Mythbusters - airplane on a conveyor belt

wowzers wrote:

wheel wrote:

If the treadmill matches the wheel speed, the plane will not take off. That's the truth.

Listen, this guy has it right.

Actually, it's impossible for the treadmill to matches the speed of the wheels if it's also matching the speed of the plane's body.

phstenning wrote:

You have missed the point. It's not a case of the treadmill "matching" the wheel speed, the wheel speed will be driven by the treadmill. Turn the treadmill up speed up, the wheels will spin faster. Given the limited friction this will make little difference to the rest of the plane which will move as it would have moved without the treadmill.

You're missing the point. again, what is this force holding the plane above the treadmill that allows it to be unaffected by the motion of the belt? there is no upward force until lift is generated.

didn't you ever see Man vs. Beast? they had a team of 40 "little people" vs. an elephant in an airplane pulling contest. if the wheels were so freely spinning and thus had negligible friction with the runway, than shouldn't the slightest force be enough to move the airplane easily? well the midgets and the elephant had to work pretty damn hard just to get the planes moving a mph or two.

Here's a question - is it possible for the treadmill to spin fast enough so that the wheel's spinning friction is enough to cause the plane to be stationary?

Basically, what are the factors that influence the spinning friction? Gravity obviously, the coefficient of friction - what else? Is the treadmill speed even a factor?

keystone light knight wrote:

again, what is this force holding the plane above the treadmill that allows it to be unaffected by the motion of the belt?

The thrust of the propellor/jet acting on the plane, obviously.

how about this for a slightly different twist-- an airplane with skates on an ice treadmill. as the treadmill goes backwards to match the speed of the plane, if there is no friction between the skates and the treadmill, the plane will accelerate forward and take off.

It would either take a lot of friction or the ice going very fast for the plane not to be able to overcome the force pushing it backwards and accelerate forwards.

The same thing is going on with freespinning wheels as with skates, but in the wheels it happens in the axles. If the axles are well enough lubricated, the plane will take off

wheel wrote:

If the treadmill matches the wheel speed, the plane will not take off. That's the truth.

Here is what the original riddle said:

"An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?"

It says nothing about the treadmill running at the same speed of the WHEELS - but rather the same speed as the AIRPLANE. At the moment of take off, both the plane and the treadmill will be "moving" at 150 MPH in the opposite direction - but the wheels will be spinning at the same speed as if the airplane was moving at 300 MPH on the normal ground.

Here's why the plane won't take off. As the treadmill speeds up to match the wheel speed, the rpm's required to overcome the planes engines will be so high that the wheel's bearings will either seize up or blow up. Now, the question becomes, can a plane take off without wheels? Not on land :)

wheel wrote:

Here's why the plane won't take off. As the treadmill speeds up to match the wheel speed, the rpm's required to overcome the planes engines will be so high that the wheel's bearings will either seize up or blow up. Now, the question becomes, can a plane take off without wheels? Not on land :)

Wouldn't the treadmill lock up then too?

Neb wrote:

wheel wrote:

If the treadmill matches the wheel speed, the plane will not take off. That's the truth.

Here is what the original riddle said:

"An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?"

It says nothing about the treadmill running at the same speed of the WHEELS - but rather the same speed as the AIRPLANE. At the moment of take off, both the plane and the treadmill will be "moving" at 150 MPH in the opposite direction - but the wheels will be spinning at the same speed as if the airplane was moving at 300 MPH on the normal ground.

to add one more thing - the riddle also doesn't limit how much force the engines are producing. Someone help me here if I'm wrong - but the engines would only have to produce the same amount as it normally would to get the plane to 150 MPH plus what ever force friction is acting upon the wheels - which should be minimal in comparison.

Neb wrote:

to add one more thing - the riddle also doesn't limit how much force the engines are producing. Someone help me here if I'm wrong - but the engines would only have to produce the same amount as it normally would to get the plane to 150 MPH plus what ever force friction is acting upon the wheels - which should be minimal in comparison.

Hallelujah!

A plane is able to take off due to the lift that is created by the pressure differential produced by the flow of air over the wing. Putting it simply -- the shape of the wing causes air to move faster over the top of the wing than it does below the wing. Faster moving air has less air pressure than slower moving air and that differential "lifts" the plane. The engines provide the thrust to make it go forward. In other words...no air moving over the wing, no take-off regardless of how fast the treadmill is running.

amen! Correct me if I'm wrong but kinetic friction force on the axle bearings is a function of the weight of the object being dragged and the friction constant. In other words, it's a CONSTANT, FINITE force. There is no reason it should be able to hold back the variable, potentially limitless thrust from the engines. Isn't that the reason the wheel is such a great invention to start with?

dingle wrote:

wheel wrote:

Here's why the plane won't take off. As the treadmill speeds up to match the wheel speed, the rpm's required to overcome the planes engines will be so high that the wheel's bearings will either seize up or blow up. Now, the question becomes, can a plane take off without wheels? Not on land :)

Wouldn't the treadmill lock up then too?

Of course not. The treadmill is hypothetical. Hypothetical treadmills the size of runways don't have limitations on how fast they can spin. Airplanes, on the other hand, are real.

phstenning wrote:

keystone light knight wrote:

again, what is this force holding the plane above the treadmill that allows it to be unaffected by the motion of the belt?

The thrust of the propellor/jet acting on the plane, obviously.

you do realize that the thrust of the engines only acts in a horizontal direction, right? unless we are talking about thrust-vectoring or VTOL aircraft, then there is not net upward force until it has reached takeoff speed.

there is a definite interpretation problem with the original question since i think it was poorly asked. let's get some things straight. the question clearly defines the initial situation as a stationary plane sitting on a motionless treadmill. now, from a dead stop, the plane's engines switch on and the treadmill belt begins to move at the same moment. this is where the riddle gets cloudy. talking about simply the "speed" of the airplane compared to the treadmill is too ambiguous, but maybe that's why it is considered a riddle. the question should have been more specific - does it mean the acceleration of the wheels? clearly, there is some sort of idea of equal forces going on here. i suppose if we take it 100% literally, and the speed of the airplane (relative to a stationary observer) is the same as the speed of the treadmill (belt going backward), then it simply means the airplane is applying twice as much thrust as it would normally apply to reach take-off speed, in order to counter the backward motion of the treadmill and accelerate beyond that point of equilibrium. that is a pretty stupid question and perhaps that is why it is posed as a riddle and not a physics question, but i suppose in that case then yes, obviously the plane will fly - but this frictionless/free-spinning wheels/engines hold the plane off the runway idea is false and not the reason. it would simply be a trick question and thus the treadmill is just a red herring.

but, if you take "speed of the airplane" to mean "force that would normally be required to achieve the same speed on a standard runway," then no, the plane will not fly, for reasons that i have stated.

wheel - the wheels would only have to spin the same speed as they would to go 300MPH on normal ground - the bearings wouldn't bust at that speed - would they?

Cujo wrote:

A plane is able to take off due to the lift that is created by the pressure differential produced by the flow of air over the wing. Putting it simply -- the shape of the wing causes air to move faster over the top of the wing than it does below the wing. Faster moving air has less air pressure than slower moving air and that differential "lifts" the plane. The engines provide the thrust to make it go forward. In other words...no air moving over the wing, no take-off regardless of how fast the treadmill is running.

I think the plane is able to "fly" because of the differential in air pressure on the wings. "take off" is another matter. Somewhere in there we should consider conservation of angular momentum, i.e. with the wheels. They won't be turning when the plane is flying, but just before takeoff they will.

The plane will take off. Doesn't matter how fast the treadmill is moving backward. Imagine a plane with wheels moving "forward" at an infinite speed, yet the plane itself remaining in place. Can that plane still move forward enough to produce lift? I say yes. It would involve a hell of a lot of screeching and burning rubber as the engine thrust overrides the wheel-treadmill friction, but it would still work.

It's the exact equivalent of trying to have a plane take off with its wheels locked (WHEEL revolution speed = GROUND movement speed). PLANE speed can still exist. Think about it.

Even if the wheels have some friction, the treadmill's force on them will accelerate the wheels, not the airplane. The question is trying to force the answered to realize the difference in acceleration forces for a car and an airplane--

In a car, the acceleration force is applied to the ground so when a car engine applies that force to through the wheels to the ground, the car accelerates.

In an airplane, the acceleration force is applied to the air via the engine (jet or propeller). The wheels are devices to reduce the friction against the ground since gravity is holding the plane against the ground, creating friction.

This is why the question is not just a red herring. The question of how lift is generated is really irrelevant.

Ohio Rulz wrote:

yet the plane itself remaining in place. Can that plane still move forward enough to produce lift? I say yes.

The plane itself remains in place, yet it moves forward to produce lift? Make up your mind first, then decide if it flies.

Wording is the most important part of this little riddle.