Deja IBU

by Tom Altenbach

With the posting of the Tinseth alpha acid equations on the Internet, we now have three methods to calculate estimated hop bitterness (in IBU) for homebrew. Rager published the first method (Zymurgy Special Issue 1990). His equations were adopted, updated, complicated, and possibly improved by Garetz in his book Using Hops. Then Tinseth produced new curves based on his research which will eventually be published formally. In the September 1995 Draught Notice, Bob Jones compared the formulae, highlighting the new Tinseth methods. I would like to follow up on that article with some of my own observations.

In Using Hops, Garetz introduces some interesting new ideas to adjust the alpha calculation. Unfortunately, no data or footnoted references are provided so the only justification available for the various factors are the author's own statements. Although the factors seem to make sense, the author's rather limited brewing experience doesn't aid his credibility.

Using Hops was reviewed in Zymurgy (Spring 1995) by Al Korzonas, National BJCP Judge, homebrew shop owner, and frequent contributor to the Homebrew Digest. The book review was highly critical, and Al's experiments seem to favor the original Rager calculations over the Garetz approach. The main knock on Garetz is that his equations call for too much hops, leading the homebrewer to overshoot on bitterness.

The new Tinseth utilization curve is an exponential fit to the yet unpublished data. For short boil times it approaches a linear relationship starting from zero utilization at time zero. The s-shape of the Rager and Garetz curves implies a threshold effect, with a constant utilization for some initial time period. When the threshold time is reached, utilization then increases. Garetz assumes a utilization of zero preceding the threshold boil time, while Rager assumes a utilization of about 5% during this time.

All the authors claim to have some data to support their assumptions in the short boil time region. While we can't sort out the answer here, this controversy has precedence in other fields. For example, in radiation health physics a debate has raged for decades over the effects of low level radiation on cells. One side proposes a linear relationship that assumes that any level of nuclear radiation, no matter how small, will cause some cell damage. The other side proposes a threshold theory, whereby small radiation levels cause no damage until the exposure threshold is reached. Both sides can present data to support their claims. My point here is that neither the linear nor threshold approach to low boil time hop utilization is inherently more logical than the other.

Wort boil gravity has an important effect on utilization. The higher the gravity, the harder it is to dissolve and isomerize the alpha acids. All the authors have a correction factor for wort gravity, but the Rager/Garetz factor differs from Tinseth. When trying to correct for boil gravity it is important to realize that the gravity is constantly changing, and it is the time dependent gravity that really determines the utilization correction. In my brewery, the wort gravity changes by 30% from the start to end of boil.

To keep the formulae simple, it's desirable to use a single value for the gravity correction. When I asked at Hop Tech which gravity to use in the Garetz equation, the response indicated the end of boil gravity. When I asked Tinseth, he responded that the average gravity during the boil would be appropriate for his formula. On this point the Tinseth approach makes more sense. I plotted the utilization correction factor as a function of the wort specific gravity at the end of the boil for Tinseth and Rager/Garetz so the two can be compared on equal footing. However, this knockout gravity is adjusted to the average kettle gravity over the hop boil time in the Tinseth equation. Two Tinseth curves are shown for a 90-minute hop boil and a 10-minute hop boil. The crossing of the curves at a gravity of 1.080 tends to bring the Tinseth and Garetz utilization estimates together for high gravity brews.

The plot in Bob's article showed alpha acid utilization as a function of boil time for a single wort gravity of 1.050 for the three methods of Rager, Garetz, and Tinseth. Since utilization decreases with wort gravity, the values obtained from Bob's plot must be multiplied by the gravity correction factor obtained in my plot, for wort gravities over 1.050. Garetz uses the same gravity correction factor as

Rager, so there is only one correction curve for both. It only applies to gravities over 1.050.

It is based on the gravity at the end of boil. Tinseth uses a different gravity correction factor, based on the average gravity during the boil. This depends on the end of boil gravity and the length of boil. Therefore the Tinseth correction plotted as a function of end of boil gravity is actually a family of curves.

I have shown two of these, for 90-minute and 10-minute boils, which cover the range of interest. The Tinseth correction also covers the full range of gravities, above and below 1.050.

For example, if we have boiled a barley wine down to a gravity of 1.100 with hops boiling for 90 minutes, the base utilizations from Bob's plot are Rager = 0.3 , and Garetz = 0.22. From my plot, the correction factor is 0.8, so the actual utilizations are Rager = 0.3 * 0.8 = .24 and Garetz = 0.22 * 0.8 = 0.18. Since the Tinseth gravity correction factor is not normalized to 1.0 at gravity 1.050, it's not correct to follow this same procedure to get the actual Tinseth utilization. The easiest way to do it is to pick the value off of the table in Bob's article.

First, compute the average gravity over the boil time, which is about 1.091. Then, pulling the value off the table for SG = 1.090, we get a Tinseth utilization of about 0.17. Or, to use my plot, first normalize the base Tinseth utilization by taking the table value for 90-min SG= 1.050 (0.247), and divide by 1.053. This is the 90-min Tinseth gravity correction for end of boil SG = 1.055 or average SG = 1.050. This gives a value of 0.247 / 1.053 = 0.235. Then, from my plot, apply the 90-min SG=100 gravity correction factor of 0.73 to get the Tinseth adjusted utilization of 0.235 * 0.73 = 0.17. Then, for this high-gravity example, Tinseth estimates the lowest utilization. This is because his gravity correction curves are steeper than Rager/Garetz. As we see in Bob's plot of lower gravity wort (1.050), there the Garetz equation will produce the lowest estimate. Rager is on the high side in both of these examples. No one ever said comparing apples and oranges was easy.

Let me finally relate my experiences in using the equations for IBUs. I have been using the Rager estimates for a long time and have noticed some trends. For highly-hopped (especially high gravity) beers, the Rager method seems to overestimate utilization. That is, for an IPA, Pilsner, or Steam beer, I need to add more hops than Rager predicts in order to get the appropriate bitterness. For a Barley Wine I add lots more hops. I would tend to favor Tinseth or Garetz for these brews, as their lower utilization estimates will call for more hops to achieve the desired bitterness level. Aim high, it's hard to overhop these beers. For lightly hopped beers like Wheat beer, Bock, or Scotch ale, I have had good success following Rager. I would be very cautious using Garetz for fear of overhopping these beers and blowing the style guidelines. Aim low here, it's hard to underhop these styles. For balanced beers like Oktoberfest and Vienna, look at all three calculations and hope for the best. Tinseth seems to cover the middle ground between the Rager and Garetz estimates for many recipes. When in doubt, aim toward the low side.

My last three brews provide examples of how the formulae compare to each other and the style guidelines.

Dortmunder Export Lager - AHA range 23 to 29 IBU. My OG = 67. My hop additions calculated to: Rager = 40, Tinseth = 26, Garetz = 22, average ò 29.

Dopplebock - AHA range 17 to 27 IBU. My OG = 95. My hop additions calculated to: Rager = 27, Tinseth = 18, Garetz = 17, average ò 21.

Oktoberfest - AHA range 22 to 28 IBU. My OG = 64. My hop additions calculate to: Rager = 32, Tinseth = 22, Garetz = 20, average ò 25.

The equations relate differently in short boil utilization vs. long boil utilization, as well as gravity corrections. Late hopping boosts the Rager and Tinseth estimates. High gravity boosts the Rager and Garetz estimates.

A final note. In judging beer, if there are no obvious flaws like gushing, sourness, or astringency, then inappropriate bitterness level for the style becomes a very easy attribute to critique. Hitting the correct bitterness can often be the difference between a drinkable beer and a prize winner.