Right, im not saying my method is perfect because of it reliance on the balling formula, but I do believe that the only error that is inherent in my method comes from the balling formula. Their are no other additional approximations or assumptions made other than the balling formula gives accurate ABV.
You are making a couple of assumptions beyond that the Balling formula is not perfect. You are assuming that the Balling formula is independent of OG. It isn't. For the case of 1.100 wort fermented down to 1.000 gives, using your constant factor formula 125*(1.100 - 1.000) = 12.5% for the ABV. Balling's formula gives 0.443*(23.77 - 0)/0.797 = 13.2%. For a 12°P beer (1.048) fermented to 3°P (1.012) the constant formula would give 125*(1.048-1.012) = 4.5% whereas the Balling formula would give 0.419*(12-3)/0.797 = 4.73%. Much closer but still a bit different. Also Balling's formula is based on extract - not specific gravity. Extract is very nearly a linear function of specific gravity but is not exactly a linear function. Part of the 'error' in the above comparisons is due to that. Also you are assuming that adding extract does not change the volume of the beer/wort. It does. In addition when you use apparent extract in the Balling formula you are accepting not only the errors inherent in the Balling formula but the deviation of the real world from the statement of Tabarie's principle. Each of these is small but cumulatively they add up. It is easy to deal with each of them.
1. Recognize the dependence of the mulitiplier on OE. This is quite simple. The multiplier is
0.48394 + 0.0024688*OE + 0.00001561*OE*OE
for true extract (°P) and
0.39661 + 0.001709*OE + 0.000010788*OE*OE
for apparent extract (°P).
2. Use extract, not specific gravity (the Balling factor formulas require this anyway).
3. Use true extract - this eliminates the additional innacuracy due to Tabarie
4. Look at total extract and final volume.
Initial volume can be easily measured with a ruler and a calculator
Can it? I can't do that. I can get approximate wort volume measurements by measuring down from the rim of the vessel but just assuming the vessel is a cylinder of known diameter doesn't give a terribly accurate answer. I've gotten around this by weighing the tared vessel at various depths and that helps but the temperature corrections are based on water (not wort) and while this is another small source of uncertainty is is, nevertheless, an uncertainty.
and evaporation does not matter when taking sg.
Yes it does because it isn't the specific gravity in the fermenter that counts. It's the
effective specific gravity. If you brew a beer and get it into the fermentor such that there are 12 pounds of extract in 120 pounds of wort that's 10 °P. Now suppose that the ferment is really vigorous and 5 pounds of water go off with the CO2. Now you have 12 pounds of extract in 115 pounds of wort and that's 10.43 °P and your beer will be stronger as a result. Then what about starter's? What about volume hung up in the chiller? Did you push that through with water? We've listed quite a few error sources here and they do mount up.
BTW, do you have a link or something about the manner of the inaccuracy of the balling formula? Im interested in reading up on it.
It's based on the assumption that 2.0665 grams of extract produce 1 gram of ethanol, 0.9565 grams of CO2 and 0.1100 grams of yeast biomass. Obviously they don't always do exactly that as some strains will produce more or less biomass and they also produce things like esters and acids.
Somewhere at home I have data on the comparisons between alcohol levels calculated from OG as best I can measure it and what the actual alcohol levels turned out to be. I'll look into that when I get home next week (if I can remember a whole week back).
You might want to have a look at
http://en.wikipedia.org/wiki/Gravity_(alcoholic_beverage) and the reference to DeClerck which is mentioned there if you have it.
One thing in engineering that we like to talk about is alot of times is how accurate is accurate enough?
Sometimes it's clear. The accuracy of the terminal guidance system at an airport is an example of that. Here it isn't so clear. It is whatever it takes to make you comfortable. For some reason late in my career I started chasing errors, doing error propagation, error budgets etc. and it became kind of a campaign for me as I found too few of my colleagues ever gave it a thought. If the meter said 12 dBm it must be 12 dBm.
Is this model good enough? Is it worth the time and resources to pursue it further? For instance say if my method gives accuracy within 1% to .5% vs being off by 4% to 5% by not taking dilution into account I would say that my method is an improvement.
You certainly took a step in the right direction by considering volume. As to whether the model is accurate enough that is really up to you to decide. Whenever this comes up I always go through the extract based method and always push people writing brewing software etc. to use it but I don't usually try to push it on the casual home brewer. For most purposes I think points per pound per gallon is accurate enough but problems where the wort/beer is subsequently diluted or where extract is added really, IMO, need to consider the things we've discussed. It is, ultimately, simple conservation of mass.
