When was the last time you actually measured the amount of tonic going into a Gin and Tonic? Chances are, like many other rational bartenders, you simply filled up your glass with ice, poured a standard serving size worth of gin into the glass, and topped up the rest with tonic.
But how much tonic are you actually adding? That amazingly simple question is not so simply answered. The key, usually, is in the completely random arrangement of ice cubes in a highball glass. We have all seen how we get less ice cubes in a glass when, by complete chance, they happen to stack into a perfect little column of ice cubes.
In order to answer this question, we can look at a feature called packing density. This number is representative of how much of a space a particle utilizes when packed into a given container. Obviously, particles smaller in size will fill up a container more efficiently, so they have a packing density closer to one, which means that the packed particles have very little empty space in between them. Large particles, with irregular shapes are terribly inefficient at filling up a space because their irregularities get in the way of each other so the packing density is closer to zero. Think of the difference being akin to how flour will fill a container perfectly, but large pebbles will fill the same container with a lot of gaps in between the rocks.
In this paper, mathematicians have analyzed through statistics and computer modelling the packing densities of various 3D shapes. In summary, they have found that randomly packed cubes (e.g. ice cubes packed into a glass) have a maximum packing density of 0.78, which means that cubes can be randomly arranged and still take up more than 3/4 of the space they are packed into. Unfortunately, these numbers are taken through the assumption that the 3D shapes are not confined by boundaries. In real life, the walls of the glass interfere with the packing of the ice cubes, we find that the effective packing density is, at most, closer to 0.5. The average packing density, howeve, can be taken as 0.35 (found through the tedious experimentation by yours truly) This means that for regular ice cubes in a regular glass, you can expect that the remaining space for liquid is at least half of the original volume of the glass, but more likely 2/3 of the total glass volume.
That being the case, most glasses in a bar tend to be within 9-12oz, or 270-360ml. Given the packing density of ice, and a standard serving of alcohol of around 45ml, we find that the remaining space for tonic is about (for a 10oz/300ml glass);
300[total space in glass] – (300 x 0.35)[space taken by ice cubes] -45[serving of alcohol]= 150[remaining space for tonic]
This means that if you have a 10oz glass, you are serving 150ml of tonic for every 45ml of alcohol, which is a 10:3 ratio, which is more or less a 3:1 ratio. Personally, I think that makes for a touch strong G&T. Personally, my ideal ratio of spirit to mixer is more akin to a 4:1 ratio, which is pretty light, I know. Sue me.
To get that ratio, you have three options
1) adjust your serving size to match the ratio
2) switch out your glasses to be able to add more mixer
3) control the amount of ice you put into the glass to achieve the ratio
Option 3 is a fairly unreasonable option, as busy nights mean less time for bartenders to pay attention to such a finicky task. Also, I personally dislike the aesthetics of a glass only half full of ice. Option 2 is easy, but costly for the business owner. Option 1 is the easiest choice to make, because it improves business margins, which makes everyone except the customer happy. To continue with the example of the bar with 10oz glasses, the proper serving size for them would be, rearranging the above equation with basic algebra:
300[total space in glass] – (300 x 0.35)[space taken by ice cubes] / (1 + 4)[parts of spirit added to parts of mixer] = 39ml
Nobody in their right mind would want to measure 39ml of liquid. If instead, I wanted to maintain a serving size of 45ml, I would find that the size of glass I need is
(45+180)[total amount of spirit and mixer] + (V x 0.35)[space taken up by glass]=V[total capacity of glass]
Solving for V, we find that for my preferred, watery, weak-ass G&T, I would need to use a 11.5oz glass. If we give the glass some extra room to avoid spillage, we find that we can use a 12oz glass, which is very easy to source.
Thereby, using the power of mathematics, I have shown what every bartender knows, that starting a good bar starts with getting the right glassware for the job.