What Is the Power to Run Through Football Players — from “How To”

Photo: Rhett Allain

I’m continuing to work on explanations for the Randal Munroe book How To — Absurd Scientific Advice for Common Real-World Problems (Penguin Press). Basically, it’s a book that just has a ton of fun answering weird questions with some cool cartoons.

There is a chapter about scoring in an NFL football game. One idea is to just use a horse and literally plow through the opposing team. It’s just like a scene from Lord of the Rings with a horse running through a sea of orcs. Honestly, I can’t remember exactly which movie this was.

So, here’s the stuff from How To. First he uses the orcs as though they were a drag force with the following equation (for the magnitude of the drag force).

In this expression:

• ρ is the density of the medium. If you were moving through air, it would be the density of air. In this case, it’s the crowd density of orcs.
• A is the cross sectional area of the object. For a horse, this would be the front surface area.
• C is a drag coefficient that depends on the aerodynamic shape of the thing.
• v is the relative velocity of the object with respect to the medium.
• Oh, the 1/2 is the number 0.5. Ha.

Using that, he gets the following equation for the power needed to move through the orcs.

Finally, he uses some estimated values to get a power of 130 hp (which is more than the power from 1 horse).

OK, let’s go over these things.

Drag Force

I think a horse moving through orcs is a great way to visualize the drag force — it’s the same drag force your car experiences as it moves through the air. In both cases, there are collisions between things (orcs or molecules) and these collisions exert a net force on the object.

Here is a diagram to help us model this collision force. Instead of having the object move, I have it at rest with the orc-air balls moving towards it.