Brain Teaser

[TheOneKEA]

"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).

The question is:

Will the plane take off or not? Will it be able to run up and take off?"

[maurits]

The plane will take off.

A plane doesn't push itself forward relative to the ground (like cars, trains, bikes etc. do) but it pushes against the air to get forward movement. The plane will still move forward (and eventually up) although the conveyor belt underneath it will reach insane speeds.

This is by the way the same reason a plane prefers to take off with a headwind, it's not groundspeed that's important but airspeed. With a headwind you get the speed of the wind as a free gift.

[TheOneKEA]

Agreed. Having read the forum thread I found the teaser in, I also thought that the plane would take off as well.

The only thing I can't figure out is how much faster than normal the plane would have to go in order to get sufficient lift.

[maurits]

theonekea said:

The only thing I can't figure out is how much faster than normal the plane would have to go in order to get sufficient lift.

No faster at all. Speed relative to the ground is irrelevant. The conveyor belt makes the groundspeed 'zero' but since only speed relative to the air is important it won't make a difference. The speed a plane has to reach to get lift is entirely dependent on wind speed.

Taxiing on the conveyor belt may be impossible though because I believe there is some sort of pushing by the wheels involved in that. I had the infamous 15 minutes taxiing to Amsterdam's fifth runway last night and it sounds as if there is a small extra motor involved.

The only question I still have is what speed the conveyor belt will reach.

A helicopter would have no trouble, nor would a Harrier.

However, assuming the "ground" upon which the plane is standing is always moving in exactly the opposite direction to the plane and at exactly the same speed then a conventional fixed wing aircraft will make nil airspeed and will not be able to achieve lift so will not take off.

[Phil]

Brilliant question!!

The answer is: the conveyor belt is irrelevant.

As stated above it is airspeed that matters. Assuming zero headwind this is equal to groundspeed. But the plane is not driving itself along the ground by (tyre) friction - it is thrust against the air. So assuming the wheels are totally free to rotate the plane will take off in the normal way.

I like that one !!

[tubeprune]

If the plane wheels are turning only because it is being driven forward by its engines, and the conveyor belt is responding equally in reverse to the wheel rotation, the aircraft will remain fixed relative to the ground. It will receive no lift because it isn't moving through the air so it will stay on the ground. There won't be much air getting into the engines either.

[DrJimi]

Exactly. The only thing this will accomplish is to wear out the tyres. There is zero relative wind over the wings. Try flying with a tailwind equivalent to your groundspeed. You will fly exactly the way a brick doesn't.

[Oracle]

In theory of the headwind was equal to the take-off speed required the 'plane will take off provided there is enough air flow into the engines. A Fiesler Storch has high-lift anti-stall devices and thus can actually hover in the air relative to ground because its stall speed is less than wind speed, and if wind speed was say 40 mph then it will hover. My late fatherin law actualy did one better than tghat once in an RAF Chipmunk and flew backwards, as wind speed was so strong that as stall speeds was exceeded, the 'plane flew and the speed was high enough to beat the prop thrust! An observer would see the 'plane fly backwards!

Oh! If a 'plane could actually temporarily lift off from the conveyor, the lack of resistance from the tyres would enable it to hop in the air, and then engine thrust would enable forward speed to increase airflow over and under the wings.

[maurits]

tubeprune said:

If the plane wheels are turning only because it is being driven forward by its engines, and the conveyor belt is responding equally in reverse to the wheel rotation, the aircraft will remain fixed relative to the ground.

No, it will still move forward because it is irrelevant what the conveyor belt does, as long as the wheels can turn. The wheels will turn twice as fast though, the plane moves forward and the belt backwards.

It will receive no lift because it isn't moving through the air so it will stay on the ground. There won't be much air getting into the engines either.

Since the plane will move forward just like it would on a regular runway it will gain speed and eventually lift.

[TheOneKEA]

maurits said:

No, it will still move forward because it is irrelevant what the conveyor belt does, as long as the wheels can turn. The wheels will turn twice as fast though, the plane moves forward and the belt backwards.

Exactly! That's why I want to know how much faster the plane would have to go in order to get sufficient traction to begin moving air over its wings.

[Oracle]

It all depends on wind speed and direction. It depends on the plane as well: whether it has high-lift devices or not. The nearest analogy I can think of is the old WW2 aircraft carriers, before catapults. The ship would turn into wind, and would try and achieve say 35 mph wind over the deck say, which was basically the carrier's speed + wind speed. Planes would then virtually fly themselves off the deck with little forward speed. A forward speed over just 10 mph say may be sufficient to launch a plane off the conveyor. Of course an Autogyro, an aircraft with a rotary wing powered by the wind, can take off virtually straight away with just a few mph forward speed as the pilot manually turns the rotors, and even a small push from the rear prop will get it airborne.

Actually on reflection, an aircraft could in fact take off without even moving! If there is sufficient wind speed, as experienced in hurricanes or storm cells, then the wings will lift even though the plane is stationery. If however the plane is on the conveyor, and there is nil wind or less than 4 knots, something I have only experienced one in a Piper PA28, then it ain't going anywhere! It is stalled on the ground. That's what you aim to achieve when landing, rounding out at the height of a double-decker bus, throttle back, and controlling descent with the stick. The air cushioned under the wings acts in the wing-in-ground-effect and the plane then stalls on the ground: if not the plane will bounce!

theonekea said:

That's why I want to know how much faster the plane would have to go in order to get sufficient traction to begin moving air over its wings.

Aircraft don't have traction. The wheels are only there to allow a plane to roll along the ground (In some parts of the world, aircraft have floats or skis for operating from water or snow.) Movement is the result of the jet thrust or airscrew acting on the atmosphere.

Hence an aircraft needs air moving backwards (relatively) over the wings to acquire and maintain flight. This is the principle a kite uses to fly.

Thus the "conveyor belt" moving in the opposite direction will prevent the aircraft from moving forward and create an airflow over the wings.

maurits said:

Since the plane will move forward just like it would on a regular runway it will gain speed and eventually lift.

If the belt is matching the a/c's speed(but in the oppposite direction) how will that happen?

[Oracle]

My closing thoughts are well they were but I have risen to a challenge!:

a) There will always have to be a time delay between the aircraft speed increasing through thrust, propellor wash or air flow and the belt speeding up to comenstae. This means that it would be theoretically possible to move forward for a limited period of time. This might be sufficient to take off.
b) Even if the aircraft is stationary relative to ground, if windspeed can be increased it will take off if the lift component is sufficient. It is thus irrelevant if the aircraft is for all intents and purposes not advancing.

As I said before, this analogy does happen in the real world, when forward speed is matched or exceeded by wind or air speed. It is the air flow above and below the wing and the pressure differential that matters. That differential provides lift, or in the reverse direction, groundforce as in a racing car's airofoils. If a powerful fan was put in front of the ensemble, sufficient air flow could be induced to cause the 'plane to lift off. The same would apply if we had to use as I mentioned before an aircraft carrier, or even a fast-moving road vehicle [that has been done..to take off and land]. It's the wind or air speed over the wings that determines whether it can take off or not.