would a plane take off if..

[MrRiplEy[H]]

The relative speed is not 0 because the myth stated 'opposite rotation'. The myth is based on the false assumption that the plane cannot move because the acceleration is done by turning the wheels like in a regular automobile and hence plane allegedly cannot move if wheel spin is exactly matched at all times (like going to measure the engine power in a dyno except this one doesn't resist at all) or imagine trying to run on wet glass-surface ice - you'll just flap around not moving anywhere.

But this is not a problem because a) The plane does not generate or need any thrust using the wheels b) The maximum wheelspin would be double the regular takeoff speed, hardly a problem. c) plane still moves on conveyor belt despite belt rolling in opposite direction in accelerating motion exactly matching aeroplane speed in reverse, remember if plane is not moving, neither is conveyor belt. All motion is generated as counter motion of the plane itself d) when enough airspeed is  reached the plane takes off normally.

Imagine having your car roll in a dyno that has zero resistance. You can spin the wheels all you want and it wont move since wheel speed is always matched in opposite. Push it with your hand gently and it will move despite of rotational speeds. Put 20 000lbs of thrust in it and it'll fly with no wings.

[RTHolmes]

err by "myth" I assume you're referring to the Mythbusters plane/conveyor belt problem. their assertion was "An airplane cannot take off from a runway which is moving backwards (like a treadmill) at a speed equal to its normal ground speed during takeoff."

although it looks similar at first glance, this problem is completely different.

[sluggish]

The relative speed is not 0 because the myth stated 'opposite rotation'. The myth is based on the false assumption that the plane cannot move because the acceleration is done by turning the wheels like in a regular automobile and hence plane allegedly cannot move if wheel spin is exactly matched at all times (like going to measure the engine power in a dyno except this one doesn't resist at all) or imagine trying to run on wet glass-surface ice - you'll just flap around not moving anywhere.

But this is not a problem because a) The plane does not generate or need any thrust using the wheels b) The maximum wheelspin would be regular takeoff speed, hardly a problem. c) plane still moves on conveyor belt despite belt rolling in opposite direction in accelerating motion exactly matching aeroplane speed in reverse, remember if plane is not moving, neither is conveyor belt. All motion is generated as counter motion of the plane itself d) when enough airspeed is  reached the plane takes off normally.

Imagine having your car roll in a dyno that has zero resistance. You can spin the wheels all you want and it wont move since wheel speed is always matched in opposite. Push it with your hand gently and it will move despite of rotational speeds. Put 20 000lbs of thrust in it and it'll fly with no wings.

the conveyor doesn't match the airplane's speed, it matches the wheel's speed.

I honestly think you guys are dismissing the premise because you think you've got it figured out.  but you don't.

[kotrenin]

The relative speed is not 0 because the myth stated 'opposite rotation'. The myth is based on the false assumption that the plane cannot move because the acceleration is done by turning the wheels like in a regular automobile and hence plane allegedly cannot move if wheel spin is exactly matched at all times (like going to measure the engine power in a dyno except this one doesn't resist at all) or imagine trying to run on wet glass-surface ice - you'll just flap around not moving anywhere.

But this is not a problem because a) The plane does not generate or need any thrust using the wheels b) The maximum wheelspin would be regular takeoff speed, hardly a problem. c) plane still moves on conveyor belt despite belt rolling in opposite direction in accelerating motion exactly matching aeroplane speed in reverse, remember if plane is not moving, neither is conveyor belt. All motion is generated as counter motion of the plane itself d) when enough airspeed is  reached the plane takes off normally.

Imagine having your car roll in a dyno that has zero resistance. You can spin the wheels all you want and it wont move since wheel speed is always matched in opposite. Push it with your hand gently and it will move despite of rotational speeds. Put 20 000lbs of thrust in it and it'll fly with no wings.

Wrong

imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.

Can the plane take off?

[MrRiplEy[H]]

the conveyor doesn't match the airplane's speed, it matches the wheel's speed.

I honestly think you guys are dismissing the premise because you think you've got it figured out.  but you don't.

The wheel turns only as fast as the aeroplane moves. The conveyor belt duplicates that movement in reverse.

I don't know, could it be then that the final wheel spin is takeoff speed to the second order (magnified by matching belt speed?) in which case the wheels woult bust apart before takeoff.

[RTHolmes]

nope, the wheels start with a rotational speed of 0 at rest, and continue with rotational speed 0 throughout the takeoff.

[MrRiplEy[H]]

nope, the wheels start with a rotational speed of 0 at rest, and continue with rotational speed 0 throughout the takeoff.

Lol if the belt rotates in the opposite direction how do you get rotational speed of 0? That would happen only if the rotation was happening in the same direction as plane moves.

[kotrenin]

someone mention that earlier.


No the conveyor belt acts like a break.  But instead of using friction like in a caliper brake or drum brake it acts like a wheel chock.  It is more like a hill or incline.

[MrRiplEy[H]]

someone mention that earlier.


No the conveyor belt acts like a break.  But instead of using friction like in a caliper brake or drum brake it acts like a wheel chock.  It is more like a hill or incline.

The way I see it any wheelspin is generated by the aircraft actually moving. Unless aircraft is not moving there is no wheelspin and hence no counter rotation.

The instant a/c moves, wheels start to turn and this is counteracted by treadmill. Result is speed x speed afaik so in the end takeoff speed would mean that wheels and the treadmill would spin at speed of takeoff speed to the second order (i.e. 140 knots x 140 knots = 19600 knots). At that speed the wheels would burst and friction from bearings etc. would be considerable but given enough thrust it should still make it.

[Oleg]

err by "myth" I assume you're referring to the Mythbusters plane/conveyor belt problem. their assertion was "An airplane cannot take off from a runway which is moving backwards (like a treadmill) at a speed equal to its normal ground speed during takeoff."

although it looks similar at first glance, this problem is completely different.

Not actually. It just set limit of speed with conveyor belt can move, but it doesnt change the fact what conveyor belt cannt prevent plane from moving forward.