Airplane on a conveyer belt problem.
September 3rd, 2010 at 8:46:00 PM
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An airplane is standing on a huge conveyor belt runway. A controller moves the conveyor belt at the same speed of the airplane, but in the opposite direction. Can the airplane ever take off?
No cheating by looking up the answer, please.
No cheating by looking up the answer, please.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 3rd, 2010 at 9:13:56 PM
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Am I crazy? [as if talking to tin men isn't enough evidence]. What wind is passing over the wing to create lift?Quote: WizardAn airplane is standing on a huge conveyor belt runway. A controller moves the conveyor belt at the same speed of the airplane, but in the opposite direction. Can the airplane ever take off?
No cheating by looking up the answer, please.
That asked, the answer is yes, if there is a steady head wind caused by a Kansas tornado of the appropriate velocity.
Now, how does a rocket propel itself in space if there is nothing for the exhaust to push against?
--Dorothy
"Who would have thought a good little girl like you could destroy my beautiful wickedness!"
September 3rd, 2010 at 9:16:13 PM
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Mike, are you saying that the airplane is being moved by the runway instead of its own power?
When I think about the answer, I think about aircraft carriers which effectively launch the planes of the deck of the carrier using the cables. So, I think the answer is yes. The runway would need to move at the necessary velocity, the plane's engines would have to be full throttle, and the flaps would need to be in the position to provide the necessary lift. The runway would also have to run in the direction against the wind to assist in takeoff. We would also assume that the landing gear would be fixed (otherwise the runway would simply move the wheels and the plane would stand still or go much slower than the runway).
When I think about the answer, I think about aircraft carriers which effectively launch the planes of the deck of the carrier using the cables. So, I think the answer is yes. The runway would need to move at the necessary velocity, the plane's engines would have to be full throttle, and the flaps would need to be in the position to provide the necessary lift. The runway would also have to run in the direction against the wind to assist in takeoff. We would also assume that the landing gear would be fixed (otherwise the runway would simply move the wheels and the plane would stand still or go much slower than the runway).
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September 3rd, 2010 at 9:29:15 PM
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The Mythbusters managed to get a small airplane airborne that way.
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September 3rd, 2010 at 9:44:36 PM
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First, assume no wind at all.
Second, let's assume the runway runs north to south. The airplane is at the south end, facing north. The conveyor on the runway moves north to south. The speed of the conveyor is adjusted to exactly match that of the plane. So if anything the plane is fighting against the conveyor, as opposed to the conveyor propelling the airplane. It is a normal plane that is powered by a propeller or jet engines.
Second, let's assume the runway runs north to south. The airplane is at the south end, facing north. The conveyor on the runway moves north to south. The speed of the conveyor is adjusted to exactly match that of the plane. So if anything the plane is fighting against the conveyor, as opposed to the conveyor propelling the airplane. It is a normal plane that is powered by a propeller or jet engines.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 3rd, 2010 at 10:06:33 PM
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Quote: WizardFirst, assume no wind at all.
Second, let's assume the runway runs north to south. The airplane is at the south end, facing north. The conveyor on the runway moves north to south. The speed of the conveyor is adjusted to exactly match that of the plane. So if anything the plane is fighting against the conveyor, as opposed to the conveyor propelling the airplane. It is a normal plane that is powered by a propeller or jet engines.
You said that the conveyer belt "is adjusted to the speed of the plane". Does that mean, CONTINUALLY adjusted? It has the ability to negate whatever speed the aircraft achieves, and thus keep it effectively stationary? If THAT is the case, then no, the plane will not become airborne---but the conveyer belt would have to be moving several hundred miles an hour.
The problem is perhaps obfuscated by having the subject vehicle be an aircraft. You could equally ask the question, could a race car on a conveyor belt ever reach 120 MPH if the conveyor was moving backwards as fast as the car could go? The answer would seem to be no.
There are also some factors coming into play re coefficient of friction of the aircraft's tires, but I don't want to know how to calculate that. If the coefficient was near-zero (like on ice), then the conveyor belt's speed would hardly matter at all.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
September 3rd, 2010 at 10:46:29 PM
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Quote: mkl654321You said that the conveyer belt "is adjusted to the speed of the plane". Does that mean, CONTINUALLY adjusted?
Yes.
Quote: mkl654321It has the ability to negate whatever speed the aircraft achieves, and thus keep it effectively stationary? If THAT is the case, then no, the plane will not become airborne---but the conveyer belt would have to be moving several hundred miles an hour.
I didn't say the conveyor can negate the plane's speed. That is more like the question than the information given. Yes, the conveyor can move several hundred miles per hour.
Quote: mkl654321The problem is perhaps obfuscated by having the subject vehicle be an aircraft. You could equally ask the question, could a race car on a conveyor belt ever reach 120 MPH if the conveyor was moving backwards as fast as the car could go? The answer would seem to be no.
Are you sure the answer is the same for a car and airplane?
Quote: mkl654321There are also some factors coming into play re coefficient of friction of the aircraft's tires, but I don't want to know how to calculate that. If the coefficient was near-zero (like on ice), then the conveyor belt's speed would hardly matter at all.
You can ignore those factors.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 3rd, 2010 at 11:02:01 PM
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The Mythbusters did experiment with this riddle and although it was a scale model airplane on a moving runway being pulled by an ATV (or some such vehicle) the plane took off... as you would expect it should.
The wheels don't provide the forward thrust for the airplane. The wheels are used to reduce friction as the plane moves forward with thrust provided by its engine - either propellers or jet engine propulsion. To compare this to a car moving forward is apples and oranges... the car's engine provides power to the wheels so if the road moved backward at the same speed the car was being pushed forward by its wheels, to the observer the car would not be moving forward at all. The plane's engine simply pushes the airplane forward by pushing against the air surrounding it and unless someone can show how the surrounding air is somehow attached to the conveyor belt (which they obviously cannot because it obviously isn't) then the means of propulsion causing forward movement is not affected or impeded by the backward-moving conveyor belt. The plane will move forward as fast as it normally would and as usual the air moving over the curved wing creates lift and... voila, the plane lifts off.
Think of it another way if it helps... you are sitting in a soap box racer on a conveyor belt. There is a long piston behind you that will push you forward at 5mph. As it pushes you forward the conveyor belt moves in the opposite direction at 5mph. It is not reasonable to think that the little racer will stop moving forward or even slow down at all as the wheels will simply move (revolve) twice as fast but that piston behind you will keep on pushing you at a constant 5mph. Now, put wings on the car, speed the piston up to 200mph or so and regardless of that conveyor belt beneath you moving at 200mph in the opposite direction, you're airborne... followed quickly by a horrendous crash due to your poor aerodynamics.
The wheels don't provide the forward thrust for the airplane. The wheels are used to reduce friction as the plane moves forward with thrust provided by its engine - either propellers or jet engine propulsion. To compare this to a car moving forward is apples and oranges... the car's engine provides power to the wheels so if the road moved backward at the same speed the car was being pushed forward by its wheels, to the observer the car would not be moving forward at all. The plane's engine simply pushes the airplane forward by pushing against the air surrounding it and unless someone can show how the surrounding air is somehow attached to the conveyor belt (which they obviously cannot because it obviously isn't) then the means of propulsion causing forward movement is not affected or impeded by the backward-moving conveyor belt. The plane will move forward as fast as it normally would and as usual the air moving over the curved wing creates lift and... voila, the plane lifts off.
Think of it another way if it helps... you are sitting in a soap box racer on a conveyor belt. There is a long piston behind you that will push you forward at 5mph. As it pushes you forward the conveyor belt moves in the opposite direction at 5mph. It is not reasonable to think that the little racer will stop moving forward or even slow down at all as the wheels will simply move (revolve) twice as fast but that piston behind you will keep on pushing you at a constant 5mph. Now, put wings on the car, speed the piston up to 200mph or so and regardless of that conveyor belt beneath you moving at 200mph in the opposite direction, you're airborne... followed quickly by a horrendous crash due to your poor aerodynamics.
Happiness is underrated
September 4th, 2010 at 12:06:32 AM
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Quote: WizardYes.
I didn't say the conveyor can negate the plane's speed. That is more like the question than the information given. Yes, the conveyor can move several hundred miles per hour.
Are you sure the answer is the same for a car and airplane?
You can ignore those factors.
I was trying to see the question in terms of ground speed, since the essential question is, can the plane reach takeoff velocity? And this would be realtive velocity, as in relative to the air. In theory, a plane sitting still, but facing directly into a, say, 140 MPH wind, would be able to lift off from that alone.
Then another poster on this thread made me see what was wrong with my thinking. The aircraft does not DRIVE the wheels on the landing gear. The wheels only serve to lessen friction as the aircraft tries to accelerate. The conveyor belt wouldn't add any additional friction (versus a stationary runway), so it is actually immaterial whether it is moving or not. In fact, the opposite-moving conveyor exerts a force on the tires that has the same vector as the force the aircraft engines are trying to impart to the entire assemblage, so the conveyor may actually SHORTEN takeoff distance. Gotta try this sometime.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
September 4th, 2010 at 12:52:50 AM
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As I recall the Mythbusters thought it wouldn't take off, but it did. They also thought 2 cars in a head-on collision, both going 50mph, had the same impact force of a car going 100mph hitting a stationary wall. They proved that the 2 50mph cars had the same force of hitting a wall going 50mph, much to their chagrin. I think our friend Issac Newton comes into play here, again.
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September 4th, 2010 at 2:15:57 AM
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If I understand this correctly, no wind would be moving over the wings if the conv. belt goes the same speed as the airplane. Thus it never goes airborne.
the mythbusters must have been doing a separate experiment
the mythbusters must have been doing a separate experiment
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell! She is, after all, stone deaf. ... Arnold Snyder
September 4th, 2010 at 2:48:00 AM
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>Am I crazy?
I don't know, but probably not. If people say you are crazy, you are probably simply perceived as being happier than they are or leading a life of greater scope and daring of which they are envious and therefore accuse you of being crazy.
>as if talking to tin men isn't enough evidence
Talking to tinkers or any other type of metal smith is not evidence that is in any way relevant to your mental state.
>What wind is passing over the wing to create lift?
Yes. You are quite correct. Relative wind is what counts. The plane could even be moving backwards on that conveyor belt but still get airborne if the wind moving over its wing was sufficient.
>the answer is yes, if there is a steady head wind caused by a Kansas tornado of the appropriate velocity.
No. A tornado is a vortex, its winds would be highly variable in speed and direction. It might flip the airplane or blow it laterally but it would be unlikely to offer an opportunity for controlled flight since there would be no laminar flow over the surface of the airfoil. Indeed, a vortex would be similar to a helicopter's turbulent downwash pinning a fixed wing aircraft on the ground during a take-off roll.
Think of all the thousands of deaths that took place in the Island Hopping Campaign in the Pacific Ocean during World War Two. All that time and effort and expense to obtain sufficiently long runways sufficiently close to the Japanese home islands. What nonsense. They had very long runways in Alaska! Glaciers and other surfaces existed once you add to the "runway" length the vertical distance that a plane would "fall". A long glacier provided insufficient distance for an actual take off, but the high speed taxi off the edge of the glacier followed by the high altitude "fall" meant that the bomber would be flying before it crashed into the ground. The sole factor was wind speed over the wings. Nothing else. Can't convince pentagon paper pushers of that though!!
>how does a rocket propel itself in space if there is nothing for the exhaust to push against?
A rocket or jet engine gets its thrust from the expulsion of the generated gases, not from those gases pushing against anything. Except for any air needed for the combustion of the fuel, a rocket or jet would be even more efficient if there were no air there to provide resistance to its forward motion.
I don't know, but probably not. If people say you are crazy, you are probably simply perceived as being happier than they are or leading a life of greater scope and daring of which they are envious and therefore accuse you of being crazy.
>as if talking to tin men isn't enough evidence
Talking to tinkers or any other type of metal smith is not evidence that is in any way relevant to your mental state.
>What wind is passing over the wing to create lift?
Yes. You are quite correct. Relative wind is what counts. The plane could even be moving backwards on that conveyor belt but still get airborne if the wind moving over its wing was sufficient.
>the answer is yes, if there is a steady head wind caused by a Kansas tornado of the appropriate velocity.
No. A tornado is a vortex, its winds would be highly variable in speed and direction. It might flip the airplane or blow it laterally but it would be unlikely to offer an opportunity for controlled flight since there would be no laminar flow over the surface of the airfoil. Indeed, a vortex would be similar to a helicopter's turbulent downwash pinning a fixed wing aircraft on the ground during a take-off roll.
Think of all the thousands of deaths that took place in the Island Hopping Campaign in the Pacific Ocean during World War Two. All that time and effort and expense to obtain sufficiently long runways sufficiently close to the Japanese home islands. What nonsense. They had very long runways in Alaska! Glaciers and other surfaces existed once you add to the "runway" length the vertical distance that a plane would "fall". A long glacier provided insufficient distance for an actual take off, but the high speed taxi off the edge of the glacier followed by the high altitude "fall" meant that the bomber would be flying before it crashed into the ground. The sole factor was wind speed over the wings. Nothing else. Can't convince pentagon paper pushers of that though!!
>how does a rocket propel itself in space if there is nothing for the exhaust to push against?
A rocket or jet engine gets its thrust from the expulsion of the generated gases, not from those gases pushing against anything. Except for any air needed for the combustion of the fuel, a rocket or jet would be even more efficient if there were no air there to provide resistance to its forward motion.
September 4th, 2010 at 5:17:11 AM
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I must be slow this morning -- I'm still not sure what the question is asking. It seems to me that the wording "moves the conveyor belt at the same speed of the airplane" implies that the airplane is actually moving rather than standing still (or that the belt is standing still too). If the plane reaches 100 mph, then the belt is going 100 mph in the other direction for a 200 mph relative speed. But who cares and why? The important thing for aerodynamic lift is the relative speed between the airplane and the air. Since the Wizard confirmed that there is no wind, the plane-air relative speed is whatever the speed of the plane is. There should be no more problem with takeoff than in any other takeoff. But this answer is so simple that I'm still not certain I have understood the question.
Apparently I view this variant of the question differently, mkl. The conveyor is not "moving backwards as fast as the car could go." It is moving backward as fast as the car is actually going. In order for the car to reach 120 mph, the engine and drive train would need to operate in a manner equivalent to driving 240 mph. That's 240 mph relative to the belt, with the car going 120 mph forward and the belt going 120 mph toward the rear. I think some race cars may have 240 mph capability, though they are not generally operated in that manner.Quote: mkl654321The problem is perhaps obfuscated by having the subject vehicle be an aircraft. You could equally ask the question, could a race car on a conveyor belt ever reach 120 MPH if the conveyor was moving backwards as fast as the car could go? The answer would seem to be no.
September 4th, 2010 at 5:29:21 AM
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Oh jeez.
Of course it takes off. the engines are working against the air, not the belt. The wheels spin twice as fast to make up the difference.
Next.
Of course it takes off. the engines are working against the air, not the belt. The wheels spin twice as fast to make up the difference.
Next.
A falling knife has no handle.
September 4th, 2010 at 5:30:16 AM
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You've opened a can of worms here, Wizard. This problem was discussed on another board that I frequent, and the debate lasted several thousand posts. Many could not accept the correct answer, but eventually got tired of arguing.
September 4th, 2010 at 5:31:06 AM
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Quote: MoscaOh jeez.
Of course it takes off. the engines are working against the air, not the belt. The wheels spin twice as fast to make up the difference.
Next.
Correct and concise. Nicely done.
September 4th, 2010 at 6:13:19 AM
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Quote: FleaStiffA rocket or jet engine gets its thrust from the expulsion of the generated gases, not from those gases pushing against anything.
Every action produces an equal but opposite reaction. It's not just a good idea, it's the law. And in physics you can't break the law. A rocket's exhaust pushes against the rocket's combustion chamber. That's why a rocket is a reaction drive.
Quote:Except for any air needed for the combustion of the fuel, a rocket or jet would be even more efficient if there were no air there to provide resistance to its forward motion.
Rockets don't need air, they carry an oxidizer which is mixed with fuel. The shuttle's external tank is made up of two tanks. One carries liquid hydrogen, which is the fuel, the other carries liquid oxygen (LOX) which is the oxidizer. Solid boosters incorporate oxidizer and fuel, except for hybrid boosters which use a liquid oxidizer on solid fuel. Spaceship One and Spaceship Two use a hybrid rocket engine.
From time to time you may hear about "air-breathing" rockets. They've been around for a long time, but are better known as turbo-jet engines.
And yes, rockets work bets in a vacuum because there is neither air resistance nor drag to slow it down.
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September 4th, 2010 at 6:53:57 AM
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I totally agree with the logic presented here.Quote: MoscaOh jeez.
Of course it takes off. the engines are working against the air, not the belt. The wheels spin twice as fast to make up the difference.
Next.
However the reality is, the wheels or the belt will malfunction due to excessive friction before the plane takes off. The plane may end up taking off with damaged wheels. It might be 'kiss your ass goodbye' time on landing....
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September 4th, 2010 at 7:30:54 AM
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I believe there may be 2 answers to the problem, depending on whether the airplane in question is propellor-powered, or jet-powered.
In the case of a propellor-driven aircraft, the lift is caused by air being pushed backwards from the propellor blades, over the wings, creating lift. So, it doesn't matter if the plane is moving forward with respect to the ground or not (though, in common experience, it generally is), if the propellor is turning, air is being pushed backwards, and the plane can take off.
In the case of a jet-powered aircraft, the jet engines are behind the plane, pushing the plane forward through the air to create lift. In this case, presumably, the conveyor belt would prevent the plane from moving forward (though, I'll admit, I'm not positive of this point), and therefore, no lift, so no takeoff.
In the case of a propellor-driven aircraft, the lift is caused by air being pushed backwards from the propellor blades, over the wings, creating lift. So, it doesn't matter if the plane is moving forward with respect to the ground or not (though, in common experience, it generally is), if the propellor is turning, air is being pushed backwards, and the plane can take off.
In the case of a jet-powered aircraft, the jet engines are behind the plane, pushing the plane forward through the air to create lift. In this case, presumably, the conveyor belt would prevent the plane from moving forward (though, I'll admit, I'm not positive of this point), and therefore, no lift, so no takeoff.
September 4th, 2010 at 7:36:19 AM
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You lose on both points. The air exhausted by the propellers is negligible for lift. How would you explain airplane designs with propellers mounted aft of the wings? For the jet (and for the propeller craft), the belt does not prevent the plane from moving forward -- how could it possibly hold back the plane unless the wheel brakes are applied?Quote: CapnDaveI believe there may be 2 answers to the problem, depending on whether the airplane in question is propellor-powered, or jet-powered.
In the case of a propellor-driven aircraft, the lift is caused by air being pushed backwards from the propellor blades, over the wings, creating lift. So, it doesn't matter if the plane is moving forward with respect to the ground or not (though, in common experience, it generally is), if the propellor is turning, air is being pushed backwards, and the plane can take off.
In the case of a jet-powered aircraft, the jet engines are behind the plane, pushing the plane forward through the air to create lift. In this case, presumably, the conveyor belt would prevent the plane from moving forward (though, I'll admit, I'm not positive of this point), and therefore, no lift, so no takeoff.
September 4th, 2010 at 8:03:01 AM
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The movement with respect to the ground and conveyor ought to be disregarded, as that has nothing to do with lift.
Lift is a function of air moving over the wings. There were some experimental early jet designs that blew bleed air off the engines over the wings for additional lift. Anyway, a small plane with a forward-mounted propeller may push enough air over the wings fast enough to take off even if it remains motionless relative to the ground. Think a light, one man plane above the ultralight stage. Something heavier like a WWII fighter wouldn't. A plane with a pusher prop may not get off the ground on a treadmill.
I'd say then it depends on the type of plane, i.e. weight, means of propulsion, etc. The Mythbusters succeeded using a very light plane with a tractor prop.
Lift is a function of air moving over the wings. There were some experimental early jet designs that blew bleed air off the engines over the wings for additional lift. Anyway, a small plane with a forward-mounted propeller may push enough air over the wings fast enough to take off even if it remains motionless relative to the ground. Think a light, one man plane above the ultralight stage. Something heavier like a WWII fighter wouldn't. A plane with a pusher prop may not get off the ground on a treadmill.
I'd say then it depends on the type of plane, i.e. weight, means of propulsion, etc. The Mythbusters succeeded using a very light plane with a tractor prop.
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September 4th, 2010 at 9:08:39 AM
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Quote: CapnDaveI believe there may be 2 answers to the problem, depending on whether the airplane in question is propellor-powered, or jet-powered.
In the case of a propellor-driven aircraft, the lift is caused by air being pushed backwards from the propellor blades, over the wings, creating lift. So, it doesn't matter if the plane is moving forward with respect to the ground or not (though, in common experience, it generally is), if the propellor is turning, air is being pushed backwards, and the plane can take off.
In the case of a jet-powered aircraft, the jet engines are behind the plane, pushing the plane forward through the air to create lift. In this case, presumably, the conveyor belt would prevent the plane from moving forward (though, I'll admit, I'm not positive of this point), and therefore, no lift, so no takeoff.
No. The only difference would be if the plane were air driven (jet or prop) or ground driven (wheel, but then it wouldn't be an airplane, it would be a car).
A falling knife has no handle.
September 4th, 2010 at 9:12:13 AM
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Quote: NareedSomething heavier like a WWII fighter wouldn't. A plane with a pusher prop may not get off the ground on a treadmill.
I'd say then it depends on the type of plane, i.e. weight, means of propulsion, etc. The Mythbusters succeeded using a very light plane with a tractor prop.
Wrong. All that matters is what the force is acting against. Pushers and WW2 prop planes would both fly in this hypothetical experiment.
A falling knife has no handle.
September 4th, 2010 at 9:15:46 AM
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Quote: odiousgambitIf I understand this correctly, no wind would be moving over the wings if the conv. belt goes the same speed as the airplane. Thus it never goes airborne.
the mythbusters must have been doing a separate experiment
Correct, in that you do not understand this correctly. Instead of a treadmill and wheels, imagine water and pontoons. Or stationary ground (ice) and skids (which do not rotate). Planes still fly out of those conditions.
A falling knife has no handle.
September 4th, 2010 at 11:07:06 AM
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First: I know the plane will takeoff. I've seen the experiment, I've understood the physics.
My post: I like the notion that the conveyor belt moving in the opposite direction could actually shorten the takeoff distance (relative to stationary ground). That could be practical for aircraft carriers and other tiny runways. I'm just not sure the effect is strong enough to make a material difference. Comments?
It would be really neat if it also worked on landing, so that if you landed an airplane on a conveyor belt going the opposite direction, it would shorten the landing distance.
My post: I like the notion that the conveyor belt moving in the opposite direction could actually shorten the takeoff distance (relative to stationary ground). That could be practical for aircraft carriers and other tiny runways. I'm just not sure the effect is strong enough to make a material difference. Comments?
It would be really neat if it also worked on landing, so that if you landed an airplane on a conveyor belt going the opposite direction, it would shorten the landing distance.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
September 4th, 2010 at 11:07:31 AM
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What if the system started out with the plane's engine merely idling, and the conveyor already moving it backwards?
Then it would simply be a matter of getting the engines thrust up so that the conveyor doesn't send the plane off the end of the runway. As long as you overcome the inertia, then the plane WILL move forward and eventually take off.
But, as I said before, in a real world scenario, the conveyor and/or the landing gear will probably malfunction due to excessive friction before takeoff is achieved.....
Then it would simply be a matter of getting the engines thrust up so that the conveyor doesn't send the plane off the end of the runway. As long as you overcome the inertia, then the plane WILL move forward and eventually take off.
But, as I said before, in a real world scenario, the conveyor and/or the landing gear will probably malfunction due to excessive friction before takeoff is achieved.....
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September 4th, 2010 at 11:17:46 AM
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As a practical matter -- if the conveyor belt moved sufficiently fast and the plane required a sufficiently long runway, the tires would overheat and the wheel bearings would fail before take-off. There would surely be a practical threshold beyond which this would be infeasible.Quote: dwheatleyI like the notion that the conveyor belt moving in the opposite direction could actually shorten the takeoff distance (relative to stationary ground). That could be practical for aircraft carriers and other tiny runways. I'm just not sure the effect is strong enough to make a material difference. Comments?
We wanted to try a similar thing with balloons here in Kansas -- but there were no vertical conveyor belts.
--Dorothy
"Who would have thought a good little girl like you could destroy my beautiful wickedness!"
September 4th, 2010 at 12:18:54 PM
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Quote: DJTeddyBearWhat if the system started out with the plane's engine merely idling, and the conveyor already moving it backwards?
Then it would simply be a matter of getting the engines thrust up so that the conveyor doesn't send the plane off the end of the runway...
Is that what would happen? Maybe the conveyor would just make the wheels rotate, but the plane would stay in place. It would seem that less energy would be required to rotate the wheels than move the whole plane. As always, someone correct me if I'm wrong.
Quote: DorothyGaleAs a practical matter -- if the conveyor belt moved sufficiently fast and the plane required a sufficiently long runway, the tires would overheat and the wheel bearings would fail before take-off. There would surely be a practical threshold beyond which this would be infeasible.
I contend that if this were actually attempted, then the wheels could handle it. At some point, yes, they would overheat, but I don't think it would come to that. For one thing, don't planes travel much faster upon landing than just before takeoff? That should go to show the wheels are pretty sturdy.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 4th, 2010 at 12:26:24 PM
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From Answers.com:Quote: WizardI contend that if this were actually attempted, then the wheels could handle it. At some point, yes, they would overheat, but I don't think it would come to that. For one thing, don't planes travel much faster upon landing than just before takeoff? That should go to show the wheels are pretty sturdy.
For an average-sized commercial jetliner with typical fuel and payload, the "takeoff speed" is around 130-140 knots, or about 155 miles per hour. The landing speed is more or less the same, usually a few knots slower. This is the average takeoff speed for a Boeing 737-series aircraft.
I think that you will start having structural problems, but I am just guessing. Maybe an engineer can chime in here ... or we can make a small wager ... some honor maybe?
--Dorothy
"Who would have thought a good little girl like you could destroy my beautiful wickedness!"
September 4th, 2010 at 12:52:23 PM
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No, Wizard, if there were any friction in the wheel/axle, the plane would move backward. The conveyor would be putting an unbalanced backward force on the plane, even if the wheel turned fairly freely (a real-world wheel/axle), giving an acceleration toward the rear of the plane. Part of the energy provided by the belt to the tire would go into increasing rotational kinetic energy of the wheel/axle, part into translational kinetic energy of the plane, and part into thermal energy due to friction. (This assumes no thrust from the plane's propulsion system.)Quote: WizardIs that what would happen? Maybe the conveyor would just make the wheels rotate, but the plane would stay in place. It would seem that less energy would be required to rotate the wheels than move the whole plane. As always, someone correct me if I'm wrong.
Edit: Even if there were no friction at all in the wheel/axle, the plane would accelerate backward. This assumes that the wheel has mass and moment of inertia, so that there must be some tangential force between the belt and the tire to rotate the wheel. This force is an unbalanced rearward force on the plane (with no thrust), so the plane accelerates backward even with a theoretical frictionless wheel assembly.
I think I agree with you about the wheels handling this. In fact, in the situation of the original problem, as the plane gains velocity with respect to the air, lift forces begin. The load on the wheels is reduced, even before liftoff, so there is less friction than some people have been assuming in this thread.Quote: WizardI contend that if this were actually attempted, then the wheels could handle it. At some point, yes, they would overheat, but I don't think it would come to that. For one thing, don't planes travel much faster upon landing than just before takeoff? That should go to show the wheels are pretty sturdy.
September 4th, 2010 at 1:02:41 PM
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The answer is, the wheels don't drive the plane, the prop does. As long as the wheels aren't locked and can spin, the plane will take off.
"It's not called gambling if the math is on your side."
September 4th, 2010 at 2:01:32 PM
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Yes. The last few posts have not addressed the original question but instead ensued from DJTeddyBear's post saying, "What if the system started out with the plane's engine merely idling, and the conveyor already moving it backwards?", followed by the Wizard's comments.Quote: EvenBobThe answer is, the wheels don't drive the plane, the prop does. As long as the wheels aren't locked and can spin, the plane will take off.
September 4th, 2010 at 8:27:06 PM
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Quote: WizardAn airplane is standing on a huge conveyor belt runway. A controller moves the conveyor belt at the same speed of the airplane, but in the opposite direction. Can the airplane ever take off?
No cheating by looking up the answer, please.
Although others seem certain the plane would quickly move off the conveyor and take off, I am not so sure.
Planes fly because of air moving around their wings. If the conveyor prevents the plane from rolling through the relatively still air, where does the lift come from? Think about a child holding his hand out of a car window on the highway. The car moving his hand through the relatively still air makes it possible for him to "fly" his hand up and down. Now imagine the same car (or plane) on the conveyor. If the child were to hold his hand out of the window, there would be no air moving to push his hand. Same with the plane, it would not get off the conveyor since it would not be moving through the still air.
Simplicity is the ultimate sophistication - Leonardo da Vinci
September 4th, 2010 at 8:30:53 PM
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This is kinda similar (or the opposite, depending on your point of view), of the old Knight Rider gimmick where he drove the car up a ramp hanging of the back of a moving truck.
The MythBusters tried this, both in scale, and full size. When the car hits the ramp, the wheels skid briefly, but the inertia keeps the car moving at the same speed. (Or it handled exactly as the driver expected.)
Here's the 5 minute MythBusters clip: http://www.youtube.com/v/uV292LPLz6U
The MythBusters tried this, both in scale, and full size. When the car hits the ramp, the wheels skid briefly, but the inertia keeps the car moving at the same speed. (Or it handled exactly as the driver expected.)
Here's the 5 minute MythBusters clip: http://www.youtube.com/v/uV292LPLz6U
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Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
September 4th, 2010 at 8:35:23 PM
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Your premise is based on a very big 'IF'.Quote: AyecarumbaIf the conveyor prevents the plane from rolling...
The reality is, the conveyor will do nothing but make the wheels spin faster.
Your car premise is correct, but that's only because a car gets it's thrust thru it's wheels.
I invented a few casino games. Info:
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Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
September 5th, 2010 at 2:34:04 PM
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Quote: WizardAn airplane is standing on a huge conveyor belt runway. A controller moves the conveyor belt at the same speed of the airplane, but in the opposite direction. Can the airplane ever take off?
Literally, no. You said the airplane is "standing", which means the controller moves the belt at speed = 0. A plane just sitting there doesn't take off.
However, I think your premise is whether an airplane can start on a conveyor belt which negates its speed relative to the ground. To put it in clearer perspective, imagine that instead of the conveyor belt, the plane's tail was chained to a building. If the plane remains stationary relative to the ground, but the air speed *over the wings* is sufficient to produce lift, then the plane "takes off" -- by definition. In other words, does the plane achieve sufficient "air speed" to take off, even though its "ground speed" is zero? I'm not sure whether airplane propulsion systems can produce sufficient air speed over the wings of a plane if the plane is not moving, but if so, yes, the plane will lift off the ground.
Instead of a conveyor belt, think of a wind tunnel. A plane is bolted to a platform (it's not going anywhere) and a giant fan blows over the wings. The platform can measure the lift force generated by the wind speed. If the fan blows hard enough, the lift force is enough to overcome the weight of the plane. (This is actually why wind tunnels were invented.) If the plane itself can generate the same force as the fan, the lift force should be the same.
The problem with the conveyor belt statement is that it introduces issues like whether the plane can "overcome" the belt and start moving forward.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
September 5th, 2010 at 2:42:51 PM
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Maybe I asked the problem badly, but I meant that the plane starts out standing still, but doesn't necessarily stay that way. The pilot starts to give the plane gas and tries to take off normally. Can he succeed?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 5th, 2010 at 3:31:34 PM
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Ofcourse, all he has to do is have air moving over the wing at a high enough speed. Nothing else counts. A wing flys because of the air it actually encounters, not theoretical air or foreseeable air. If the airplane is being moved forward by the conveyor, its the same as if its being moved backwards by the conveyor or standing still. Its air flow over the lifting and control surfaces. Thats it! Nothing else counts. Spectators can watch the airplane moving forward or back or standing still. The wing does not pay attention to the spectator's field of vision. The wing pays attention to the air flowing over it.Quote: WizardThe pilot starts to give the plane gas and tries to take off normally. Can he succeed?
Now I don't know of many pilots who would want to fly from a conveyor belt and I don't know of many conveyor belts that would reliably support the weight of an airliner much less move it at a high rate of speed or withstand the various blasts of air that are involved, but whether its a real world situation or a theoretical situation: its air flow over the wing! Nothing else.
The plane can be standing still in relation to the observer or the plane can be going backwards in relation to the observer, its still one and only one thing that concerns the wing. The sum of those air molecules. Blow enough air from a great big fan and the plane can take off while moving backwards at a high rate of speed. I won't be a passenger at the time. Only an experimental test pilot would do this sort of thing, not just an ordinary test pilot, but it could be done.
September 5th, 2010 at 4:35:56 PM
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Quote: WizardMaybe I asked the problem badly, but I meant that the plane starts out standing still, but doesn't necessarily stay that way. The pilot starts to give the plane gas and tries to take off normally. Can he succeed?
Doesn't necessarily stay that way how? If the purpose of the conveyor belt is to ensure that the plane stays still relative to the ground, then the only way the plane takes off is if it can generate enough air speed past the wings to cause lift.
Go to the beach and watch seagulls hovering in the headwind. Same concept, just that if there's no wind in the environment, the plane itself has to cause it.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
September 5th, 2010 at 5:11:25 PM
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Quote: MathExtremistIf the purpose of the conveyor belt is to ensure that the plane stays still relative to the ground, then the only way the plane takes off is if it can generate enough air speed past the wings to cause lift.
I never said that was the purpose. Maybe that is not what would happen.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 5th, 2010 at 6:48:59 PM
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Quote: WizardI never said that was the purpose. Maybe that is not what would happen.
I guess that's why I'm struggling with the notion of "A controller moves the conveyor belt at the same speed of the airplane, but in the opposite direction". If that doesn't mean "to ensure the plane stays still relative to the ground" then I'm not sure what it would mean. If there's no conveyor belt at all, the plane gains velocity over time as it taxis and eventually hits takeoff speed (again, based on air speed past the wings). If the conveyor belt is perfectly effective at slowing the plane down (relative to ground) but the air speed past the wings is still sufficient to cause lift, then you'll still get lift without taxiing. The same is true if the plane is tethered to something really heavy behind it. The difference between a tether and the conveyor is that at some point, assuming the plane's propeller can create enough wind to produce lift, the conveyor belt will cease to have any effect at all. The practical effect would be to have the plane slowly rise vertically from the conveyor belt and then take off forward. But again, this assumes the plane can self-generate lift when not moving forward. I don't know if any plane can do that, but I'd suppose it's possible.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
September 5th, 2010 at 7:48:36 PM
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Quote: MathExtremistI guess that's why I'm struggling with the notion of "A controller moves the conveyor belt at the same speed of the airplane, but in the opposite direction". If that doesn't mean "to ensure the plane stays still relative to the ground" then I'm not sure what it would mean.
The problem doesn't specify what the conveyor is meant to accomplish. You seem to be thinking of the airplane like a car. Maybe an airplane would be different. Other posts have already addressed this.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 5th, 2010 at 8:53:29 PM
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Aha. I've figured out what is happening with this "conundrum". Wiz, you earlier deflected my comment about coefficient of friction of the wheels on the conveyer belt surface. But this MUST be considered when addressing the problem.
The force that must be overcome before the wheels can start to move is static friction. This friction, in the case of a tire on a runway, has a high coefficient. You did not specify the material that the conveyor was made of, but let's assume it has a similarly high coefficient. In the case of the aircraft moving forward, or in the case of the conveyor making the aircraft move backward, the lateral force that must overcome static friction, before anything moves, in other words, is the same.
Let's set aside our disbelief about whether a conveyor belt exists that has enough driven power to move the aircraft backwards to negate the forward movement impelled by the thrust of tha aircraft's engines--that is a stated condition of the problem. The aircraft benefits from the bearings in the wheels translating the static friction into kinetic friction, then rolling friction: the friction that must be overcome is gradually turned from the greater to the lesser form(s). By contrast, the conveyer only transforms the static friction on the conveyor-tire contact to kinetic friction; it does not benefit from the bearings in the wheels, because it is not connected to them.
Therefore, I conclude that the conveyor CANNOT move the plane back as quickly as the plane can move itself forward. The plane will therefore be able to move forward, and will be able to lift off.
Again, I wonder if this system might actually shorten takeoff distance.
The force that must be overcome before the wheels can start to move is static friction. This friction, in the case of a tire on a runway, has a high coefficient. You did not specify the material that the conveyor was made of, but let's assume it has a similarly high coefficient. In the case of the aircraft moving forward, or in the case of the conveyor making the aircraft move backward, the lateral force that must overcome static friction, before anything moves, in other words, is the same.
Let's set aside our disbelief about whether a conveyor belt exists that has enough driven power to move the aircraft backwards to negate the forward movement impelled by the thrust of tha aircraft's engines--that is a stated condition of the problem. The aircraft benefits from the bearings in the wheels translating the static friction into kinetic friction, then rolling friction: the friction that must be overcome is gradually turned from the greater to the lesser form(s). By contrast, the conveyer only transforms the static friction on the conveyor-tire contact to kinetic friction; it does not benefit from the bearings in the wheels, because it is not connected to them.
Therefore, I conclude that the conveyor CANNOT move the plane back as quickly as the plane can move itself forward. The plane will therefore be able to move forward, and will be able to lift off.
Again, I wonder if this system might actually shorten takeoff distance.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
September 6th, 2010 at 5:23:21 AM
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Why do you think small planes are tied down when parked at an airport? They ain't moving forward, but wind moving over the wing surface can still generate lift! That is ALL that counts.Quote: MathExtremistBut again, this assumes the plane can self-generate lift when not moving forward. I don't know if any plane can do that, but I'd suppose it's possible.
September 6th, 2010 at 8:52:32 AM
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Quote: FleaStiffWhy do you think small planes are tied down when parked at an airport? They ain't moving forward, but wind moving over the wing surface can still generate lift! That is ALL that counts.
Right, but I think the OP stated "no wind". By that, I assumed no environmental wind. I also assumed that the conveyor belt kept the plane from moving forward while it was on the belt, though recent posts by Wizard have left some doubt in my mind as to that. Regardless, the only way a plane takes off with no wind and without moving forward is if the engines can push/pull enough air over the wings to generate lift. Like I said, I don't know of any planes designed to do that, but I don't see why it couldn't happen.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
September 6th, 2010 at 12:10:06 PM
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Nope. Only air of a specific speed can create enough lift. The speed is relative to the ground, not relative to the speed of the conveyor - unless the conveyor creates air turbulence (which is doubtful).Quote: mkl654321Again, I wonder if this system might actually shorten takeoff distance.
Jets create exhaust which is translated into thrust and forward motion. It does not create wind over the wings.
Prop planes DO create wind which does go over the wings, but the volume of that wind, compared to the total volume of wind required for lift over the entire wingspan is minimal. The props primarily create forward motion which creates acceleration. The acceleration eventually creates enough forward speed to get the required volume of air to pass over the wings to create enough lift for takeoff.
Only a head wind can cause lift. Any other sort of wind, at high enough velocity, can cause the plane to tilt and/or move around, and possibly hit other planes or roll over. THAT'S why small planes are tied down.Quote: FleaStiffWhy do you think small planes are tied down when parked at an airport? They ain't moving forward, but wind moving over the wing surface can still generate lift! That is ALL that counts.
FYI: Yeah, I realize that tilt is a sideways version of lift....
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Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
September 6th, 2010 at 12:51:02 PM
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Quote: DJTeddyBearNope. Only air of a specific speed can create enough lift. The speed is relative to the ground, not relative to the speed of the conveyor - unless the conveyor creates air turbulence (which is doubtful).
I know about the aerodynamics of lift. If the plane is moving relative to the ground, and the air is still, then the net effect will be that of forward motion through the air at that speed. In this case it is irrelevant whether the plane or the air itself is moving---only the sum of their two movement vectors matters.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
September 6th, 2010 at 1:50:50 PM
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Understood. Maybe I should have said that the air speed is relative to the wing...Quote: mkl654321I know about the aerodynamics of lift. If the plane is moving relative to the ground, and the air is still, then the net effect will be that of forward motion through the air at that speed. In this case it is irrelevant whether the plane or the air itself is moving---only the sum of their two movement vectors matters.Quote: DJTeddyBearNope. Only air of a specific speed can create enough lift. The speed is relative to the ground, not relative to the speed of the conveyor - unless the conveyor creates air turbulence (which is doubtful).
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
