A harmless little riddle

You are the smartest person that has posted on this topic. People have been saying that the situation is different because the plane does not get its thrust from its wheels like a car does, but a car with wings would be able to take off as well in this situation. It would just be twice as hard because it would have to move 300 mph relative to the treadmill. Heck, even a person with wings could take off if he/she could run fast enough.

Aerospace guy: maybe you should look into a new career? Or maybe just stop posing as an aerospace guy on the internet.

You people are ignoring my BRILLIANT argument.

If the plane ever does begin to move forward (relative to the ground), what does that mean? It means that the planes speed relative to the treadmill is GREATER than the treadmills speed. THAT DEFIES THE RIDDLE! The treadmills speed to the ground must ALWAYS equal its speed relative to the plane. The ONLY speed at which that occurs is if the plane is NOT MOVING. Relative speed of the treadmill and plane HAS to equal the treadmills true speed! That is the condition of the riddle. So basically the riddle is saying, in different and confusing words, that the treadmill will always act to halt the plane, will the plane take off?

This is NOT a physics problem. This is entirely a LOGIC problem.

It SHOULD be worded this way: The treadmill will always speed up to match the EQUIVALENT SPEED OF THE THRUST of the plane. That is, if at 100% thrust the plane will reach 200mph under NORMAL conditions, then at 100% thrust on the treadmill the treadmill will go backwards at 200mph. Will the plane take off? Otherwise the riddle is circular and presents an impossibility.

The above question is what you all should be arguing over.

However, the riddle DOES make sense under a different interpretation. that is if you interpret the definition of speed in the riddle to mean the ground speed of the airplane. if thats the case, the answer IS IN THE RIDDLE ITSELF. The riddle states the airplane begins to move forward. IT IS THE AIRPLANES FORWARD GROUND SPEED THAT IS MATCHED BY THE TREADMILL. Since many people can't seem to get over the friction problem of the planes wheels, think about a runner on a treadmill. It works just the same. If your jog speed is 8mph and you start running on this treadmill at 8mph it will move in the opposite direction at 4MPH!!!! In that way you are moving FORWARD at 4mph while the treadmill is moving backwards at 4mph. That is what is meant by the treadmill matching your speed. If you increased your pace to 9mph the treadmill will move backwards at 4.5 mph and your ground speed will increase to 4.5 mph. Your ground speed will always equal the treadmill speed, which is what is meant by the riddle.

THE SOLUTION wrote:

Since many people can't seem to get over the friction problem of the planes wheels, think about a runner on a treadmill. It works just the same. If your jog speed is 8mph and you start running on this treadmill at 8mph it will move in the opposite direction at 4MPH!!!! In that way you are moving FORWARD at 4mph while the treadmill is moving backwards at 4mph. That is what is meant by the treadmill matching your speed. If you increased your pace to 9mph the treadmill will move backwards at 4.5 mph and your ground speed will increase to 4.5 mph. Your ground speed will always equal the treadmill speed, which is what is meant by the riddle.

Surely if you have a net ground speed of 4.5mph and the treadmill is stationary, you're going to run off the treadmill. Am I missing something - doesn't the treadmill have to move in the opposite direction at the exact same speed as you are running in order for both you and the treadmill to remain stationary.

And another question doesn't a jet engine that relies on thrust for power, still require faster air movement over the top of its wings in order to create a net upward force (assuming its thrust is directed horizontally as most jets are)?

No it doesn't. You must have failed physics, logic and reading comprehension.

Maybe this will simplify things for you:

1. The plane moves forward. (says so right in the riddle)

2. The treadmill moves at the same speed as the plane.

Pay attention now. This is the tricky part.

3. The treadmill DOES NOT AFFECT THE SPEED OF THE PLANE. 4. Thus the plane continues to move forward.

5. Moving forward, the plane takes off.

As was mentioned a few time before, the treadmill is a red herring, designed to catch people like you.

Let me give you another hint: if the plane is moving, that means it is NOT stationary. How much clearer can it get?

No Not Agree wrote:

No it doesn't. You must have failed physics, logic and reading comprehension.

Maybe this will simplify things for you:

1. The plane moves forward. (says so right in the riddle)

2. The treadmill moves at the same speed as the plane.

Pay attention now. This is the tricky part.

3. The treadmill DOES NOT AFFECT THE SPEED OF THE PLANE. 4. Thus the plane continues to move forward.

5. Moving forward, the plane takes off.

As was mentioned a few time before, the treadmill is a red herring, designed to catch people like you.

Let me give you another hint: if the plane is moving, that means it is NOT stationary. How much clearer can it get?

You are a MORON who didn't understand ANYTHING I said. How could you disagree with me when I am agreeing that the plane will take off??????? Moron.

In fact the treadmill DOES affect the speed of the plane. But the amount the plane is slowed by the treadmill is negligible. My point with the runner on the treadmill example is that even if you aren't able to understand that the treadmill does not effect the speed of the plane and you think the treadmill would slow down the ground speed of the plane, IT WOULD STILL TAKE OFF.

HOWEVER, if you interpret the question the other way, that it is the relative speed between the plane and treadmill that is matched, then you have a situation where the plane stays still. that is because if the plane accelerated to 200mph at 100% thrust the treadmill would go 200mph the other way. the relative speed now is 400mph!!! that alone would not be able to stop the plane BUT it would slow down the plane. say the incresaed friction caued the plane to slow down to 190mph. now you have a situation where the plane is moving to the right at 190mph, and the treadmill is moving to the left at 190mph for a speed differential of 380mph!!!! that would slow down the plane again in the same manner and all this would happen instantaneously. that is to say that the plane would never be able to move forward in the first place.

now piss off.

i meant to add that eventually the plane and treadmill would get down to 0mph. and it would happen instantaneously meaning the plane would never be able to move in the first place

experience wrote:

Surely if you have a net ground speed of 4.5mph and the treadmill is stationary, you're going to run off the treadmill. Am I missing something - doesn't the treadmill have to move in the opposite direction at the exact same speed as you are running in order for both you and the treadmill to remain stationary.

yes you are missing something. speed is RELATIVE. when you are running on a treadmill you have a relative speed to everything around you. your speed relative to the treadmill is one thing, your speed relative to the ground is something else. in the riddle the treadmill moves in the opposite direction at the speed you are running relative to the GROUND. you would not run off the front of the treadmill obviously because the treadmill in the riddle is of indefinate length.

let it go already

No Not Agree wrote:

No it doesn't. You must have failed physics, logic and reading comprehension.

Maybe this will simplify things for you:

1. The plane moves forward. (says so right in the riddle)

2. The treadmill moves at the same speed as the plane.

Pay attention now. This is the tricky part.

3. The treadmill DOES NOT AFFECT THE SPEED OF THE PLANE. 4. Thus the plane continues to move forward.

5. Moving forward, the plane takes off.

As was mentioned a few time before, the treadmill is a red herring, designed to catch people like you.

Let me give you another hint: if the plane is moving, that means it is NOT stationary. How much clearer can it get?

another way to think of the problem is this.

the planes ground speed = P

the treadmills speed = T

the relative speed between the plane and treadmill = P-T

the riddle states that T = P-T ( that the treadmill will always match the planes RELATIVE speed )

in a motionless state the values are 0 = 0-0

and because the treadmill always moves to the left it will always have a negative value.

when the plane starts moving P would have a positive value. BUT P CANNOT HAVE A POSITIVE VALUE because for any non-zero value of P the treadmills speed CANNOT equal the relative speed. For any P value greater than 0, P minus T cannot equal T, no matter what T is (remember, T can only have a negative value because it moves in the opposite direction).

this is what i was explaining by the phrasing of the riddle being ambiguous and how one interpretation is impossible.

You piss off. My point is only a moron would interpret the the question another way. Quit wasting our time and bow down to the truth.

man, you people are crazy. well--the ones who are getting all worked up anyway.

seriously, if people can't understand that a plane won't take off if it gets up to 150mph on a treadmill really have a screw loose.

aerospace isn't my specialty, but if this "debate" keeps up, i'll get an engineer in that field to dumb this down and explain it for you guys who believe it's possible.

cuhd wrote:

man, you people are crazy. well--the ones who are getting all worked up anyway.

seriously, if people can't understand that a plane won't take off if it gets up to 150mph on a treadmill really have a screw loose.

aerospace isn't my specialty, but if this "debate" keeps up, i'll get an engineer in that field to dumb this down and explain it for you guys who believe it's possible.

and i can't believe that you idiots are still arguing over this after a link to the answer was posted on page 3:

(YES, the plane will take off)

i encourage all who doubt this to go buy a little wooden plane with a rubber band propeller. wind it up and put it on a treadmill. see what happens.

wow, this has been explained a thousand times. why dont the people who say the plane doesnt take off use this riddle as an example to disprove newtons third law of motion... for every action there is a reaction. the propellers create thrust (this is a force) the reaction to this force is the plane moves forward through the air. the treadmill cannot be another force used to negate this forward motion because the acceleration of the treadmill can only spin the wheels. the wheels on a plane have no driveshaft, they dont propel or slow down the plane. they just spin freely. since the treadmill cant decellerate and therefore be a force on the plane, the plane doesnt remain still. how many different ways do u need the same thing explained to u?

THE SOLUTION wrote:

another way to think of the problem is this.

the planes ground speed = P

You keep harping on about the plane's ground speed.

A plane (any plane) has airspeed. That is, speed relative to the air.

Its speed relative to the ground is immaterial.

The fact that it's on the ground makes no difference, WHATSOEVER.

If a plane, say a light aircraft, was sitting on the ground, anchored, and facing into the teeth of a hurricane, will it take off? Remember, that before you answer, it has NO GROUNDSPEED. You can try this experiment with a toy or paper plane.

Now, people, repeat after me (just take it as read until you can understand it):

The groundspeed doesn't matter; the airspeed matters.

That's why A/C have airspeed indicators.

Lulu wrote:

Jack,

Here's the thing. A plane moves by pulling itself through the air, not pushing itself off of the ground. You are right, the plane would roll off of the back of the treadmill if the engines weren't on and we were taking friction into account. But once the engines are on, it doesn't need the ground to move, it just needs the air, and it will be able to pull itself forward.

I agree that it pushes itself off the the air, but the plane rests on the ground right? As long as it is on the ground the treadmill will push the air plane in the direction it is moving. Then you turn on the engines and the force generated by the engines will negate the movement the plane is getting in the opposite direction by the treadmill. But the plane does not move foward it just sits there because the force of the treadmill and the force of the engines is equal and in opposite directions, thus creating no movement fowards or backwards and I think we all agree what happens when their is no movement.

Big huge gigantic tall guy wrote:

You keep harping on about the plane's ground speed.

A plane (any plane) has airspeed. That is, speed relative to the air.

Its speed relative to the ground is immaterial.

The fact that it's on the ground makes no difference, WHATSOEVER.

If a plane, say a light aircraft, was sitting on the ground, anchored, and facing into the teeth of a hurricane, will it take off? Remember, that before you answer, it has NO GROUNDSPEED. You can try this experiment with a toy or paper plane.

Now, people, repeat after me (just take it as read until you can understand it):

The groundspeed doesn't matter; the airspeed matters.

That's why A/C have airspeed indicators.

you are another moron. in my explanation it doesn't matter if i am referring to the planes air speed or ground speed. what i meant by ground speed is the speed of the plane relative to the environment, that is, NOT relative to the treadmill.

the same holds true if you are talking about the planes airspeed.

if the plane has an airspeed of 150mph the equation would look like this

T = 150 - T (with T being a negative value)

you can see that no negative value of T will satisfy that equation

in words it goes like this: if the plane was moving at 150mph then the treadmill would be moving backwards at 150mph, but then the speed differential between the plane and treadmill would be 300mph. so the treadmill would speed up to 300mph, but then the differential would grow and it would have to speed up even further, until the treadmill is at an infinite speed, impossible. THIS IS WHY THE ONLY SPEED THAT SATISFIES THE EQUATION IS AN AIR SPEED/GROUND SPEED/ENVIRONMENT SPEED for the plane OF ZERO!!!

This explanation is only meant to point those who think it will NOT fly in the right direction. knowing that the above interpretation is impossible that leads to the 2nd interpretation. with the 2nd interpretation which i've explained numerous times, THE PLANE FLIES

Please stop using that article from avweb. First, it is a dot com site. Any idiot with half a brain can make a dot com site and make it look like it knows what it is talking about. Any college research class will tell you this. If it is not from a dot edu or dot gov site don't use it to prove a point. Second, Rick uses no scientific thoughts to back up his believe that the plane will no fly. He is just some guy rambling on about his beliefs like everyone here.

The Rick article is wrong and should be publishing a correction/retraction. He starts off with a comment:"Notice that the question does not state that the conveyor's movement keeps the airplane over the starting position relative to the ground, just that it moves in the direction opposite to any movement of the airplane. " But the question does NOT state that the conveyor's movement doesn't keep the airplane over the starting position either!

He asserts that the conveyor is irrelevant and offers this one sentence proof:

"It was an interesting argument, but as things progressed, more rational heads prevailed, pointing out that the airplanes do not apply their thrust via their wheels, so the conveyor belt is irrelevant to whether the airplane will takeoff." That's great physics, Rick!

Then he makes the same error that many others make by simply stating:

"....the airspeed indicator comes off the peg at about 10 mph. At that moment the conveyor is moving at 10 mph to the east and the tires are whirling around at 20 mph because the prop has pulled it to an airspeed, and groundspeed, of 10 mph, westbound. The airplane is moving relative to the still air and the ground at 10 mph, but with regard to the conveyor, which is going the other way at 10 mph, the relative speed is 20 mph. " Now if you assume that any movement of the plane has to mean movement away from a stationary observer then this interpretation predisposes the problem in that you've already declared it moving away from the stationary observer net of all other forces and that just isn't an interesting question after that. It is like saying "If I always move away from you no matter how hard you pull on me, will I continue to move away from you?".

Under those conditions, ordinary laws of physics will get the plane flying, yet he brings up the usual babble (no scientific support) about the plane being different from a car or person on a treadmill because it gets propulsion from the air and also throws in the fact that the wheel friction force is less than 40 lbs. So...where's any scientific support for the relevance of either of those in the problem. He's also wrong that a plane is somehow different. F=ma It doesn't make a difference what supplies the F, could be a plane, a truck, or dog sled, the force require to accelerate the plane to a faster speed is the same regardless what supplies it. The force required to overcome rolling friction is also the same regardless of what supplies it. There's nothing magical about the fact that it is supplied by a prop.

I see that Rick is a pilot (ATP) and a lawyer. But his approach to this problem makes me question whether he ever took a course in mechanics and relative motion.

Start this problem off like you would a relative motion problem in 1st semester college physics class. No forces, coefficients, masses are given nor do you need them. Only two things, the speed of the plane is matched by an opposite speed of the conveyor. The problem initially states that the plane is ON the runway/conveyor which provides a natural frame of reference for the speed of the plane to be relative to the conveyor, just like 100s of similar problems that you would see in 1st semester physics. You'll quickly see that the equal but opposite relative speeds sum to zero, therefore the plane will be stationary with respect to the outside and not flying because there's no airspeed.

Listen people, beside the fact that the plane would be moving at ZERO mph on a traditional treadmill set up and could in no way take off....

You are not paying attention. The original poster did not say the plane's engines were pushing in opposition to the direction of the treadmill! The normal set up. BUT, If the plane was facing backward on the treadmill it could take off more than twice as fast as if it was on the ground. You have to listen to what the poster didn't say.

OUT!

Please stop. Your argument assumes that the treadmill/conveyer keeps the plane stationary relative to the air. It does not.Look at the problem! The tread mill is going the SAME speed as the plane is MOVING. There may be a speed that the treadmill could go to keep the plane from moving forward, but the same speed is not it. The force applied to the plane by the treadmill is dissapated by the circular motion of the wheels. The force that the treadmill can apply to the plane will ALWAYS be less than the force the plane can apply as thrust--assuming, as the problem state, the treadmill runs at the same speed as the plane is moving. "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?"