Will it take off?

Original Question:


A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

I see all of this talk about wheel speed, but it's not really an issue, and it's being confused. First, I do not think it would be disagreeable to say that in this case a wheel is in someway attached to a plane. That is to say, the wheel is going just as fast as the plane, in the direction the plane is going.

Second, with respect to the wheel's rotation Under normal flying circumstances, the wheel's RPM is independent of the engine's RPM. For example, a stationary plane could rev its engine quickly, creating a lot of RPMs, but not creating a full rotation in any wheel.

Third, for a plane to taxi under normal circumstances, it must have enough power to drag itself using air (push or pull on air) between two points. I use the word drag because of the first two ideas: The wheel is attached to the plane, and wheel RPM is independent of engine RPM; the plane does not roll itself, although while dragging itself, the wheels do begin to roll via friction.

I don't have the stats for airplane tires, but, the coefficient of friction for normal car tires is .015 (www.howstuffworks.com...). Let's assume our plane is 500lbs, meaning, it would take 7.5lbs (500*.015) to drag the plane on level surface.

Let's start up the treadmill. Neglecting air for now, if I were to drag this plane of a stationary treadmill, the friction between the wheels and the treadmill would be the same as if the treadmill were on, and going the same speed as I was dragging the plane. The same would be true no matter how fast I go:

Part of the standard model of surface friction is the assumption that the frictional resistance force between two surfaces is independent of the velocity of relative movement.

hyperphysics.phy-astr.gsu.edu...

The main point of all of the above:
Friction will not increase as the wheel continues to spin faster.

Now, I have a handy-dandy calculator for air friction that I've been using from www.exploratorium.edu... -- Using the weight of 500lbs, and 90MPH speed we come to a drag of 212.93 newtons. Allowing that 1 newtons = 0.224808943 pounds force, 212.93 newtons = 47.8685683 pounds force.

So, to move forward on this treadmill while initially going that spead, the engine must produce more than 47.9lbs + 7.5lbs of thrust. Which is interesting, since a covair engine can produce over 300lbs of thrust. (www.flycorvair.com... )

Granted this math was very rough using car tires, bicyclist air dynamics, and a 500lbs plane, but it illustrates the plane overcoming air and ground drag in order to move forward on a hypothetical treadmill. It's late, so please forgive any mistakes.

-Radardog

Originally posted by radardog
I see all of this talk about wheel speed, but it's not really an issue, and it's being confused.

Yes and no.

It's relevant because many people are/were under the assumption that the conveyer can/does match the plane's wheel speed, allowing the conveyer to reach an equilibrium that "holds the plane in place".

But, all the conveyer can do is add to the wheel speed (of the plane) and, as long as that's the case, the wheel speed will always be faster than the conveyer which proves that the plane will be moving forward.

This is just a "simple" way to prove the plane will move forward and gain airflow.

Originally posted by radardog
First, I do not think it would be disagreeable to say that in this case a wheel is in someway attached to a plane.

Correct.

Originally posted by radardog
That is to say, the wheel is going just as fast as the plane, in the direction the plane is going.

Incorrect.

While this would basically apply on a normal runway (still, it depends on a head, or tail, wind since plane's measure air speed), the conveyer changes the rules.

The wheel speed will be (roughly) double the plane's speed.

Even though the conveyer is going the opposite direction, it will still spin the wheels in the same direction as the plane's independent "pull/thrust".

2mph (plane speed) + 2mph (conveyer speed) = 4mph (wheel speed)

The conveyer doesn't hinder (or help) the plane's speed, it's energy is just "lost" (as excess wheel speed) in the free-spinning wheels.

Originally posted by radardog
Friction will not increase as the wheel continues to spin faster.

I'll take your word for it on the tires, and "one up" ya, that the tire friction will actually reduce as the plane starts to gain airflow/lift, however, the bearing friction will increase as the tires spin faster, but as long as they (the bearings) can withstand spinning twice the normal takeoff speed, all will be fine.

[edit on 2/21/06 by redmage]

On topic of the length/time on the conveyor:

Yes, there is friction to overcome, but it is no different than on a static runway. The belt doesn't move until the plane does, and once it's moving (and the belt starts moving), that force has been overcome. The only other forces that are different on the conveyor than on a normal runway would be the additional friction in the wheel/bearing/strut combination. I have no idea how much friction typical wheel assembly components have, but I would think that it would cause at least enough of a force (since the wheels will be rotating twice the speed of normal) to factor into the equation.

HOWEVER, the belt still only matches the speed of the aircraft. While the thrust is trying to overcome this friction, the belt is also moving at the same speed. To me it seems as if the plane could take off on the exact same LENGTH of runway, but might take a bit LONGER in time to get up to speed. I haven't done the math in physics equations, but I think that would contradict (as time and distance are cornerstones of acceleration/velocity equations ... changing one of the two usually changes the other). Anyone got any ideas? I'll look into my equations later tonight.

Try thinking of it this way. let's say that you have a car in a wind tunnel. The speed control on the fan is set to match the forward speed of the car. Can the car drive into the wind? Of course it can.

the plane fires up it's jets and begins to move forward. the conveyor matches the planes SPEED and in the opposite direction it begins ACCELERATING as the plane accelerates. the wheels turning at whatever speed are negated by the belt, but the engines are pushing on AIR, so the plane will move forward. so, whatever the takeoff speed of the jet, the belt only needs to turn that fast, maybe 120 miles an hour?(i'm not a pilot)(remember, it's MATCHING the SPEED of the AIRPLANE, in the reverse direction, so the wheels would be going 240 mph(well, spinning to accomadate that velocity based on their diameter), which isn't even unreasonable!).

the above was my answer for physorg.(with extra stuff just for ATS) i see others saying the same thing, but i thought i'd throw my vote on this side of the argument.

[edit on 21-2-2006 by billybob]

Ya got it all right except this:

Originally posted by billybob
the wheels turning at whatever speed are negated by the belt,

It's more like "the belt is negated by the wheels".

Other than that, perfect.

Originally posted by redmage
Ya got it all right except this:

Originally posted by billybob
the wheels turning at whatever speed are negated by the belt,

It's more like "the belt is negated by the wheels".

Other than that, perfect.

heehee! cheers.

To Those who would argue that the Thrust of the plane's prop or Jet exhaust "is pushing against the air", I recommend that you consult a physics text.

Or more simply:

The "thrust" generated by an airplane's engine, no matter What Type of Engine it Is does NOT "push Against The Air. A vehicle's engine pulls or pushes against the vehicle itself. Air is not solid, it is a gas, which although unlike a true fluid, is compressable, does not present a surface against which one can impart force.

The "thrust" you all seem to be refereing to is nothing more than the higher pressure opposing the low pressure created by the prop on the front surface of the prop blade as it slices through the air. It is in fact the lower pressure created by the prop ahead of the prop (and by extension, the plane) which is actually pulling the plane through the air!

This "thrust" as you call it is merely a by-product of the actual force responsible (in the case of a prop-driven vehicle) for the motion of the vehicle.

Hoping, for the sake of my ever diminishing faith in the modern educational system, that we can all agree that the same law of physics would apply to an airplane whether that plane was powered by a propeller, a jet engine or a rocket engine; how is it then that a rocket is able to propell a vehicle, winged or otherwise through the vaccuum of space - - where there is NO air to "push against"!?

The law of physics involved Does Not Change with the Method Used to Demonstrate that law!

Originally posted by Bhadhidar
Newtonian Physics 101
.....

That's lovely

Although, you're really just, incorrectly, arguing semantics here.

Originally posted by Bhadhidar
It is in fact the lower pressure created by the prop ahead of the prop (and by extension, the plane) which is actually pulling the plane through the air!

Incorrect, it is in fact the higher pressure created by the prop (behind the prop), which is forcing (or pushing) it ahead into the low pressure area (ahead of the prop), that actually pulls the plane through the air.

The blades of the prop are just "mini wings" creating forward lift.

www.aeromuseum.org...
The wing is forced into the region of reduced air pressure above the upper surface of the wing by the higher air pressure beneath the wing.

Forced=pushed, by the higher air pressure behind (in a props case), which in turn pulls the rest of the plane.

Don't get me wrong, the low pressure helps, but it doesn't create nearly enough of a "vacuum" to solely pull the plane.

I'm just hoping, "for the sake of my ever diminishing faith in the modern educational system", that you have been able to grasp the independant nature of that thrust, how it will allow the plane to move forward (regardless of the conveyer) to gain airflow under (and over) the wings, and in turn take flight.

Originally posted by Bhadhidar
how is it then that a rocket is able to propell a vehicle, winged or otherwise through the vaccuum of space - - where there is NO air to "push against"!?

How is it that you got so far off topic? :shk:

The rocket pushes against the mass of the "ship".

And, there's a reason that they don't use "props" in the vacuum of space.

There is no air pressure to push them (the props) forward as they spin, even though a "vacuum" (ahead of the prop) would already be there.

Your own example effectively disproves your theory that low pressure, ahead of a prop, is all that is required to "pull" the vehicle forward, and shows the nescessity of the high pressure "push" wonderfully.

[edit on 2/21/06 by redmage]

Originally posted by Bhadhidar
To Those who would argue that the Thrust of the plane's prop or Jet exhaust "is pushing against the air", I recommend that you consult a physics text.

Or more simply:

The "thrust" generated by an airplane's engine, no matter What Type of Engine it Is does NOT "push Against The Air. A vehicle's engine pulls or pushes against the vehicle itself. Air is not solid, it is a gas, which although unlike a true fluid, is compressable, does not present a surface against which one can impart force.

The "thrust" you all seem to be refereing to is nothing more than the higher pressure opposing the low pressure created by the prop on the front surface of the prop blade as it slices through the air. It is in fact the lower pressure created by the prop ahead of the prop (and by extension, the plane) which is actually pulling the plane through the air!

This "thrust" as you call it is merely a by-product of the actual force responsible (in the case of a prop-driven vehicle) for the motion of the vehicle.

there are no gears on landing gear. the same force that drives the plane forward(the propellor or jet) when there is no conveyor belt, will drive the plane forward at the same rate as if there IS a conveyor belt reverse matching the speed of the airplane, except the wheels will spin twice as fast. in the latter case.

no need to get into the technical aspect of suck vs. blow for this argument, methinks. you're right, though, of course. propellors are pushed by air, but as newton said, for every force there is an equal and opposite force, so i think it's fair to say the engines push on the air, but, hey, that's just me.

on the other hand, you're wrong, though. flight is not achieved by engines thrusting on airplanes, it is achieved by creating a low pressure zone in front of the blades using bernoulli's principle, which gives the blades 'lift', but ina vertical position. the air pushes the blades, and the plane that is attached follows.

Originally posted by Kruel


"Matches the speed of the plane" is quite vague. This could be the speed of the plane in relation to the ground, the belt, or the air. But which? It doesn't specify.

I know I'm dipping into semantics here, and you do get the gist of my argument, but I would say its not vague at all, if the 'speed of the plane' is matched then the plane must have some speed to BE matched, if the plane is stationary, it has no speed. That is perfectly clear and according to the rules of english if you want to mean something else then you have to spell it out, ie say 'the speed of the plane relative to the belt it is on but independant of the ground speed' etc. Because it does not say this there is no reason to try and place this interpretation on the question. Anyway, thats is my view of course and the argument will rage on.

The wheel can only spin as fast as the surface the wheel is in contact with. It just blows me away that alot of you think the wheel is spinning at double the rate that the conveyor and the plane are moving.

The plane is moving forward at 3ms- the wheel is moving forward at 3ms. If the conveyor was not moving ie just on the tarmac then the wheel would travel in position 3 meters from Point A to Point B in one second.

BUT

Since the conveyor is moving at 3ms in the opposite direction (lets say turn based) Plane moves forward 1 second at 3ms, plane travels from point A to point B (3 meters) now its the conveyors turn, the conveyor moves 3ms in the opposite direction, so then in this phase the plane (not moving now) moves from Point B back toward Point A 3 meters in one second. The plane is now back to point A where it started its last turn.

When both the plane and the conveyor move in the same phase, the wheel moves at 3ms (or whatever the rate the plane is pushing it or trying to pull it forward) and the ground underneath it is moving back towards point A at the same rate.

if you have a roller between two drive belts one on the top and one on the bottom, the roller does not turn at a rate that is twice as fast as the belt moving past it.

Look at any belt driven automobile pulley that is at the end of a loop. On each side the belt is moving in opposite directions one forward and one reverse, does the pulley stay in place or is it driven off. Is not the rate the same on the top of the pulley as is the bottom. The pulley can only turn as fast as the media that is moving past it.

Originally posted by robertfenix
The wheel can only spin as fast as the surface the wheel is in contact with. It just blows me away that alot of you think the wheel is spinning at double the rate that the conveyor and the plane are moving.

the speed of the wheel is measured along it's ROTATION, not 'forward speed', which would of course, be the same speed as the plane. the plane moves forward at 10 mph, the belt backwards at 10 mph, then the surface of the wheel, where it contacts the belt, will have to spin at 20 mph. anything else is impossible.

what people seem to be missing is that the wheels spin freely whether there is a belt or ground beneath the plane. the wheels do not drive the plane forward, nor are they capable of pulling it backwards. the engines propel the plane forward, and as long as the wheel bearings don't overheat and seize up, the plane will just take off normally.
i think it unlikely that the takeoff speed for a plane, times two, would be enough to overheat wheel bearings on a vehicle which is SUPPOSED to go several hundred miles an hour.

Robertfenix. re your last post. Imagine a normal factory conveyor belt travelling at 10pmh, now, imagine yourself beside it, stood on the ground, walking in the opposite direction, also at 10mph, whilst holding, for the sake of argument, a toy car in your hand and pressed to the belt. Do you disagree that the car is travelling forwards at 10mph with you but that the force of the belt acting on the wheels is making them spin twice as quickly because the 'relative' speed between the belt and you (or the rate of separation between you and the point on the belt where you started from)is 20mph?

If you can't grasp this simple concept there's no wonder you don't get what we're on about, but please, don't mock our 'ignorance'.

It just blows me away that alot of you think the wheel is spinning at double the rate that the conveyor and the plane are moving.

And you would be right to be blown away if anyone had made this ridiculous claim, but nobody has.

What is being claimed is that the rate of wheel rotation is equal to the speed of the plane travelling forwards plus the speed of the belt going the other way, as spelled out in the example above.

You seem fixated on an image of the plane standing still with the belt running furiously underneath it (and thinking that others are claiming the wheels are going twice as fast as the belt).

Again, there is no wonder you can't grasp what is being said. Go back to the original question and it cvan be seen that the plane is not still, because if it was the belt would also be still. The 'speed' of the plane that is being matched is its forward velocity, not the rate at which its wheels are spinning.




[edit on 21-2-2006 by waynos]

Originally posted by redmage

Originally posted by radardog
That is to say, the wheel is going just as fast as the plane, in the direction the plane is going.

Incorrect.


The wheel speed will be (roughly) double the plane's speed.

Incorrect. The speed of the wheel would be the same as the plane. I am NOT talking about the wheel's rotation. It's the same concept as an airplanes nuts and bolts going the same speed as the plane, in the same direction. If I am in an airplane, I can spin a wheel in its place at a different rotation speed than the airplane speed, but the wheel itself is going the same speed as the airplane (and so would I, as fate would have it).


I'm with you that the wheel rotation rate would be very high, but I don't think it should be an issue to the question. The main issue should be movement on the treadmill, which I showed should be easily possible.

What's not to get?

The only reason the conveyor belt moves is because the plane is moving forward under the pressure of its prop or jets.

The plane moves forward, generating lift.

The plane takes off.

Think of it this way:

If the plane was being powered by its wheels, what is going to keep it in the air once it has taken off?

At first I went with the "no" answer, but that Straight Dope explanation was obvious and simple.

Originally posted by radardog
The speed of the wheel would be the same as the plane. I am NOT talking about the wheel's rotation.

You're right , my confusion occured because; most people here are using the terms, "wheel speed" and "wheel's rotational speed", as one and the same (like on a car).

It can just as easily be stated that, on the conveyer, the planes "wheel rotational speed" will be twice that of the "wheel speed", but I think that would just add to the confusion for many.

I just thought it would be more important (and simple) to help some people understand the concept, and concequences, of the independent thrust (by using their own terms) before delving into deeper "semantic" arguments.

Originally posted by radardog
I'm with you that the wheel rotation rate would be very high, but I don't think it should be an issue to the question. The main issue should be movement on the treadmill, which I showed should be easily possible.

I'm not trying to say that it's the issue, it's just another way to demonstrate (since, for some, other methods were not "sinking in") that the plane will be moving forward.

Because, as long as the wheel's rotation will always be faster than the belt's speed (when an independent thrust is applied), the plane will be moving forward.

[edit on 2/21/06 by redmage]

Hi everyone,

had a stab at this one early on, then changed my mind Can't even remember what I thought in the end without going back and looking Don't know if anyone's interested, but there's a load of Physics buffs argueing about it here -

forum.physorg.com...

Some of them are doing experiments as well! It's a looooooooong thread - 289pages and they still can't agree In fact they've been at it since July! Stumbled across it looking for something else and thought I'd let you all know. Apologies if it's already been posted.

[edit on 23-2-2006 by maldives01]

Originally posted by maldives01
Hi everyone,
Don't know if anyone's interested, but there's a load of Physics buffs argueing about it here -

forum.physorg.com...

Some of them are doing experiments as well! It's a looooooooong thread - 289pages

and they still can't agree

In fact they've been at it since July! Stumbled across it looking for something else and thought I'd let you all know. Apologies if it's already been posted.

i'm 'newton' on that thread. i think that thread is about to stop flying, lol. just read the last pages(where i joined in the discussion, HEEHEE!)

people misunderestimate the question, lol!

Hi billybob,

thought there may be someone here on there, but wasn't sure. I found it purely by accident - just skipped through at random and found the page where the guy was setting up something with a train and a conveyor, and another one where they were calling each other all sorts of names Had some great mental pictures! btw, what IS the answer?