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Old 10-11-2013, 06:08 PM   #1
helgibelgi
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Default ABV calculator question

Hi all

I was wondering about the formulas that ABV calculators use to give you the ABV of your beer. I'm really interested in this for some reason. I got the idea in my head that the gravity reading after fermentation is probably skewed, so that my ABV calculations may be wrong.

I have found tvo different versions of the formula that calculators use:

1) ABV = (og – fg) * 131.25

2) ABV = (76.08 * (og-fg) / (1.775-og)) * (fg / 0.794)

Can anyone tell me what the constants represent? And/or explain to me how these formulas make sense?

Thank you

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Old 10-11-2013, 10:00 PM   #2
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Carl Balling came up with alcohol estimation figures years ago based on the differences between original and apparent or true extract. Obviously the true extract formula is going to be more accurate than the apparent extract one as apparent extract relies on Tabarie's principle which I believe (based on some tests) to be shakey.

Balling found that ABW (easily converted to ABV) depends on the difference between original and true or apparent extract with the proportionality factor depending on the original gravity. The factors are easily computed from simple polynomials and are tabulated in DeClerck. I don't have that with me here but I do remember the factor for AE 12°P beers is 0.421. Thus for a 12 °P beer fermented down to 3 °P (75% apparent attenuation)

ABV = 0.421*(12 - 3) = 0.421*9 = 3.789 ABW

Converting this to ABV gives 3.789*1.012/0.791 = 4.85%

0.791 is the SG of pure ethanol and 1.012 is the approximate SG of beer fermented to 3 °P ( 3 x 4 = 12).


Converting to points is done by multiplying the Plato numbers by 4 and dividing by 1000 i.e by multiplying by 250. Thus 0.421(OE - TE) = 0.421*250(OG - FG). This gives ABW. Multiplying by 1.012/0.791 gives (OG - FG)*0.421*250*1.012/0.791 = 134.7*(OG - FG) which is pretty close to your first formula which, as its difference multiplier does not depend on OG, can only be 'correct' at some one unknown OG which is apparently not 12 °P (1.040). Your 2) does have a difference multiplier which depends on OG is potentially more accurate. It also recognizes that ABV depends on not only the extract difference and original extract but on the finsihed beer's specific gravity.

Thus the constant 131.25 represents approximately 250*0.421*1.012/0.791 with 250 being the (approximate) factor for converting between points extract difference and Plato extract difference, 0.421 being the Balling factor for a 12 °P, 1.012 being the approximate final SG of a nominally attenuated 12 °P beer and 0.791 being the SG of pure ethanol. I'm relying on memory here so maybe it is 0.794 as 2) implies. The 0.003 discrepancy might also be because of differences in the definition of specific gravity based on the change to the ITS of 1994.

The formulas make sense because the amount of alcohol produced is a function of the amount of extract consumed and the OE - TE difference reflects that.

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Old 10-20-2013, 03:03 PM   #3
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Thank you, ajdelange, for that detailed answer!

But I'm still a bit lost :P

Am I right in thinking that the final gravity reading, using a hydrometer, will be skewed? Because the solution is now not only water and sugars, but also alcohol which is lighter than both water and sugar.

The way I see it if, you simplify the problem, it looks like this:

Solution before fermentation (wort) = water + sugars (this gives you OG)

Solution after fermentation (beer) = water + sugars + alcohol (this gives you FG)

So I understand that by comparing OG to FG you get Apparent Attenuation. But that number seems to me to be useless. What you want is Actual (or Real) Attenuation. That way you can know exactly the amount of sugars that have been converted into alcohol.

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Old 10-21-2013, 02:14 AM   #4
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Quote:
Originally Posted by helgibelgi View Post
Am I right in thinking that the final gravity reading, using a hydrometer, will be skewed? Because the solution is now not only water and sugars, but also alcohol which is lighter than both water and sugar.
You are absolutely right.


Quote:
Originally Posted by helgibelgi View Post
So I understand that by comparing OG to FG you get Apparent Attenuation. But that number seems to me to be useless.
Stand by on this for a moment.

Quote:
Originally Posted by helgibelgi View Post
What you want is Actual (or Real) Attenuation. That way you can know exactly the amount of sugars that have been converted into alcohol.
Yes, that is what you want if you are willing to do the extra work to get the true extract. Reunited with my library now so

ABW = (.48394 +0.0024688*p + 1.5609E-%*P*P)*(P-n)

where P is the original extract and n the true extract.

But if you don't have the true extract another, even more approximate, formula is available which take into account the effects of alcohol on the AE measurement

ABW = (0.39661 + 0.0017091*P + 1.0788E-5*P*P)*(P-m)

where m is the apparent extract.

The formulas for the difference multipliers are fits to "Ballings Table", Table 15, DeClerck Vol II p 428
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Old 10-21-2013, 11:26 AM   #5
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Quote:
Originally Posted by ajdelange View Post

ABW = (.48394 +0.0024688*p + 1.5609E-%*P*P)*(P-n)

where P is the original extract and n the true extract.
I was reading Kaiser's wiki and found a method to get true readings after fermentation. It's pretty clever imo. You take a sample (about 100ml) and boil off the alcohol, then add back water to reach the same volume. Now you can measure gravity and calculate °P and thereby knowing exactly the drop in sugar level. Can I use this formula along with this method? Is n (true extract) gonna be the °P after fermentation?

Btw, thanks for clearing these things up for me. I was unconsciously making the mistake of equaling gravity to sugar level, but of course that's not really true, especially after fermentation.
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Old 10-21-2013, 05:23 PM   #6
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Quote:
Originally Posted by helgibelgi View Post
I was reading Kaiser's wiki and found a method to get true readings after fermentation. It's pretty clever imo. You take a sample (about 100ml) and boil off the alcohol, then add back water to reach the same volume. Now you can measure gravity and calculate °P and thereby knowing exactly the drop in sugar level. Can I use this formula along with this method? Is n (true extract) gonna be the °P after fermentation?
What you have described is, with one minor omission, the method for obtaining the true extract number, n. When the alcohol is boiled off this is usually being done in order to measure the alcohol content of the beer thus much of the water is boiled off as well to make sure that all the alcohol is recovered and little remains to contaminate the residue. In the standard ASBC practice 50 mL of water are added to 100 mL of beer and 95 mL of distillate are recovered. The extract is then made back up to 100 mL and the specific gravity measured. This number is converted to °P and that value is the percentage of the weight of the reconstituted residue which is extract. The weight of extract is thus density_water*SG_residue*°P_residue. But the true extract of the beer is the percent of the weight of the beer (density_water*SG_beer) which is extract i.e.

density_water*SG_residue*°P_residue/density_water*SG_beer

the density of water cancels out so

n=°P_residue*(SG_residue/SG_beer)

After measuring the °P of the reconstituted residue be sure to multiply by the ratio of the specific gravities. This is the omission I referred to.
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