Right. My understanding is that the overspeed failures are mostly from centrifugal force, not heat. I was told this by a guy who flew the Concorde. He said you had to be quite careful to rotate and lift off the runway at the right speed, as there was often less than 10kts of safety margin for tire failure.
Bingo. I’m a member on the board where this question (to my knowledge) was originally posted, before the avweb guys caught wind of it. It is a pilot forum, flightinfo.com. Anyways, there are 2 types of people who read this question.
Person A reads it as: airplane moves forward at 5 knots (with reference to a stationary object), belt moves backward at 5 knots, wheels turn at ten knots. The airplane will take off shortly.
Person B reads it as: airplane begins to move forward (again, with reference to a stationary object), the belt speeds up to the point where friction from the wheel bearings equals the airplane’s thrust. Obviously, this is practically impossible, but if the belt is infinitely fast and the wheels and bearings are infinitely strong, the airplane goes NOWHERE.
The whole debate is confused because half of the people are talking speeds and the other half are talking forces. Seeing as how we are talking about a 200’ wide conveyer belt that is capable of infinite speed, I’m going to say that we can also have superwheels and superbearings, and as a result I take side with the force people.
Assuming no skidding, the belt does match the speed of the wheels.
More precisely, at the point of contact between a wheel and the surface of the treadmill, there is no relative motion between the wheel and the surface. That’s how wheels work.
To illustrate, take the treadmill out of the situation, and consider a wheel on normal pavement. If a car (or plane) is moving forward at 30 mph, then the linear velocity of the wheel at the point of contact is -30 mph (30 mph backwards) relative to the car. Relative to the ground, the linear velocity of the tire at the point of contact is zero (30 mph due to the forward motion of the auto minus 30 mph due to the rotation of the wheel, which is backwards relative to the car at the point of contact).
Note that the linear velocity of the top of the tire is 30 mph forward relative to the car, and as the car’s velocity is 30 mph, the linear velocity of the top of the tire is 60 mph forward relative to the ground.
True - but it doesn’t need to. It simply uses its engine to accelerate to a normal takeoff airspeed. The fact that the wheels are spinning unusually rapidly is, to a first approximation, irrelevant.
Here’s another way to explain why the plane will move and will take off.
Imagine the conveyer is designed, not just to meet, but to exceed the plane’s wheels’ speed. So even when the plane is standing still, the conveyer is moving.
(As has been mentioned, frictionless wheel mechanisms should be assumed here to stay within the spirit of the thought experiment.)
Will the conveyer’s movement cause the plane to go backwards when the plane’s engine is not providing thrust? No–the plane’s wheels will turn but the plane itself will stay in place.
This means the movement of the conveyer belt has no effect on the motion of the plane.
And nothing changes about this fact just because the engine starts up and provides forward thrust.
(BTW I started out thinking the plane would stay still but posts on this thread showed me otherwise.)
-FrL-
Person B’s interpretation does not match the problem as stated in the OP, though:
The problem as stated in the OP said nothing about an infinitely fast belt. It said that it exactly matched the speed of the wheels. And since real airplanes do not have to travel infinitely fast to take off, this seems like a silly interpretation of the problem.
In any event, I don’t get the impression that anyone in the discussion so far pictured the situation as depicted by Person B.
IMHO, it’s much more likely people are imagining how an automobile or a runner acts on a treadmill, which is not a valid comparison, as I noted previously.
First of all, propellor planes do not fly because they blow air over the wings. They work because the propellor accelerates air backwards, producing a reactive force forwards. Have you ever seen a plane with the propellor at the rear of the plane? How do you think those work?
I’m am sure that you are incorrect.
Why do you think there is no forward movement?
Why do you think that these two situations (a tether and the treadmill) are analogous?
What does this have to do with anything?
I think many posters are misunderstanding the OP and complicating the problem w/
such things as wheel failure.
I believe the basic hypothesis is that the forward thrust of the engine(s), whether prop
or jet, is being negated by the treadmill. I maintain that an aircraft, assuming no wind
factor, needs forward movement, provided by the engine(s) thrust, to create an
airflow over the wings, thereby providing the lift necessary for flight. If the aircraft
remains stationary, relative to the ground AND the ambient air, then no lift will be
created and no flight is possible.
My aircraft carrier analogy points out that the maximum thrust of the jet engines is
insufficient to create lift because the aircraft is prevented from forward movement by
the arresting cable.
Don’t we have any aeronautical engineers on the board?
It’s really cool. 
If there was no forward movement then you would certainly be correct, however there will be forward movement and so the plane can fly.
Again, you must keep in mind that because the rotation of the wheels is NOT what moves the plane around, the wheels can spin at any speed, totally independent of how fast the plane is moving with respect to the fixed earth.
The jet engine produces a certain amount of force which pushes the plane forward, and this force is completely unrelated to how fast the treadmill is spinning. That’s why I used the analogy of a cable pulling the plane forward rather than the exhaust “shoving” it forward, it’s a little easier to visualize.
Here’s a more familiar example to show why the wheels can spin at any speed you want, so long as they are not providing the force that moves the vehicle.
Get your roller blades (Perfect Physics rollerblades…no friction in the wheel bearings) and go over to the gym. Put on the skates and hop on a level treadmill. Turn on the treadmill.
No matter how fast the treadmill is spinning, you won’t go anywhere - the wheels spin at the same speed as the treadmill surface and you stay at 0mph with respect to the fixed floor.
In other words, it’s EXACTLY like you were standing on a smooth, frictionless surface. Play with the treadmill speed all that you want, it makes no difference, you don’t move. There is NO FORCE causing you to move backward. Set the treadmill to 1mph or 100mph, you don’t go anywhere, even though the skate wheels will be spinning like mad.
Now let’s apply some forward thrust. Your buddy comes up behind you, standing on the floor, and starts to shove you forward. You begin to move up the treadmill at exactly the speed he is pushing. If he pushes you at 1mph, you move at 1mph, even though you’ve got the treadmill moving at 100mph.
And that’s exactly what happens with the airplane on the conveyor belt - it’s just a plane on a frictionless runway. The jet engine provides thrust which causes forward motion regardless of how slippery the runway is. The wheels can revolve at 1mph, 100mph or 1000mph, it makes no difference at all.
I’d say that’s a correct statement.
This is the crux of your misunderstanding of the situation. The airplane is not attached to the treadmill! It has wheels which are free to spin.
In the ideal situation, there is no wheel bearing friction. If the treadmill starts up, in that case, the wheels turn, and the plane does not move. In the real situation, the plane does have to apply some thrust to remain stationary, and with a bit more thrust, it will start to move forward with respect to the ground.
This is why your comparisons to a tether or arresting wire don’t make sense.
Ahhhh.
My mistake was assuming that like a car, matching the wheel speed meant jet not moving. I see now that the jet can have forward movement and the wheels still match the belt speed.
Thanks, Frylock and robby
Airflow over the lift surfaces is all that matters for getting a plane to lift off.
If the treadmill is moving 600 mph backwards and the jet engines of the plane are producing enough thrust to move the plane 600 mph forwards you have a net speed of zero. This equals zero lift, and no chance to take off.
If it was otherwise aircraft carriers would have treadmills instead of catapults to assist with launching planes.
Now if you were to put a plane in a wind tunnel that could generate airflow equivalent to takeoff speed on an otherwise stationary plane, it would lift off.
It might help if you try to picture how exactly the treadmill supposedly counteracts the forward thrust of the engines.
If “appealing to authority” works for you, I’m an engineer (not aeronautical, though), and a former physics instructor. In my opinion, though, as a thought experiment, this is not an engineering problem. It’s a basic physics problem.
But the OP specified the treadmill will match the speed of the wheels, so the plane would be standing still no matter how fast the plane accellerated or decellerated.
I understand what you’re trying to get at, but to do that the plane would have to exceed the speed of the treadmill by its takeoff speed, or it would not generate enough lift to take off.
If not, please try and explain for this bozo who is just not getting this.
(Sigh.)
How exactly is a treadmill moving 600 mph backwards going to move the plane backwards at that speed? Especially since in the next sentence, you note that treadmills are not a particularly effective means of moving a plane?
The treadmill will turn the wheels. Period! Assuming no wheel bearing friction, this wheel motion does not exert a backwards force on the plane.
You folks need to draw a “free-body” diagram of the plane, and consider each of the forces acting on the plane.
Regardless of the treadmill’s velocity, what FORCE can it exert on a plane with wheels that are free to turn?
Okay, let’s turn it around a little bit, then. Assuming a perfectly frictionless bearing system, place the plane on the treadmill and start the treadmill going. Since it’s a perfectly frictionless bearing system, the plane doesn’t move.
Turn the treadmill up to eight billion miles an hour.
The plane doesn’t move.
Turn on the jet engines. They generate thrust.
The plane can’t go eight billion miles an hour, but something has changed. What has changed? The plane is generating thrust, so it starts to go forward, just as if the treadmill were turned off. Or going the other direction. Whether or not the plane moves forward or back has absolutely no connection to whether or not the treadmill is running.
Maybe this will help:
The speed of the plane with respect to ground is NOT the same as the speed of the wheels. If the plane needs 200 mph to take off (with respect to the ground), and the treadmill is going backwards at 200 mph, then the wheels have a linear speed of 400 mph.
If the plane needs 200 mph to take off (with respect to the ground), and the treadmill is going backwards at 1,000 mph, then the wheels have a linear speed of 1,200 mph.
If the plane needs 200 mph to take off (with respect to the ground), and the treadmill is going backwards at 1 mph, then the wheels have a linear speed of 201 mph.
That’s one possible interpretation of the OP.
But it’s not physically possible for the treadmill to do this job unless you presume the plane’s brakes are locked. If the wheels are free to act as wheels, they won’t allow the treadmill to exert anything like enough force to balance the thrust of the engine(s). Thus, the plane accelerates with respect to the air, gains flying speed, and takes off.
I don’t get this part. Why wouldn’t the plane move backwards. The earth is just a giant treadmill too and all planes go right along with it when they are “sitting still”.
Of course, if the treadmill was moving on earth then that would result in a serious tailwind and the plane with just flip over and not be able to take off.