Tinseth? Rager?

[SacoDeToro]

It really doesn't matter what you use as long as you've correlated your calculations with your palate. I use ProMash and have things set to use the Rager formula for all of my beers. I see the theoretical IBU level and I know how that's going to play out in my beers before I brew them. It's like using Metric vs. English units - just understand that your dick is smaller than you think.

[BigNastyBrew]

It really doesn't matter what you use as long as you've correlated your calculations with your palate. I use ProMash and have things set to use the Rager formula for all of my beers. I see the theoretical IBU level and I know how that's going to play out in my beers before I brew them. It's like using Metric vs. English units - just understand that your dick is smaller than you think.

Damn! I thought it was pretty small already.

I'll continue to "play" with it. I'm brewing a Vienna lager Saturday and this will be my first Rager brew. I'm pretty balanced with a .52 BU:GU ratio Rager but .46 Tinseth. I brew a lot of balanced beers like this so we'll see if I can taste a difference. If not, I'll probably just keep my recipes Rager because it seems as though that's the popular choice for recipes.

[ajdelange]

This is an interesting question which motivated me to go back and look at the last 24 beers I've brewed and compare the planned BU's to the BU's actually realized. When I did this I found that the average error was -15.5% (i.e. if I calculated, on average, 50 BU in planning the beer I measured, on average, 42) with standard deviation of 15.5% for an rms error of 21.6%. IOW I was overly optomistic about the utilizations I would achieve and indeed the numbers I used were 34% utilization for hops boiled for an hour (irrespective of gravity), 18% for half an hour, 9% for 15 minutes and 8% for anything less than 15 minutes (based on the fact that the hops stay in the hot wort during the time it takes to drain the kettle through the chiller which is typically about 15 minutes). As a good junior scientist I know that the thing to do here is scale all these utilizations by the factor which minimizes the rmse which I did. The recalculated estimates (based on 29.6% utilization for 1 hr, 15.7% for 1/2 hour, 7.8% for 1/4 and 7% for < 1/4 hr) now give me differences which average -3% with rmse of 17.6% and a standard deviation of about the same. This represents a better "model" but it is a stretch to glorify the method I had been using by calling it a model at all.

The Tinseth model has lots of appeal. It is simple* to compute in a spreadsheet or with calculator, factors the utilization into parts which depend on the boil time and the wort strength, gives results generally intermediate between the Garetz and Rager models and is apparently based on some real data. So I recalculated all my predictions based on the Tinseth model tweaking the 4.15 factor to get the mimimum rmse, as he advises doing on his website. The result was a set of prediction errors whose mean was -2.65% with a standard deviation of 16.5% for an overall rmse of 16.5%. Tinseth's model is clearly better than my "model" (as adjusted) but hardly dramatically so (1% improvement in rmse but it does reduce error for the few strong beers I've done). So how do we explain this?

What do we do with the utilization number? Multiply it by the AA% value on the hops package. If we are a big commercial operation and have just ordered several bales from Hop Union which we know are coming directly to us via refrigerated truck from thier cold storage facility we migh have some confidence that the number on their certificate of analysis, with the analysis done just before shipping, has some validity. But if the hops come in Oz [i.e. 1 ounce - I don't mean they come from Australia here] bags from our local HBS with uncertainty as to how they have been shipped and stored or even, in some cases, which year's crop they represent or if they come to us from a buddy who had some left over with the AA number written in Magic Marker on a baggie we cannot be so confident. Note that hops labeled 3.5% that actually retain only 3% AA represent a 15% error in predicted BU's even if the utilization model is flawless. Note also that this level of loss is not at all unexpected if the finer varieties of hops are stored at 20 °C for even a relatively short period. It is quite clear that the analysis which leads to the number on the package is done before the hops are put in the package and it is thus not surprising that my data show, on average, lower yields than the labeling indicates. Then there are all the other variables to consider such as whether the yeast is bruch or staub, total AA concentration etc.

So what does all this mean? To me it suggests that you might as well pick a model you like and stick with it. The Tinseth model has, as noted above, lots of appeal. It doesn't have you chasing half percent (percent of percent or percent of calculated BU) corrections in a scheme that overall is likely to at best yield a number that is within 15% of the truth. Consistency is probably more important than accuracy because it will allow you to draw conclusions about hop additions for a beer you are plannng based on whether you want it more or less bitter than a previous one. As has been noted here by others it doens't really matter whether your scale of bitterness is accurate or not as long as it is consistent (the beer with the higher number is always more bitter than the beer with the lower).

*Tinseth publishes his formulas as F1 = (1-exp(-0.04*minutes)/4.15 which represents the time factor. Note that it has value 0.241 for long boil times. The other factor he calls the "bigness" factor; F2 = 1.65*0.000125^(SG-1). Note that for pure water (SG =1.000) this factor has a value of 1.65. Multiplying F1*F2 gives a maximum utilization of 39.7%. It would feel better to me if F1 = (1-exp(-0.04*minutes)/4.15/1.65 and F2 = 0.000125^(SG-1) so the two represent separate reductions in utilization but perhaps he has a good reason for doing it the way he did.

[BigNastyBrew]

Thanks, brotha! Lots of good info there. Some of it I can use now, the rest I'll have to store away for the moment. All of my beers have been Tinseth so far. I'm brewing a Vienna with Rager on Saturday. Seems like Rager uses less hops to achieve the expected IBU (given the input itno the formulae are strictly taken from the bag).

[GrahamW]

*Tinseth publishes his formulas as F1 = (1-exp(-0.04*minutes)/4.15 which represents the time factor. Note that it has value 0.241 for long boil times. The other factor he calls the "bigness" factor; F2 = 1.65*0.000125^(SG-1). Note that for pure water (SG =1.000) this factor has a value of 1.65. Multiplying F1*F2 gives a maximum utilization of 39.7%. It would feel better to me if F1 = (1-exp(-0.04*minutes)/4.15/1.65 and F2 = 0.000125^(SG-1) so the two represent separate reductions in utilization but perhaps he has a good reason for doing it the way he did.

I agree that the Tinseth formulae makes more sense than the other two in most respect, particularly when plotted out and compared. The fact that there are no offsets or discontinuities in the Tinseth formula is the most obvious point in its favour. However, perhaps Mr. Tinseth's maths were not up to it, because his formula is more complicated than it needs to be, and has several interrelated constants all muddled together such that it is not intuitive as what needs to be done to adjust it to match various peoples systems or experiences.

Some time ago, for something else that I was doing, after making similar observations to Mr. Delange, I simplified Tinseth's approach and split it into distinct sections to make it much simpler to adjust.

This is how it ended up:

Utilisation = Su x Gc x Bc

Where:
Su = Start utilisation, in per cent. This is a figure that represents an upper limit for utilisation - the very maximum utilisation that could (possibly) be achieved under ideal, or better-than-ideal, conditions (such as infinite boil time and zero original gravity). To match Tinseth this is set to 39.75. This number happens to match the 39.7 mentioned by Mr. Delange (except that I came up with it by trial and error - I did not see the relationship that Mr. Delange pointed out, so it shows that my maths are not that good either). This figure is then modified by the other two factors to incorporate his "bigness factor" and the boil-time factor.

*****

Gc = Gravity Compensation Factor, represents Tinseth's Bigness Factor - a number between 0 and 1. This is generated by an exponential function. 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. In my version it is given by: Gc = e^(-degrees_grav /Scale_Factor) The degrees gravity is the O.G. expressed in degrees (1.045 = 45 degrees). The scale factor is the adjustment factor. To match Tinseth the Scale Factor is set to 112.

I personally do not think that an exponential function is appropriate here. It is believed that the greatest and most variable influence on hop utilisation versus "bigness" 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 it would seem, although I doubt if it is quite that simple. In point of fact, the Tinseth implementation is right down on the linear-most part of the exponential curve and the results differ very little from a simple linear implementation.

*****

Bc = Boil Time Compensation Factor, another number between 0 and 1. This is again an exponential function, and is given by Bc = 1-e^(-t/T). T is the boil time in minutes and "t" is the scale factor, which is in fact the time it takes for isomerisation to reach 63%. Many electrical/electronics engineers will recognise the formula as the same as the time constant for a capacitor. To match Tinseth "t" is set to 25 (actually the reciprocal of Tinseth's 0.04).

Although the exponential curve is the identical shape as a utilisation graph published by one hop merchant, I have a possible theoretical objection to the shape of the curve in that it starts at time-zero with isomerisation occurring immediately at its maximum rate, which may not be true. My 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 (as in one of the other workers' formulae). Of course, in defence of the hop merchant, commercial brewers do not shove bittering hops in the copper for ten minutes, and it would not be an issue if it were not for the habit of home brewers using the same formulae for predicting the bitterness contribution for late hops. The curve represents the duration from time zero, whereas late hops are added towards the end of the boil. Clearly, different utilisations would apply. A sigmoid curve would go a long way to equalising this.

*****

With Su set to 39.75, the Gc scale factor set to 112, and t set to 25, it matches the Tinseth table spot on. The advantage is just one obvious number needs to be adjusted to tailor each of the parameters. The 39.75 can be adjusted to move the whole utilisation up and down bodily. The scale factor (112) can be adjusted to independently move the "bigness" factor up and down. t can be adjusted to independently move the boil factor up and down. Arguably, pellet hops and whole hops should have different values for t anyway.

[vejgaardzoo]

I've been really confused by the various ways of computing the IBUs. I found some advice on the web (can't find it now, of course) saying to use Tinseth for all-grain and Garetz for extract so I've been switching back and forth. But there seems to be agreement that

Consistency is probably more important than accuracy

Point taken.

The Tinseth model has lots of appeal. It is simple* to compute in a spreadsheet or with calculator,

Agree. Tinseth it is.