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The Straight Dope

"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?"


At 10:36 AM, Blogger Miguel said...

Jesus, Paul - what are you doing up reading Cecil Adams at 6.50AM? (Not that there's anything wrong with that.)

Also, if the plane's engines are never turned on, and brakes are never turned on, and the conveyor belt starts moving at 20 mph or so, how much does the plane move? Do the wheels just start spinning?

At 11:24 AM, Blogger oded said...

The article suppoeses that you have frictionless wheels. I think it makes sense for the question that was posed. The coefficant of friction changes with the speed that two surfices rub against each other. if the belt started to move at 20 mph right away I think that, yes the wheels would just start spinning, albeit at a slowwer rate than the belt.

At 11:37 AM, Blogger Paul Boyer said...

I think that we must assume that all the plane's systems and the belt (or other plane:) are both working perfectly and against the laws of thermodynamics.

At 1:32 PM, Blogger Ivan said...

Planes fly because of air passing over their wings. Wings are curved on top and flat on the bottom. Air takes a longer trip across the top than bottom, so moves faster. Faster moving air creates lower pressure, and you have lift.

Unless the belt generated some kind of wind, you'd have no lift.

Now I'll read the article.

At 1:50 PM, Blogger Ivan said...


Straight dope is good.

Here is the original, by the way:

"The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way."

I love that I read it "add 5 to the value of A". From programming.

Assuming no static or kinetic friction in the wheels, the plane will not move back. The wheels will just spin.

If there is friction, the plane will initially move back at a speed according to how much of a static friction force was needed to get the wheels moving. After they start moving, kinetic friction will not only allow for more force upon the plane, but also slow down the plane to an equilibrium.

If the acceleration of the belt is smaller than force to overcome the the static friction given the mass of the plane, then the wheels won't spin.

My guess is that there is closed form solution for how far back a plane of mass M moved with N wheels of kinetic friction Fk, with certain distribution of mass, etc...

Infinite acceleration to 20mph would certainly be enough to overcome the static friction.

Oded, all that matters is that at some point the wheels are spinning at the same speed as the belt. They dont accelerate further, and all the force of the plane goes into making the plane move forward.

At 2:37 PM, Blogger Miguel said...

I was wondering about a real plane - there is friction, but it's minimized.

"but also slow down the plane to an equilibrium"

Is there then an equilibrium with a plane moving at a speed <20mph, with the wheels spinning a bit?

"all that matters is that at some point the wheels are spinning at the same speed as the belt."

That never occurs - since the plane is moving forward and the belt backward, the wheel-spinning show a much higher "speed" than the plane is travelling, because they're covering a lot of extra ground.

At 3:07 PM, Blogger Ivan said...

yah, there might be an equilibrium. The plane will only stops (with wheels rolling) if the force from the engines is equal to the force from kinetic friction with the wheels.

that would probably have to either be a very heavy plane or very high friction or very low force.

let's say that the plane provides a force that would normally accelerate it from 0 to 100m/s in 100s. The belt also accererates to 100m/s in 100s.

If the wheels were frictionless, the plane would take off normally.

Also, I forgot that rolling tires actually have static friction, not kinetic, but that only matters for labels.


I think I need to make a simulation rather than commenting further. I'll post a video of the result, or maybe even an app, when I get around to it.

At 3:31 PM, Blogger oded said...

not holding my breath

At 9:33 PM, Blogger Ivan said...

Digg has at it:


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