Splish, Splash, I Was Takin' a Drink...

[bluesbassdad]

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.

Definitions:

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!

Yours truly,

Dave Morefield

[Speedy_John]

Actually, your math is spot on. But, I think you can make it a bit easier if you limit your equation to finding out how much water per ounce of bourbon you need to add to reach your desired drinking strength. Then, the equation becomes:

X = A/B - 1

A = Proof of bourbon

B = Desired drinking proof

X = Amount of water to add per ounce of bourbon.

Example: You have Stagg at 138 proof, but you want to drink it at, say--pulling any old number randomly out of the air--101 proof. In this case,:

X = (138/101) - 1 = 1.37 - 1 = .37 (approximately)

Therefore, you would add about .37 ounces of water to each ounce of Stagg to reach a drinking strength of 101 proof. If you're pouring two ounces of Stagg, you would add .74 ounces of water.

Whew, too much thinking. Me thirsty. Me drink Stagg. Water?

SpeedyJohn

[jeff]

Thanks you guys for figuring this out. I had wanted to do it, but didn't want to spend the time thinking about it

[Forbes]

Last night I was helping my son with his algebra homework. I often have told him that algebra was important because in life you use it all the time. Now is this not the perfect example of the use of algebra to solve an important issue! I like the formula except I usually do not like to add water to my bourbon…

[bluesbassdad]

Actually, your math is spot on.

I was sure that something looked wrong in my post. Last night while channel-surfing, it came to me.

A PBS station was doing a fund drive, interspersed with a feature called "Mack the Knife", the hit song by Bobby Darin (about 40 years ago). At least I got the "i" right.

Your mention of a proof of 101 has started me thinking about the effects of the expected degree of error in the measurements. For most of us, who are likely to use commonly available kitchen implements, a series of attempts to reach 101 is likely to produce a distribution ranging from around 95 to around 105. Perhaps it's time to revisit the recent thread that touched on graduated flasks as used in chem labs.

Yours truly,

Dave Morefield

[Marvin]

Very Scientific!!! Your formula is correct, I think. Who knows???Maybe, Probably - Not Quite Sure!!!!But very, very interesting!!!!! Well, I am going to go pour me another one!! Here's to you .

Cheers,

Marvin

[Vinnie]

Very interesting. It seems we share the very same exact scientificly correct recipe except i leave out the water.....hehe