Possible error in the ABV calculator

Discussion in 'Recipe Editor' started by Brewer #77733, Nov 9, 2016.

1. Neubierig New Member

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#1
Hi all,

just quickly signed up to post about what might be an error in the ABV calculator. I have been discussing this with a pro-brewer here in Germany, and given a starting OG and FG, he gets a markedly lower ABV. I assumed he was using what the website here refers to as the Standard Formula, while I was being a good boy and using the more compicated Alternate one.

He then showed me his source, which wasn't the simple one at all, and I started looking into the source for this website (Zymurgy, Summer 1995, vol. 18, no. 2). It appears that that article is not without some mistakes. The equation the pro-brewer has been using is the same Plato-based one as appears in the article. The problem comes when this is converted to use specific gravity. The article does not use the complicated cubic equation shown elsewhere on this site and also in the article itself, but rather the simplified version (SG points divided by 4). The article acknowledges that this simple version is only good up to about SG 1.060 (15°P), and yet it uses it in the ABV formula, and it is this incorrect formula that is used here on this site.

The article makes two further mistakes, which are of considerably lesser effect:

1. The above-mentioned formula gives alcohol by weight (ABW), which is converted to ABV by dividing by the SG of pure alcohol. This is 0.789 @20°C, whereby the article uses 0.794, which itself states is the SG at 15°C. This itself is not an error, but users of the formula need to make sure their readings at taken at 15°C - it would be better to use the SG of alcohol at the same temperature for which your hydrometer is calibrated (mine is 20°C for example).

2. The article states that ABV is calculated not only by diving ABW by the SG of ethanol, but by then multiplying by the final gravity. I'm sticking my neck out here - the guy is after all a PH.D. - but I do not think that's correct. I believe the conversion involves simply diving ABW by the SG of ethanol. I'm happy to be corrected on this. I'm of course happy to be corrected on any of it.

Sorry it's a bit of a brain dump, but the results that come out for my bigger beers are considerably different. Here's one example:

OG = 1.080
FG = 1.014

Corrected formula gives 8.72%ABV
Standard equation on this site gives 8.66%ABV
Advanced formula on this site gives 9.23%ABV

As I say, the main problem is that the original ABW formula was based on Plato, but Plato was expressed in gravity using an inaccurate simplified conversion.

Cheers,

Keith

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2. amaggs New Member

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#2
Guys, this dude Keith is totally right. I did the math and your "Advanced" formula is totally wrong. What you did is take the formulas from the Michael L Hall article and mix them up. He explains quite plainly that the "easy" and "complicated" formulas shouldn't be mixed. But you totally mixed them up! You guys are using the "complicated" formula alongside the "simplified" formulas which leads to overestimation of alcohol content. You need to consistently use the authors formulas, otherwise you end up with overestimation. Send me a message and I can send you the math involved.

3. Lenard New Member

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Without going into to the detail of said article. I also think the ABV calculation is wrong.
I did a simple test in the receipe calculator:
• Batch size 10 liter
• 1.985kg dextrose (1.907kg for Alternate ABV calculation)
• custom attenuation @ 100%
• results in a calculated ABV of exactly 10.0%
• results in a calculated FG of exactly 1.000 ... (but that is 100% water !!)
That can't be as as 10% of the volume is alcohol at 0.7983kg/ltr
so FG should be (90%x1)+(10%*x0.7983)=0.979

It looks as if the FG calculation does not take the specific gravity of the final alcohol content into account.
This lines up with my experience that my real brews' FG is always lower than calculated. Especially with lighter ones. (For the heavier beers I think that the standard 72.5% attenuation may be a bit high, but that is to be expected.)

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