Hooligan Science: Intoxication and Beer Consumption

I had lost the original version of this during a server move, so had to resurrect it from the WayBack Machine. What was stored there was incomplete, so a few of the images are missing. And of course since I was a little bit (ok, a lot) plastered at the time, I don't recall what equations were represented by the missing images. One of these days I'll have to make something up (or else get drunk again) to fill in the missing equations.

Intoxication and Beer Consumption
A while ago, the Chronicler and the Black Creature, being a couple of math and physics minded types attempted to derive a mathematical relationship between beer consumption and intoxication. The work was never completed though, because both researchers ended up getting drunk while performing experiments to test their theories.

Let Intoxication Factor be defined as where φ represents the amount of beer consumed,

Beer Consumption
The function is a complex function representing the amount of beer consumed

where
n = number of people present
α = alcohol content of beer (vector quantity)
t = time spent in the bar
= amount of food consumed
p = probability that a certain beer with alcohol content is chosen

To simplify things, we make the assumption that only beer is involved. If hard alcohol is included, the equation becomes more complex. Since most beers are of similar alcohol content, and people tend to stick with a single brand of beer, we can assume that α is a constant and p = 1. This equation simplifies to
image missing

Further, if blood is donated prior to beer consumption, an additional multiplicative factor (determined empirically) of

is applied.

Intoxication Factor (IF)
Intoxication factor is a rather complicated non-linear integral-differential equation incorporating beer consumption, metabolism and the complex Hooligan Factor.

Obviously, IF will depend on φ, so we'll start with that,

Now, we must include metabolic effects, which will act to decrease the amount of alcohol,
image missing
where
m = mass of the person
E(t) = energy expenditure during drinking period

E(t) takes into account whether or not the person has been dancing, moving around or wrestling in the bar. We can simplify this by assuming that the majority of time is spent sedentary. In this case, M(t) becomes a constant factor. Incorporating this, we get
image missing

Theoretically, IF can increase without bound, because of the positive exponential dependence on alcohol consumption. But, empirically, it has been observed that after a certain time, depending on the rate and amount of alcohol consumed, a critical point is reached and a phase change occurs where a violent expulsion of the person's stomach contents takes place. This critical point is represented by a rapidly decreasing exponential that dominates at high t.