I think the confusion is that the conveyor belt is running at a fixed speed, which is the aircraft’s takeoff speed. That just dictates how fast the wheels spin, but since the plane generates thrust with its propeller, the wheels just end up having to spin at double takeoff speed. Since they’re relatively frictionless, that’s easy.
The more confusing myth is the one where the speed of the conveyor belt is variable, and it always moves at the same speed as the wheels. So, at the beginning the conveyor belt isn’t moving, but as soon as the plane starts to move, and its wheels start to spin, the conveyor belt movies in the opposite direction. In that case, the plane can’t take off. That’s basically like attaching an anchor to the plane’s frame, so no matter how fast the propeller spins, the airplane can’t move.
Except it’s not like attaching an anchor. The plane isn’t physically attached.
The wheels will just roll double whatever the current ground speed is. If the plane has enough thrust to take off with the treadmill moving an inverse of its take off speed, then it has enough force to start rolling, too.
At most, the force applied by the treadmill would be sufficient over enough time to lengthen the take off roll, but given enough space to do so, the plane will take off.
To keep the plane from rolling forward; the treadmill would have to be able to apply an equal force as the engines, it can’t do that through the wheels- the wheels can only apply a force equal to their rolling resistance and friction in its mechanics.
If the conveyor moves at the same speed as the wheels, it is exactly like attaching an anchor. That isn’t the myth they were testing, but it’s a more interesting myth.
it can’t do that through the wheels- the wheels can only apply a force equal to their rolling resistance and friction in its mechanics.
It can do that if it can spin the wheels fast enough. Picture the ultra-light airplane from the episode with big, bouncy wheels and a relatively weak propeller. If the treadmill was moving 1000 km/h backwards, that little propeller could never match the force due to rolling resistance from the wheels.
Just to clarify; you understand that because the engines are pushing on the plane itself and not the wheels, by the time the wheels start moving, the plane is already moving relative to ground and air alike.
Which, said another way, this thought problem appears confusing because it’s being considered from otherwise irrelevant reference frames.
An anchor sufficient to keep the plane from rolling forward is different because the force it is apply is significantly greater.
Sure, you can deflate the tires and increase the rate of spin on the wheels. But at that point, you might as well ask “can we creat a scenario where planes can’t take off”
To which the answer is definitely “Yes”,
And as a side note, if we assume the wheels are indestructible, which I’d argue is only fair, then even if what you’re saying is true and we ramp up the drag induced by the wheels sufficient to counter the engines… then the wind generated by the rolling treadmill would be producing a sufficient headwind for the plane to take off. (Remember, the air resistance of the treadmill’s belt moving will accelerate the air some.)
But again, the wheels have almost zero drag to begin with, the speed at which the roll is independent of both the actual groundspeed and the airspeed of the airplane.
If it has the thrust to over come friction at take off speeds, and at standing, then it has enough power to get to take off velocity eventually.
On the other hand, this entire conversation assumes the thrust to weight ratio is less than 1. If it’s more than one, well they just…. Go straight up.
Just to clarify; you understand that because the engines are pushing on the plane itself and not the wheels, by the time the wheels start moving, the plane is already moving relative to ground and air alike.
The wheels are attached to the plane so they move at the same time as the plane. But, I get what you’re trying to say, that the wheels are effectively being dragged by the plane, they’re not powering the movement. But, what you need to think about is that if you oppose that dragging by moving the conveyor belt in the opposite direction you can prevent the plane from moving at all. Yes, the wheels are merely dragging and there isn’t a lot of friction there, but friction increases with speed. And, if you move the conveyor belt fast enough, you can stop the plane from moving relative to the ground, which can stop it from moving relative to the air, which can prevent it from taking off.
An anchor sufficient to keep the plane from rolling forward is different because the force it is apply is significantly greater.
No, by definition it’s the same. The conveyor moves with however much speed is necessary to stop the forward motion of the plane. The conveyor would eventually go so fast that it generated enough force to stop the plane from moving, so it’s indistinguishable from an anchor.
Sure, you can deflate the tires and increase the rate of spin on the wheels.
You don’t need to deflate the tires, you merely need to increase the speed at which the conveyor moves to match the speed of the wheels.
if we assume the wheels are indestructible, which I’d argue is only fair, then even if what you’re saying is true and we ramp up the drag induced by the wheels sufficient to counter the engines… then the wind generated by the rolling treadmill would be producing a sufficient headwind for the plane to take off
That seems like an unfair assumption because you’re assuming that the conveyor belt has second-order effects on the air (i.e. generating a “wind” over the wings of the plane), while ignoring the second-order effects the conveyor would have on the wheels (massive heat from friction leading to failure).
On the other hand, this entire conversation assumes the thrust to weight ratio is less than 1. If it’s more than one, well they just…. Go straight up.
I mean, the discussion is of a plane, not a helicopter or a rocket. Even jet fighters with a thrust-to-weight ratio of more than 1 typically have engines that only have that ratio once they’re at high speed, not from a standing start. That’s why even fighter jets on carriers need a catapult-assisted takeoff. A VTOL aircraft like a Harrier wouldn’t need that, but then its takeoff speed is zero, and the myth isn’t very interesting when the conveyor belt doesn’t move.
The wheels are attached to the plane so they move at the same time as the plane. But, I get what you’re trying to say, that the wheels are effectively being dragged by the plane, they’re not powering the movement.
no. I’m saying that by the time the wheel is rolling, the plane’s is already moving forward, the engines have already overcome the drag in the wheels. the treadmill is locked to the wheels, not the plane. The plane would continue accelerating even as the wheels reported weird rates of turning.
As for the (very brief) time delay, that’s a function of the plane’s gear’s suspension that is quite well sprung.
the rate of roll on the tire is, effectively, decoupled from the airspeed (and groundspeed) of the plane. which makes this:
No, by definition it’s the same. The conveyor moves with however much speed is necessary to stop the forward motion of the plane.
… entirely different. an affixed anchor does not allow the free motion that a wheel would.
You don’t need to deflate the tires, you merely need to increase the speed at which the conveyor moves to match the speed of the wheels.
And one of a few things happen. Either the plane has enough engine thrust to overcome the acceleration induced by the wheels, and therefore takes off, or it does not.
In the case that it does not, the wheels would continue spinning in increasing RPM until the plane begins moving backwards. because, again, the airspeed of the airplane is not dependent on the wheel’s RPM. Assuming the airplane doesn’t crash from suddenly becoming incredibly difficult to control… eventually it would take off anyhow. because the airflow over the wings would still generate lift. (though they would become horribly inefficient.) and therefore take off.
this is of course ignoring the whole “can a pilot actually control that and manage a take off like that” thing. If you don’t want to grant godlike piloting skills, we could then just make the treadmill irrelevant and leave the brakes on.
I’m saying that by the time the wheel is rolling, the plane’s is already moving forward
The wheels are attached to the plane, so they move at the same time. There’s going to be slight flex due to rubber and metal not being insanely stiff, but essentially as soon as the plane starts moving forward through the air, the wheels start rolling forward along the ground. Since the conveyor belt cancels the forward movement of the wheels, the movement of the plane ceases too.
The plane would continue accelerating even as the wheels reported weird rates of turning.
Initially, for a few tenths of a second, or a few seconds sure. But, during that time, the conveyor belt would be moving faster and faster as it matched the speed of the wheels. The faster the conveyor moved, the more friction there would be, and the more drag there would be from that friction. Eventually you’d reach an equilibrium where the drag from the wheels was equal to the thrust from the engine, and the plane would cease moving forward. It would be exactly like the plane being anchored to the ground, except instead of a stationary anchor, the anchor would be a spinning treadmill in contact with a spinning wheel. In a world without a magic conveyor belt that could instantly adjust to the speed of the wheels, there would be some slight forward and backward movement of the plane, but that’s just like being attached to an anchor with a bungee rather than a rigid rope.
an affixed anchor does not allow the free motion that a wheel would.
The wheel doesn’t have free motion. By definition, the conveyor is moving at the same speed as the wheel, so the wheel is locked in place. With a real conveyor belt there would of course be some lag as the motors of the conveyor accelerated the belt, but using the hypothetical as defined, the axle of the wheel couldn’t ever move because every rotation of the wheel would be matched by a movement of the conveyor belt.
And one of a few things happen. Either the plane has enough engine thrust to overcome the acceleration induced by the wheels, and therefore takes off, or it does not.
The thrust would have to be infinite because, by definition, the conveyor is always going to match the velocity of the wheels. If the wheels were truly frictionless, then the conveyor belt would have no effect at all. But, any real wheel will have some friction that will increase with speed, so there will always be some speed where the force backwards from the friction of the spinning wheels matches the force of the engine.
As an aside, my guess is that most real airplane wheels would probably fail pretty quickly at just double the normal takeoff / landing speed. The centripetal force acting on the spinning parts of the wheel and tire increase with the square of the velocity, so 2x as fast means 4x as much force. 3x as fast and 9x as much force. So, if you did this with a real wheel, you’d destroy the wheel pretty quickly. Of course, the same applies to the conveyor belt, but I’m going to assume that it’s specially engineered to survive this challenge.
the wheels would continue spinning in increasing RPM until the plane begins moving backwards
The plane wouldn’t move backwards because if the wheels slowed down, the conveyor belt would slow down too. Of course, that’s in a world where the conveyor belt could adjust its velocity instantaneously, but for this thought-experiment you can say that if the pilot cuts the engine or something, the wheels don’t spin as fast, so the conveyor belt slows down, and the plane remains in one spot.
eventually it would take off anyhow. because the airflow over the wings would still generate lift
In the thought-experiment world, there wouldn’t be any airflow over the wings because the plane would be stationary. In reality, there would be some airflow due to the movement of the conveyor belt, but the wheels would probably melt long before that was enough air to give the plane lift while stationary relative to the world around.
I think the confusion is that the conveyor belt is running at a fixed speed, which is the aircraft’s takeoff speed. That just dictates how fast the wheels spin, but since the plane generates thrust with its propeller, the wheels just end up having to spin at double takeoff speed. Since they’re relatively frictionless, that’s easy.
The more confusing myth is the one where the speed of the conveyor belt is variable, and it always moves at the same speed as the wheels. So, at the beginning the conveyor belt isn’t moving, but as soon as the plane starts to move, and its wheels start to spin, the conveyor belt movies in the opposite direction. In that case, the plane can’t take off. That’s basically like attaching an anchor to the plane’s frame, so no matter how fast the propeller spins, the airplane can’t move.
Except it’s not like attaching an anchor. The plane isn’t physically attached.
The wheels will just roll double whatever the current ground speed is. If the plane has enough thrust to take off with the treadmill moving an inverse of its take off speed, then it has enough force to start rolling, too.
At most, the force applied by the treadmill would be sufficient over enough time to lengthen the take off roll, but given enough space to do so, the plane will take off.
To keep the plane from rolling forward; the treadmill would have to be able to apply an equal force as the engines, it can’t do that through the wheels- the wheels can only apply a force equal to their rolling resistance and friction in its mechanics.
If the conveyor moves at the same speed as the wheels, it is exactly like attaching an anchor. That isn’t the myth they were testing, but it’s a more interesting myth.
It can do that if it can spin the wheels fast enough. Picture the ultra-light airplane from the episode with big, bouncy wheels and a relatively weak propeller. If the treadmill was moving 1000 km/h backwards, that little propeller could never match the force due to rolling resistance from the wheels.
Just to clarify; you understand that because the engines are pushing on the plane itself and not the wheels, by the time the wheels start moving, the plane is already moving relative to ground and air alike.
Which, said another way, this thought problem appears confusing because it’s being considered from otherwise irrelevant reference frames.
An anchor sufficient to keep the plane from rolling forward is different because the force it is apply is significantly greater.
Sure, you can deflate the tires and increase the rate of spin on the wheels. But at that point, you might as well ask “can we creat a scenario where planes can’t take off”
To which the answer is definitely “Yes”,
And as a side note, if we assume the wheels are indestructible, which I’d argue is only fair, then even if what you’re saying is true and we ramp up the drag induced by the wheels sufficient to counter the engines… then the wind generated by the rolling treadmill would be producing a sufficient headwind for the plane to take off. (Remember, the air resistance of the treadmill’s belt moving will accelerate the air some.)
But again, the wheels have almost zero drag to begin with, the speed at which the roll is independent of both the actual groundspeed and the airspeed of the airplane.
If it has the thrust to over come friction at take off speeds, and at standing, then it has enough power to get to take off velocity eventually.
On the other hand, this entire conversation assumes the thrust to weight ratio is less than 1. If it’s more than one, well they just…. Go straight up.
The wheels are attached to the plane so they move at the same time as the plane. But, I get what you’re trying to say, that the wheels are effectively being dragged by the plane, they’re not powering the movement. But, what you need to think about is that if you oppose that dragging by moving the conveyor belt in the opposite direction you can prevent the plane from moving at all. Yes, the wheels are merely dragging and there isn’t a lot of friction there, but friction increases with speed. And, if you move the conveyor belt fast enough, you can stop the plane from moving relative to the ground, which can stop it from moving relative to the air, which can prevent it from taking off.
No, by definition it’s the same. The conveyor moves with however much speed is necessary to stop the forward motion of the plane. The conveyor would eventually go so fast that it generated enough force to stop the plane from moving, so it’s indistinguishable from an anchor.
You don’t need to deflate the tires, you merely need to increase the speed at which the conveyor moves to match the speed of the wheels.
That seems like an unfair assumption because you’re assuming that the conveyor belt has second-order effects on the air (i.e. generating a “wind” over the wings of the plane), while ignoring the second-order effects the conveyor would have on the wheels (massive heat from friction leading to failure).
I mean, the discussion is of a plane, not a helicopter or a rocket. Even jet fighters with a thrust-to-weight ratio of more than 1 typically have engines that only have that ratio once they’re at high speed, not from a standing start. That’s why even fighter jets on carriers need a catapult-assisted takeoff. A VTOL aircraft like a Harrier wouldn’t need that, but then its takeoff speed is zero, and the myth isn’t very interesting when the conveyor belt doesn’t move.
no. I’m saying that by the time the wheel is rolling, the plane’s is already moving forward, the engines have already overcome the drag in the wheels. the treadmill is locked to the wheels, not the plane. The plane would continue accelerating even as the wheels reported weird rates of turning.
As for the (very brief) time delay, that’s a function of the plane’s gear’s suspension that is quite well sprung.
the rate of roll on the tire is, effectively, decoupled from the airspeed (and groundspeed) of the plane. which makes this:
… entirely different. an affixed anchor does not allow the free motion that a wheel would.
And one of a few things happen. Either the plane has enough engine thrust to overcome the acceleration induced by the wheels, and therefore takes off, or it does not.
In the case that it does not, the wheels would continue spinning in increasing RPM until the plane begins moving backwards. because, again, the airspeed of the airplane is not dependent on the wheel’s RPM. Assuming the airplane doesn’t crash from suddenly becoming incredibly difficult to control… eventually it would take off anyhow. because the airflow over the wings would still generate lift. (though they would become horribly inefficient.) and therefore take off.
this is of course ignoring the whole “can a pilot actually control that and manage a take off like that” thing. If you don’t want to grant godlike piloting skills, we could then just make the treadmill irrelevant and leave the brakes on.
The wheels are attached to the plane, so they move at the same time. There’s going to be slight flex due to rubber and metal not being insanely stiff, but essentially as soon as the plane starts moving forward through the air, the wheels start rolling forward along the ground. Since the conveyor belt cancels the forward movement of the wheels, the movement of the plane ceases too.
Initially, for a few tenths of a second, or a few seconds sure. But, during that time, the conveyor belt would be moving faster and faster as it matched the speed of the wheels. The faster the conveyor moved, the more friction there would be, and the more drag there would be from that friction. Eventually you’d reach an equilibrium where the drag from the wheels was equal to the thrust from the engine, and the plane would cease moving forward. It would be exactly like the plane being anchored to the ground, except instead of a stationary anchor, the anchor would be a spinning treadmill in contact with a spinning wheel. In a world without a magic conveyor belt that could instantly adjust to the speed of the wheels, there would be some slight forward and backward movement of the plane, but that’s just like being attached to an anchor with a bungee rather than a rigid rope.
The wheel doesn’t have free motion. By definition, the conveyor is moving at the same speed as the wheel, so the wheel is locked in place. With a real conveyor belt there would of course be some lag as the motors of the conveyor accelerated the belt, but using the hypothetical as defined, the axle of the wheel couldn’t ever move because every rotation of the wheel would be matched by a movement of the conveyor belt.
The thrust would have to be infinite because, by definition, the conveyor is always going to match the velocity of the wheels. If the wheels were truly frictionless, then the conveyor belt would have no effect at all. But, any real wheel will have some friction that will increase with speed, so there will always be some speed where the force backwards from the friction of the spinning wheels matches the force of the engine.
As an aside, my guess is that most real airplane wheels would probably fail pretty quickly at just double the normal takeoff / landing speed. The centripetal force acting on the spinning parts of the wheel and tire increase with the square of the velocity, so 2x as fast means 4x as much force. 3x as fast and 9x as much force. So, if you did this with a real wheel, you’d destroy the wheel pretty quickly. Of course, the same applies to the conveyor belt, but I’m going to assume that it’s specially engineered to survive this challenge.
The plane wouldn’t move backwards because if the wheels slowed down, the conveyor belt would slow down too. Of course, that’s in a world where the conveyor belt could adjust its velocity instantaneously, but for this thought-experiment you can say that if the pilot cuts the engine or something, the wheels don’t spin as fast, so the conveyor belt slows down, and the plane remains in one spot.
In the thought-experiment world, there wouldn’t be any airflow over the wings because the plane would be stationary. In reality, there would be some airflow due to the movement of the conveyor belt, but the wheels would probably melt long before that was enough air to give the plane lift while stationary relative to the world around.