Mythbusters recently busted that weird viral video that seems to depict shrimp being cooked by firing them out of an air cannon, through sprays of flour, egg, and bread crumbs, and then a fireball. If you haven’t seen it, check it out here: https://www.youtube.com/watch?v=lkaIoH6Um60

If you have any familiarity with barbecues, it won’t surprise you that the shrimp ends up completely raw. (If you have any familiarity with air cannons, it may not surprise you that it also ends up rather shredded in a lot of cases) The Mythbusters ramped it up by shooting the shrimp through twelve feet of sword forges, at a temperature of 2000 degrees F (around 1350 Kelvin, which is what we’ll be working in from here on out). Still, the shrimp remained unwarmed.

So, the natural question to ask is: what would it actually take?

Stepping through the footage from the Mythbusters episode, the shrimp take about seven frames — 0.25 seconds — to travel through the forges. That doesn’t leave much time for cooking. The internet recommends that shrimp be cooked to an internal temperature of 335 K. The Mythbusters start out with shrimp at room temperature, roughly 295 K.

Now we’ll need some physical properties of a typical shrimp. A jumbo shrimp weighs around 20 grams. SInce a shrimp is basically neutrally buoyant in water, it thus has a volume of 20 cm^3. If we model it as a meat cylinder which has a length about 5 times its diameter, we can then calculate it to be roughly 1.7 cm wide and 8.6 cm long, with a surface area of 50 cm^2. This is the important number, since heat is transferred into an object via its surface.

Another important number is the specific heat capacity of the shrimp – the amount of energy it takes to warm it up. Water has a high specific heat, and shrimp is mostly water, so we’ll estimate that it will be not too far off. (Cooking involves breaking and reshaping proteins, which takes some amount of heat, and indeed the internet does indicate that the specific heat of meats tends to increase with temperature, but it’s still not going to be significantly different from water). It takes 4.2 Joules to raise the temperature of 1 gram of water by 1 K. So for our 20 grams and 40 K, we’ll need about 3.7 kiloJoules. Since that energy has to be transferred in 1/4 of a second, we’ll require 15 kilowatts of power. Since it has to be transferred through 50 square centimeters, we’ll need 3 megawatts per square meter.

Now let’s take a step back. There are three ways by which heat is transferred to an object: conduction, convection, and radiation. Conduction involves direct contact with a hot surface (i.e. a frying pan), so we can’t use it for cooking shrimp in mid-air. Convection involves heat transferred from a fluid, such as air or water. Radiation uses, well, electromagnetic radiation (typically infrared). So we need to consider two ways in which the shrimp will be heated.

Convective heat transfer is proportional to the difference in temperature between the object and its surroundings. Radiant heat transfer is proportional to the difference of the fourth powers of the temperatures. Since we know that the temperature is going to be quite high, it is reasonable to imagine that convection will therefore be negligible. So we really only need to consider radiant heat.

Power per unit area is equal to the Stefan-Boltzmann constant times the difference of the fourth powers of the temperatures.

And there we have it. Shrimp should be cooked for a quarter of a second at 2700 Kelvin or 4400 degrees Fahrenheit.

Who’s up for some seafood?