would a plane take off if..

[vorticon]

where we're going, we don't need runways.

[1701E]

The wheels would always move in the opposite direction of the moving conveyor belt, at the speed of the conveyor belt, until the wheels had no more contact with the conveyor belt ... the wheels are "free wheeling" on their axle.

I was never good at anything above basic thinking, so I didn't expect to be right on all, or any accounts.

[eagl]

The rolling resistance on a free-wheeling axle would not become a factor soon enough to prevent eventual rotation.

The plane can't go "forward" through the air without the wheel rotating faster than the treadmill, but the premise is that the treadmill always matches the speed of the wheel rotation.  That is why the treadmill will accelerate essentially instantaneously to an extremely high speed.

Example.  The treadmill is stationary, and the plane moves forward at .5 mph, so the wheel is rotating at .5 mph faster than the treadmill.  The treadmill will begin to rotate at the same speed as the wheel.  Rotational drag goes up a bit, and the plane (assuming no further thrust increase) stops it's forward motion, but the wheel and treadmill are now both going at .5 mph.  Thrust is increased to whatever level is required to get the plane moving again, but once again, the treadmill instantly speeds up as fast as necessary to cause enough of an increase in rolling resistance to exactly counteract the engine's thrust, which brings the plane to a halt again.  If the plane is moving through the air, then by definition the wheel is rolling faster than the treadmill is turning, which can't happen according to the question.  So the treadmill will instantly accelerate to whatever speed is necessary to create enough rolling drag to exactly counteract the thrust, thereby keeping the plane stationary.

[eagl]

And that's where the mythbusters test went wrong...  They assumed that since the plane takes off at 60mph (or whatever), all they had to do was put the plane on a 60mph treadmill.  But for the plane to get to 60mph airspeed on a 60mph treadmill, the wheels would have to be rotating at 120mph!  Which can't happen in the original question.  The wheels always rotate at the treadmill speed plus the speed of the plane through the air.  Since the treadmill speed is always equal to the wheel speed, the airspeed must remain zero (assuming no wind).

Again, the only way this can be changed is if the wind created by the treadmill surface is enough to create enough wind over the wings to lift the plane off of the treadmill.  But the thickness of that wind is very very very thin over the moving surface, so I'm not sure enough wind would be produced by the time the rolling resistance equalled the max thrust of the engine.

If there was no rolling resistance, the treadmill would accelerate to an infinite speed due to a divide-by-zero condition.  Do the math...

[eagl]

X = tire rotation speed
Y = treadmill speed
Z = ground speed at takeoff

By definition, X = Y, since that is how the question is worded.  HOWEVER...

For the plane to take off, X must equal any hypothetical surface speed (the ground or a treadmill) plus the speed through the air required to get off the ground.

For a plane to take off, X = Y + Z, so Y would have to be some amount lower than X, violating the conditions of the test.  For X to continue to equal Y, ground speed at takeoff would have to be 0.  The only way for Z to be 0 at liftoff would be if there was some wind, but again the test condition specifically states that wind is zero.  The only way to create a wind condition is to move the treadmill fast enough for the surface effect to generate enough moving air over the treadmill surface to create enough lift over the wings for the plane to lift off.  I don't think you can get a treadmill moving fast enough to do that (for a human-sized aircraft), using current materials technology.  Obviously since hard drive read/write heads "fly" over the surface of the platter using this same effect, it could be possible on a small enough scale.

[eagl]

And oh by the way, HT posted basically the same conclusion the last time this came up   Assuming that it was possible to reproduce the conditions of the test (which isn't possible for a human sized aircraft), the plane can't fly and the very basic math formula I posted above proves it conclusively.  Add in other factors as I describe, and it maybe could be tested with a small enough plane where the forces involved aren't so strong that they exceed the strength of the treadmill, wheel, tire, and bearings.

[Vulcan]

So the treadmill will instantly accelerate to whatever speed is necessary to create enough rolling drag to exactly counteract the thrust, thereby keeping the plane stationary.

then the wheels will simply drag. There is no way the treadmill + wheel bit would be enough to overcome the thrust of an aircraft.

[SlapShot]

The plane that they used in the Ghost Busters had a take off speed of 60 mph ... Jamie could pull that tarp at 200 mph and that plane would still have taken off within it's designated rotation distance ... rolling resistance would have no effect.

The conveyor belt and the wheels have no direct influence on the thrust provided by the propeller ... there is no frictional drag that will stop the plane from moving forward.

Answer me this ... if what your saying is true, then the fact that Jamie was providing the concept of the conveyor belt (but not to your exact specifications) ... why did the plane take off in the exact distance it rotated when there was no conveyor belt ... you would have thought that Jamie's actions would have at least provided some sort of a disruption in it's normal rotation distance ... yet it didn't.

[eagl]

Another way to look at it...

Plane on treadmill that isn't moving, takes off.  At liftoff, it has 60 mph ground speed.  What was the tire rotation speed at liftoff?  60mph.  Easy huh?

Ok, now the treadmill is moving at 100,000mph.  The plane again takes off, at the same 60mph relative to the ground that the treadmill is sitting on.  How fast are the tires rotating at liftoff?  100,060 mph.  See?  For the plane to take off, the wheels have to be rotating faster than the surface they're sitting on.  No matter how fast you turn that treadmill, if the wheel is rotating exactly as fast as the treadmill is going, then the wheel moves... nowhere.  It just sits there.  If you try to drag it forward down the treadmill, you just made it turn faster than the treadmill.  But by the test condition, the treadmill will instantly accelerate to match the tire rotation speed, so you simply can't drag, push, whatever, the wheel down that treadmill because the treadmill will keep accelerating to an infinite speed if necessary, to keep you from making that tire rotate faster than the treadmill is going.  If rotational drag is zero (impossible), then the treadmill will instantly go to an infinite speed (impossible).

Therefore, the test can't be carried out on a human sized aircraft using current materials technology.  And if it could, the plane still couldn't budge an inch because the treadmill would keep increasing it's speed.

[eagl]

then the wheels will simply drag. There is no way the treadmill + wheel bit would be enough to overcome the thrust of an aircraft.

Nonsense.  You're not bothering to read the test condition.  The treadmill always exactly matches the tire speed.  The tire speed cannot exceed the treadmill speed.  If you say rolling resistance is negligible, then the treadmill simply keeps accelerating to an infinite speed, before the plane budges an inch, because that's how the test is set up.

The wheels cannot drag because the treadmill moves at the same speed as the wheel rotation.

I suppose you can cheat the test by locking the wheels and dragging them along the treadmill surface, but the test also assumes that the wheels can rotate.  If you say that the wheels being allowed to skid on the treadmill is an allowable deviation from the test conditions, then you might as well be asking if a plane on skids can take off from a treadmill rotating at an infinite speed (or from a normal surface), because now your engine must simply overcome the friction of the dragging wheels on the treadmill.

[eagl]

The plane that they used in the Ghost Busters had a take off speed of 60 mph ... Jamie could pull that tarp at 200 mph and that plane would still have taken off within it's designated rotation distance ... rolling resistance would have no effect.

The wheels would have been rotating at 260mph, which violates the test condition that the wheels rotate at the same speed as the treadmill.

The conveyor belt and the wheels have no direct influence on the thrust provided by the propeller ... there is no frictional drag that will stop the plane from moving forward.

The frictional drag will increase to infinity if you have infinite thrust, because the treadmill speed exactly matches the wheel speed.  The plane can not move unless the wheel speed is faster than the treadmill speed!  This is the point you are completely ignoring.  How can you explain the wheels moving faster than the treadmill, since that violates the test condition?  There is no explanation you can give for the plane moving an inch that does not require the wheel to rotate faster than the treadmill.  Name any condition where the plane takes off that does not involve skidding (you might as well put the plane on skis if that is allowable) and you will find that the wheels are moving faster than the treadmill.  Which is not allowable because the treadmill will always accelerate to keep the speeds the same.

Answer me this ... if what your saying is true, then the fact that Jamie was providing the concept of the conveyor belt (but not to your exact specifications) ... why did the plane take off in the exact distance it rotated when there was no conveyor belt ... you would have thought that Jamie's actions would have at least provided some sort of a disruption in it's normal rotation distance ... yet it didn't.

Because the treadmill in the test was moving at maybe 60mph, the plane took off at 60mph, so the wheels were turning at only 120mph.  Rolling resistance is significant at that speed (probably around a hundred pounds of force) but it wouldn't show up in their test conditions because that's still a fraction of the engine thrust.  Move the treadmill at, say, 100,000 mph, and the wheels would have to spin at 100,060 mph...  That would be a massive amount of rolling resistance, and it STILL violates the test conditions which state that the wheels can't rotate faster than the treadmill.

[trax1]

The plane that they used in the Ghost Busters had a take off speed of 60 mph

I don't remember that scene.

[Sombra]

http://www.straightdope.com/columns/read/2638/an-airplane-taxies-in-one-direction-on-a-moving-conveyor-belt-going-the-opposite-direction-can-the-plane-take-off

As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed.   Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

[SlapShot]

X = tire rotation speed
Y = treadmill speed
Z = ground speed at takeoff

By definition, X = Y, since that is how the question is worded.  HOWEVER...

For the plane to take off, X must equal any hypothetical surface speed (the ground or a treadmill) plus the speed through the air required to get off the ground.

For a plane to take off, X = Y + Z, so Y would have to be some amount lower than X, violating the conditions of the test.  For X to continue to equal Y, ground speed at takeoff would have to be 0.  The only way for Z to be 0 at liftoff would be if there was some wind, but again the test condition specifically states that wind is zero.  The only way to create a wind condition is to move the treadmill fast enough for the surface effect to generate enough moving air over the treadmill surface to create enough lift over the wings for the plane to lift off.  I don't think you can get a treadmill moving fast enough to do that (for a human-sized aircraft), using current materials technology.  Obviously since hard drive read/write heads "fly" over the surface of the platter using this same effect, it could be possible on a small enough scale.

You have got to be kidding me ... you're gonna create your own formula to prove your theory.

Wheel rotation (X) and treadmill speed (Y) are disconnected from ground speed at takeoff (Z) because X is free-wheeling. The wheels on a plane have nothing to do with take off speed ... they only make it easier to reach takeoff speed because they are ... free-wheeling. Put skids on a 747 instead of wheels ... it will take off but it will take a hell of a lot more runway than it would need if it had wheels.

It's more like ...

X = thrust
W = wheels speed (which are free-wheeling)
Y = conveyor belt speed
Z = distance needed to travel to obtain ground speed at takeoff

X - (W-Y) = Z

When you take off in a plane, is your ground speed measured by how fast your wheels are rotating on the runway ? or is it how fast you are being thrusted forward ?

How is that Bush planes are able to rotate off bog marshes with skids ... imagine that ... they have no wheels.

[vorticon]

i'm probably completely off base here but...seems to me...
to stop the plane going forward, the conveyor belt would need to be moving in a way that counteracts the thrust of the engines...regardless of what the wheels are doing. which, i believe, would require going massively faster, not matching  what the wheels or plane itself is doing. but it is possible.

eagls looks fine if the belt is matching the wheels rotational speed...and what the mythbusters did is correct, if the belt matches the wheels forward speed.