Physics Question

[eber]

Originally posted by: mugs

Originally posted by: Bigsm00th

the thurst created by the engines is counter-acted by the friction of the wheels. that is the whole point of this hypothetical problem. the "station wagon on the treadmill" scenario is a perfect example of this. the "thurst" is the same thing as the car moving the wheels with an engine. you guys are very wrong by stating the plane would lift off because it is still stationary with respect to the ground. that is how the question is asked so the answer is no, it doesnt lift.

The question said that the treadmill moves at the same speed as the plane in the opposite direction, it did not say the plane remains stationary. There'd have to be a hell of a lot of friction in those wheels to counteract the thrust of the jet engines. The wheels would simply be rotating twice as fast as the plane is moving.

I got ya...it is a tricky question. But then not only would there have to be a hell of a lot of friction, it would have to be a hell of a good conveyor belt system.

 

[dawks]

Originally posted by: Bigsm00th

Originally posted by: letdown427

Originally posted by: Armitage

Originally posted by: letdown427
"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?"

waaait a minute. a plane is not a car right? Right. A plane is not moved forward by it's wheels right? Right. For the plane to move forwards, air is sucked into the engines (i'm not thinking of a propeller driven plane here, but like, a commerical airliner, irrelevant though) Neway, for it to move forward, this must happen, it mustbe sucking the air into the engine, generating thrust n stuff, fine i don't know for sure the exact technical details, but i actually think it can take off. The plane actually moves forward independent of the ground. its wheels stop it from dragging on the floor nothing more. so if the plane is moving forward at say 140mph (to take off) yes, the conveyer is moving at 140 opposite direction, but this just means that the wheels are moving at 280mph. the planes speed is created in the air if u will, by the engines, not by the wheels. therefore, i think it can take off. contrary to my initial assumption of this is a duuuuumb post. do i win? lol

like, imagine a strong fan, on wheels, blowing air backwards on one of these conveyers. say it blows air out at a rate sufficient to get it to move forward at 10mph. now, assuming there is no resistance as we always do in simple physics, it will move forward at 10mph whether it is in thea air, on the ground on its wheels, or even in the sea (sticking to NO RESISTANCE here). if it was on this conveyer, all that would happen is that it would still be moved forward by the fan at 10mph, but the wheels would be traveeling at 20mph, ass they conveyer would be moving opposite to the wheels under it.

OMG, I can't believe there are 3 pages of posts on this. No I haven't read them all, but letdown got it right on the first page.

The speed of the ground/conveyer belt under the plane is completely irrelevant. As everybody says, it's the speed of the plane through the air that matters. Well, the plane moves forward by thrust from the engines - it is accelerating forward regardless of what the ground is doing underneath it. Assuming the brakes are off of course

The wheels will be spinning at twice the forward velocity of the plane of course, but the plane will be moving forward relative to the air.

Draw a free body diagram of the plane. You have thrust from the engines. What is counteracting that thrust to keep the plane motionless?

Not the conveyer belt - there will be some rolling resistance of the wheels across the belt of course - just like a normal takeoff. Though a bit higher due to the higher wheel speed.

But it is moving and will takeoff.

Thank You. lol.

you arent right and neither is armitage. this is a very simple question with a very simple answer. it has been said many times.

the thurst created by the engines is counter-acted by the friction of the wheels. that is the whole point of this hypothetical problem. the "station wagon on the treadmill" scenario is a perfect example of this. the "thurst" is the same thing as the car moving the wheels with an engine. you guys are very wrong by stating the plane would lift off because it is still stationary with respect to the ground. that is how the question is asked so the answer is no, it doesnt lift.

You're wrong.

If you put a wagon on a treadmill, then hold it there with your hand, no matter how fast the treadmill belt goes, the wagon will remain stationary, since the wheels will just spin faster to match the belt. If you start pushing forward on the wagon with your hand, it wouldnt matter if the belt was spead up, becasue again, the wheels would just speed up too. As you push forward, the wagon moves forward.

The same happens with an airplane. But instead of a hand pushing the plane, you have turbofan engines pulling it forward. No matter how fast the belt goes underneath, the wheels will match it.

As I said before, in this case, its pretty well the same as being in the air already, the only difference here is that the wheels are holding the weight of the aircraft until it can be transferred to the wings.

 

[silverpig]

Depending on how technical you want to get, you could have it go either way.

The plane would normally be able to take off, but if you can get the treadmill going as fast as you wanted, you could make it so that the plane didn't take off. If you get it going fast enough, the wheels would be spinning so fast that the tires would come apart, destroying the wheels, making the plane crash onto the treadmill and go shooting off the back of the runway. Sure it's kind of lame, but it'd sure be fun.

 

[SVT Cobra]

I am taking a model airplane to a treadmill and testing this. While all my physics classes tell me it should not take off, I still believe with a jet engine it can still generate airflow over the wings.

EDIT: No it would not take off, airflow would be generated, but it would still be stationary to the air.

 

[Mark R]

Of course the plane will take off.

The plane's engine pushes on air, not on the runway. As a result the plane will be propelled forward, generating lift on the wings.

That the runway is itself propelled is irrelevant.

 

[g8wayrebel]

No , and I sure as hell hope none of the idiots who oppose you on the answer are future leaders of anything more than a boyscout troup.
In fact , maybe they better stick to taking care of the goldfish.

 

[dawks]

Originally posted by: g8wayrebel
No , and I sure as hell hope none of the idiots who oppose you on the answer are future leaders of anything more than a boyscout troup.
In fact , maybe they better stick to taking care of the goldfish.

Explain why.

Its been explained clearly, numerous times why it would..

I thought it wouldn't at first too, but if you actually think it through, it would work just fine.

 

[mugs]

Originally posted by: g8wayrebel
No , and I sure as hell hope none of the idiots who oppose you on the answer are future leaders of anything more than a boyscout troup.
In fact , maybe they better stick to taking care of the goldfish.

Quoted so you can't edit this when you realize how stupid it makes you look.

 

[Armitage]

Once again - If the plane doesn't take off, what force is opposing the thrust of the engines such that the plane remains stationary?

 

[Armitage]

Originally posted by: 911paramedic
OK, a friend of mine frequently posts brainteasers for us on our site. (400+ members, all veterans or active duty) This is his latest question and we are deeply divided on the answer, just about down the middle. I would like to put this out there so I can get a very simple answer to explain it to him. (I am sure of my answer, but dont want to post it for fear of contamination) Here is his question:

"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?"

Thanks in advance. (no, its not homework, you guys know me...duh)

Back to the OP ... note that it doesn't say that the plane is stationary - just that the conveyer belt is moving backwards at the same speed the plane is moving forward. Seems very clear and unambiguous to me.

The wheels are turning twice as fast as they would be on a normal runway, but it accelerates and takes off just fine.

 

[bootymac]

.

 

[allies]

I find it funny that there are a lot of people who still say the plane won't take off. The plane WILL be experiencing airspeed due to it moving forward, but it's wheels moving twice as fast as they normally would on a stationary "conveyor belt".

 

[slpaulson]

No, it has to be moving at a certain speed with respect to the air around it, but the belt is keeping it from moving at all.

 

[imported_Baloo]

Doh!, letdown427 got it.

 

[KillerCharlie]

ARGGGHGHGHHH!!!

THE WORDING OF THE QUESTION IS HORRIBLE. IF IT IS WORDED MORE CLEARLY THE ANSWER IS STRAIGHTFORWARD!!!

IF THE PROBLEM DICTATES THAT THE PLANE DOES NOT MOVE WITH RESPECT TO THE FIXED REFERENCE FRAME (you sitting inside a building watching this thing on the conveyor), THEN IT WILL NOT TAKEOFF. NO AIRFLOW OVER WINGS = NO LIFT.

IF THE PROBLEM DOES NOT CONSTRAIN THE PLANE IN THIS FIXED REFERENCE FRAME THEN IT CAN TAKEOFF.

I AM A PROFESSIONAL AERODYNAMICIST. BOEING WOULD HAVE FIRED ME A LONG TIME AGO IF I DIDN'T KNOW WHAT I WAS TALKING ABOUT.

THIS THREAD MAKES ME WANT TO KILL MYSELF. WHOEVER CAME UP WITH THIS QUESTION SHOULD BE SHOT FOR WORDING IT SO POORLY.

AHHHHHHHHHHHHHHHHH!!!!

 

[mugs]

Originally posted by: KillerCharlie
ARGGGHGHGHHH!!!

THE WORDING OF THE QUESTION IS HORRIBLE. IF IT IS WORDED MORE CLEARLY THE ANSWER IS STRAIGHTFORWARD!!!

IF THE PROBLEM DICTATES THAT THE PLANE DOES NOT MOVE WITH RESPECT TO THE FIXED REFERENCE FRAME (you sitting inside a building watching this thing on the conveyor), THEN IT WILL NOT TAKEOFF. NO AIRFLOW OVER WINGS = NO LIFT.

IF THE PROBLEM DOES NOT CONSTRAIN THE PLANE IN THIS FIXED REFERENCE FRAME THEN IT CAN TAKEOFF.

I AM A PROFESSIONAL AERODYNAMICIST. BOEING WOULD HAVE FIRED ME A LONG TIME AGO IF I DIDN'T KNOW WHAT I WAS TALKING ABOUT.

THIS THREAD MAKES ME WANT TO KILL MYSELF. WHOEVER CAME UP WITH THIS QUESTION SHOULD BE SHOT FOR WORDING IT SO POORLY.

AHHHHHHHHHHHHHHHHH!!!!

What about the wording is ambiguous in that respect? The question never says the plane doesn't move. It's up to you to figure out whether it can move or not.

You're basically complaining that the question doesn't give away the answer.

Edit: And as a PROFESSIONAL AERODYNAMICIST, you ought to know that an airfoil does not need to move to produce lift, it simly has to have air passing over it. i.e. a big gust of wind.

In conclusion, Boeing should fire you.

 

[Evadman]

This totaly depends on what the teacher is teaching. Seriously.

In real life, the plane would take off just fine. The plane does not push against the ground for power like a car. If this were a car, then the net speed of the car would be zero.

Since a plane pushes against the air, the wheels can be turning at any rate they want, forwards, backwards, sideways, it doesn't matter. (though steering and premature wear would be issues)

If the plane is moving forward at 170 mph, and the conveyor is moving backward at 170, then the wheels are moving at a relitiveistic speed of 340 mph (remember, they are not pushing against the ground, they are basicly freewheeling). However, the plane is still moving at 170 though the air, and getting the lift that it would get at 170 mph.

Those who are discussing the friction of the bearing are not taking into account the power most planes create. Remember, we are in real life. With enough power and the corect angle of attack it is possible to make a brick fly. My truck at 140 is proof of that.

Unless the wheels were bolted to the conveyor, and a speed differential between the conveyor and the air is impossible, the plane will fly. The plane only havs to make slightly more power than a regular take off to make up for the friction loss of the bearings.

 

[MrCodeDude]

0.9999999999... = x
100 * x = 99.9999999999

99.9999999999 - x = 99 <-- where does this come from?

 

[KillerCharlie]

Originally posted by: Evadman

Unless the wheels were bolted to the conveyor, and a speed differential between the conveyor and the air is impossible, the plane will fly. The plane only havs to make slightly more power than a regular take off to make up for the friction loss of the bearings.

Interestingly, the resistance from the wheels (to a high order of accuracy) depends just on the normal force (weight) of the aircraft, not the speed of the wheels. Given that the aircraft is not constrained in the fixed reference frame, then the conveyor speed actually has 0 effect on the airplane.

This means the ODE governing the aircraft velocity is:

m(dv/dt)=T-D-mu*(W-L)

T=thrust
D=drag
mu=coefficient of rolling friction
W=weight
L=lift

Of course thrust, drag, and lift are functions of velocity. Drag is also a function of lift, but because of ground effect the induced drag changes quite a bit, meaning you'd need a simple numerical ODE solver for this.

The wheel resistance does not depend on the speed, so the conveyor speed is irrelevant (once again, only if the airplane is not constrained in the fixed reference frame). If the aircraft is fixed in the reference frame as per some interpretations, then the thrust needed to cancel out the wheel resistance and keep the plane stationary is constant.

 

[mugs]

Originally posted by: KillerCharlie

If the aircraft is fixed in the reference frame as per some interpretations, then the thrust needed to cancel out the wheel resistance and keep the plane stationary is constant.

Again, how can you read the question and possibly interpret it to mean that the airplane is "constrained to a fixed reference frame"?

 

[91TTZ]

Originally posted by: 911paramedic
OK, a friend of mine frequently posts brainteasers for us on our site. (400+ members, all veterans or active duty) This is his latest question and we are deeply divided on the answer, just about down the middle. I would like to put this out there so I can get a very simple answer to explain it to him. (I am sure of my answer, but dont want to post it for fear of contamination) Here is his question:

"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?"

Thanks in advance. (no, its not homework, you guys know me...duh)

No. Unless it's a Harrier. Wheel speed doesn't matter, it's air over the wings which make it fly.

 

[mugs]

Originally posted by: 91TTZ
No. Unless it's a Harrier. Wheel speed doesn't matter, it's air over the wings which make it fly.

:frown:

 

[Armitage]

Originally posted by: KillerCharlie
ARGGGHGHGHHH!!!

THE WORDING OF THE QUESTION IS HORRIBLE. IF IT IS WORDED MORE CLEARLY THE ANSWER IS STRAIGHTFORWARD!!!

IF THE PROBLEM DICTATES THAT THE PLANE DOES NOT MOVE WITH RESPECT TO THE FIXED REFERENCE FRAME (you sitting inside a building watching this thing on the conveyor), THEN IT WILL NOT TAKEOFF. NO AIRFLOW OVER WINGS = NO LIFT.

IF THE PROBLEM DOES NOT CONSTRAIN THE PLANE IN THIS FIXED REFERENCE FRAME THEN IT CAN TAKEOFF.

I AM A PROFESSIONAL AERODYNAMICIST. BOEING WOULD HAVE FIRED ME A LONG TIME AGO IF I DIDN'T KNOW WHAT I WAS TALKING ABOUT.

THIS THREAD MAKES ME WANT TO KILL MYSELF. WHOEVER CAME UP WITH THIS QUESTION SHOULD BE SHOT FOR WORDING IT SO POORLY.

AHHHHHHHHHHHHHHHHH!!!!

All your chest pounding about your aerodynamics degree is pointless - nobody is arguing that the plane has to have takeoff velocity relative to the air to take off. The argument is whether the plane moves or not.

Again, please explain what force is balancing the thrust of the engines to prevent the plane from moving? Seriously ... draw the free body diagram.You have forward thrust from te engines ... if the plane isn't moving, what force is opposing this thrust?

And while you're at it, take another look at the OP and show me where it says the plane remains stationary WRT (With Respect To) the earth? In fact the OP states that the plane is moving:

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).

You were going on about the proper cordinate frame earlier - the coordinate frame has to be relative to the earth - let's call it inertial. Otherwise the controller is divergent. Try this little though experiment with me...

Lets assume the statement in the OP that I've quoted above means that the conveyer tries to match the speed of the plane WRT the conveyer. Let's look at this as discreet steps:

1. The plane and conveyer are both at rest WRT the inertial cordinate frame.

2. Something accelerates the plane so that it has a speed of 1mph WRT the inertial frame (and still stationary conveyer)

3. The conveyer controller (CC) measures the speed of the plane WRT the conveyer and commands the conveyer to go -1mph (ie. in the opposite direction).

4. The CC measures the speed of the plane WRT the conveyer again - now it is 2mph (the plane is still only moving 1mph WRT inertial). So the CC bumps the conveyer speed up to -2mph

5. The CC measures the speed of the plane WRT the conveyer again - now it is 3mph. So the CC bumps the conveyer speed up to -3mph

Do you see where this is going? The controller is impossible if we assume the OP is refering to the speed of the plane relative to the conveyer. Now a controller the moves the conveyer backwards WRT inertial at the same rate as the plane moves forward WRT inertial is possible, so I have to take that as what is meant.

 

[Mo0o]

No. the "lift" comes from the air passing through the wings and creating a pressure difference . If the plane is not cutting through the air it will NOT lift off. Another question can be, if you're running on a treadmill holding one of thoes 50c glittering foil fans like 6 year old girls like, will that fan spin?

This is based on the assumption the plane is stationary to begin with and any acceleration attempt forward is countered completely by the coveyer belt carrying it back, essentially keeping hte plane in place

 

[91TTZ]

Originally posted by: 911paramedic
OMFG, now there is a website posted saying it CAN take off...

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

The "straight dope" is smoking dope.

The argument is largely just a matter of the wording. The people who say it can't take off are right as they state it. The people like Dr. Pizza are also right, but for a different reason.

To make it simple, a plane needs air over the wings to fly. Let's say a plane's takeoff speed is 100 mph indicated airspeed. If this conveyor thing was in place and moved backwards at the same rate which the plane moved forwards, this would NOT stop the plane from moving forwards, it would just double the tire speed. So the plane would still take off at 100 mph indicated airspeed, but 200 mph tire speed.