Question of the Week

Treadmill runway?

Sun, 27th Jan 2008

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Kian Pham, Australia asked:

A plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?


Tim Sabey, Pilot & Ex-physicist:
In order to take off, an aircraft must have sufficient vertical forces to counteract its weight. The major component of this upwards force is lift. Lift is generated by airflow over the wings creating a lower pressure distribution on the upper surface compared with the lower. This has the effect of deflecting air downwards as it passes over the wing. The equal and opposite reaction force of this is upwards and called lift. Lift is dependent on the aircraft speed so the aircraft must be at sufficient speed, typically 130-150kts for a commercial jet to take off. The second upwards force is the vertical component of the engine’s thrust as when the aircraft nose is pitched up part of the thrust vector will be vertical.

The aircraft will accelerate down the runway by its engines. These accelerate air backwards and again the equal and opposite reaction force on the plane is in the forwards direction, known as thrust. In the situation described there is a conveyor belt which automatically tracks the aircraft ground speed and moves at that speed but in the opposite direction. Since the aircraft is not accelerated by means of contact with the ground (like a car does) the only effect will be that the wheels spin faster so there is more friction. The aircraft will still be able to accelerate to a speed that produces enough lift to take off. This will increase the runway length required but given that is sufficient it will still be able to take off.

Diana: If a plane was to reach take-off speed from motorised wheels:

Terry Holloway, Marshall Cambridge, Group Support Executive:
In this particular instance the assumption is that the aeroplane is sitting on this mobile conveyor belt runway. As the aeroplane gains speed and goes forward so the conveyor goes backwards at an identical speed. Let us say hypothetically that this particular aeroplane that we’re talking about would normally take off at 100 miles per hour. When it reaches a forward speed of 100mph, in other words its wheels on the runway, the conveyor is going backwards at 100mph but the aeroplane’s speed through the air is zero. There’s no air flowing over the aerofoil section of the wing which produces the lift. Therefore the aeroplane won’t fly.


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The question is bad expressed. When you say "The plane moves in one direction" and "the conveyor moves in the opposite direction" you have to specify with respect to what they moves. If you mean that the plane moves with respect to the conveyor, which moves with respect to air, then the plane is stationary with respect to air, so it won't take off. lightarrow, Tue, 22nd Jan 2008

Won't the plane still move forward as the wheels aren't driven? Even if the conveyor moves, the wheels will be free to move and the plane will still go forward.

The wings need an airflow to provide lift.
turnipsock, Tue, 22nd Jan 2008

Imagine, for a moment, that there's no air resistance (It's OK, I will come back to that one).
Also imagne the wheels are perfect and have no friction at their bearings and are of negligible mass.

Leave the plane's engines off and start the conveyor. No force acts on the plane so it says still.
For what it's worth, set the conveyor going the other way and the plane will still stay still.
OK so, without friction or air resistance, the plane "doesn't know the conveyor is there" . If you fire up the engines, it will take off just the same as usual.
OK if there is some friction at the wheel bearings then the conveyor moving backwards (from the passengers' point of view) will tend to push the plane back.
If you could get the belt moving fast enough, this friction would drag the plane backwards just as hard as the engines push it forwards so the plane could be made to stand still. (until the wheel bearings overheated and melted).
OK, now lets put air resistance back into the quetion.
The only way to stop the plane taking off is to have the belt move backwards much faster than the plane usually moves forwards (the wheel bearings are not that bad, so it would take a lot of speed to provide as much force as the engines do). If you do that it will drag a lot of air along with it. This air will be dragged past the wings amd cause lift so the plane starts to rise. At that point the drag on the wheels is greatly reduced and the plane flys off anyway.

Unless anyone can show me a flaw in that I'm afraid you might have to talk amongst yourselves 'till the 27th.

Here are a couple of questions you might want to think about.
Can you stay upright riding a bicyle on a treadmill?
If so, why,
If not, why not?

And, more related to the original question.
Imagine you are in a plane- to give a nice concrete example let's say one of these
OK, you are about to take off, the engines are running at full pelt, the airstrip is level and, for the sake of this question, the air is at standard temperature and pressure (in effect the runway is at sea level), the plane is fully loaded and the runway is flat.

At the moment you take the brakes off to start moving, at what rate is power transfered from the engines to the plane to move it forward?

Bored chemist, Tue, 22nd Jan 2008

Same question last month in another forum:

iko, Tue, 22nd Jan 2008

If there is no friction between the plane an the runway then the runway can have no effect because it cannot impress a force on the plane, forwards or backwards. Wheel bearings are pretty good and, let's face it, would only have to work at twice their normal rate if the runway is running 'backwards'. Simplest, ideal case - no effect at all. The plane uses air being pushed backwards(reaction) to produce its thrust. If it tried to use driven wheels to aid its takeoff then the runway might have an effect. lyner, Wed, 23rd Jan 2008

The plane will not take off as all will be equal. (providing "take off" also means flying)

But, it don't say how the plane is powered, with jets or a prop?

If powered by props and they were big enough then the air flow from them over the wings may be enough to lift the plane. It still wont take off though as it will then be subject to stall speed and it will just drop down again.

that mad man, Thu, 24th Jan 2008

"But, it don't say how the plane is powered, with jets or a prop?"
I didn't say whether it was prop or jet driven (or rocket for that matter) because it makes no difference. The plane will take off as I explained earlier- the wheels are near frictionless so the plane simply doesn't know if the runway is moving or not.

As for "It still wont take off though as it will then be subject to stall speed and it will just drop down again."
How does that work? HOw does the plane know that it's just left a moving runway, rather than an ordinary one?
Since planes take off perfectly well from stationary runways and stay in the sky there's no reasone why a plane that takes off from a moving runway would not stay up. What's the difference? Bored chemist, Thu, 24th Jan 2008

If there were significant drag between the runway and the air I think you could see the runway pulling some air at low level back with it but the air higher up, unaffected by the runway, would be still wrt the ground and so the plane migt be able to take off by remaining stationary relative to a (very fast moving) runway because of the air flow it induced, but then rise above the level of the disturbed air, into the air that was still, and discover that it had suddenly "stopped" at which point it would fall back to earth.
It would have to be a very big treadmill... but my fluid dynamics isn't up to working out how big and therefore just how impossible it might or might not be. rosy, Thu, 24th Jan 2008

  The treadmill is irrelevant.  Aircraft fly because of air molecules moving over the wing. So airspeed is relevant, ground speed is irrelevant.  If bearning friction on the wheels is minimal even if the wheels locked up from overheated bearings it would still be possible to take off.  Given good bearings of for the sake of argument assuming (no friction in the bearings) there would be no real difference.  Dick Smith flew across Australia in a Hot air balloon.  There's a picture of him sitting on to of the fiber-glass gondola on a deck chair.  His ground speed was over 200mph (in the jet stream) but as the balloon was moving at the same speed 0 difference. 

There is an optical illusion that pilots flying low can get into that often causes accidents.  If they are flying around a tree (mustering cattle) on the ground then to fly a circle around the tree they have to turn much tighter going from downwind to upwind because the wind makes them drift if they maintain a constant circle relative to the wind.  This can cause them to stall as they bank and once sideways they use the elevator (pull back on the stick to increase the rate of turn) pull back too far and they stall and crash.  But as far as the air is concerned it doesn't know how fast the ground is, (until it hits it).  The aircraft only knows how fast it is going relative to the air so ground speed increases but airspeed is only relative to the aircraft. 

There would be a slight effect from the friction of the conveyor belts friction with the air causing it to drag some air with it this would be reduced as the aircraft got further away from the ground.  This is know as wind gradient and pilots have to take ground friction with wind into account but it's nothing you can't fix by adding a little more speed.

If you want to understand this a little better try drawing a circle on a piece of paper.  Now try drawing the same circle while moving the paper, look at the shape you've drawn. 

The other way to think about this is to imagine a boat chugging along at 10 knots in a 10 knot current.  With the current the boat speed relative to water is still 10 knots but relative to a nearby island it will be 20 knots.  If you go against the current your boats speed (relative to the water) is still 10 knots, but relative the island is now 0 knots.  Same with air and aircraft. Cameron Lapworth, Sat, 26th Jan 2008

"the plane migt be able to take off by remaining stationary relative to a (very fast moving) runway because of the air flow it induced, but then rise above the level of the disturbed air, into the air that was still, and discover that it had suddenly "stopped" at which point it would fall back to earth."
At the point where the plane leaves the moving runway it no longer has the friction pulling it back and the engines are pushing it forwards so it takes off just as a normal plane would. Bored chemist, Sat, 26th Jan 2008

    But it would have to be a very rough runway.  Wind gradient in flying is caused not only by grass, but trees, buildings etc.  And it can catch you unawares if you don't know about it.  Even though the aircraft is flying relative to the air and given any time in any given layer of slower air everything will equal out it's kinetic energy descending through the progressively slower air means an effective drop in airspeed.  As you land very close to stall this can tip the balance if you are not aware. But even in a 30mph wind the gradient may only need you to add another 5 to 10mph to your usual speed for still air.  And that's with trees grass and other stuff slowing the airmass close to the ground and friction from that airmass slowing the air above it with progressively lower effects I couldn't imagine a runway providing a huge effect here, but it'd be there all the same. 

In practice on take off you go through something similar as you leave ground effect.  The aircraft flies better a few feet above the ground (ground effect) then performance drops as you climb out.  You climb out (if you are a good pilot) at your aircrafts best L.D. lift to Drag ratio.  This is the speed that provides the most efficient compromise between the lift of the wing and the drag induced by whatever angle of attack you have.  With unlimited power you could fly a very high angles of attack close to stall and produce more lift but generally the best climb is achieved well below this as you just don't have the power to handle any more so that's your best L.D. this will be a fair bit over the stall speed so as you raised above the layer of air your climb rate would fall off momentarily as your airspeed dropped but as your prop speed in the now slower air would now be accelerating the aircraft you'd quickly catch up and climb out normally. Cameron Lapworth, Sun, 27th Jan 2008

Makes no difference as the wheels free wheel,the plane will move forward and take off as if it was on a normal runway.

The only thing the engines have to overcome is the standing weight of the aircraft , slight friction from the wheels and air once that is done the plane will move forward.

The conveyor could move backwards at a million times the speed of the forward motion of the plane if it liked and all the engines would need to do to hold the plane still and prevent it moving backwards with the conveyor is apply the same amount of thrust equivalent to the weight of the plane, which is a tiny fraction of what would be available from the engines.Once the thrust is increased beyond that point the plane will move forward,increase the thrust to take off values and it will move forward along the coveyor until it reached the required airspeed for take off to be achieved.
The only thing which will be affected by the conveyor moving will be the rotation speed of the wheels.

ukmicky, Sun, 27th Jan 2008

" couldn't imagine a runway providing a huge effect here, but it'd be there all the same.  "
If the runway was a belt running under the wheels fast enough that the (small) frictional force was equal to the thrust of the engines I think you would see an effect. My guess is the belt would have to be traveling well over the speed of sound. It would also need to be big enough to put the plane on so it would move a lot of air. It would be like the wind gradient in a tornado; a pretty big effect. Bored chemist, Sun, 27th Jan 2008

Agreed,  I was being nit-picky.  Aircraft fly from airspeed, ground speed is irrelevant unless you fly into it (tree, mountain etc). Cameron Lapworth, Mon, 28th Jan 2008

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