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The Plato tables express conversion from specific gravity to degrees Plato. The following equation is a quadratic curve fit to the table, from deClerck:
E = 668.72*SG - 463.37 - 205.347 * SG * SGA simplified version of the equation, rounded to a more reasonable (for homebrewing) number of significant figures, and recast in terms of points = 1000 * (SG - 1), is
E = 0.258*(1-0.0008*Pts)*Pts + 0.003
To go the other way, use
Pts = 0.082636 + 3.8480*E + 0.014563*E^2This differs from the "true equation" by less than 0.1 in the range E=0..19, and by about -1.0 at E=30.
Here's a quick conversion table
Plato Points Plato Points Plato Points 0 0 10 40 20 83 1 4 11 44 21 87 2 8 12 48 22 92 3 12 13 53 23 96 4 16 14 57 24 101 5 20 15 61 25 105 6 24 16 65 26 110 7 28 17 70 27 115 8 32 18 74 28 119 9 36 19 78 29 124 10 40 20 83 30 129
AA = 1 - AE / OE, AE = Apparent Extract of beer, as measured by a hydrometer OE = Original Extract of the wort.However, the specific gravity of the beer is depressed by the lower specific gravity of alcohol (0.8, approximately), so the measured apparent extract is smaller than the real extract (sugars remaining in the finished beer). Real extract, RE, can be measured by dealcoholizing the beer (typically by boiling gently), adding distilled water back to the original volume, and then taking the specific gravity. Or, we can use an approximation (due to Balling):
RE = .1808*OE + .8192*AE,
With this approximation, we can compute an approximation to the real attenuation as
RA = 1 - RE / OE, RA = 1 - (.1808*OE + .8192*AE) / OE.
Balling gives the following, more accurate formula:
A = (OE-RE)/(2.0665-.010665*OE) (% weight)
Then, there are the old favorites for % alcohol by volume.
A = (OG - FG) * 125 * 1.05, or A = (OG - FG) * 1000 / 7.5Both of these estimate a little bit high for most worts, but only by 0.1 to 0.2 percent.
Ralph Snel (ralph@astro.lu.se) wrote: A quite simple way that will give accuracy up to 0.1% is to boil off all the alcohol and substitute by water. This means boiling down to less than a third of the original volume in most cases, it's not that hard to smell if there are alcohols in the vapour. Fill with water so you have your original volume and take the difference in gravity, then look up alcohol content in the table:
SG Alcohol SG Alcohol SG Alcohol diff. vol % diff. vol % diff. vol % 0 0.00 10 7.18 20 16.00 1 0.64 11 7.98 21 17.00 2 1.30 12 8.80 22 18.00 3 1.98 13 9.65 23 19.00 4 2.68 14 10.51 24 20.00 5 3.39 15 11.40 25 21.00 6 4.11 16 12.30 26 22.00 7 4.85 17 13.20 8 5.61 18 14.10 9 6.39 19 15.10 10 7.18 20 16.00From: Technisch handboek voor de amateur wijn- en biermaker by Leo van der Straten ISBN 90-245-0969-6
Caloric content of beer
Fix writes:
Walter Gude asked in HBD#878 about the determination of calories in
beer. The following empirical formula is remarkably accurate, and
widely used to check direct measurements. Let A, FG, and RE be
defined as follows:
A = alcohol content of finished beer in % by wt. RE = real extract of finished beer in deg. Plato FG = final gravity of finished beer.Then the number of calories per 12 oz. bottle is the following:
(6.9*A + 4.0*(RE - .1))*3.55*FG .
To take Walter's specific case, first note that from Plato tables an OG of 1.045 is equivalent to
OE = 11.25 deg. Plato,
while a FG of 1.010 is equivalent to
AE = 2.5 deg. Plato.
Therefore,
RE = .1808*11.25 + .8192*2.5 = 4.08 deg. Plato,
and
A = (11.25 - 4.08)/(2.0665 - .010665*11.25) = 3.68 % wt.
We conclude that there are
( 6.9*3.68 + 4.*3.98)*3.55*1.010 = 148.12
calories in Walter's beer. Note that 61.5% come from alcohol, and 38.5%
come from the residual extract. Errors in the formula for calories using A and RE will be under 1%. Errors in Balling's approximations can be as large as 3-5%.