Planes On A Treadmill

Boingboing has a post up that gets the pedantic science nerd in me going. I’ll need to reproduce it almost in full so you can understand. It begins:

David Pogue at the NYT has presented this classic airplane on a giant treadmill problem, and people are arguing about whether or not the plane would take off or not.

Here’s the set-up from Pogue, quoting someone else:

”Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off? I say no, because the plane will not move relative the the ground and air, and thus, very little air will flow over the wings. However, other people are convinced that since the wheels of a plane are free spinning, and not powered by the engines, and the engines provide thrust against the air, that somehow that makes a difference and air will flow over the wing.” (Here’s Pogue’s original post.)

Continue if you like such thought problems.


Boingboinger Mark Frauenfelder has his say:

I say yes. Let's assume the friction in the wheel bearings is negligible. Putting a plane on a treadmill is like putting it on an icy lake. When you fire up the jets, the plane is going to shoot down the lake and take off just like it would on a runway.

Some commenter then disagrees. But I have to say I’m a bit surprised this is a problem for anyone, really. Jets generate thrust by expelling hot air, which pushes back on the plane in a simple demonstration of Newton’s third law of motion. It shouldn’t matter what’s happening with the wheels; they don’t supply any power in our example. They just let the plane roll.

Now, if the plane sped up via power from the wheels, like a car with wings attached, sitting on a treadmill that matched the rotational speed of the wheel would be a problem. But the plane speeds up by pushing air out. Maybe the wheels would be spinning twice as fast as they would be if the plane were not on treadmill, but so what?

Think of it this way: the plane could be disconnected from the ground all together. Say it has a rotor blade like a helicopter’s that suspends it above the ground. The jets will still push the plane forward. To me, this doesn’t seem hard to understand at all (see? pedantic nerd), so I am surprised this issue generates a lot of online discussion.