The problem is that (approximately) the level of thrust required to maintain a certain speed does not depend on the speed itself. So, for example, suppose you need 50 pounds of thrust to keep the plane stationary on a treadmill moving 2 mph. If the treadmill’s moving 3 mph, the you need about 50 pounds of thrust to keep the plane stationary. If the treadmill’s moving 10 mph, then you need about 50 pounds of thrust to keep the plane stationary. If the treadmill’s moving 100 mph, then you need about 50 pounds of thrust to keep the plane stationary. And on and on and on.
So. What happens when the engine produces 51 pounds of thrust?
There’s no speed where the additional 1 pound of thrust will be balanced. So the additional 1 pound of force goes into accelerating the wheels. And as long as you keep the engine lit at 51 pounds, the wheels (and the treadmill) keep accelerating and accelerating and accelerating until the tires blow or the engine runs out of fuel.
Nope. Only if the wheels have (effectively) infinite friction. If they have the realistic friction of real landing gear, they just spin a little and the plane takes off almost unimpeded, unless the treadmill is going fast enough to blow the tires (or the axles fuse or the treadmill breaks)
As much as I hate to dive in here, I think what is in this paragraph is the source of your confusion.
This is one of the ways on interpreting the “the speed of the treadmill matches the speed of the plane”, and it’s perfectly valid. But you then make this assumption:
which is probably not correct.
Consider a plane going down the runway at 5 mph. Lets say the wheels have to rotate once per second at this speed (I have no idea of the real speed).
Now the plane drives up on a treadmill running backward at 5 mph. What happens? Does the plane stop relative to the ground?
Almost certainly not. What happens is the plane continues to move forward at about 5 mph relative to the ground, but the wheels are now turning twice as fast (twice per second instead of only once).
Now imagine a car going 5 mph drives up on that same treadmill. What happens? Does it continue forward like the plane?
No, unlike the plane, it stops moving forward relative to the ground.
Why the difference? With the car, the thrust of the engine is transmitted through the tires pushing back on the ground. By counteracting that movement with the treadmill, the car no longer moves forward relative to the ground.
But the plane is pushed by the engines directly, not through the wheels. The thrust is not transmitted through the tires. They just freewheel. It’s as if the plane is pushing directly against the air. It’s not, it’s an action/reaction kind of thing, but in this case the effect is the same. So all that happens on the treadmill is that the wheels freewheel at a higher speed to make up for the fact that the treadmill is going backward, while the plane continues moving forward relative to the ground pretty much as if nothing had changed.
So it takes off normally.
Now if you make one of the other assumptions about “the speed of the treadmill matches the speed of the plane”, things can be different. But in your specific example, I think this is where you go wrong.
**Sorry if this has been explained elsewhere, but I haven’t seen this covered… **
This is a different look at why this seems to be highly problematic…
Okay, a typical commercial jet needs to reach a speed of 150 to 180 miles/hour to lift off from the ground.
If the plane achieves this speed on the treadmill (which is standing still relative to the earth), and it achieves takeoff speed, how does the plane suddenly go from 0 mph (again, relative to the earth) to 180 mph…
This would be less of a takeoff and more of a launch. And even in scenarios where a rocket launches, the physics are much different.
Someone please explain to me how the plane would make this seemingly miraculous jump from 0 to 180mph. :smack:
This is the point where the slight chortles crept in…
…aaand this is the point where I actually laughed out loud. I don’t mean that in the much abused and completely false ‘lol’ sense, I mean actually laughed out loud.
This is indeed where I get confused. And i think that both quotes are hinging on the same fact that I don’t get. Why is it that 50 foot pounds of thrust move the same plane 2, 3, even 10 miles per hour? Is it the same reason that moving onto the treadmill from a “normal ground” speed of 5 miles per hour will not actually stop when the ground underneath it starts moving back at 5 miles per hour?
I do understand a difference between the thrust being transmitted to the air by the engines of a plane vs the thrust being transmitted to the ground. I just don’t see, when the airplane has less not reached takeoff levels of air moving over it’s wing, how that matters. Whether the thrust is being transmitted through the wheels or the air doesn’t seem to matter to me. I am still seeing this as “the ground is moving backward at x miles per hour, the thrust of the plane is moving it forward at x miles per hour, x from both sides cancel each other out.”
So is there some fact you are utilizing or step that you’re not explaining? Is there something so implicit to your explanation that is just so very obvious (to those who do know it) that you’re not explaining it (to those that don’t get it)?
Agreed that realistic tires and realistic friction leads to blown tires and so forth.
However, I think Fzplus is interpreting the problem more as a thought experiment. In other words, he’s ignoring the real-life effects on tires and bearings, and he’s explicitly assuming a frictional torque that increases with speed.
There’s no need for infinite friction here, just wheel assemblies that will withstand the entire engine power being dumped into them as frictional heat. A tall order, yes, but a perfectly valid thought experiment.
I don’t think anyone’s saying that. It’s just that different people have been using “speed” to mean different things: speed with repect to the treadmill or speed with respect to the ground. For the most part, anyone who comes to the conclusion that the jet takes off is arguing that the jet isn’t standing still with respect to the ground, for various reasons.
Thank you, thank you. I will (apparently) be here all week.
Okay, Assuming that plane is on a treadmill, and it is moving at a speed which progressively increases to 180 mph on that treadmill, but if you are not on the tredmill (say standing and watching from 50 ft away) the plane is moving at 0 mph relative to your position - when the plane “takes off” it suddendly should be moving at an airspeed of 180 mph relative to your position.
There seems to be a basic problem with relativity here; or am I missing something?
Careful here. There’s a difference between moving the plane at X miles per hour on a runway and keeping the plane stationary on a treadmill that moves X mile an hour.
Here’s the issue. You’re looking at it as if the basic impetus is a speed rather than a force.
Perhaps the fact I’m not explaining is this: F=ma. Force equals mass times acceleration. If the forces aren’t balanced, the object (plane, car, whatever) must accelerate.
Let’s back up to a more intuitive analogy. You’re sitting in your car, cruising down the highway at a steady speed. Your foot’s on the gas, the engine’s delivering torque to the wheels, and the wheels are applying force to the road. With me so far?
But you’re not accelerating; you’re staying at a steady speed. That’s because the wheel force is exactly balanced by opposing forces: hysteresis force in the tires and air resistance forces being the two big ones. All forces add to zero, and you don’t accelerate. If any of those forces change, your speed will change (because F=ma, or rather a =F/m).
For example, you let off on the gas. The force pushing the car forward is now less than the force opposing the car, and you slow down (because F=ma, and negative total F means a negative total a). The nice thing here is that the air resistance force is a function of your velocity, So, as you slow, the air resistance force decreases, and eventually the forces are again equal, and you’re travelling at a constant velocity.
Likewise, if a tailwind suddenly springs up, the air resistance decreases, the forces are no longer equal, and (unless you let off the gas) your car accelerates (because F=ma).
Now, back to the airplane. Look at it from a force point of view, not a speed point of view. During a normal take off (on a runway, not a treadmill), the engines produce a force. That force is resisted by wheel friction, tire hysteresis, and air resistance. Normally the engine thrust is greater than the resisting forces and the plane accelerates (F=ma, right?).
However, you could probably roughly match engine thrust force to some steady speed. If the engine produces just a little bit of force, the plane will accelerate to (say) 1 mph, at which time the air resistance force increases just enough to completely balance the thrust, and the plane stays at a constant 1 mph until it plows off the end of the runway.
With a little more thrust force, the plane will accelerate to 2 mph, at which time the air resistance force increases just enough to completely balance the thrust, and the plane stays at a constant 2 mph until it plows off the end of the runway. And on and on and on.
But once you put the plane on a treadmill, this force balance is no longer valid, because if the plane stays stationary, there is no air resistance.
Suppose you fire the engine up to produce a little bit of force–the same little bit of force that pushed the plane to go a constant 1 mph on the runway. What happens?
The thrust force is the same, but the opposing forces are different: there’s no air resistance. So the forces don’t balance when the treadmill goes 1 mph. It’s a different set of forces.
So what does happen to the plane on the treadmill? Well, it depends on what you assume happens to the other forces–the hysteresis and the bearing friction and so forth. Different assumptions lead to different answers…but one thing that’s for sure is that in this case, the overall forces are different from the non-treadmill case, so the acceleration (and the velocity) must be different too.
Anywhere in this discussion, to avoid misunderstanding, we must specify (1) what object we are talking about (plane, treadmill, ground, air) and (2) what the speed is relative to (plane, treadmill, ground, air). No assumptions should be made, or confusion will result.
So, “If the plane achieves this speed on the treadmill (which is standing still relative to the earth)…”, WHAT is standing still? The treadmill or the plane? And it is standing still relative to WHAT? The air? The ground? The treadmill? WHAT is achieving this speed? Relative to WHAT? The air? The ground? The treadmill?
Using different assumptions will get you different answers.
No one (well, almost no one) claims that a jet which is on a moving treadmill but is stationary with respect to the ground will take off. But some people claim (for various, but perfectly valid, reasons) that the plane will be moving with respect to the ground.
No, the plane is progressively increasing to 180 mph relative to my position. The crux of the problem is that, barring some incredibly unphysical situations[sup]*[/sup], the treadmill can’t stop, nor even slow down, the plane. The treadmill can get the wheels spinning very, very fast, but the plane basically doesn’t care how fast its wheels are spinning, it’s going to just keep on going forward through the air.
*And even in those situations, the plane still takes off, though for different reasons. But let’s not get into that right now.
That is indeed the crux of the matter that I don’t GET at all. The phrase “the treadmill can get the wheels spinning” has to be alluding to the something I don’t get.
Strictly from a mind experiment, how I’m seeing it, no physics formulas at all, IANAPOAE (I am not a physicist or aeronautics expert) point of view… at low speeds (where the plane is traveling slowly relative to the ground), the force of the engines is overcoming not air resistance, but gravity and inertia.
Unless there is some force I’m not aware of acting here, it takes a pretty significant speed of air moving over the wings of the airplane before there’s enough lift for air resistance to become one of the major factors. Until that lift is present, I don’t care if the engine is attached to the wheels or not, it’s still transmitting that force in part through those wheels, and the treadmill moving backward at the same rate as the plane is moving forward will prevent that lift from ever occurring.
To all those who say the plane takes off with the wheels going twice as fast: You seem to be forgetting that it is the speed of the wheels we are measuring, not the speed of the plane. And by speed of the wheel, I am interpreting it as (distance around the circumference of the wheel that has rotated) / (time in which it has taken to do this). ie, if the circumference of the wheel was 3m, and it takes 3 seconds to perform a complete turn, the speed of the wheel as I interpret it is 1m/s.
If the question had said that the belt matches the speed of the plane, then yes - it would take off with the wheels going twice as fast. But it matches the speed of the wheels, so with the wheels going twice as fast… the belt goes twice as fast also, keeping the plane still.
I’m very much in the ‘plane does not take off’ camp!
Oh… and Mr. Emerson, your scenario is not my scenario. At least from my point of view it doesn’t matter how quickly the wheels are rotating, it’s a matter of whether the plane is moving forward or not. I’m still in the plane not taking off camp, but I’m also pretty sure that the place taking off camp knows something that they have not expressed in a way to enlighten me.
Ok… i may have gotten a glimmer of that elusive “something” I’m missing. In another thread on another board, someone said “take the treadmill, this long flag impersonating the ground moving backward thing out of the mental picture and replace it with metal rollers like you would use to test tire rotation” Now if I picture a plane with it’s wheels on those, I’m having somewhat less of a mental issue seeing the plane hopping itself right out of those, no matter how fast they are rotating.
Yet, I’m still not seeing the same thing happening if I make the mental switch back to the treadmill.
Lets take the closest thing to a real world version of this scenario… a pontoon plane vs. a pontoon boat. Both having the same weight, both having the same displacement in the water. The pontoon boat is acting against the water with a prop propeller in the water. the pontoon plane is acting against the air.
Put both of these things in a fast moving river, point them upstream and start the engines.
Prior to the point that the plane’s speed decreases it’s water displacement, what difference is there in the amount of force to move the pontoon plane upriver against the current compared to the pontoon boat.
Similar to the treadmill exercise, the plane is not acting against the ground/water, it’s acting against the air. A boat or car is acting against the ground/water.
Are these similar enough for whatever the “something” is I don’t get to become clear enough for someone to point out?
The plane’s engines push directly on the plane. They push the same if the plane is on the ground or in the air, or on skis on the water. The wheels do nothing but spin, their only function is to reduce friction between the plane and the ground.
Imagine it like this. The plane has no engine. Way down at the far end of the runway is a winch, with a two-mile long cable that comes all the way back and attaches to the nose of the plane.
The winch starts to pull the plan the plane forward at 5 mph relative to the ground.
At the one mile mark, the plane rolls up onto a treadmill that is running at a constant 5 mph backwards. What happens?
Does the plane stop relative to the ground? Of course not. The winch doesn’t care about the treadmill, it just keeps sucking that cable in at 5 mph relative to the ground. The only way the plane could stop is if the cable pulled the nose off.
The only thing that changes is that the wheels on the plane have to spin twice as fast to account for the fact that the plane is moving forward at 5 mph relative to the ground, while the treadmill is moving backward at 5 mph relative to the ground.
So the plane happily rolls right across and off the treadmill and on down the runway.
So the thing to understand here is that the plane’s thrust comes from the action / reaction of pushing the air backward, and the “push” is directly on the part of the plane where the engines are attached, just as if there actually were a cable tied to plane and pulling it.
The only way the plane could stop is if the engines break off, just as with the cable.
The wheels are only along for the ride, and under anything like normal circumstances, you couldn’t possibly impart enough force to the plane by spinning them to slow the plane down much at all.
Sorry, But I’m confused at what is being said here.
If the plane is moving on a treadmill (I’m assuming that the treadmill is used so the plane will not move forward (off the treadmill) until it has reached takeoff speed). For example, lets say the “footprint” of the plane is 200 feet long, and the tredmill is 210 ft. (so the plane doesn’t leave the treadmill, but the treadmill “spins” to accomodate the idea that the relative surface (and spin) of the treadmill allows the plane to move “forward” at 180 Mph without moving across the length of the runway.
If this is the case, the plane is moving 0 mph relative to anyone (or anything) that is not on the treadmill (this is what relativity is all about).
Please explain how the plane is progressively increasing to 180 mph relative to the position of someone not on the treadmill, because the increase in speed in the relative space of the tredmill doesn’t apply to anything not on the treadmill.
Now this one I really don’t get. Take my water example above, add a third element… a pontoon boat, with no engine, and it’s attached to a cable/winch that’s 2 miles up stream.
Is the force required (provided by the plane’s engine, the winch pulling, the boat/s propeller) to move all three of these things 2 miles upstream the same? Because unless there is something that causes the boat to exert more force to move that distance than the other two options, then I’m still missing whatever factoid, point of view or advance physics formula you’re using to say that the plane still moves independent of the ground before it gets lift.
Personally, I can see where the winch might actually require less, but I think that the plane, at best, exerts a level of force between that of the winched boat and the propeller in the water driven boat.
At least from my point of view it doesn’t matter how quickly the wheels are rotating, it’s a matter of whether the plane is moving forward or not. I’m still in the plane not taking off camp, but I’m also pretty sure that the place taking off camp knows something that they have not expressed in a way to enlighten me.