Imagine a plane is sitting on a treadmill

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction. The engines are running at take-off thrust, the brakes are off, etc. Everything is normal save for the fact the plane is on a treadmill.

Can the plane take off?

Yes.

Are the engines running?

100% NO!

no, there isnt any lift.

Yes, if the engines are running

(And if the wheels can rotate at twice the take-off speed without oblitterating themselves)

Depends on whether the air moves with the conveyer belt or not.

I guess the answer DW is looking for is that a plane needs a certain air speed to take off, ground speed is incidental to the issue.

i agree

What exactly is going to stop the plane moving forwards once the jets are fired up?

explain then, why there is no lift? (edit: aka, what sGb27 said)

yup

No. Air traffic control are too busy wondering how on earth anybody managed to make the runway into a treadmill and won't give clearance for such an idiotic airline operator.

Actually the whole problem is wrongly expressed. The problem would make sense if it derived its forward acceleration from the wheels turning against the runway/belt. But planes don't. They use propellers/jets.

In fact the plane could keep its brakes on, fire up its jets, and have the conveyer belt move at the same speed as it, and take off nicely.

But the aircraft will reach normal ground speed. The fact that there's a giant conveyor belt would only matter if the wheels were providing the propulsive force, and they aren't.

Edit: too slow.

The movement of the plane over the conveyor belt is equivalent to the movement of the plane over a smooth surface without friction, thus the plane is not moving respect to the world reference frame. As there is no movement respect to that reference frame there is no increase on the velocity of wind speed under the wings of the plane so there is no sustentation force to lift the plane. So no, as said before by a few others.

Edit: the piece on the wheeels is true. So probably all the jabber-jibber from above is wrong.
Second Edit: and Tom17 is right.

as per newton’s first law : a body at rest will remain at rest, or a body in motion will continue in straight-line motion unless subjected to an external applied force.
dynamic lifting force of air on the wings are essential for take-off

But the plane is propelled by thrust, not by the wheels. Its acceleration is in respect to the "world reference frame" and not the "treadmill reference frame" and therefore there IS an increase on the velocity of wind speed under the wings of the plane do there IS force to lift the plane

No, because the thrust is produced by acting against the air, not the ground. Imagine if it was a giant ice-rink instead of a conveyor belt - no friction on the wheels, but the aircraft would still be able to take off. The engines provide thrust against the air, not the ground.

Edit: and again

Sorry, could you explain what is preventing the plane from accelerating forwards relative to the air/earth once the engines are fired up (assuming the pilot has taken off the brakes)? The friction in the wheel bearings is tiny compared to the power from a jet engine, for all intents and purposes it will take off as normal.

yes

I still think the wheels spinning at twice their rated take-off speed is going to be the big problem here

I once spun a 10" Mini wheel up to 200mph and it ballooned out like a bastard!

Just look at both the edits on my post. I was wrong.

Ahaha excellent bit of "outside the box" thinking there

I'm pretty sure aircraft wheels will be designed to spin at *far* higher than normal take off speeds. And unlike a car, the faster you go the vertical load gets significantly less...

its irrelevant if the tires, conveyor belt, ice rink, etc move. All that is relevant is that the wind on the wings of the plane get high a high enough MPH (lift) to break gravity. In this scenario all that is moving is the tires and the threadmill and some wind through the jets, not on the wings. No way it could take off. This is why aircraft carriers have catapaults instead of conveyer belts.

No forward motion and therefor no lift generated by airflow over the wings so no, UNLESS the aircraft has a thrust to weight ratio of greater than 1 and then yes.

Edit : Just saw tbfb's pic, perfect example of greater than 1:1 thrust/weight

Why does everyone think that an airplane's wheels spinning have anything to do with flying? Sheesh! The only thing that matters is how fast air is going over (and under) the wing.

I've flown a plane backwards. It's easy. All you need is a plane that can fly r-e-a-l slowly (like a Cessna 172 with a slowflight kit) and some strong wind. I found winds over 40kt and slowed the plane down to 32kt so I was flying backwards at a rate of around 8kt.

I didn't look to see if the wheels were spinning or not.

woof.

Don't forget: there are two major forces of concern here: the thrust (minus aerodynamic drag) produced by the engines and the lift (minus gravity) generated by the wings.

If the thrust is not high enough to produce an airflow of a certain velocity over the wings, there won't be enough net lift to get the aircraft into the air.

So, nope, the plane stays on the ground.

EDIT: Somebody got to it before me...

The plane doesn't care what the wheels do though - it will move as normal 'cept harder to steer.

I'm sure they do, and I have no real idea about this, but do you think they would design a tyre to spin at 600mph if the maximum take-off/landing speed would never exceed 300mph? I dont actually know anything about the take-off/landing speeds or the tyre tolerances used but it would seem silly to have twice as much in reserve.

edit: To clarify why I am talking about the wheels so much... If you get blowouts on all the wheels, you may be looking at a crash into the runway rather than actually taking off (unless you have sufficient lift before the tyres blow out, if they do at all)

What's worrying me is that we have so many enginerds on TT but they can't agree on the answer!

This is a very active topic, but I haven't seen DW even looking in. Hope he's pleased with the answers.

BTW I agree that the wheels would not be designed to be capable of rotating at twice the speed they will ever rotate at in normal operation. But a wheels maximum stress is as the plane lands, and the wheel goes from stationary to landing speed in a fraction of a second, and dumps some rubber on the end of the runway

But it will move normally - the engines work against the air, not the ground. The wheels will just be spinning very quickly.

dolfan, bluedave & JerseyBoy, you're all wrong. Please tell me, what force is equalling those of the engines to stop the plane moving forwards as it does normally during a take off?

Exactly. Newton's *mumble* law, innit?

I'm please with some of the answers

This thread was intended to get the geeks all excited and it appears to be working!



BTW, I'm trying to capture people's initial, unedited posts as best I can. I'm going to stay entirely quiet about any solution to the question - for now at least.

Ahh good point about the landing stresses... Given the HUGE short duration/high load stresses at that point then rotatin at twice the designed speed would prolly be fine..

So the answer is a definate yes..

I'm not really understanding how some people seem to think it would not take off at all though...

In the example quoted the plane ( and therefore it's wings too ) is not moving forward and therefore no airflow is travelling over it's wings.

Without lift from the wings a plane will not take off with thrust alone UNLESS, as i already qualified, the thrust to weight ratio is greater than 1:1.

You're misssing the point. The engines on any aircraft are used to propel the craft forward, so that lift on the wings can be generated. If the aircraft is not moving forward, due to the conveyor belt, there is no airflow over the wings. No airflow, no lift.

Nothing is stopping the plane from moving forward on its wheels. The conveyor belt just keeps the craft in place with respect to the person not standing on the conveyor belt.

EDIT: I am assuming, of course, that the airflow is stationary w.r.t. the observer.

Why? Whats stopping it from moving forward?
Does it say its not moving forward or that something is stopping it from moving forward?

Engines throw vast amounts of air out backwards - plane accelerates forwards at the same rate. What the wheels do doesn't come into it at all.

Edit: unless the brakes are on, but even then it would come unstuck eventually.

What makes you think it's not moving forwards? All it said was the conveyor is moving the same speed as the plane. So plane goign forwards at 100mph (airspeed), conveyor going back at 100mph (relative to ground). Plane can still take off, just wheels are spinning at 200mph.

the conveyor belt. or i read it completely wrong. it moves at exactly the same speed as the planes wheels do, except in the opposit direction. so the poor engines are going ten to the dozen but in effect not moving the plane forward and through the air to create the necessary lift at all. no lift no take off.

plane 350 mph ---------->
conveyor belt 350 mph <-----------
ground speed 0mph -
air speed 0 mph
lift 0

Bugger, got me worried now, you're right, if the wheels aren't driven then what stops it moving forward. ?

D'ohh, to the back of the class for me

But gideon, there's nothing which joins the thrust of the engines to the wheels. They are freewheeling.

Come on, think about it, how does that apply a force to the plane though? The only force will be from the friction in the wheel bearings, which is tiny compared to the power of a jet engine. The engines push against the *AIR* not the ground.

Wrong. The plane does not accelerate forward at the same rate. The thrust out of the engines is not only dependent on exit velocity, but also the amount of mass being expelled from the engine. A very fast flow produces very little thrust if the mass flux of the working fluid is very low, i.e. hydrogen.

Correction...

plane *AIR SPEED* 350 mph ---------->
conveyor belt 350 mph <-----------
ground speed relative to us on a day with no winds 350mph -------->
ground speed relative to the treadmill 700mph -------->

If the belt matches the speed exactly of the intended forward motion of the aircraft the aircraft will not have any air speed. The Aircraft requires forward motion relative to the air to produce lift. So no, it will stay on the ground.

Ignoring any ground effects!

Where do you get plane air speed as 350 mph? I would put it as 0mph, while ground speed relative to the conveyor belt = 350mph.