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Hop Utilisation
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Hop Utilisation Defaults

Introduction

The bitterness of a beer can be expressed numerically by a magic number known as European Bitterness Units. Technically, one EBU represents one milligram of alpha-acid in one litre of beer. The bitterness of a beer can be represented numerically by:

                  Weight X Alpha-acid X Utilisation
EBU    =     ———————————————————
                    Volume Brewed X 10

Where:
EBU = European Bitterness Units.
Weight = the weight of hops in grams.
Alpha-acid = the alpha-acid content of the hops in per cent.
Volume = the volume of beer brewed in litres.
Utilisation = hop alpha-acid utilisation in per cent.

Home brewers tend to use the above formula to determine the quantity of hops to use to achieve a given bitterness in a beer, or the other way round to estimate bitterness from a give quantity of hops. This application is not really what it was intended for; it was intended as an internal quality-control measure for commercial breweries, and does not really lend itself to being worked backwards as we home brewers try to do. However, it is all we have, and would be straight-forward enough, if it was not for a major snag called hop alpha-acid utilisation.

Hop alpha-acid utilisation, usually called hop utilisation, or even just utilisation, is a variable in the above formula. Although a given variety of hop may contain, say, five per cent alpha-acid (bittering power), we only manage to extract, or isomerise, a small fraction of that. The amount of alpha-acid we get from the hop, compared to the total alpha-acid contained within the hop is known as hop alpha-acid utilisation, and is expressed in per cent. The amount of alpha-acid we put into the copper is not the same amount that ends up in the beer. Frustratingly, hop alpha-acid utilisation is not an easily defined fixed number, but a highly variable parameter that is affected by just about everything; equipment design, recipe, wort protein, original gravity, boil time, boil vigour and many more things - even atmospheric pressure. Determining a figure for individual hop utilisation is one hell of a headache because different equipment setups and different recipes will produce a different figure.

There are at least half a dozen formulae kicking about in the home brewing community that attempt to predict alpha-acid utilisation, but all of them give widely differing results and none of them consistently match laboratory-measured figures. There have been a number of tests whereby home-brewed beers have had their bitterness measured in a laboratory and the results have been compared to the predicted values given by the various formulae and they just do not match up, apart from the occasional fixed point, but even a stopped clock is correct twice a day. None of them are particularly reliable. In fact, they are possibly less accurate than the old AA units introduced by Dave Line in the early 1970s.

One of the reasons for writing Beer Engine was the issue of hop utilisation. The standard utilisation formulae used in other software packages, the ones that I looked at least, use an inflexible one-size-fits-all approach. Although some software packages do provide some (often bizarre) tweaks, none of them allow the parameters of the formula itself to be tweaked. Even if the authors of the various hop utilisation formulae had got things absolutely right, as they all thought they had, all the respective authors openly state in their work that the numbers will need tweaking to suit individual circumstances. Consequently the hop utilisation approach in Beer Engine is flexible and tweakable, which has the disadvantage that it makes the defaults set up in Beer Engine a little difficult to understand.

Internally, Beer Engine derives alpha-acid utilisation from:

Utilisation = Bu x Gc x Bc

Where:
Bu = Base utilisation, in per cent
Gc = Gravity Compensation Factor, an internally-generated number between 0 and 1 (such as 0.6)
Bc = Boil Time Compensation Factor, another internally-generated number between 0 and 1.

Base Utilisation

This is a figure that represents an upper limit for utilisation - the very maximum utilisation that could ever be achieved under ideal, or better-than-ideal, conditions. This is typically around 35%, but varies between different utilisation formula and methods due to various assumptions that have to be made. This figure is then modified (lowered) by the Gravity Compensation Factor and the Boil Time Compensation Factor. If both the Gravity Compensation and Boil Time Compensation are set to 'None', then the Base Utilisation will represent a fixed utilisation that is applied to all hops irrespective of anything else. The Base Utilisation provides a simple method of adjusting the overall hop utilisation to suit your system, as part of the tweakability concept. If, for example, the perceived bitterness of your beers is consistently too high, increase the Base Utilisation figure and the perceived bitterness of your beer (the amount of hops demanded) will reduce.

Gravity Compensation Factor

Internally this is a number between 0 and 1, which actually represents a percentage between 0 and 100%, but expressed as a decimal. Hop utilisation is roughly proportional to the original gravity of the beer, so it is called gravity factor or something similar by most workers. However, gravity compensation is a bit of a misnomer because the greatest and most variable influence on hop utilisation is the amount of protein in the wort during the boil, not the actual gravity of the wort. The solubility of alpha-acid does not vary much with gravity, but protein has the effect of absorbing alpha-acid and dragging it out of solution with the trub. Different beers, particularly beers of different recipe (and strength), will have different amounts of protein and therefore different hop utilisation. Twice as much pale malt = twice as much protein = twice as much alpha-acid absorbed - a more or less linear function. Different types of malt contain different amounts of protein, flakes and grits contain a lot more protein than does malt, sugar contains none. Ideally, 'gravity compensation factor' would be termed 'trub compensation factor' and would be linearly proportional to the amount of protein or trub in the wort.

The utilisation formulae currently used by home brewers do not base gravity factor on trub levels. It seems that few of the authors were aware of its influence, or at least did not mention it if they were; thus their formulae were based upon incorrect assumptions. Although, technically, gravity factor should be based on protein content of the malt, original gravity is a fair enough approximation to it in the absence of better information, but nevertheless accuracy would be improved if nitrogen-free ingredients, like sugar, were omitted from the gravity figure. The major point is that the function should be substantially linear, whereas with many of the utilisation formulae it is not. For example, Tinseth's gravity factor function is exponential, but Garetz's is linear.

The Trub Compensation Box in the defaults popup has three possible settings; linear, exponential and none. None obviously means that compensation is switched off. SFL and SFE are scale factors (Scale Factor Linear and Scale Factor Exponential). These enable one to tailor the gravity compensation, independent of anything else, should it be felt that the compensation is out of step with the reality of the situation. Changing these will change the slope of the function, independent of anything else, and slide utilisation up and down as appropriate.

Linear: The linear method of approximating gravity factor is probably a more realistic scenario than Tinseth's exponential function. Certianly, British commercial brewers treat the (so called) gravity factor as if it were linear. It is the method I used (from 1991) long before many of the other methods surfaced. In reality the results do not differ substantially from the Tinseth curve anyway. The scale factor (SFL) can be used to independently fine-tune the linear function to adjust it to your system.

Exponential Tinseth uses an exponential function (a power of 'e') to predict gravity factor in his formula. It seems that Tinseth was not aware that his function was exponential, judging by his convoluted formula, but when one examines it, exponential is what it turns out to be. Although Tinseth uses an exponential function, the numbers are at the bottom, linear-most part of the curve (the curve is the same shape as in the graph shown below) and at normal gravity ranges deviates very little from a linear function. Indeed, when comparing the linear method (using the default values) side by side with the Tinseth method, there is a worst-case difference of less than 3EBU over typical gravity ranges, which is beyond human taste perception. Indeed, there is just a 1 EBU difference between Linear and Tinseth for an O.G. 1.050 40EBU beer. The linear-function parameters can probably be tweaked to match Tinseth even closer, should anyone feel the need to do so. Tinseth and linear figures begin to diverge significantly at very high gravities, above about 1.100, but at those gravities it is anybody's guess as to which one is more accurate. With the Scale Factor (SFE) set to 112 and the Base Utilisation set to 39.75, the exponential function matches the Tinseth figures (The Tinseth button preloads those values). The scale factor can be used to independently fine-tune the exponential function to adjust it to your system.

Trub Based The trub-based function is currently disabled, but may be a linear function that takes the amount of grist nitrogen / protein / trub into account when calculating gravity factor. It may just as likely be removed from the next version too.

Boil-Time Compensation Factor

Alph-acid is just about insoluble in beer. To make it soluble it needs to be converted into isomerised alpha-acid by boiling. Isomerisation is a slow process; the longer the boil the more alpha-acid is extracted from the hops, which is why it takes a ninety-minute or so boil to get the most out of the hops. Thus hop utilisation is a function of boil time; the longer the boil the higher is utilisation.

It is documented in commercial sources that hop isomerisation plotted against time is a pseudo first-order kinetic function at constant pH (wort pH is not constant but drops during the boil). Indeed, it makes logical sense that it should be. Utilisation Graph The most obvious implementation of first-order kinetics is the exponential function, an example of which is shown in the accompanying graph. Indeed, a similar-shaped curve is shown in some hop merchant's data sheets and an exponential function is used in the Tinseth formula. Therefore an exponential boil-time function is currently the only boil-time option provided in Beer Engine apart from 'None' which merely switches it off.

A theoretical objection to the shape of the graph is that the curve starts at time-zero with isomerisation starting immediately at its maximum rate, which may not be true. The argument being that isomerisation is a slow, time-related, process, like most cooking processes, and does not instantaneously occur at maximum rate. There would at least be a significant delay before isomerisation begins, but is more likely to gradually build up from zero, reaching maximum rate after several minutes. An S-shaped (sigmoid) curve is a far more likely scenario. Some of the other hop utilisation formula do indeed use a sigmoid curve, but the jury is out on whether an exponential or sigmoid curve is the most appropriate. This would not be an issue if it were not for the habit of home brewers (inadvisably) using such formulae for attempting to determine the alpha-acid contribution for late hops. The curves represent the duration from time zero, whereas hops are actually towards the end of the boil, which is a different kettle of fish entirely.

Anyway, back to the hop utilisation defaults box. T is the frig-factor or scale factor for the exponential boil time function. It is called T because it is in fact a time. It is the time in minutes that it takes to extract 63.2% of whatever is the maximum that you are ever going to get from your hops. That is 63.2% of what is in the Base Utilisation box. With T set to 25, it matches the Tinseth numbers, so 25 is the default setting, even though I think it is rather on the low side. As with the other scale factors, adjusting this figure will slide the Boil-Time Compensation up and down the scale so that you can set it to whatever you want.

'Set To Tinseth' Button

Of the various methods that attempt to predict hop alpha-acid utilisation by the home brewing community, the Tinseth formula seems to be the most popular method. The Tinseth button loads preset parameters that will cause Beer Engine to emulate the Tinseth method. It is the only 'named' method that is included as a preset.

Set To Linear Button

A linear approach to predicting hop alpha-acid utilisation is another valid method. The 'Set To Linear' button loads preset parameters that produce numbers that do not differ substantially from the Tinseth numbers over normal gravity ranges. Boil-time compensation is switched off when the linear button is pressed (so that it matches the stuff. Should you require boil time compensation you will need to select it separately. See the 'Late Hop' section below.

And Finally

It should be realised that estimating bitterness in this way, no matter whose formula you use, is only an approximation and a rough approximation at that. The authors of the most popular formula have all been accused of extrapolating scant laboratory information, overgeneralising, and making inappropriate assumptions. None of them have supplied the original data which they (presumably) used to derive their formulae or even given references, so it is not possible to double-check their work. The whole concept of EBUs and bitterness, although not exactly a pseudo-science, is very empirical and woolly. The alpha-acid of hops cannot be measured to any great precision, normally to just one significant digit and one decimal place, and the measurement of bitterness in beer is notoriously inconsistent. There are several analytical techniques to measure bitterness, but different techniques give markedly different figures for the same beer, and other constituents of beer can interfere with the results, so different types of beer with identical hop rates can give unexpectedly different results even when using the same analytical technique. Needless to say, measured bitterness, calculated bitterness and perceived bitterness are three entirely different things. A beer that has twice the EBUs of another will not taste twice as bitter, because the palate, like hearing (decibels), is logarithmic, whereas the EBU formula is linear. In the end it is down to taste, getting to know your system and technique, and adjusting the parameters accordingly.

Note that, as with all the default settings, any changes will need to be saved for them to apply to future sessions, otherwise the changes will only remain valid for the current session.


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Text copyright (C) 2009 Graham Wheeler.