The "Aeroplane on treadmill" conundrum...
 

Folks,
I wonder if any of you have seen this article (or any of the many versions of this so-called conundrum doing the rounds):
http://www.straightdope.com/columns/060203.html
Anybody care to post an appropriate response?
TPK:ok:

Providing of course that the tyres don't exceed their rated rotational speed and shag themselves in the process.

The speed of the conveyor belt would not be relevant to the aircraft's air speed. If the air speed was sufficient, it would fly.

Bit of a stupid question.

In answer to the initial request for an appropriate response:

What a load of old b@ll@cks.

Quite appropriate, methinks.

Hi guys,

Clearly it's bull. I was angling for replies to the original web site. However, a pretty active discussion is now underway! :ouch:

TPK:ok:

This one got me the first time - can't believe I thought it wouldn't take off! :} :{

I'll ask the fat plumber, He has a conveyor belt. He uses it for stacking bales of stupid questions which keep coming back

What about the other one I've seen doing the rounds:

If an aircraft is in flight and inside it, a bird is also in flight, does the aircraft feel the weight of the bird?

HWD, dont, just please for all man kind, dont!:eek:

This question came up a few months ago at work. After much discussion, everyone at work agreed that the question was flawed.What speed are we talking about here? Are we talking about the speed of rotation of the aircraft's wheels? If the aircraft moves forwards at 5kt, the conveyor would then have to start moving backwards at 5kt. But this would of course increase the speed of the aircraft's wheels to 10kt, which would then cause the conveyor to speed up... and before long, the conveyor would be going infinitely fast. This is the answer that is given on the website.

Or are we talking about the airspeed of the aircraft? In which case, if the aircraft starts moving forwards through the air, the conveyor would start moving backwards. Now we need to know some more about the aircraft's wheels. If they are perfect, i.e. no friction, the wheels would be spun backwards, but this would not slow the aircraft's movement through the air, so it would take off at its normal rotate speed.

If the wheels have friction (as all real-world wheels do), then the action of the conveyor on the wheels would cause the aircraft to move backwards, whilst the propellor would continue to move the aircraft forwards. (If you don't believe me, think about an aircraft without its engine running sat stationary on the conveyor, and get the conveyor to move backwards - the aircraft moves with the conveyor. Having the prop running would not affect this.) Since most wheels only have a little friction in them the prop would probably overcome the conveyor, i.e. close to the no-friction case. The aircraft would still rotate at its normal rotate speed, but it might take a little longer to reach this speed than it would if the conveyor wasn't slowing it down. So your conveyor would have to be at least as long as a runway to avoid the aircraft going off the end of it.

FFF
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If the aeroplane is not moving THROUGH THE AIR it cannot fly. If it's on a conveyor belt, the belt doesn't care what speed the air is moving and the belt won't move the air to move (OK, it could be argued that the "boundry layer" of air to the belt has a velocity, but realistically it's enough to ignore in this case).

All the time the belt is moving "backwards" at the same speed the a/c wing is moving forwards, nothing will happpen.

Think of yourself running on a treadmill (unpleasent thought, I know...!)....when "running" at the same speed as the belt, you are stationary - your relative wind = 0, therefore no angle of attack, therefore no lift.

Good one though, has got me thinking about how to word an answer.

tKF

And If the aircraft is flying at, say, 500 kts and the bird has a max speed of 100 kts - will the bird manage to fly from the back to the front of the aircraft?

Makes me think of one my old physics master said to us...(sorry, diverging from the original thread somewhat..)

If you're in a space craft (theoretically) travelling JUST under the speed of light, and you run from the back to the front of the spacecraft (enough to make up the difference from space craft speed to the speed of light), are you then travelling at the speed of light? What then happens if, while you are still running, the rocket accelerates to a speed GREATER than the speed of light....?

tKF

Three things happen as you approach the speed of light:

1. You get heavier
2. Time slows down
3. You get foreshortened in the direction of travel

In other words, you won't have anywhere to run.

Also, of course, the speed of light is a constant for all observers, yadda, yadda, yadda...

QDM

Correct, however the conveyor belt has no means of stopping the aircraft from moving through the air. The aircraft does move through the air, and it does take off.

No

Yes

Nothing. Prove me wrong!

Easy ;)

tKF

Well, yes. That was my original thought when I posted this thread. However, in reading some of the arguments on the original site, I am now convinced that the aircraft will fly.

The basic argument says that since the wheels of the aircraft are free to rotate (i.e. not powered like a car) the movement of the conveyor belt will do nothing except cause the wheels to rotate. Assuming no friction, the aircraft will remain stationary. Now... start its engine, and it will pull itself forward through the air until it gains sufficient speed to take off. The difference between this and a similar question involving a car is that a car powers itself by pushing against the ground, while an aeroplane powers itself by pushing against the air.

TPK:ok:

OH I see! It's a looooong treadmill, loooong enough to accelerate through the air to gain lift (with the tyres spinning like mad) sufficient to take off and climb over the ubiquitous 50ft barrier ...
Now.... what about the landingon aforesaid treadmill? :p