From the HBD Archive
From: gjfix@utamat.uta.edu (George J Fix)
Subject: unknown
Date: 1992-06-08 16:25:58 GMT

Subject: Origin of Calorie Formula; Numerical Examples (George Fix)

The calorie formula I quoted was derived by the committee on analysis
of the European Brewing Congress (EBC). They started with the postulate
that the formula should have the following form:

cal. = 3.55*( c1*A + c2*(RE - 0.1)).

In this formula A is the % alcohol by weight (they report this as
grams per 100 grams which is our degrees Plato). RE is the real extract
measured in the same units, and the term RE - 0.1 represents the residual
extract corrected for the ash content. The number 3.55 was a factor
associated with the units used (i.e., grams and kcal). It was introduced
so that the numbers c1 and c2 would be dimensionless. The latter were
determined by a least squares fit using standard mathematical techniques.

The unit used for calories was kcal/1000g (calories per kilogram). This is
how beer calories are reported in EC countries. All I did was to was to convert
it into other units. Multiplication by FG (beer specific gravity) takes it
to kcal/l, and the liter-oz. conversion factor takes it kcal/12 oz. This is
the form I reported, which I rewrite as follows:

cal. = (24.495*A + 14.2*(RE - 0.1))*FG.

The problems that bothered many was the nonlinear formula for A. Rob Bradley
brought this out nicely. Boy if people get worked up by the alcohol formula,
they should see what we use for hops. There is not anything even remotely
linear about any of them.

As far as the other issue is concerned, I personally do not see anything
wrong with the "factor of 4" conversion from Plato to spec. gr. The only
point I wanted to make was that it was not exact. In particular, Mike Hall's
analysis seems entirely reasonable.

Perhaps the following examples might clarify these issues a bit. The data
was taken from the German trade journal Brauindustrie. Their column "500
Biere aus aller Welt" gives numerical profiles of beer brewed throughout
the world. The measurements were done at Weihenstephan so the numbers are
very good. The only exception was Michelob whose data I got from AB. The
numbers are in % by weight ( grams per 100 grams), except those for calories.

Paulaner Salvator
- ------------------
Measured data:
OE = 18.3 (1.076 or 1.073 for the factor of four types)
RE = 6.78 (1.027)
AE = 4.24 (1.017)
A = 6.17% wt.
kcal/1000g = 693
kcal/12oz. = 693*1.017*12/33.8144 = 250.1
Balling's formulas:
RE = .8192*4.24 + .1808*18.3 = 6.78
A = (18.3 - 6.78)/(2.0665 -.010665*18.3) = 6.16% wt.
EBC formula:
kcal/12 oz. = (24.495*6.16 + 14.2*6.68)*1.017 = 249.9

By the way the linear wine formula A=100*(OG-FG) gives

A = 100*(1.073 - 1.017) = 5.6% wt.

I frankly feel most homebrewers could have gotten a better estimate
by actually tasting a glass of Salvator and guessing. The wine formulas
do better at lower OGs, but my interest in accuracy wanes as well. Having
said this I should also say that "acceptable accuracy" falls into the area
of personal opinion, and thus is not amenable to rational analysis.

My main interest in formulas for alcohol and calories is for dopplebocks and
barley wines. I wanted something better than "sloppy Joe" numbers not only
to monitor personal consumption, but also as a reference for friends and
neighbors who help me drink the beer I brew.

Michelob
- ----------
Measured data:
OE = 12.0
RE = 4.53
AE = 2.89
A = 3.81% wt.
kcal/12 oz. = 156
Calculated data:
RE = 4.53
A = 3.85% wt.
kcal/12 oz = 158

EKU 28 (!):
- ------------
Measured data:
OE = 28.8 (1.124; here the factor of 4 gives 1.115)
RE = 12.22
A = 9.42% wt.
kcal/12oz. = 416.5
Calculated data:
You are not going to believe this, but the formulas for A and kcal/12oz.
are almost exact. I leave this as a homework exercise!

The nonlinear term in Balling's formula is also of historic significance.
The classical Gay-Lussac theory (see page 161 of my book) predicts a formula
like

A = (OE - RE)/c,

where c is a constant near 2. (Note that OE - RE is the amount of extract
fermentated in grams per 100 grams). This is only the case for liquids
like wine, which for this purpose may be considered as a simple mixture of
glucose (dextrose) and water. Beer wort is far more subtle! This lead to
the modern Embden-Meyerhof-Parnas theory of fermentation (pages 175-184).

There is a practical issue here as well. Note that the denominator

c = 2.0665 - .010665*OE

decreases as OE increases. Folks,there is more alcohol in our homebrews
than many may realize, especially those with high OEs. Take care.

Off to Milwaukee!

George Fix



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