Looking at this from a broad POV you have an observable, the refractive index which obviously depends on the amount of alcohol in the solution:
RI = f(A)
But you don't really know what f is. You know that it depends on True Extract, of course,
RI = f(A;TE)
but it also depends on a lot of other things so the formula really needs to be written
RI = f(A;TE, OE, q1,q2,q3.....)
where everything to the right of the semicolon is a 'consider parameter' i.e. something which needs to be considered) such as the original extract, the concentration of long chain dextrines, the amount of protein, soluble hops products......i.e. any optically active substance in the beer. You also know that True Extract depends on Apparent Extract and Original Extract so
RI = f(A; AE, OE, q1, q2, q3, ...)
It's a simple matter to get an estimate of A from an RI measurement
A_ = F_inv(RI; AE, OE, q1, q2, q3...)
In the MEBAK and ASBC approaches, f_inv is assumed linear in AE and RI and it is further assumed that for some group of beers the variations between beers in the other consider parameters is small. The error in the estimate has 2 terms. The first is attributable to error in measurement error in RI (note that you cannot use ATC in making these measurements as the ATC algorithm in a refractometer is designed for sucrose solutions and beer is demonstrably different). The second is due to variance in the consider parameters of which only measurement of AE should be significant for a small group of like beers. You are really doing a Taylor series expansion about some unknown vector of q's and assume that no beer in the ensemble has a q vector appreciably different from the one about which you are expanding). If these assumptions are good you get a nice linear formula for A_ and all is well. The ASBC has you determine the slope and offset of this formula and MEBAK gives you one for Vollbier and one for Starkbier. Louis Bonham did the same thing.
The problem is that the q parameters are too variable over the ranges of all beers and even, in my experience, over the range of voll or stark in the MEBAK method. That consider parameter covariance term becomes a large contributor to the variance in the estimate A_.
I cannot get any of the published formulae to give me errors which I consider acceptable. There is a big difference between the way this old body responds to a couple of pints of 5.0 ABV and a couple of pints of 6.0%.
Given my experiences with refractometry as a means of determining ABV, the positions of MEBAK and ASBC, the experiences of others and a basic understanding of estimation theory it wasn't really necessary for me to read about the details of your approach (but I did go back and do so anyway once I realized it was out there).
What I don't want to do is discourage investigation. You apparently have means to measure actual ABV and given that you don't need my opinion. You need data. At some point you should be able to say "I have a method that, over an ensemble of X beers gave, ABV estimates with rms error Y %" Potential users then can decide whether Y % is good enough for them or not.
Hi! I feel like we're communicating 'round each other, and not to each other. I'm interpreting your comments as being about my proposed analytical method for
measuring %ABV, and not on the Calculator that tries to model it from pre-fermentation and post-fermentation Brix -- right? It would help if we could be sure we're referring to the same thing.
So let's just focus, for now, on my proposed analytical technique -- sample Brix compared with Brix on a boiled/reconstituted version of that same sample.
If I just use the
difference in those two Brix values, isn't the difference just the EtOH that got boiled off? Aren't all those other equation terms the same in both samples?
Before boiling,
RI = f(A;TE, q1,q2,q3.....)
(I don't see why you had OE in there). Brix on the sample is a function of A, TE, and a bunch of other things that aren't extract but contribute to Brix. Yes, TE and all those other things are functions of OE, but we don't care about that at this point. The sample is what it is It has A, TE, and a bunch of other things in it that could contribute to Brix).
After boiling/reconstituting,
RI = f(TE, q1,q2,q3.....)
where TE, q1, q2, q3, etc. have the same values in both samples.
If so, then the crux of what I have done -- my assumption -- is that EtOH contribution to Brix is independent of the rest of the matrix and contributes linearly to Brix. I found the contribution to be linear and constant when comparing EtOH in water to EtOH in water with sucrose.
Yes, I have the capability to measure %ABV via GC/FID with megabore capillary column. I'd have to kick someone off one of my lab's instruments to install the appropriate column, but I can do it. It was my feeling, however, that comparing my analytical method to standards was superior to comparing it to GC analysis. Thus far, all I've done is to compare to standards of EtOH/sucrose/water. What I can do is to create standards in post-fermentation wort (distilled of pre-existing EtOH) and measure those, rather than comparing two analytical techniques with each other. Or, even simpler, is that I can see if the contribution of EtOH to Brix is the same in EtOH/wort as in EtOH/sucrose.
Finally, I'll note that if the number i use for "Brix per %ABV" is wrong, then it will affect the Calculator used to model %ABV from pre- and post-fermentation Brix differently than it will affect my proposed analytical technique (the boil/reconstitution method). An erroneously large "Brix per %ABV" will cause over-estimation of %ABV with the Calculator and will cause under-estimation of %ABV analytically. The fact that the Calculator tends to gives similar %ABV as found "analytically" suggests I can't be too far off in wort, at least in terms of that "Brix per %ABV" contribution from EtOH.
And now, I think I'll go have a beer!
