no it isn't its just a stupid hypothetical question with insufficient information to draw a positive conclusion.

What if the plane moves no faster than say 5mph, it isn't going to fly anywhere....

 

agreed

if the plane does not physicaly move, there is no air accross the wings, and no lift

 

and even if it does move- the question says it moves, who's to say it will move fast enough to take off?

If it does, then it will- if it doesn't no amount of non-science in the world is going to make it fly

 

All the information needed to solve the problem is in the problem statement. No matter what vehicle is moving over the treadmill, the solution is that it its interface with the treadmill moves at twice that absolute velocity of the body.

Take the person running on a treadmill case... Set the treadmill for 5 mph (so it's moving backwards at 5 mph). Can you imagine a scenario where you're moving forward relative to stationary ground at 5 mph? Sure, it happens when you try to run 10 mph on the treadmill.

This is exactly the same as the plane, except the force on the plane is further decoupled from the wheel rotation rate since it doesn't rely on the wheels to generate the thrust force.

The plane goes ahead and accelerates and takes off. The only difference is its wheels spin at twice the normal rate.

And while we're on the subject, the idea that the plane stays stationary while the treadmill moves doesn't even make sense in light of the problem statement. If the plane wasn't moving, then neither would the treadmill. The plane needs some finite forward velocity for the treadmill to move backwards in the opposite direction.

 

Hate to tell you but you are wrong, the problem statement makes no claim to any rate of accelleration or velocity of the plane, only that it moves and the conveyor moves faster.

Now if it said that the plane accellerates in a forward direction to its take-off speed, then you would be correct, but the problem statement as given does not say anything other than "the plane moves"

 

Ignore the treadmill/conveyor issue at all, reworded this way:

A plane is standing on a runway. The plane moves in one direction.

The question is:

Will the plane take off or not?

You can't answer that, just like you can't answer it with all the conveyor crap thrown in, it is a question with insufficient given information.

 

Fair enough. I think people will always argue different points on this, so we can all agree to disagree

 

Hey, you're the mechanical engineer . I think I was trying to say the same thing as you but just used an analogy that did not add-up to yours.

I guess I should have said what I was thinking without trying to compare it to something else. What I’m trying to say is that if you always remain at point zero, then there's no other miraculous force creating wind for lift. Basically, if you speed the treadmill/thrust to 1000mph or 0mph the weather around you remains the same which creates no lift.


Why don't you *****es email this to Mythbusters and wait for their real world experiment?

 

Good idea.

BTW, my plans are finally done. I should get quotes in the next 2-3 weeks and then I'll have that paperwork on it's way to you.

 

I think the point of the problem statement is obvious. Clearly the plane is attempting to accelerate to take off, and whatever velocity it has relative to stationary ground, a control system moves a conveyor underneath it backwards at the same rate.

Given that statement, the plane will take off, because the force exerted on the plane from the faster moving ground beneat it is negligible compared to the large thrust force of the engine.

 

Here's my opinion.

As was stated, an airplane flies when it's wing generates lift due to the difference in air pressure between the top of the wing and the bottom.

Because the wing is not moving relative to the air, nothing is acting upon the wing to lift.

I guess another scenario might explain it best.

An F1 car can literally be driven upside down in a tunnel because it generates so much downforce due to the air pressure acting on its wings. However, if you introduce it to an upside down conveyor belt that moves fast enough so that the car stays in place, there will be no increased air pressure to apply downforce on its wings; much like how there is no increased air pressure on the wings to lift it.

I guess what everyone is confused about is the difference between velocity and speed (and the theory of relativity).

 

This is the common incorrect opinion that most people have. The plane does generate speed and therefore lift, because the force that the conveyor belt applies to the plane through the wheels is negligible compared to the engine thrust.

It's a coordinate transformation trick. Let's look at the case of the F1 car driving on a conveyor. Let's fix the conveyor for a minute so it's not moving. Now drive the F1 car up to 200 mph (speedo reads 200 mph). Now start moving the conveyor belt backwards at 100 mph. How fast is the F1 car moving relative to the motionless ground? It's moving at 100 mph forward, while the conveyor is moving 100 mph backward, and the speedo still reads 200 mph. You can trace this all the way back to starting from a stop with a conveyor that matches speed. The trick is that the F1 car just has to drive twice as fast on the moving conveyor as it would on a motionless conveyor to achieve the same absolute speed.

Same goes for the plane...

 

But the problem statement was that the conveyor is moving in an opposite direction and identical speed to the plane's wheels. Therefore, the plane never achieves a positive relative speed.

If the plane does indeed go faster than the conveyor, then, yes, at some point it will achieve enough relative speed to generate lift and thus take off.

The problem statement is no different than putting the plane on stands that hold it in place. Even with the engines at max thrust, the plane is going nowhere. If you instantly take the stands away, the plane will not take flight.

 

I think the confusion is coming from the measurement of velocity. You can't mix reference frames. People seem to be measuring the vehicle speed relative to the treadmill, and then the treadmill speed relative to the earth. You need to measure them both relative to a fixed inertial reference frame (the earth). That has gone without saying in my explanations.

 

This is what I was trying to say with the brakes.