An airplane on a treadmill: will it take off?

[TimberWolf]

No it isn't. The treadmill is always irrelevant. The real question is whether or not the aeroplane's engines are on, something which wasn't mentioned in the original post. The mistake is in thinking planes work like cars, or runners. They don't. Propulsion is nothing to do with the wheels.

I guess a plane on a treadmill with its brakes on would be moving the same direction as the treadmill, and if that was backwards it might take a bit longer for it to reach take off speed going forwards.

The engines would have to be on to keep pace with the treadmill, unless you want to add a third interpretation of the problem. Wheels are not like ice, and if there is an incline you'd also need to counter gravity to keep pace with the treadmill. You must have a small amount of thrust to be able maintain speed with the treadmill. To summarize, the treadmill is not irrelevant and neither it nor the wheels are frictionless.

[VectraMan]

Vectra - if you replace the treadmill with a mythical treadmill which can be used to efficively keep the plane stationary

How would a treadmill keep a plane stationary? I'd bet that even with the brakes on, the force of the engines would be enough to overcome any backwards force being exerted via the wheels. Without the brakes the wheels would just turn backwards as the plane moved forwards.

[VectraMan]

The engines would have to be on to keep pace with the treadmill, unless you want to add a third interpretation of the problem. Wheels are not like ice, and if there is an incline you'd also need to counter gravity to keep pace with the treadmill. You must have a small amount of thrust to be able maintain speed with the treadmill. To summarize, the treadmill is not irrelevant and neither it nor the wheels are frictionless.

Okay I'll give you that. Not "irrelevant", but "negligible".

[TykeMerc]

I've watched Harriers take off, hover and land vertically several times during engine tests, they use special hard standings as they rip the hell out of tarmac or bog standard concrete. Any loose stuff becomes a shower of high speed projectiles.
Once the water tanks are empty anything other than a fairly controlled verticle landing is all but impossible as there's not enough reaction mass to provide sufficient vertical thrust.

Since the original post makes no mention of engines existing, let alone them running, the answer is no it won't take off as assuming the aircraft has wheels rather than skids it will simply freewheel more or less in place until the velocity of the wheels overcomes the limits of the wheel bearings and the plane is thrown off the rear of the treadmill.
Assuming the aircraft has engines which are running at a suitable speed and the treadmill is long enough it will take off if the treadmill isn't running too fast which would again overcome the freewheel ability of the wheel bearings.

[TimberWolf]

Okay I'll give you that. Not "irrelevant", but "negligible".

Small is a better word than negligible. The frictional force at the wheels is proportional to the weight of the plane. It would be hard to pull a plane along the ground by hand for instance. E.g. If the plane were sitting still on a stationary treadmill, and the treadmill started, the wheels would not turn to keep pace with the treadmill (unlike ice, very, impossibly slippery ice), the engines would have to be on to keep pace with the treadmill surface.

[Mich the Tester]

I’ve seen a top class sprinter using an adapted treadmill for ‘overspeed’ training. The treadmill is cranked up to a slightly higher speed than the sprinter can run on the track so that he can run with reduced wind resistance, thereby training his nervous system to move his legs forward very quickly in the hope of increasing his top speed. No, the sprinter did not take off. Not that I expected he would.

[Churchill]

I’ve seen a top class sprinter using an adapted treadmill for ‘overspeed’ training. The treadmill is cranked up to a slightly higher speed than the sprinter can run on the track so that he can run with reduced wind resistance, thereby training his nervous system to move his legs forward very quickly in the hope of increasing his top speed. No, the sprinter did not take off. Not that I expected he would.

I've seen a fat lass fall off a treadmill.

[TimberWolf]

A related question, if anyone has the stamina, is whether it is easier to run on a powered treadmill than on normal unpowered ground.

[Mich the Tester]

I've seen a fat lass fall off a treadmill.

I've been going to the wrong gyms; too many fit, competent people for that to happen. I'd love to see it though.

[Churchill]

A related question, if anyone has the stamina, is whether it is easier to run on a powered treadmill than on normal unpowered ground.

easier on a treadmill, as mentioned, no wind-resistance. Also, most treadmills are sprung.