Attention Math Magicians:

[DrBrewDC]

here is a question I have not seen asked nor answered in this forum, yet (of course, it may be out there and I have just not come across it)...

If my OG was 1.078 (which it was) and my FG is 1.020 (and it is) and therefore, the ABV calculates to a glorious 7.73% (which I must presume) and I add precisely 10ozs of 40% alc/vol bourbon to approximately 5 (but probably a bit more), how would I go about predicting the final ABV?

 

[HawksBrewer]

My fuzzy math and fuzzy logic seems to say that it will add approximately .625% to your final ABV... but I've been wrong before.

 

[weirdboy]

5 gallons = 640 fluid ounces

(7.73 * 640 + 40 * 10)/(640 + 10) = 8.22% ABV

 

[bernerbrau]

5gal * 7.73% + 10 fl oz * 40% = .3865 gallons + 4 oz = .41775 gallons.

.41775 gal / 5 gal (rounding down) = 0.08355 = Roughly 8.35%.

 

[passedpawn]

damn it I keep getting 11.3%

[woops, wrongo, I guess there are more than 16 ounces in a gallon... duh, argh. you guys were fast]

 

[DrBrewDC]

So 7.73 + .625 = 8.335 therefore (8.335 + 8.22 + 8.35) / 3 = 8.30 ABV

(my math skills are great enough to be able to calculate the mean).

Thank y'all!!

 

[HawksBrewer]

So 7.73 + .625 = 8.335 therefore (8.335 + 8.22 + 8.35) / 3 = 8.30 ABV

(my math skills are great enough to be able to calculate the mean).

Thank y'all!!

Close enough for government work... enjoy

 

[flyfisherwes]

I get 8.25%

 

[weirdboy]

5gal * 7.73% + 10 fl oz * 40% = .3865 gallons + 4 oz = .41775 gallons.

.41775 gal / 5 gal (rounding down) = 0.08355 = Roughly 8.35%.

Where the heck does that 4oz come from?





It is not 8.3% it is 8.22%

You have to account for the additional volume you add with the bourbon.

 

[flyfisherwes]

1578ml alcohol in 5.05 gallons of liquid. about 8.25%

 

[HawksBrewer]

8.25% vs 8.3%? If you can taste (or feel) a difference you are a better man than I. At least OP has a ballpark for reference... i.e. don't pretend it's BMC and chug 4 really quick.

 

[passedpawn]

10oz = 0.078125g

( (5g*7.73%) + (0.078125g*40%) ) / (5g + 0.078125g) = 8.23%

 

[DrBrewDC]

Ahhhhh the controversy.

 

[DrBrewDC]

8.25% vs 8.3%? If you can taste (or feel) a difference you are a better man than I. At least OP has a ballpark for reference... i.e. don't pretend it's BMC and chug 4 really quick.

But how 'bout 3??

 

[slarkin712]

I agree with wierdboy:
In beer: 7.73%*640 oz = 49.472 oz of alcohol
Addition:40%*10 oz = 4 oz alcohol
Total alcohol: 53.472 oz

New volume: 640+10 = 650 oz

New ABV: 53.472/650 = 8.22%

 

[weirdboy]

10oz = 0.078125g

( (5g*7.73%) + (0.078125g*40%) ) / (5g + 0.078125g) = 8.23%

This is basically the same number as what I got. I just truncated at 8.22 instead of rounding the last digit up, which I guess I should have done but was lazy.

 

[passedpawn]

This is basically the same number as what I got. I just truncated at 8.22 instead of rounding the last digit up, which I guess I should have done but was lazy.

I figured that. I just wanted to make sure we had ever number between 8.20 and 8.30 covered

 

[brewit2it]

8.23 ABV it is.

53.472 oz of pure EtOH in 650 oz total volume.

 

[jmf143]

Roughly 8.2261538% or so, give or take a bit here or there, approximately.

 

[Bernie Brewer]

I agree with wierdboy:
In beer: 7.73%*640 oz = 49.472 oz of alcohol
Addition:40%*10 oz = 4 oz alcohol
Total alcohol: 53.472 oz

New volume: 640+10 = 650 oz

New ABV: 53.472/650 = 8.22%

This.

 

[bernerbrau]

Where the heck does that 4oz come from?

4oz of alcohol, which is 40% of 10 oz.

It is not 8.3% it is 8.22%

You have to account for the additional volume you add with the bourbon.

Yes, assuming infinite precision. But he stated his volume is "approximately 5 (but probably a bit more)". So we're talking maybe +/- a quart or two. So to account for a range of most likely results, you could give him a margin of error if you wanted to get really technical.

But since his total volume is an approximation anyway, 8.3% and 8.22% are both approximations and both probably in the right ballpark. I could have accounted for the additional 10oz of bourbon, but that's 1.6% of his stated initial volume, which given the precision of his measurement is somewhat negligible to the actual result, since it's not going to be accurate to a tenth of a percentage point anyway.

 

[bernerbrau]

So to clarify, let's assume his beer is somewhere between 4.75 and 5.5 gallons.

Then the initial range of volume of alcohol is given by:

7.73% * [608..704] = [47..54].

He then adds 4 oz (40% of 10 oz) with the bourbon, giving him a total alcohol volume range of:

[51..58]

Dividing back into the total volume:

[58 / 714..51 / 618] = [8.12%..8.25%]

Ah. Well, I take my crow grilled medium well and lightly seasoned then.

 

[DrBrewDC]

So to clarify, let's assume his beer is somewhere between 4.75 and 5.5 gallons.

Then the initial range of volume of alcohol is given by:

7.73% * [608..704] = [47..54].

He then adds 4 oz (40% of 10 oz) with the bourbon, giving him a total alcohol volume range of:

[51..58]

Dividing back into the total volume:

[58 / 714..51] = [8.12%..8.25%]

Ah. Well, I take my crow grilled medium well and lightly seasoned then.

I enjoyed the entire debate. The best part? A man able to admit when he is wrong; a rarity these days. Kudos to you, bernerbrau!

 

[passedpawn]

I enjoyed the entire debate. The best part? A man able to admit when he is wrong; a rarity these days. Kudos to you, bernerbrau!

I agree. That was refreshing. (how was that crow?)