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The Airplane on a Treadmill

February 3, 2015

Can an airplane take off on a treadmill going as fast as the top speed of the aircraft?

The answer to the question is yes, but that’s not the interesting part. The interesting part is the explanation, which is notoriously difficult.

Airplanes take off by moving forward first, then up. They don’t take off right away; this is why runways are so long. So to simplify the original question, let’s ask “Will a treadmill stop an airplane without wings from moving forward?”. To stop the plane from moving, the frictional force from the treadmill acting on the wheels pushing the plane backwards must equal or exceed the thrust of the engines pushing the plane forward.

plane without wings

Moving Forward
Aircraft engines don’t push on the ground to generate movement, like cars do. They push on the air. Obviously, when you’re flying, there’s no ground to push on, so this has to be the case. So with or without wheels, an aircraft’s engines will push the plane forward.

Airplane engines generate a tremendous amount of thrust. Keep in mind, they are designed to take a vehicle weighing several tons and throw it through the air at 500 mph.

Watch this video to get an idea of just how powerful jet engines are:

How much force does a treadmill exert?
Aircraft wheels are free spinning. When an airplane lands, the wheels go from stationary to 200 mph in a fraction of a second. If they were not extremely low friction, they would be ripped off. An airplane’s engine doesn’t connect to the wheels in any way. They are more like a skateboard or a furniture dolly than a car.

An airplane, basically:
furniture dolly

Suppose someone took a small airplane and put it on a treadmill and then tied a rope to its nosecone and handed the other end of the rope to a normal human being.

treadmill plane with rope

If the treadmill were slowly brought up to speed, could the human hold on to the rope? They’d have to pull a bit, but they could hold it. Now try the same stunt with a car and their arm would be ripped off.

The Verdict
So, we have a huge force pushing the plane forward and a tiny force holding it in place. According to the laws of physics, if you have a net force applied in one direction, acceleration will occur. The plane will move forward.

Theoretically, if the treadmill were moving at an insane speed, like 2,000 mph, the friction from the wheels might generate enough friction to substantially slow the aircraft’s acceleration. However, at the speeds where friction would generate substantial amounts of friction, the wheels would melt and the landing gear would rip off and the plane would be torn apart by the insanely fast treadmill beneath it. Landing gear is not strong enough to hold together against the forces the engines can generate.

Moving up
Now that we’ve established that the plane moves forward, it will eventually reach the critical speed, and the lift from the wings as well as the thrust from the engines will push the plane upwards. The faster the plane moves, the less its weight pushes down on the runway, and the less friction the wheels will generate.

Reducing the problem down to whether the plane moves forward makes it much easier to solve and sidetracks any nonsense about lift or airflow or anything like that.

The Mythbusters actually tested this, so if you just want to watch a video as proof, here you go:

Another article about this problem

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