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Three Experiments on Alpha-Acid Utilization and IBUs

Abstract
This post summarizes three experiments I conducted in order to explore factors that might affect alpha-acid utilization and IBUs.  I found that (a) the use of a mesh bag to contain whole-cone hops had no noticeable impact on IBUs, (b) alpha-acid utilization is probably linear with initial alpha-acid concentration up to roughly 260 ppm, above which an increasing alpha-acid concentration has little effect on utilization, and (c) the age of the beer can have a noticeable impact on IBUs during the first few months.

Introduction
When I was writing the post “A Summary of Factors Affecting IBUs“, the cumulative error in an early version of the quantitative model was suspiciously high.   In my mIBU experiments, measured IBU values were always lower than predicted values when using the recommended Tinseth scaling factor of 4.15.  It seemed that the model was missing some factor (or factors) that affects IBUs.  After going over the data several times, I thought of two possibilities: (1) alpha acids, being notably sticky [e.g. Malowicki, p. 20], might adsorb much more to the aluminum kettle I was using than to the stainless steel kettles that most people use, thereby greatly decreasing utilization, or (2) my use of a mesh bag to contain the hops in the wort might be having a much greater impact on utilization than the 10% correction factor suggested by Garetz [Garetz, p. 141].  While neither of these options seemed very likely, the first experiment in this series tested both of these hypotheses.  Although neither hypothesis ended up showing any significant impact on IBUs, the results here might be of interest to others who are considering such factors.  I also tested IBUs from this experiment at four and five weeks after the start of fermentation, to see if IBUs might be decreasing more quickly than I expected in fresh beer.

After the results of the first experiment showed that neither kettle material nor the use of a mesh bag was significantly impacting IBU values, I thought (in some desperation) that the hopping-rate correction factor described by Garetz [Garetz, p. 137] might be an underestimate.  The second experiment checked to see if the hopping rate has a larger-than-expected impact on IBUs.  Results from the first experiment indicated that IBUs can decrease noticeably in the space of one week, so I also used several of the conditions from this second experiment to look at changes in IBUs over time.  Finally, Shellhammer has written that malt polyphenols contribute 1 to 3 IBUs to beer [Shellhammer, p. 177].  In order to test this statement using my brewing setup, the second experiment had a final condition with no added hops, to see if there could be a measurable impact of malt polyphenols on IBUs.  These experiments showed that the hopping rate and age of the beer can have a large impact on IBUs (enough to explain the discrepancies in my earlier experiments).  I did not see any impact of malt polyphenols on IBUs.

The third experiment was designed to continue to tease apart the influence of isomerized alpha acids from other components that affect IBUs, for estimating the solubility limit of alpha acids at boiling.  (Unfortunately, I have no way to measure the concentration of isomerized alpha acids directly.)   Based on the results from the second and third experiments, I concluded that the solubility limit of alpha acids in boiling wort is approximately 260 ppm, under the assumption that alpha acids in the boil and above this concentration are very quickly degraded.  (I’ve since conducted several more experiments along these lines, and the more recent experiments indicate a limit of 230 ppm under the assumptions that (a) alpha acids above this threshold are converted to isomerized alpha acids following a first-order reaction with a higher rate constant, and (b) the isomerized alpha acids that are not in solution quickly degrade.  A better explanation will have to wait for a future blog post.)

In all of these experiments, IBU values were measured by Oregon BrewLab.  I’ve been very happy with the enthusiasm, support, and quantitative results from both Analysis Laboratory and Oregon BrewLab; I switched to Oregon BrewLab for this set of experiments for a couple of minor, more personal, reasons.  I highly recommend having your beers tested, at least so that you can calibrate your typical brewing process and resulting IBU levels with a formula such as Tinseth’s.  I’ve also found laboratory measurements of pH, original gravity, final gravity, and color very informative.  Testing is easy, affordable, and quick.

Utilization Experiment #1
The first utilization experiment looked at the impact on IBUs from the material the kettle is made from (aluminum vs. stainless steel) and the use of a nylon mesh bag to contain the hops in the kettle.  This experiment also measured IBUs at four and five weeks after the start of fermentation, to see if IBUs can change noticeably during this period.

The alpha acids in hops are known to be sticky, so they readily adsorb to many surfaces [e.g. Malowicki, p. 20]. I thought that the aluminum kettle I use might have some properties that increase the adsorption of alpha acids (relative to the more common stainless steel kettle used in brewing), which would lead to lower alpha-acid utilization and therefore lower IBU values.  Conditions X and Y of the first experiment test this hypothesis: Condition X was identical in all respects to Condition Y, except that X was boiled in a stainless steel kettle and Y was boiled in an aluminum kettle.

Garetz has published a number of modifications to predicted IBU values based on a wide variety of factors.  In particular, he says that “if you use a hop bag to boil your hops in, then your utilization will be decreased by about 10%” [Garetz, p. 141].  I thought that a reduction of 10% might be an underestimate, and so Conditions Y and Z tested the effect of using a mesh bag to contain whole-cone hops:  Condition Y had the hop cones floating loose in the kettle, while Condition Z kept the hops in a nylon mesh bag.   (I’ve found that using such a mesh bag greatly simplifies my cleanup, so it’s my preferred mode of brewing.  Marshall Schott at the awesome Brülosophy site also tested bagged vs. loose hops.  He found that while the impact on IBUs was small to negligible, there was a statistically significant impact on flavor, with the loose hops being generally preferred.)

(I’ve labeled the conditions in this Experiment X, Y, and Z (instead of A, B, and C) in part to avoid confusion with Experiments #2 and #3.)

Experiment #1: Methods
Three batches of beer were brewed for this experiment: Conditions X, Y, and Z.  I made one batch of wort and divided it into equal portions for each condition.  In this case, 8.60 lbs (3.90 kg) of Briess dry malt extract was added to 7.25 G (27.44 liters) of water to yield 7.88 G (29.83 liters) of wort, with a specific gravity of 1.051.   For each condition, 1.75 G (6.62 liters) was taken from this larger pool of wort and heated to boiling.  When boiling was reached, 0.75 oz (21.26 g) of Cascade hops (package rating of 8.1% alpha acids, 7.6% beta acids) were added.

For this experiment, I used hop cones from YCH Hops, which are claimed to be stored in nitrogen packaging, although this was not stated directly on the packages I used.  An analysis of the same batch of hops 6 weeks later (for Experiment #2) showed an AA rating of 7.9%, a beta-acid value of 7.1%, and an HSI of 0.247, indicating that these hops were, in fact, stored extremely well.  YCH provides information about the lot number, and this lot (PR2-YLUCAS5069) was harvested in 2015, so it was about 10 months old at the time of this first experiment (July 2016).

The wort was boiled for 20 minutes (with the kettle covered), stirring approximately every 5 minutes.  When the 20-minute mark was reached, 1.5 quarts (1.42 liters) were removed and quickly cooled in an ice bath to 75°F (24°C) and sealed.  After about 30 more minutes of settling, almost all of this wort was decanted into a sterile 1 G (4 liter) container and sealed.

Once all conditions were ready, 0.26 oz (7.42 g) of Safeale US-05 yeast was mixed with 2.6 oz (74 g) of 80°F (27°C) water.  Each condition was aerated by vigorous shaking for 90 seconds, and 0.41 oz (11.6 g) of the yeast slurry was added.

Airlocks were applied, yeast proceeded to ferment sugars into alcohol, and wort was magically transformed into beer.  After three weeks of fermentation and conditioning, 0.80 quarts (0.76 liters) of each condition were decanted and bottled with 0.10 oz (2.83 g) of sucrose.  IBU values were measured at approximately 4 and 5 weeks after the start of fermentation.

The conditions were different in only the following ways: Condition X was boiled in a stainless steel kettle with loose hops; Condition Y was boiled in an aluminum kettle with loose hops, and Condition Z was boiled in an aluminum kettle with hop cones contained within a nylon mesh bag.

Experiment #1: Results & Analysis
Table 1 (below) shows measured and modeled IBU values for each of the conditions in Experiment 1, along with a variety of other measured parameters (e.g. original gravity).  Gravity readings were obtained by a hydrometer.  Post-boil volume was computed by taking the ratio of pre-boil gravity points divided by post-boil gravity points, and multiplying that by the initial volume.

The measured IBU values show about the same variation across the one-week measurement interval as they do across conditions.  The IBU values decreased by an average of 2.0 in the one week (5%), and the average difference between conditions was also 2.0.   The maximum difference between conditions was the change from 34 to 37 IBUs with the stainless steel and aluminum kettles, respectively.  This difference is probably not significant, and is also in the opposite direction of what I’d expect if alpha acids adsorb more readily to aluminum than to stainless steel.  The difference of 1 IBU between loose hops and a mesh bag is definitely within the type of random variation I’ve seen in measured IBU values, and so the use of a mesh bag did not demonstrate any real impact on IBU levels.  The difference across time was consistent for all three conditions, and the time period of one week is small, and so these results, while inconclusive, suggest that IBUs might change quite a bit with age of the beer.

The alpha-acid concentrations of about 283, 294, and 299 ppm for conditions X, Y, and Z, respectively, are somewhat higher than the threshold that I determined later to be the approximate limit for a linear increase in IBU values with alpha-acid concentration.  In addition, I assume that Tinseth measured his IBU values soon (e.g. one week) after fermentation, and my results were measured after more time had elapsed.  Therefore, with the benefit of hindsight, I’d now expect the Tinseth IBU estimates (using the recommended scaling factor of 4.15) to be a bit on the high side, since the Tinseth formula doesn’t account for alpha-acid concentration or age of the beer.  Results from the Tinseth formula are provided in Table 1.

In a separate blog post, I present a more detailed model of IBUs; the values obtained from that model for this experiment (at week 4) are also given in Table 1.  This more detailed model takes into account factors such as original gravity, hopping rate, age and storage conditions of the hops, alpha/beta ratio, age of the beer, and form of the hops.  Using this model, the AA rating at harvest was 8.1% (the same as the value on the package) and the estimated degradation factor was 0.95 (generally comparable with the HSI value of 0.247).  The estimated alpha/beta ratio was 1.0, a bit lower than the ratio of 1.07 from the package rating.  The root-mean-square (RMS) error from this model was 2.73 IBUs, with a maximum difference of -3.6 IBUs (Condition Z).  According to this model, isomerized alpha acids contributed 58%, 57%, and 54% to the IBU values of conditions X, Y, and Z, respectively.  These values are somewhat lower than the 67% contribution estimated by this model for the Tinseth equation at 20 minutes using “typical” brewing values, presumably due primarily to the concentration of alpha acids in this experiment being somewhat higher than the estimated threshold of solubility.

condition
X: stainless steel, loose hops
condition
Y: aluminum, loose hops
condition
Z: aluminum, mesh bag
original gravity
1.056 1.058 1.059
post-boil volume 1.61 G / 6.09 l 1.55 G / 5.87 l 1.52 G / 5.75 l
final gravity
1.009 1.009 1.009
measured IBUs: week 4 (from OBL)
34 37 36
measured IBUs: week 5 (from OBL)
33 34 34
IBUs from Tinseth formula
 37.4  38.2  38.6
IBUs from detailed model (week 4)
 33.6  34.0  32.4

Table 1. Measured and modeled values of the three conditions in the first utilization experiment.  Results provided by Oregon BrewLab are indicated by “OBL”.

Experiment #1: Conclusion
The use of stainless steel vs. aluminum, the use of a mesh bag vs. loose hop cones, and the impact of one week of age (between 4 and 5 weeks after the start of fermentation) all had a small and inconclusive impact on measured IBU values.   The good news is that kettle material and the use of a mesh bag don’t seem to require special attention when developing a quantitative model of IBUs.

Utilization Experiment #2
The second experiment looked at three factors that might have an influence on IBUs: (1) the hopping rate (the relative amount of hops, and especially alpha acids, in the wort), (2) the age of the beer, and (3) malt polyphenols.

There is consensus in the literature that “simply adding more and more hops does not produce a linear increase in the amount of bitterness produced” [Daniels, p. 85].  Garetz provides the only quantitative model for this effect that I’ve found [Garetz, p. 137], but he notes that some of his correction factors are “new and still largely unproven” [Garetz, p. 128].  Based on the IBU data I’d collected so far, I thought that his model might underestimate the impact of a high hopping rate.  This experiment was designed to look at the impact on IBUs resulting from adding larger and larger amounts of hops to the wort.

I’ve heard that IBUs decrease with age, but the time scales I’ve read about are on the order of six months to a year.  For example, Peacock [Peacock, p. 164] reports a study of 25 commercial beers that showed a 14% relative loss of IBUs after 8 months at 72°F (22°C).   I wanted to see how IBUs change during a beer’s first weeks in my homebrew bottled beer, which is different from commercial beer in that there is probably less filtering, more active yeast, and more oxygen in the headspace.

Finally, Shellhammer has stated that “the [IBU] measurement yields a finite value in the range of 1 – 3 [IBU] for unhopped beer” [Shellhammer, p. 177].   To test this, I evaluated a condition made without any hops additions, to test the contribution of malt polyphenols to IBU levels with the malt extract, specific gravity, and bottle conditioning used in this set of experiments.

Experiment #2: Methods
In this experiment, seven batches of beer were brewed in one very long day.  The first six (Conditions A through F) had an increasing amount of hops in the same volume of wort, and the seventh (Condition G) had no hops added.  Two (identical) batches of wort were created, each with 8.60 lbs (3.90 kg) of Briess Pilsen Light Dried Malt Extract added to 7.25 G (27.44 liters) of water, yielding 7.85 G (29.72 liters) of wort with specific gravity 1.051.  The first four conditions were taken from the first batch, and the remaining three conditions were taken from the second batch.

For each condition, 1.75 G (6.62 liters) were taken from the larger pool and heated to boiling.  Once boiling was reached, the wort was boiled for 7 minutes (uncovered) before adding (loose) hop cones (if any).  After that, the wort was boiled for an additional 12 minutes, covered.  The wort was stirred twice during this time.  When the 12 minutes of boiling were finished, the wort was quickly cooled to 75°F (24°C) by transferring it into an empty pot sitting in an ice bath; a sieve was used during transfer to remove most of the hop cones, and the wort was stirred in order to cool it quickly.  The cooled wort then sat for 5 minutes before 3½ quarts (3.31 liters) were decanted into a sterile 1 G (4 liter) container (plastic milk jug).  After all conditions were ready, 0.74 oz (21 g) of Safeale US-05 yeast was added to 6.10 oz (173 g) of 80°F (27°C) water.  Each condition was aerated by vigorous shaking for 90 seconds.  Then, approximately 1 oz (28 grams) of the yeast slurry was pitched into each condition, airlocks were applied, and wort fermented into beer.

The hops were the same Cascade hops (i.e. the same lot number) as Experiment #1, from YCH Hops, with a package rating of 8.1% AA.  The hops were analyzed by Alpha Analytics within four days of brewing, with (as mentioned above in Experiment #1) an AA rating of 7.9%, a beta-acid value of 7.1% and an HSI of 0.247.

For Conditions A through F, the amount of hops added was 0.37 oz (10.49 g), 0.74 oz (20.98 g), 1.11 oz (31.47 g), 1.48 oz (41.96 g), 1.85 oz (52.45 g), and 2.22 oz (62.94 g), respectively.  In other words, each condition had 0.37 oz (10.49 g) more than the preceding condition, and so the rate of increase of hops in each condition was linear.

The beers were decanted and bottled after 3 weeks of fermentation and conditioning.  Conditions C and F had no priming sugar, and the other conditions were primed with 0.42 oz (11.9 g) of sucrose to target 2.1 volumes CO2.

IBU values were measured over time, relative to the start of fermentation.  Condition A was measured at 3, 7, and 13 weeks.  Condition B was measured at 3 and 7 weeks.  Condition C was measured at 1, 2, 3, 6, 7, and 13 weeks.  Conditions D and E were measured at 3 and 7 weeks.  Condition F was measured at 1, 2, 3, 6, 7, and 13 weeks.  Condition G was measured at 3 weeks.

Experiment #2: Results & Analysis
Table 2 (below) shows measured and estimated values for Conditions A through F.   Specific gravity values are from hydrometer readings.  (By this point in my brewing, I’d upgraded to a hydrometer scaled from 1.000 to 1.070, so I attempted readings with greater precision than in previous experiments.)  The measured IBU values in Table 2 are labeled with the age of the beer in weeks from the start of fermentation.  Note that the predicted IBU values from the Tinseth equation increase linearly (a constant increase of 13.2 IBUs per condition), because this equation doesn’t account for any effects of hopping rate.  The values from the “detailed model” were obtained using the quantitative model developed in a previous blog post, A Summary of Factors Affecting IBUs.

Malt Polyphenol Contribution to IBUs
For Condition G, with no hops, the original gravity was 1.0565 and the final gravity was 1.0087.  The measured IBUs for Condition G at 3 weeks from the start of fermentation was 0.

Modeling the Decrease in IBUs as a Function of Age
In general, the measured IBU values change smoothly as a function of time and hopping rate.  The measured IBU values at week 3, however, were all higher than expected when compared with other weeks, for reasons that are unclear to me.  It’s possible that I did something different when collecting these samples for analysis and bottling, e.g. decant the finished beer in such a way as to increase the levels of bitter compounds.  Figure 1 plots IBUs from Conditions C and F as a function of age of the beer.  It can be seen that at week 3, the IBU values are about 16% higher than would be expected (since IBU values should not quickly increase and then decrease; they should only decrease over time).  Because of this anomaly, I estimated “corrected” IBU values for week 3, by taking the measured values and multiplying by 0.8625.  The corrected values are also shown in Figure 1.   These corrected values for week 3 are close to the values from week 7 multiplied by 1.09, again indicating that results from all samples from week 3 were off by a constant factor.  In subsequent analyses using IBU values from week 3, I use the corrected values.  In addition, for Condition B at week 7, the measured IBU value was only 13, which was very surprising given that at week 3 the measured (and corrected) value was 24.15.  Oregon BrewLab re-measured this sample, coming up with 14 IBUs, indicating that there was a problem with the sample I took, not the analysis.  I sent in one more sample from Condition B at week 8, which came back at 23 IBUs.  Interpolating between 24.15 at week 3 and 23 at week 8, a corrected value for Condition B at week 7 is 23.25.  In subsequent analyses using this data point, I use this corrected value.

utilExp2-Figure1-correctedIBUs

Figure 1. Measured IBU values for Conditions C and F (dark lines) and corrected values for week 3 (light lines).

Figure 2 shows the measured IBU values as a function of the age of the beer, in weeks, for Conditions C and F.   The rate of decrease is greater for the hoppier beer, which suggests that we may be able to use a single correction factor (i.e. a multiplication factor) to account for the age of the beer when modeling IBUs, independent of the initial IBU level.  I fit the data to an exponential decay function with age measured in weeks.  For Condition C, the best fit was obtained with IBU(age) = 24.6 × e-0.0228×age + 7.7 (with IBU(age) being the age-adjusted IBU value and age being the age of the beer, in weeks), yielding a value at time 0 of 32.3 IBUs.  For Condition F, the best fit was obtained with IBU(age) = 14.8 × e-0.1306×age + 41.2, yielding a value at time 0 of 56.0 IBUs.  I then converted all IBU values to relative values by dividing by the estimated IBU level at time 0, yielding age-related multiplication factors at each age.  The best fit to the relative values of both sets was obtained with factor(age) = 0.32 × e-0.08×age + 0.68,  where factor(age) is the age-related IBU correction factor, as a function of age of the beer.  The IBU value at time age can then be estimated from IBU(age) = IBU0 × (0.32 × e-0.08×age + 0.68), where IBU0 is the (hypothetical) IBU value at time 0.  If you know the IBU level at week w, you can compute IBU0 from IBU(w) / (0.32 × e-0.08×age + 0.68), and thus an IBU value at any time point.

Figure 2 also shows the estimated IBUs for Conditions C and F that are obtained by multiplying the time-zero IBU estimates (32.3 and 56.0, respectively) by the age-related correction factor.  The fit of the model to the data appears reasonable, although there is a very limited amount of data to judge this by.  Table 2 provides the IBU estimate at week 1 for all conditions, based on values from weeks 3 and 7 and this formula.  If we assume that isomerized alpha acids and other components are affected by age at the same rate (which is probably an incorrect assumption [Peacock, p. 164], but not unreasonable as a first approximation), we can model the loss factor for isomerized alpha acids using the same formula.

I then had measurements of all conditions made after 1 year.  The IBU levels seemed to have stabilized before the year was up, because the exponential decay model predicted values at 52 weeks that were lower than observed.  Using IBU values from both weeks 3 and 7 to compute IBU0 values, the exponential decay model reached the measured 52-week IBU level after an average of 16 weeks.  So, IBU values seem to decrease with an exponential decay for about 16 weeks, after which they remain stable.

utilExp2-Figure2-IBUvsAge

Figure 2. Measured IBU values for Conditions C and F, and estimated IBUs based on IBU estimate at time 0 and age-related IBU factor with an exponential decay.

Modeling a Hopping-Rate Correction Factor
Garetz has proposed a hop-rate correction factor (described by both Hall and Daniels) that depends on volume and “desired IBU” to determine the weight of hops needed [Garetz, p. 137; Hall, p. 63; Daniels, p. 86]. If we focus on full boils (instead of boiling a higher-gravity wort and then adding water), we can write the Garetz correction factor as HF(IBU) = (IBU/260) + 1, where HF is the hop-rate correction factor that depends on the (desired) IBU value, IBU. If the IBU value is to be estimated from the weight of hops, Hall provides a method to compute this correction factor in two steps rather than through the iterative process suggested by Garetz [Hall, p. 63].  Table 2 shows the IBU values predicted by the Tinseth equation, the IBU correction factor computed for each condition using Hall’s modification of the Garetz method, and IBU values predicted from the Tinseth equation and then modified by the Garetz correction factor.

In Figure 3, the measured IBUs at weeks 3 and 7 are plotted as a function of weight of the hops added.  Figure 3 also plots, in addition to the measured IBU values, the IBU values predicted from the Tinseth equation, and the predictions from the Tinseth equation modified by the Garetz hopping-rate correction factor.  It can be seen that the correction factor provided by Garetz does underestimate the decrease in IBUs as a function of weight of the hops.  (In other words, the IBU values predicted from the Garetz correction factor are still too large when compared with measured IBU values.)  Because measured IBUs are only available for all conditions at weeks 3 and 7, and because Tinseth may have measured his IBUs much sooner after the start of fermentation, I estimated IBU values for week 1, based on the measured values from weeks 3 and 7 and the age-related correction factor described above.  It can be seen that even the IBU values at 1 week are lower than values predicted by the Garetz correction factor.

utilExp2-Figure3-IBUvsWeight

Figure 3. Measured IBU values for Conditions A through F (week 3: dark blue line; week 7: light blue line), estimated IBU values for the same conditions at week 1 (very dark green line) based on age-related decay factor, IBU values predicted by Tinseth equation (red line), and IBU values predicted by Tinseth equation with Garetz hopping-rate correction factor (light green line).

Rather than make adjustments to the Garetz correction factor, it seems that a simpler explanation (and model) may be possible.  This explanation depends on the fact that IBUs measure a combination of both isomerized alpha acids (IAAs) and bitter components other than IAAs (nonIAAs).  As explained by Peacock, this relationship can be expressed as IBU = 5/7 × (IAA + nonIAA) [Peacock, p. 157].  It may be that after the solubility limit of alpha acids is reached, adding more alpha acids to the wort doesn’t contribute any more IAAs to the beer.  (In other words, isomerization only occurs for the alpha acids that are dissolved in wort.)  However, adding more and more nonIAAs may continue to provide a linear contribution to the IBU measurement.  This would explain the increase in IBUs in Figure 3 looking like two separate lines: up to around 0.75 oz (21 g) in this experiment, the IAAs and nonIAAs both contribute linearly and equally to the IBU, in agreement with the Tinseth formula; above 0.75 oz (21 g), the IAA level is constant but the nonIAA level continues to increase linearly, resulting in a line with a more shallow slope.

Figure 4 illustrates this concept, with initial concentration of alpha-acids (in parts per million) on the X axis instead of weight of the hops.  (Note that the small dip in the plot for Condition D in Figure 3 is no longer present, and the measured IBU values for Conditions B through F have an increase very close to linear.  This change is due to the switch from weight of the hops in Figure 3 to alpha-acid concentration in Figure 4; concentration depends on the weight, AA rating, and volume.)  In Figure 4, IAAs and nonIAAs contribute equally to the IBU at lower alpha-acid concentrations (and at the boil time of 12 minutes).  At concentrations above 260 ppm, the IAA contribution (dark blue line) remains constant, but the nonIAA contribution (light blue line) continues to increase linearly.  The sum of the IAA and nonIAA concentrations, multiplied by 5/7, gives the estimated IBU value (red line), as described by Peacock.  With these assumptions (equal contributions from IAA and nonIAA at lower concentrations, and an alpha-acid limit of 260 ppm), estimated IBU values (with a mapping of 0.06 from initial alpha-acid concentration to bottled-beer IAA and nonIAA concentrations) have a surprisingly good fit to the measured IBU values from week 7 (green line).

utilExp2-Figure4-IAAvsConcentration

Figure 4. Measured IBU values for Conditions A through F at week 7 (green line), hypothetical concentration of isomerized alpha acids (IAA) for beer (dark blue line), hypothetical concentration of other bitter components in beer (nonIAA) (light blue line), and predicted IBU obtained by combining IAA and nonIAA components according to Peacock’s IBU formulation (red line).  The IAA and nonIAA concentrations assume equal contributions after a 12-minute boil at low alpha-acid concentrations, and the IAA level assumes that no isomerized alpha acids make it into the beer once the initial alpha-acid concentration exceeds 260 ppm.

The last row of Table 2 provides IBU values estimated from the detailed model described in A Summary of Factors Affecting IBUs, with an age of 7 weeks.  In this model, the AA rating at harvest was 8.1% (the same as the value on the package) and the estimated degradation factor was 0.99 (generally comparable with the HSI value of 0.247).  The estimated alpha/beta ratio was 1.10, very close to the ratio of 1.07 from the package rating.  The root-mean-square (RMS) error from this model was 0.40 IBUs, with a maximum difference of 0.67 IBUs (Condition D).  According to this model, isomerized alpha acids contributed 50%, 48%, 39%, 33%, 28%, and 24% to the IBU values of conditions A through F, respectively.  (Note that the 50% contribution of IAA in Condition A is the same as the hypothetical equal contributions of IAA and nonIAA in Figure 4.)

Experiment #2: Conclusion
Experiment #2 indicates that the IBU level in a home-brewed beer can be modeled as a function of age of the beer with the formula IBU(age) = IBU0 × (0.32 × e-0.08×age + 0.68), where age is the age of the beer in weeks and IBU0 is the IBU value at time 0.  This formula can be used up to about 16 weeks, after which the IBU values remain stable.  It also indicates the potential for a hopping-rate correction factor being modeled by (a) a limit on the solubility of alpha acids in boiling wort at 260 ppm and (b) the assumption that non-soluble alpha acids do not convert into isomerized alpha acids that are present in the finished beer.  The resulting hopping-rate correction model simply limits the (effective) initial amount of alpha acids in the wort to 260 ppm.

condition
A
condition
B
condition
C
condition
D
condition
E
condition
F
weight of hops
0.37 oz /
10.49 g
0.74 oz /
20.98 g
1.11 oz /
31.47 g
1.48 oz /
41.96 g
1.85 oz /
52.45 g
2.22 oz /
62.94 g
post-boil volume
1.64 G / 6.21 l 1.62 G / 6.13 l 1.62 G / 6.13 l 1.65 G / 6.25 l 1.61 G / 6.09 l 1.61 G / 6.09 l
original gravity
1.0545 1.0550 1.0550 1.0540 1.0555 1.0555
final gravity
1.0088 1.0084 1.0084 1.0096 1.0099 1.0104
initial alpha-acid concentration 135.5 ppm 274.3 ppm 411.5 ppm 538.7 ppm 690.1 ppm 828.1 ppm
measured IBUs, week 1
32 54
measured IBUs, week 2
31 53
measured IBUs, week 3 (orig)
16 28 36 45 53 60
measured IBUs, week 3 (corrected)
13.8 24.15 31.0 38.8 45.7 51.75
measured IBUs, week 6
29 48
measured IBUs, week 7
12 13 (orig) or 23.25 (corr.) 29 34 41 47
measured IBUs, week 13
12 26 44
measured IBUs, week 52
11.5 19.5 25.5 31.5 37.0 43.0
estimated IBUs, week 1
14.01 25.64 32.62 39.52 47.09 53.65
IBUs: Tinseth
12.71 25.62 38.43 50.76 64.16 76.99
Garetz correction factor
0.955 0.917 0.884 0.857 0.830 0.807
IBUs: Tinseth with Garetz
12.14 23.5 33.99 43.49 53.25 62.14
IBUs: detailed model (week 7)
12.4 24.3 29.7 34.8 40.7 46.1

Table 2. Measured and modeled values of the first six conditions in the second experiment.

Utilization Experiment #3
In looking at Figure 4, with the benefit of hindsight and knowing good parameter values, it seems clear that an alpha-acid concentration limit of 260 ppm and an equal contribution of IAA and nonIAA to the IBU after 12 minutes of boiling provide a good fit to the data, but this was not obvious to me after finishing Experiment #2.  Also, measured IBUs from different boil times might produce results that contradict this simple hopping-rate correction model.  Therefore, I conducted a third experiment, with varying boil times and amounts of hops, in order to get additional data for estimating the amount of alpha acids that contribute to isomerization as a function of initial alpha-acid concentration.  Under the assumption that only soluble alpha acids contribute to the IAA levels in finished beer, this will tell us the solubility limit of alpha acids at boiling.

Experiment #3: Approach to the Problem
This experiment had five conditions (labeled here as Conditions H through L, respectively, to avoid confusion with Experiment #2).  Each condition varied in the amount of hops, duration of the boil, and (for Condition L) the temperature at which hops were steeped.  The steep times for Conditions H through L are listed in Table 4 (below).  I was fortunate enough to obtain hops from the same lot number as in Experiments #1 and #2, keeping that factor fairly constant.

Conditions H through L were designed to yield an IAA level that is some multiple of the IAA level in another condition, as summarized in Table 3 (below).  In particular, the amount of hops and steep time of Condition H were designed to yield twice the amount of isomerized alpha acids when compared with Condition A from Experiment #2.  The amount of hops and steep time of Condition I were designed to yield twice the amount of IAA when compared with Condition C.  Condition J was designed to be identical with Condition C in Experiment #2, to check IBU values across the two experiments.  Condition K was designed to yield 1.5 times the amount of IAA when compared with Condition F.  Condition L was designed to be the same as Condition K, but with a steep temperature that yields less than 5% of the isomerization at boiling, in order to look at the impact of nonIAA components.

cond. H
cond. I
cond. J
cond. K
cond. L
relative IAA level
2 × cond. A 2 × cond. C 1 × cond. C 1.5 × cond. F < 0.05 × cond. K

Table 3. Targeted relative IAA levels for conditions H through L.

The relative amount of IAA produced (and therefore the amount of time needed for each boil) was determined from an equation by Malowicki [Malowicki, p. 27] (also reported by Huang et al. [Huang, p. 51]):

[IAA]wort = [AA]0 (k1(T)/(k2(T)-k1(T))) (ek1(T)t-ek2(T)t)

where [IAA]wort is the concentration of isomerized alpha acids in the wort after time t and temperature T (in Kelvin).  [AA]0 is the initial concentration of alpha acids, and k1(T) and k2(T) are temperature-dependent rate constants determined by Malowicki.  As long as the initial concentration of alpha acids is the same, the level of IAA at 26.9 minutes is twice that of the IAA level at 12.0 minutes, and the level of IAA at 19.0 minutes is 1.5 times that at 12.0 minutes (with all cases at boiling).  Also, according to this equation, with a 19-minute boil at 145°F (62.8°C), the IAA produced will be only 3.4% of that at boiling.

The goal of this experiment was to estimate the amount of alpha acids that contribute to isomerization, as a function of the initial alpha-acid concentration (when added to the wort).  Based on data from Experiment #2, I expected that these amounts would increase linearly up to some point and then level off once the alpha-acid solubility limit is reached.  In other words, I hypothesized that the solubility of alpha acids limits the amount of alpha acids that can isomerize, and this solubility limit is responsible for the hopping-rate correction factor noted by others.  Because I can’t measure IAA levels directly (I can only measure IBUs, which are a combination of IAA and nonIAA components), the first step is to estimate levels of nonIAA components in each condition.

I assumed that nonIAA levels increase linearly with the concentration of hop particles in the wort, which is the same as assuming that nonIAA levels increase linearly with the alpha-acid concentration, given a constant alpha-acid rating, alpha/beta ratio, and hops deterioration factor.  (I also assumed that oxidized alpha and beta acids produced during the boil are all present after 12 minutes of boil time (the minimum boil time used here).)  By making these assumptions, we can have an (unknown) factor map from initial alpha-acid concentration to nonIAA levels in the finished beer.  For example, if the initial alpha-acid concentration is 200 ppm from a weight of 0.5 oz (14 g) of hops in 1.6 G (6 liters) of wort, and the mapping factor is 0.10, then there will be 20 ppm of nonIAA in the finished beer; if the alpha-acid concentration doubles to 400 ppm by doubling the amount of hops, then there will be 40 ppm of nonIAA.

Next, using the equation for IBUs proposed by Peacock [Peacock, p.157], namely

IBU = 5/7 × (IAA + nonIAA)

we can take measured IBU values and the (still unknown) mapping factor in order to determine the levels of IAA and nonIAA in each condition.  For example, if we have an alpha-acid concentration of 200 ppm, a measured IBU value of 30, and an assumed mapping factor of 0.10, then

nonIAA = [AA]0 × factor = 200 × 0.10 = 20 ppm
IAA = (7/5 × IBU) – nonIAA = (7/5 × 30) – 20 = 22 ppm

The next question is how to determine the mapping factor with some method better than randomly guessing at a value.  Because the boil times in each condition were varied in order to obtain exactly 1.0, 1.5, or 2.0 times the IAA levels in certain conditions in Experiment #2, we know what IAA differences to expect between certain conditions.  For example, in Condition C, an IBU level of 31.86, [AA]0 level of 411.49, and mapping factor of 0.10 yields an IAACondC value of 3.45.  In Condition I, an IBU level of 48.00, [AA]0 level of 406.55, and mapping factor of 0.10 yields an IAACondI value of 26.55.  But we also know that IAACondI should be twice that of IAACondC because of the different boil times.  Therefore, in this case, the difference in expected values is (26.55 – (2×3.45)), or 19.65.  Keeping everything else the same but changing the mapping factor from 0.10 to 0.06, IAACondC becomes 19.91 and IAACondI becomes 42.81, for a difference in expected values of (42.81 – (2×19.91)) = 2.99.  Therefore, in this one case, a mapping factor of 0.06 is a much better fit to the data than 0.10.  We can then search over a large number of mapping factors and all expected differences, and find the mapping factor that minimizes the error in expected IAA differences.

Given an optimal (in the minimal-error sense) value for the mapping factor, we can use the initial alpha-acid concentrations and IBU values to compute IAA and nonIAA for each condition.  Also, for Condition A, we can compute the ratio of initial alpha-acid concentration to (estimated) IAAs.  If we assume that Condition A has [AA]0 less than the solubility limit, we can then multiply this ratio by the IAAs estimated for other conditions to determine the level of alpha acids contributing to isomerization as a function of initial alpha-acid concentration.

Experiment #3: Methods
One large batch of wort was created from 10 lbs and 1.36 oz (4.57 kg) of Briess Pilsen light DME added to 8.5 G (32.2 liters) of water, yielding 9.25 G (35.0 liters) of wort with specific gravity 1.051.  Similar to Experiment #2, for each condition, 1.75 G (6.62 liters) were taken from the larger pool and heated to boiling (with an average of 17 minutes to reach boiling).  For Conditions H through K, once at boiling, the wort continued to boil for another 7 minutes (uncovered) before adding (loose) hops.  For Condition L, the wort was boiled for 7 minutes, then cooled with a wort chiller to the target temperature of 145°F (62.8°C) before hops were added.  After the hops were added, the hops steeped in the wort with the cover on for the target steep time, with stirring about every 5 minutes.  Once the steep time was reached, the wort was quickly cooled to 75°F (24°C) by transferring it into an empty pot sitting in an ice bath; a sieve was used during transfer to remove most of the hop cones, and the wort was then stirred in order to cool it quickly.  The cooled wort then sat for 5 minutes before 3½ quarts (3.31 liters) were decanted into a sterile 1 G (4 liter) container.  After all conditions were ready, 0.74 oz (21 g) of Safeale US-05 yeast was added to 6.10 oz (173 g) of 80°F (27°C) water.  Each condition was aerated by vigorous shaking for 90 seconds.  Then, approximately 1 oz (28 grams) of the yeast slurry was pitched into each condition, airlocks were applied, and wort fermented into beer.

The hops were the same Cascade hops (i.e. the same lot number) as Experiments #1 and #2, from YCH Hops, with a package rating of 8.1% AA.  The hops were again analyzed by Alpha Analytics within four days of brewing, with an AA rating of 7.7%, a beta-acid value of 6.8% and an HSI of 0.231.  These values are similar enough to the values from Experiment #2 (especially considering the variation I’ve seen in measured AA values of hops from the same bine) that it seems fair to treat the hops between Experiments #2 and #3 as essentially the same.

IBU levels were measured at two weeks after the start of fermentation.  Measurements were again provided by Oregon BrewLab.

Experiment #3: Results & Analysis
Table 4 (below) shows measured and estimated values for Conditions A through F (Experiment #2) and Conditions H through L (Experiment #3).   For Conditions A through F, the IBU values are estimated values at week 2 (using the formula developed in Experiment #2) in order to have IBU values comparable with Experiment #3.  Specific gravity values are from hydrometer readings.  The values from the “detailed model” in this table are taken from the quantitative model developed in a previous blog post, A Summary of Factors Affecting IBUs.

The optimal mapping from initial alpha-acid concentration to nonIAA was 0.06, with a root-mean-squared error of 3.11 over four comparisons (Condition H IAA is 2 times Condition A; Condition I IAA is 2 times Condition C; Condition J IAA equals Condition C IAA; Condition K IAA is 1.5 times Condition F).  This mapping value is heavily dependent on the hops used, age of the beer, and other factors during and after the boil, and will probably not generalize to other beers.

If the level of alpha acids that contribute to isomerization (i.e. yield IAAs in the finished beer) was always linear with the initial alpha-acid concentration, then there would be no need for a hopping-rate correction factor; if I added twice as much hops between one condition and the next, I’d get twice as much IAA and twice as much nonIAA, yielding twice as many IBUs.  If, however, the alpha acids that contribute to isomerization rise linearly up to some (initial) concentration and then level off, then this function may be a good model for the hopping-rate correction that is needed.  We can also postulate a reason for such a rise and then leveling off: the solubility of alpha acids. By this reasoning, once the solubility limit is reached, the addition of more alpha acids (that do not dissolve in the wort) has little impact on IAA levels.

In Table 4, the row labeled “AA solubility” is an estimate of how much of the alpha acids were dissolved in solution for each condition.  This solubility level was determined from the estimated amount of IAA in a condition multiplied by a conversion factor from IAA to initial alpha-acid concentration.  This conversion factor was obtained by dividing the initial alpha-acid concentration for Condition A by the IAA level estimated for Condition A, under the assumption that Condition A had less alpha acids than the solubility limit.  Therefore, for Condition A the alpha-acid solubility (in ppm) is the same as the initial alpha-acid concentration.  For other conditions, under the assumption that only soluble alpha acids contribute to the isomerized alpha acids in the finished beer, the IAA level after a 12-minute boil multiplied by the conversion factor yields the estimated solubility of alpha acids for this condition.  The IAA level after a 12-minute boil is obtained either (a) directly from the value of a condition with a 12-minute boil, or (b) from the estimated IAA level divided by the expected relative IAA level for that condition, e.g. 1.5 or 2.0.

Figure 5 plots the alpha acids that contribute to IAA levels as a function of initial alpha-acid concentration, at boiling.  Under the assumption that only soluble alpha acids contribute to isomerized alpha acids in the finished beer, the Y axis can be interpreted as the alpha-acid solubility level at boiling, in ppm.  Averaging all conditions except A and H (expected to be below the solubility limit), the average alpha-acid solubility limit is 262.41 ppm.  The dashed green line in Figure 5 shows the proposed model of alpha-acid solubility, in which solubility increases linearly up to 260 ppm, and then remains constant at higher initial alpha-acid concentrations.  It can be seen that, similar to the alpha-acid solubility at room temperature and pH 5.2 found by Malowicki [Malowicki, p. 53], solubility doesn’t reach an abrupt limit at a certain concentration, but continues to increase slightly with higher concentrations.  The same phrasing from Malowicki applies to these results: “Although the curve did not completely plateau, there was a distinct knee in the curve” [Malowicki, p. 52].  The boil time does not have a clear effect on the estimated solubility limit; Conditions H and K (with boil times 26.9 and 19 minutes) have estimated values less than Conditions A and F (12-minute boils), respectively, but Condition I (boil time 26.9 min) is slightly greater than Condition C (12 minutes).

For Condition L, 2.22 oz (62.94 g) of hops were steeped at approximately 145°F (62.8°C) for 19 minutes. An average temperature of 146.5°F (63.6°C) was maintained (minimum 141.8°F (61.0°C) , maximum 150°F (65.6°C)) for 19 minutes.  The measured IBU value was 27.  At this temperature, the amount of IAA produced should be only 3.7% of the IAAs produced at boiling, according to Huang’s equation.  Condition K was identical to Condition L, except for the steeping temperature.  With Condition K producing an estimated 32.41 ppm of IAA, Condition L should have only about 1.20 ppm of IAA (3.7% of 32.41).  Therefore, the IBU value of 27 in Condition L is comprised of about 1.20 ppm of IAA and 36.6 ppm of nonIAA (with 27 = 5/7 × (1.20 + nonIAA)).  This 36.6 ppm of nonIAA is less than the 48.79 ppm of nonIAA estimated for Condition K (at boiling).

The nonIAA components include oxidized alpha acids, oxidized beta acids, and polyphenols.  Both oxidized alpha and beta acids are produced during the boil [Parkin, p. 11, Algazzali, p. 17; Dierckens and Verzele, p. 454; Oliver p. 471] (in addition to being a product of hop oxidation).  For example, Stevens and Wright note that “after heating colupulone with boiling wort for 2 hr., as much as 10% of the beta acid had been converted into cohulupone.” [Stevens and Wright, p. 500].  (Note: colupulone is one of the four components of the beta acids; cohulupone is the oxidized form of colupulone.)  The results from Conditions K and L imply that the production of oxidized alpha and beta acids during the boil is temperature-dependent, with less production at lower temperatures.  The results also imply that oxidized alpha and/or beta acids produced during the boil contribute significantly to the nonIAA value, and that they are a notable component of the overall IBU value, especially at shorter boil times.  It’s also quite clear that even with almost no isomerization (at 145°F (62.8°C)) and the use of very well-preserved hops, sizeable IBU levels can still be found in the finished beer.

Table 4 also shows the IBU values of Experiment #3 estimated from the detailed model described in A Summary of Factors Affecting IBUs.  In this model, similar to the previous experiments, the AA rating at harvest was 8.1% (the same as the value on the package) and the estimated degradation factor was 0.96 (generally comparable with the HSI value of 0.247).  The estimated alpha/beta ratio was 1.10, very close to the ratio of 1.07 from the package rating.  The root-mean-square difference was 1.35 IBUs, and the maximum difference was 2.6 IBUs (Condition H).  According to this model, isomerized alpha acids contributed 66%, 57%, 39%, 33%, and 3% to the IBU values of conditions H through L, respectively.

utilExp2-Figure5-AAsolubility

Figure 5. Estimated alpha-acid solubility (for Conditions A through F and H through K) plotted as a function of the initial concentration of alpha acids (at the start of the boil). The dashed green line shows the model of alpha-acid solubility at boiling based on these data points, with solubility increasing linearly from 0 up to the limit of 260 ppm.  A number of assumptions were made to arrive at these values, as described in the text.

Experiment #3: Summary and Conclusion
This third experiment separated IAA from nonIAA components in measured IBU values by targeting relative levels of IAA through different boil times.  The relative levels were computed from work on alpha-acid utilization by Malowicki and Huang.  The determination of IAA levels depended on the assumptions that (a) IAA values in the finished beer are less than those produced during the boil by some multiplication factor, (b) nonIAA components did not reach their solubility limit in this experiment and therefore increased linearly with amount of hops added, (c) the level of oxidized alpha and beta acids produced during the boil had reached its maximum by 12 minutes of boiling, and (d) there is a linear mapping between nonIAA concentrations in the final beer and initial alpha-acid concentrations, as long as the same hops are used.   The estimated IAA levels in the finished beer were than mapped to alpha-acid solubility under the assumptions that (e) alpha acids in the boil and above the solubility limit are very quickly degraded and (f) Condition A had an initial alpha-acid concentration below the solubility limit.  Of these assumptions, the weakest two are probably (c) and (e), but they still seem to me to be reasonable first approximations.  Given these assumptions, the results indicate a solubility limit of around 260 ppm at boiling.

This experiment also found evidence which suggests that the production of oxidized alpha and beta acids during the boil is temperature dependent, and that these oxidized acids can make a significant contribution to IBU values.

cond. A cond. B cond. C cond. D cond. E cond. F cond. H cond. I cond. J cond. K cond. L
weight of hops
0.37 oz /
10.49 g
0.74 oz /
20.98 g
1.11 oz /
31.47 g
1.48 oz /
41.96 g
1.85 oz /
52.45 g
2.22 oz /
62.94 g
0.37 oz /
10.49 g
1.11 oz /
31.47 g
1.11 oz /
31.47 g
2.22 oz /
62.94 g
2.22 oz /
62.94 g
boil time (min)
12.0 12.0 12.0 12.0 12.0 12.0 26.9 26.9 12.0 19.0 19.0
post-boil volume
1.64 G / 6.21 l 1.62 G / 6.13 l 1.62 G / 6.13 l 1.65 G / 6.25 l 1.61 G / 6.09 l 1.61 G / 6.09 l 1.59 G / 6.02 l 1.59 G / 6.02 l 1.62 G / 6.13 l 1.59 G / 6.02 l 1.63 G / 6.17 l
original gravity
1.0545 1.0550 1.0550 1.0540 1.0555 1.0555 1.0562 1.0563 1.0550 1.0562 1.0546
final gravity
1.0088 1.0084 1.0084 1.0096 1.0099 1.0104 1.0087 1.0093 1.0090 1.0098 1.0088
initial alpha-acid concentration (ppm)
135.5 274.3 411.5 538.7 690.1 828.1 135.5 406.6 399.0 813.1 793.1
measured IBUs
13.68 25.04 31.86 38.61 46.00 52.40 18 48 32 58 27
IBUs from detailed model
20.6 47.3 32.4 59.2 27.5
IAA (ppm)
11.02 18.60 19.91 21.73 23.00 23.67 17.07 42.81 20.86 32.41 1.20
nonIAA (ppm)
8.13 16.46 24.69 32.32 41.40 49.69 8.13 24.39 23.94 48.79 36.6
IAA percent of total (%) 57.6 53.0 44.6 40.2 35.7 32.3 67.7 63.7 46.6 39.9 3.2
AA solubility (ppm)
135.9 228.58 244.79 267.14 282.66 291.01 104.91 263.09 256.40 265.62 N/A

Table 4. Measured and modeled values of the first six conditions in the second experiment (Conditions A through F) and all five conditions in the third experiment (Conditions H through L).

Overall Summary
This blog post reports on three experiments that were designed to assist in the development of parameters of a detailed model of IBUs.  Results indicate that the use of a mesh bag for hops during the boil has a negligible impact on IBUs, and that the kettle material (stainless steel vs. aluminum) also has a negligible impact.  No effect of malt polyphenols was seen on IBU levels for a 3-week old beer.  The IBU levels in a beer can decrease fairly quickly during the initial weeks after fermentation, and this can be modeled with the formula IBU(age) = IBU0 × (0.32 × e-0.08×age + 0.68), where age is the age of the beer in weeks and IBU0 is the IBU value at time 0.  After 16 weeks, the IBU values seem to stabilize.  The alpha acid solubility limit at boiling appears to be approximately 260 ppm, under the assumption that alpha-acid concentrations above this limit do not contribute to isomerized alpha acids in the final beer.  This limit provides a simple explanation and model for a hopping-rate correction factor, with a better fit to the current data that the Garetz correction factor.  It also seems likely that oxidized alpha and beta acids produced during the boil can make up a sizeable fraction of the total nonIAA components, and nonIAA components can contribute significantly to the IBU.

None of these conclusions have been definitively proven, but they are plausible explanations based on the observed data.  The suggested solubility limit of 260 ppm is lower than the limit of 300 ppm estimated by Spetsig for boiling and at a pH of 5.2 [Spetsig, p. 1423], but Spetsig’s limit was determined by extrapolating from two data points at lower temperatures (25°C and 40°C) [Spetsig, p. 1424].

Acknowledgements
Many thanks to Dana Garves at Oregon BrewLab for her valuable feedback on this post!

References

  • V. A. Algazzali, The Bitterness Intensity of Oxidized Hop Acids: Humulinones and Hulupones, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2014.
  • R. Daniels, Designing Great Beers: The Ultimate Guide to Brewing Classic Beer Styles.  Brewers Publications, 2000.
  • J. Dierckens and M. Verzele, “Oxidation Products of Humulone and Their Stereoisomerism,” in Journal of the Institute of Brewing, vol. 75, pp. 453-456, 1969.
  • M. Garetz, Using Hops: The Complete Guide to Hops for the Craft Brewer. HopTech, 1st edition, 1994.
  • M. L. Hall, “What’s Your IBU,” in Zymurgy.  Special Edition, 1997.
  • Y. Huang, J. Tippmann, and T. Becker, “Kinetic Modeling of Hop Acids During Wort Boiling,” in International Journal of Bioscience, Biochemistry, and Bioinformatics, vol. 3, no. 1, January 2013.
  • M. G. Malowicki, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2005.
  • D. R. Maule, “The Fate of Humulone During Wort Boiling and Cooling”, in Journal of the Institute of Brewing, vol. 72, pp. 285-290, 1966.
  • G. Oliver, The Oxford Companion to Beer, Oxford University Press, 2011.
  • E. J. Parkin, The Influence of Polyphenols and Humulinones on Bitterness in Dry-Hopped Beer, Master of Science thesis (advisor: T. H. Shellhammer), Oregon State University, 2014.
  • V. Peacock, “The International Bitterness Unit, its Creation and What it Measures,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • T. H. Shellhammer, “Hop Components and Their Impact on the Bitterness Quality of Beer,” in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium, ed. Thomas H. Shellhammer, Master Brewers Association of the Americas, 2009.
  • L. O. Spetsig, “Electrolytic Constants and Solubilities of Humulinic Acid, Humulone, and Lupulone,” in Acta Chemica Scandinavica, vol. 9, pp. 1421-1424, 1955.
  • R. Stevens and D. Wright, “Evaluation of Hops [Part] X. Hulupones and the Significance of β Acids in Brewing,” in Journal of the Institute of Brewing, vol. 67, 1961.
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mIBU Experiments #1 and #3

Abstract
This post summarizes two of the three experiments I conducted in order to evaluate the accuracy of the mIBU approach described earlier, specifically Experiments 1 and 3. (The second experiment is described in a separate post, “An Analysis of Sub-Boiling Hop Utilization“.)  The results from the current two experiments show that when estimating IBUs, it’s important to have good estimates of (a) the alpha-acid rating of the hops, (b) storage conditions of the hops, (c) alpha-acid concentration in the wort, and (d) age of the beer.  If these factors are accounted for, the IBU estimates in these experiments are fairly close to measured IBU values.  When the wort is allowed to cool naturally after flameout for (in this case) 15 minutes, the use of the mIBU approach yields much better estimates for hop additions at flameout and with short boil times.

Introduction
For the first experiment, I brewed four batches of beer with hops added at different times during the boil and with forced cooling at flameout, in order to calibrate my brewing setup and resulting measured IBU values with the Tinseth IBU formula.  For the third experiment, I brewed five batches, each with 15 minutes of post-flameout natural cooling, to compare the measured IBU values with values predicted by the Tinseth formula and the mIBU approach.

In both of these experiments, IBU values were measured by Analysis Laboratory.  Scott Bruslind from Analysis Laboratory was very responsive and encouraging, providing a full set of measurements (including gravity, pH, and attenuation, in addition to IBUs) as well as alpha-acid measurement of hops.

Experiment #1
The first experiment calibrated measured IBUs obtained from my brewing setup with the standard Tinseth IBU formula.  As a result of this experiment, I got some idea of how much variation to expect in IBU measurements, and I found that several factors inadvertently impacted both measured and modeled values.

Experiment #1: Methods
In this experiment, four batches of beer were brewed with forced cooling at flameout.  Each batch was brewed separately: 2.0 lbs (0.91 kg) of Briess dry malt extract in 2 G (7.6 liters) of water, with 0.60 oz (17.0 g) of Cascade hop cones (in a loose mesh bag) and a slurry of 0.08 oz (2.3 g) of Safeale US-05 yeast.  The boil time of the wort for all conditions was 60 minutes.  The hops were added at 60 minutes (condition A), 40 minutes (condition B), 20 minutes (condition C), and 10 minutes (condition D) prior to flameout.  All batches had the following targets: pre-boil volume of 2.15 G, pre-boil specific gravity of 1.043, post-boil volume of 1.45 G, and (post-boil) original gravity (OG) of 1.060.  The wort was quickly force-cooled and the hops were removed immediately at flameout.  The wort was left to sit, covered, for several minutes, and then 3½ quarts were decanted into a 1 G (4 liter) container.  After 90 seconds of aeration (a.k.a. vigorous shaking), the yeast was pitched.  Fermentation and conditioning proceeded for 19 days.  The beers were bottled (with 0.46 oz (13 g) of sucrose per condition as priming sugar) and left to bottle condition for an additional 8½ weeks before IBU values were measured.

The Cascade hops, purchased in June, had an alpha-acid (AA) rating on the package of 8.0%.  I had the alpha acids measured close to the time of the experiment by both Analysis Laboratories (AL) and subsequently by KAR Labs (KAR).  The AL alpha-acid rating was 6.25% (with 7.25% beta acids and a Hop Storage Index (HSI) of 0.45), and the KAR rating was 4.11% (with 5.40% beta acids).  An HSI of 0.45 indicates 28% loss or 72% AA remaining, which translates into an AA rating on brew day of 5.76% if the harvest AA rating was 8.0%, or a harvest AA rating of 8.7% if the level was 6.25% at the time of the experiment.  From the AL numbers, the alpha/beta ratio is 0.862 and the from the KAR numbers, the alpha/beta ratio is 0.761, both on the low side for Cascade.  From these various numbers, two things are clear: (1) the actual AA rating at the time of brewing could easily have been anywhere from about 4% to 6.25%, which is a pretty wide variation, and (2) I had inadvertently used hops that had been improperly stored.  Afterwards, I had a nice chat with my LHBS, and they confirmed that while the hops were stored in very good mylar bags, they spent at least part of the year in an air-conditioned room at the back of the store.  I’ve since become much more concerned and proactive about the storage conditions of my hops.  At any rate, Glenn Tinseth recommends, if needed, adjusting the linear scaling factor (4.15) in his equation to fit the current conditions, so we can pick our best guess of the AA rating and adjust the scaling factor to fit the data.  Equivalently, we can pick one scaling factor (e.g. the recommended 4.15) and adjust the AA rating to fit the data.

Experiment #1: Results
Table 1 (below) shows measured and modeled IBU values for each of the conditions in Experiment 1, along with a variety of other measured parameters (e.g. original gravity).  The observed and modeled IBU values are plotted below in Figure 1.

Determining the post-boil volume was a little tricky… if the hops are in the wort they will increase the measured volume by displacement, and if they are removed from the wort they will decrease the volume by soaking up wort.  In the end, I took the ratio of pre-boil gravity points divided by post-boil gravity points, and multiplied that by the initial volume.  The post-boil specific gravity (i.e. the OG) measured by Analysis Laboratory was determined from the original extract reading in degrees Plato.

The average alpha acid concentration of about 210 ppm for all conditions is less than the threshold of 230 ppm that seems to be the cutoff for a linear increase in IBU values with alpha-acid concentration.  Therefore, the Tinseth equation should still yield good results at this concentration.

For IBU values from the Tinseth equation, I used the recommended scaling factor of 4.15 and the average specific gravity of the start and end of the boil, as recommended by Tinseth, and adjusted the AA rating to minimize the error.  This yielded an AA rating of 5.79%, about the middle of the range between 4.00% and 6.25%, and a root-mean-squared (RMS) IBU error of 4.32 IBUs.  How good (or bad) is this error?  It’s hard to say, but it’s within the reported perceptual threshold of 5 IBUs, with one condition having a difference of about 7 IBUs.  The problem in getting a better fit is that the modeled IBU value at 60 minutes is higher than the measured IBU, and the modeled IBU at 10 minutes is lower than measured; a linear scaling factor can’t fix that.  These differences at high and low steeping times may be due to the large amounts of oxidized alpha and beta acids in the poorly-stored hops that I used.

In a separate blog post, I present a more detailed model of IBUs; the values obtained from that model for this experiment are also given in Table 1.  This more detailed model takes into account factors such as original gravity, hopping rate, age and storage conditions of the hops, alpha/beta ratio, age of the beer, and form of the hops.  Using this model, the estimated AA rating at harvest was 8.0% (the same as the value on the package) and the estimated degradation factor was 0.82 (somewhat higher than the HSI-based factor of 72%), yielding an AA rating on brew day of 6.6%.  An AA rating of 6.6% is higher than the AA rating estimated from the Tinseth equation (5.79%) but close to the value from AL (6.25%).  The estimated alpha/beta ratio was 0.75, somewhat lower than the value from AL (0.86) but very close to the KAR value (0.761).  The RMS error from this model was 2.93 IBUs (about two-thirds the error of the Tinseth model), with a maximum difference of 3.7 IBUs.  According to this model, isomerized alpha acids contributed 67%, 61%, 48%, and 36% to the IBU values of conditions A through D, respectively.  The low percentage for even the 60-minute boil is due to the age, poor storage conditions, and low alpha/beta ratio of the hops.  I used the average boil gravity and average volume over the other four conditions to estimate 4.9 IBUs at a boil time of 0 minutes (0% from isomerized alpha acids); this value is higher than it would typically be, because of the poor storage conditions of the hops.

condition
A
condition
B
condition
C
condition
D
pre-boil SG (from hydrometer)
1.042 1.0425 1.042 1.042
pre-boil volume
2.11 G / 7.99 l 2.13 G / 8.06 l 2.15 G / 8.14 l 2.15 G / 8.14 l
time of hops addition
60 min 40 min 20 min 10 min
post-boil SG (from hydrometer)
1.059 1.058 1.061 1.063
post-boil SG (measured by AL)
1.05986 1.05891 1.06337 1.06417
post-boil volume 1.49 G / 5.64 l 1.54 G / 5.83 l 1.44 G / 5.45 l 1.42 G / 5.38 l
FG (measured by AL)
1.01134 1.00863 1.00928 1.00950
measured IBUs (from AL)
35.7 34.3 27.1 22.0
IBUs from Tinseth
40.0 34.0 24.7 14.9
IBUs from detailed model
38.9 32.1 24.9 18.2

Table 1. Measured and modeled values of the four conditions in the first experiment.  Results provided by Analysis Laboratories are indicated by “AL”.

mIBU-exp1

Figure 1. Measured IBU values (red line), IBU values from the Tinseth model (blue line), and IBU values from the detailed model (green line). The model values were fit to the measured values by minimizing the error, which was necessary because the AA rating at brew day was basically unknown.

Experiment #1: Conclusion
A number of issues came up when analyzing the data from this experiment.  The point of this first experiment was, in some sense, to discover such issues and be able to address them in subsequent experiments.   (Regardless of the numerical results, all of these experiments have been a wonderful learning opportunity.)  Here’s a list of bigger issues with the first experiment: (1) I don’t have a reliable estimate of the AA rating of the hops on brew day, which obviously impacts any modeled IBU value; (2) the hops were improperly stored, which drastically decreased the amount of alpha acids and increased the amount of oxidized alpha and beta acids, impacting the measured IBU values; (3) I used a digital kitchen scale to measure 0.60 oz of hops, which was OK but not ideal… I’ve since upgraded to a more precise jewelry scale; and (4) boiling a small amount of wort for 1 hour yields a large change in specific gravity and an evaporation rate that is very difficult to control, leading to unwanted variability.

Despite these issues, fitting the AA rating to the IBU data yielded a not-terrible fit to the Tinseth model (with an RMS error of 4.32 IBUs).

Experiment #3
The third experiment was similar to the first, except that the wort was left to sit and cool naturally for 15 minutes after flameout.  The purpose of this experiment was to compare measured IBU values with IBU values predicted by the Tinseth formula and the mIBU approach.

Experiment #3: Methods
In this experiment, five batches of beer were brewed with 15 minutes of natural cooling at flameout, and forced cooling when the 15-minute mark was reached. This time, I made one batch of wort and divided it into equal portions for each condition.  In this case, 9.25 lbs (4.20 kg) of Briess dry malt extract was added to 7.0 G (26.5 liters) of water to yield 7.75 G (29.34 liters) of wort, with a specific gravity of 1.057.  This wort was boiled for 30 minutes and left to cool with the lid on. The specific gravity of the wort after the 30-minute boil was 1.062, with a volume of about 7 G (26.5 liters).  The wort for each condition was taken from this larger pool of wort, to guarantee the same specific gravity at the start of the boil.  The hops were boiled for 60 minutes (condition A), 30 minutes (condition B), 15 minutes (condition C), 7½ minutes (condition D), and 0 minutes (condition E).

For each condition, 1.3 G (4.92 liters) was heated to boiling.   When the wort reached boiling, 0.80 oz (22.7 g) of Cascade hops were added.  The wort was boiled for the amount of time specified for each condition, and the boil was conducted with the lid on, in order to minimize evaporation losses and keep the boil gravity from increasing too much.  At flameout, the lid was removed (to make it easier to measure the change in temperature over time) and the hops remained in the wort.  At 15 minutes after flameout, the hops were removed and the wort was quickly cooled.  The wort was left to sit, covered, for several minutes, and then 3½ quarts (3.31 liters) were decanted into a 1 G (4 liter) container.  After 90 seconds of aeration (a.k.a. vigorous shaking), a slurry with 1.5 oz (42.5 g) of Safeale US-05 yeast was pitched into each condition.  Fermentation and conditioning proceeded for 21 days.  The beers were bottled (with 0.45 oz (12.75 g) of sucrose per condition as priming sugar) and left to bottle condition for an additional 5 weeks before IBU values were measured.

In order to have better control over the hops in this experiment, I used some of my precious home-grown Cascade.  The AA rating at harvest, measured by KAR Labs, was 6.64% (with a beta acid percentage of 5.38%).  While they were nearly 8 months old at the time of the experiment, I had stored them in vacuum-sealed bags in a freezer at  -6°F (-21°C).  Around the time of the experiment, I sent samples to both KAR Labs and Alpha Analytics.  This time, KAR Labs reported an AA rating of 6.66% and beta acid level of 5.51%; Alpha Analytics reported an AA rating of 7.70% and beta acid level of 6.80%.  The HSI value from Alpha Analytics was 0.22, indicating no significant degradation over the 8 months.  Once again, there was a surprising lack of clarity in the AA rating from the laboratory-measured values… it could be anywhere from 6.6% to 7.7%, or even outside this range.  The alpha/beta ratio was approximately 1.1 to 1.2.  Fortunately, the data from both KAR Labs and Alpha Analytics indicate that the hops were well preserved, so the hop degradation factor should be close to 1.

Experiment #3: Results
Table 2 provides measured and modeled IBU values for each of the conditions in Experiment 3, along with a variety of other measured parameters. The observed and modeled IBU values are plotted below in Figure 2. The post-boil volume and specific gravity were determined using the same methods as in Experiment 1.

I thought that by keeping the lid on the kettle during the boil, there would be almost no evaporation and therefore almost no change in specific gravity between conditions.  Instead, I found a fairly large change in original gravity between the different conditions, probably because I did take off the lid occasionally to stir the wort.  In the future, I’ll have to take this source of variability into account.

In this experiment, the alpha-acid concentration of about 345 ppm was (unfortunately) well above the estimated threshold of 230 to 260 ppm.  (The alpha-acid concentration can be computed as AA × W × 1000 / V, where AA is the alpha-acid rating of the hops (on a scale from 0 to 1), W is the weight of the hops (in grams), and V is the volume of the wort (in liters).  Therefore, the Tinseth equation will predict IBU values higher than measured IBU values, unless this concentration is taken into account.

I kept a minute-by-minute record of the decrease in temperature after flameout for each condition.  Since the volume of each condition was similar, the temperature decay was also similar for each condition.  I used a single temperature-decay function, fit to the temperatures from all five conditions, to model post-flameout temperature decay in this experiment:  temp = 0.1065t2 – 5.1294t + 211.682, with temperature temp measured in Fahrenheit and time t measured in minutes.  (While larger volumes seem to fit well with a straight line, these small volumes had a temperature decay that fit much better with a quadratic function.)

The recommended scaling factor of 4.15 in the Tinseth model did, in fact, yield predicted IBU values that were much higher than measured values.  In the first experiment, it seems that the default value worked well as a compromise between the age of the beer (which, unaccounted for in the Tinseth model, would have yielded larger predicted values than measured values) and the degradation of the hops (which, given the storage conditions and alpha/beta ratio less than 1, would have yielded smaller predicted values than measured values).  In this third experiment, the storage conditions and alpha/beta ratio are probably closer to what Tinseth used when he developed his model, and so the combination of hopping rate and age of the beer yielded predicted values much greater than measured values when using the default scaling factor.  The purpose of this experiment is to compare the Tinseth and mIBU models, and so we can adjust the scaling factor in both models to fit the data, and see which model produces values closer to the measured values given the best scaling factor.  In this case, a scaling factor of 6.15 with the AA rating estimated by the detailed model (6.0%, as described below) provided the best fit of the Tinseth model to the measured IBU values.  With this scaling factor, there is an RMS error of 8.33 IBUs and a maximum difference of 16.1 IBUs (at the 0-minute condition).  (If a different AA rating is used, the same error is obtained with a different scaling factor.)

Another option for fitting the data is to explicitly account for the hopping rate and age of the beer, and use the recommended scaling factor of 4.15 in both the Tinseth and mIBU models.  We can approximate the alpha-acid solubility limit by simply limiting the alpha-acid concentration in the Tinseth equation to 260 ppm.  (Computationally, we can adjust the weight of the hops to an “effective” weight that limits the alpha-acid concentration to no more than 260 ppm at the beginning of the boil.)  We can estimate the impact of age on IBUs using an adjustment factor developed in a separate blog post: 0.32 × e0.08 ageweeks + 0.68, where ageweeks is the age of the beer in weeks.  With these modifications to the Tinseth formula and the recommended scaling factor of 4.15, there is an RMS error of 8.24 IBUs and a maximum difference of 16.1 IBUs (at the 0-minute condition).

For the mIBU model, a scaling factor of 6.60 provides the best fit to the data when not accounting for alpha acid concentration or age of the beer.  In this case, there is an RMS error of 1.92 IBUs, with a maximum difference of 3.41 IBUs (at the 0-minute condition).   When accounting for these two factors and using a scaling factor of 4.15, there is an RMS error of 1.89 IBUs, with a maximum difference of 2.74 IBUs (at the 30-minute condition).

For the more detailed model, the best fit was obtained by adjusting the AA rating, alpha/beta ratio, and decay factor to fit the data.  An AA rating of 6.0% (somewhat lower than the value of 6.64% reported by KAR), an alpha/beta ratio of 1.6 (higher than the value of 1.21 reported by KAR), and a decay factor of 0.95 provided the best fit to the data.  With these values, there is an RMS error of 1.36 IBUs and a maximum difference of 2.5 IBUs (for the 60-minute condition).  According to this model, isomerized alpha acids contributed 75%, 67%, 56%, 44%, and 23% to the IBU values of conditions A through E, respectively. Given the good storage conditions of the hops, the fairly low iso-alpha percentage for even the 60-minute boil is, in this case, due to the alpha-acid concentration above the solubility limit.

condition
A
condition
B
condition
C
condition
D
condition
E
pre-boil SG (from hydrometer)
1.062 1.062 1.062 1.062 1.062
pre-boil volume
1.30 G / 4.92 l 1.30 G / 4.92 l 1.30 G / 4.92 l 1.30 G / 4.92 l 1.30 G / 4.92 l
time of hops additions
60 min 30 min 15 min 7.5 min 0 min
post-boil SG (from hydrometer)
1.075 1.069 1.067 1.069 1.065
post-boil SG (measured by AL)
1.0760 1.0720 1.0685 1.0689 1.0658
post-boil volume 1.06 G / 4.01 l 1.12 G / 4.42 l 1.18 G / 4.47 l 1.17 G / 4.43 l 1.22 / 4.62 l
FG (measured by AL)
1.01190 1.01114 1.01008 1.01016 1.00944
measured IBUs (from AL)
46.4 35.4 26.1 21.2 16.1
IBUs from Tinseth, scale 6.15
49.2 36.6 22.6 13.0 0.0
IBUs from Tinseth, scale 4.15
44.6 35.0 22.8 13.0 0.0
IBUs from mIBU model, scale 6.60
46.8 37.1 26.3 19.3 12.7
IBUs from mIBU model, scale 4.15
45.5 38.1 28.5 20.7 14.2
IBUs from detailed model
48.9 35.8 26.1 20.6 14.6

Table 2. Measured and modeled values of the five conditions in the third experiment.  Results provided by Analysis Laboratories are indicated by “AL”.

mIBU-exp3-new

Figure 2. Measured IBU values (red line), IBU values from the Tinseth model (blue line), IBU values from the mIBU model (black line), and IBU values from the detailed model (green line).  The Tinseth, mIBU, and detailed-model values take into account the initial alpha-acid concentration and the age of the beer.

Experiment #3: Conclusion
Results obtained (a) by adjusting the scaling factor to fit the data, or (b) by using the default scaling factor and incorporating modifications to the Tinseth formula to account for alpha-acid concentration and age of the beer, were similar.  In both cases, the mIBU approach showed an improved estimate, especially at the 0-minute and 7½-minute conditions.  In these two cases, the differences between the two models (14.2 and 7.7 IBUs, respectively) seem to be outside the range of typical random variation, with the mIBU results much closer to measured IBU values.

The detailed model also showed a good fit to the observed data.  I find it interesting that a complicated model with many parameters performed about as well, in this case, as the simpler mIBU model, after accounting for alpha-acid concentration and age of the beer.

Overall Summary
Analysis of the results indicates: (1) In the first experiment, the poor storage conditions of the hops, the low alpha/beta ratio, and the age of the beers probably caused the values predicted by the Tinseth formula (with the recommended scaling factor) to be somewhat different from the measured IBU values, but an inability to get a good value for the alpha-acid rating of the hops on brew day prevents more specific conclusions; (2) Accounting for the hopping rate, storage conditions of the hops, alpha/beta ratio, age of the beer, and other parameters in a much more detailed model of IBUs provided a better fit to the data; (3) In the third experiment, the mIBU method provided good estimates with the recommended scaling factor of 4.15, after taking into account the alpha-acid concentration and age of the beer (and with the use of well-preserved hops); and (4) Results from the third experiment show the expected increase in IBUs caused by post-flameout utilization, and that this increase was modeled well by the mIBU method.

A Summary of Factors Affecting IBUs

This blog post is excessively long.  In order to make it somewhat more manageable, here are links to the various sections:
1. Introduction
2. Definitions of IBUs
xxxxx2.1 IBU Definition from the American Society of Brewing Chemists (ASBC)
xxxxx2.2 IBU Definition from Val Peacock
3. A General Description of Factors Affecting IBUs
xxxxx3.1 Concentration of Isomerized Alpha Acids (IAA) Under Ideal Conditions
xxxxx3.2 Accounting for Post-Boil Utilization
xxxxx3.3 Adjustments to the Concentration of Isomerized Alpha Acids
xxxxx3.4 A Revised IBU Formula for nonIAA Components
xxxxxxxxxx3.4.1 Oxidized Alpha Acids
xxxxxxxxxx3.4.2 Oxidized Beta Acids
xxxxxxxxxx3.4.3 Polyphenols
xxxxxxxxxx3.4.4 Solubility of nonIAA Components
4. Available Data, Parameter Estimation, and Results
xxxxx4.1 Overview
xxxxx4.2 Sources of IBU Data
xxxxxxxxxx4.2.1 Tinseth Utilization
xxxxxxxxxx4.2.2 Peacock Hop-Storage Conditions
xxxxxxxxxx4.2.3 Personal Experiments
xxxxx4.3 Parameter Estimation and Results
5. Discussion of Results
6. Summary
References

1. Introduction
This blog post presents a summary of some of the factors that affect the measurement of International Bitterness Units (IBUs) (or simply “Bitterness Units” (BU) if you’re already international).  In order to provide as cohesive a summary as possible, I provide both qualitative and quantitative descriptions of these factors.  The purpose of the quantitative model is descriptive, not predictive.  In other words, the information here may be helpful in understanding how certain factors affect IBU values, but it may not be sufficient to predict the IBU level of your beer much better than existing predictive formulas (e.g. the Tinseth formula).  With so many interrelated factors and guesses of appropriate values for many factors, there is a very good chance that IBU values predicted from this quantitative description will not be the same as measured IBU values.  If, however, you simply want to get a better understanding of what components contribute to an IBU value, how the storbuage conditions and amount of hops used may impact IBUs, or how late hopping may decrease the relative proportion of isomerized alpha acids, then this might be the blog post for you.

The more I learn about hops, the more complex the topic becomes, with a seemingly never-ending level of detail. If you’re familiar with Alice In Wonderland, then this blog post goes only one level down the IBU rabbit hole, and it looks briefly through a number of open doors at that level without going through them.  In other words, there’s a lot of research, chemistry, opinions, known unknowns, unknown unknowns, and contradictions that I’m not going to touch on.  If you’re not familiar with Alice In Wonderland, then think of this post as an impressionist painting: if you stand back far enough, you should be able to see a complete picture.  If you look too closely and focus too much on the details, however, things that make sense in their relationship to other things may become, when isolated from the larger context, meaningless splotches.

The IBU measurement itself is not always highly regarded.  While it is often reported to be correlated with the bitterness of beer (e.g. [Priest and Stewart, p. 266]), the perception of bitterness is not linear (especially at high bitterness levels [Hieronymus, p. 184]), bitterness may have different qualities not captured by the IBU measurement [Peacock, p. 163], and the correlation between IBU levels and bitterness doesn’t hold up under every circumstance (e.g. with dry-hopping [Maye et al., p. 25]).  On the other hand, it is a universally-known and (sometimes grudgingly) accepted quantitative measurement.  This post doesn’t touch on the pros and cons of the IBU, but, accepting it at face value, tries to break it down into various components and relationships.

This post provides a summary of a large number of sources, including Val Peacock’s article “The International Bitterness Unit, its Creation and What it Measures” in Hop Flavor and Aroma (ed. Shellhammer); Mark G. Malowicki’s Masters thesis, Hop Bitter Acid Isomerization and Degradation Kinetics in a Model Wort-Boiling System; Michael L. Hall’s article “What’s Your IBU” in Zymurgy (1997); Michael J. Lewis and Tom W. Young’s chapter “Hop Chemistry and Wort Boiling” in Brewing; Mark Garetz’ article “Hop Storage: How to Get – and Keep – Your Hops’ Optimum Value” in Brewing Techniques, and his book Using Hops; Stan Hieronymus’ book For the Love of Hops; J. S. Hough et al.’s Malting and Brewing Science (volume 2); and many other theses, print, and internet sources.  If you look at the bibliography, you’ll see many publications produced under the guidance of Thomas Shellhammer.  I’ve tried to cite appropriately, and I’ve put the full bibliography at the bottom of this post.  I’ve omitted a lot of interesting details from these sources, in order to maintain a more focused narrative.

2. Definitions of IBUs
2.1 IBU Definition from the American Society of Brewing Chemists (ASBC)
Because of the complexity of hops and IBUs, it’s probably a good idea to start at a high level of description, which is deceptively simple but not very informative: An IBU is a measurement of the amount of absorption of light at 275 nm (abbreviated as A275nm) in a liquid, multiplied by 50.  The liquid in this case is not just any liquid, but beer that has been combined with twice as much iso-octane (TMP) and also diluted in octyl alcohol and hydrochloric acid [American Society of Brewing Chemists], i.e. “acidified beer.”  In mathematical form, we can say:

IBU = A275nm(beer) × 50 [1]

where IBU is the resulting IBU value, “beer” indicates the substance being analyzed (after proper acidification), and A275nm(beer) is the amount of light absorbed at 275 nm from a sample of acidified beer [Peacock, p. 158].

This measurement has been found to correlate well with the perception of bitterness in beer.  As Lewis and Young state, “the value for [IBU] is a good representation of the sensory bitterness of beer” [Lewis and Young, p. 266].  Why does this correlation exist?  There are three intertwining factors: (1) the absorption of light at a particular (ultraviolet) frequency (275 nm) through a sample, (2) the concentration of certain substances in this acidified beer that absorb light at this frequency, and (3) the perception of bitterness that is associated with these substances.  This blog post pretty much ignores the first and third factors, assuming that it is predominately those substances that absorb more light at this frequency that have a bitter taste in beer.  What this post focuses on, then, is the second factor: the concentration of substances in acidified beer that absorb light at 275 nm.  In the development of the IBU measurement, there was a deliberate decision to include not only the bitter isomerized alpha acids (abbreviated here as IAA) that are produced during the boiling of hops in wort, but also other “bittering substances” that contribute to the perception of bitterness [Peacock, p. 159], and which happen (by happy circumstance) to absorb light at 275 nm (as isomerized alpha acids do).

The amount of absorption of light at 275 nm by a sample of acidified beer, multiplied by 50 (or, more precisely, 51.2), was found to provide a good approximation to the concentration of isomerized alpha acids in typical beer of the 1960s (when the IBU measurement was developed) [Peacock, p. 161].   So, we can say:

[IAA]beer1960s = A275nm(beer1960s) × 51.2 [2]

where [IAA]beer1960s is the concentration of isomerized alpha acids in the 1960s beer (in mg of isomerized alpha acid per kg of beer, or parts per million (ppm)), and “beer1960s” on the right-hand side of the equation indicates that we’re measuring the absorption of a certain type of beer.  (Note that beer contains a number of types of substances that absorb light at 275 nm; IAA is the usually predominant, but not only, substance [Peacock, p. 159].)  The IBU value can approximately equal the concentration of IAA (i.e. Equations [1] and [2] can be approximately equal), but generally only for hops and boiling times typical of the 1960s, because of the relative concentrations of other bittering substances.

If one has a solution that contains only isomerized alpha acids and no other substances that absorb light at 275 nm, the concentration of IAA can be estimated with the following equation [Peacock, p. 161]:

[IAA]IAAsolution = A275nm(IAAsolution) × 69.68 [3]

where [IAA]IAAsolution is the concentration of isomerized alpha acids in this solution, and “IAAsolution” on the right-hand side of the equation indicates that the solution being analyzed contains only isomerized alpha acids as the relevant (light-absorbing) substance.

Figure 1(a) shows hypothetical (i.e. completely made up) data that represent absorption of light at 275 nm on the horizontal axis and the measured concentration of a substance X on the vertical axis.  (The data are fake, but the figure will hopefully be useful to illustrate some concepts.)  In this case, a line can be fit through the data to predict concentration given absorption: concentration = (69.68 × absorption) + 0.  The offset of this line is 0 (meaning that the predicted value for an absorption of 0 is a concentration of 0), and so we can ignore the offset, characterizing the relationship with a single multiplication factor (69.68).

absorptionVsConcentrationALL

Figure 1. Concentration as a function of light absorption for various circumstances. (a) Concentration of X is approximated by light absorption multiplied by 69.68.  (b) Both X and Y can have their concentration predicted by multiplying absorption by 69.68.  (c) The concentration of substance Z is predicted by light absorption multiplied by 696.8 (10 × X).  We can model the concentration of Z multiplied by a scaling factor (0.10) as a function of absorption, which allows us to treat it like substances X and Y (with a multiplication factor of 69.68).

2.2 IBU Definition from Val Peacock
This background leads us to a second high-level description of IBUs:  An IBU is an estimation of the concentration of isomerized alpha acids in typical 1960s beer, based on the combined concentration of isomerized alpha acids and other bittering substances in beer, multiplied by 5/7 [Peacock, p. 161].  In mathematical notation:

[IAA]beer1960sIBU = 5/7 × ([IAA]beer + [nonIAA]beer) [4]

where [IAA]beer1960s is the concentration of isomerized alpha acids in 1960s beer, [IAA]beer is the concentration of IAA in the beer being analyzed, “nonIAA” are “other bittering substances that aren’t isomerized alpha acids” in beer (which is not the same as “non-isomerized alpha acids,” despite the abbreviation), and [nonIAA]beer is the concentration of these substances in the beer being analyzed.

Why is there the multiplication by 5/7 in Equation [4]?  We can derive it from Equations [2] and [3] if we make three assumptions: (1) For substance X in an appropriate solution, if the absorption of light at 275 nm is zero (A275nm(X) = 0), then the concentration of X is zero ([X] = 0).  (2) There is a linear relationship between the absorption of light at 275 nm and the concentration of relevant bittering substances in beer, at least within the range of interest.  (3) The linear relationship between absorption and concentration is the same for all relevant substances in beer, namely 69.68.  The first two assumptions were made by the 1967 Analysis Committee of the European Brewery Convention that developed the unit that became the IBU [Peacock, p. 160-161], so they seem reasonable.  The third assumption is not necessarily true, but we can modify it for those cases where it isn’t true, so let’s assume it’s true for now.

Let’s start by looking at two beers that have the same amount of absorption of light at 275 nm (i.e. the same level of bitterness): one beer is a (cryogenically preserved) 1960s beer with this bitterness level, and the other beer is something you just brewed:

A275nm(beer1960s) = A275nm(beer) [5]

where beer1960s is our 1960s beer, and beer is the one just brewed.

We can then multiply the numerator and denominator of the left-hand side by 51.2, and multiply the numerator and denominator of the right-hand side by 69.89, and the relationship still holds:

(A275nm(beer1960s) × 51.2) / 51.2 = (A275nm(beer) × 69.68) / 69.68 [6]

The relevant bittering substances in beer are IAA and nonIAA (by definition), so we can replace beer in Equation [6] with (IAA + nonIAA):

(A275nm(beer1960s) × 51.2) / 51.2 = (A275nm(IAA + nonIAA) × 69.68) / 69.68 [7]

From Equation [3], we can multiply absorption of light at 275 nm by 69.68 to predict the concentration of IAA in a solution that contains only IAA as the relevant substance.  From our third assumption, nonIAA substances have the same relationship between absorption and concentration, so we can also multiply the absorption of light at 275 nm by 69.68 to predict the concentration of nonIAA in a solution that contains only nonIAA as the relevant substance.  This is illustrated in Figure 1(b), showing two different substances that have the same mapping between absorption and concentration.  Since the relevant bittering substances in beer are IAA and nonIAA, we can predict the combined concentration of (IAA + nonIAA) from the absorption of light at 275 nm in a solution containing both substances.  (For example, if we have 30 mg of IAA in 1 kg of solution, we have 30 ppm and light absorption of 0.43.  Likewise, if we have 21 mg of IAA and 9 mg of nonIAA in 1 kg of solution, we have a total of 30 mg of (IAA + nonIAA), or 30 ppm.  That 30 ppm will also have a light absorption of 0.43.)  Now we can map from absorption to concentration, using Equation [2] for the left-hand side and the third assumption for the right-hand side:

[IAA]beer1960s / 51.2 = [IAA + nonIAA]beer / 69.68 [8]

We can then bring the 51.2 from the left to the right by multiplying both sides by 51.2, and note that the combined concentration of both IAA and nonIAA in beer ([IAA + nonIAA]beer) is equal to the sum of the concentrations of the individual substances ([IAA]beer + [nonIAA]beer) :

[IAA]beer1960s = (51.2 / 69.68) × ([IAA]beer + [nonIAA]beer) [9]

Next, we can simplify 51.2/69.68 to 5/7, and note that then the right-hand side equals Peacock’s definition of an IBU, and the left-hand side indicates that this is approximately equal to the concentration of IAA in the 1960s beer:

[IAA]beer1960sIBU = 5/7 × ([IAA]beer + [nonIAA]beer) [4] = [10]

Let’s look at a quick example… say we brew a beer with pure isomerized alpha acids, and we end up with [IAA]beer equal to 10 ppm.  In this case, [nonIAA]beer is zero, and the measured IBU value will be 7.  A beer with the same bitterness level brewed in the 1960s would have had, typically, 7 ppm of IAA and (the equivalent of) 3 ppm of nonIAA, with the same net concentration of bittering substances (10 ppm).  As another example, let’s say we brew a beer with poorly-stored hops, and we end up with equal concentrations of IAA and nonIAA, at 10 ppm each.  Now our beer will have an IBU value of 14.  A typical beer with the same bitterness level brewed in the 1960s would have had an IAA level of 14 ppm and a nonIAA level of 6 ppm.

Now let’s revisit the assumption that the concentration of nonIAA substances can be predicted from light absorption with a scaling factor of 69.68.  For the sake of explanation, let’s consider a hypothetical case where nonIAA substances have a scaling factor of 696.8, ten times that of IAA, as illustrated in Figure 1(c).  We can then plot the concentration of nonIAA substances divided by 10 (i.e. [nonIAA]/10) as a function of light absorption (Figure 1(d)), and return to our desired IAA scaling factor of 69.68.  We then just need to note in our equation that we’re no longer modeling the actual concentration of nonIAA, but the scaled concentration [nonIAA]beer × scalenonIAA:

[IAA]beer1960sIBU = 5/7 × ([IAA]beer + ([nonIAA]beer × scalenonIAA)) [11]

where scalenonIAA is the scaling factor needed to convert the absorption-to-concentration relationship of nonIAA (696.8 in our example) to the absorption-to-concentration relationship of IAA (69.68).  In our example, scalenonIAA is 0.10.  In a similar way, we can consider nonIAA as a group of substances, each with its own scaling factor.  If nonIAA consists of three different substances, nonIAA1, nonIAA2, and nonIAA3, we can write the relationship like this:

[IAA]beer1960sIBU = 5/7 × ([IAA]beer + (([nonIAA1]beer × scalenonIAA1) + ([nonIAA2]beer × scalenonIAA2) + ([nonIAA3]beer × scalenonIAA3))) [12]

where scalenonIAA1 is the scaling factor for the first nonIAA substance, scalenonIAA2 is the scaling factor for the second nonIAA substance, and scalenonIAA3 is the scaling factor for the third nonIAA substance.

The IBU value was designed to be approximately equal to the concentration of isomerized alpha acids (in ppm), given the boiling time, alpha acid levels, and storage conditions of 1960s beer and hops [Peacock, p. 161].  At that time, hops seem to have been stored for long periods of time at cellar or room temperature without special packaging [Peacock, p. 160 and 162].  As Peacock explains, for a typical beer made from typical hops with a typical age and duration of hop boiling, the relative concentration of IAA to all bittering substances (IAA + nonIAA) was about 5/7, or about 71%.  In more recent times, it is much more likely that hops are stored at freezing temperatures with less oxygen for less time, which makes the relative concentration of IAA (with a typical 1960s hop boiling time) much higher.  So, an IAA concentration of 14 ppm from a 60-minute boil might yield an IBU value closer to 12.  On the other hand, it is also common now to add a lot more hops much closer to flameout, which increases the relative concentration of nonIAA components in the beer (compared with longer boiling times), as discussed below.

3. A General Description of Factors Affecting IBUs
The preceding descriptions of IBUs actually helped us.  Now we know that there are only three things we need to worry about when modeling IBUs: the concentration of isomerized alpha acids (IAA), the concentrations of other bittering substances (nonIAA), and the scaling factors for the nonIAA substances.  Thanks to Peacock’s formulation, we’ve moved from the absorption of light at 275 nm (which is very difficult for a homebrewer to  predict) to the concentrations of different substances (which we can approximate).  This section looks at these three items in more detail.

Before getting too far into this section, this might be a good place to define some terms related to alpha acids and beta acids.  Alpha acids are part of the soft resins in the hop lupulin gland, and the alpha acids contain humulone, cohumulone, and adhumulone  [Oliver, p. 34].   Older work may refer to all alpha acids as humulones [Oliver, p. 462].  The oxidized alpha acids contain humulinone as their most important component [Algazzali, p. 13].  The soft resins also contain beta acids, which are also called lupulones [Oliver, p. 462].  The beta acids are composed of colupulone, adlupulone, lupulone, and prelupulone [Oliver, p. 260].  The oxidized beta acids contain mostly hulupones [Algazzali, p. 15].  The oxidized form of colupulone is called cohulupone [Stevens and Wright, p. 496].

3.1 Concentration of Isomerized Alpha Acids (IAA) Under Ideal Conditions
A lot of research has been conducted on modeling isomerized alpha acids.  We can use this work to estimate the IAA concentration that we need to model IBUs.  Mark Malowicki [Malowicki] provides a model for both the conversion of alpha acids into isomerized alpha acids and the subsequent conversion of isomerized alpha acids into other “uncharacterized degradation products”, as functions of time and temperature, under fairly ideal laboratory conditions (with pH 5.2 and an alpha-acid concentration of 80 ppm).  (These degradation products include humulinic acid, isobutyraldehyde, and iso-hexenoic acid [Hough et al., p. 480].)  Malowicki describes the conversion of alpha acids into isomerized alpha acids as a first-order reaction following an Arrhenius equation with a temperature-dependent rate constant k1:

k1(T) = 7.9×1011 e-11858/T [13]

where k1(T) is the rate constant for the conversion of alpha acids into isomerized alpha acids and T is the temperature in degrees Kelvin.  A first-order reaction is of the form [X] = [X]0ekt (where [X] is the concentration of substance X at time t, [X]0 is the initial concentration of X (at time 0), and e is the constant 2.71828…), so we can describe the reduction of alpha acids (due to their conversion into isomerized alpha acids) as:

[AA]wort = [AA]0 ek1(T)t [14]

where [AA]wort is the resulting concentration of alpha acids in the wort at time t (in minutes), [AA]0 is the initial concentration of alpha acids (at the start of the boil), and k1(T) is the rate constant from Equation [13].  We can assume that the reduction in alpha acids is mirrored by a corresponding increase in isomerized alpha acids (see [Malowicki p. 6]).  Second, Malowicki describes the subsequent conversion of isomerized alpha acids into degradation products, also as a first-order reaction with a temperature-dependent rate constant:

k2(T) = 4.1×1012 e-12994/T [15]

where k2(T) is the rate constant for the conversion of isomerized alpha acids into other products (and T is still in degrees Kelvin).

Both Malowicki [Malowicki, p. 27] and Yarong Huang et al. [Huang 2013] show how to combine these equations into a single model of the cumulative concentration of isomerized alpha acids as a function of time and temperature:

[IAA]wort = [AA]0 (k1(T)/(k2(T)-k1(T))) (ek1(T)t-ek2(T)t) [16]

where [IAA]wort is the concentration of isomerized alpha acids in the wort at time t and temperature T.  We can plot this equation in Figure 2, with time on the horizontal axis, relative concentration of isomerized alpha acids (compared with the initial concentration of alpha acids) on the vertical axis, and a few different steeping temperatures represented with different colors:

isoAlphaAcidConcentraion

Figure 2.  Theoretical relative concentration of isomerized alpha acids in water, as a function of time and temperature.

This plot at 100°C (212°F) looks reassuringly similar to the utilization of alpha acids in the Tinseth equation for predicting IBUs [Tinseth]; the scale is different, and the shape is somewhat different, but the general trend at boiling is similar.

Equation [16] relies on the initial concentration of alpha acids at the beginning of the boil, which we can determine from the volume of wort (in liters), the weight of hops added (in grams), and either (a) the measured percentage of alpha acids at the time of the boil or (b) the measured percentage of alpha acids at the time of harvest and the degradation of alpha acids over time.  These values will give us the concentration of alpha acids in wort (in ppm):

[AA]0 = AA × W × 1000 / V [17]

where AA is the alpha acid rating of our hops, scaled to the range 0 to 1 (i.e. AA is the proportion of the hop (cone, pellet, or extract) that is alpha acids, from 0 to 1; e.g. an alpha acid rating of 7% becomes 0.07), W is the weight of the hops in grams, the factor of 1000 converts from grams to milligrams, and V is the volume of the wort in liters.  These units combine to give us milligrams of alpha acids per kilogram of wort (since 1 liter of water equals 1 kg; we’ll ignore the extra weight of the extract), or approximately parts per million.

Is V the volume at the beginning, middle, or end of the boil?  While [AA]0 indicates the initial level of alpha acids (at the beginning of the boil), we don’t have a factor that adjusts for volume changes between the beginning and end of the boil.  If we did have such a factor, it would describe the difference between the pre-boil volume and the post-boil volume, since the final concentration of isomerized alpha acids is determined by the post-boil volume (before racking losses that reduce the volume but don’t change the concentration).  Instead of having a separate factor and applying it explicitly, we can specify that V is the post-boil volume, and the numbers will come out the same as if we started with pre-boil volume and then accounted for evaporation.  In short: V should be post-boil wort volume (not including the volume of hops or trub).

If we don’t know the alpha acid rating of the hops when we brew our beer, we can use the initial (harvest) estimate with a model of how alpha acids degrade over time, developed by Mark Garetz [Garetz article] to estimate the alpha acid rating for hop cones:

AAAAharvest × AAdecayfactor = AAharvest × 1/ek×TF×SF×D [18]

where AAharvest is the alpha acid rating of the hops after harvest and drying, AAdecayfactor is a multiplication factor for how much the AA level has decayed over time (1.0 for fresh hops), k is a value that depends on the percent of alpha acids lost after 6 months at room temperature (which in turn depends on the variety of hops), TF is the temperature factor that describes how degradation is affected by temperature, SF is the storage factor that describes how degradation is affected by storage conditions, and D is the age of the hops, in days.  The full definition of all terms is provided in Garetz’s article [Garetz article].  For hop pellets, the rate of deterioration is much slower.  Hieronymus says that while whole hops can lose up to 100% of their alpha acids when stored at 68°F (20°C) for one year, pellets lose only 10% to 20% under the same conditions [Hieronymus, p. 230].  If you use pellets that were made immediately after harvest, and they’ve been stored in the refrigerator or freezer, it’s probably safe to assume that losses are somewhere between 5% and negligible, yielding a correction factor between 0.95 and 1.0.  If you don’t know how long the hops in your pellets were in whole-cone form, or what the storage conditions were, predicting the losses becomes quite difficult.

3.2 Accounting for Post-Boil Utilization
It’s clear that at flameout, the wort (unfortunately) does not instantaneously cool to pitching temperature.  According to Equation [16], there can still be measurable isomerization even at 158°F (70°C).  Therefore, as the wort cools after flameout, there can be a significant increase in the concentration of isomerized alpha acids.  I’ve suggested in a previous blog post that we can model this post-flameout increase in IBUs by multiplying the change in IAA concentration at time t by a temperature-dependent factor at t (with a factor of 1.0 for boiling), and then integrating the instantaneous values over time to arrive at a cumulative IAA concentration that reflects post-flameout temperature changes. In the current framework, we have a function (Equation [16]) that is already dependent on temperature, so we can take the derivative with respect to time, compute the instantaneous change in concentration at time t and temperature T, and then integrate over time t to arrive back at total concentration of IAA.  While the temperature is boiling, we will arrive at the same answer as if we didn’t take the derivative and then integrate.  As the kettle cools after flameout, we change the rate constants to reflect the lower rate of isomerization.  This can be implemented in less than 20 lines of programming code, and I’ve since noticed that Malowicki suggests this very approach, saying “for conditions in which the rate constants change with a changing temperature profile, the concentrations of iso-humulones formed during kettle boiling can be calculated using [equations] which define the differential change in alpha-acid, iso-alpha-acid, and degradation product concentrations with respect to time” [Malowicki, p. 27].

We  can take the derivative of Equation [16] in order to compute the change in IAA concentration at time t:

d([IAA]wort)/dt = [AA]0 (k1/(k2k1)) (k2e-k2tk1e-k1t) [19]

where d([IAA]wort)/dt is the rate at which the IAA concentration changes, in ppm per minute.  However, instead of using [AA]0 to compute the change at any time t, we can use the equations defined by Malowicki [p. 27] to compute the change in concentration at time t using current concentration levels:

d([AA]wort)/dt = –k1 [AA]wort [20]
d([IAA]wort)/dt = k1 [AA]wortk2 [IAA]wort [21]

By using these equations, we only need to know the total concentration of these substances at the previous time step in order to compute the concentrations at time t.  Only at t=0 do we need to know the initial concentration of alpha acids.  Since we’re integrating the instantaneous values anyway, Malowicki’s formulation of the derivatives ends up being just as easy to program and incredibly more efficient at dealing with multiple hop additions.

A model of how temperature decreases after flameout can be obtained by bringing the desired volume of water to a boil, turning off the heat, measuring the temperature at one-minute intervals, and then fitting a line or polynomial to the data.  I’ve found that the temperature decrease of a 6-gallon (23-liter) volume (no lid on the kettle) can be modeled fairly well with a straight line, at least for the first 20 minutes or so:

TF(tf) = -1.344 tf + 210.64          (for temperature in Fahrenheit) [22a]
TC(tf) = -0.74667 tf + 99.244    (for temperature in Celsius) [22b]
TK(tf) = -0.74667 tf + 372.394  (for temperature in Kelvin) [22c]

where TF is the estimated temperature in Fahrenheit, -1.344 is the rate of change (°F per minute), tf is time after flameout (in minutes), and 210.64 is the approximate temperature at flameout (when tf = 0, in °F). Likewise, TC is the estimated temperature in Celsius, -0.7466 is the range of change (°C per minute), and 99.244 is the approximate temperature at flameout (in °C); TK is temperature in Kelvin modeled with -0.74667 degrees Kelvin per minute and a flameout temperature of 372.394 Kelvin.  (Note that this formula will only yield reasonable results for a typical home-brewing system with a 6-gallon (23-liter) volume and an uncovered kettle, and even these “reasonable” results will be affected by factors such as kettle material and size.  To maximize accuracy, one should measure the temperature decay of their own system and determine a formula based on system-specific data.  Fortunately, the data I’ve collected so far indicates that this function is not significantly dependent on ambient temperature or relative humidity, so this function only needs to be constructed once per brewing system.)

We can model total concentration of IAA by integrating the change in [IAA] at each instant, where this amount of change is dependent on the steep time and temperature of the wort.  Rather than expressing this as a formula, I think a short amount of pseudo-code will be easier to understand (referred to as Code [1]), even if you’re not a programmer:

integrationTime = 0.001;
AA = AA0;
IAA = 0.0;
time = 0.0;
while (time <= totalTime) {
    if (time <= boilTime) 
        temp = 373.15; 
    else 
        temp = (-0.74667 * (time - boilTime)) + 372.394;
    k1 = 7.9 * pow(10,11) * exp(-11858.0/temp);
    k2 = 4.1 * pow(10,12) * exp(-12994.0/temp);
    dAA = -1.0 * k1 * AA;
    AA = AA + (dAA * integrationTime);
    dIAA = (k1 * AA) - (k2 * IAA);
    IAA = IAA + (dIAA * integrationTime);
    time = time + integrationTime;
}

where the integration time of 0.001 (called integrationTime) is sufficient for accuracy to at least two places past the decimal point.  The variable AA0 is the initial concentration of alpha acids, in ppm (see Equations [17]).  Here, AA is the total concentration of AA, or [AA], after time time (in minutes).  Likewise, IAA is the total concentration of IAA, or [IAA], after time time.  The value of totalTime is the length of the boil in minutes (boilTime) plus any time after the boil when isomerization might be happening (postBoilTime).  A loop is set up to evaluate (and integrate) all time points from 0.0 to totalTime in increments of 0.001 minutes, with time representing the current time instant.  The temp variable is temperature at the current time, in Kelvin.  The k1 and k2 variables are the rate constants from Equations [13] and [15].  The variable dAA is the derivative of [AA], or change in [AA] per minute, as defined in Equation [20].  Likewise, the variable dIAA is the derivative of [IAA], or change in [IAA] per minute, as defined in Equation [21].  The pow() function raises the first argument to the power of the second argument; the exp() function computes the exponent of its argument.  After finishing the loop, IAA will equal the total concentration of isomerized alpha acids, accounting for both time and (post-flameout) temperature.

3.3 Adjustments to the Concentration of Isomerized Alpha Acids
Now we know how to measure the concentration of IAA in wort during the boil under ideal conditions.  We can use this as the basis for a quantitative model of IBUs.  What we need next is a way to describe the differences between ideal laboratory conditions and (home) brewery conditions.  Many factors affect the rate or amount of conversion from alpha acids to isomerized alpha acids: temperature (e.g. boiling at high altitudes), pH of the wort, form of the hops (e.g. extract, pellet or cones; loose or bagged), and alpha-acid concentration in the wort.  Other factors can be described as losses of IAA that are produced in the boiling wort but never make it into the pint glass: losses due to high wort gravity, other losses during the boil, and losses due to fermentation, filtration, and aging.  We’ll look at each of these briefly in this section.  In general, if we have a loss of x%, the loss factor will be (1 – (x%/100)); for example, a loss of 10% will become a loss factor of 0.90.

Before getting into too much detail, this is a good place to define a high-level term, “utilization.”  Hop utilization, U, is the ratio of the amount of isomerized alpha acids in finished beer, divided by the amount of alpha acids added to the kettle, and then multiplied by 100 to convert to percent [e.g. Lewis and Young, p. 266]:

U = 100 × (isomerized alpha acids in beer) / (alpha acids added to kettle) [23]

It should be noted that utilization refers only to the creation and loss of isomerized alpha acids, not to IBUs.

Isomerization as a Function of Temperature and pH: According to Malowicki’s equations (above), a decrease in temperature (e.g. below 100°C) will decrease utilization.  If you live at a high enough altitude, your wort will boil at less than 100°C, in which case you might want to adjust k2 and k2 in Equations [13] and [15], or include a temperature-dependent rate factor, RFtemp(T).  Post-flameout temperature dependencies are discussed above.  (Lewis and Young, Palmer, Hieronymus, and others note that the intensity of the boil affects utilization [Lewis and Young, p. 266; Palmer p. 55; Hieronymus, p. 188], which is presumably related to wort temperature.)

It is generally accepted that an increased wort pH will increase utilization [e.g. Lewis and Young, p. 266].   This was demonstrated by Kappler (at pH levels of 4.0, 5.0, and 6.0) and by Huang (at pH levels of 4.5, 5.2, 5.5, and 6.5), looking at the degradation of isomerized alpha acids added to the boil [Kappler, p. 334; Huang, p. 50].  However, Malowicki looked at isomerized alpha acids produced and degraded during boiling at pH values of 4.8, 5.2, 5.6, and 6.0, and found that “the dataset did not show a significant effect of pH on rate of iso-alpha-acids produced” [Malowicki, p. 38].  The typical homebrewer should aim for a mash pH in the ballpark of 5.2 to 5.4 [Palmer and Kaminski, p. 60; Noonan, p 144; Fix, p 49; Troester citing Kunze (2007) and Narziss (2005)], although a pH as high as 5.8 is still acceptable [Troester].  Since Malowicki’s work looked at both the production and degradation of isomerized alpha acids, and since this work didn’t show a significant effect of pH in the range of interest, the model of IBUs that is built in this post does not have a dependency on pH.  Therefore, the rate factor for wort pH, RFpH(pH), is set to be 1 for all values of pH.

Isomerization as a Function of Form of the Hops: It is often said that whole hops do not provide as much utilization as hop pellets [e.g. Daniels p. 78].  According to Lewis and Young, “the alpha acids dissolve most easily from extracts, less easily from pellets …, and least with whole hops” [Lewis and Young, p. 266].  The higher rate at which alpha acids from pellets dissolve, compared with whole cones, is because “the pelletization process ruptures the lupulin glands and spreads the resins over the hop particles, giving a larger surface area for isomerization” [Hall, p. 58].  Noonan says that “with pelletized hops, ruptured and better-exposed lupulin glands give greater utilization” [Noonan, p. 154].  Garetz indicates that pellets have better utilization up to a boil time of 30 minutes (after which utilization is the same), because after 30 minutes all of the alpha acids have been dissolved, regardless of whether they come from cones or pellets [Garetz book, p. 131].

Hough et al. say that alpha-acid extracts are actually much less efficient than whole or pelletized hops: “the solubility of humulone was the limiting factor in its utilization.  … In trials using pure humulone, only 50-60% of the resin added was isomerized during [the] 1.5 h boil.  In contrast, 65-75% of the alpha acids present in hops are isomerized in the same period, which supports the view that the isomerization of humulone is catalyzed by the presence of hop cones, break, or even an inert surface such as Celite.” [Hough et al., p. 489, citing Maule, p. 288].  Since Malowicki used alpha-acid extract in his experiment (with no added surfaces to serve as a catalyst), the correction factor for the form of the hops in our quantitative description is 1.0 for extracts and about 1.27 (70%/55%) for non-extract forms.  (Note that there is 57% isomerization of alpha acids at 90 minutes according to Equation [16], which is very much in line with the statement by Hough et al.)

Expressing whole hops as less efficient than pellets, Noonan provides a whole-hop correction factor (in table form) that varies from 0.66 to 1.0, based on boil time and gravity [Noonan, p. 215].  Garetz recommends a correction factor of 0.90 for boil times up to 30 minutes, otherwise a correction factor of 1.0 [Garetz book, p. 141].  Hieronymus says that hop pellets are 10% to 15% more efficient than cones [Hieronymus, p. 188], translating into a correction factor between 0.87 and 0.91 when using whole cones.  According to Michael Hall, Mosher specifies a correction factor of 0.75 [Hall, p. 62].  This leaves a wide range of possible correction factors for the use of whole hops compared with pellets (from 0.66 to 1.0), with a median factor of 0.91.  For the model of IBUs being built, I’ll assume a factor of 0.91.  This whole-hop vs. pellet correction factor is in addition to (i.e. multiplied by) the correction factor for non-extracts, 1.27.  Therefore, pellets have a correction factor of about 1.27 and whole hops have a correction factor of about 1.16.

Garetz also says that hops kept in a mesh bag during the boil have lower utilization than loose hops, with a correction factor of 0.91 for loosely-stuffed hops and 0.83 for a full bag. Whole hops in a loosely-packed mesh bag will then have a combined correction factor of 1.05 (1.27 × 0.91 × 0.91) [Gartez book, p. 141].  I recently looked at the effect of a mesh bag vs. loose hops on measured IBUs, and found no significant difference (blog post to come in the future).  Marshall Schott at Brülosophy also looked at bagged vs. loose hops, and found 25 IBUs for the bagged hops and 27 IBUs for the loose hops [Schott].  While this difference is not significant, this ratio of 0.926 (25/27) is close to Garetz’s correction factor of 0.91.  In short, it’s not clear if hop cones in a mesh bag really do have lower utilization, but I’ll keep the suggested correction factor of 0.91.  For the model being developed, I’ll assume that bagged hops are always loosely bagged, for a “bagging” correction factor of 0.91.

Isomerization as a Function of Alpha-Acid Concentration: Along with the form of the hops, the relative amount of hops (and therefore also the relative amount of alpha acids) in the wort affects utilization.  As Lewis and Young say, “a high hopping rate reduces extraction efficiency” [Lewis and Young, p. 267].  Daniels phrases this as “simply adding more and more hops does not produce a linear increase in the amount of bitterness produced” [Daniels, p. 85].  Fix also notes that the utilization rate is affected by hop concentration [Fix, p. 47].  Hough et al. say that “hops are utilized more efficiently at low rates” [Hough et al., p. 489].  Maule determined that reduced utilization at higher hop rates can only be accounted for by the “difficulty with which [isomerized alpha acid] enter[s] solution when wort [is] boiled with large amounts of [alpha acid]” [Maule, p. 290], and that “only a small portion of the resin present on the hot break … can be claimed to be truly adsorbed” [Maule, p. 289].

Garetz provides the only source I’m aware of with a quantitative model of the relationship between amount of hops and utilization.  He proposes a hop-rate correction factor (also described by Hall and Daniels) that depends on volume and “desired IBU” to determine the weight of hops needed [Garetz book, p. 137; Hall, p. 63; Daniels, p. 86].  When I was initially developing this blog post, I used a modified form of his equation to estimate a correction factor based on volume, weight of hops, and alpha acid rating of the hops, since we don’t know the desired IBU when trying to predict an IBU value.  However, after some difficulty fitting the IBU model developed in this post to available data, and after further experimentation, I concluded that Garetz’s correction factor underestimates the effect of alpha acid concentration on utilization.

A better fit to the data available to me can be obtained by either (a) simply limiting the alpha acids available for conversion to about 260 ppm, or (b) limiting the alpha acids in solution to 230 ppm, increasing Malowicki’s rate constant k1(T) (Equation [13]) by a factor of 3.9, and increasing the rate constant k2(T) (Equation [15]) to some very large value, e.g. 1000.  (Increasing k1(T) means that alpha acids not yet in solution are converted more quickly into IAA, but increasing k2(T) means that those IAA that are created while not in solution are nearly instantly degraded.)  (I will provide more detail about the second suggested limit on alpha acid solubility in a future blog post.)  These limits are greater than the solubility of alpha acids at room temperature (around 90 ppm [Malowicki, Appendix A, pp. 51-54]), but Spetsig’s paper on the solubility of humulone indicates an approximate limit of around 300 ppm at boiling and pH 5.2 [Spetsig 1955, p. 1423-1424].  Using this approach, utilization increases linearly with alpha-acid concentration until the solubility limit is reached (e.g. 230 ppm or 260 ppm); at higher concentrations utilization increases either much less or not at all.  The values for the solubility limit and the increase in k1(T) were obtained using the model described in this blog post, so these are two unknown parameters in the model development; they will be referred to as [AA]limit and k1_scale.

Instead of providing a formula to show how the model of alpha-acid isomerization is affected by alpha-acid solubility, I think that modifications to Code [1] that set the solubility limit to 230 ppm and include changes to the rate constants will be more helpful in understanding how the modified model works.  This new code will be referred to as Code [2]:

integrationTime = 0.001;
AA_limit = 230;
k1_scale = 3.90;
if (AA0 > AA_limit) {
    AA_sol = AA_limit;
    AA_unsol = AA0 - AA_limit;
} else {
    AA_sol = AA0;
    AA_unsol = 0.0;
}
IAA = 0.0;
time = 0.0;
while (time <= totalTime) {
    if (time <= boilTime) 
        temp = 373.15; 
    else 
        temp = (-0.74667 * (time - boilTime)) + 372.394;
    k1_sol = 7.9 * pow(10,11) * exp(-11858.0/temp);
    k2_sol = 4.1 * pow(10,12) * exp(-12994.0/temp);
    dAA_sol = -1.0 * k1_sol * AA_sol;
    AA_sol = AA_sol + (dAA_sol * integrationTime);
    if (AA_sol < AA_limit AND AA_unsol > 0) {
        AA_sol = AA_sol - (dAA_sol * integrationTime);
        AA_unsol = AA_unsol + (dAA_sol * integrationTime);
    }
    dIAA_sol = (k1_sol * AA_sol) - (k2_sol * IAA_sol);
    IAA_sol = IAA_sol + (dIAA_sol * integrationTime);
    k1_unsol = k1_sol * k1_scale;
    k2_unsol = k2_sol * 1000.0;
    if (AA_unsol > 0.0) {
        dAA_unsol = -1.0 * k1_unsol * AA_unsol;
        AA_unsol = AA_unsol + (dAA_unsol * integrationTime);
        dIAA_unsol = (k1_unsol * AA_unsol) - (k2_unsol * IAA_unsol);
        IAA_unsol = IAA_unsol + (dIAA_unsol * integrationTime);
        if (IAA_unsol < 0) IAA_unsol = 0.0;
    } else {
        AA_unsol = 0.0;
        dAA_unsol = 0.0;
        dIAA_unsol = 0.0;
        IAA_unsol = 0.0;
    }
    time = time + integrationTime;
}

where the variables are the same as in Code [1], but dAA, AA, dIAA, IAA, k1, and k2 now have two parts: the part that is related to alpha-acids that have been dissolved in the wort (dAA_sol, AA_sol, dIAA_sol, IAA_sol, k1_sol, and k2_sol) and the part that is related to the alpha-acids that are not yet dissolved in the wort (dAA_unsol, AA_unsol, dIAA_unsol, IAA_unsol, k1_unsol, and k2_unsol).  If we start with an alpha-acid concentration above the solubility limit [AA]limit, the part that is less than the limit (dissolved in wort) isomerizes and is destroyed at the same rates as described by Malowicki.  As dissolved alpha acids are converted into isomerized alpha acids, lowering the concentration of dissolved alpha acids, some of the alpha acids not yet dissolved go into the wort solution to maintain the solubility limit.  The not-yet-dissolved alpha acids are converted into isomerized alpha acids at a higher rate (k1(T) × k1_scale), and the not-yet-dissolved isomerized alpha acids are quickly destroyed and don’t contribute to the final concentration of isomerized alpha acids.

Isomerization as a Function of Kettle Size and/or Geometry: The kettle size and/or kettle geometry may also impact utilization [Daniels, p. 78; Fix, p. 47].  As Hieronymus says, “larger kettles are more efficient, and the difference between a five-gallon homebrew system and even a 10-barrel (310-gallon) commercial brewery is startling” [Hieronymus, p. 188].  There are other claims, however, that recipes should scale linearly with kettle size, indicating no impact on utilization [e.g. Spencer].  If there is an impact, the reason for the change in utilization is not clear to me, especially since Malowicki used only tiny volumes of wort (12 ml) [Malowicki, p. 19] and obtained high utilization rates at boiling (see Figure 2).  The only quantitative description I’ve seen of this impact on utilization is in an article on BeerSmith, which says that “Hop utilization is much higher at craft brewing scales, because large boils simply extract more bitterness. … The Hop Utilization Factor … can easily be 125%, 150% or possibly more for a multi-barrel brewing system” [Smith].  It may be that the observed increase in utilization with kettle size is a reflection of longer times between flameout and cooled wort, which is already accounted for in the current model with post-boil utilization.  In short, kettle size (or wort volume) may (or may not) have an impact on utilization, with a scaling factor ranging from 1.0 (no impact) to 1.5 (large impact).  Because of the difficulty of reconciling Malowicki’s use of tiny volumes and resulting high utilization, I assume that kettle size has no impact on utilization.  Therefore, the rate factor for kettle size, RFsize(V), is assumed to be 1.

Losses Due to Wort Gravity: Utilization decreases with increasing wort gravity, at least at higher gravities [e.g. Lewis and Young, p. 266; Hieronymus, p. 188; Hall, p. 62; Daniels, p. 78; Palmer, p. 55; Malowicki, p. 44; Garetz book, p. 130; Hough et al., p. 489; Kappler, p. 334].  As Lewis and Young state, “iso alpha acids react with proteins of wort whence they are partially removed as trub or hot break” [Lewis and Young, p. 266].  As the gravity increases, the concentration of wort proteins increases, implying a greater loss of isomerized alpha acids with increasing gravity.  Kappler found losses of isomerized alpha acids at higher gravities when adding (already) isomerized alpha acids to the boil [Kappler, p. 335], indicating that higher gravity causes more isomerized alpha acids to bind with trub and settle out of solution (as opposed to slowing the rate of conversion from alpha acids to isomerized alpha acids).  Malowicki did not find a significant change in utilization at specific gravities of 1.000 and 1.040 [Malowicki, p. 39], and Garetz indicates that the lower limit for this effect is a specific gravity of 1.050 [Garetz book, p. 130].  Greg Noonan [Noonan, p. 215] provides a table of utilization as a function of boil time, original gravity, and form of the hops.  (His table simply lists “wort density” and “specific gravity”, but he defines wort density as original gravity [Noonan, p. 204].) The original gravity in his table seems to be an independent scaling factor of the other two parameters, with scaling factors of about 1.0, 0.921, 0.865, 0.842, and 0.774 at averaged gravities of 1.040, 1.058, 1.070, 1.080, and 1.090, respectively.  A line can be fit through these points to determine an original-gravity correction factor as a function of original gravity:

LFOGN(OG) = (-4.944 × OG) + 6.166    if OG > 1.045, else 1.0 [24]

where LFOGN(OG) is Noonan’s gravity loss-correction factor (expressed as an equation instead of the original table form) and OG is the original gravity.  If OG is less than or equal to 1.045, LFOGN(OG) is defined as 1.  Glenn Tinseth models the  gravity correction factor as LFWGT(WG) = 1.65 × 0.000125(WG − 1), with a scaling factor of 1.0 at around a (typical) wort gravity (WG) of 1.055.  (Tinseth uses the term “wort gravity” and suggests using the average of the (initial) boil gravity and original gravity for wort gravity [Tinseth].)  Because Malowicki measured the production of isomerized alpha acids in water (with a specific gravity of 1.0), we want to think of any increase in gravity as a reduction in the production of isomerized alpha acids, when compared with Malowicki’s work.  Since Noonan’s formula describes higher gravity as always yielding less utilization, his original-gravity correction factor is more suitable for our purposes; it also provides a compromise between the correction factors proposed by Tinseth, Rager, and Garetz [Hall, p. 61].

Other Losses During the Boil:  Isomerized alpha acids are lost during the boil in ways that are not dependent on the wort gravity.  Malowicki says that “trub, and specifically the formation of trub, leads to greatly increased losses of bitter acids” [Malowicki, p. 8; emphasis mine].  He cites work by H.O. Askew in which the use of pre-formed trub produced losses of only 5% to 9%, but the formation of trub created losses of 35% [Malowicki, p. 7-8].  Malowicki also cites Laufer and Brenner who found a 38% loss of bitter acids to trub and a 35% loss to spent hops.  Spetsig reports that about 25-30% of the bitter substances are found in the spent hops and 25-40% are found in the trub [Spetsig 1968, p. 346].  Hall cites Hough et al., who cite Maule (1966), saying that “about 7% of the iso-alpha acids are removed with the breaks” [Hall, p. 57; Hough et al., p. 489].  Garetz says that “8-10% of the iso-alpha acids are adsorbed (meaning they cling to the surface of) the hot and cold breaks.  This number appears to be fairly constant, even given wide variations in the amount of break, composition of the wort, and the method and length of cooling” [Garetz book, p. 126].  In short, the estimated loss of isomerized alpha acids during the boil ranges from 7% to 73%, yielding a correction factor from 0.27 to 0.93, which is a bit too large of a range to be of practical value.

Losses During Fermentation: Isomerized alpha acids are also lost during fermentation [e.g. Hieronymus, p. 190]. Lewis and Young say that “during fermentation, iso-alpha-acids associate with the surface of the yeast cells present… Iso-alpha-acids, being surfactants, react with inert surfaces of all sorts and for example separate on gas bubbles to be deposited on the fermenter walls” [Lewis and Young, p. 267].  Hall describes the same process, saying that “during the fermentation process, iso-alpha acids are scrubbed by the rising CO2 and collect in the foam of the kraeusen.  This sticky foam can be blown off, skimmed off or stuck on the sides of the fermenter … Iso-alpha acids also are bound up by the yeast cells and removed when the yeast flocculates out” [Hall, p. 57].  Daniels says that the amount of loss is dependent on the amount of yeast pitched and the “extent of yeast growth during fermentation” [Daniels, p. 78].  Garetz says that there are two factors, “the total growth of the yeast crop and the amount of time the yeast stays in suspension”, and that there is a 5% variation depending on the flocculation characteristics of the yeast [Garetz book, p. 126].  He also says that if the alpha acids are mixed back into the beer at the right time, utilization is increased by 18% [Garetz book, p. 126], implying typical losses of 18%.  Fix (citing Garetz) estimates loss to yeast sediment at 10% to 20% [Fix, p. 49]. Malowicki (citing Laws et al.) reports losses during fermentation from 5% to 17% [Malowicki, p. 8] and also (citing Laufer and Brenner) losses to yeast of 10% [Malowicki, p. 7].  Spetsig reports losses of 10% to 15% [Spetsig, 1968].  Hieronymus reports losses during fermentation and packaging of 20% [Hieronymus, p. 191].  Tom Nielsen (from Sierra Nevada Brewing Co.) measured the IBUs of wort and finished beer made from 10 types of hops (9 aroma hops and 1 bittering hop) and found a fairly consistent fermentation loss of about 18% (standard deviation approximately 1.6%) [Nielsen, p. 65].  To summarize, there is IAA loss during fermentation ranging from 5% to 20%, yielding a correction factor between 0.80 and 0.95.  A factor of around 0.85 is probably the best compromise between all reported values, and so the model being developed here uses 0.85.  The flocculation factor suggested by Garetz is 0.95 for high-flocculation yeast and 1.05 for low-flocculation yeast [Garetz book, pp. 140-141].

Losses Due to Filtration and Aging:  According to Daniels, “any filtration will remove some bitterness … The addition of clarifying agents such as gelatin or PVPP may have a similar effect.” [Daniels, p. 79].  Garetz says that filtering will reduce utilization by 1.25% to 2.5%, for a filtration loss factor of about 0.98 [Garetz book, p. 141]:

LFfiltering(filtering) = 0.98 for filtered beer or 1.0 for unfiltered beer [25]

where LFfiltering(filtering) is the loss factor due to filtering, if any.

Hall says that “there are oxidation reactions that can reduce the bitterness of beer over extended storage periods” [Hall, p. 58].  According to Kaltner and Mitter, “over a storage time of 12 months, a degradation of bitter substances in various beers in a range of 10% to 15% could be analyzed” [Kaltner and Mitter, p. 37].  According to Peacock, citing results from Forster et al. (2004), beer loses 18% of  isomerized alpha acids and 14% of measured IBUs after 8 months at room temperature [Oliver, pp. 132-133, Peacock p. 164].  I am unaware of an existing model of how IBUs decrease with age for home-brewed beer stored in bottles at room temperature (which may have greater oxidation, less filtering, and other differences with commercially-bottled beer).  I therefore measured the decrease in IBUs for two home-brewed beers after 1, 2, 3, 6, 7, and 13 weeks from the start of fermentation, and fit the measured IBU decrease over time with an exponential-decay function.   If we assume that isomerized alpha acids and non-IAA components are affected by age at the same rate (which is probably an incorrect assumption [Peacock, p. 163], but not unreasonable as a first approximation), we can model the loss factor for isomerized alpha acids using the same age formula determined for IBUs:

LFage(ageweeks) = 0.32 × e0.08 ageweeks + 0.68 [26]

where LFage(ageweeks) is the loss factor due to age of the beer (in weeks).

Summary of IAA Adjustments: We can now express the concentration of IAA in the beer as a function of the concentration of IAA in the wort, multiplied by the various isomerization rate adjustment factors and IAA loss factors discussed above:

RFIAA(T, pH, hopsForm, V) = RFtemp(T) × RFpH(pH) × RFform(hopsForm) × RFsize(V) [27]
LFIAA(OG, flocculation, filtering, ageweeks) = LFOGN(OG) × LFboil × LFferment(flocculation) × LFfiltering(filtering) × LFage(ageweeks) [28]
[IAA]beer = [IAA]wort × RFIAA(T, pH, hopsForm, V) × LFIAA(OG, flocculation, filtering, ageweeks) [29]

where RFIAA is the isomerization rate factor adjustment of isomerized alpha acids, LFIAA is the loss factor for isomerized alpha acids, and [IAA]beer is the concentration of isomerized alpha acids in the finished beer.  The rate factor RFIAA is expressed as a combination of other factors, where RFtemp is a rate factor for temperature (with temperature T still in degrees Kelvin), if desired; RFpH is a rate factor for wort pH (currently a constant 1.0); RFform is the rate factor for the form of the hops (where hopsForm is “pellet”, “loose whole cones”, or “bagged whole cones”); and RFsize is the rate factor for kettle size (specified in this case with volume V).  The loss factor LFIAA is expressed as a combination of other factors, where LFOGN is Noonan’s loss factor as a function of original gravity; LFboil is the loss factor during the boil; LFferment is the loss factor due to fermentation (with flocculation being “high”, “medium”, or “low”); LFfiltering is the loss factor due to filtration (with parameter filtering being “unfiltered” or “filtered”); and LFage is the loss factor due to age (which varies with the age of the beer, ageweeks).  The concentration of IAA in the wort, [IAA]wort, can be computed using Code [2].

The only problem remaining for modeling [IAA]beer is that while we have a good idea of some factors (RFtemp, LFOGN) and a rough approximation of others (RFform, LFferment, LFfiltering, and LFage), we have very little basis for determining the remainder (LFboil,  [AA]limit, and k1_scale).  But we can come back to that problem later.

3.4 A Revised IBU Formula for nonIAA Components
At this point, we have as complete a description as we’re going to get of the concentration of isomerized alpha acids in beer.  The other factor in the IBU formula (Equation [12]) is the concentration of “other bittering substances,” which we call nonIAA.

Alpha acids (before isomerization) are neither soluble [e.g. Lewis and Young, p. 259] nor bitter [Shellhammer, p. 169], but as they age and become oxidized, the resulting oxidized alpha acids (oAA) are soluble in wort and bitter [Algazzali, pp. 14-15, p. 19, p.45; Maye et al, p. 23; Hough et al., pp. 435-436; Hough et al., p. 439; Lewis and Young, p. 265].  Oxidized alpha and beta acids are also produced during the boil [Parkin, p. 11, Algazzali, p. 17; Dierckens and Verzele, p. 454; Oliver p. 471].  Oxidized beta acids (oBA) are also soluble [Algazzali, p. 16] and may be produced and contribute to bitterness in the same way as oxidized alpha acids [Malowicki, p. 2; Peacock, p. 157; Fix, p. 36; Lewis and Young, p. 265; Hall, p. 55; Lewis and Young p. 265; Oliver, p. 132; Oliver, p. 470; Parker, p. 11; Algazzali, p. 17; Hough et al., p. 489].  The formulation of the Hop Storage Index (HSI) implies that oxidized alpha (and beta) acids have optical density at 275 nm [Algazzali, p. 19].  Finally, polyphenols may be a contributing factor to the nonIAA components [e.g. Krogerus]; as Shellhammer states, “the contribution of polyphenols to beer bitterness can not be overlooked” [Shellhammer, p. 177].

I haven’t been able to find definitive (e.g. more than one source) claims on the bitterness or A275nm properties of other substances that might be considered nonIAA.  That leaves us with oxidized alpha acids, oxidized beta acids, and polyphenols as the only nonIAA components that influence the measurement of IBUs.  We can then re-write Equation [12] to be more specific, replacing the generic nonIAA1, nonIAA2, and nonIAA3 with oxidized alpha acids (oAA), oxidized beta acids (oBA) and polyphenols (PP):

IBU = 5/7 × ([IAA]beer + (([oAA]beer × scaleoAA) + ([oBA]beer × scaleoBA) + ([PP]beer × scalePP))) [30]

where [oAA]beer is the concentration of oxidized alpha acids in the beer (in ppm), scaleoAA is the non-IAA scaling factor specific to oxidized alpha acids,  [oBA]beer is the concentration of oxidized beta acids in the beer (in ppm), scaleoBA is the non-IAA scaling factor specific to oxidized beta acids, [PP]beer is the concentration of polyphenols in the beer (in ppm), and scalePP is the non-IAA scaling factor specific to polyphenols.  (Note that we can compute [IAA]beer using Code [2] and Equation [29].)

3.4.1 Oxidized Alpha Acids
As hops age, the alpha and beta acids become oxidized.  The “most important group of oxidized alpha acids formed during hop aging is the humulinones” [Algazzali, p. 13].  The rate at which alpha acids oxidize during storage is determined by the form of the hops (e.g. cones or pellets), hop variety, age, temperature, and amount of exposure to oxygen [Garetz article].  Garetz has a model that predicts the amount of alpha acids remaining in hop cones, given these factors [Garetz article].  (As long as they are properly stored, pellets undergo oxidation at a much slower rate [Hieronymus, p. 230], and so Garetz’s model should only be used for whole hop cones.)  A decrease in the amount of alpha acids is mirrored by a corresponding increase in the amount of oxidized alpha acids.  The alpha acids also undergo some amount of oxidation while still on the bine [Hieronymus, p. 233] and further during the warm and highly oxygenated conditions of hop drying [e.g. Hieronymus, p. 126], and so the level of oxidized alpha acids when we get our newly-dried hops soon after harvest can be greater than zero [Maye, p. 23].  Finally, oxidized alpha acids are created during the boil [Algazzali, p. 17; Dierckens and Verzele, p. 454].

We can model the level of oxidized alpha acids (oAA) in the wort as the sum of three contributions: (1) the oAA present in the freshly-dried hops as a result of oxidation on the bine and during drying, (2) the oAA that accumulate as the hops age and deteriorate, and (3) oAA that is produced during the boil:

oAA = oAAfreshoAAstorageoAAboil(t) [31]

where oAA is the level of oxidized alpha acids (as percent of weight of the hops), oAAfresh is the level of oxidized alpha acids in freshly-dried hops, oAAstorage is the level of oxidized alpha acids produced during storage, and oAAboil(t) is the level of oxidized alpha acids produced during the boil as a function of boil time t; all components are expressed as percent of weight of the hops.

Based on data from Maye et al. [Maye, p. 24], I fit the level of oAA for fresh hops (with a Hop Storage Index (HSI) of 0.25 [Hough et al., p. 434]) to the model of alpha-acid decay proposed by Garetz [Garetz article], and determined that oAAfresh can be modeled reasonably well for the available data with a storage factor of 1 (loose hops), a temperature factor of 1 (20°C or 68°F), and a duration of 0.5 days.  I then fit the data in the Maye paper for higher HSI values to the loss predicted from the Garetz formula multiplied by a scaling factor of 0.022.  (I will go into much more detail on this in a future blog post.)  This leaves oAAboil(t) as the only unknown parameter that must be searched for, expressed as the amount of alpha acids that undergo oxidation relative to the amount of available alpha acids in the boil.  Given a lack of information about oAAboil(t), I’ll assume that it increases linearly from when the hops are added until some time toAAmax, after which it remains at a constant value, oAAboilMax.  These two parameters allow approximation of a wide variety of plausible oxidized alpha acid concentrations produced during the boil.  We can then re-write oAA using different functions to replace oAAfresh, oAAstorage, and oAAboil(t):

oAAboil(t) = oAAboilMax × t / toAAmax if t < toAAmax; otherwise oAAboilMax [32]
oAA = (1 – 1/ek×1×1×0.5) + (oAAagescale × (1 – AAdecayfactor)) + (AA × oAAboil(t)) [33]

where oAAboil(t) is the relative amount of alpha acids that undergo oxidation during the boil, oAA is the same level of oxidized alpha acids in Equation [31], k is the variety-specific hop decay factor from the Garetz model, oAAagescale is the age-related scaling factor of 0.022, AAdecayfactor is the alpha acid decay factor from Equation [18], and AA is the level of alpha acids at the start of the boil (Equation [18]).  This equation is specific to hop cones; some modification would be required for hop pellets, presumably a larger value of oAAfresh but a value close to zero for oAAstorage.  Since oxidized alpha acids are soluble, all of the oxidized alpha acids in the hop cones are in the wort shortly after being added to the kettle, and the oxidized-alpha-acid level peaks at toAAmax.

That leaves us with two other oAA factors that we still need to account for: losses and a scaling factor.  I have not yet been able to find any description of the losses of oxidized alpha acids during the boil and fermentation, so this is a completely unknown factor. It seems reasonable to assume that oxidized alpha acids are lost to trub, yeast, and in other ways, just as isomerized alpha acids are lost in the process of turning wort into beer.  Therefore, because the same types of losses probably occur for oxidized alpha acids as for isomerized alpha acids, we can model the oxidized alpha acid losses as the losses that affect isomerized alpha acids multiplied by some (unknown) scaling factor.  The scaling factor is a high-level correction factor for differences between losses found in isomerized alpha acids and oxidized alpha acids.  In other words,

[oAA]wort = oAA × W × 1000 / V [34]
[oAA]beer = [oAA]wort × LFIAA(OG, flocculation, filtering, ageweeks) × scaleoAAloss [35]

where [oAA]wort is the concentration of oxidized alpha acids in the wort, [oAA]beer is the concentration of oxidized alpha acids in the finished beer, W is (still) the weight of the hops in grams, V is (still) the post-boil volume of the wort in liters, LFIAA is the same IAA loss factor from Equation [28] and scaleoAAloss is the (unknown) loss scaling factor.

We also need a scaling factor in Equation [30] that scales the factor for absorption of light at 275 nm of oxidized alpha acids (unknown) to the factor for absorption of light at 275 nm of isomerized alpha acids (69.68).  Fortunately, Maye et al. provide this data; based on their Figure 7 [Maye, p. 25], the scaling factor is 0.0142/0.0130, or 1.093:

scaleoAA = 1.093 [36]

Despite the large number of parameters for modeling oAA, we end up needing to obtain estimates of only three: oAAboilMaxtoAAmax, and scaleoAAloss.

3.4.2 Oxidized Beta Acids
As with alpha acids, the beta acids oxidize as the hops age.  The most bitter and most prevalent components of the oxidized beta acids are called hulupones [Algazzali, p. 15-16].  The oxidized beta acids are thought to contribute more to beer bitterness than the oxidized alpha acids; as Peacock notes, the “nonIAA bitterness is mostly from oxidation products of the alpha and especially the beta acids of the hops formed during hop storage”. [Peacock, p. 157; emphasis mine].

We can model oxidized beta acids in a way similar to oxidized alpha acids: there are oxidized beta acids occurring in fresh hops, created during storage, and produced during the boil [Algazzali, p. 17; Stevens and Wright p. 496; Hough et al., p. 490]:

oBA = oBAfreshoBAstorageoBAboil(t) [37]

where oBA is the level of oxidized beta acids in the hop cone, oBAfresh is the level of oxidized beta acids in freshly-dried hops, oBAstorage is the level of oxidized beta acids produced during storage, and oBAboil(t) is the level of oxidized beta acids produced during the boil; all components are expressed as percent of weight of the hops.

Stevens and Wright say that oxidized beta acids are present at not more than 0.5% of the weight of the cone [Stevens and Wright, p. 500], Spetsig and Steninger note up to 3% [Spetsig and Steninger, p. 413], and Mussche found oxidized beta acids up to 1% of the weight [Mussche, p. 13].  Peacock implies that the beta acids undergo oxidation losses at approximately the same rate as the alpha acids [Peacock, p. 162].  Given the wide range of reported values of (oBAfreshoBAstorage), I’ll assume that oxidized beta acids are produced at the same levels as oxidized alpha acids both in fresh hops and during aging, but that this sum should be in the ballpark of 0.5% to 3%.  Stevens and Wright provide an estimate of the oxidized-beta-acid boil factor, noting that “after heating colupulone with boiling wort for 2 hr., as much as 10% of the beta acid had been converted into cohulupone.” [Stevens and Wright, p. 500]. I’ll assume that the time to convert beta acids to oxidized beta acids during the boil is the same as for alpha acids, i.e. toBAmax = toAAmax, and Stevens and Wright give the ballpark estimate for oBAboilMax, namely oBAboilMax = 0.10. All of this gives formulas similar to Equations [32] and [33]:

oBAboil(t) = oBAboilMax × t / toBAmax if t < toBAmax; otherwise oBAboilMax [38]
oBA = (1 – 1/ek×1×1×0.5) + (oBAagescale × (1 – AAdecayfactor)) + ((AA / ABratio) × oBAboil(t)) [39]

where oBAboil(t) is the relative amount of beta acids that undergo oxidation during the boil; oBAboilMax is approximately 0.10; oBA is the same level of oxidized beta acids in Equation [37], k is the variety-specific hop decay factor from the Garetz model, oBAagescale is the age-related scaling factor of 0.022, AAdecayfactor is the alpha acid decay factor from Equation [18], AA is the level of alpha acids at the start of the boil (Equation [18]), and ABratio is the ratio of alpha acids to beta acids (see, for example, Tables 2.1 through 2.3 in Principles of Brewing Science [Fix, pp. 60-62]).  This equation is also specific to hop cones; some modification would be required for hop pellets.  As with oxidized alpha acids, since oxidized beta acids are soluble, all of the oxidized beta acids that are present in the hop cones are in the wort shortly after being added to the kettle, and the oxidized-beta-acid level peaks at toBAmax.

That (again) leaves us with two other oxidized beta acid factors that we still need to model: losses and a scaling factor.  It seems reasonable to assume that oxidized beta acids are lost to trub, yeast, and in other ways, just as isomerized alpha acids and (presumably) oxidized alpha acids are lost.  With that assumption, we can model the oxidized beta acid losses as the losses that affect isomerized alpha acids multiplied by some (unknown) scaling factor.  In other words,

[oBA]wort = oBA × W × 1000 / V [40]
[oBA]beer = [oBA]wort × LFIAA(OG, flocculation, filtering, age) × scaleoBAloss [41]

where [oBA]wort is the concentration of oxidized beta acids in the wort, [oBA]beer is the concentration of oxidized beta acids in the finished beer, W is (still) the weight of the hops in grams, V is (still) the post-boil volume of the wort in liters, LFIAA is the same IAA loss factor from Equation [28] and scaleoBAloss is the (unknown) loss scaling factor.

We also need a scaling factor in Equation [30] that scales the factor for absorption of light at 275 nm of oxidized beta acids (unknown) to the factor for absorption of light at 275 nm of isomerized alpha acids (69.68).  Lewis and Young state that “during storage of hops alpha acids decline but presumably new bitter compounds are formed, largely from beta acids.  … if the alpha-acid to beta-acid ratio is about unity as is commonly the case, sensory bitterness remains more or less constant with storage.” [Lewis and Young, p. 261].  Since sensory bitterness and IBUs are correlated [Lewis and Young, p. 266], and since oxidized beta acids are believed to be the second-largest contributor to IBUs (after isomerized alpha acids), this statement implies that the oxidized beta acids have a relationship between light absorption and concentration that is similar to that of the isomerized alpha acids (69.68).  So, the scaling factor for oxidized beta acids (scaleoBA) should be approximately 1, with emphasis on the “approximately”.  According to Hough et al., “hulupones exhibit 80-90% of the absorption of the iso-alpha-acids at [275nm in acid solution]” [Hough et al., p. 491].  In order to convert this absorption to be the equivalent for IAA, a scaling factor of about 1/0.85 or 1.176 is implied:

scaleoBA = 1.176 [42]

Due to the large number of assumptions made and estimates obtained from the literature, we only need to obtain an estimate for three oBA parameters: oBAagescale, oBAboilMax, and scaleoBAloss.  We can also constrain (oBAfresh + oBAstorage) to be between 0.005 and 0.03, and oBAboilMax to be 0.10 or somewhat less.

3.4.3 Polyphenols
The other nonIAA component we need to consider consists of polyphenols, which are “an extraordinarily diverse group of compounds;” the majority of those in brewing are flavonoids [McLaughlin, p. 1].  Polyphenols can come from both barley and hops [Hough et al., p. 471], so we should separate the PP component into PPhops and PPbarley, where PPhops is the amount of polyphenols contributed by the hops and PPbarley is the amount of polyphenols contributed by the barley.

According to Shellhammer, IBUs are in the range of 1 to 3 for unhopped beer [Shellhammer, p. 177].  I brewed a beer with no hops (OG 1.056) and sent it out for IBU analysis three weeks after the start of fermentation; the result was 0 measured IBUs.  For the model being developed, I’ll assume a constant value of 0.5 IBU from barley polyphenols and ignore the potential decrease in IBUs over time.  Setting the other components in Equation 29 to zero, the scaled concentration of barley polyphenols then becomes 0.5 × 7/5 = 0.7:

[PPbarley]beer × scalePPbarley = 0.7 [43]

where [PPbarley]beer is the concentration of barley polyphenols in the finished beer and scalePPbarley is the scaling factor for light absorption at 275 nm.  We don’t need to determine the separate values of these parameters; knowing that their product is 0.7 is sufficient.  We can then update our estimate of IBUs in beer to separate the contributions from hops and barley polyphenols:

IBU = 5/7 × ([IAA]beer + (([oAA]beer × scaleoAA) + ([oBA]beer × scaleoBA) + ([PPhops]beer × scalePPhops) + ([PPbarley]beer × scalePPbarley))) [44]

Hop polyphenol levels are often reported in the range from 2% to 6% of the weight of the hops [Shellhammer, p. 169; Hough et al., p. 422; Algazzali, p. 5], although McLaughlin reports a higher range, from 4% to 14% [McLaughlin, p. 3].  After having been added to the wort, polyphenols are removed “extensively by precipitation with proteins during wort boiling”; 80% of hop flavanols are removed in the trub when boiling hopped wort [McLaughlin, p. 7].  As Noonan phrases it, “the rolling motion of the boil causes the malt proteins to collide with and adhere to the sticky hop polyphenols” [Noonan, p. 158].  (It may be that the polyphenols are not so much removed as largely insoluble in wort.  The largest polyphenol group in hops (prenylflavonoids) are not soluble in water; all other hop polyphenol components are “soluble in water, preferably in hot water” [Forster, p. 124].  The prenylflavonoids make up about 75% to 85% of all hop polyphenols [Forster, p. 124], so only about 20% of the hop polyphenols are soluble, corresponding to 80% removal.)  Then, polyphenols are removed during fermentation, and “it seems possible that this could occur in much the same way as it does with the iso-alpha-acids” [McLaughlin, p. 7].

From this, we can construct a rough model of the concentration of hop polyphenols in wort and in beer, with an initial level of polyphenols at about 4% of the weight of the hops, a loss factor (or solubility factor) for polyphenols in the wort during the boil (LFPP) estimated at 0.20, and the same loss factors for fermentation and packaging that we have for isomerized alpha acids, LFferment and LFpackage:

[PPhops]wortPPrating × W × 1000 / V [45]
LFPP = 0.20 [46]
[PPhops]beer = [PPhops]wort × LFPP × LFferment(flocculation) × LFpackage(filtering, ageweeks) [47]

where [PPhops]wort is the concentration of hop polyphenols in the wort, PPrating is the percent of the hop weight that consists of polyphenols (similar to the AA rating for alpha acids, on the scale from 0 to 1; a value of 0.04 is a reasonable estimate), LFPP is the loss factor for polyphenols precipitated out of the wort (estimated at 0.20), [PPhops]beer is the concentration of hop polyphenols in the finished beer, and LFferment and LFpackage are the same loss factors for isomerized alpha acids.

Finally, we need a scaling factor to use the concentration of hop polyphenols in Equation [44].  According to Ellen Parkin, “an increase of 100 mg/L of polyphenols was predicted to increase the BU value by 2.2” [Parkin, p. 28], so that 1 ppm of hop polyphenols should increase the IBU by 0.022 (Equation [48]). We can consider Equation [44] in terms of hop polyphenols only, with an IAA component of zero, an oAA component of zero, an oBA component of zero, a non-zero hop polyphenol (PPhops) component, and a PPbarley component of zero (Equation [49]).  Since Equations [48] and [49] both measure IBUs from the contribution of only hop polyphenols, we can determine the value of the scaling factor for hop polyphenols (Equation [50]):

IBU = [PPhops]beer × 0.022 [48]
IBU = 5/7 × (0 + 0 + 0 + ([PPhops]beer × scalePPhops) + 0) [49]
scalePPhops = 7/5 × 0.022 = 0.0308 [50]

here [PPhops]beer is the concentration of hop polyphenols in the finished beer (in ppm) and scalePPhops is the scaling factor for hop polyphenols relative to the scaling factor for IAA.

3.4.4 Solubility of nonIAA Components
The nonIAA components (specifically, oxidized alpha and beta acids, and soluble hop and barley polyphenols) are soluble in water [e.g. Lewis and Young, p. 265; Forster, p. 124].  They do not require isomerization, which (for alpha acid isomerization) takes a significant amount of time.  Therefore, they probably contribute quickly to the measured IBU value.  This is of particular significance for hops that are added late in the boil (or at flameout, or after flameout), since they will have a significant amount of their nonIAA components quickly dissolved and contributing to IBUs, whereas the IAA level will be low due to insufficient time for isomerization.  As a result, the ratio of IAA to all bittering substances can be much lower for hops added close to flameout, even for very fresh hops.  In short, the 1960s finding that the concentration of IAA is 5/7 of the total concentration of all bittering substances reflects not only the age and storage conditions of 1960s hops, but also the typical time(s) at which hops were added to the boil in the 1960s.  Freshly-dried hops added at flameout (with 10 minutes of cooling after flameout) may yield 15 IBUs, but only 50% of that from isomerized alpha acids.

4. Available Data, Parameter Estimation, and Results
4.1 Overview
The quantitative description we now have of IBUs is still incomplete, because we don’t have useful estimates for a number of the factors (specifically: LFboil, [AA]limit, k1_scale, oAAboilMaxtoAAmax, scaleoAAloss, oBAagescale, oBAboilMax, and scaleoBAloss).  We do, however, have Tinseth’s model for predicting IBUs under normal circumstances [Tinseth], results from a study by Val Peacock that looks at IBUs and IAA concentration as a function of hop storage conditions [Peacock, p. 162], and results from ten experiments where I’ve measured IBUs with varying hop steeping times, amounts, and temperatures (to be published later on this blog).  We can make assumptions about the conditions of these studies as needed (i.e. boil gravity, post-boil volume, beta acid level, etc.) and use the data and assumptions, along with common techniques for searching a parameter space, to obtain a rough estimate of the nine unknown values.

4.2 Sources of IBU Data
4.2.1 Tinseth Utilization
The Tinseth model is widely used for predicting IBUs.  Tinseth had “access to some handy tools and knowledgeable friends at the USDA hop labs and the Flavor Perception labs at Oregon State University,” [Tinseth] and he has “had quite a few worts and beers analyzed” [Tinseth].  Therefore, whatever model we develop should come up with estimates close to those predicted by the Tinseth model given similar conditions.  Tinseth provides a detailed description of his model and parameters at realbeer.com.  He based his model on a review of the literature and on data from the pilot brewery at Oregon State University and small breweries; he then verified the model by brewing small batches and testing the results [Hieronymus, p. 185].  In the experiments he conducted in order to validate his model, he used hops from vacuum-sealed oxygen barrier bags stored in a freezer, resulting in very low hop degradation [Tinseth emails].  Also, he took small samples at intervals throughout the boil and immediately cooled them, yielding almost no post-boil utilization [Tinseth emails].

4.2.2 Peacock Hop-Storage Conditions
In an article describing IBUs, Peacock provides results of a study that looked at how the storage conditions of hops affected IBU levels [Peacock, p. 162].  He lists four storage conditions (ranging from -20°F (-29°C) to 70°F (21°C)), the relative percent of alpha and beta acids lost (based on the Hop Storage Index), the IAA levels in the finished beer, and the IBUs of the finished beer. He also provides the alpha/beta ratio of the hops used, but not the amount of hops, wort volume, or original gravity.

4.2.3 Personal Experiments
I conducted a series of ten experiments (one in two parts) that look at IBUs as a function of hop steeping time, amount of hops, and wort temperature.  Experiment 1 was a set of “standard” beers with boil times ranging from 10 to 60 minutes and immediate post-flameout cooling, in order to sync up with the Tinseth formula.  Experiments 2a and 2b were a set of beers with hops added only at flameout and held at a constant temperature for 10 or 20 minutes (from 145°F (63°C) to 212°F (100°C)), in order to evaluate the degree of utilization at sub-boiling temperatures.  Experiment 3 was a set of beers with hops added at varying times during the boil (from 0 to 60 min) and a 15-minute post-flameout natural cooling (a.k.a. a hop stand) before forced cooling.  Experiment 4 looked at utilization as a function of kettle material (stainless steel vs. aluminum) and loose vs. bagged hops.  Experiment 5 looked at the decrease in IBUs over time and utilization as a function of the amount of hops, and Experiment 6 varied some factors from Experiment 5 (amount of hops, boil time, and steep temperature) in order to estimate IAA concentrations from IBU values.  Experiments 7 through 10 looked at IBUs as a function of both alpha-acid concentration and boil time.  I will write about Experiments 7 through 10 in more detail in the future.

One of the biggest difficulties in these Experiments 1, 2, and 3 was obtaining accurate alpha-acid levels of the hops at harvest.  As a result of that difficulty, for these three experiments I allowed the IBU model parameter search (Section 4.3) to evaluate ±1 percentage point around the best estimate of alpha-acid levels at harvest.  In all of these personal experiments,  I also provided some flexibility in the alpha-beta ratios (based, when possible, on estimates from analysis of the hops at around the time of brewing) and the value of AAdecayfactor (based on estimates of how well-preserved the hops might be).  Experiments 7 through 10 used hops from the same bag, and so I constrained the alpha-beta ratio and AAdecayfactor to be the same for all four experiments.

4.3 Parameter Estimation and Results
Using 9 IBU values based on Tinseth’s utilization function (from 10 minutes through 90 minutes at 10-minute intervals) (with typical or assumed values for AAharvest, OG, W, and V, and the values of AAdecayfactor and ABratio fit to the data), the 4 IBU values and 4 IAA values from Peacock (assuming values for original gravity and volume, and fitting the boil time, post boil time, and weight of the hops to the data), and 71 measured IBU values from my ten experiments, there are 88 data points with which to estimate the nine unknown parameter values, as well as a number of source-specific parameter values (e.g. weight of the hops in Peacock’s study).  This really isn’t enough data for a reliable estimate of all parameters, but it’s better than nothing.  It helps that these sources of data cover a number of scenarios of interest, including boil time, storage conditions of the hops, weight of hops used, and hop steeping temperature.

Tables 1 through 11 (below) provide the known values, assumptions, estimated values, and IBU (or IAA) results for each set of data.  In addition, flocculation was set to “normal” and filtering was set to “none”.  All other parameters not being estimated were given the best-guess values noted in the previous sections.  For oxidized alpha and beta acids produced during the boil, I previously found that below-boiling temperatures may produce fewer oxidized alpha and beta acids.  I assumed a linear decrease with temperature, from full oxidized-acid production (scale factor 1.0) at boiling to zero production (scale factor 0.0) at room temperature.  For Tinseth and Peacock, I assumed loose whole hops, so that RFform(hopsForm=loose cones)=1.16; for my experiments, I used RFform(hopsForm=loose cones)=1.16 or RFform(hopsForm=bagged cones)=1.05, depending on the form of the hops.  The alpha-acid decay factor in Tables 1 and 2, AAdecayfactor, is the result of the Garetz formula ek×TF×SF×D; I constrained the search range for this factor based on best guesses of the variables k, TF, SF, and D in each condition.

I used an iterative brute-force search over the parameter space to minimize the squared error, starting with the approximate range of each parameter and a coarse search interval.   After each iteration, I used the best estimates of each parameter to specify a smaller range, along with a smaller search interval.  The search process was stopped when best estimates were obtained with a typical search interval of 0.01.  A nested recursion was used to constrain the five unknown model parameters in an iteration to be the same for all data sources, while the unknown parameters from each experiment were searched for individually.  (I will provide java and C-code procedures of the complete IBU model, after I have a chance to publish the remaining experiments and clean up the code.)

The result of this parameter search is not an ideal solution!  We have a very large number of assumptions, a fairly large number of unknown parameters, and a relatively small amount of data.  As a result, the estimates of the parameter values will almost certainly be wrong at some level.  My hope, however, is that a slight overestimate of one factor will be balanced by a small underestimate of another factor, and on average the model will provide a cohesive, general description of the factors that contribute to IBUs.  The model and parameter settings provide a “most likely” set of values given the (limited) data.  Because of the lack of held-out test data, the resulting description of IBUs is descriptive, not predictive.  In other words, I make no guarantee of how well this model will predict your IBU values, even if you know all of the input parameter values (hops weight, volume, alpha acid level at harvest, alpha-beta ratio, storage conditions, steep time, etc.).  This model may, however, help with understanding the various factors and relative contributions of these factors to the IBU measure.

The results of the search for the nine parameters are: LFboil = 0.58, [AA]limit = 230 ppm, k1_scale = 3.9, oAAboilMax = 0.35, toAAmax = 12 minutes, scaleoAAloss = 0.04, oBAagescale = .01, oBAboilMax = 0.08, and scaleoBAloss = 0.76.  The estimated value of LFboil is fairly close to that of Malowicki’s report that the formation of trub causes losses of 35% (translating to a scaling factor of 0.65) [Malowicki, p. 7-8].  The alpha-acid solubility limit of 230 ppm is lower than Spetsig’s estimate of 300 ppm at boiling [Spetsig, p. 1423], but he notes that the value of 300 is an approximation based on extrapolation from two data points at 25°C and 40°C [Spetsig, p. 1424].  The small value of scaleoAAloss, compared with the larger value of scaleoBAloss, results in a smaller contribution of oxidized alpha acids compared with oxidized beta acids, which is also in agreement with the literature (e.g. [Peacock, p. 157]).  The value of oBAagescale, when used to compute oBAstorage, yields (oBAfresh + oBAstorage) in the ballpark of 1% for typical values of oBAfresh, which is in line with reported values from 0.5% to 3% [Stevens and Wright, p. 500; Spetsig and Steninger, p. 413; Mussche, p. 13].  The value of 0.08 (8%) for oBAboilMax is also in line with the reported value of 10% [Stevens and Wright, p. 500].

Tables 1 and 2 provides the known, assumed, and estimated values of parameters that could vary between the sources of data.  Parameters that could vary were constrained to a reasonable search range based on available data. Note that several values in the Tinseth column do not need to be the same as what Tinseth used in his experiments; as long as the same values of these parameters are used in the comparison with the current model, any values can be used.  For the Peacock study, the alpha acid rating at harvest was determined based on the data he published.  I assumed a two-barrel (62 G or 234 liter) volume for Peacock’s experiments; if this assumption is incorrect, then the estimated weight of the hops can be scaled proportionally to give the same results.  I also assumed a fairly slow post-flameout temperature decay for Peacock’s experiments (reaching 200°F (93.5°C) after 30 minutes), under the assumption that a large volume of wort cools slowly; if the actual temperature decay was different, the weight of hops, boil time, and/or post-boil time may need to be adjusted.

Tinseth Peacock Exp. #1 Exp. #2a Exp. #2b Exp. #3
AA at harvest
8.65% (?) 3.9% 8.0% 7.9% 8.4% 6.0%
α/β ratio 1.00 1.35 0.75 1.45 1.0 1.6
AA decay factor
0.95 0.07 to 0.83 0.82 0.87 0.99 0.95
boil time
10 to 90 min 90 min
10 to 60 min 0 min 0 min 0 to 60 min
post-boil time
0 min 50 min 0 min 10 to 20 min 10 min 15 min
post-boil temp.
N/A slow decay N/A 185°F to 212°F 145°F to 212°F fast decay
hops weight
13.0 oz 13.0 oz 0.60 oz 1.60 oz 1.60 oz 0.80 oz
wort volume
62 G (?) 62 G (?) 1.37 to 1.50 G 1.10 to 1.24 G 1.05 to 1.20 G 0.88 to 1.15 G
boil gravity
1.055 (?) 1.035 (?) 1.059 to 1.064 1.064 to 1.066 1.063 to 1.065 1.065 to 1.075

Table 1. Known values, assumed values, and best estimates of parameters that were allowed to vary between the sources of data, for the first six sources of data. If a value has no markings, it is a known value.  If a value has a question mark after it (?), it is an assumed value.  If a value is in bold face and red, it is the best estimate as determined by the parameter search.

Exp. #4 Exp. #5 Exp. #6 Exp. #7 Exp. #8 Exp. #9 Exp. #10
AA at harvest 8.1% 8.1% 8.1% 13.3% 13.3% 13.3% 13.3%
α/β ratio 1.0 1.10 1.10 3.31 3.31 3.31 3.31
AA decay factor 0.95 0.99 0.96 0.55 0.55 0.55 0.55
boil time 20 min 12 min 0 to 26.9 min 0 to 100 min 0 to 103 min 0 to 100 min 0 to 100 min
post-boil time 0 min 0 min 0 to 19 min N/A (0) N/A (0) N/A (0) N/A (0)
post-boil temp. N/A N/A 145°F N/A N/A N/A N/A
hops weight 0.75 oz 0.37 to 2.22 oz 0.37 to 2.22 oz 1.15 oz 2.923 oz 4.25 oz 6.25 oz
wort volume 1.52 to 1.61 G 1.61 to 1.65 G 1.59 to 1.63 G 8.14 to 7.78 G 8.23 to 7.73 G 8.25 to 7.65 G 8.06 to 7.51 G
boil gravity 1.056 to 1.059 1.054 to 1.056 1.055 to 1.056 1.048 to 1.051 1.049 to 1.052 1.048 to 1.052 1.049 to 1.052

Table 2. Known values, assumed values, and best estimates of parameters that were allowed to vary between the sources of data, for the remaining seven sources of data. If a value has no markings, it is a known value.  If a value has a question mark after it (?), it is an assumed value.  If a value is in bold face and red, it is the best estimate as determined by the parameter search.

Tables 3 through 11 show results from the Tinseth, Peacock, and personal experiments.  Table 3 shows the results of IBU estimation based on the Tinseth formula and based on the estimates obtained from the current model:

time 10 min
20 min 30 min 40 min 50 min 60 min 70 min 80 min 90 min
formula 10.9 18.1 23.0 26.3 28.5 29.9 30.9 31.6 32.0
estimate 11.6 17.2 21.2 24.7 27.5 29.9 31.9 33.4 34.7
diff. .07 -1.0 -1.8 -1.6 -1.0 0.0 0.9 1.8 2.6

Table 3. IBU estimates from the Tinseth formula and the current model, as a function of hop steep time, and the difference (error) between the two.

Table 4 shows the IAA and IBU measured values reported by Peacock, and the results of IAA and IBU estimation from the current model:

condition -20°F 25°F 40°F 70°F
measured IAA 19.8 ppm 18.1 ppm 14.4 ppm 2.9 ppm
measured IBU 13.5 12.0 13.5 11.0
estimated IAA 17.6 ppm 15.5 ppm 11.5 ppm 1.5 ppm
estimated IBU 17.0 16.1 14.2 9.7
IAA difference
2.2 ppm 2.6 ppm 2.9 ppm 1.4 ppm
IBU difference
3.6 4.1 0.7 -1.3

Table 4. IAA and IBU measured values and estimates from the current model, as a function of hop storage conditions.  The difference (error) between measured and estimated values is also shown.

Table 5 shows the measured and estimated IBU values from my experiment #1 (mIBU experiment #1), meant to sync up with the Tinseth formula.  The estimate of the alpha-acid rating at harvest (8.0%) is equal to the value written on the package I bought.  The estimate of the alpha/beta ratio (0.75) is not too far off from an estimate obtained by analysis of the hops’ alpha and beta values (0.862).  The degradation factor of 0.82 is reasonably close to the degradation factor estimated from the Hop Storage Index (0.72).

steep time 10 min
20 min
40 min
60 min
measured IBU
22.0 27.1 34.3 35.7
estimated IBU
18.2 24.9 32.1 38.9
IBU difference
-3.8 -2.2 -2.2 3.3

Table 5. Measured IBU values and estimated IBU values from personal experiment #1, as a function of hop steep time.  The difference (error) is also shown.

Table 6 shows the measured and estimated IBU values from my experiment #2 (mIBU experiment #2), which looked at utilization as a function of steep temperature.  In most cases, the steep time was 10 minutes, but in one case the steep time was 20 minutes.

temp/
time
212°F/
10m
200°F/
10m
190°F/
10m
185°F/
10m
192°F/
20m
212°F/
10m
175°F/
10m
165°F/
10m
155°F/
10m
145°F/
10m
meas. 33.3 28.9 30.8 25.5 35.9 40.6 23.6 24.5 23.1 21.8
est. 35.9 30.6 27.9 26.4 33.3 39.4 26.6 24.5 22.4 20.7
diff. 2.6 1.7 -2.9 0.9 -2.6 -1.2 3.0 0.0 -0.7 -1.1

Table 6. Measured IBU values and estimated IBU values from personal experiment #2, as a function of hop steeping temperature and time.  The difference (error) is also shown.

Table 7 shows the measured and estimated IBU values from my experiment #3 (mIBU experiment #3) which combined various hop boil times with a 15-minute hop stand.  The wort was allowed to cool naturally during this 15 minutes, after which it was force-cooled.

time 0 min
7.5 min 15 min 30 min 60 min
measured
16.1 21.2 26.1 35.4 46.4
estimated 14.6 20.6 26.1 35.7 48.9
difference -1.5 -0.6 0.0 0.3 2.5

Table 7. Measured IBU values and estimated IBU values from personal experiment #3, as a function of hop boil time.  The difference (error) is also shown.

Table 8 shows the measured and estimated IBU values from my experiment #4 (utilization experiment #1), which looked at utilization as a function of kettle material and form of the hops.

kettle material,
hop form
stainless steel,
loose
aluminum,
loose
aluminum,
bagged
measured
34 37 36
estimated
33.6 34.0 32.4
difference
-0.4 -3.0 -3.6

Table 8. Measured IBU values and estimated IBU values from personal experiment #4, as a function of kettle material (stainless steel or aluminum) and hop form (loose cones or bagged cones).

Table 9 shows the measured and estimated IBU values from my experiment #5 (utilization experiment #2), which looked at utilization as a function of weight of the hops.

weight
0.37 oz
0.74 oz
1.11 oz
1.48 oz
1.85 oz
2.22 oz
measured
12 23 29 34 41 47
estimated 12.4 23.3 29.1 34.7 40.8 46.6
difference 0.4 0.3 0.1 0.7 -0.2 -0.4

Table 9. Measured IBU values and estimated IBU values from personal experiment #5, as a function of hop weight.  The difference (error) is also shown.

Table 10 shows the measured and estimated IBU values from my experiment #6 (utilization experiment #3), which looked at variety of conditions: Condition H had hop weight of 0.37 oz and boil time of 26.9 min; Condition I had hop weight of 1.11 oz and boil time of 26.9 min; Condition J had hop weight of 1.11 oz and boil time of 12 min; Condition K had hop weight of 2.22 oz and boil time of 19.0 min; and Condition L had hop weight of 2.22 oz, with no boiling but a 19-minute hop stand held at 145°F.  Conditions H through K were immediately cooled upon flameout.

Condition
H
I
J
K
L
measured
18 48 32 58 27
estimated 20.6 47.3 32.4 59.2 27.5
difference 2.6 -0.7 0.4 1.2 0.5

Table 10. Measured IBU values and estimated IBU values from personal experiment #6, as a function of hop boil time.  The difference (error) is also shown.

Table 11 shows the measured and estimated IBU values from my experiments #7 through #10, which looked at IBUs as a function of both boil time and alpha-acid concentration.


Exp. #7
Exp. #8
Exp. #9
Exp. #10
10 min
meas. = 8.0
est. = 7.4
diff. = -0.60
meas. = 19.5
est. = 17.8
diff. = -1.70
meas. = 20.5
est. = 24.1
diff. = 3.62
meas. = 34.0
est. = 30.9
diff. = -3.10
20 min
meas. = 11.0
est. = 10.3
diff. = -0.67
meas. = 27.5
est. = 25.2
diff. = -2.27
meas. = 30.0
est. = 34.4
diff. = 4.38
meas. = 43.0
est. = 41.8
diff. = -1.21
30 min
meas. = 14.5
est. = 12.7
diff. = -1.82
meas. = 32.5
est. = 31.2
diff. = -1.31
meas. = 39.0
est. = 42.6
diff. = 3.60
meas. = 53.0
est. = 51.3
diff. = -1.72
40 min
meas. = 16.5
est. = 14.7
diff. = -1.82
meas. = 38.0
est. = 36.3
diff. = -1.74
meas. = 48.5
est. = 49.6
diff. = 1.08
meas. = 64.0
est. = 59.9
diff. =-4.10
50 min
meas. = 19.5
est. = 16.4
diff. = -3.13
meas. = 42.5
est. = 40.6
diff. = -1.89
meas. = 51.5
est. = 55.5
diff. = 3.99
meas. = 68.0
est. = 67.2
diff. = -0.81
60 min
meas. = 22.5
est. = 22.8
diff. = 0.29
meas. = 48.0
est. = 44.3
diff. = -3.69
meas. = 59.0
est. = 60.5
diff. = 1.50
meas. = 72.5
est. = 73.3
diff. = -2.22
70 min
meas. = 28.0
est. = 27.7
diff. = -0.28
meas. = 47.5
est. = 47.3
diff. = -0.14
meas. = 62.0
est. = 64.6
diff. = 2.58
meas. = 81.0
est. = 78.4
diff. = -2.63
80 min
meas. = 32.5
est. = 31.3
diff. = -1.21
meas. = 50.0
est. = 49.9
diff. = -0.11
meas. = 66.5
est. = 68.0
diff. = 1.47
meas. = 83.0
est. = 82.6
diff. = -0.43
90 min
meas. = 33.5
est. = 34.3
diff. = 0.80
meas. = 54.0
est. = 52.0
diff. = -1.95
meas. = 69.5
est. = 70.8
diff. = 1.25
meas. = 79.0
est. = 85.9
diff. = 6.93
100 min
(103 for Exp #8)
meas. = 37.0
est. = 36.8
diff. = -0.16
meas. = 52.5
est. = 54.1
diff. = 1.60
meas. = 72.5
est. = 72.9
diff. = 0.46
meas. = 74.0
est. = 88.7
diff. =14.67

Table 11. Measured IBU values and estimated IBU values from personal experiments #7 through #10, as a function of hop boil time.  The difference (error) is also shown.  The values from Experiment #10 at times 90 and 100 minutes were not included in the model fitting, because the model is not capable of predicting such a decrease in IBUs.  At this point, I conjecture that the decrease in IBUs is due to changing pH at very high alpha-acid concentrations and long boil times.

5. Discussion of Results
The average difference between observed (or Tinseth model) IBU and IAA values and current model estimates is -0.04, with a standard deviation of 2.0 and a maximum difference of 4.4.  The fact that all 10 IBU values from Experiment #9 are overestimates and all 8 IBU values used in Experiment #10 are underestimates indicates something sub-optimal in the model or in the parameter estimation.  From the data I’ve seen, observed IBU values can deviate quite a bit from expected values (for reasons that are still unclear to me), and so the overall results from the model do not seem excessively bad.  With a human detection threshold of 5 IBU [Daniels, p. 76], none of the errors in the model (with a maximum difference of 4.4 IBU) would be detectable by a human palate. While few, if any, of the model parameters have been estimated with great precision, the overall fit suggests that errors in one parameter estimate are, for the most part, balancing out errors in another estimate.

To the extent that parameter estimation has been reasonable, we can use this model to look at how various factors affect IBUs.  If we assume some typical brew parameters (OG 1.055, volume 5.25 G or 20 liters, a typical AA rating of 8.65%, an alpha/beta ratio of 1.4, exceptionally well-preserved hops with AAdecayfactor of 1.0, post-flameout natural cooling for 10 minutes, and taking IBU measurements one week after the start of fermentation), we can vary the amount and timing of hops additions in the model to look at the impact on IBU and IAA.  For example, 2 oz added at flameout will create 15.6 IBUs with a concentration of 10.4 ppm of IAA (47% of the IBU total), 1.4 ppm of oAA, 7.4 ppm of oBA, and 18.9 ppm of hop polyphenols.  The same 2 oz added at 60 minutes will create 55.9 IBUs with a concentration of 65.2 ppm of IAA (83% of the IBU total), 1.6 ppm of oAA, 8.6 ppm of oBA, and 18.9 ppm of hop polyphenols.  If we triple the amount of hops, from 2 oz to 6 oz, the IBUs only increase from 55.9 to 90.1 (88.2 ppm of IAA, representing 70% of the total; 4.9 ppm of oAA, 25.6 ppm of oBA, and 56.8 ppm of hop polyphenols).  If we add those 6 oz at flameout, we’ll get 31.0 IBUs, with only 10.4 ppm of IAA (24% of the IBU total).  If we have somewhat degraded hops (say, stored at room temperature in airtight packaging for six months) yielding an AAdecayfactor of 0.82, the 2 oz of hops added at 60 minutes will yield 48.9 IBUs, with 53.9 ppm of IAA representing 79% of the IBU total.  Adding these degraded hops at flameout will produce 15.7 IBUs, but with only 8.8 ppm of IAA representing 40% of the IBU total.  The lack of a strong impact on IBUs when using somewhat degraded hops is in line with reported experience [Peacock, p. 162].

Another interesting thing we can do is estimate the contribution of nonIAA components to the Tinseth formula.  While the Tinseth formula uses only the weight and alpha-acid rating of the hops to compute IBUs [Tinseth], the utilization function was fit to observed data [Pyle], which includes nonIAA components.  We can use the current detailed model to separate out the actual IAA contribution to utilization from the (implicit) nonIAA contribution.  For example, at 10 minutes before flameout, the detailed model predicts 14.75 IBUs in a (post-boil volume) alpha-acid concentration of 168.74 ppm using the Tinseth source of data.  (The Tinseth formula predicts 14.20 IBUs using the same data.)  If the IBU value was equivalent to the concentration of isomerized alpha acids, as assumed by the Tinseth equation, then at the final boil volume there would be utilization of 14.75 ppm / 168.74 ppm = 0.0874 (or 8.74% utilization).  The detailed model tells us, however, that at 10 minutes the relative contribution of IAA to the IBU is only 0.50, and that the IAA concentration is 10.30 ppm, for a utilization of 0.0610.  The nonIAA components contribute an “IAA equivalent” 10.35 ppm (obtained by the sum of their estimated concentrations multiplied by their scaling factors), for a total of 20.65 ppm of IAA-equivalents in 168.74 ppm of alpha acids, or an IAA-equivalent utilization of 12.24%.  If we multiply 0.1224 by 5/7, we get the 0.0874 that we estimated by assuming that IBUs are equivalent to the concentration of IAA.  (As a quick example, 6.94 ppm of oBA multiplied by the scaling factor of 1.176 yields 8.16 ppm of IAA equivalents obtained from oBA; the remaining 2.19 ppm comes from oAA and polyphenols.)  In the Tinseth formula, therefore, at 10 minutes about 4.22% of the 8.41% utilization is coming from nonIAA components.  At 5 minutes, 2.58% of the 4.68% utilization is from nonIAA components, and at 12 minutes and above, about 5% is from nonIAA components.

In general, one can think of the nonIAA components as contributing up to 5% of the utilization in the Tinseth formula.  (In other words, if the Tinseth utilization is 0.22 (22%), then 0.05 (5%) can be thought of as coming from nonIAA components, and the remaining 0.17 (17%) from IAA.)  This corresponds fairly well with the Rager IBU formula [Pyle], which has a non-zero and roughly constant utilization of 5% (0.05) from 0 to 5 minutes, presumably accounting for nonIAA components at short boil times.

6. Summary
This post has described the various factors that contribute to the IBU, and quantified each factor as much as possible. Estimates of parameter values that could not be determined from the literature were obtained by fitting a model to the available data.

Despite the length of this post, many things have been left undiscussed.  The current model is restricted to full boil of the wort (i.e. not performing the boil at higher gravity and then diluting).  The topic of dry hopping and its impact on bitterness is left entirely to Ellen Parkin [Parkin], Maye et al. [Maye], and others.  The model is probably much less effective when it comes to the IBUs of darker beers and stouts, since dark malts may affect bitterness and the IBU value (although I’ve seen surprisingly lower-than-expected IBU values in my stouts).  The perception of bitterness is left out entirely (especially at high IBU values), as is the large topic of different bitterness qualities.  I’ve also put off a number of topics (e.g. alpha acid concentration limit at boiling, rate of alpha-acid oxidation based on Maye et al.’s paper [Maye]) for future blog posts.

What’s the take-away message of this post?  If you’re adding hops late in the boil (or at flameout), you will probably not get a lot of bitterness from alpha acid isomerization.  You can, however, get a significant number of IBUs (and bitterness) from this hop addition, with most of the IBU value coming from nonIAA components.  Likewise, if you’re using a large amount of hops, the IBU value may be smaller than you’re expecting (due to what appears to be the solubility limit of alpha acids in boiling wort), but much of that IBU value may come from nonIAA components.  To the extent that the model development and parameter estimation has been correct, most of the contribution to nonIAA components is from oxidized beta acids, and a significant amount of the oxidized beta acids are produced during the boil (or during post-boil steeping).  Hopefully this post and model will help in understanding the relative contributions of isomerized alpha acids and nonIAA components to the IBU.

References

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An Analysis of Sub-Boiling Hop Utilization

Abstract
In a previous post, “A Modified IBU Calculation (Especially for Late Hopping and Whirlpool Hops)“, one of the components of the modified Tinseth IBU formula is an estimation of relative α-acid utilization at below-boiling temperatures.  The current experiment investigates this relative utilization as a function of temperature.  One result of this experiment is that the measured IBU at 145°F (63°C) is about half the measured IBU value at boiling.  However, IBU values are not the same as iso-α-acid concentrations (especially at low temperatures and short steep times), due to the presence of oxidized alpha acids, oxidized beta acids, and polyphenols.  Therefore, IBU values cannot be used to directly estimate relative α-acid utilization.  Instead, the data from this experiment are applied to a detailed model of IBUs developed in another post to estimate iso-α-acid concentration and, from that, relative α-acid utilization is estimated.  It is shown that this estimate of relative α-acid utilization is consistent with a formula proposed by Malowicki, although because of some dependencies, this estimate is not an independent verification of the formula.  While Malowicki’s formula is also time-dependent, a reasonable time-independent representation of relative utilization as a function of temperature can be expressed as Urel(T) = 2.39×1011 × e-9773/T (where T is temperature in degrees Kelvin).  Note that this utilization is relative to the amount of utilization at boiling.

Introduction
Hop utilization is defined as isomerized α-acids (iso-α-acids, or IAA) in finished beer divided by total α acids added.  It would be nice to have a model of this utilization as a function of (sub-boiling) temperature, in order to better predict the increase in IBUs that happens after flameout.

I’ve seen reports that utilization decreases as a function of temperature, from maximum utilization at boiling, down to zero utilization at around 180°F (82°C).  (I’ve seen two numbers: 175°F (79°C) according to BYO and a discussion at theelectricbrewery, and 185°F (85 °C) according to a homebrewersassociation discussion and a probrewer discussion).  However, just knowing a maximum (full utilization) and a minimum (zero utilization) doesn’t mean that a straight line is the best fit to the actual utilization.  In addition, I haven’t seen any justification for this lower limit; just because I read it on the Internet doesn’t necessarily mean it’s true.

Next, let’s look at isomerized α-acids, which are the biggest contributor to IBU values and the numerator of the utilization definition.  Malowicki, Huang et al., Kappler et al., and others (e.g. Jaskula) have done a lot of work looking at α-acid isomerization at temperatures other than boiling.  Malowicki provides formulas for the temperature dependence of the loss of α acids (converted into iso-α-acids) and the loss of iso-α-acids (converted into other “uncharacterized degradation products” due to the continued presence of heat).  For the loss of α acids, this first-order reaction has a rate constant k1 = 7.9×1011 e-11858/T (T in degrees Kelvin), e.g. [iso-α-acids] = [iso-α-acidsinitial]ek1, where angle brackets ([]) indicate concentration.  For the loss of iso-α-acids, this first-order reaction has a rate constant k2 = 4.1×1012 e-12994/T (T in degrees Kelvin).

One can take Malowicki’s function for the loss of α acids as a function of temperature and assume a corresponding decrease in utilization.  For example, k1 = 0.01249 at 212°F (100°C) and k1 = 0.00622 at 198°F (92°C), and so the rate of the reaction is halved (reaction time is doubled) at 198°F (92°C).  If one assumes that the concentration of α acids is directly (and inversely) tied to alpha-acid utilization, one can conclude that utilization is also 50% at 198°F (92°C), relative to utilization at 212°F (100°C).

We can improve upon this assumption by including the loss of iso-α-acids during the boil, referring to work by Malowicki (and also reported by  Huang, Tippmann, and Becker (2013)). Malowicki (on page 27) provides an equation for the concentration of iso-α-acids as a function of time (t) and temperature by combining the two rate constants into a single formula: [iso-α-acids] = [α-acidsinitial](k1/(k2k1))(e-k1t-e-k2t). (The temperature dependence is implicit in the values of k1 and k2.)  We can then plot the concentration of iso-α-acids (relative to the initial concentration of α-acids, not taking into account volume changes produced during the boil) as a function of time for various temperatures (see Figure 1, below).  It can be seen that at 30 minutes, the relative iso-α-acid concentration is 0.2976 at 212°F (100°C) and 0.1696 at 198°F (92°C).  The value 0.1696 is 14% larger than would have been predicted by our first assumption (half the value at boiling, or 0.1488).  Also, according to this formula, there is still noticeable utilization happening at 175°F (79°C), with 5% to 10% utilization between 30 and 60 minutes.

isoAlphaAcidConcentraion

Figure 1: iso-α-acid concentration, relative to initial α-acid concentration, as a function of time and temperature, according to a formula by Malowicki.

We can use this formula to plot relative utilization as a function of temperature for different steep times (Figure 2).  In this case, regardless of the steep time, the relative utilization at boiling is defined to be 1.0, and utilization at other temperatures is relative to 212°F (100°C).

HuangUtilAsFunctionOfTemp

Figure 2: Relative utilization as a function of temperature (boiling = 1.0) and various steep times, according to equation by Malowicki (2005).

These values of relative utilization are dependent on both time and temperature, although the temperature component has a much larger impact than the time component.  We can approximate this as a function of only temperature, by choosing a single steep time to represent the general case, e.g. 40 minutes.  We can then fit the relative utilization data to an equation.  In this case, a root-mean-squared fitting error of 0.013 can be obtained with the Arrhenius function Urel(T) = 2.39×1011 e-9773/T (where T is temperature in degrees Kelvin).  In this case, at 373.15 Kelvin (or 212°F or 100°C), Urel(T) is close to 1.00; at 194°F (90°C), the utilization is half that of boiling.

The experiment that follows measured IBU values as a function of (sub-boiling) temperature, with hops steeped for 10 minutes, to compare measured IBU values with utilization prediction by this equation.  IBU values are not, however, a substitute for isomerized α acid levels (except for the boil times, hop concentrations, and hop storage conditions of the 1960’s), and so the measured IBU values need to then be converted into estimated isomerized α-acid levels.  This conversion is done using a detailed model of IBUs developed in a separate blog post.  This model uses, in part, the formula from Malowicki to estimate utilization at sub-boiling temperatures.  Therefore, the IBU values from the model are dependent upon the assumption that this formula is correct.  Because of the dependence of the model on the formula, the results of this experiment don’t provide independent verification of the formula.  However, the results do show that the model can be used to find good estimates of measured IBU values, and therefore this formula can provide a reasonable estimate of temperature-dependent utilization.

Methods
Conditions
Each condition in this experiment consisted of a small batch (1.3 G (4.92 liters) pre-boil volume) of beer brewed with a single 10-minute addition of hops, as described below.  The hops were added (and maintained) at a different target temperature for each condition within a set.

Because of constraints on my time and energy, I divided this experiment into two sets (brewed in September and January).  Within a set, each condition sampled from the same batch of wort and hops.  Since the wort and hops varied between sets, one condition in each set was the reference point, with a target temperature of 212°F (100°C) and a relative utilization (compared with other temperatures) of 1.0.  Other target temperatures ranged from 145°F (63°C) to 200°F (93°C), as listed in the Table 1 (below).

Finished beer from each condition was sent to Analysis Laboratory for analysis of IBUs and original gravity.  (Scott Bruslind from Analysis Laboratory has been very responsive and encouraging with these experiments, providing a full set of measurements (including gravity, pH, and attenuation, in addition to IBUs.))  The IBU level of each condition was divided by the IBU level of the reference condition (target temperature of 212°F (100°C)) in order to obtain a relative IBU level.  Since all other conditions were held as constant as possible (including boil volume, specific gravity, pH, hop steeping time, α acids, oxidized β acids, polyphenols, and fermentation conditions), any difference in IBU levels is due to decreased utilization at the target temperature, an error in measurement (as explained below), or some combination of both. By fitting a smooth function to the data, we’d like to be able to average out errors and estimate utilization in finished beer as a function of temperature.  The problem is that the IBU is not just a measurement of isomerized α acids; it includes other bitter substances that don’t increase at the same rate as isomerized α acids during the boil.  We’ll come back to this problem later in this post.

Sources of Error
This experiment relies on just nine IBU values, with only one value at each sub-boiling temperature, due to limited time and effort.  If one had the luxury (and energy) to repeat this experiment 10 times, one would get a variety of different relative IBU values at a given target temperature, hopefully all clustered together fairly closely.  These differences can be considered errors with respect to the “true” relative IBU value at each temperature.  What causes these errors?   First (and maybe less significantly), there may be errors in the sample analysis.  Second (and maybe more significantly), the small batch size (1.3 G (4.92 liters) pre-boil) makes it very difficult to maintain a consistent target temperature, evaporation rate, and concentration of alpha acids and other bitter substances.  Measured IBU values that do not conform to a simple pattern are very likely off due to such errors, and these errors are unavoidable with my current methodology.  The methods used here are probably sufficient, however, to find a “reasonable” fit to the data by minimizing the error.

Recipe
There were two sets, Set 1 (Conditions A, B, C, and D) and Set 2 (Conditions F, G, H, I, and J).  (No, I’m not very good at fanciful names for these things.  Yes, there was a Condition E, but it was not entirely relevant to this analysis and is omitted here.  The data for Condition E is included in a separate blog post.) Each condition maintained (close to) a target temperature for steeping, listed below in Table 1.

The wort for each set was prepared with 9¼ lbs (4.2 kg) Briess DME dissolved in 7 G (26.5 liters) of water, yielding about 7⅔ G (29 liters) of pre-boil wort.  This wort was heated, boiled for 30 minutes uncovered, and then cooled with a wort chiller.  The cooled wort was stored with a lid on, in order to minimize chances of infection.  For Set 1, the measured specific gravity prior to boiling each condition was 1.060; for Set 2, the specific gravity was 1.061.  For each condition, ~1.3 G (4.9 liters) was taken from the larger pool of wort, heated to boiling, and then cooled to the target temperature.  Once the target temperature was reached, 1.60 oz (45.36 g) of Cascade hops were added, within a large mesh bag.  (The hops were collected in advance from a larger mixture of 8 oz to 9 oz (227 g to 255 g) per set.)  The kettle was covered, and the target temperature was maintained as closely as possible for 10 minutes.  (Temperature readings were taken at one-minute intervals with a long thermometer probe stuck through a very small hole in the lid.)  After 10 minutes, the hops were removed and the wort was cooled as quickly as possible.  This wort was left to settle for 5 minutes, after which 3½ quarts (3.31 liters) were decanted into a 1-gallon (~4 liter) container.  This container was sealed until all conditions within the set were ready.  Once ready, 1½ packets of Safeale US-05 yeast were added to ~0.9 cups of water.  Each condition was aerated for 90 seconds by vigorous shaking, and 1½ oz (42.5 g) from the pool of yeast slurry was added.  Airlocks were applied.  Time passed and beer bubbled.  After 3 weeks, each condition was bottled with a small amount of simple syrup to target about 2.1 volumes CO2.  After 3 more weeks, samples were taken from the bottles (leaving behind the yeast sediment), degassed, and sent for analysis at Analysis Laboratory.   The original gravity and IBU values in Table 1 come from this analysis; the original gravity is converted from degrees Plato.

target temp. average temp. original gravity post-boil volume measured IBUs relative IBUs
Condition A
212°F
100°C
212°F
100°C
1.0658 1.18 G
4.47 l
33.3 1.0
Condition B
200°F
93.3°C
198.8°F
92.7°C
1.0645 1.20 G
4.54 l
28.9 0.868
Condition C
190°F
87.8°C
191.1°F
88.4°C
1.0645 1.23 G
4.66 l
30.8 0.925
Condition D
185°F
85.0°C
185.4°F
85.2°C
1.0641 1.24 G
4.69 l
25.5 0.766
Condition F
212°F
100°C
212°F
100°C
1.0645 1.23 G
4.66 l
40.6 1.0
Condition G
175°F
79.4°C
176.4°F
80.2°C
1.0628 1.26 G
4.77 l
23.6 0.581
Condition H
165°F
73.9°C
166.3°F
74.6°C
1.0628 1.26 G
4.77 l
24.5 0.603
Condition I
155°F
68.3°C
155.6°F
68.7°C
1.0624 1.27 G
4.81 l
23.1 0.569
Condition J
145°F
62.8°C
145.6°F
63.1°C
1.0624 1.27 G
4.81 l
21.8 0.537

Table 1. Target temperature, measured average temperature, original gravity, measured IBU values, and (measured) relative IBU values for each of the nine conditions.

Raw Results
Table 1 shows the target temperature, measured values, and relative IBU values for each condition in the experiment.  (The post-boil volume was computed from the ratio of pre-boil gravity points to post-boil gravity points, multiplied by the initial volume of 1.3 G (4.9 liters)).  The measured IBU values were converted to relative IBU values by dividing the measured IBU of that condition by the IBU value at boiling in that set (Condition A or F).  A plot of these relative IBU values as a function of average steep temperature is shown below in Figure 3.

mibu_exp2_relativeibu

Figure 3. Relative IBU values as a function of temperature (in °C).

Other than the results at 191°F (88.4°C) and 176°F (80.2°C), the data fit quite well to an exponential function.  I assume that the relatively large differences for these two extreme values are due to a relatively higher or lower concentration of α acids (and other components) in the wort, compared with the reference condition, as explained above in the section Sources of Error.  Fitting an exponential function to the eight available data points of relative utilization, we get U(T) = 0.11245 e0.01031T (where T is temperature in °F) or U(T) = 0.15642 e0.01856T (where T is temperature in °C).  The root-mean-squared error of either function is 0.059.

Data Analysis
When comparing the theoretical relative utilization (with about 50% utilization at 194°F (90°C), expressed by the formula above for Urel(T) and plotted in Figure 2) with the relative IBU values from Table 1, it quickly becomes clear that the relative IBU values are quite a bit larger (with a 50% value at around 140°F (60°C)) than the theoretical values.  This puzzled me for quite a while, but it can be explained by the components of the IBU measurement that are not isomerized α acids.  (See “The International Bitterness Unit, its Creation and What it Measures” by Val Peacock, in Hop Flavor and Aroma: Proceedings of the 1st International Brewers Symposium; BYO has an online article by John Palmer that discusses several of the same points as the Peacock article.)

The IBU measures contributions from both isomerized α acids (IAA) and other “interfering substances” (non-IAA components, including oxidized α and β acids and polyphenols, all of which contribute to bitterness).  Normally, the contribution of non-IAA components is much lower than the contribution of IAA.  (In the 1960’s, about 70% of the IBU value was from IAA and 30% was from non-IAA components.  With improvements in the storage conditions of hops over the past decades, the IAA proportion with a 60-minute or greater boil time is now generally higher.)  In this experiment, however, the short boil time (10 minutes), high boil gravity (about 1.064), and relatively large hop additions (1.6 oz in 1.3 G, or 45 g in 4.9 liters) caused the non-IAA contribution to the IBU to be much greater than the IAA contribution, even for the condition at boiling.  As the temperature decreased with each experimental condition, the contribution of IAA to the IBU also decreased, but the non-IAA contribution remained more constant.  Therefore, the IBU values from this experiment cannot be used to directly estimate relative α-acid utilization.

Estimating Alpha-Acid Utilization with a Model of IBUs
In another blog post, I present a model of IBUs that accounts for both α-acid isomerization and the effects of oxidized α acids, oxidized β acids, and polyphenols on IBU values.  This model uses the equation from Malowicki to estimate the temperature-dependent isomerization of α acids.  It also takes into account the age of the hops, the fact that oxidized α and β  acids are produced during the boil (Algazzali, p. 17), and various losses that impact IBUs.  The model can estimate the IBU values from this experiment with a maximum difference of 3.0 IBUs.  The IBU values in Table 1 vary by as much as 3.5 IBUs from the expected smooth line, and so the error from the model is more or less in line with the observed measurement error.  This model can also be used to  estimate the concentrations of isomerized α acids and non-IAA components in the finished beer.  This gives us two ways to use the measured IBU values (and other data from the experiment) to estimate relative α-acid utilization, both of which produce similar results: (1) determine utilization directly, by dividing the estimated iso-α-acids in the finished beer by total α acids added, or (2) multiply the measured IBU value by the estimated percent of the IBU that comes from isomerized α acids.  In both cases, the result at each temperature is divided by the result at boiling to determine a relative utilization.

In the search for model parameter values, I allowed allowed some flexibility in the AA rating of the hops, the ratio of α to β acids, and the degradation factor due to the age and storage conditions of the hops.  The reason for this flexibility was that I couldn’t determine reliable values for these parameters.  The AA rating on the packages of hops was 8.4% for Set 1 and 7.9% for Set 2.  I set aside some of each set of hops for testing at KAR Laboratories, which came back with 5.75% AA for Set 1 and 6.25% AA for Set 2.  At first I thought that the decrease was caused by degradation of the hops over time, and that the hops in Set 1 that I bought in September were not fresh but just over a year old (and poorly stored, as well).  This would make interpretation of Set 2 values difficult, though: if Set 1 had 31% degradation over 12 to 13 months, Set 2 (purchased in late December) would have 21% degradation over either 3 months or 15 months, which would either be too much (over 3 months) or too little (over 15 months) relative to Set 1.  After sending other samples in for analysis over a longer time period, it seems that there is a wide variation in laboratory-measured AA values; I’ve even seen older hops with a higher AA rating than fresh hops from the same bine (grown in my back yard).  It seems that either the analysis of α-acid percent by weight is not reliable, or that this value is accurate but can vary greatly even between different 30-gram samples taken from the same bine.  (Hough, Briggs, Stevens, and Young say that “sampling of hops is extremely difficult due to their heterogeneous nature” (p. 432).)  Because I can’t determine the AA rating reliably, the ratio of α to β acids is also uncertain.  Finally, without analysis of the Hop Storage Index (HSI), the value for the hop degradation factor is also unknown.  As a result, I allowed the search for model parameters to vary the harvest AA rating within one percentage point of the AA rating on the package, the α/β ratio to vary between 1.1 and 1.5 (a range of expected values for Cascade hops), and the degradation factor to vary between 0.50 and 1.0.  Results of fitting the model to the data yielded an AA rating of 7.9%, an α/β ratio of 1.45, and a degradation factor of 0.87 for Set 1, and an AA rating of 8.4%, an α/β ratio of 1.0, and a degradation factor of 0.99 for Set 2.  (By coincidence, the estimated harvest AA rating of Set 1 equals the package rating of Set 2, and vice versa.)

Table 2 provides, for each condition, (a) the concentration of pre-boil α acids in the volume of wort  at the end of the boil (α-acid concentration, in parts per million (ppm)); (b) IBU values estimated from the model; (c) estimated iso-α-acid concentration (in ppm) in the finished beer; (d) estimated ratio of iso-α-acids contributing to the IBU value (range 0 to 1); and (e) relative utilization determined by multiplying the measured IBU value by the estimated ratio of iso-α-acids contributing to the IBU value.

alpha acid concentration(ppm)
model IBUs
estimated IAA (ppm)
ratio of IAA contributing to IBU
relative utilization
Condition A
697.9 35.9 11.6629 0.2317 1.0
Condition B
686.3 30.6 6.3279 0.1476 0.553
Condition C
669.6 27.9 4.3487 0.1115 0.445
Condition D
664.2 26.4 3.3007 0.0891 0.295
Condition F
810.1 39.4 11.7465 0.2132 1.0
Condition G
790.9 26.6 2.1232 0.0569 0.155
Condition H
790.9 24.5 1.2866 0.0375 0.106
Condition I
784.6 22.4 0.7693 0.0245 0.065
Condition J
784.6 20.7 0.4858 0.0167 0.042

Table 2. Values related to relative utilization that have been determined by fitting the IBU model to available data.

Figure 4 shows the relative utilization determined by two of the three methods discussed above; it can be seen that they all yield similar results, and that these results are close to the values predicted by Malowicki’s equation.

mIBU_exp2_relativeIAA_newMalowicki

Figure 4. Relative utilization as a function of temperature, estimated by two methods described in the text (method 1 in green; method 2 in blue), and relative utilization predicted from the Malowicki formula (red).

Discussion: What I’d Do Differently Next Time
I used such a large amount of hops in these experiments in order to get higher IBU values and thereby (marginally) increase the accuracy of the relative values.  However, I’ve since found that “a high hopping rate reduces extraction efficiency” (Lewis and Young, p. 267), and I now think that the concentration of α acids I used (660 ppm to 815 ppm) was much greater than the α-acid solubility limit at high temperatures (230 to 260 ppm), greatly reducing the amount of isomerized α acid produced but increasing the concentration of non-IAA components.  This experiment used a steep time of 10 minutes, which at boiling would yield a utilization factor of only 0.074 according to the Tinseth model (which doesn’t take into account a high hopping rate).  The greatly reduced degree of α-acid utilization in this experiment, compared with typical beers, resulted in a much lower ratio of IAA to non-IAA components in the resulting IBU values.  If I were to re-do this experiment, I would increase the boil time instead of the hop concentration in order to increase utilization, and target an α-acid concentration of about 200 ppm.  Even better, I would use α-acid extract instead of hops, if I could get it, in order to avoid the non-IAA components entirely… failing that, I’d use the highest α-acid hop I could get.

Conclusion
One obvious result from this experiment is that IBU values can not be directly substitued for isomerized α-acid values, especially at short steep times, high hopping rates, and sub-boiling temperatures.  This is because IBU values reflect not only isomerized α-acid values, but also contributions from oxidized α and β acids and polyphenols.  The function of relative utilization estimated in this blog post is for α-acid utilization, and does not include the contributions of these other components to the IBU.

The results of this experiment don’t provide an independent verification of relative utilization based on Malowicki’s equation.  However, the results do show that this equation can be used as part of a larger model to provide good estimates of measured IBU values, and that the iso-α-acid levels and relative utilization estimated from measured IBU values conform well to expectations.  By converting Malowicki’s equation from absolute to relative values and removing the time dependency (using a single representative time point), relative utilization can be modeled with the function Urel(T) = 2.39×1011 e-9773/T (where T is temperature in degrees Kelvin).

Techniques for Maximizing Hop Flavor and Aroma

Introduction
This blog post provides a summary of the techniques I’ve found for maximizing hop flavor and aroma, based on my experimental results and general experience.  Others have said many of these things before, and in some cases with better writing skills.  I am not claiming that anything here is a new discovery; I’m just reporting what I’ve found from my personal brewing experience.  (As usual with this blog, the contents of this post may change over time as I revise and update what I’ve learned.)

1. Add Hops Late in the Boil.  Like Really, Really Late
Hops should be added late in the boil.  How late?  That depends on when you start cooling your wort and how quickly it cools.  According to Papazian (The Home Brewer’s Companion, p. 68), flavor is maximized at 10 minutes before flameout.  I’ve found increased hop flavor by adding hops at flameout and then letting the wort cool naturally (with the lid on) for 10 minutes.  There is a lot of room for experimentation here.

Also, according to Greg Noonan, “the bitterness derived from long boiling is coarser than that from a more moderate period” (Noonan, New Brewing Lager Beer, p. 154), which also suggests that more hops for a shorter time in the boil is advantageous.

It seems that boiling temperatures will decrease hop flavor if applied long enough (e.g. greater than 15 minutes), but it may also be that that (near) boiling temperatures are needed in order to bring out hop flavor.

2. Don’t Use Hop Stands for Long Periods of Time
Keeping hops in the wort at various sub-boiling temperatures for 60 minutes adds maybe some extra body, but little to no additional hop flavorA 45-minute hop stand at 170°F seems to add no hop flavor.  On the other hand, a 10-minute hop stand (with hops added at flameout) can produce very nice hop flavor.  The take-away message seems to be that long hop stands (45 minutes or more) don’t add hop flavor; shorter hop stands (around 10 minutes) do, although temperature may also be a factor.  Even at sub-boiling temperatures, steeping for too long removes (or fails to produce) that wonderful hop flavor. Are the sub-boiling temperatures of a hop stand beneficial to flavor, or do the flavor benefits come mostly from the amount of time of the steep?  I don’t know.

3. Cover the Kettle After Late-Hop Additions
The effect is very small, but covering the kettle after late-hop additions (i.e. no greater than 10 minutes before flameout) may provide some increase in hop flavor.  For hop-forward ales, there is minimal risk of high DMS levels caused covering the kettle for a few minutes.

4. Dry Hop for Aroma
I haven’t yet done any controlled experiments on hop aroma, but at this point I’ve found that small to moderate hop aroma requires a large amount of late-hop or flameout additions.  But a big aroma can be obtained through dry hopping with an ounce or two (about 25 to 60 grams).   (Noonan says it better: “the full, fresh aroma of hops is only captured by ‘dry-hopping’.”  (Noonan, New Brewing Lager Beer, p. 78.)

5. Dry Hop using a Weighted Mesh Bag
When I dry hop with whole cones, I sometimes put the hops in a very large mesh bag along with some weights.  The bag makes for easy removal of the hops, and the weights force all of the hops to be submerged.  The large mesh bag allows the hops to move around in the wort.  If you have a narrow-necked carboy, you should probably rack the beer to the keg or bottling bucket before removing the hops.  Removing the hops by squeezing them through a narrow neck, with the beer still in the carboy, may add too much grassy flavor to the beer.  More to come when I have time for a formal experiment.

6. Dry Hop for Shorter Periods of Time
As Palmer notes, dry hopping may yield “a dry aftertaste, like old tea” (Palmer, How To Brew, p. 44).  Strong comments that “it can produce a lingering grassy, vegetal note that some may not like” (Strong, Brewing Better Beer, p. 72). He recommends “limiting the contact time of dry hops in beer to 3 to 7 days” (ibid, p. 72).  More to come on this topic, but a week of dry hopping is not too long, in my experience.

7. Use a Lot of Hops Very Late in the Boil
When using too much hops there is the risk of tannins that can cause a grassy taste (Palmer, How to Brew, p. 44) and of course excessive bitterness.  But big, hoppy beers seem to require (strangely enough) lots of hops.  In a 5-gallon (19-liter) batch, six ounces (170 g) of hops very late in the boil (and/or at flameout) and an additional two ounces (57 g) for dry hopping is good, but maybe even on the low side for a really big beer.

Some beers that I’ve brewed with lots of hops do tend to have what I think is referred to as a “grassy” flavor, as noted by Palmer.  It’s not necessarily bad, but it’s not the character of the hops that I’m looking for.  At this point, I think that this flavor was caused by using improperly-stored hops.  In a six-gallon (23-liter) boil, I’ve added one ounce (28 g) at 15 minutes before flameout, 11 ounces (312 g) at flameout (with 10 minutes of post-flameout natural cooling), and an additional 2 ounces (57 g) during dry-hopping, and not noted any grassy flavor (but lots of wonderful citrusy flavor).  All of these additions were made with properly-stored hops, which may have been a critical factor.  (In fact, that beer turned out quite well and measured only 41 IBUs.)

By adding lots of hops late in the boil, IBUs are difficult to predict using standard models.  On the one hand, additions close to flameout will produce more IBUs than predicted by standard formulas because of continued heat after flameout; on the other hand, once you get above 2 ounces (57 g) of AA 10% hops in a 6-gallon (23-liter) boil, IBUs increase less than standard models will predict.  The mIBU model addresses flameout additions but not high levels of alpha-acid concentration.  More to come on this topic when I have more time.  In the meantime, I’ve learned to not fear large amounts of well-preserved flameout hops with a 10-minute rest period before forced cooling.

Other Techniques
I’ve heard about, but not yet had time to try, the following techniques:
Hop Tea: Add a homemade “hop extract” or “hop tea” to the secondary.  Noonan gives fairly detailed instructions (Noonan, New Brewing Lager Beer, p. 160) and recommends the practice.
Hop Bursting: Divide the flavor hops into several additions, with each addition made at a slightly different time.  For example, instead of adding 2 oz of hops at 10 minutes before flameout, try ½ oz each at 15 min, 10 min, 5 min, and 0 min.

Dry Hopping in a Weighted Mesh Bag

Dry hopping, or adding hops in the secondary fermenter, is the best way I’ve found to get good hop aroma.  When I first started dry hopping, I would push the hop cones through the narrow neck of my 5-gallon glass carboy.  To my dismay, the hops floated on top and most of them didn’t seem to ever touch the beer.  Stirring the beer helped a bit, but the contact between hops and beer was still limited.  And cleaning the hops out of the carboy was a mess.  A lot of people use hop pellets for dry-hopping, but since I grow my own Cascade, I’m interested in using the whole cones.

I now use a large mesh bag for dry hopping, with weights in the bag to pull all of the hops into the beer.  It seems like a good idea that I haven’t seen written about elsewhere, so I’m writing a blog post about the technique.

[Edit, Oct 2015:  I’m having second thoughts about removing the hops before racking, especially with a narrow-necked carboy… the aroma is great, but it might add too much grassy flavor to the beer.  To be safe, I’d rack to the keg/bottling container before removing the bag of hops.  More to come when I have time for a formal experiment.]

[Edit, March 2016: I just read on Norm Pyle’s Hops FAQ: “some brewers use a sanitized hop bag and marbles to sink the hops for maximum contact.”  So, apparently it’s true that “what has been done will be done again; there is nothing new under the sun.”]

1. Large Mesh Bag
I use a large nylon mesh straining bag to hold the hops.  I prefer a fairly large bag, so that the hops are free to roam about within the confines of the mesh enclosure.  Figure 1 shows the mesh bag I use, approximately 15″ × 8″ (38 cm × 20 cm).  I thoroughly wash it and soak it in Star-San before each use.

Large Mesh Bag

Figure 1. Large mesh straining bag for holding weights and hops.

2. Weights
Before adding the hops to the sanitized mesh bag, I add two weights.  The purpose of the weights is to drag the bag down into the beer and drown the hops in beer.  (I clean and sanitize the weights before adding them to the bag.)  The weights must satisfy several criteria: (1) they need to fit through the (small) opening of the carboy; (2) they need to be heavy enough to cause the bag and hops to sink; (3) they should ideally not contain iron or lead.  In my case, I took two brass compression caps measuring about ⅞” (2.22 cm) to 1″ (2.54 cm) across and filled them with lead-free solder.  Each filled cap weighs 1.6 oz (45 g), and the two weights together are just about sufficient to weigh down one ounce of hops.  For two ounces of hops, use two bags and four weights total.  These weights are just small enough to fit through my glass carboy when they are inside the mesh bag.  If you have a secondary fermenter with a large opening, the size of the weights probably doesn’t matter.

Brass weights (compression caps) with lead-free solder.

Figure 2. Brass weights (compression caps) filled with lead-free solder.  A ruler (in inches) shown for scale.

dryHop_brassWeights3

Figure 3. Brass weights (compression caps) filled with lead-free solder and a US quarter shown for scale.

3. Fishing Line
I use fishing line for two purposes: (1) to keep the weights in the bag separate from each other and from the hops, and (2) to provide a “lifeline” to remove the bag when the dry-hop time is up.

I found that allowing the hops and weights to mix together caused clumping, and made removal of the bag a bit difficult.  I now add one weight to a bottom corner of the mesh bag, tie it off with fishing line, add the second weight, tie that off with fishing line, and then add the hops.  This makes adding and removing the bag a little easier.  The result of adding weights and tying them off is shown in Figure 4, using a dry (not sanitized) bag and no hops.

009

Figure 4. The mesh bag with two weights tied into a corner.  40-lb green fishing line is used for visual effect, but 8-lb line works well, too.

Once the bag is filled with hops, I pull the drawstrings of the bag closed and knot them together.  I then tie some fishing line to the bag drawstring (near the knot) and let this line come along the edge of the rubber stopper and outside the carboy.  The rubber stopper seals around the fishing line nicely, allowing no air to escape except through the air lock.  When the time comes to remove the bag, I remove the stopper and pull on the fishing line to pull the bag out of the beer.

008

Figure 5. The mesh bag with fishing line tied to one of the drawstrings.

4. Adding the Hops to the Beer
The procedure of adding the hops is pretty much what you’d guess it is:  I remove the rubber stopper from the carboy, then add the mesh bag filled with weights and hops (starting with the weights).  I let one end of the fishing line tied to the drawstring remain outside the carboy.  I replace the rubber stopper.

xx

Figure 6. Mesh bag containing weights and hops (mostly) sinks into the beer.

dryHop_bagInCarboy2

Figure 7.  Closeup of mesh bag inside the carboy.  (This is a different batch of beer.)  You can see the fishing line extending from the opening of the carboy.

5. Stirring the Hops
I stir the hops in the beer at 12-hour intervals, by tilting the carboy on an edge and sloshing the beer around a small amount.  The idea is just to mix the hops with the beer a little more.  I have no idea if this is really useful or not.

6. Removing the Hops
I used to remove the hops before racking to the next container, but that might yield excessive grassy notes.  Instead, I’ll recommend that you rack the beer to the next container and then remove the hops.

When it’s time to remove the hops, I wash and sanitize my hands, remove the rubber stopper, and pull on the fishing line.  When the hops come out of the carboy, the small neck squeezes most of the beer out of the hops and back into the carboy.  Some beer will rise up and flow over the opening, but by going slowly this can be minimized and wiped up with a paper towel.  The weights come out last, and since they haven’t mixed with the wet hops, they are easily removed.  The fishing line can be easily cut off and discarded.

 

Late Hop Experiment #1 (a.k.a. Hop-Stand Experiment #3)

Abstract
In my quest for lots of hop flavor, I previously found that a hop stand did not provide the increase in flavor I expected.  The current experiment looks at several aspects of the brewing process that might provide an increase hop flavor: covering the pot during the last minutes of the boil, varying the time of late-hop additions, and hop stands with a somewhat different technique than I used previously.

I found that covering the pot to prevent oils escaping with the steam may provide some improvement, but this result was not definitive.  A late-hop addition at flameout (followed by 10 minutes of natural cooling with the lid on) contributed much more hop flavor than additions at 5 or 10 minutes.  Holding the wort (and hops) at 170°F (77°C) for an additional 45 minutes may have contributed something, but not an increase in hop flavor.  It seems that hop flavor is lost with extended contact time with boiling wort, and not increased with below-boiling temperatures.

I’ve also created a summary blog post that describes the techniques I’ve found to be useful at maximizing hop flavor and aroma.

Background
Flameout Hops Additions and Hop Stands

When I first started brewing, I would immediately cool the wort when the 60-minute boil time was up.  That was fine, until I started reading about hops additions at zero minutes/flameout.  Why add a whole bunch of hops, only to immediately cool down the wort and remove them?  I came across a discussion on BeerSmith about adding hops at flameout and then letting the wort sit for a while.  There’s another interesting discussion at BeerAdvocate about how long to let the wort sit before cooling.  There’s also an excellent article in BYO on hop stands, in which it’s explained that “pro brewers [give] their flameout hops extended contact time with the wort“.  Last but not least, there’s an interesting discussion on ProBrewer about how long professional brewers whirlpool their hops after flameout.  In short, the wort is often not cooled immediately, which creates a hop stand (whether or not hops are added at flameout, due to any hops already in the wort that have not yet reached maximum utilization).  This extended contact gives flameout hops time to contribute something to beer flavor (and bitterness) at below-boiling temperatures.  In my previous hop-stand experiments, I added post-flameout hops only after the target temperature (e.g. 170°F (77°C)) had been reached, and steeped for a relatively long period of time (60 minutes).  Since those experiments didn’t demonstrate an increase in hop flavor, maybe higher temperatures or shorter steep times are critical for hop flavor.  In the current experiment, I let all batches sit for 10 minutes after flameout, with the lid on.  (I chose 10 minutes pretty much by chance, but I now think that 10 minutes is a really good time for steeping hops.)

Balancing Bitterness Across Conditions
The goal of the current experiment was to look at hop flavor, but I wanted to examine hop flavor independently of bitterness.  In other words, I wanted to vary the timing of late-hop additions and keep the wort at high temperatures after flameout, but hold the bitterness level of all conditions relatively constant.   If one uses a standard formula for computing IBUs (e.g. Tinseth’s formula), hops additions at 0 minutes contribute no bitterness to the beer.  This is true if one immediately force-cools the wort at flameout, but since I allowed the wort in this experiment to sit for 10 minutes after flameout at high temperatures, there was bitterness that was not accounted for by this formula.  In order to keep the conditions in this experiment at roughly the same bitterness level, I developed a modified version of Tinseth’s IBU formula that predicts bitterness contributions after flameout.  I used this formula to vary the timing and amount of hops added to each condition, in an attempt to equalize bitterness levels. There was a bug in my code at the time I used it for this experiment, and I didn’t have the finished beer tested for IBUs, so despite my good intentions I have no idea how well bitterness was kept constant.

Introduction
This experiment looked at three techniques that may contribute to hop flavor: (1) covering the pot during the last minutes of the boil, (2) varying the time of late-hops additions, and (3) a 45-minute hop stand held at 170°F (77°C), with hops added at flameout instead of when the target temperature is reached.  In all cases, the wort was left to stand for 10 minutes after flameout, which may be a critical detail.

(1) Covering the Pot
It’s well known that volatile oils from the hops escape with the steam during the boil (e.g. Daniels, Designing Great Beers, p. 101; Fix and Fix, An Analysis of Brewing Techniques, p. 33; Lewis and Young, Brewing, 2nd ed., p. 271; Papazian, The Homebrewer’s Companion, p. 63). However, an uncovered boil is essential to drive off the precursors of DMS (e.g. Palmer, How to Brew, p. 82; Fix and Fix, An Analysis of Brewing Techniques, p. 50).  Under the assumption that the risks of DMS outweigh any benefits, I usually leave my pot uncovered during the entire brewing process, in accordance with Papazian’s instructions to “never cover a boiling wort with a lid”. (Papazian, p. 138).  Most ales, however, “have DMS levels well below threshold” (Fix and Fix, p. 50).  Because SMM and DMS are reduced more at ale fermentation temperatures than at lager fermentation temperatures, “any hint of DMS in ales is likely from technical brewing errors, most notably contamination” (Fix, p. 75).  This then brings up the question:  will covering the pot during the last additions of hops yield more (good) hop flavor in the (hop-forward) beer than (bad) DMS?  There’s only one way to find out:  brew one condition with the pot uncovered during the entire boil, then brew a nearly identical batch with the pot covered after the last addition of hops.

(2) Varying the Time of Late Hops Additions
Late hop additions are also well known to provide more hop flavor than early additions.  I’ve seen many general statements to the effect of “Thirty minutes is a traditional cut-off point for flavor hops” (Daniels, p. 101) or “Flavor hops additions are considered to be in the last 10 to 20 minutes of the boil” (Strong, p. 65).  Papazian provides an informative graph, showing an increase in flavor starting at 0 minutes, peaking at 10 minutes, and decreasing to zero at 45 minutes (Papazian, The Homebrewer’s Companion, p. 68).  This graph is a “general guide,” though, and I wanted to examine the effect of hops additions in the final 10 minutes, and include a 10-minute stand after flameout.  Therefore, the current experiment looks at the effect on flavor when adding hops at 10 minutes, 5 minutes, and 0 minutes before flameout.  In all cases, I let the wort cool for 10 minutes after flameout.  This post-flameout wait provided at least a brief hop stand for all batches, but it means that my results will be different from someone who does late hopping and then cools their wort at flameout.

(3) Hop Stand
In my previous attempts at a hop stand, I found that the hops added during the stand contributed very little hop flavor, and that the resulting fuller-bodied beer was most likely the result of non-enzymatic browning of the wort.  Not what I was looking for.  But I added the hops only after the wort had reached the target temperature.  Some (or most?  nearly all?) people conduct a hop stand by adding the hops at flameout, bringing the temperature down (either naturally or by forced cooling), and then (possibly) holding the wort at a target temperature.  In the current experiment, there is an additional condition in which I added the hops at flameout, let the wort cool naturally (while covered) for 10 minutes, force-cooled the wort to the hop-stand target temperature, and then held that temperature for 45 minutes. This allows a direct comparison of how effective a hop stand is for longer time periods at lower temperatures.

Methods
This experiment used five conditions:
(A) The baseline: a beer with a late-hop addition at 10 minutes and no covering of the pot.  This was a pretty generic beer.  The “bittering” hop addition of 0.25 oz in 1.3 G of wort (7 g in 4.9 liters) was made at around the ~20 minute mark (instead of the normal 60 minute mark), under the assumption that at 20 minutes and more, the contribution to hop flavor is minimal.
(B) A late-hop addition at 10 minutes, with the pot covered during the final 10 minutes.  The bittering hop addition of 0.25 oz (7 g) was also around the 20-minute mark.
(C) A late-hop addition at 5 minutes, with the pot covered during the final 5 minutes.  The bittering hop addition was slightly more hops (0.30 oz or 8.5 g) at around the 30-minute mark, to attempt to keep the bitterness level about the same as in other conditions.
(D) A late-hop addition at flameout (0 minutes).  The bittering hop addition was even more hops (0.35 oz or 10 g) at the 45-minute mark, to try to keep the bitterness level about the same as in other conditions.
(E) A late-hop addition at flameout.  The hops additions (amount and timing) were the same as in Condition D.  This condition was different from Condition D in that it was followed by holding the wort at 170°F (77°C) for 45 minutes after the 10-minute natural cooling period.

For all conditions, the wort was left to cool for 10 minutes after flameout with the pot covered. The target OG of all conditions was 1.060.  More details are provided below in Table 1.

Comparisons
Condition A can be compared with B, to determine if covering the pot during the last hop addition (at 10 minutes, in this case) improves hop flavor.  Conditions B, C, and D can be compared with each other to determine which late-hop time (10 minutes, 5 minutes, 0 minutes) yields the most hop flavor (given the subsequent 10-minute hop stand).  Conditions D and E can be compared to determine if a 45-minute hop stand at 170°F (77°C) contributes to increased hop flavor.

I originally intended to compare the bitterness levels across all conditions, as a test of a modification to Tinseth’s IBU formula.  However, due to a bug in my initial calculations, the bitterness level will probably be somewhat different across the batches.  I report on the perceived bitterness levels in the Results: Comparisons section, below.

Recipes
As usual in these experiments, a very simple recipe of Briess liquid malt extract, Cascade hops (8.9% AA), Citra hops (13.9% AA), and Safeale US-05 yeast was used.  Rather than brewing the best beer possible, the idea was to keep things as simple and as replicable as possible.  The target volume of the wort at the end of each boil was 1.3 G (4.9 liters).  The goal was to end up with more than 1 G (3.8 liters) per condition, and to ferment only 3½ quarts (3.3 liters), as it’s better to throw wort away (including wort used in SG readings and settled trub) than to not have enough.  The 3½ quarts (3.3 liters) leaves (just) sufficient head room for fermentation.

condition
A
condition
B
condition
C
condition
D
condition
E
Extract:
2½ lbs (1.13 kg) Briess light LME 2½ lbs (1.13 kg) Briess light LME 2½ lbs (1.13 kg) Briess light LME 2½ lbs (1.13 kg) Briess light LME 2½ lbs (1.13 kg) Briess light LME
Initial Water: 1.80 G
(6.8 liters)
1.68 G
(6.3 liters)
1.80 G
(6.8 liters)
1.95 G
(7.4 liters)
2.0 G
(7.6 liters)
Boil Time: 30 min 30 min 35 min 45 min 45 min
Bittering Hops Addition: 0.25 oz (7 g) Cascade (8.9% AA) at 19 min 0.25 oz (7 g) Cascade (8.9% AA) at 21.3 min 0.30 oz (8.5 g) Cascade (8.9% AA) at 30.5 min 0.35 oz (10 g) Cascade (8.9% AA) at 45 min 0.35 oz (10 g) Cascade (8.9% AA) at 45 min
Aroma/
Flavor Hops Addition:
0.4 oz (11 g) Cascade (8.9% AA) and
0.4 oz (11 g) Citra (13.9% AA)
at 9.3 min,
not covered
0.4 oz (11 g) Cascade (8.9% AA) and
0.4 oz (11 g) Citra (13.9% AA)
at 9.3 min,
covered
0.4 oz (11 g) Cascade (8.9% AA) and
0.4 oz (11 g) Citra (13.9% AA)
at 5.0 min,
covered
0.4 oz (11 g) Cascade (8.9% AA) and
0.4 oz (11 g) Citra (13.9% AA)
at 0 min,
covered
0.4 oz (11 g) Cascade (8.9% AA) and
0.4 oz (11 g) Citra (13.9% AA)
at 0 min,
covered
Hop Stand:
no no no no 45 minutes at 170°F (77°C)
Final Target Volume:
1.3 G
(4.9 liters )
1.3 G
(4.9 liters )
1.3 G
(4.9 liters )
1.3 G
(4.9 liters )
1.3 G
(4.9 liters )
Yeast:
~3.4 g Safeale US-05 in 1.6 oz water added to 3½ quarts (3.3 liters) ~3.4 g Safeale US-05 in 1.6 oz water added to 3½ quarts (3.3 liters) ~3.4 g Safeale US-05 in 1.6 oz water added to 3½ quarts (3.3 liters) ~3.4 g Safeale US-05 in 1.6 oz water added to 3½ quarts (3.3 liters) ~3.4 g Safeale US-05 in 1.6 oz water added to 3½ quarts (3.3 liters)
Priming Sugar:
0.5 oz (14 g)
corn sugar
0.5 oz (14 g)
corn sugar
0.5 oz (14 g)
corn sugar
0.5 oz (14 g)
corn sugar
0.5 oz (14 g)
corn sugar
Target OG:
1.060 1.061 1.061 1.060 1.061

Table 1. Recipes and predicted values for the five conditions.

These recipes assumed an evaporation rate of 0.90 G/hr (3.4 liter/hr) during the uncovered boil, 0.35 G/hr (1.3 liter/hr) at temperatures less than boiling (uncovered), and 0.10 G/hr (0.38 liter/hr) for a covered boil or stand.  (The value for the covered boil was a guess, and assumed some small amount of loss due to various factors.)  The amount of water, the weight of bittering hops, and the timing of all hops additions were varied to attempt to achieve about the same OG, the same post-boil volume, and the same bitterness levels.

At 10 minutes after flameout, each condition was cooled to 75°F (24°C) using a wort chiller and let sit for an additional 10 minutes.  After transferring 3½ quarts (3.3 liters) into a sterile 1 G (4 liter) container (a.k.a. milk jug), the jug was shaken vigorously for 90 seconds, the yeast was pitched, and an airlock was applied.  Fermentation and conditioning proceeded for 3 weeks at around 64°F (18°C), followed by bottling and bottle conditioning for an additional 3 weeks (also around 64°F (18°C)).  Priming used 0.50 oz (14 g) of glucose per condition to yield 2.11 volumes CO2. The yield was 8 12-oz bottles per condition.

I don’t think that the level of precision indicated in these recipes is required in order to obtain perceptually identical beers; a point or two of OG difference or a variation of 5 IBUs (Daniels, p. 76) probably won’t be perceptible.  I tried my best to obtain the target numbers indicated, however, and hoped that any measurement errors would, on average, cancel each other out.

Results
Results: (In)Ability to Follow the Recipes (a.k.a Mistakes)
If I had been able to follow the recipes above to the letter and not had any bugs in my software, then this sub-section wouldn’t be necessary.  But nothing new ever goes completely according to plan, and so there were some unintended deviations from the recipes.  This part discusses what went differently and if I think there may be an impact on results.

(1) Evaporation Rates: Apparently, the 0.90 G/hr (3.4 liter/hr) evaporation rate that I’ve measured in the past (when making 5-gallon batches) was larger than my observed evaporation rate in this experiment.  This may have been because I used a smaller pot (which had a smaller opening), or because I’ve been so worried about too much evaporation that I applied less heat overall.  Likewise, the below-boiling evaporation rate seems to have been slightly overestimated.  Finally, the evaporation rate when the pot was covered was probably much closer to zero.  I realized something was off when Condition A was finished with the boil.  My solution for conditions B, C, D, and E was to wait an additional 5 to 10 minutes during the boil before adding any hops.  Even so, my measured OG values were 1.059 to 1.060 instead of 1.060 to 1.061.  I don’t believe that I can detect the difference of a few points of OG, and the over-estimation of evaporation rate was roughly the same for all conditions, so I don’t think that this will affect results.

(2) Condition A: I mistakenly used 1.85 G (7.0 liters) of water instead of 1.80 G (6.8 liters).  In addition, because the assumed evaporation rates were incorrect, I ended up with 1.75 G (6.6 liters) of wort after the boil instead of 1.60 G (6.0 liters).  My solution was to use a hop-less stand after the boil (at 170°F (77°C)) for 30 minutes in order to evaporate the extra 0.15 G (0.57 liters).  This meant that Condition A probably had a little bit more body than Conditions B, C, and D due to non-enzymatic browning, but body is not one of the factors I’m intending to evaluate in this experiment.

(3) Condition E: By the time I got to Condition E, apparently I was starting to really increase the heat in order to increase evaporation.  I ended up with an OG of 1.061.  Since the other conditions ended up with OGs around 1.059, I added ¼ cup (60 ml) of water to the final 3½ quarts (3.3 liters), which resulted in an OG of 1.060.

(4) Post-Flameout Temperature Decrease: Before brew day, I did a quick experiment in my kitchen to measure how quickly temperatures decrease after flameout.  This test showed that for 1.6 G (6.0 liters) in an uncovered pot, the temperature after 10 minutes was 182°F (83°C), and for 1.6 G (6.0 liters) in a covered pot, the temperature after 10 minutes was 201.5°F (94°C).  Since I planned to keep the lid closed after flameout, I used a line based on the second measurement to predict post-flameout bitterness.  What I forgot to take into account was the minute or so immediately after flameout, when I stirred the wort one last time and took a sample for SG reading.  In this brief time, the temperature quickly dropped while the pot was uncovered.  Also, the temperature in my kitchen (68°F (20°C)) was much greater than in my garage where I brew (around 60°F (15.5°C)).  As a result, I ended up with temperatures between 190°F (88°C) and 195°F (90.5°C) at 10 minutes after flameout.  Because of lower observed temperatures, I achieved less hop utilization during the 10 minutes after flameout than I had predicted.

(5) Bug in the Calculations: While this batch was fermenting, I worked on a blog post to explain a modification to the prediction of IBU values that takes into account post-flameout bitterness.  In the course of this writeup, I found a bug in my code.  As a result of this bug, I was computing less post-utilization flameout than I should have been for earlier hops additions, and so the (hopefully) more correct bitterness levels (mIBU values) decrease with the later hops additions instead of being constant.

After all those mistakes, here is a table summarizing the observed original gravity and final gravity for each batch:

condition
A
condition
B
condition
C
condition
D
condition
E
Original
Gravity
 1.059  1.060  1.059  1.059  1.060
Final
Gravity
 1.013  1.014  1.013  1.013  1.013

Table 2. Measurements of Each Condition

Results: Comparisons
The following table summarizes the results of the comparisons.  The top right half of the table (in blue) is for the “hops flavor” comparison, and the bottom left half of the table (in green) is for a “relative bitterness” comparison. The letter in each box indicates which of the two conditions was preferred; a question mark indicates that no difference could be reliably detected.  Multiple values indicate multiple comparisons of the two conditions, which I did to detect possible random variation.

Condition A
Condition B Condition C Condition D Condition E
Condition A
   ?,B,?  –
 –  –
Condition B  ?,?,A    ?,C,C  D,D  –
Condition C  –  ?,?,?    D,D,D  –
Condition D  –  ?,?  ?,D,C     ?,?,?
Condition E  –
 –  –  ?,?,?
 

A/B Comparison Notes. First tasting: condition A had slightly more body, as expected by the non-enzymatic browning caused by the extra time for evaporation. Condition B had very slightly more hops/citrus flavor, but not enough to be a reliable difference.  It seemed that covering the pot during the last 10 minutes had a negligible effect on flavor.  Second tasting:  Condition B had a very slightly crisper, more citrus flavor than A, as one would expect from Cascade and Citra hops.  The beers were very, very similar, but there was a reliable, detectable difference.  Bitterness levels were the same.  Third tasting:  This time, A seemed slightly more bitter; B more “mellow.”  (In hindsight, it’s likely that I was hallucinating the difference in bitterness; I’m also not sure what would make B more “mellow”.)  I could detect only a very slight difference in hops flavor, with B having slightly more but not enough for me to consider it a reliable difference. In short: B was preferred for hops flavor all three times, but only once did I think it noticeable enough to be considered a “reliable” difference.

B/C Comparison Notes. First tasting: these beers had nearly identical taste.  At first I decided that C was ever so slightly more bitter than B; a half glass later, I decided that B was just slightly more bitter than C.  So I marked it as “no detectable difference” in terms of bitterness.  At first, I could detect no difference in hops flavor.  By the end of the first tasting, I thought that C had slightly more hops flavor than B, but not much.  Second tasting: this time, I could reliably detect a small amount of more hops flavor in C, even from the first sips.  Bitterness levels were about the same, although C seemed maybe just a little more bitter than BThird tasting: C had distinctly more hops flavor than B, although not dramatically more.  The difference was small but noticeable.  I thought B might have been a little bit more bitter than C (the opposite of my second tasting result), but not enough to make it a reliable difference.  In short: bitterness levels were about the same, and C had consistently more hop flavor than B.

C/D Comparison Notes. First tasting: OK, this was the first clear and compelling difference!  D definitely had more hops flavor.  This was a real plus.  On the other hand, it also had more of a tannin flavor.  I had a hard time deciding which was more bitter.  D might have been a tad sweeter, but it also seemed like it might have had more of a tannin or “astringent” bitterness, in contrast with the “clean” bitterness of C.  So in the end the bitterness level seemed about the same.  One unanswered question is whether the astringent bitterness was caused by the longer boil time of the “bittering” hops or the later addition of the “flavor” hops.  Second tasting: D had much more hops flavor, by a wide margin.  C had a definite citrus-hop character, but D brought it out much more.  I thought that D was more bitter, in contrast with the predicted bitterness levels.  Third tasting: Again, and without question, D had more hops flavor.  C seemed to be slightly more bitter, but the bitterness was a “cleaner” bitterness rather than an “astringent” or “grassy” bitterness.   Since these tastings, I’ve found a relevant comment by Greg Noonan: “the bitterness derived from long boiling is coarser than that from a more moderate period” (Noonan, New Brewing Lager Beer, p. 154).  Condition D had a larger amount of bittering hops in the boil for a longer time, and so the difference in bitterness quality probably came from the bittering hop addition rather than the late hop addition.  In short: D clearly had more hop flavor than C; bitterness levels were difficult to judge but about the same.

D/E Comparison Notes. First tasting:  There was almost no difference between these beers.  There was a very slight and subtle difference, but I couldn’t figure out if it E was slightly more astringent, or had more body, or what.  In short, there was no difference between D and E that I could label with any category.  Second tasting:  Same results as the first.  I thought there might be some difference between the two conditions, but I couldn’t quite place what it was.  More bitter?  Fuller?  More sweet?  Crisper?  I really didn’t know.  They were not identical, but not reliably different in either hops flavor or bitterness.  Third tasting:  This time I was able to pin a label on the difference: E was slightly smoother than D.  Once I had decided on that label, I could distinguish them.  Since “smooth” is neither hop flavor nor bitterness, I marked this comparison as “?” in both categories.  The “smoothness” description fits in well with the flavor effects of a hop stand that I observed in Hop Stand Experiment #1In short: bitterness and hop flavor levels were about the same for D and E; E was slightly “smoother”.

B/D Comparison Notes. After the main comparisons (A/B, B/C, C/D, D/E), I had enough bottles left to compare B and D twice, so I did.  First tasting: As expected, D had more hops flavor than B, but I couldn’t detect a difference in bitterness… if anything, D seemed slightly more bitter.  Second tasting: Once again, D had more hops flavor than B.  At first I thought that B was more bitter, then I decided that I really couldn’t tell.  In short: D had more hops flavor than B.

Summary
Covering the lid during the final 10 minutes of the boil (immediately after the last hops addition) had a small impact.  There might be some benefit to covering the pot, resulting in a barely detectable increase in hops flavor.  Certainly there was no downside, and no extra effort.

A hops addition at flameout, with a 10-minute stand, contributed much more hops flavor than otherwise identical additions at 5 and 10 minutes.  A hop addition at 5 minutes contributed more hops flavor than a 10-minute addition, but much less than the flameout addition.  This may be compatible with Papazian’s graph showing a peak in hops flavor at 10 minutes, since his graph may assume cooling at flameout, whereas my batches were kept hot for 10 minutes after flameout.

Holding the hops in the wort at 170°F (77°C) for 45 minutes yielded no reliably-quantifiable effect on hops flavor or bitterness, except for the possibility that the wort held at 170°F (77°C) was slightly smoother.  Unless you’re really trying to squeeze every last possible iota of goodness from your process, when the wort cools to ~180°F (82°C), you might as well force-cool to pitching temperature and get on with the day.

Conclusion and Future Work
Within the constraints of this experimental setup, the best way to maximize hop flavor is to add hops at flameout, cover the pot, and let the wort cool naturally for at least 10 minutes.  Longer hops additions are not as effective as flameout additions.  Covering the pot provides a very small increase in flavor.  Holding the wort at 170°F (77°C) may provide some benefit, but is probably not worth the effort.

Future work: I’d like to see if there is some temperature between boiling and ~180°F (82°C) that maximizes hop flavor, and for how much time the hops should be steeped at that temperature.