Will a plane take off on a conveyor belt?

From conveyor belts?

If the belt is not moving then you are correct the plane and wheels do 100 mph (belt = ground for all intents and purposes when belt is stationary)
If the belt does 100 mph backwards then the "ground" (in your case 3, but not air) might as well be doing 100 mph backwards = no forward motion of the aircraft.
The OP states

If the wheel speed is matched exactly to the conveyor then they do not move forward, relative to the air (or ground), nor does the aircraft. No lift.

 

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By stating that the conveyor belt will move as fast as the wheels do, you are essentially locking the wheels to the groung, thereby chaining the plane in place.

 

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My thoughts exactly.

I just Googled this, and there are two camps apparently - Fly and No Fly, each with as many solutions and posts as the other.

I know, of course, I'm in the correct camp

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.

Ho hum. Another SF argument to rage forever.

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No from any runway, since the pilot always observes his plane to not be in motion...

nonono, only if its relative to the ground which it isnt in my solution to the problem

The belt does 100mph backward relative to the pilot who is dong 100mph forward relative to the ground, thus relative to the ground the conveyor is still not moving, but the conditions of the scenario are still satisfied when everything is checked relative to the pilot.

Heres the math:
Condition:
relative to unspecified observer:
perihperal speed=conveyer speed+plane speed

answer:
for plane relative to ground:
if groundpeed>0 lift
if groundspeed<=0 no lift

Now, if the plane is moving 100mph relative to the ground, we have groundspeed and lift. If this can fit the condition above, then its a good solution:
plane is moving 100mph relative to ground,
conveyor is stationry relative to ground
relative to convayer, plane is moving 100mph
relative to plane, convayer is movng 100mph in oposite direction

from the planes perspective; wheel perihperal motion is 100mph
when all is relative to the plane:
perihperial motion=100mph
plane speed=0
convayer is moving 100mph
sub this into original equation
100mph=100mph+omph

problem solved.

-Andrew

 

the wheels are not coupled to the plane.
they spin freely because of wheelbearings.
turning the wheel has no effect on the axle.

 

Ha-ha-ha! Some of you people are down-right amusing. Not just you, Leo, I just replied to your post because it was the last one.

Actually Oli and Leo are both closest to the correct answer - but each in a different way.

First, consider someone running on a treadmill. They are stationary relative to the ground AND the surrounding air as long as they are keeping perfect pace with the conveyor. And if you strapped perfect airfoils on their outstretched arms NO lift would be generated since there is no airflow relative to the runner. (Believe me, there is NO air passing over your body while doing that - I get very, very hot because of it!) You don't even need that parenthetical statement because you can clearly see there's no movement of the air generated.

All the business about the observer being on the ground or in the pilot seat is just a bunch of red herrings. It makes no difference WHERE the observer is.

With that out of the way, we do still have to consider two things though - one is a plane which will not take off and the other is a plane that will.

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The one that won't take off is a jet. As long as we maintain the proper speed on the conveyor to match the thrust/speed developed by the jet engine, all we can do is burn out the bearings on the wheels. That's because there is STILL no airflow over the wings (just like our stationary runner on the treadmill) to create any lift.

However, a prop-driven plane WILL succeed in taking off. And that's because the backwash from the prop(s) flow across and under the surfaces of the wings. When that happens, lift IS generated, the plane will rise straight up (more or less) from the surface of the belt and begin to take off in normal flight.

So, since the type of plane was not specified in the original question - jet or prop - the answer is both yes and no. It all depends on the plane.

 

Read Only, it makes a complete difference as to who the observer is. Read my above post...

 

read-only,
wrong, wrong, wrong,
first of all a person on a treadmill isn't even close to what we are talking about.

okay, try this.
you tie a kite to a skateboard.
you have the very same scenario as the first post.
now the wind starts blowing and starts to move the skateboard forward.
there is no why in hell a conveyor belt is going to make any difference

 

If the plane is on the treadmill, the plane can not move forward, therefore the wind is NOT blowing.

 

But the pilot observes the ground to be in motion - backwards, and the air also. If the belt matches the wheel speed then the aircraft cannot be moving forward, so no ground or air motion backwards to generate lift.

Wheel speed = conveyor speed. As stated in the OP. Whatever speed the wheels (and therefore plane) is trying to move forward the conveyor negates it.
Therefore whatever speed the plane WOULD generate the peripheral speed increases and is matched exactly by the conveyor. No forward motion.
The pane cannot generate a ground speed, only a "conveyor speed" which would be twice whatever the ground speed "should" be.

No forward motion, no lift.

Leopold:

If the wheel speed is matched by the conveyor then the axle isn't going anywhere, so neither is the aircraft.

 

You are mixing things, you keep remeasuring axel speed relative to the ground, when I have stated and shown mathematicly that the solution is valid given the pilot as the observer...
once gain: because axel speed relative to the pilot is always 0, and in a non moving convayer(relative to the ground), the perihperal speed is both equal to the convayor speed and the ground speed (relative to the pilot)... and do i also need to point out the OP never stated relative to what the speeds needed to be taken? Thus fullfilling all conditions, and letting any plane to take off...
-Andrew

 

will the skateboard move forward like i suggested?

 

Read_only:

Not true, (unless we have a massively overpowered aircraft and accompanying large prop). Spitfires etc. require(d) forward motion to take off. A typical prop will not generate enough airflow to cause sufficient lift, even with fancy devices like boundary layer blowing/ Coanda effect/ Fowler flaps etc.
Tethered prop aircraft have shown little propensity to rise vertically even under 110% power during ground-running trials.

 

Not wrong in the least. Go back and read it carefully - it EXACTLY compares to someone on a treadmill (the jet plane does).

What's the "wind starts to blow" bit?? There's no wind blowing in the original question. And besides, you still have a basic flaw in that example. If the wind DOES start to blow and moves your skateboard, it will still have no forward motion as long as the belt precisely matches it's speed in the opposite direction. Simple algebraic additives - a positive and a negative, both being equal results in zero forward motion.

 

Not unless the skateborad lifts off the treadmill.

 

On second thought...

Put Billy in front of the tradmill, give him the end of the string and have him run away from the tradmill, and the skateboard WILL follow him, regardless how fast the tradmill is running.

Now I'm not sure...

 

Because axle speed needs to be relative to the ground, it's the forward motion of the aircraft, wheel, axle and pilot that causes lift. The pilot observes the ground moving backwards - that's what generates lift.
Pilot = (1/2)wheel = axle = aircraft. The conveyor cancels out the forward motion.

Non-moving conveyor? The OP states the belt moves backwards at wheel speed.

 

We should write an email to the Myth Busters and link to this thread!

 

you're coming around, you're getting it.

 

Oli,

What's up with little Billy and the skateboard?
You're an aerospace engineer, aren't you?