All my equations and numbers come from "How to Brew" by John Palmer. This is the first time I've ever brewed a beer strictly by using numbers and I wanted to see how everything looks. I used to teach algebra to 9th graders so I skipped writing out a lot of the math so if there's confusion, let me know.
The goal was an ABV of 9% and a 5 gallon batch size. I assumed an FG of 1.010.
ABV = (OG - FG)(.129) *OG and FG measured in gravity points.
9 = (OG - 10)(.129)
70 = (OG - 10)
Therefore, the OG is 80 or 1.080
Now I need to find the attenuation which will show me what type of yeast to use.
FG = OG(1 - AA) *OG and FG measured in gravity points.
10 = 80(1 - AA)
AA = .875
With an AA of .875 or 87.5 in the real world, I need to use a strong ale yeast with an AA between 80 and 100.
I decided to use 3 types of grains for this. I'm not entirely sure how it will taste but experimentation is the best part.
The ratio of lbs grain to points per gravity equation with multiple grains is as so where the grain is measured in lbs and the PPG is a constant I found in the book assuming 75% efficiency:
[ ((Grain1 * PPG1)/Batch Size) + ((Grain2 * PPG2)/Batch Size) + ((Grain3 * PPG3)/5) ](.001) + 1 = OG
I know my OG is 1.080 and I have a 5 gallon batch size so...
[ ((Grain1 * PPG1)/5) + ((Grain2 * PPG2)/5) + ((Grain3 * PPG3)/5) ](.001) + 1 = 1.080
Subtract 1 from both sides then divide by .001 and you get...
[ ((Grain1 * PPG1)/5) + ((Grain2 * PPG2)/5) + ((Grain3 * PPG3)/5) ] = 80
Multiply both sides by 5 to get rid of the denominators...
(Grain1 * PPG1) + (Grain2 * PPG2) + (Grain3 * PPG3) = 400
I swear I totally randomly picked these grains and somehow it came out to equal 400 on the second try. I picked 6 - row, Crystal 40L and Carapils.
Grain, Weight, PPG
6 - row, 11lbs 26
Crystal 40L, 4lbs, 25.5
Carapils, .5lbs, 24
(11 * 26) + (4 * 25.5) + (.5 * 24) = 400
So in a perfect world with everything happening perfectly, this would yield my 9% beer.
I'm thinking about trying it. I don't expect a whole 9% but I should be close and may toss in a little extra grain to help toward getting there. Anyone see any obvious flaws in this (aside from the lack of hops- probably go cascade) Like I said earlier, this is my first time paying any attention toward this side of brewing but if it is accurate, it opens up a whole new world of things to occupy my time at work