Mythbusters - airplane on a conveyor belt

Working Engineer wrote:

I am one of the people that agrees that the plane will take off, for obvious reasons. But, I do also believe that the treadmill is capable of holding the plane in place, in a very idealized envionment:

Since there is actually friction in the wheels it is theoretically possible for the force of the treadmill against the wheels to counteract the thrust of the engine. The problem is, the frictional coefficient in the wheels is extremely tiny. This would mean the speed of the treadmill would have to be extremely fast (hundreds of thousands of MPH, if not millions). The wheels would then have to spin along the treadmill at the same pace.

This is wrong. There are two forces opposing the forward motion of the plane - 1) rolling resistance between the treadmill and plane wheel, and 2) internal bearing friction of the wheel itself.

1) Rolling resistance is indepenant of speed. Increasing the speed of the treadmill WILL NOT increase the rolling resistance of the wheel/treadmill interface.

2) The static coefficient of friction is greater than the dynammic coefficient of friction. Therefore, once the wheels are spinning, the frictional term is less than that of a stationary plane. The speed of the treadmill does not increase the frictional term either.

The fact is, the treadmill cannot impart a force upon the plane that will impede its forward motion.

The only case that the "no-fly" camp has is that once the plane starts moving forward relative to the ground, the boundary conditions of the riddle have been violated - that is, the riddle states that the treadmill must be going the same speed as the plane. If the plane is moving forward on the treadmill (as it very well will and as is needed to fly) the conditions of the riddle are not met.

My explanation here is the END ALL BE ALL OF THIS RIDDLE. THERE IS NO NEED FOR FURTHER POSTING. EVERY POSSIBLE QUESTION YOU HAVE ABOUT THIS RIDDLE HAS BEEN ANSWERED BY MY POST.

Thanks, and have a great day.

"The only case that the "no-fly" camp has is that once the plane starts moving forward relative to the ground, the boundary conditions of the riddle have been violated - that is, the riddle states that the treadmill must be going the same speed as the plane. If the plane is moving forward on the treadmill (as it very well will and as is needed to fly) the conditions of the riddle are not met."

Correct.

I needed to get the last word though.

justinbobby:

The fact is, the treadmill cannot impart a force upon the plane that will impede its forward motion.

this is very true.

justinbobby:

The only case that the "no-fly" camp has is that once the plane starts moving forward relative to the ground, the boundary conditions of the riddle have been violated - that is, the riddle states that the treadmill must be going the same speed as the plane. If the plane is moving forward on the treadmill (as it very well will and as is needed to fly) the conditions of the riddle are not met.

This is not true. The riddle states that the treadmill must be going at the same speed as the PLANE - not the WHEELS! The speed of any plane is measured by how it flows through the air - not how it moves in relation to the treadmill belt. There is NO argument that holds water by the "no-fly camp".

Tre1nt wrote:

Dude, if the plane is moving through the air at a speed that generates enough lift to counteract drag then

it

will

fly.

Why even discuss a treadmill if that's the supposition?

Just call the riddle "Can a plan fly?"

You're very wrong...check the forces. Thrust opposed DRAG ads in they both act in the same direction. A plane will lift off when the total lift generated by the plane exceeds the total WEIGHT of the plane. Thusly the plane will accelarate forward if thrust exceeds drag and will accelerate upwards if lift exceeds weight.

Neb wrote:

This is not true. The riddle states that the treadmill must be going at the same speed as the PLANE - not the WHEELS! The speed of any plane is measured by how it flows through the air - not how it moves in relation to the treadmill belt. There is NO argument that holds water by the "no-fly camp".

A valid point. However, it is not inconcievable that someone may interpret "speed" as "wheel speed." If you do, the alternate interpretation holds water.

Bottom line: we have solved the riddle. Please let this thread die because I am addicted to it again, just as I was the first time.

The whole point of the riddle is that you understand the difference between airspeed and "wheel speed." Who measures the speed of a plane by how fast its wheels are spinning?

What a lot of people don't seem to understand is that when you run on a treadmill, you actually have no speed. The treadmill is moving, but you aren't. That's not the situation the riddle poses. The riddle states that the treadmill moves in the opposite direction as the plane with the same speed. If the plane isn't moving (and there is no airflow over the wings to generate lift) then the treadmill wouldn't be moving either. Thus the plane has to have an airspeed for the treadmill to be moving also.

And you don't need a really long runway to takeoff either. The only difference from taking off from a typical runway, as many before have stated, is the airplane's wheels would be spinning twice as fast as normal. I hope that helps, but I kind of doubt it will.

IMPOSSIBLE!!!!

There will be NO AIR going over the wings! Even University of Michigan engineering students know this! If the plane was able to take off from the treadmill, US Air Craft carriers would have used this technique YEARS ago!

You can't fool me! I'm an aerospace engineering major who just took a test on this shit yesterday.

QFE wrote:

Big Ten Engineering wrote:http://youtube.com/watch?v=-EopVDgSPAk

this needs to be watched by the naysayers. I will continually quote/post this link until you ignorant people SHUT THE F*CK UP. Learn things.

Dude, stop posting that. I agree the plane will fly but that video doesn't prove it. The main problems are:

1) That string is obviously holding the plane in place. 3:50 into the video the plane should be flying off the back of the treadmill. It's not. That's the first clue that something is amiss.

2) We don't know the speed of the plane. If the plane goes 20 mph and we turn the treadmill to 4 mph, of course it will go forward. If we turn the treadmill to 10 mph, of course the plane will still go forward. Someone who believes that a plane moves like a car (tires generating the force) could still argue that this is happening in this video.

waltter wrote:

IMPOSSIBLE!!!!

There will be NO AIR going over the wings! Even University of Michigan engineering students know this! If the plane was able to take off from the treadmill, US Air Craft carriers would have used this technique YEARS ago!

You can't fool me! I'm an aerospace engineering major who just took a test on this shit yesterday.

God you're dumb. No one thinks the plane is going to take off from a standing still position like a helicopter.

We are arguing the plane can move forward. From there it will encounter all the air going over the wings it needs.

This entire issue is - will it move forward or not. We all know the plane can't take off without air on the wings. You're so stupid.

The "no-fly" people do. And its an understandable, but no less wrong, interpretation.

Yes, exactly. That is why it takes no energy to run on a treadmill. (Can you feel the sarcasm?)

You are wrong on this. You are moving, you do have speed. You just have to be looking at the correct frame of reference.

Just because you use the word "thus," it doesn't mean you are intelligent.

You are wrong on this point. Refer to the link to "frame of reference" above. The treadmill can most definately be moving (and the wheels of the plane as well) with no plane airspeed. This is a fundamental concept necessary to understand this riddle and you don't get it.

Well, at least you were right about one thing...

I know what frame of reference means. I also know about relative speed.

What you are defining as speed is actually the speed of the airplane relative to the treadmill. But if you measure the speed of the airplane relative to the treadmill how can you say the treadmill and plane are moving at the same speed?

You have to define a third external reference point, which we normally pick as the earth, and define the treadmill and airplane's speed relative to this stationary point.

I agree that if you held the airplane in place, you could turn on the treadmill and the only the wheels would spin. But then the treadmill would have a speed and the airplane wouldn't, which violates the riddle. The bottom line is that we almost always measure speed relative to the earth. So if the plane is moving in one direction, relative to the earth, and the treadmill is moving in the opposite direction at the same speed relative to the earth, then do you agree the plane could take off?

if you were going by wheel speed,than once the plane starts going and gets airspeed, the wheel's on the plane will always be faster than the treadmill, meaning they will both go to infinity and the wheels will melt off. This is just a dumb scenario and no one would have ever thought of a riddle where this would be the case.

Once again, another idiot presumes that a planes engines drive it's wheels.

That third external reference point you refer to as "normally the earth", in the case of a plane which relies on thrust to accelerate, would be the atmosphere.

Watch the damn youtube vid, simpleton. The only thing that has violated the riddle so far is the presumptuous ignorance of those who think that "reading between the lines" somehow trumps the simple dictates of the riddles circumstance.

"An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?"

Answer this: Can a wheel/bearing spin faster than the vehicular structure affixed to said wheel/bearing, assuming no force applied.

Yes or no?

You cannot possibly be that stupid.

Redd wrote:

"A plane will lift off when the total lift generated by the plane exceeds the total WEIGHT of the plane. Thusly the plane will accelarate forward if thrust exceeds drag and will accelerate upwards if lift exceeds weight."

That is how a rocket works, not a plane. Plane fly because of lift generated by wings.

I searched around a bit and found this good explanation:

Get your roller blades (Perfect Physics rollerblades...no friction in the wheel bearings) and go over to the gym. Put on the skates and hop on a level treadmill. Turn on the treadmill.

No matter how fast the treadmill is spinning, you won't go anywhere - the wheels spin at the same speed as the treadmill surface and you stay at 0mph with respect to the fixed floor.

In other words, it's EXACTLY like you were standing on a smooth, frictionless surface. Play with the treadmill speed all that you want, it makes no difference, you don't move. There is NO FORCE causing you to move backward. Set the treadmill to 1mph or 100mph, you don't go anywhere, even though the skate wheels will be spinning like mad.

Now let's apply some forward thrust. Your buddy comes up behind you, standing on the floor, and starts to shove you forward. You begin to move up the treadmill at exactly the speed he is pushing. If he pushes you at 1mph, you move at 1mph, even though you've got the treadmill moving at 100mph.

And that's exactly what happens with the airplane on the conveyor belt - it's just a plane on a frictionless runway. The jet engine provides thrust which causes forward motion regardless of how slippery the runway is. The wheels can revolve at 1mph, 100mph or 1000mph, it makes no difference at all.

Tre1nt wrote:

Redd wrote:

"A plane will lift off when the total lift generated by the plane exceeds the total WEIGHT of the plane. Thusly the plane will accelarate forward if thrust exceeds drag and will accelerate upwards if lift exceeds weight."

That is how a rocket works, not a plane. Plane fly because of lift generated by wings.

?????

The lift he's talking about IS caused by the wings.

The forward acceleration he's talking about is forward horizontal movement - not forward vertical movement. By drag he means whatever force is caused by the treadmill.

boredman, I never said that a plane's engines drive its wheels...I don't know where you got that from. I have also seen the youtube video and I think it clearly shows how a plane could take off in a real-world scenario. The thrust generated by the model plane's propeller is easily enough to overcome the friction of the wheels and accelerate the airplane forward (relative to the earth).

I have no clue what your "vehicular structure" question is trying to ask. Its official, I must be that stupid.

Here's the other part of the riddle (other than our definition of a treadmill) that makes it "fun".

One of Einstein's greatest ideas was that there is no experiment that can be done to prove that an object is at rest or is moving. As you said we can only speak of an object moving in relation to another object.

So, yes I was running 8MPH in relation to the belt of the treadmill - but I was running 0MPH in relation to the ground underneath the treadmill.

The "tricky" part of the riddle is that it doesn't state what the speed of the plane is in relation to - is it in relation to the belt? or to the air around it?

For me it can only be the earth/air around it - for two reasons.

1) An airplane has a speedometer on its instrument panel. That speedometer won't show the plane as having a forward speed unless it is moving through the air (the speedometer uses two gauges measuring air pressure - one exposed to the air flow and one not - the speed is found by taking the difference in air pressure readings between these two gauges).

2) The drag of friction caused by the treadmill cannot keep the plane stationary. The riddle cannot mean that the plane is moving relative to the belt of the treadmill and is stationary to the earth/air around it - because a treadmill cannot overcome the force of the engines. The treadmill can only act upon the wheels of the plane - and the wheels have basically no effect on the body of the plane. 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.

Exactly...lift acts in the vertical direction opposite of weight, think about it...it is lifting into the sky. Drag is caused by skin friction and pressure drops across the body of the plane and acts in the horizontal direction same as the thrust. So when drag is less than thrust the plane will accelerate down the runway and eventually into the air.

A rocket generally does not generate lift. It creates a tremendous amount of thrust to overcome weight and drag forces. It's simple to visualize if you draw it out in a free body diagram neglection other minor forces.

Tre1nt you obviously have no idea what you're talking about or you wouldn't say such obviously wrong things.