Engineering question
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If an airplane is positioned on a conveyor belt as wide as a runway, and this conveyor belt is designed to exactly match the speed of the wheels, but moving in the opposite direction, ... Can the airplane take off?
In general, no. The movement of the wheels has no effect on lift. To take flight, a craft needs either sufficient airflow across the wings or enough thrust to overcome gravity. A plane can take off from a stationary position, without a conveyor, if there is enough wind and the engine has enough thrust to counteract the drag; the plane would simply rise straight off the ground. Additionally, air craft with very powerful engines, like an F-16, can accelerate vertically. In this case, the wings do not generate lift; the engine itself provides all the lift. Theoretically, an F-16 could take off from a stationary but vertical position. Again, the wheels would not be used for this.
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The ONLY way the airplane can take off is if the speed of air respect of the airplane's speed is equal to the minimum speed the airplane needs to take off when the wind is absolutely calm. That is, because the conveyor makes the plane to be static respect to the ground, the only way the plane will take off is if there is a really hard hurricane that accelerates de wind to the plane's take off speed.
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Ignoring the possibility of a head wind strong enough to take of on the spot (or very close to it): No, it will not take off. The engines will obviously apply a force to the aircraft. To match the speed of the wheels, the conveyer belt would have to keep the plane still - if the plane is moving forward, the wheels much move faster than the belt (ignoring maximum friction, so the wheels will not slip). This means the belt will have to apply enough reverse force on the tires that the increased tire rolling friction and bearing friction transferred to the landing gear is identical to the force applied by the engine. This would quickly require the wheels to spin so fast the centrifugal force will rip them apart - first the ties, then the wheel or bearings. Then anything remaining of the landing gear will be ripped off, and the aircraft will crash on its belly on top of a conveyer belt moving it rapidly backwards. Kind of hard to get in the air from that position. Any limit to the available friction between belt and tires will allow the tires to slip over the belt - this means the aircraft could be moving forward while the belt is still matching the speed (but not position) of the wheels. But any friction available will be "used" to accelerate the wheels - so anything but the most minuscule friction would not allow the plane to reach takeoff speed before the wheels collapse. To take of, you should basically be able to do it with the breaks applied (ignoring the pesky nose or tail wheel without breaks).
The conveyor stuff is just complication. The entire point of the conveyor is to prevent lateral movement. Mythbusters had no budget for a real conveyor and their facsimile wasn't a conveyor and didn't prevent lateral movement. The weight of the plane and the stretch of the material allowed for lateral movement. A dynamometer would have been better. Sure, the wheels don't matter. So take the wheels off and jack the plane onto cinder blocks. Same concept, only without the fake-conveyor nonsense that lets people think you can have lift in no wind with no lateral movement. Jet, plane, whatever... If you prevent it moving forward, it's not going to move upward just because you tilt a control surface. Tie a sea plane off by its rear to a dock. Throttle slightly to get all the slack/stretch of the line out, then push to full. It would remain more or less stationary. "Prop wash" lift is a thing in R/C aircraft where thrust-to-weight blows pretty much all real planes out of the water. You can hover some R/C planes like a helicopter. You might be able to do that with some real sport planes, but I doubt it.
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Of course you are right. I realized (late) that engines push the air back and, hence, the airplane forward irrespective of wheels moving or not (or even not existing at all as in the case of seaplanes). Seems my brain was taking a day off yesterday :laugh:. Luckily it was a weekend day.
Mircea
I hear you. My brain takes frequent breaks, and not just on weekends. :wtf: I just happened to have argued this same scenario a few years ago (and was on the wrong side at first) and recalled the facts.
If you think 'goto' is evil, try writing an Assembly program without JMP.
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The engines don't directly cause the airflow. The engines push the airplane, whose movement through the air causes the airflow over the wings.
So there will be an airflow, and the plane will lift into the air. The airflow is a consequence of the engines pushing the plane into speed, exactly as at a "standard" take off. The only difference is that the free running wheels will be spinning twice as fast when the plane leaves the ground, but the speed of the plane - relative to the surrounding air and the solid ground - will be exactly as for a normal take off. The air flow in the same.
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If an airplane is positioned on a conveyor belt as wide as a runway, and this conveyor belt is designed to exactly match the speed of the wheels, but moving in the opposite direction, ... Can the airplane take off?
No. The reason being
Amarnath S wrote:
match the speed of the wheels
the result of which is that, no matter how hard the plane pushes forward, the conveyor belt pushes the same wheels, with a nonzero mass, back exactly as fast as the wheels are moving forward relative to the conveyor belt, a process which is not limited by anything (say, the wheels will spin at an incredible rate, and they it were a real-world situation, the wheels would explode from centrifugal forces); so that the total speed of the plane relative to the ground is zero. So the plane's thrust is used completely to drive the wheels' reaction force. It cannot be anything different, or else the exactly matching speed in the opposite direction would no longer hold true. So the wings do not catch any wind and the plane stays on the ground. All the force used by the plane for its attempt to take off is put into the wheels spinning. And this conveyor belt, having to make those same crazy speeds in the other direction, would be a mighty impressive piece of work. This is why it is important that you carefully read the question, be precise in what it states and what it does not state, not read carelessly, and not jump to conclusions.
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No. The reason being
Amarnath S wrote:
match the speed of the wheels
the result of which is that, no matter how hard the plane pushes forward, the conveyor belt pushes the same wheels, with a nonzero mass, back exactly as fast as the wheels are moving forward relative to the conveyor belt, a process which is not limited by anything (say, the wheels will spin at an incredible rate, and they it were a real-world situation, the wheels would explode from centrifugal forces); so that the total speed of the plane relative to the ground is zero. So the plane's thrust is used completely to drive the wheels' reaction force. It cannot be anything different, or else the exactly matching speed in the opposite direction would no longer hold true. So the wings do not catch any wind and the plane stays on the ground. All the force used by the plane for its attempt to take off is put into the wheels spinning. And this conveyor belt, having to make those same crazy speeds in the other direction, would be a mighty impressive piece of work. This is why it is important that you carefully read the question, be precise in what it states and what it does not state, not read carelessly, and not jump to conclusions.
Martijn Smitshoek wrote:
No.
unless it is a plane designed to take of completely vertically.
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No. The reason being
Amarnath S wrote:
match the speed of the wheels
the result of which is that, no matter how hard the plane pushes forward, the conveyor belt pushes the same wheels, with a nonzero mass, back exactly as fast as the wheels are moving forward relative to the conveyor belt, a process which is not limited by anything (say, the wheels will spin at an incredible rate, and they it were a real-world situation, the wheels would explode from centrifugal forces); so that the total speed of the plane relative to the ground is zero. So the plane's thrust is used completely to drive the wheels' reaction force. It cannot be anything different, or else the exactly matching speed in the opposite direction would no longer hold true. So the wings do not catch any wind and the plane stays on the ground. All the force used by the plane for its attempt to take off is put into the wheels spinning. And this conveyor belt, having to make those same crazy speeds in the other direction, would be a mighty impressive piece of work. This is why it is important that you carefully read the question, be precise in what it states and what it does not state, not read carelessly, and not jump to conclusions.
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If an airplane is positioned on a conveyor belt as wide as a runway, and this conveyor belt is designed to exactly match the speed of the wheels, but moving in the opposite direction, ... Can the airplane take off?
Could be my view is too simplistic but I imagine a plane sort of like a submarine, needing to be buoyant in much lighter fluids (air). For this to happen you need quite a volume of air flowing under the wings as opposed to over it, giving it 'lift'. Having no significant flow of air while basically staying in one place, I think, is not gonna help. Maybe you'd need a vertical vortex?
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If an airplane is positioned on a conveyor belt as wide as a runway, and this conveyor belt is designed to exactly match the speed of the wheels, but moving in the opposite direction, ... Can the airplane take off?
If memory Serves Mythbusters did that and tried it with a very light plane and a really long tarp, the pilot was amazed. If I recall the wheels are not powered and only the engine which forces wind over and under the wing matters. Non-trival question! Full marks have a look on Amazon+ or You Tube for the episode. ;)
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Could be my view is too simplistic but I imagine a plane sort of like a submarine, needing to be buoyant in much lighter fluids (air). For this to happen you need quite a volume of air flowing under the wings as opposed to over it, giving it 'lift'. Having no significant flow of air while basically staying in one place, I think, is not gonna help. Maybe you'd need a vertical vortex?
JP Reyes wrote:
Having no significant flow of air while basically staying in one place,
Are you saying that with the engines under the wings running at full power, those free-running will have the power to hold back the plane with the same force (but in the backwards direction) as the thrust from the engines in the forwards direction, to make the plane stand still? I guess that would cause so much stress on those wheels that the would break apart. With no wheels on that conveyer belt, the plane would be free to fly away :-)
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JP Reyes wrote:
Having no significant flow of air while basically staying in one place,
Are you saying that with the engines under the wings running at full power, those free-running will have the power to hold back the plane with the same force (but in the backwards direction) as the thrust from the engines in the forwards direction, to make the plane stand still? I guess that would cause so much stress on those wheels that the would break apart. With no wheels on that conveyer belt, the plane would be free to fly away :-)
Well if I understood correctly, the conveyer belt is meant to match the speed of the wheels even at full engine thrust. I Don't know if the wheels have a speed threshold with all that weight, one would imagine the rubber does have it's limits (heck I even bet the conveyer belt would buckle long before the jet engines go to full power) Realistically I can only imagine the most catastrophic take off (I think the wheels would be useless for landing and the huge conveyer belt tarmac, broken and in tatters). Nonetheless I would have to agree with you. But referring the original (very hypothetical) question:
Quote:
If an airplane is positioned on a conveyor belt as wide as a runway, and this conveyor belt is designed to exactly match the speed of the wheels, but moving in the opposite direction, ... Can the airplane take off?
Barring the unlikely existence of such a conveyer belt and matching powerful set of wheels, I would still say it doesn't take off. Unless convinced otherwise, it's the volume of the air flowing under the wings that matter, not the volume of air flowing through the turbines.
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No. The reason being
Amarnath S wrote:
match the speed of the wheels
the result of which is that, no matter how hard the plane pushes forward, the conveyor belt pushes the same wheels, with a nonzero mass, back exactly as fast as the wheels are moving forward relative to the conveyor belt, a process which is not limited by anything (say, the wheels will spin at an incredible rate, and they it were a real-world situation, the wheels would explode from centrifugal forces); so that the total speed of the plane relative to the ground is zero. So the plane's thrust is used completely to drive the wheels' reaction force. It cannot be anything different, or else the exactly matching speed in the opposite direction would no longer hold true. So the wings do not catch any wind and the plane stays on the ground. All the force used by the plane for its attempt to take off is put into the wheels spinning. And this conveyor belt, having to make those same crazy speeds in the other direction, would be a mighty impressive piece of work. This is why it is important that you carefully read the question, be precise in what it states and what it does not state, not read carelessly, and not jump to conclusions.
Martijn Smitshoek wrote:
So the plane's thrust is used completely to drive the wheels' reaction force.
Do you happen to have a model (toy) airplane with free running wheels? If you also have an option to mount the the spare tire of you car so it can spin around, it can serve as a model conveyor belt. Now start the tire (/conveyor belt) spinning, with the model plane on top of it, let your hand serve as model engines. You claim that there is no way that your hand can give the plane a thrust forward to throw it into the air. Even though the wheels are free running, in some magical way, they will convey a counter force against your hand making it impossible for the hand (/the engines of the plane) to push the plane forwards at a speed enough to give the plane a lift. Obviously you can push the model plane forwards, even with the tire spinning ahead beneath it. You claim that if your hand is replaced with real engines, providing same thrusting power as your hand did, that thrust will be unable to move the plane ahead the way your hand did. I do not see what makes the principal difference between the thrust from your hand on the plane body and the thrust from the engines on the plane body. You maintain that there is a principal difference, or alternately, that as long as those free running wheels touch the rotating tire conveyor belt, your hand can't possibly move the model plane forward. I'd certainly like to know which one of these two alternatives you go for, along with a good justificaytion.
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The conveyor stuff is just complication. The entire point of the conveyor is to prevent lateral movement. Mythbusters had no budget for a real conveyor and their facsimile wasn't a conveyor and didn't prevent lateral movement. The weight of the plane and the stretch of the material allowed for lateral movement. A dynamometer would have been better. Sure, the wheels don't matter. So take the wheels off and jack the plane onto cinder blocks. Same concept, only without the fake-conveyor nonsense that lets people think you can have lift in no wind with no lateral movement. Jet, plane, whatever... If you prevent it moving forward, it's not going to move upward just because you tilt a control surface. Tie a sea plane off by its rear to a dock. Throttle slightly to get all the slack/stretch of the line out, then push to full. It would remain more or less stationary. "Prop wash" lift is a thing in R/C aircraft where thrust-to-weight blows pretty much all real planes out of the water. You can hover some R/C planes like a helicopter. You might be able to do that with some real sport planes, but I doubt it.
jochance wrote:
If you prevent it moving forward
But what would prevent it from moving forward? The engines, whether jet engines or propellers, thrust the plane in the forwards direction, and there is nothing from stopping it. The free running wheels will not stop it, even if they are spinning at a fairly high speed.
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The ONLY way the airplane can take off is if the speed of air respect of the airplane's speed is equal to the minimum speed the airplane needs to take off when the wind is absolutely calm. That is, because the conveyor makes the plane to be static respect to the ground, the only way the plane will take off is if there is a really hard hurricane that accelerates de wind to the plane's take off speed.
gervacleto wrote:
because the conveyor makes the plane to be static respect to the ground,
How does it do that, with free running wheels? The wheels are the conveyor belt's only contact with the plane, and I cannot see how you can enforce a thrust of the same magnitude (but opposite direction) as the plane engines, through free running wheels.
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The airplane does or does not lift off owing to the upward airflow forces on the wings. If the air does not move relative to the airplane (or vice versa) the plane will stay on the ground. And the speed of the conveyorbelt relative to the air close by will cause some drag, therefore some lift, but it is likely to be way too little, unless you add a quite signifant ventilator to help. That should be pretty obvious, but I miss the joke - if there is one?
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The speed of the wheels is irrelevant - they aren't powered or driven in any way. The speed of the airflow over the wings is the source of lift, along with the wings angle of incidence. Assuming the conveyor is moving at the same speed (but in the opposite direction) as the aircraft would be on a normal runway then the aircraft would actually be stationery and the airflow over the wings would effectively be zero and thus not generating any lift?
Leo56 wrote:
Assuming the conveyor is moving at the same speed (but in the opposite direction) as the aircraft would be on a normal runway then the aircraft would actually be stationery and the airflow over the wings would effectively be zero and thus not generating any lift?
I sure would like to see that airplane sitting there on the runway with the engines running at full power, but the plane is standing completely still because its wheels are spinning around. Nothing else is holding the plane back, and the wheels are free running, but in some magical way they still manage to cancel out the full power of the engines. I'd sure like to see that happen. And also to have a reasonable explanation how it can be possible.
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Why wouldn't the engines provide exactly the same thrust on the plane body, giving it the same forward acceleration as on a non-belted runway?
My understanding was that the engines were not used. If I took that one wrong, sorry. But engines give forward thrust irrespective of the behavior of the wheels (assuming they can turn), so in that case the plane would go forward anyway, the wheels just having to turn faster in response to the belt.
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Well if I understood correctly, the conveyer belt is meant to match the speed of the wheels even at full engine thrust. I Don't know if the wheels have a speed threshold with all that weight, one would imagine the rubber does have it's limits (heck I even bet the conveyer belt would buckle long before the jet engines go to full power) Realistically I can only imagine the most catastrophic take off (I think the wheels would be useless for landing and the huge conveyer belt tarmac, broken and in tatters). Nonetheless I would have to agree with you. But referring the original (very hypothetical) question:
Quote:
If an airplane is positioned on a conveyor belt as wide as a runway, and this conveyor belt is designed to exactly match the speed of the wheels, but moving in the opposite direction, ... Can the airplane take off?
Barring the unlikely existence of such a conveyer belt and matching powerful set of wheels, I would still say it doesn't take off. Unless convinced otherwise, it's the volume of the air flowing under the wings that matter, not the volume of air flowing through the turbines.
JP Reyes wrote:
Well if I understood correctly, the conveyer belt is meant to match the speed of the wheels even at full engine thrust.
Sure, but that doesn't null the thrust. If the conveyor belt is running at takeoff speed before the engines are started, then you fire up the engines and zip down the runway (/conveyor belt), when the plane lifts off the ground the wheels is spinning at twice the takeoff speed (unless the conveyor belt has been slowed down as the plane accelerates, to maintain the 'wheels spinning at takeoff speed). I am not into construction of air planes, but I wouldn't be surprised if twice the normal takeoff speed is well within the safety margins for the wheels. In any case, it doesn't affect the principal question of whether the plane could take off.
Unless convinced otherwise, it's the volume of the air flowing under the wings that matter, not the volume of air flowing through the turbines.
The air flowing through the turbines would give the plane a forward speed that would cause an airflow over and under the wings. Or are you suggesting that the thrust from the turbines are nulled out because the free running wheels are spinning around? What are the mechanism behind this canceling? Assume that the wheels for some reason started spinning mid-air, would this cancel the thrust from the turbines as well, so the plane crashes? Or does it require the wheels to be in contact with the ground for the thrust to be nulled out?
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My understanding was that the engines were not used. If I took that one wrong, sorry. But engines give forward thrust irrespective of the behavior of the wheels (assuming they can turn), so in that case the plane would go forward anyway, the wheels just having to turn faster in response to the belt.
