Math forumula for FG
 

Hi,

I'm in an intro to programming class and each project that we've been assigned I've been making modules for a beer recipe program. Right now they're all pretty basic and just in the logic and algorithm phase. How would one determine what the potential FG is on a recipe?

Does anyone know this formula?

Also any other formulas would help me as well as I plan on maybe throwing together a complete linux compatible brewing software suite.


Thanks

Too many variables influence FG. Most brewing software just does a SWAG of 25% of OG.

The potential for the FG would be based on the potential attenuation value of the yeast and the starting gravity of fermentables. This potential of course implies that there are perfect conditions for yeast growth such as temperature, oxygen, etc.

I would say a formula such as:
FG = SGf * YAP + SGu

where:
SGf is the starting gravity of fermentables.
YAP is the yeast's attenuation potential. (Usually 70% - 80%)
SGu is the SG of unfermentables.

More detailed information on yeast attenuation can be found here: http://www.homebrewtalk.com/wiki/index.php/Understanding_Attenuation

...and a ton of other things like mash temp & schedule, mash pH, grist makeup, pitching rate, fermentation temp, wort oxygen content...

This is why most brewing software just does the 25% SWAG.

Beer Tools Pro will re-calculate the FG if you change the attenuation percentage.

Not to mention how all of this, and much more, changes over the course of a perhaps week long fermentation. There are simply too many variables to reasonably expect that any calculation would be accurate. I don't see this happening.

You will find plenty of formulae on gravity measurement and its applications at www.wetnewf.org under Specific Gravity Measurements and Applications in Brewing. This set of notes was put together with programmers as the intended audience.

Nothing on FG. I always advise taking the OE and reducing it by the midrange attenuation listed by the yeast packager for the strain in question. E.G. if the yeast is stated to attenuate between 68 and 72% just multiply the OE by (1 - *(0.68 + 0.72)/2). If the OE is 12 °P the estimated AE would be, in this case, 12*0.3 = 3.6°P. This will give an idea of what can be expected. A dextrinous wort might be expected to come in at the low end of the anticipated attenuation, 12*(1-.68) = 3.8°P and a highly fermentable one at the high end, 12*(1 - .72) = 3.4 °P.

This is what I do, and have been very successful in predicting FG, at least for the yeast I have used so far (S04, 1056, S33, 3944, 1084, S05, 1007, 1028 and 3068):
FG=1+EFF*( (1-AT*F1)*PPG1*W1 + (1-AT*F2)*PPG2*W2 + (1-AT*Fn)*PPGn*Wn )
Where:
EFF=Mashing efficiency. Example 75%, enter 0.75
AT= yeast attenuation = (50+800/(T-130))/100
T=Mashing temperature (valid from 150 to 160F)
F1=fermentability of grain1. For base malts=1, for dextrin or lactose = 0, for Crystal malts until 30L = 0.65, for Crystal malts above 40L = 0.5, for highly toasted malts (>120L) = 0
PPG1= points per pound per gallon of grain 1
W1= weight in pounds of grain 1

same for grain 2 until grain "n"

I use a ferm chamber, so my temps are within 1F of my setpoint. I also pay a very close attention to the mashing temp and my mash tun drops only 1F in 1h.

I think the problem with a general formula for FG is because the variations of equipment and methods by the homebrewers, like mash tun design that affect the temperature drop, fermentation temp control, inaccuracy when measuring temp, volumes and gravity.

Thanks, this looks like it will come in handy. Like I said I'm not trying to go pro and am just a new programmer and really with FG I can only just get in the ball park anyway. At least with something like this I can give a good rough estimate.