A jet plane on a large treadmill

[Squatch]

Thanks guys. It's this collective lack of knowledge that got me 12 credits worth of AP Physics, merely by sleeping through class only half the time. It's that credit that lets me shit around in school and go skiing.

[Telenater]

Nater-
If the velocity vector and acceleration are always equal in magnitude and opposite in direction the sum of each respectively is always zero

Vplane + Vtreadmill = Vplane - Vplane = 0

dVplane + dVtreadmill = dVplane - dVplane = 0

Ahh, there's the problem.

Vplane + vTreadmill(surface) = 0
dVplane + dVtreadmill(surface) = 0

But Vplane <> 0 so, what is it moving in relation to? It's moving in relation to the ground (and the base of the treadmill)

The only case in which Vplane relative to the ground = 0 is one in which the plane is stationary and so is the treadmill's belt.

If Vplane = -Vtreadmil(surface) then the relative velocity is actually 2Vplane.

If you're standing in a fixed location observing, the plane will move in one direction at a speed relative to you. The belt will move the opposite direction at the same speed, and the wheels on the plane will be rotating as if the plane were moving twice as fast as it appears to be to you. As the plane applies thrust, it will accelerate relative to you (because it's pushing against the air which may be assumed to be stationary in relation to the ground) and the belt will mirror the acceleration. The wheels will exhibit double the acceleration. But, because the plane is acceleration in relationship to the assumed still air it can reach take off speed.

Definitions
Vpg = velocity of plane relative to ground
Vtg = velocity of treadmill surface relative to ground and oriented such that -Vtg - Vpg
Vpt = Velocity of plane relative to the treadmill surface.
Apg Accelerations with the same frames of reference.
Atg
Apt

Key points:
The airplane has a V that is not zero.
force of friction from the rotating wheels is negligible compared to the thrust
Vpg = - Vtg and Vpt = Vpg - Vtg = 2 Vpg = 2|Vtg|
The same applies to acceleration.
This is absolutely critical. Vplane = Vpg it the plane is moving in relation to the ground.

The plane is accelerating with relation to the ground therefore it will barring anything more unusual than a plane being on a conveyer belt be able to reach a take off speed with it's wheels acting as if it were moving at twice that speed.

Consider a plane at rest on the treadmill. It begins to accelerate at 10m/s^2 by thrusting against the air.
at 1 second, the plane is moving 10m/s and has traveled 5m while the spot on the belt that it started at has moved 5 m back creating a distance of 10 m between the two.

at 10 seconds, the plane is moving at 100m/s relative to the ground (not the belt) and has traveled 500m while the belt spot is now 1000m behind it also moving at 100m/s relative to the ground.

The plane is then moving at approximately 225 mph which might be close to its take off speed and it's wheels still on the belt are rolling as if they were doing 450mph.

If the plane were using it's wheels to accelerate, it's acceleration would be inrelationship with the surface providing the propulsive force (ie the tread, and it would therefore have gone nowhere), but because the plane accelerates by pushing on the air mass not the belt, it's velocity differential is with regards to the air mass not the belt.

[Storm11]

Ya know, It really is threads like this that make this board so god damn funny sometimes.Bunch of ski bums arguing about physics....classic

[Telenater]

Bunch of ski bums arguing about physics....classic

Any athlete is an exceptional amature physicist.

[PulverSchwein]

Yeah, its really the hall of fame nerd threads that keep me here at TGR. Skiing's alright but physics, well.....let's just say I'm stoked.

[cj001f]

Key points:
The airplane has a V that is not zero.
force of friction from the rotating wheels is negligible compared to the thrust
Vpg = - Vtg and Vpt = Vpg - Vtg = 2 Vpg = 2|Vtg|

We argued whether that was true on pages 2 and 5

Your math is correct if you assume the velocities are planeground and treadmill surfaceground. If you assume plane treadmill surfac and treadmill surface to ground mine is. Both can be read from the problem one of it's many inadequacies (but it makes for fantastically revelatory and amusing internet debate)

[ill-advised strategy]

i'm not even reading it all. I can't believe this shit went 7 pages in one day.

on a related note. I once turned the treadmill at the fire station up to 15 mph and tried to ride a bike on it no handed hanging onto the railings..heh...tomfoolery and shenanigoats ensued.

[Mrthemike]

I havent even read through the thread except for the first page.



Here's my answer.




NO LIFT! NO FLY!

[shmerham]

The speed of the treadmill doesn't make any difference. Imagine an ice treadmill and the plane is on skis. The plane will just start skipping over the treadmill. And sure the treadmill will go faster and faster but there isn't much force to couteract the forward thrust of the engines.

I think this is the right answer. Initially I wanted to point out the difference between the fricition in the wheel bearings and the friction of the tires, in order to show that the friction of the tires is necessary to make the plane move forward, but then I remembered that the wheels don't drive, they simply provide a low-friction platform for the plane. The wheels don't need to roll, but allowing them to provides an even lower friction factor.

I'm not sure I can prove that the plane will take off, but I can prove that it will get moving.

All the engines have to do is produce enough thrust to overcome the initial plane/treadmill friction. Once they do the treadmill will start adding more drag by turning on, but it can never stop the plane, because if it does provide enough fricition to slow down the plane, it will slow down as the plane slows down, thus lowering the drag and the plane always has the option of adding more thrust as it slows down.

[stayhigh]

PAGING OGRE

[bagtagley]

NO LIFT! NO FLY!

Oh my God! That's it! Guys, he has it, that's the answer.

Thanks dude, I can't believe that wasn't covered at all in those 6 pages of amateur physics and nerd hate that you conveniently skipped.

[focus]

Jesus fucking christ.

the treadmill won't even begin to move until the plane moves forwards, it's linked to the plane's forward movement, not the movement of the wheels.

there is no power being applied to the wheels, friction doesn't have anything to do with it, nothing will ever be moving at the speed of light. If the plane isn't moving forwards THROUGH THE AIR nothing will be moving. The entire fucking scenario will be static. we'll hear the fucking crickets.

why the hell would any of you think the wheels would be spinning and the plane wouldn't be moving? what would make the wheels spin? the treadmill? why is the treadmill spinning? because the plane is moving? but if the plane isn't moving, how will the treadmill, that's hooked up to the plane's speed, know that it's time to move -- with enough force through friction to counter the power of those jet engines?

back to the wheelchair/treadmill analogy -- if i'm pulling you forwards off a treadmill, and the treadmill senses your forward speed and counters it with an equal backwards speed, the wheels will turn twice as fast -- but i still won't have any problem pulling you off. IF the treadmill's turning is too much, and i stop moving you forwards, the treadmill will stop turning backwards, and i'll be able to pull you forwards again.

edit: speed of treadmill = speed of jetplane. if speed of treadmill = a billion gajillion million then the speed of the jetplane MUST equal a billion gajillion million. and i think we can all agree that a billion gajillion million is probably fast enough to take off. the wheels will be spinning at two billion gajillion million.

and FINALLY, even if it WAS a car -- forward motion isn't measured by how fast the wheels are spinning, that's just a tool we use to guess. when i'm in a snowbank, with four wheel drive, and all four wheels are spinning at 60 and i'm goin nowhere -- do you think i'm really going 60? (i think this is where most of you are hung up) if this fucking treadmill was hooked up to a car, the car would drive right off the fucking end. wheel speed = forward velocity + opposite velocity of the surface they're on. most of the time the opposite velocity is 0.

[DJSapp]

Ok, so I was too busy tuning my skis last night to write the proof, but here's the just of it:

1. An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

2. Net force equals mass of the object times acceleration of the object F=ma

3. For every action, there is an equal and opposite reaction i.e. you push on a table, the table pushes back

Motion of the aircraft as dictated by newton's laws:

F of engine thrust ACTING UPON STATIONARY AIR = 95,000 lbs/engine
Total thrust = 95,000 * 4 = 380,000 lbs
F of rolling friction from the conveyor acting on wheels = u/radius of wheel * m*g = u/2 ft * 910,000 lbs
(assuming 4' diameter wheels, couldn't find actual size in google)

NOTE THAT ROLLING FRICTION IS INDEPENDENT OF WHEEL SPEED

If thrust is greater than rolling friction, the plane will have an unbalanced force (read: plane will be accelerating reltative to air) acting upon it, causing it to move forward down the runway, giving it airflow and lift. It is simple to verify that for the plane to be held still

u/2 * 910,000 lbs = 380,000 lbs

u = .835164 !!!!!

That is 83% of the force applied to a 747 is lost to rolling friction. Imagine being on a bike and only getting 17% of your energy put into forward progress. (A side note, sliding friction of rubber tires is close to .85, the 747 could in theory take off on a regular runway provided it's long enough, with it's wheels completely locked up!) In the real world, rolling friction losses are closer to 0.5%. The plane will accelerate reltative to the stationary air due to an unbalanced force between the engine thrust from the plane acting on the air and the force of friction due to the conveyor moving at any speed.

The conveyor cannot stop the 747. Bow to its might.

[The General]

NOOOOO!!!! Let this thread die

http://forums.flightinfo.com/showthread.php?t=66860

just read this..... it's up to 32 pages.....

[cj001f]

fucking engineers

[DJSapp]

the wheels don't drive, they simply provide a low-friction platform for the plane.

DING DING DING DING DING

edit cj001f = pwned

[cj001f]

cj001f = pwned

I am impervious to the psyops of the people who can't read

[Core Shot]

[dbp]

NOOOOO!!!! Let this thread die

http://forums.flightinfo.com/showthread.php?t=66860

just read this..... it's up to 32 pages.....

The first pro-takeoff post on that thread is well worded. End of the post quoted below...

The Plane Will Take Off.


The reason you think it won't, if you are one of those people, is because you are thinking of it like a car. A car with wings WOULD NOT take off in this scenario, because a car's motion comes from traction power from the wheels, and the car must necessarily travel the same distance traveled by the outside of the wheel on the ground. Thus, the car moves at speed 0 relative to someone off the treadmill while the wheels move at speed V (which would be the spedometer reading) and the treadmill moves backwards at speed V.

A plane's power is not generated at the wheels, and thus they can spin freely at 2V, allowing the plane to move forward at speed V (relative to an observer not on the treadmill) while the treadmill moves backwards at V.

[Dantheman]

The conveyor doesn't matter and there is no spoon. Shit, it doesn't even need to be a 747, a Cessna would probably be able to take off in this scenario.

[focus]

The reason you think it won't, if you are one of those people, is because you are thinking of it like a car. A car with wings WOULD NOT take off in this scenario, because a car's motion comes from traction power from the wheels, and the car must necessarily travel the same distance traveled by the outside of the wheel on the ground. Thus, the car moves at speed 0 relative to someone off the treadmill while the wheels move at speed V (which would be the spedometer reading) and the treadmill moves backwards at speed V.

This is still WRONG. This will only be true if the treadmill is hooked up to the car's speedometer. If the treadmill is hooked up the FORWARD SPEED OF THE CAR then the car will still move, albeit at half the speed registered on the speedometer.

[The Suit]

I googled "jet plane treadmill" and found that this thread has been duplicated on:

- about a gazillion physics forums
- the Bad Astronomy forum
- Motonews.com
- Ford XR6 Turbo.com
- PaGaLGuY.com - India's largest MBA forum
- RV.net Open Roads Forum
- and, best of all, the Texas Fishing Forum (where it's hit 38 pages)

The bass fishermen seem to understand physics about as well as everyone else.

I also learned that President Bush has added a treadmill to Air Force One.

[Telenater]

We argued whether that was true on pages 2 and 5

Your math is correct if you assume the velocities are planeground and treadmill surfaceground. If you assume plane treadmill surfac and treadmill surface to ground mine is. Both can be read from the problem one of it's many inadequacies (but it makes for fantastically revelatory and amusing internet debate)

Ok, that would be true. Except that because the plane is pushing air to accelerate it is accelerating relative to the air and not to the treadmill. Because of this fact, the treadmill has no impact on it's ability to accelerate the mass of the airplane. Unless the plane is tied down to the ground it cannot apply thrust while on a treadmill and not accelerate. So, if the plane is staked out to the ground, you are correct(and in which case taking off has bigger problems than the treadmill). If it's not tied down, the rest of us are.

[This End Up]

So if a Wasatch Powderturds helicopter is loaded with a pilot, a guide (~180lbs each) and 4 middle aged investment bankers (assume they average 275 lbs each), how many dirty hippies, weighing approximately 120 lbs each, would have to hold on to the to chopper’s skids to prevent it from taking off? Assume the helicopter is powered by a JET engine that produces 1.21 Jigga-Watts of power.

[TomK]

As the problem is written, no takeoff.

Relevent part of the problem:
"This conveyor...tracks the planes speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction)."

Think about getting the plane moving forward in the first place.
Even an infintesimally small amount of forward aircraft motion is 100% canceled by the conveyor's movement in the opposite direction, so the conveyor will speed up to the point where the wheel bearings frictional drag will prevent the plane from moving forward thru the air, therfore the plane will not move a single nanometer forward. So no airspeed, no lift, and no takeoff.

Every argument for YES assumes "speed" is ground-speed as measured by the wheel rotations. Nowhere is this stated in the problem.

In the real world, of course it would take off, but this isn't a real-world problem. It's a "gedankexperiment" (thought experiment).