Conveyor Belts, Airplanes, Skateboards

Thursday, February 09 2006

Jason’s Case of the Plane and Conveyor Belt riddle is confusing very smart people, so I thought I might explain it. First, go read Jason’s post, then come back here.

So, a lot of people assume that the thrust of the airplane is somehow effected by the speed of the magical conveyor belt it rides on. Let me first say this: it’s not, and rather than talk about how the thrust only acts on the air, and not the conveyor belt (the two are totally unrelated) I’ll talk about something I know well: skateboards.

Picture this – you’re standing on a skateboard that is riding on a treadmill. One person is standing in front of the skateboard on firm ground, and the two of you are holding a rope. This person pulls on the rope that you’re holding so that the rope moves exactly an inch per second, advancing you forward. No matter what speed the treadmill is going, as long as that person maintains the same rate of pull, you’ll advance forward an inch per second. Your skateboard wheels might go faster or slower in relation to the speed of the belt, but you’ll pretty easily advance forward. Change the rope to a stick, and the conveyor belt can travel in either direction at either speed and be just as irrelevant.

The airplane’s engines provide the forward force, pushing against the air behind their outputs. The air is like the person standing firm (as firm as air can be) and the engines pushing against that air provide the same kind of force that someone pulling on the rope provides. In both cases, the speed of the conveyor belt has no correlation with the force that the rope or engines produce against the air or the person standing firm.

Granted, in both cases, wheel friction will come into play. With a skateboard and treadmill, friction might be noticeable. With the kind of forces a jet turbine can produce the wheels would probably melt off before the engines noticed anything.