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12/06/2006 01:35:45 PM · #51 |
Originally posted by Raziel:
Originally posted by LoudDog:
Yes it will.
The plane moves relative to the air, not the ground. Thus the planes wheels will just turn a lot faster. |
As the plane is on a treadmill it is stationary with respect to the ground. If you assume no wind, the air is stationary relative to the ground. Since the difference in air pressure over the top and the bottom of the wing is what generates lift, if no air is moving over and under the wings there will be no lift and hence the plane cannot take off. |
Seems I'm a bit tired today and not thinking properly. When a plane takes off the force from the engines is applied directly to the air "pulling" it through the air. Unlike a car it doesn't rely on applying torgue to the wheels to get it up to speed. The plane will take off. It will also move off of the treadmill. The moving treadmill will just cause the wheels to spin faster than they would normally, assuming the increased speed doesn't cause any problems, the treadmill will not impede the take off at all. |
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12/06/2006 01:43:02 PM · #52 |
Originally posted by legalbeagle:
An interesting problem:
A plane equipped with fixed horizontal engines and wheel landing gear is placed on a huge treadmill runway. The treadmill has a clever design and always matches the speed of the plane, but runs in the opposite direction. Will the plane take off and fly or not?
Any takers? |
There are a couple of key phrases in here that need to be understood. As others point out, the treadmill always matches the speed of the plane, but in the opposite direction. The other on is fixed horizontal engines.
This is similar to an engineering test problem I had in college. The engines only produce horizontal thrust. The airplane lifts off the ground (takeoff) because of the air passing over its wings (Bernoulli's effect) which creates a vertical force (which we call lift).
Assuming the treadmill doesn't affect the air (ie it doesn't cause wind) the air over the wings will not move, so there will be no lift. Since there is no force on the wings, the airplane will not takeoff any more than a truck would. The wings create lift, and "hold the plane up". You can see this force in action-- when a plane is at rest on the ground, the wingtips are lower than they are when the plane is flying.
If you took the wings off the plane, and kept the engines horizontal (assume they are on the tail section) you could use the engines to move the plane as fast as you wanted, the wheels would spin as fast as they could, but the plane wouldn't take off.
If the airplane were in a wind tunnel with no treadmill, and a strong enough wind were created, then the airplane would "take off" even though its wheels were not moving and its engines were off. In this situation, a plane with no engines (i.e. a glider) would take off.
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12/06/2006 01:44:00 PM · #53 |
remove the airplane
put a car on instead ..
would a car fly ? ... nope ... |
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12/06/2006 01:47:28 PM · #54 |
Originally posted by Raziel:
The moving treadmill will just cause the wheels to spin faster than they would normally, assuming the increased speed doesn't cause any problems, the treadmill will not impede the take off at all. |
Yes, but every time the wheels are about to move forward, the treadmill matches that acceleration by speeding up.
Thrust applies forward force to the plane, which normally would translate into acceleration. However, in this case the treadmill is matching that acceleration. The wheels speed up, the treadmill speeds up... Does it reach a point where the force of the thrust is used up trying to overcome the friction of the wheels?
i.e. the acceleration matching effect and friction quickly become significant to the point where the plane might as well be glued to the runway. |
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12/06/2006 01:55:21 PM · #55 |
Originally posted by jhonan:
The wheels speed up, the treadmill speeds up... Does it reach a point where the force of the thrust is used up trying to overcome the friction of the wheels?
i.e. the acceleration matching effect and friction quickly become significant to the point where the plane might as well be glued to the runway. |
Imagine that the plane travels at an airspeed of 100mph forwards. The runway would be travelling at 100mph backwards. The wheels would be spinning at 200mph, the difference between the airspeed and the groundspeed. As the plane speeds up, the reverse groundspeed also increases. However, this does not impede the plane's acceleration and take off - only the speed of the wheels turning (assuming the wheels could take it, and ignoring the slight decrease in efficiency that you would tend to see in the wheel bearings at higher speeds).
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12/06/2006 01:56:39 PM · #56 |
Originally posted by ralph:
remove the airplane
put a car on instead ..
would a car fly ? ... nope ... |
Would you ever expect the car to fly?
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12/06/2006 01:58:20 PM · #57 |
Originally posted by jhonan:
Originally posted by Raziel:
The moving treadmill will just cause the wheels to spin faster than they would normally, assuming the increased speed doesn't cause any problems, the treadmill will not impede the take off at all. |
Yes, but every time the wheels are about to move forward, the treadmill matches that acceleration by speeding up.
Thrust applies forward force to the plane, which normally would translate into acceleration. However, in this case the treadmill is matching that acceleration. The wheels speed up, the treadmill speeds up... Does it reach a point where the force of the thrust is used up trying to overcome the friction of the wheels?
i.e. the acceleration matching effect and friction quickly become significant to the point where the plane might as well be glued to the runway. |
Your assessment would be correct if the thrust were applied to the runway/treadmill, as is the case with a car, but with a plane the engine thrust is pushing against the air.
The wheels on the plane will simply turn twice as fast on the treadmill as they would on a normal runway. |
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12/06/2006 02:03:10 PM · #58 |
Originally posted by legalbeagle:
Imagine that the plane travels at an airspeed of 100mph forwards. The runway would be travelling at 100mph backwards. The wheels would be spinning at 200mph, the difference between the airspeed and the groundspeed. |
My argument is that the plane never reaches *any* speed relative to the air. It remains stationary. The thrust applied is not enough to overcome the friction created by the wheels/treadmill.
If I attach a rope to an ice-skater and start pulling them towards me, but at the same time the ice rink they're standing on starts moving backwards at a very high speed. The friction between the skater and the rink increases dramatically. If I try to apply more force to the rope, the rink accelerates even more to match me, increasing the friction. So I never manage to move the ice skater forwards.
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12/06/2006 02:05:18 PM · #59 |
Originally posted by jhonan:
My argument is that the plane never reaches *any* speed relative to the air. It remains stationary. The thrust applied is not enough to overcome the friction created by the wheels/treadmill. |
I'm sure in a world where we could create such a treadmill we have the technology to design frictionless wheels...
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12/06/2006 02:11:02 PM · #60 |
| The airplane is already on a treadmill of sorts. THE EARTH. |
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12/06/2006 02:11:31 PM · #61 |
Originally posted by DrAchoo:
Originally posted by jhonan:
My argument is that the plane never reaches *any* speed relative to the air. It remains stationary. The thrust applied is not enough to overcome the friction created by the wheels/treadmill. |
I'm sure in a world where we could create such a treadmill we have the technology to design frictionless wheels... |
But is the problem supposed to use 'real world' physics? Because if you're allowing frictionless wheels, then I'm allowing a faster-than-light treadmill. ;-) |
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12/06/2006 02:12:14 PM · #62 |
I agree with those that state the plane will fly. I disagree with any statement that the plane will fly even if the plane does not move forward relative to the ground (I think I read that a couple times).
It is an interesting problem - and I think one that is confused by the way other vehicles, like cars, are propelled. I considered a vehicle at rest on a frictionless surface (a hypothetical zero friction ice surface). With a car, no matter how hard you hit the accelerator, the wheels would simply spin and the car would not go anywhere. This is because a car's engine is coupled to the wheels and relies on friction between the wheels and road for propulsion. The engine drives the wheels which grab the road to move the car. There is no other force component moving the car forward (at least nothing of significance).
A plane's engines, however, are not coupled to its wheels. With a plane, the thrust created moves the entire plane forward - the wheels turn due to friction with the runway, but the engine is not directly powering the wheels. So, even on a frictionless surface where the plane's wheels would simply slide helplessly along and would not even spin, a plane's engines will generate thrust that will move the plane along the frictionless surface thereby providing the air flow over the wings and resulting lift.
So, in the question posed, the plane will move relative to both the ground and the treadmill as a result of the engine thrust - the wheels will spin faster than they otherwise would, but the thrust will move the plane forward relative to the ground - that is how the plane sees sufficient air flow over its wings to generate the lift needed for take-off.
I typed more than I intended - does any of it make sense?? :-) |
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12/06/2006 02:16:24 PM · #63 |
I don't think the parameters are fullly given. Just as well, I suppose, as we're meant to be puzzled.
Treadmills have a moving surface, while they are themselves stationary. If it's one of those things you use in a gym, then the movement is rotary, so that part of the belt is moving in the opposite direction to the bit on top.
So there's the bit about horizontal engines. Providing horizontal thrust, I presume this is supposed to mean, so it can't take off like a rocket or a jump jet. If it were a jump jet, then it would have vertical speed, which the treadmill would have to match in the only way it can. Ah well, we've all suffered on treadmills, maybe it's time one of them did some work for itself. It does all rather depend on the so-called 'clever design' though. If it's by the same geezer that is held responsible for 'intelligent design', then all bets are off, obviously.
I think the boys have it right (unless they're girls, I didn't check). The horizontal (?) thrust of the jet (?) engines is against the air and 'speed' of aeroplanes is measured as air speed, i.e. the passage of the plane through the air, which passage and which air will cause the difference in pressure above and below the wings that will, in turn, facilitate lift-off.
If speed is relative to the ground then so is the speed of the treadmill. That still allows the plane to take off.
If the speed is relative to the surface of the treadmill and vice versa then I hope you didn't pay the designer a lot because the relative speeds of a runway and a plane travelling along it are always equal and opposite.
I'll take the boat.
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12/06/2006 02:25:00 PM · #64 |
I'm going to have to disagree with most of the resposes here, and say that the plane will not take off.
In order for a plane to take off, it needs to be moving forward, relative to the ground, so that there is airflow over the wings. If the plane is on a treadmill moving the opposite direction, the net speed of the plane is zero, and hence, no airflow.
Think of it like this: When you are running full speed on a treadmill, say at 10mph, is there "wind in your face"? No, there isn't. And that's why the plane won't take off--there is no airflow over the wings. The plane needs "wind in its face" to generate lift. |
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12/06/2006 02:31:05 PM · #65 |
Originally posted by Zal:
Think of it like this: When you are running full speed on a treadmill, say at 10mph, is there "wind in your face"? No, there isn't. And that's why the plane won't take off--there is no airflow over the wings. The plane needs "wind in its face" to generate lift. |
But the plane isn't 'running' (i.e. it's not using it's wheels to create forward motion)
Imagine yourself running on a treadmill, and someone starts pushing a pole into your back - pushing so hard that you're pushed off the front of the treadmill; you'd have wind in your face then! :)
That's the 'pro-takeoff' argument anyway. |
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12/06/2006 02:44:18 PM · #66 |
Originally posted by jhonan:
Originally posted by Zal:
Think of it like this: When you are running full speed on a treadmill, say at 10mph, is there "wind in your face"? No, there isn't. And that's why the plane won't take off--there is no airflow over the wings. The plane needs "wind in its face" to generate lift. |
But the plane isn't 'running' (i.e. it's not using it's wheels to create forward motion)
Imagine yourself running on a treadmill, and someone starts pushing a pole into your back - pushing so hard that you're pushed off the front of the treadmill; you'd have wind in your face then! :)
That's the 'pro-takeoff' argument anyway. |
YES! There we go, the pole in the back. That is the variable that 90% of the internet seems unable to understand. The jet accelerates by pushing air against air so the plane will accelerate and take off just like normal, the wheels will be spinning twice as fast as they normally would but that is really inconsequential apart from the minimal amount of drag produced by their rotation on the axles (might knock a couple knots off the air speed, but not alot).
Unless I'm missing something big here... |
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12/06/2006 02:45:48 PM · #67 |
A plan has to be moving forward (V) to achieve liftoff. Just as with a car the wheels are not what makes it go forward. In a car you have an engine that turns the drive shaft that makes the tires rotate propelling it forward. In a plane you have engines that rotate the turbine that makes the tires/skids/etc. move forward.
If the Plane's velocity is at 100% (PV) and the the treadmills velocity is at 100% but in reverse direction that would be (-TV), both would equal out each other. The plane would be at V=0. V=0 is a terminology that aviation uses to describe no forward motion on the runway. Even if the plane made it to V1 (stall speed) it could not get off the ground. The only way the plane could get off the ground is if it reaches V2 (minimum speed for take off) with forward motion grater than gravity so it could climb and not stall. And the only way this could happen is forward motion. But with the OP saying the clever treadmill would alway go in reverse equal to the planes speed then the plane would always be a V=0 (no velocity). No velocity means no headwind which means no lift.
Still I say it will not fly with the information we have been provided.
Message edited by author 2006-12-06 14:49:17. |
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12/06/2006 02:48:46 PM · #68 |
Originally posted by ShorterThanJesus:
Originally posted by jhonan:
Originally posted by Zal:
Think of it like this: When you are running full speed on a treadmill, say at 10mph, is there "wind in your face"? No, there isn't. And that's why the plane won't take off--there is no airflow over the wings. The plane needs "wind in its face" to generate lift. |
But the plane isn't 'running' (i.e. it's not using it's wheels to create forward motion)
Imagine yourself running on a treadmill, and someone starts pushing a pole into your back - pushing so hard that you're pushed off the front of the treadmill; you'd have wind in your face then! :)
That's the 'pro-takeoff' argument anyway. |
YES! There we go, the pole in the back. That is the variable that 90% of the internet seems unable to understand. The jet accelerates by pushing air against air so the plane will accelerate and take off just like normal, the wheels will be spinning twice as fast as they normally would but that is really inconsequential apart from the minimal amount of drag produced by their rotation on the axles (might knock a couple knots off the air speed, but not alot).
Unless I'm missing something big here... |
You need lift. The weight of that plane needs to be lifted off the ground. Air does this over the wings. No lift, no fly. |
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12/06/2006 03:03:06 PM · #69 |
Originally posted by jhonan:
Imagine yourself running on a treadmill, and someone starts pushing a pole into your back - pushing so hard that you're pushed off the front of the treadmill; you'd have wind in your face then! :)
That's the 'pro-takeoff' argument anyway. |
But the whole point of the treadmill is that the plane isn't pushed to the front--the treadmill will speed up such that the net speed of the plane is zero. Hence, no lift. |
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12/06/2006 03:04:01 PM · #70 |
Let's break down the problem. Assume this is a jet airplane. The engines fire horizontally rearward. For a moment, consider just one engine. That engine is mounted to one thing, the plane. It creates thrust by accelerating the mass of air that moves through it. This thrust is transmitted to the aircraft via the engine mount.
So, considering the above, we can see that the motive force is in no way dependent on the surface on which the plane is sitting. Surely, as the plane moves forward, there is some friction from the bearings in the wheels. Should the wheels be forced to move faster, as by a treadmill running toward the rear, the friction will surely be doubled, if speed is doubled. Still, the friction of the wheels is very small compared to engine thrust. Thus, forward headway will not be appreciably slowed. The plane is accelerating through the *air*.
At takeoff speed, the plane lifts from the runway, the lift being generated from the wings offsetting the weight of the craft. Now, the craft continutes to accelerate through the *air*, yet it is not in contact with the ground; this is agian due to the fact that the thrust of the engines is due to their interaction with the air, not the ground. This last fact should convince any skeptics that still believe the presence of the hypothetical treadmill will have an effect. |
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12/06/2006 03:06:48 PM · #71 |
Originally posted by boomtap:
You need lift. The weight of that plane needs to be lifted off the ground. Air does this over the wings. No lift, no fly. |
Lift is generated by air moving over the wing, which is generated by forward movement, which is generated by the thrust of the engines against air. None of these elements are hampered by the movement of a treadmill in the opposite direction.
Originally posted by Zal:
But the whole point of the treadmill is that the plane isn't pushed to the front--the treadmill will speed up such that the net speed of the plane is zero. Hence, no lift. |
The treadmill can do nothing to stop the plane from being pushed to the front. If the plane were pushed by the wheels, then yes, the treadmill would stop the movement. But the plane is pushed by the engine thrust, on which the treadmill has no effect.
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12/06/2006 03:07:18 PM · #72 |
The plane will not take off. It is in fact stationary, the wheels are travelling forward, ie rotating in a forward direction. The treadmill is moving in the opposite direction equalling the speed. If thrust is increased, the treadmill speds up to counter any possible movement. Even if there is a concrete wall behind the engine, giving the thrust of the engine added impetus, the treadmill will always increase speed to match it.
Put a car on a rolling road and you can accelerate as hard as you like, and a passenger can step out of the car as it is stationary. Likewise the plane, it is static. Friction doesn't even come into the equation as frictionless will still be countered by the treadmill. No movement, no airflow, no fly. |
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12/06/2006 03:11:35 PM · #73 |
I haven't seen these posted yet, so here you go.
//www.straightdope.com/columns/060203.html
And some more info if you are still skeptical...
//www.straightdope.com/columns/060303.html |
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12/06/2006 03:13:04 PM · #74 |
Originally posted by Southern Gentleman:
A plan has to be moving forward (V) to achieve liftoff. Just as with a car the wheels are not what makes it go forward. In a car you have an engine that turns the drive shaft that makes the tires rotate propelling it forward. In a plane you have engines that rotate the turbine that makes the tires/skids/etc. move forward. |
The mistake in your reasoning is that the thrust moves the plane forward, independent of the wheels. The wheels then rotate against the ground, but those wheels are not providing the forward motion. In the case of a car the engine drives the wheels, and the friction between the ground and rotating wheels moves the car forward.
The plane does not move forward due to the wheel/ ground interaction.
So the treadmill, no matter what speed it goes it, does not stop the plane from moving. It rotates the wheels (which as we've discussed, are independent of the forward motion of the plane)
Consider a plane once it is flying. More thrust is applied. Does the plane move forward because of what the wheels are doing ? Are the wheels even out ? No. The wheels have nothing to do with the acceleration of the plane - spinning at any speed.
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12/06/2006 03:15:12 PM · #75 |
Originally posted by ShorterThanJesus:
Lift is generated by air moving over the wing, which is generated by forward movement, which is generated by the thrust of the engines against air. None of these elements are hampered by the movement of a treadmill in the opposite direction. |
Ok, here's where we can break it down.
Lift is generated by air moving over the wing
Correct.
which is generated by forward movement
Correct
which is generated by the thrust of the engines against air
NOT correct. The engines do generate thrust, but this thrust is converted to kinetic energy by the wheels on the runway to generate forward motion. It is this forward motion that moves the air over the wings to create lift, and hence, take off.
On the treadmill, the wings are not moving through the air. Yes, the engines are generating thrust, but thrust is not what makes a plane take off. Lift is. In the original scenerio, there is no lift.
Picture yourself as an observer standing on the tarmac watching the plane on the treadmill. The wings are NOT MOVING THROUGH THE AIR.
So, would someone who thinks the plane will take off please explain where the lift comes from? |
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