Mythbusters - airplane on a conveyor belt

Good Job Neb and Tre1nt. Finally it's over. For all of you non-believers, or Michigan students (just kidding mpokora, I know you'll eventually come around, even though your football team may not), here are some links to look at, or scenarios to think about:

1. How easy is it to push a rolling pin on a treadmill?

2.

http://www.straightdope.com/columns/060203.html

(this link explains the whole myth, even the scenario where the conveyor matches exactly the speed of the wheels, and how it is impossible)

3.

http://www.youtube.com/watch?v=-EopVDgSPAk&feature=related

4. Free Body Diagram:

http://www.youtube.com/watch?v=siYQU99VaAM&feature=related

And finally, for some comic relief:

http://www.youtube.com/watch?v=cDliz-YinyY

Neb wrote:

So, if the riddle meant the treadmill kept the plane in place relative to the earth and air around it the riddle would be flawed because that's not physically possible.

oh, but it's possible to put a 747 on a treadmill though? great. i never saw a treadmill that big, but i guess you have.

you shouldn't sound so smug. because again, you are just making assumptions. if you just state that you are assuming the plane will move forward, then fine, it can take off. If you're going to argue the semantics of "air speed" and "wheel speed" and the wording of the riddle, then you can draw your conclusions based on your set conditions. but don't claim that others are just plain dumb b/c they don't see that it's impossible for a real treadmill to hold it in place. obviously this is a hypothetical treadmill, and people can read the problem to mean that the airplane does not move relative to an observers standing next to the treadmill.

aguywhoknowsaguy wrote:If you're going to argue the semantics of "air speed" and "wheel speed" and the wording of the riddle, then you can draw your conclusions based on your set conditions. but don't claim that others are just plain dumb b/c they don't see that it's impossible for a real treadmill to hold it in place.

It's not a matter of semantics at all. And yes, people who cannot see this are dumb.

aguywhoknowsaguy wrote:

obviously this is a hypothetical treadmill, and people can read the problem to mean that the airplane does not move relative to an observers standing next to the treadmill.

Then why place any restrictions on the hypothetical? A treadmill keeping a plane "stationary" is just as possible as a plane taking off without any air rushing under its wings to provide lift.

If you state that the plane is kept stationary by the treadmill than you can't say with any certainty that the plane won't take off - because you have created a La La land where physical laws don't mean anything.

But, building a giant treadmill - even though it doesn't exist - doesn't break any law of physics.

A planes wheels are it's only interface with the treadmill. A planes wheels may spin independantly of it's movement, which is caused by thrust against the atmosphere.

Any forward movement caused by the thrust of the planes engines will move the plane beyond the influence of the treadmill. Speed would not be a factor. The first part of the riddle is just subtrefuge, as I said in my first post "the planes wheels/ treadmill are not factors".

Can the plane take off? Yes.

plane speed = x

treadmill speed = -x

wheel speed 2x

2x-x = x (net positive speed)

Imagine one more scenario to understand why the plane takes off:

Picture a regular car, on a regular road. Now add extra wheels on the roof of the car. The car's transmission is not tied to these wheels, they spin freely. Now picture an upside down treadmill resting on these wheels.

If the treadmill spins backward it will not affect the car's movement. If somebody steps on the gas, the car will still move forward.

This is the same reason the airplane takes off.

Ying Yang Twins wrote:

Imagine one more scenario to understand why the plane takes off:

Picture a regular car, on a regular road. Now add extra wheels on the roof of the car. The car's transmission is not tied to these wheels, they spin freely. Now picture an upside down treadmill resting on these wheels.

If the treadmill spins backward it will not affect the car's movement. If somebody steps on the gas, the car will still move forward.

This is the same reason the airplane takes off.

I thought of this scenario with one additional detail.

The car would be parked under a (fixed to the ground) frame which the upsidedown treadmill was attached as to contact the free spinning roof wheels.

I have followed this riddle since it appeared on letsrun and find it remarkable how stubborn ostensibly intelligent people can be about something so very obvious and simple. Read through some of the "plane won't fly" arguments and see how far some will go to argue that which does not matter. Seems like for some people science is akin to politics where truth and critical thought must yield to distraction and ambition.

Let me try.

Say you are in a plane. The plane requires an airspeed of 150 mph to produce enough lift over the wings to take off. The plane is on a treadmill. The treadmill is infinitely long. The treadmill is running under you at 150 mph. You look down at the treadmill, and it does not appear to be moving (you are stationary on it, moving backwards at 150mph). You have a wheel speed of zero (in reality this is meaningless in real life, the riddle brings it up to throw you off). You look to the side of the treadmill. You see the landscape rushing by (from back to front) at 150 mph. The airspeed over your wings is -150mph. You have no lift, actually it would read as negative lift (since the air is rushing over your wings from back to front, and assuming your wings are not configured to produce lift while moving backwards through the air). You will not take off.

Now you start your plane's engine. You throttle up to what would normally produce 150 mph of airspeed. You look down at the treadmill. You see the treadmill going past you (in a backwards direction) at 150mph. You have a wheel speed of 150mph. You look to the side of the treadmill. You see that the landscape is standing still. You have no air moving over your wings. Thus you have no lift (this time it is really zero, not negative with a zero effect). You will not take off.

Now you rev your plane up to what would normally produce 300 mph of air speed. You look down at the treadmill. It is zooming from front to back at 300 mph. You look to the landscape beside the treadmill. It is zooming past, from front to back, at 150 mph. The air is moving over your wings at 150mph. You have lift. You take off.

This is if the treadmill is already running and the plane has built up a negative (relative to the air) speed that must first be shed.

But wouldn't the 150 mph of negative airspeed be acting against your plane, pushing it along the treadmill, though not at 150 mph?

Better stated: wouldn't friction from the air keep you from reaching -150mph, and in fact you would be rolling forward on the treadmill? Could you be going forward on the treadmill at say, 50 mph, while going backwards relative to the landscape at 100 mph, while your engine is still off, because of wind resistance?

Here is what is wrong with your hypothetical:

You say that "You throttle up to what would normally produce 150 mph of airspeed." If the plane's engine is producing the amount of thrust required to go 150 mph than the plane will go 150 mph relative to the air around it and the ground besides the treadmill. The only thing that would slow it down relative to the air and ground is if the treadmill transferred any force to the plane's body - but it doesn't.

Now you might say - "the treadmill made the plane go backwards at 150 mph, so it must have some effect on the body of the plane." I'm not sure that it would be so easy to get the plane moving backwards that fast unless the wheels were locked or the belt accellerated to 150 mph relatively slowly. Remember an object at rest stays at rest unless acted upon by a force - free spinning wheels aren't exactly the most efficient way to transfer force.

It would take a little longer to get to 150 mph of forward motion since it started from a speed of 150 mph going backwards - but once the plane engines start creating force the treadmill no longer has any effect on the body of the plane. Again, the treadmill can only effect the speed of the wheels - and the wheels have no real effect on the body of the plane, especially when the engines of the plane are creating forward thrust.

The riddle states that the treadmill only matches the the speed of the plane. Not that it would matter, the plane would still take off because its engines thrust acts against the atmosphere, not the treadmill. If you started the treadmill first, then the plane probably would back up. As soon as you started and applied the engines, the thrust against the atmosphere would move the plane forward with hardly any more frictional resistance than on a regular runway.

If you'd like to create a riddle where the plane does not take off, knock yourself out. Maybe the treadmill is going 1000+ mph and the bearings are fried, either way it wouldn't be very clever.

This riddle was very simple and definitely solved.

The prop is generating a certain amount of forward force, which is exactly equal to the force that would have to be applied to the wheels of a car for it to stay on the treadmill, if it weighed the same amount as the plane.

It makes no difference whether the thrust is applied to the air or not.

You do agree that a car would have to create some forward thrust to stay on the treadmill, don't you? And you do agree that you could put the car in neutral and generate the same thrust with a prop mounted on the car, don't you? And you do agree that the car still wouldn't fly, don't you?

Everyone who thinks the plane would take off should be required to fly in a 100 mph tailwind to see what they learn.

OK, you win. The plane won't fly, the earth is flat, and the government has nothing to hide.

Actually the point of the riddle is exactly that - it DOES matter where the force generated by the object is applied.

You are basically saying that if I were on a skateboard that it wouldn't matter if I pushed my back foot off of the treadmill or the ground beside it. If I push my foot off the treadmill I stay stationary compared to the ground. If I use the exact same amount of force on the ground beside the treadmill (while the skateboard is on the still on the treadmill) I go forward compared to the ground (and the air).

Why? because the force of the treadmill can only act upon whatever is in contact with the treadmill. If the thrust is applied to the treadmill (through wheels or feet) - than the treadmill can counteract it. If the thrust is applied to the air or the ground beside the treadmill - there is nothing the treadmill can do to counteract that force.

Of course not - unless of course you put wings on your "prop car" ; )

This argument boils down to how one interprets the problem statement. It's fairly safe to say that we all know the plane's lift is caused by the air foils (wings) passing through the air fast enough to produce lift that overcomes the weight of the plane, right? Moving on. So, does the problem statement tell YOU that the plane is traveling forward, relative to the surrounding air? Forget all of the mechanics of the wheels and treadmill, it's the red herring. The riddle hinges on this interpretation.

turkey leg wrote:

This argument boils down to how one interprets the problem statement. It's fairly safe to say that we all know the plane's lift is caused by the air foils (wings) passing through the air fast enough to produce lift that overcomes the weight of the plane, right? Moving on. So, does the problem statement tell YOU that the plane is traveling forward, relative to the surrounding air? Forget all of the mechanics of the wheels and treadmill, it's the red herring. The riddle hinges on this interpretation.

Yes - but only one interpretation is possible physically. Because it's IMPOSSIBLE for a treadmill to counteract the thrust of an engine on the air. The treadmill CAN'T keep the plane stationary in relation to the earth and air and therefore the plane MUST move forward.

If the wheels are touching the treadmill, the plane cannot move forward unless wheel speed is greater than treadmill speed. The origin of the force does not change this fact.

With a due sense of dread and futility, let me be the milionth person to attempt to "resolve" this question (by agreeing, for the most part, with some earlier posts). If it helps my credibility, I do have a PhD in physics, although that doesn't really mean anything in this context.

Some true statements:

(a) The answer to the hypothetical riddle depends on the interpretation of the question.

(b) If the treadmill accelerates in such a way as to keep the plane stationary with respect to the ground no matter how high the thrust is, the plane will not take off BUT the treadmill is a hypothetical construct that does not exist in real life.

(c) If the treadmill is designed to move at a speed that is equal and opposite to the speed of the plane with respect to the ground, the plane will move forward (with wheels spinning at twice the speed of forward movement), and is CAPABLE of taking off.

(d) If we try to move the experiment from hypothetical to real-world, as MythBusters have apparently done, the plane will be CAPABLE of taking off. But whether it actually does or not will depend critically on the various friction parameters of the wheel and treadmill surface, as well as on factors such as the length of the runway. (If friction is relatively high, perhaps because the treadmill surface is softer than asphalt, then you could imagine the plane moving forward but with reduced acceleration, so that it doesn't reach take-off speed by the end of the treadmill.)

So if MythBusters doesn't get the plane to take off, they've only proved something about their specific set-up.

the plane remains stationary relative to the air surrounding it.

Bernoulli's equation shows that no pressure differential created, and hence no lift.

STFU.