If your treadmill is going so ludicrously fast that the bearing friction (plus rolling resistance I guess) provides a backwards force that is equal to the force being applied by the engines, then I guess the plane will not be moving forward.
Again, this requires magic, infinite friction between the tires and the treadmill surface. Also your wheels will explode, unless they are magic non-exploding wheels.
Maybe read point 3 here of this appropriately named xkcd blog entry.
The only way to shorten landing length is for the plane to decelerate more quickly. Deceleration happens three ways. First, there’s wind drag, which is proportional to the square of the plane’s speed relative to the air. This has nothing to do with ground speed or wheel speed. Second, there’s reversing the thrust of the engines. This also has nothing to do with ground speed or wheel speed. Third, there’s the mechanical brakes in the wheels. Essentially, the brakes suck kinetic energy from the plane and convert it to heat energy in the brake pads (and the tires). The limiting factor is how quickly the brake pads can dissipate the heat. Landing on a treadmill would merely make the wheels spin faster. I don’t see how that would increase the efficiency of the braking system. You still have the same limitation that you had before, which is the fact that if you step on the brakes too hard the brake pads will overheat. You still have the same amount of kinetic energy that needs to be transferred. It still takes the same amount of time. If the plane decelerates in the same amount of time, it must cover the same distance, regardless of how fast the wheels are spinning.
Replacing the runway with a treadmill is totally useless for either takeoff or landing because the treadmill would have to be exactly the same length as the runway it would replace.
The xkcd blog entry fails to address the OP. The question we are here to discuss is not whether you can replace a runway with a treadmill. You can. The question is would that accomplish anything? The answer is NO. The treadmill needs to be exactly the same length as the runway it replaces. The treadmill offers no advantage. This explains why aircraft carriers use catapults and arresting cables instead of treadmills.
Have you read this crazy thread? It’s way past the OP.
No, I’m asking in your scenario where the plane takes off, what do I see when looking at the wheel/treadmill video? The only answer that makes any kind of sense is that the wheel speed is greater than the treadmill speed, which is also a violation of the premise.
So all this boils down to is that if it’s a possibility to have the treadmill always move as fast as or faster than the wheels.
The argument against is that the wheels’ speed is a function of the treadmill and plane speed, so you can’t instantly adjust the treadmill speed based on said adjustment’s result.
My argument is that it is possible to adjust the treadmill speed as a function of the plane’s thrust. In a simplified, ideal world, it wouldn’t be much of an argument to state if the thrust was split and pointed in opposing directions the plane would not move. But also, if 1/2 thrust force was applied to the plane and 1/2 to the treadmill speed (with no energy loss), the plane would remain stationary also.
Read point 3 of the blog post.
No, this would only be true if the wheel was glued to the treadmill.
I’m trying quixotically to steer the conversation back to the OP.
Right, so if the only answer that makes sense doesn’t make sense, then the question is flawed.
That is a valid question. The answer is no.
Correct, because the only way for that to happen is at 0 or at infinity.
What does “applying half the thrust to the treadmill speed” mean in this context? Are you saying that the treadmill will be powered by the 1/2 the engine power? In that case, the plane only has 1/2 the power to take off, so may or may not take off, depending on how much power reserve it has. The moving treadmill would have no effect. If you are saying that the treadmill is moving at the exhaust velocity, well, the treadmill is moving really really fast, but is still not having any effect.
The original, interesting, and correct premise is that the treadmill moves in the opposite direction at the same speed of the airplane, not the wheels. That’s the premise.
The other premise, the one that you’re pushing, and was already addressed in Cecil’s column, is that the treadmill moves in the opposite direction at same speed as the wheels. This premise is impossible.
Under the original formulation, the wheels go faster than the treadmill – the plane moves at 100 mph, the treadmill moves in the other direction at 100 mph, and the wheels spin at an equivalent rate of 200 mph.
Under the second premise, the wheels and treadmill instantly go to infinity as the treadmill tries to increase to the speed of the wheels, making the wheels spin faster, making the treadmill spin faster. This is uninteresting and impossible, but if there really was no friction in the bearings, and the wheels were made out of unobtanium, I guess the plane would take off as usual.
And, with that, I predict this thread will come to its natural end.
Only if the plane isn’t moving. And the plane moves as soon as the engines apply thrust because the wheels don’t impact the plane’s speed.
Alright, I think I’ve wasted enough of my and ya’ll’s time on this. I think most of us actually agree on the physics of the scenario, I just diverge on whether or not it’s possible to have the treadmill keep up with the wheel speed. Some believe the plane would still take off under this scenario, which I really don’t get, but whatever. I appreciate everyone’s responses. Now, I’m off to see if anyone on the dope boards remembers this alternate ending to Big where Susan comes back as a little girl. I saw this once when I was a kid.
Nice!
And, now, finally, this thread will skid to a halt, since it’s on a treadmill moving in the other direction.
No, we can’t. It is impossible for the treadmill speed to exceed the wheel speed under the conditions of the setup, so the statement is meaningless. You can’t have logical consequences from an impossible premise.
I don’t know why this is so difficult. You seem to have cause and effect muddled up. The wheels do not rotate by magic, you cannot specify their speed of rotation as an independent parameter. Their rotation is determined by what the treadmill and the aircraft are doing.
(1) Under thrust, the aircraft will move forward, regardless of what the treadmill does.
(2) The aircraft speed and the treadmill speed determine the speed of the wheels: it is the sum of the two. If the aircraft speed is positive, then the wheels rotate faster than the treadmill speed.
Your hypothetical “treadmill speed > wheel speed” might as well be saying, “well, what if force does not equal mass times acceleration?”, or “what if two plus two equals five —what then?” (dramatic music).
ETA: If some other force (reverse thrust from the engines, say) were making the aircraft move backwards then the wheels would rotate more slowly than the treadmill as a consequence of the the aircraft’s backward motion. But let’s be clear about cause and effect: that’s a consequence of what the aircraft is doing. Again, you cannot specify the speed of rotation of the wheels as an independent parameter. The wheels simply do what the movement of the aircraft and the movement of the treadmill tell them to do.
The wheels/treadmill have no impact on the plane if the engines are running; either moving forward or taking off. Until you grasp this fundamental part of the scenario then we don’t all agree on the physics.
If the treadmill moved in the direction of engine thrust, would the takeoff area be shortened?
If the treadmill moved backwards at the engine’s maximum thrust speed before the engines are started, could the plane develop enough thrust to take off?
Hmm. Yes, it would shorten the takeoff distance slightly. Takeoff distance depends entirely on acceleration, which is thrust minus drag minus rolling resistance. Rolling resistance is a constant and does not depend on the speed of the treadmill. But if the treadmill spins the opposite way, the rolling resistance would add to acceleration instead of subtracting. So, yes, the plane would accelerate slightly faster and take off slightly sooner.
There are two scenarios. #1 the treadmill spins forward at a speed higher than the plane’s takeoff speed, so that the airplane’s wheels are spinning backwards. In this case, acceleration equals thrust minus drag plus rolling resistance. #2 the treadmill spins forward at a speed slower than the plane’s takeoff speed. In this case, acceleration is initially thrust minus drag plus rolling resistance and then switches to thrust minus drag minus rolling resistance when the plane exceeds the treadmill’s speed. In either case, the total time required to reach takeoff speed is less than what it would have been with no treadmill at all.
This would be most effective leaving the plane’s brakes on and slowly ramping up the treadmill’s speed as the plane accelerates. Essentially you’d be turning the treadmill into a catapult.
This question makes no sense because you’re attempting to equate thrust and speed. The speed of the treadmill is irrelevant because rolling resistance is a constant. If the plane’s wheels are turning forward, the rolling resistance will slightly slow down the plane. Making the wheels spin faster doesn’t increase the resistance at all. There is no such thing as a wheel speed which could match the engine’s thrust. The engine has more than enough thrust to overcome the wheels’ rolling resistance, or else it would never be able to move on a runway. Rolling resistance is a constant.
But turning the treadmill forwards instead of backwards does reverse the direction of the rolling resistance vector. Yes, pushing the plane forwards with a treadmill would shorten the takeoff distance slightly*. Perhaps you could replace a 2,000 foot runway with a 1,950 foot treadmill. That would be an awfully expensive installation just to save a few feet. You are much better off with a catapult.
Can an airplane successfully take off with its wheels locked?
That would be difficult but not impossible. The airplane just needs enough air speed, which is the relative speed of the wings through the air (or air over the wings, depending on your point of view). All the wheels do is increase or decrease friction relative to the ground. Putting on the brakes maximizes friction with the ground. But under certain conditions, that friction would be small enough that the engine’s thrust could overcome it and the plane could accelerate to takeoff speed.
Here are several options I thought of which would allow a plane to take off with its brakes on:
Note that option 4 requires a treadmill which is almost as long as a conventional runway.
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