Plane on a Treadmill (puzzle question)

[echelon6]

This has been floating around the web a lot lately, anyone heard of this one?

If a plane is traveling at takeoff speed on a conveyor belt, and the belt is matching that speed in the opposite direction, can the plane take off?

i.e. A plane starts from a standstill and as it goes faster, the conveyor belt it''s on matches that speed, but in the opposite direction. Can the plane ever take off?

(assume 0 resistance, infinite length conveyor belt, speeds relative to the ground or anything non-moving)

 

[Delster]

echelon I sent this to my BF, who has a degree in aeronautical engineering -- I thought he''d get a chuckle out of it and I might get an interesting reply with an explanation of why yay or nay... eh, the reply I got was...

"no"

 

[zdrastvootya]

Date: 10/22/2007 11:50:16 AM
Author: Delster
echelon I sent this to my BF, who has a degree in aeronautical engineering -- I thought he''d get a chuckle out of it and I might get an interesting reply with an explanation of why yay or nay... eh, the reply I got was...

''no''

I''ve heard some pretty qualified people have been fooled by this one. The wheels and the treadmill don''t make a difference - on a car it would (turning of wheels makes the car go), but on a jet the engines blowing against the air make the plane go. It doesn''t matter that the wheels have no traction. The plane still moves forward and takes off. (The wheels are turning twice as fast, if that helps.) I believe that''s the correct answer.

Z.

 

[Delster]

Date: 10/22/2007 12:43:43 PM
Author: zdrastvootya

Date: 10/22/2007 11:50:16 AM

Author: Delster

echelon I sent this to my BF, who has a degree in aeronautical engineering -- I thought he''d get a chuckle out of it and I might get an interesting reply with an explanation of why yay or nay... eh, the reply I got was...


''no''

I''ve heard some pretty qualified people have been fooled by this one. The wheels and the treadmill don''t make a difference - on a car it would (turning of wheels makes the car go), but on a jet the engines blowing against the air make the plane go. It doesn''t matter that the wheels have no traction. The plane still moves forward and takes off. (The wheels are turning twice as fast, if that helps.) I believe that''s the correct answer.


Z.

Ha ha! After a 15 minute very convoluted and confusing explanation of why he is right, and reading your post about ten times, BF has now managed to work out that he was... wrong!!! He''s very amused. He''s going around grinning to himself and plans on passing this on to his pals at work. They all have PhDs in engineering. This is gonna be entertaining!

 

[belle]

Date: 10/22/2007 12:43:43 PM
Author: zdrastvootya

Date: 10/22/2007 11:50:16 AM
Author: Delster
echelon I sent this to my BF, who has a degree in aeronautical engineering -- I thought he''d get a chuckle out of it and I might get an interesting reply with an explanation of why yay or nay... eh, the reply I got was...

''no''

I''ve heard some pretty qualified people have been fooled by this one. The wheels and the treadmill don''t make a difference - on a car it would (turning of wheels makes the car go), but on a jet the engines blowing against the air make the plane go. It doesn''t matter that the wheels have no traction. The plane still moves forward and takes off. (The wheels are turning twice as fast, if that helps.) I believe that''s the correct answer.

Z.

of course, that would be correct!

 

[ladypirate]

The MythBusters did an episode on this! They discovered by actually doing it that the plane did indeed take off...man, that show is awesome.

 

[zdrastvootya]

Date: 10/22/2007 1:14:15 PM
Author: Delster

Date: 10/22/2007 12:43:43 PM
Author: zdrastvootya

Date: 10/22/2007 11:50:16 AM

Author: Delster

echelon I sent this to my BF, who has a degree in aeronautical engineering -- I thought he''d get a chuckle out of it and I might get an interesting reply with an explanation of why yay or nay... eh, the reply I got was...


''no''

I''ve heard some pretty qualified people have been fooled by this one. The wheels and the treadmill don''t make a difference - on a car it would (turning of wheels makes the car go), but on a jet the engines blowing against the air make the plane go. It doesn''t matter that the wheels have no traction. The plane still moves forward and takes off. (The wheels are turning twice as fast, if that helps.) I believe that''s the correct answer.


Z.

Ha ha! After a 15 minute very convoluted and confusing explanation of why he is right, and reading your post about ten times, BF has now managed to work out that he was... wrong!!! He''s very amused. He''s going around grinning to himself and plans on passing this on to his pals at work. They all have PhDs in engineering. This is gonna be entertaining!

I''m pretty sure I got the wrong answer the first time. The treadmill is a very distracting piece of information.

A pretty well-known phd/lecturer was thrown by this question. He had a very long explanation, but he was wrong.

The 15 minute explanation and reading my post 10 times ==> tee hee.

Z.

 

[partgypsy]

I know I''m already wrong (I''m not an engineer) but I would have guessed no, because a plane rises because of lift. Doesn''t seem there would be any lift if the plane was not moving relative to the ground

 

[echelon6]

Date: 10/22/2007 1:14:15 PM
Author: Delster

Date: 10/22/2007 12:43:43 PM
Author: zdrastvootya

Date: 10/22/2007 11:50:16 AM

Author: Delster

echelon I sent this to my BF, who has a degree in aeronautical engineering -- I thought he''d get a chuckle out of it and I might get an interesting reply with an explanation of why yay or nay... eh, the reply I got was...


''no''

I''ve heard some pretty qualified people have been fooled by this one. The wheels and the treadmill don''t make a difference - on a car it would (turning of wheels makes the car go), but on a jet the engines blowing against the air make the plane go. It doesn''t matter that the wheels have no traction. The plane still moves forward and takes off. (The wheels are turning twice as fast, if that helps.) I believe that''s the correct answer.


Z.

Ha ha! After a 15 minute very convoluted and confusing explanation of why he is right, and reading your post about ten times, BF has now managed to work out that he was... wrong!!! He''s very amused. He''s going around grinning to himself and plans on passing this on to his pals at work. They all have PhDs in engineering. This is gonna be entertaining!

Hah! I too originally thought no, but now I think yes.

has mythbusters done this already? I thought it was still an ep in the making...

Interestingly, there''s apparently a peer-reviewed paper published by a PHD Physicist out there which answers this problem definitively.

I actually originally got this from another forum I frequent. One of the responses involved a black-hole being formed due to the wheels instantly accelerating to infinite. Hilarious

 

[cara]

The original phrasing of the question is a little confusing, but the key is the little bit thrown in at the end about speeds being relative to the ground. If the plane is traveling at takeoff speed relative to the air around the wings then it can take off. That is what the "lift" formula is based on - the relative velocity of airflow around the wings.

This is why its easier for planes to take off into a headwind - the plane speed relative to the ground can be lower for the same effective air speed around the wings.

If the plane is a takeoff speed relative to the conveyer belt and the conveyer belt is at an equal and opposite velocity relative to the ground, such that the plane is basically at rest relative to the ground and more importantly at rest relative to the air mass around the plane, then the plane cannot takeoff. Not if it is a fixed wing aircraft.

While the jets provide forward thrust that accelerates the plane along the runway and straight ahead in the air, unless they are aimable (such as jets on the space shuttle or a satellite that can reorient), they do not provide "lift" to get off the ground. The lift is provided by interactions between the air and plane as the air is forced to flow around various shapes - mainly the wings and the steering flaps (need technical term for flaps here).

 

[ladypirate]

It''s possible it hasn''t aired yet--I heard them do a keynote address where they talked about the episode, so it might be on this season.

 

[strmrdr]

Date: 10/22/2007 9:44:20 AM
Author:echelon6
This has been floating around the web a lot lately, anyone heard of this one?

If a plane is traveling at takeoff speed on a conveyor belt, and the belt is matching that speed in the opposite direction, can the plane take off?

i.e. A plane starts from a standstill and as it goes faster, the conveyor belt it''s on matches that speed, but in the opposite direction. Can the plane ever take off?

(assume 0 resistance, infinite length conveyor belt, speeds relative to the ground or anything non-moving)

sure it would take right off.
The speed the wheels are traveling is not relevant to the air speed.
The wheels would just turn 2x as fast at take off speed.
The key is that aircraft wheels are free wheeling.
An aircraft without power could stay stationary on a moving conveyor belt by using flaps and reversers if the air drag overcame the relatively small amount of friction between the wheels and the spindles they turn on.

 

[zdrastvootya]

If the plane is a takeoff speed relative to the conveyer belt and the conveyer belt is at an equal and opposite velocity relative to the ground, such that the plane is basically at rest relative to the ground and more importantly at rest relative to the air mass around the plane, then the plane cannot takeoff. Not if it is a fixed wing aircraft.

"Such that the plane is basically at rest .......". This is impossible. The conveyor belt cannot keep the plane at rest when the engines are engaged.

The speed of the conveyor belt is irrelevant, because the wheels are assumed to be frictionless (in the bearings, let''s say). The belt can go 5x the takeoff speed in the opposite direction, but it offers no resistance to the jet moving forward and reaching takeoff speed. (The wheels just spin faster, as the esteemed stormraider has pointed out.)

That''s the "trick" to this question.

Z.

 

[cara]

Why is it impossible for the plane to be at rest with the conveyer belt spinning under it? Yes if the engines are engaged the plane will go forward but I don't see that in the problem. Either way, stating the problem more clearly would still make the right answer more clear - presumably the first interpretation with velocities relative to the ground.

but the no resistance claim is a little tricky as well. don't you need air resistance in order to have lift?

 

[lyra]

My husband is an expert in this field. I''ll ask him for his input next time I see him, although I''m sure I''ll get the rolling eyes gesture mostly.

Is it a jet or piston aircraft? If it''s a VTOL, there is no issue at all AFAIK.

Also, what if the plane is mounted on skis?

 

[aljdewey]

Date: 10/23/2007 1:33:26 PM
Author: cara
Why is it impossible for the plane to be at rest with the conveyer belt spinning under it? Yes if the engines are engaged the plane will go forward but I don't see that in the problem. Either way, stating the problem more clearly would still make the right answer more clear - presumably the first interpretation with velocities relative to the ground.

but the no resistance claim is a little tricky as well. don't you need air resistance in order to have lift?

Because it's not stationary. The act of the convey belt spinning will move the plane (forward or back) even though the plane's wheels aren't moving.

Think of you standing in the center of a treadmill that's not turned on. You're not walking and the treadmill isn't turning, so you will remain at the center of the treadmill.

You can change that in two ways: by taking a step forward or back (even if the treadmill remains turned off) or by turning on the treadmill (even if you never move your feet.) Two actions will cause movement - you initiating the movement or the treadmill initiating movement. If either of those two things creates movement, you are no longer stationary.

Regarding the quiz, the reason the plane will still take off is this: 'an object at rest tends to stay at rest, and an object in motion tends to stay in motion." It doesn't matter how the object (in this case the plane) achieves the velocity required to be sufficiently 'in motion". In daily life, the runway doesn't move at all, so all the velocity has to be generated by moving the plane along the stationary runway (so 0% runway power, 100% plane power). In the example above, the burden of achieving the needed velocity for liftoff is simply split/shared between the movement of the plane and the movement of the treadmill (50% 'runway', 50% plane).

 

[cara]

Date: 10/23/2007 12:05:30 PM
Author: zdrastvootya

If the plane is a takeoff speed relative to the conveyer belt and the conveyer belt is at an equal and opposite velocity relative to the ground, such that the plane is basically at rest relative to the ground and more importantly at rest relative to the air mass around the plane, then the plane cannot takeoff. Not if it is a fixed wing aircraft.

''Such that the plane is basically at rest .......''. This is impossible. The conveyor belt cannot keep the plane at rest when the engines are engaged...

Z.

Aljdewey, my question was in reference to this alternate senerio above, in which the plane''s velocity is given relative to the top of the conveyer, and the conveyer''s velocity is given relative to the ground, such that the plane IS at rest relative to the ground. I realize this is not what the initial poster asked, but it was what I was imagining until that last bit at the end in which the poster says "velocities are relative to ground".

In this alternate scenerio, Z. says it is impossible IF the engines are engaged and there is no friction from the conveyer or plane wheels spinning.

This I get - but the problem doesn''t say the engine is on. If the engine is off the plane can sit pretty, at rest relative to the ground, with its wheels spinning furiously and the conveyer running opposite underneath. Like standing on a treadmill on a roller skates. Treadmill spins, skate wheels spin, person still. Unless I am missing something else - this is the misinterpretation I imagine many people make that answer the problem wrong.

If the engine is ON, spitting air out of the back, then it should accelerate forward, and the wheels and conveyer can spin as they want.

Regarding your last bit, the law is "at object at rest will remain at rest, and an object in motion will remain in motion, unless acted upon by an outside force". Motion in this instance means constant speed and direction. If the plane is to take off, it must accelerate up, not remain moving in a straight line. To accelerate, you need "lift" - a force acting on the plane that is generated by air as it flows over the wings and other shapes of the plane. No air flow, no lift. Speed of ground beneath plane doesn''t matter, speed of air over wings does matter. The tricky part is throwing out "air resistance" but still getting lift. I am not sure that is possible. But we were probably supposed to keep air resistance but only throw out kinetic friction for the bearings on the wheels and conveyer when given the "0 resistance" instruction.

OK enough. Back to my regular work.

 

[zdrastvootya]

Regarding the quiz, the reason the plane will still take off is this: ''an object at rest tends to stay at rest, and an object in motion tends to stay in motion.'' It doesn''t matter how the object (in this case the plane) achieves the velocity required to be sufficiently ''in motion''. In daily life, the runway doesn''t move at all, so all the velocity has to be generated by moving the plane along the stationary runway (so 0% runway power, 100% plane power). In the example above, the burden of achieving the needed velocity for liftoff is simply split/shared between the movement of the plane and the movement of the treadmill (50% ''runway'', 50% plane).

50% runway, 50% plane ==> untrue. You''re equating the wheels spinning with velocity of the plane. The velocity of the plane has nothing to do with the treadmill or the wheels.

Cara''s right though about the fact that with planes it''s really about velocity of air over the wings, not the velocity of the plane relative to the ground. But without wind, it''s kind of the same thing.

I guess the plane can be at rest on the treadmill (going the opposite direction), if you run the engines the right amount, but there wouldn''t be any air rushing across the wings. The plane wouldn''t take off any more than it would sitting on a runway. Sorry Cara, haven''t had a chance to read your latest. Back to work! Z.

 

[strmrdr]

A better question is if you towed a large jet backwards fast enough would it rise of the ground?
How about a cesena?

 

[zdrastvootya]

Date: 10/26/2007 2:41:53 PM
Author: strmrdr
A better question is if you towed a large jet backwards fast enough would it rise of the ground?
How about a cesena?

Well, the air is going over the wings the wrong way, but I''m sure you''d get some lift. Wouldn''t think it would be very stable.

If you put the plane in an wind tunnel with the wind blowing at cruising speed into the nose, I''m sure it would rise up.

Z.

 

[Skippy123]

Date: 10/22/2007 1:32:58 PM
Author: ladypirate
The MythBusters did an episode on this! They discovered by actually doing it that the plane did indeed take off...man, that show is awesome.

I like that show too, especially the episode w/the motion sickness tests. I thought those pressure point bands would work but no people got sick.

 

[Rocksport]

Bzzzzttttt

Sorry that was the sound of a few fuses blowing upstairs.

It took a few readings to see what was actually being asked, think I have it now. Maybe not as firm a grip, but getting there.

For the bit about if a plane was dragged backwards. Would this not work the opposite way and cause plane to have the opposite of lift you get when it is going forward.

PLEASE not to complicated, I only have a few fuses left

 

[strmrdr]

Date: 10/28/2007 9:33:26 AM
Author: Rocksport
Bzzzzttttt

Sorry that was the sound of a few fuses blowing upstairs.

It took a few readings to see what was actually being asked, think I have it now. Maybe not as firm a grip, but getting there.

For the bit about if a plane was dragged backwards. Would this not work the opposite way and cause plane to have the opposite of lift you get when it is going forward.

PLEASE not to complicated, I only have a few fuses left

No it would still have lift, the Cessna would would rise off the ground.
The jet wouldn''t because no modern jet gets enough lift from the wings to fly.
They are all lifting body designs where somewhere around 40% of the lift is generated by the planes body and not the wings.

 

[lyra]

Here''s the definitive answer from my DH:

Answer 1 Zero ground friction.

If there is absolutely no ground friction, the conveyor belt becomes completely irrelevant and the aircraft would accelerate and fly.

Answer 2 Friction on a Conveyor belt (jet aircraft)

If there was friction on the wheels as there always is, but the surface of the wheels were matched but in opposite direction by the treadmill, the aircraft will not accelerate through the airmass. It will remain stationary relative to the airmass. Airflow over the wings is required to achieve lift.

This could be explained in a car. If you have your car emmission tested on a "Dyna" cart, The drive wheels move but move proportionately to the Dyna cart so the car does not move forward through the airmass. If you rolled down your window and put your arm out, you would feel no airflow thus achieving no lift.

For a prop airplane, things change slightly in that the propellor produces airflow over the wing but not enough to produce "controlled" flight.

 

[zdrastvootya]

Date: 10/28/2007 11:00:41 PM
Author: lyra
Here''s the definitive answer from my DH:

Answer 1 Zero ground friction.

If there is absolutely no ground friction, the conveyor belt becomes completely irrelevant and the aircraft would accelerate and fly.

Answer 2 Friction on a Conveyor belt (jet aircraft)

If there was friction on the wheels as there always is, but the surface of the wheels were matched but in opposite direction by the treadmill, the aircraft will not accelerate through the airmass. It will remain stationary relative to the airmass. Airflow over the wings is required to achieve lift.

This could be explained in a car. If you have your car emmission tested on a ''Dyna'' cart, The drive wheels move but move proportionately to the Dyna cart so the car does not move forward through the airmass. If you rolled down your window and put your arm out, you would feel no airflow thus achieving no lift.

For a prop airplane, things change slightly in that the propellor produces airflow over the wing but not enough to produce ''controlled'' flight.

Remember, this question fools many physicists and engineers.

Even if the wheels had friction, how fast would the treadmill spin to cause enough friction to resist forward momentum?
Let''s say takeoff speed is 100mph. You roll the treadmill the other way 100mph. For the plane to reach 100mph, the wheels would spin at 200mph. I don''t think there''s enough friction in the wheels at 200mph to stop the plane''s forward motion. The treadmill matches forward wheel speed - this means the wheel revolutions are consistently doubled as the plane accelerates. Again, I can''t see why the (free-spinning) wheels would cause enough friction for a jet to stand still.

A car is powered by the wheels. A jet has free spinning wheels (like a toy car that you can push forward or backward). A jet on a dyna cart is something completely different because no matter how you spin the rollers, the jet engine will push the plane forward off the cart. Please re-check with DH.

Z.