# Brass monkey cold

In case it should ever come up in conversation, only the picture at left shows a brass monkey. The other is a bronze statue of some sort of a primate. A brass monkey is a rack used to stack cannon balls into a face centered pyramid. A cannon crew could fire about once per minute, and an engagement could last 5 hours, so you could hope to go through a lot of cannon balls during an engagement (assuming you survived).

Small brass monkey. The classic monkey might have 9 x 9 or 10×10 cannon balls on the lower level.

Bronze sculpture of a primate playing with balls — but look what the balls are sitting on: it’s a dada art joke.

But brass monkeys typically show up in conversation in terms of it being cold enough to freeze the balls off of a brass monkey, and if you imagine an ornamental statue, you’d never guess how cold could that be. Well, for a cannonball holder, the answer has to do with the thermal expansion of metals. Cannon balls were made of iron and the classic brass monkey was made of brass, an alloy with a much-greater thermal expansion than iron. As the temperature drops, the brass monkey contracts more than the iron balls. When the drop is enough the balls will fall off and roll around.

The thermal expansion coefficient of brass is 18.9 x 10-4/°C while the thermal expansion coefficient of iron is 11.7 x10-4/°C. The difference is 7.2×10-4/°C; this will determine the key temperature. Now consider a large brass monkey, one with 10 x 10 holes on the lower level, 81 at the second, and so on. Though it doesn’t affect the result, we’ll consider a monkey that holds 12 lb cannon balls, a typical size of 1750 -1830. Each 12 lb ball is 4.4″ in diameter at room temperature, 20°C in those days. At 20°C, this monkey is about 44″ wide. The balls will fall off when the monkey shrinks more than the balls by about 1/3 of a diameter, 1.5″.

We can calculate ∆T, the temperature change, °C, that is required to lower the width-difference by 1.5″ as follows:

-1.5″ = ∆T x 44″ x 7.2 x10-4

We find that ∆T = -47°C. The temperature where this happens is 47 degrees cooler than 20°C, or -27°C. That’s 3.2°F, not a very unusual temperature on land, e.g. in Detroit, but on sea, the temperature is rarely much colder than 0°C or 32°F, the temperature where water freezes. If it gets to 3.2°F on the sea, something is surely amiss. To avoid this problem, land-based army cannon-crew uses a smaller brass monkey — e.g. the 5×5 shown. This stack holds 1/7 as many balls, but holds them to -74°F, a really cold temperature.

Robert E. Buxbaum, February 21, 2015. Some fun thoughts: Convince yourself that the key temperature is independent of the size of the cannon balls. That is, that I didn’t need to choose 12 pounders. A bit more advanced, what is the equation for the number of balls on any particular base-size monkey. Show that the packing density is no more efficient if the bottom lawyer were an equilateral triangle, and not a square. If you liked this, you might want to know how much wood a woodchuck chucks if a woodchuck could chuck wood, or on the relationship between mustaches and WWII diplomacy.