calculate OG from FG
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You do this by inverting the Balling formula which gives you ABW as
ABW = f(OE)*(OE - AE)
f(OE) is a function of the original gravity so clearly to solve for OG you would have to use an iterative procedure such as Excel's Solver. For rough work you can just use f = 0.421. I don't have the details of f(OE) with me at the moment anyway.
Original Extract (OE) and Apparent Extract (AE) should be in °P.
Thus OE = ABW/0.421 + AE
ABW = ABV*0.791/SG_beer
ABW = f(OE)*(OE - AE)
f(OE) is a function of the original gravity so clearly to solve for OG you would have to use an iterative procedure such as Excel's Solver. For rough work you can just use f = 0.421. I don't have the details of f(OE) with me at the moment anyway.
Original Extract (OE) and Apparent Extract (AE) should be in °P.
Thus OE = ABW/0.421 + AE
ABW = ABV*0.791/SG_beer
WoodlandBrew
Well-Known Member
In case you prefer working with specific gravity instead of present extract the equations would be:
ABV=131(OG-FG) => OG= ABV/131+FG
(I know AJ knows the Balling Observation [in fact I think I learned it from him] ... in case you are really really curious, the percent extract equation the 0.421 follows the Balling Observation: 2.0665g extract -> 1g EtOH + 0.9564g CO2 + 0.11g other constitutes)
If you don't know the ABV, it can also be calculated assuming a solution of alcohol, and sugar in water by measuring the refraction index and and the specific gravity of the beer. My blog has an approximation of the solution.
ABV=131(OG-FG) => OG= ABV/131+FG
(I know AJ knows the Balling Observation [in fact I think I learned it from him] ... in case you are really really curious, the percent extract equation the 0.421 follows the Balling Observation: 2.0665g extract -> 1g EtOH + 0.9564g CO2 + 0.11g other constitutes)
If you don't know the ABV, it can also be calculated assuming a solution of alcohol, and sugar in water by measuring the refraction index and and the specific gravity of the beer. My blog has an approximation of the solution.
WoodlandBrew
Well-Known Member
You do need two pieces of information, but ABV doesn't have to be one of them. Final Refraction Index (that can measured with a refractometer) and Final Specific Gravity (that can be measured with a hydrometer) will work.
See here for details:
http://woodlandbrew.blogspot.com/2013/02/abv-without-og.html
I've refined this technique since the blog post. You can find better information in my book. (It will be available very soon)
See here for details:
http://woodlandbrew.blogspot.com/2013/02/abv-without-og.html
I've refined this technique since the blog post. You can find better information in my book. (It will be available very soon)
stpug
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Thank you for this woodlandbrew!! I had recently inherited a batch from a friend in a keg in which I had to backtrack the OG using hydro and refract measurements, plus a spotty recipe. Somewhat luckily it was a partial mash. Anyway, long story short..... I had calculated about 1.095 based on my readings and spotty recipe; while your equation calculated 1.097 which works out (i.e. corresponds) very well. Within 2 points OG is perfectly fine for my purposes.
Cheers!
WoodlandBrew
Well-Known Member
You're welcome! I'm glad you were able to make use of it. It's also good to know it works for other brewers. Thanks for the feed back!
Refractometry is not a viable way of estimating the alcohol content of beer unless the beer (or rather beers similar to it) have been calibrated against the RI readings using another method (GC, gravimitry). By 'similar' I mean very similar e.g. this technique is used by breweries to measure lot to lot variation of the same product but a calibration curve for that product has been constructed using a densitometer, for example. There is an ASBC MOA which has all the details. As you can see from the formula in #3 (which has been corrected as I used the SG of alcohol instead of the Balling factor) an error of 1% in ABW would result in an error of 1/0.421 = 2.38 °P in the OE estimate. Perhaps this is good enough for the intended purpose.
As I assume that it cloning of craft beers that is of most interest and most craft brewers are not hesitant to reveal their ABV/ABW numbers you will probably do better to call the brewery and ask rather than try to estimate the ABV/ABW from a refractometer reading.
As I assume that it cloning of craft beers that is of most interest and most craft brewers are not hesitant to reveal their ABV/ABW numbers you will probably do better to call the brewery and ask rather than try to estimate the ABV/ABW from a refractometer reading.
WoodlandBrew
Well-Known Member
Yes, refractometry alone would be a pour way of estimating ABV without a calibration curve for a specific beer. However when refractometry is paired with specific gravity there is enough information to calculate the ABV content assuming the content of the beer is primarily alcohol sugar and water.
If you took enough measurements of RI on aqueous solutions of sucrose and ethanol you ought be able to estimate coefficients alpha_ij
RI = alpha_10*Ds + alpha_20*Ds^2 ...+ alpha_11*Ds*A ... + alpha_01*A + alpha_02*A^2... (1)
where Ds is the density of the aqueous solution for sucrose only IOW the density corresponding to the true extract and A is the alcohol content w/w. Given a set of alpha_ij and knowledge of the true extract one could solve (1) for A. The problem here is that esters, proteins, dextrines etc. do not influence RI in the same way that sucrose and ethanol do. In fact RI isn't even a reliable way of measuring OE unless you consider errors of more than 1 °P tolerable. This is why calibration is necessary even if you use TE. But you don't. You take it one step further and use AE. The information on AE would be present if Tabarie's principle were valid but I have found in my experiments attempting to validate it that it is only approximately so. This doesn't matter if the beers being tested are close to one another. RI alone is sufficient (because the TE is the same as are the esters, higher alcohols...) to give a good estimate of A in that case.
Now let's put the highly technical considerations aside and ask ourselves "If one could calculate A with reasonable accuracy from RI and AE measurements why would the MOA demand the arduous, time consuming calibration procedure involving expensive instruments that only the largest breweries can afford?"
Before you can assert that AE and RI are sufficient to estimate A you have to take RI, A, TE and AE measurements on a lot of beers. fit the model of (1) to them and demonstrate good residuals. Or, alternatively, find in the literature articles by people that have done that work and come to the same conclusion. Note that one must measure the alcohol content. It would not be sufficient to use alcohol content calculated from Ballings formula for AE as that relies on Tabarie's principle.
I guess I can start measuring RI (I measure the other stuff) but given the rate at which I am brewing these days it's going to be a long time before I have enough data to come to a solid conclusion. Maybe things aren't as grim as I think but based on what I have seen in just wort RI measurements I'm not too hopeful.
RI = alpha_10*Ds + alpha_20*Ds^2 ...+ alpha_11*Ds*A ... + alpha_01*A + alpha_02*A^2... (1)
where Ds is the density of the aqueous solution for sucrose only IOW the density corresponding to the true extract and A is the alcohol content w/w. Given a set of alpha_ij and knowledge of the true extract one could solve (1) for A. The problem here is that esters, proteins, dextrines etc. do not influence RI in the same way that sucrose and ethanol do. In fact RI isn't even a reliable way of measuring OE unless you consider errors of more than 1 °P tolerable. This is why calibration is necessary even if you use TE. But you don't. You take it one step further and use AE. The information on AE would be present if Tabarie's principle were valid but I have found in my experiments attempting to validate it that it is only approximately so. This doesn't matter if the beers being tested are close to one another. RI alone is sufficient (because the TE is the same as are the esters, higher alcohols...) to give a good estimate of A in that case.
Now let's put the highly technical considerations aside and ask ourselves "If one could calculate A with reasonable accuracy from RI and AE measurements why would the MOA demand the arduous, time consuming calibration procedure involving expensive instruments that only the largest breweries can afford?"
Before you can assert that AE and RI are sufficient to estimate A you have to take RI, A, TE and AE measurements on a lot of beers. fit the model of (1) to them and demonstrate good residuals. Or, alternatively, find in the literature articles by people that have done that work and come to the same conclusion. Note that one must measure the alcohol content. It would not be sufficient to use alcohol content calculated from Ballings formula for AE as that relies on Tabarie's principle.
I guess I can start measuring RI (I measure the other stuff) but given the rate at which I am brewing these days it's going to be a long time before I have enough data to come to a solid conclusion. Maybe things aren't as grim as I think but based on what I have seen in just wort RI measurements I'm not too hopeful.
