Any Bobby Darrin fans out there?
Actually this is about a different kind of splash, namely that "splash" that we all refer to from time to time when we add water to our bourbon before drinking it.
Today I decided to finish off a bottle of GTS, and for my first drink I added water in two doses before I achieved the balance of flavor and smoothness that most appealed to me today. In the process, I started wondering what proof I had achieved, knowing full well that there was no way to measure after the fact how much bourbon I started with, much less how much water I had added.
But suppose I had measured the amount of bourbon that I started with and the amount of water I added. How hard would it be, I wondered, to calculate the proof of the resulting mixture. Or, perhaps more usefully, what if I knew the quantity and proof of the bourbon I started with and the desired proof of the end-product. How could I calculate the amount of water to add?
It took me an embarrassingly long time to come up with an answer, and I know this wheel has probably rolled before. Nevertheless, here's what I came up with, albeit handicapped by my inability to use subscripts in this forum as I did originally.
q = initial total amount of bourbon
a = " " " " alcohol
w1 = " " " " water
w2= new " " " water
splash = w2 - w1
p1 (i.e. initial %abv) = a / q = a / (a + w1)
p2 (i.e. new %abv) = a / (a + w2)
A few algebraic steps later, I came to the following:
splash = a/p2 - q
Now let's suppose that my GTS is an even 138 proof. Then the initial abv% ( or p1) is 69% or 0.69.
If I start with exactly one ounce, just to make the calculation more illuminating, and if I want to end up with a drink that is 100 proof (or 50% abv), the following calculation tells me how to do that.
splash = a/p2 - q = .69/.50 - 1 = 0.38
In other words, I must add 0.38 ounces of water to one ounce of GTS at 138 proof to yield a drink of 100 proof.
If the target is 90 proof (45% abv), then
splash = .69/.45 - 1 = 0.53
If the target is 80 proof (40% abv), then
splash = .69/.4 - 1 = .73
I find the above counter-intuitive. Could it actually be that one can add almost three quarters of the original amount and still have 80 proof bourbon?
I can't see an error in my math, but, of course, I am nearing the end of my second glass of Stagg. Bleeee!