My degree was in materials

0.7 would be something like leather on wood.

µ for greased hard steel on steel is more likely <0.1, and thats not taking any fancy bearing design elements into account, which get you down to three decimal places for a roller needle bearing and the like


Output of a commercial jet engine like a RR Trent is about 90k lb thrust or 400kN each. That should get the job done.

The jet engine is thrusting against the air, which is static. Once the wheels start to rotate the plane has nothing much to keep pushing it backwards, and will accelerate forwards as its being pushed forward by the force of the engine against the air.

Read the straight dope article, its a pretty good explanation.

It does! The backwards motion of the treadmill!

Nope, once the wheels start to spin, the treadmill is just acting to spin the wheels, not to move the plane. It will just spin the wheels at 200mph while the initial thrust of the engine pushing on th static air stops the plane going backwards and then starts to drive it forwards intil its doing whatever speed it needs to do to take off, at which point the wheels will be spinning at take off speed +200.

It depends what your frame of reference is. If it's relative to a fixed point on the treadmill belt then it will have a net velocity of 0. If it's relative to a fixed point in the air or on the treadmill frame, then it will be 100 mph. I assumed the former.

So by that logic if you are sitting in a car traveling the highway at 200kmh, you are actually doing zero..relative to where you are sitting, but the rest of the countryside is rushing by at breakneck speed.


I can just see you at the side of the road "Im sorry officer, your radar must be wrong. By my frame of reference I was barely moving"

Thats one thing that is surely not going to fly

I hate this thread. It's impossible to argue it sensibly with such a badly worded question.

Anyway, it doesn't matter because I'm right.

It's good fun though, Bazz.

I just thought about it another way… if the brakes were locked on, the plane will not move even with the engines at full thrust. Therefore the thrust alone is not enough to get the plane moving - the notion that thrust goes through the airframe and not the wheels is wrong. During a take-off, the commencement of forward motion is totally dependent on the rotation of the wheels, and their subsequent movement along the runway.

If the runway is counter-rotating, the wheels would not travel any distance, effectively being geo-static. And I think we all agree that IF the plane is geo-static, it cannot take off.



And another thought - is the treadmill rotating from nose-to-tail or from tail-to-nose?? It would seem that rotation nose-to-tail would allow the plane to take off in half the normal distance, whereas only tail-to-nose would keep the plane geo-static? The thrust of the aircraft would negated by the force of the treadmill trying to roll the wheels backward?

I think!

In that case how do the brakes work if all it takes is thrust from the engine to make it move forward? the wheels are an integral part of the plot.

The original premise was that … “The conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction”….. so, it doesn’t matter what is pushing against what - as the airframe tries to react to the engine thrust the treadmill also reacts balancing out the thrust so keeping the plane stationary.

I don’t want to think too much about “match the speed” as that in itself implies something is moving at a speed other than zero.

EXACTLY you were just ahead of me there - the wheels are the key

In this case, it's probably best not to.

Unfortunatly for you and Bazz the brakes are clearly stipulated as off.


The engine thrust acts on the air, which is (relatively) static, not the conveyer.

The wheels on an aircraft are not powered, they only move as a result of the fact that the plane is being pushed along by the thrust of the engines against the air. The motion makes the wheels move, not the other way around.

So, the plane is moving due to the thrust of the engine , which in turn makes the wheels move on the treadmill / runway, which in turn starts to moves in the opposite direction according to the hypothetical rules.

The treadmill can only act on the wheels of the plane which are in contact with it, right? So its acting on the wheels, making them rotate. But in the mean time the engines are still pushing the plane along, till it reaches take off speed.

Remember, the wheels of the plane do not drive it, they move only because the plane is moving, and the engines are still driving it forward. The motion of the conveyer simply makes the wheels go faster, but does not have any serious effect on the velocity of the aircraft itself.


Look at it the other way, say the converyer was moving in the same direction as the plane...the plane could do 200mph and take off, but the wheels would be totaly still. What the wheels do relative to the runway is totally unimportant, they have no influence on the speed of the plane one way or the other, they cant, because they are not powered.

Sigh. For about the hundredth time, the wheel rotation is a red herring. The treadmill is a red herring. Think about the forces. Start the engines, thrust is acting on the airframe. The airframe MUST react to that force, unless there is a force sufficient to counter it. With the brakes on, that force is friction. But in the ORIGINAL problem, THE BRAKES ARE OFF. THERE IS NO SIGNIFICANT FORCE OPPOSING THE THRUST. If the treadmill weren't there, the plane would roll out and take off normally. The ORIGINAL question: if there is a treadmill under the plane, can the plane still roll out and take off. YES IT CAN. The moving treadmill CANNOT OPPOSE THE THRUST FROM THE ENGINES. If the plane can roll out and take off from a stationary runway, it can do the same from a moving runway. A moving runway CANNOT prevent the thrust from moving the airframe.

Being geostatic is irrelevant. If the plane were AEROstatic it could not take off. Whether or not it is geostatic doesn't matter.

Egad...

Ok. The only thing I disagree with here Bill is when you say that being geostatic wouldn't matter. I presume by geostatic we're meaning maintaining a fixed position in relation to the earth. Short of having a headwind equal to the aircrafts take off speed, a geostatic plane wont take off because it isn't moving.
Anyway, the fact remains, as bill has being saying all along, that the plane wouldn't be geostatic. The plane is moving forward at 100kts compared to the earth, not in comparison with the treadmill. the treadmill is moving in the opposite direction at 100kts, compared to the earth (the same speed as the plane but in the opposite direction). The planes wheels are therefore rotating at 200kts. The fact remains that the plane is moving at 100kts in comparison with the earth and the static air over the earth, so it will take off.

I was thinking about flying a kite in a steady wind. I'm standing still and the kite is at the end of the string. Its ground speed is zero, but it's flying. It's flying because it has air speed. All the plane needs to lift into the air is air speed. The ground speed, wheel spin, bearing friction, and so on are red herrings. The engine's thrust will create air speed.