math moron

[dickshindles]

My brain has gone into shut-down mode. Please help.

For all intents and purposes, let's say I have 1 gallon of juice. That juice weighs 2#, and is 50 brix. That means (correct if wrong) there is 1# of sugar in that juice? Right?

If so, let's also say for AIAP, I was going to add that to some beer, and I wanted to know how many degrees Plato that would contribute to my beer. I would have to assume that 1# of sugar raises the specific gravity of 1 gallon of water 1.045. That would contribute 11.25 Plato in 1 gallon of beer. Right? This leads me to assume that if I were brewing 5 gallons, I would simply divide that # by 5, to solve for x. Easy enough....but

NOW, let's say I am brewing 10 Bbl of beer, and I am adding, say, 67# of sugar to the brew. How do I devise an equasion to solve for x. Please walk me through this process as if I were an idiot.

Thanks,
Dick

[brewbonghm]

Heh,
1 gallon of just about anything septin' maybe feathers weighs more than 2#.

[jwalts]

Hey Dick, here's a variation of the ASBC formula for calculating extract:

E = (258.7+P)*P*V/100
E = Extract in lbs.
P = Degrees Plato.
V = Volume in barrels.

If you solve for gravity, you get this:

P = (-258.7+sqrt(258.7^2+4*100*E/V))/2
sqrt(blah blah) = square root of 'blah blah'
a^x = a to the xth power

The amount of gravity contributed by the sugar will depend on the gravity of the original wort. It makes sense if you think of the most extreme example: adding more sugar to a bucket of sugar will increase the volume, but the "gravity" will stay the same. What this means is that you should first calculate your total extract with the first formula, then use the result in the second formula to figure out your increase in Plato. Here's an example:

Initial gravity = 12 P
Initial volume = 10 bbl
Initial extract = (258.7+12)*12*10/100 = 325 lbs
Sugar wt = 67 lbs
Sugar solubility = 100%
Sugar extract = (sugar solubility/100)*67 = (100/100)*67 = 67 lbs
Total extract = initial extract + sugar extract = 392 lbs
Final gravity = (-258.7+sqrt(258.7^2+4*100*392/10))/2 = 14.4 P
Gravity difference = 14.4 - 12 = 2.4 P

You could change your final volume to include sugar displacement, but it's not really worth doing (especially if you add sugar to the kettle during lautering, which allows you to just stop filling at your target volume).

Joe