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Physics Question
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The Godfather
Platinum Member
I got 99 problems but a b1tch ain't one.
I'd like to take a stab at it.
First, please accept this as an addendum to the original question. Even though it was not worded as such, I believe it is within the spirit of the problem:
<addendum>
There is ample friction between the wheels and the treadmil such that traction is never lost via the plane's acceleration. Sure you could strap a saturn V on the back of the plane and incinerate the wheels as the plane heads up to escape velocity but I don't think that would follow the premise of the original problem. If traction is lost, then of course the plane will be able to move independent of the treadmill and the plane can take off. In other words, there shall be no skid marks on the treadmill.
</addendum>
It seems the schism here is between those who feel the wheels have absolutely no effect on the planes movement and those who do. Those who claim that wheel speed will simply double as the plane moves forward on the treadmill are of the "freewheel" camp. Please consider this scenario:
Plane is idle on the treadmill, engines off. Start the treadmill at 50mph. There are two possible outcomes:
1) Plane remains stationary, wheels are spinning at 50mph.
2) Wheels remain stationary, plane moves at -50mph.
I'm of the belief that the plane will be moving backwards and the wheels will be still. The freewheelers would think otherwise, the plane is stationary, the wheels are moving.
Scenario 2:
Plane is reversed on the treadmill such that they are both moving in the same direction. Takeoff speed for the plane is 200mph. Plane is idle, engines off. Start the treadmill and accelerate it to 200mph.
A) Plane remains stationary, wheels are spinning at -200mph.
B) Wheels remain stationary, plane moves at 200mph, lifts off from runway and promptly lands on runway as it quickly loses its forward speed where it is again acclerated up to 200mph, repeat. (At 200mph air resistance will likely be enough to overcome the static friction between the wheels and the treadmill causing the plane to start rolling backwards so you might have to speed up the treadmill a bit to get the plane to 200. Or, the terminal velocity of the plane may be less than 200mph and it will never take off with the wheels accepting the excess velocity but I think the logic still applies.)
Again, I see scenario B to be the more likely outcome. The freewheelers would think the plane just sits there. Going back to the first scenario and assume that the plane was moving backwards. Accelerate the plane such that it gains on the treadmill until you reach the origin. Now, back off on the accelerator so that you are no longer moving with respect to the ground. Here, I see the plane at zero speed relative to ground, treadmill at 50mph, wheels spinning at -50mph. Now, speed up the treadmill to 100mph. I would think the plane would again start moving backwards. If you can visualize this, then I think you can see that the plane can never advance if the treadmill is matching the plane's speed.
If the plane is independent of its wheels and therefore independent of the treadmill, then I can see how you think the plane can takeoff. This would only be the case if the wheels and bearings are frictionless which I don't think they are. Or if the air resistance of a stopped/low speed plane is greater than the friction between the wheels and the treadmill which I would also doubt. For example, in the first scenario if instead of air, the plane was trying to move through honey, there might be enough resistance there such that the treadmill would spin the wheels instead of move the plane. Also, I believe that whole issue of wheel driven versus thrust driven does not apply here. Those would be more relevent in the case of a dynamometer. A car on a dyno would not move. A plane on a dyno would.
As for the skateboard fan, it would not move as the fan is pushing itself backwards as much as it's pushing the board forwards. This would be the same thing as attaching a huge magnet a foot in front of your car and expecting it to move forward.
The idea behind pulling a rope is not a proper analogy. If you are on skates or whatever on a treadmill holding yourself by a rope, the rope is pulling you at the same speed that the treadmill is pushing you. If the treadmill increases speed, the rope will pull you harder. As long as traction is maintained between the wheels and the treadmill, the push/pull will be equal resulting in no net movement. If you now start pulling on the rope, you are adding a force outside of the system than can not be offset by the treadmill as any increase in the treadmill speed will still be taken care of by the rope. If the treadmill is pushing at -10mph, the rope is pulling you at 10mph. If you pull the rope at 1mph, treadmill increases to 11mph, rope pulls at 11mph, you're still pulling at 1mph, so now you're going 12mph. This cycle will continue until the rope shreds your hand or the rope breaks. The same occurs with the hand pushing the wagon from behind. If you think that the wheels spinning plays no part in the overall movement of the object, than you shouldn't need a rope or a hand to keep a wheeled object stationary on a moving treadmill.
P.S. I'm quite impressed at the discussion thus far. It has been rather civil and pretty open-minded. Hope it keeps up.
First, please accept this as an addendum to the original question. Even though it was not worded as such, I believe it is within the spirit of the problem:
<addendum>
There is ample friction between the wheels and the treadmil such that traction is never lost via the plane's acceleration. Sure you could strap a saturn V on the back of the plane and incinerate the wheels as the plane heads up to escape velocity but I don't think that would follow the premise of the original problem. If traction is lost, then of course the plane will be able to move independent of the treadmill and the plane can take off. In other words, there shall be no skid marks on the treadmill.
</addendum>
It seems the schism here is between those who feel the wheels have absolutely no effect on the planes movement and those who do. Those who claim that wheel speed will simply double as the plane moves forward on the treadmill are of the "freewheel" camp. Please consider this scenario:
Plane is idle on the treadmill, engines off. Start the treadmill at 50mph. There are two possible outcomes:
1) Plane remains stationary, wheels are spinning at 50mph.
2) Wheels remain stationary, plane moves at -50mph.
I'm of the belief that the plane will be moving backwards and the wheels will be still. The freewheelers would think otherwise, the plane is stationary, the wheels are moving.
Scenario 2:
Plane is reversed on the treadmill such that they are both moving in the same direction. Takeoff speed for the plane is 200mph. Plane is idle, engines off. Start the treadmill and accelerate it to 200mph.
A) Plane remains stationary, wheels are spinning at -200mph.
B) Wheels remain stationary, plane moves at 200mph, lifts off from runway and promptly lands on runway as it quickly loses its forward speed where it is again acclerated up to 200mph, repeat. (At 200mph air resistance will likely be enough to overcome the static friction between the wheels and the treadmill causing the plane to start rolling backwards so you might have to speed up the treadmill a bit to get the plane to 200. Or, the terminal velocity of the plane may be less than 200mph and it will never take off with the wheels accepting the excess velocity but I think the logic still applies.)
Again, I see scenario B to be the more likely outcome. The freewheelers would think the plane just sits there. Going back to the first scenario and assume that the plane was moving backwards. Accelerate the plane such that it gains on the treadmill until you reach the origin. Now, back off on the accelerator so that you are no longer moving with respect to the ground. Here, I see the plane at zero speed relative to ground, treadmill at 50mph, wheels spinning at -50mph. Now, speed up the treadmill to 100mph. I would think the plane would again start moving backwards. If you can visualize this, then I think you can see that the plane can never advance if the treadmill is matching the plane's speed.
If the plane is independent of its wheels and therefore independent of the treadmill, then I can see how you think the plane can takeoff. This would only be the case if the wheels and bearings are frictionless which I don't think they are. Or if the air resistance of a stopped/low speed plane is greater than the friction between the wheels and the treadmill which I would also doubt. For example, in the first scenario if instead of air, the plane was trying to move through honey, there might be enough resistance there such that the treadmill would spin the wheels instead of move the plane. Also, I believe that whole issue of wheel driven versus thrust driven does not apply here. Those would be more relevent in the case of a dynamometer. A car on a dyno would not move. A plane on a dyno would.
As for the skateboard fan, it would not move as the fan is pushing itself backwards as much as it's pushing the board forwards. This would be the same thing as attaching a huge magnet a foot in front of your car and expecting it to move forward.
The idea behind pulling a rope is not a proper analogy. If you are on skates or whatever on a treadmill holding yourself by a rope, the rope is pulling you at the same speed that the treadmill is pushing you. If the treadmill increases speed, the rope will pull you harder. As long as traction is maintained between the wheels and the treadmill, the push/pull will be equal resulting in no net movement. If you now start pulling on the rope, you are adding a force outside of the system than can not be offset by the treadmill as any increase in the treadmill speed will still be taken care of by the rope. If the treadmill is pushing at -10mph, the rope is pulling you at 10mph. If you pull the rope at 1mph, treadmill increases to 11mph, rope pulls at 11mph, you're still pulling at 1mph, so now you're going 12mph. This cycle will continue until the rope shreds your hand or the rope breaks. The same occurs with the hand pushing the wagon from behind. If you think that the wheels spinning plays no part in the overall movement of the object, than you shouldn't need a rope or a hand to keep a wheeled object stationary on a moving treadmill.
P.S. I'm quite impressed at the discussion thus far. It has been rather civil and pretty open-minded. Hope it keeps up.
Because if you are a pilot and have ever piloted an aircraft, then you should know that it will take off
EDIT: but then you can skid on the tredmil and still pull ytourself foreward, your landing gear can break off and at full thrust, you will still probably go foreward if the tredmill is moving
EDIT: but then you can skid on the tredmil and still pull ytourself foreward, your landing gear can break off and at full thrust, you will still probably go foreward if the tredmill is moving
Mrvile
Lifer
Alright, I only read through the first page. But here's my argument:
I know this sounds crazy but I gave it some thought.
Take Letdown's example on the first page. Picture a vehicle towing the plane on a belt. The vehicle is not part of the belt. The vehicle moves forward at 10mph, so the plane begins to move at 10mph, and the belt moves backwards at 10mph. So the plane's wheels are spinning at 20mph total. However, the belt only moves the plane's wheels, and doesn't affect the towing vehicle at all. So the towing vehicle will still be moving forward at 10mph, and so will the plane. The belt might be spinning at 1 billion mph, and the wheels 2 billion mph, but none of this affects the towing vehicle.
The engines of the plane act as the towing vehicle - they push air through the engines to propel the plane forward. The wheels aren't motorized, and exert no friction on the ground. So the conveyer belt would be doing nothing but spinning the plane's wheels - it won't actually be pulling the plane against itself.
So assuming the plane's wheels and the conveyer belt can move at infinite speeds, and there is no friction within the bearings of the wheel itself, the plane would take off.
I hope you guys understand this. This is a really cool topic.
I know this sounds crazy but I gave it some thought.
Take Letdown's example on the first page. Picture a vehicle towing the plane on a belt. The vehicle is not part of the belt. The vehicle moves forward at 10mph, so the plane begins to move at 10mph, and the belt moves backwards at 10mph. So the plane's wheels are spinning at 20mph total. However, the belt only moves the plane's wheels, and doesn't affect the towing vehicle at all. So the towing vehicle will still be moving forward at 10mph, and so will the plane. The belt might be spinning at 1 billion mph, and the wheels 2 billion mph, but none of this affects the towing vehicle.
The engines of the plane act as the towing vehicle - they push air through the engines to propel the plane forward. The wheels aren't motorized, and exert no friction on the ground. So the conveyer belt would be doing nothing but spinning the plane's wheels - it won't actually be pulling the plane against itself.
So assuming the plane's wheels and the conveyer belt can move at infinite speeds, and there is no friction within the bearings of the wheel itself, the plane would take off.
I hope you guys understand this. This is a really cool topic.
imported_Condor
Diamond Member
No! It's all about airflow, not groundspeed.
A conveyor belt cannot prevent the plane from moving forward no matter how fast it is travelling unless the wheels lock up.
I suppose you could argue that the wheels have a certain amount of friction and you could reach a speed where the wheels generate enough friction inside the wheels to actually couple the plane to the conveyor belt enough to stop the plane, but I can't imagine a real wheel not melting at that speed.
letdown427
Golden Member
The conveyer is not mimicing wheel speed. this leads to a paradox as has been said many, many times.
Second, stop discussing, oh the conveyer could get fast enough to stop the plane. Even if it could, at that speed, the plane would be flying. Please, read some of my earlier posts. The conveyers speed is relative to the speed of the plane. The speed of the plane is relative to the earth. I proved that in my earlier posts. Therefore for the conveyer to be moving at all, the plane must be moving.
For the plane to be going at say 200mph, the plane must be moving, relative to the earth, at 200mph. it would be flying at this point.
Please stop saying thrust doesn't equal lift. we all know that. Please stop argueing that airflow over the wings is needed. we all know that too. the airflow over the wings is created by the fact that the plane is moving.
hehe, this won't stop until we've converted every 135,000 odd anandtech members to the right way of thinking! hehe 🙂
Second, stop discussing, oh the conveyer could get fast enough to stop the plane. Even if it could, at that speed, the plane would be flying. Please, read some of my earlier posts. The conveyers speed is relative to the speed of the plane. The speed of the plane is relative to the earth. I proved that in my earlier posts. Therefore for the conveyer to be moving at all, the plane must be moving.
For the plane to be going at say 200mph, the plane must be moving, relative to the earth, at 200mph. it would be flying at this point.
Please stop saying thrust doesn't equal lift. we all know that. Please stop argueing that airflow over the wings is needed. we all know that too. the airflow over the wings is created by the fact that the plane is moving.
hehe, this won't stop until we've converted every 135,000 odd anandtech members to the right way of thinking! hehe 🙂
Here is a stupid example. Imagine that the conveyor belt is declined about 45 degrees. That is, it is significantly angled downward.
If it was off and you were to drop a ball on it, the ball would roll down.
If it was off and you held a plane on it, and then let go, the plane would roll off.
If it was on and you let the plane go... HOW IS IT SUPPOSED TO KEEP THE PLANE FROM ROLLING DOWNHILL?! The force on the plane from gravity will pull the plane down the incline despite the fact that the conveyor is moving.
The plane's engine provides force just like gravity. Therefore the plane will move.
If it was off and you were to drop a ball on it, the ball would roll down.
If it was off and you held a plane on it, and then let go, the plane would roll off.
If it was on and you let the plane go... HOW IS IT SUPPOSED TO KEEP THE PLANE FROM ROLLING DOWNHILL?! The force on the plane from gravity will pull the plane down the incline despite the fact that the conveyor is moving.
The plane's engine provides force just like gravity. Therefore the plane will move.
Kelemvor
Lifer
Well, I didn't read the whole thread but here's my take...
If the plane is thrusting with jets then it can take off. The conveyor cannot match the speed of the plane's wheels because the jets are pushing the plane forward through the air. The wheels are not what makes the plane go forward. So as the plane's jets fire, it will push the plane forward through the air. The wheels just move because they happen to be touching the ground. But the plane wil still move forward and if the convery starts to spin fast to try to stop the plane the converyor will eventually break beacause it's impossible.
Now if the plane was like a car and got it's movement from the tires driving, then No the plane could take off. It wouldn't matter how fast the plane is moving in relation to the converyor belt, it only matters how fast it's moving in relation to the air. The air (and air pressure) is what gives the plane lift. No movement = no fancy air pressure = no takeoff.
If the plane is thrusting with jets then it can take off. The conveyor cannot match the speed of the plane's wheels because the jets are pushing the plane forward through the air. The wheels are not what makes the plane go forward. So as the plane's jets fire, it will push the plane forward through the air. The wheels just move because they happen to be touching the ground. But the plane wil still move forward and if the convery starts to spin fast to try to stop the plane the converyor will eventually break beacause it's impossible.
Now if the plane was like a car and got it's movement from the tires driving, then No the plane could take off. It wouldn't matter how fast the plane is moving in relation to the converyor belt, it only matters how fast it's moving in relation to the air. The air (and air pressure) is what gives the plane lift. No movement = no fancy air pressure = no takeoff.
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