Apparently "Myth Busters" will be taking this little problem on so we'll finally get to see this setup in action. :-)

http://www.boingboing.net/2008/01/28/mythbusters-tackles.html

" the next episode of MythBusters (airing this Wednesday). It tackles the famous "plane on a conveyor belt problem," that has pitted brother against brother and friend against friend for years.

To get to the bottom of the thought-problem, Adam and Jamie used a real plane, in this case a 400-lb ultralight, and a large conveyor belt. Did the plane take off? You'll have to wait until Wednesday to find out, but Adam said even the pilot guessed wrong."

So, today's Wednesday.... a whole week to wait!

I would have thought that the plane would not take off, but since the airplane pilot guessed wrong.... who knows!

Several pilots on this thread have conflicting opinions. I'm a pilot, and I say it flies.

I figured they would get to this one at one point...... is that tonight....?

Watching it right now...here's what I've identified as a problem with this DVInfo thread:

The problem statement is incorrectly or ambiguously stated. The original problem statement (as far as I know):

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

Can the plane take off?

http://boards.straightdope.com/sdmb/showthread.php?t=348452

Whereas the the way it is in this forum:

If you have a large jet plane (747) sitting on a runway that was actually a giant conveyor belt (go with it). And there is also a device on the plane that communicates with the conveyor belt to tell it how fast the plane is traveling, which would then make the conveyor belt match the speed IN REVERSE.

Can the jet take off?

The difference is subtle but critical and I believe goes a long way to explain the vehement disagreement we have endured. The latter statement is ambiguous, leading to two very different interpretations.

I leave it to you to spot the difference!

I was one who said it wouldn't fly, but first test with came off showing it would, but I don't think they really matched speed with treadmill.

Did I miss it??? I thought it was next week! I assume it flew... VINDICATED!

Did I miss it??? I thought it was next week! I assume it flew... VINDICATED!

Yes, verily vindicated!

Though the way they did it was rather unscientific which doesn't suit my scientific (in)sensibilities but does suit my boys and their toys bent.

Oh - it was on at 9e, perhaps it will be on at 9p?

Cool it's on at eight pm here in California. Funny, they do a lot of their outdoor testing just up 101 from me, in the old Naval Yards.

I don't think the original statement here is 'wrong' or confusing. Even if you gave the treadmill a slight 'head start' - the plane would still accelerate independent of the speed of the treadmill.

I was hoping they'd get to this...did somebody here suggest it on their site, or was this just coincidence?

I have to agree that the question as posed in this thread is a bit confusing, only because of "And there is also a device on the plane that communicates with the conveyor belt to tell it how fast the plane is traveling". How fast the plane is traveling? That means it's moving. If it's moving forward fast enough, it can create the necessary lift to take off, so the entire point is moot, as you've just explained the thing is able to move. The more appropriate setup would be to match the speed of the wheels' rotation, as John pointed out, but that only changes the way the situation is stated, not the fundamental principles involved. The whole thing is difficult to imagine just from the question, as whether the belt matches the wheels or the body of the plane, it wouldn't have anything to match if there were not already motion, and once the plane gets moving, well, problem solved.

I think the biggest problem here is to get hung up, as I initially did, on the Bernoulli effect, and to focus on how wings generate lift, forgetting that you've already made the mistake of assuming the plane does not move forward. "Can a conveyor belt stop an aircraft from moving forward?" might be a better question, excluding of course helicopters and those pontoon-equipped dealies that land in water. Since the propulsion of the aircraft has absolutely, positively nothing to do with the wheels, I should say the answer is a definite 'no'. The wheels can spin as fast as they need to, the landing gear could snap off if it came to that, even skidding on its belly the thing would create lift if it had enough thrust behind it. I don't know if a jumbo jet is really built to overcome that kind of friction, even with four enormous engines, but you get the idea; unless this conveyor system is on the moon or underwater, there's plenty of air for the jets or propellors to send backward in the pursuit of thrust.

I think most people got hung up on the notion that wheels provide motive force for the aircraft's movement. The wings were not necessary for 'forward motion' - only for flight. You could just as easily say "If you put an airplane engine on a skateboard, and the treadmill moved in the opposite direction - would it move forward? The answer is still yes - the motive force is not connected to the ground or the wheels - it operates and applies thrust independent of wheel rotation speed.

Once its moving then the wings take over.

You could say "Moved in the opposite direction in response to wheel speed rotation" OR "Moved in the opposite direction in response to engine thrust" OR "Moved in the opposite direction in response to apparent motion as observed by a viewer off the treadmill" OR "Moved in the opposite direction in response to an airspeed indicator" OR "Moved in the opposite direction in response to a speedometer attached to the wheels" - The wheels provide no motive force, they are only there to eliminate (as much as possible) friction between the device and the ground.

EDIT - Man, its on and I think it's not the one. I must have missed an earlier showing.

EDIT - Man, its on and I think it's not the one. I must have missed an earlier showing.

They showed two episodes back-to-back here, the first at 8. The one of interest is the second one. Can't remember what the first one was about since I'd seen it before.

Hah! You're right they just showed the preview for it, two shows back to back.

Well I watched it last night, and it was fun to watch them deal with it. As smart as the guys are, sometimes they can be a little 'common sense' blind. It was obvious the treadmill was going to be too short for the model plane take off run for instance.

Still, good fun to see the myth busted.

The. Plane. Will. Fly.

...good fun to see the myth busted. The. Plane. Will. Fly.Thanks for bringing this thread back to life and giving it proper closure, guys! Much appreciated,

So in our scenario as originally posted, the conveyor sped up every time the plane would speed up, in the Myth Busters version, they just used a constant speed take off speed for the conveyer. Point of us nay sayers has always been that you have to attain air speed. If the conveyor kept speeding up the, downforce of gravity is enought to created the friction necessary to keep the plane from going forward, as the conveyor sped up, the plane would never move forward and wheels would fall off at some speed. I still say not busted, as applied to the scenario posted here.. I also note that both planes were ultra light, certainly not comparable to a 747. :)

So in our scenario as originally posted, the conveyor sped up every time the plane would speed up, in the Myth Busters version, they just used a constant speed take off speed for the conveyer. Point of us nay sayers has always been that you have to attain air speed. If the conveyor kept speeding up the, downforce of gravity is enought to created the friction necessary to keep the plane from going forward, as the conveyor sped up, the plane would never move forward and wheels would fall off at some speed. I still say not busted, as applied to the scenario posted here.. I also note that both planes were ultra light, certainly not comparable to a 747. :)

If the "downforce of gravity is enough to create the friction necssary to keep the plane from going forward", the plane would never move, even if the ground were still. This is EXACTLY what happens when the breaks are applied. "The force of gravity" never changes as a result of the treadmill speed. "The force of gravity" is the same when the treadmill is not moving as it is when it is moving.

The treadmill speed has no impact on the plane ... it could be double the plane's "speed" and not make a difference.

Think of it this way (again).....
If you have a plane chained to the ground and rev up the engines ... the plane stays still, because the chains counteract the force of the engines attempting to push the plane forward.

Now get rid of the chains.
What is there to prevent the plane from going forward when the engine is throttled up? ... Nothing. It rolls forward.

Finally ... how will the treadmill moving under the spinning wheels ever have the same force pulling backward on the plane as the chains did?
The answer is that it doesn't ... at any speed.

So in our scenario as originally posted, the conveyor sped up every time the plane would speed up, in the Myth Busters version, they just used a constant speed take off speed for the conveyer. Point of us nay sayers has always been that you have to attain air speed.

But the wheels decouple the airframe from the conveyor. Airspeed is attained. The correct version of the problem is busted.

...downforce of gravity is enought to created the friction necessary to keep the plane from going forward

The two are unrelated. On a horizontal surface (runway), gravity acts vertically and friction acts horizontally. The two are completely orthogonal.

Chris,

There were three examples on the show.

The first one consisted of the model on the treadmill. They started the treadmill, and 'held the model in place'. This meant that the wheels and the treadmill were moving AT EXAXCTLY the same speed. THEN the engine was engaged, and the plane accelerated and off the treamill. No, the treadmill did not accelerate, but the engine went from 'O' thrust to positive thrust overcoming the friction on the wheels. (From standpoint of neutral observer - plane goes from "O" to + while conveyor belt is already going 'faster' in the opposite direction)

In the SECOND example the model plane was placed on a longer 'treadmill' tarp. WATCH THE SHOW TAPE - first the tarp accellerated in reverse, THEN THE ENGINE IS ENGAGED - in those shots, the plane is already MOVING BACKWARDS while the tarp is moving - and it still ACCELLERATED IN THE OPPOSITE DIRECTION regardless of the fact that the tarp is already 'faster' than the plane. The motive force once again overcomes the directional speen of the 'conveyor belt' and the plane takes off.
(Plane goes from "-" to "+" against a faster belt starting belt)

in the THIRD example - The ultralight is sitting on the stationary tarp, when the plane and truck pulling the tarp - begin to accelerate. This is as close to the scenario described as can be achieved. Perhaps the plane accelerated faster than the truck towing the tarp, but I doubt it. I'd be willing to guess that the truck's acceleration exceeded the planes, and in fact - from the point of a neutral observer, the 'conveyor belt ' was moving faster than the plane in the beginning of the experiement. It still doesn't matter - the plane accellerates independent of the belts speed and direction, and it takes off.

Myth. Busted. Plane. Flies.


It would make no difference whatsoever if it were a jet or rocket or multi engined aircraft - all of these get their motive propusion FROM THE ENGINES not from their interaction from the ground.

Every Single Plane That Take Off from the EARTH facing WEST takes off from a 'conveyor belt' that is moving MUCH FASTER than the plane is in the opposite direction - and takes off just fine.

You'll just have to accept it. :)

You'll just have to accept it. :)



Thats what the church said to Gallileo.....

I accept the premise as presented in Myth Busters. That makes clear sense. The conveyor belt had a limited speed.

I provided an illustration based on the scenario presented at the beginning of the this game. The scenario was that the conveyor belt sped up every time the plane moved forward. We all wondered how that could be instantaneous, but the point was that it did. So in that situation, I posited that the plane could n't reach air speed, because of the mechanic of friction and gravityh. I think that is different from what was demontrated on Myth Busters.

Simple experiment: Get youself a tread mill with unlimited speed. Tie a rubber band to the nose of you plane, and start the tread mill. Pull forward on the nose using the rubber band, but at the same time speed up the tread mill to equalize the forward thrust caused by your rubber band pull, and the plane will remain stationary, and the rubber band will stretch longer, demontrating the actual forces of friction and gravity that is applied.

http://youtube.com/watch?v=0ul_5DtMLhc

For those who missed it.

You keep talking about the conveyor belt having a limited speed, but the truck and the sedgeway DIDN"T and those are the examples where the plane took off - so just dismiss the one where the belt had a limited speed AND distance.

It doesn't matter how fast the belt is moving. That was proved. In the opening shot of the sequence with the model on the tarp/belt, you can see the tarp start moving in the opposite direction.

ANY conveyor belt you build, at any speed, is already 'moving' because its sitting on the earth.

The speed and direction of the belt won't prevent the plane from moving forward.

In your rubber band experiment, the plane will continue to move forward... even if it stretches.

Youre conflating gravity and friction - they are two seperate forces at work, just as lift and drag are two seperate forces. The gravity acting on the plane is a constant - EVEN WHEN ITS IN THE AIR. Wheel friction is minimal, thats what they are designed to do (Yes, even spinning at many times the aircrafts take off speed - they have to be designed that way to land).

The plane has plenty of power to overcome the gravity and wheel friction.

To quote Gallileo "Nevertheless it moves.." - I think YOU represent the 'churchs' position in this one ;)

For reference, her is the original post language:

"If you have a large jet plane (747) sitting on a runway that was actually a giant conveyor belt (go with it). And there is also a device on the plane that communicates with the conveyor belt to tell it how fast the plane is traveling, which would then make the conveyor belt match the speed IN REVERSE.

Can the jet take off? "

demontrating the actual forces of friction and gravity that is applied.

Gravity has NOTHING to do with it except increase the contact area between the deformable wheels and the deformable conveyor. If both both had zero compressibility, gravity would do nothing.

BTW, since we are verging on the realms of Flat Earth (the Galileo reference), the Earth can't be flat by virtue of its atmosphere. :)

For reference, her is the original post language:

"If you have a large jet plane (747) sitting on a runway that was actually a giant conveyor belt (go with it). And there is also a device on the plane that communicates with the conveyor belt to tell it how fast the plane is traveling, which would then make the conveyor belt match the speed IN REVERSE.

Can the jet take off? "

That's the point I made a few posts ago - the problem statement posted on DVInfo is not the same as the one challenged by the rest of the world, including Mythbusters and is ambiguous.

The original post says the device communicates with the belt to tell it how fast the plane is going so that it will match the speed in reverse.

SO the plane is going a hundred miles an hour east, the belt is going a hundred miles an hour west, the wheels rotate at two hundred miles an hour and the plane takes off.

No problems. It doesn't say anything about 'matching the rotational speed of the wheels" - which isn't important anyway.

I can imagine a scenario where the plane will take off - WITHOUT MOVING in relation to the ground.

I can imagine a scenario where the plane will take off - WHILE MOVING BACKWARDS in relation to the ground.

(Both of those depend on headwinds. Indeed, its possible to be flying 'forward' while watching your progress on the ground move backwards... now imagine extending your landing gear down to earth and having the wheels touch.)

It has nothing to do with the wheels turning.

Simple experiment: Get youself a tread mill with unlimited speed. Tie a rubber band to the nose of you plane, and start the tread mill. Pull forward on the nose using the rubber band, but at the same time speed up the tread mill to equalize the forward thrust caused by your rubber band pull, and the plane will remain stationary, and the rubber band will stretch longer, demontrating the actual forces of friction and gravity that is applied.

Great experiment!
Try it.
The rubber band won't get longer .... it'll just pull the the plane forward. :-)

Another variant would be to simply hold the plane in place with the rubber band, and continually increase the speed of the treadmill. If the faster treadmill exerted more and more force on the plane, the rubber band would get longer and longer until it snapped.

Instead, the rubber band will barely register any speed change in the treadmill .... the treadmill doesn't "pull" on the plane.

Instead, the rubber band will barely register any speed change in the treadmill .... the treadmill doesn't "pull" on the plane.

Exactly! It just "pulls" on those parts of the aeroplane that are in contact with the treadmill due to friction. Those parts are the bottom surfaces of the wheels and the wheels turn. This completely decouples the airframe from the treadmill. The treadmill does nothing more than make the wheels spin and has no bearing (!) on the airframe which is where the thrust is generated. Ergo, wave goodbye as the 'plane ventures forth into the sky.

Exactly! It just "pulls" on those parts of the aeroplane that are in contact with the treadmill due to friction. Those parts are the bottom surfaces of the wheels and the wheels turn. This completely decouples the airframe from the treadmill. The treadmill does nothing more than make the wheels spin and has no bearing (!) on the airframe which is where the thrust is generated. Ergo, wave goodbye as the 'plane ventures forth into the sky.

I guess you are saying though the wheels are attached to the plane, by some magic of physics, they are momentarily diconnected from the airframe....

No magic. Just basic mechanics. The aircraft's wheels rotate freely about an axle unlike the wheels on a car or a train which are fixed to the axle.

The only point of the aircraft having wheels is so that it can move on the ground either by thrust from its engines or from a towing vehicle and so that it can accelerate along the runway with minimum friction between it and the ground.

The purpose of the wheels on a car or a train is to convert the energy from the engine into rotational energy, providing a force to which the friction between the wheel and the ground will react, thereby providing the forward acceleration of the vehicle's mass. (F = ma)

A good comparison is wearing roller blades on a running treadmill, hands on the rails on either side.

To "simulate" the thrust of the jets, simply pull yourself using the handrails. You will have no problem rolling yourself off the treadmill.

A good comparison is wearing roller blades on a running treadmill, hands on the rails on either side.

To "simulate" the thrust of the jets, simply pull yourself using the handrails. You will have no problem rolling yourself off the treadmill.

That's the most concise, clear and correct explanation I've seen yet!

Just to clarify... (or further confuse?)
I'm in agreement with the plane on the runway being able to take off regardless of the wheelspeed/conveyorbelt speed.

But I'd like some clarity on this scenario, just to make sure I have the physics right.

1) A small plane is sitting *STILL* on a massive conveyor belt travelling 100mph backwards.
2) The plane (sitting still, travelling backwards) has -100mph windspeed and 0mph wheelspeed (relative to the conveyor belt).
3) The plane normally needs +50mph windspeed to achieve lift.

So... The pilot kicks the throttle up to what thrust would under normal circumstances give him 50mph (I don't know plane RPM vs. speed figures at all, sorry)...

Which of the following is true?
A) The plane, not giving a rats ass about what's happening around it... simply because it is a plane and does not have a mind of its own... moves from -100mph to +50mph because the force of its engine is pushing against the universe, not the negtive windspeed nor the conveyor belt.
...and takes off!


B) The plane, again still not caring about the massive 20 mile long conveyor belt miracle of human engineering under it... generates a positive 50mph thrust... but because it is already moving backwards at -100mph airspeed... finds itself with a -50mph windspeed (still moving backwards in relation to the earth regardless of its now +50mph wheelspeed on the conveyor belt.)
And doesn't take off.

Love to hear an answer on that one.

Oh, and regarding Mythbusters... I haven't seen the full episode yet, but I wish they had experimented to see what they could have done to make the plane NOT take off.

Which of the following is true?
A) The plane, not giving a rats ass about what's happening around it... simply because it is a plane and does not have a mind of its own... moves from -100mph to +50mph because the force of its engine is pushing against the universe, not the negtive windspeed nor the conveyor belt.
...and takes off!

If it is moving with an airspeed of +50mph, it will take off. This is what you have described.

However, if at the start the plane is moving backwards with an airspeed of -100mph, it will be just like a 100 mph wind blowing up the (rat's) ass. Odds are the plane would be blown off/over etc.

B) The plane, again still not caring about the massive 20 mile long conveyor belt miracle of human engineering under it... generates a positive 50mph thrust... but because it is already moving backwards at -100mph airspeed... finds itself with a -50mph windspeed (still moving backwards in relation to the earth regardless of its now +50mph wheelspeed on the conveyor belt.)
And doesn't take off.

Love to hear an answer on that one.

Right - it won't take off.

Whether it takes off or not is all about airspeed and nothing to do with groundspeed. That's why airports switch runways/change direction according to the wind. Taking off into a wind requires less groundspeed, a shorter runway, less fuel etc.

BTW, there isn't such a thing as a 50mph thrust. Thrust is a force and makes the aircraft accelerate. As long as the thrust is maintained, the acceleration will continue. Just like a car's accelerator - you cut back on the acceleration when you get to the desired speed.

If you reverse the situation - i.e., the conveyor belt runs in the forward direction, then the aircraft will take off with less thrust required. If the belt is fast enough, no thrust will be needed.

This is just how the steam catapults on aircraft carriers work. They accelerate the aircraft quickly to take-off velocity. The speed of the ship and the head wind also contribute.

For our non-pilot friends, it can be kind of confusing, seprerating GROUND SPEED from AIR SPEED from INDICATED AIRSPEED... all of these are distinctly different things. (Indeed, apparently more than one pilot was confused over this as well... ah well, plenty of drivers don't know how an engine works either).

The important thing to remember, is that the engines apply thrust to the airframe NOT the wheels. SO its just like someone standing OFF the treamill, pushing or pulling on the skater. Also, in the original thought experiment, and pretty much on the mythbusters, there is 'no apparent wind'... that is it is assuming 'still air'.

Here are some interesting go/no go thought experiments, that illustrate the importance of the SPEED and DIRECTION of the airflow in relation to the wings, and the difference between TAS, IAS and GS.

Put your plane on the treadmill... in a wind tunnell. The treadmill, the engine and the wind flow can all be controlled independently OR simlutaneously in synch. The wind tunnell can generate flow in either direction.

Assume a nominal 'take off speed' of the aircraft at 100mph.


Is it possible for the airplane to liftoff, without 'moving forward' in relation to the observer standing outside the tunnel?

If so, describe what speed and directions the wind and belt must travel.

IS it possible for the airplane to remain stationary ON THE RUNNING TREADMILL without lifting off?

If so, describe the speed and direction of the wind and belt.

Is it possible for the plane to take off while 'travelling backwards' in relation to the independent viewer?

Again, describe speed and direction for belt and airflow re: aircraft.


Or better yet - just lock this thread and I'll get back to editing. ;)

BTW, there isn't such a thing as a 50mph thrust. Thrust is a force and makes the aircraft accelerate. As long as the thrust is maintained, the acceleration will continue. Just like a car's accelerator - you cut back on the acceleration when you get to the desired speed.


I figured it was easier to simplify it down to that rather than to go through xRPM to lb/ft-thrust to acceleration/time/velocity. :)


Anyway, thanks for the feedback, it's definitely something to wrap your mind around, especially for us non-pilots. But what none of us factored into the equation though is...

how many hours does the plane have to sit on the runway before control clears it for takeoff? :)

Put your plane on the treadmill... in a wind tunnell. The treadmill, the engine and the wind flow can all be controlled independently OR simlutaneously in synch. The wind tunnell can generate flow in either direction.

Assume a nominal 'take off speed' of the aircraft at 100mph.


Is it possible for the airplane to liftoff, without 'moving forward' in relation to the observer standing outside the tunnel?

If so, describe what speed and directions the wind and belt must travel.

IS it possible for the airplane to remain stationary ON THE RUNNING TREADMILL without lifting off?

If so, describe the speed and direction of the wind and belt.

Is it possible for the plane to take off while 'travelling backwards' in relation to the independent viewer?

Again, describe speed and direction for belt and airflow re: aircraft.


Or better yet - just lock this thread and I'll get back to editing. ;)

1. Yes, if the wind speed in the tunnel is 100mph towards the nose of the aircraft. Belt direction and speed of no consequence providing you compensate for rolling resistance of the tyres
2. Yes, if the wind speed is opposite to the direction of the belt and high enough to counteract rolling resistance of the tyres of the plane - obviously below 100mph if the wind speed is towards the nose of the aircraft.
3. Yes. The wind speed must be 100mph plus the speed it is travelling backwards in relation to an independent viewer.

Another great way to prove this is to put a little toy car on a treadmill and hold onto it. Then turn the mill on and see how easy it is to push the car forward against the treadmill. That's very similar to the type of thrust generated by an airplane engine, jet or prop.

The only way you would have any difficulty is if the toy's wheel bearings failed.

A jet flying at mach 3 crosses over laser tower on the ground. At the same precise moment a laser beam is flashed from the Jet and the tower on a target the same distance ahead. Which laser beam hits the target first ?

Sharyn

In a vacuum, the beams would hit simultaneously, because they're going the same distance and the speed of light is constant. In air, however, the tower's firing path, being at a lower altitude and therefore in thicker air, will yield a slower lightspeed, because light moves more slowly in air than in thinner air or vacuum.

Let's assume they're both in vacuum, or both at the same density altitude.

Lightspeed is the same regardless of the observer or his motion. Because of the Lorentz-Fitzgerald contraction, the distance to the target will seem (and actually be) shorter as seen by the airplane [or its crew]. To them, the laser beams travel shorter paths, so take less time, but still go equal times and distances, and arrive at the target simultaneously. The difference in distance (for the observer in the plane and the observer in the tower) is exactly the same percentage-wise as the difference in the times the observers measure. That's relativistic time dilation and distance contraction.

Bottom line: If the two beams are fired when the distances are equal, then each observer will see the two beams arrive simultaneously, and they will be right. But the two observers will not see the same distance, or measure the same time interval, or concur about the speed of the airplane.

-- Carl Hayes, Mensan since 1965. Old fuddy-duddy.

A fixed wing (Non Harrier) plane takes off based on the air flow over and under the wings. Lift off speed is typically measured in terms of speed over the ground but only for convenience. This is why the plane takes off into the wind, and air craft carriers point into the wind, and power head.

If the airflow over/under the wing is not sufficient to create lift, the plane will not take off

Sharyn
Having flown turbo prop/jet aircraft for years ;-)

This deserves a somewhat deeper analysis, although Sharyn is precisely correct.

(1) The question is ambiguous. Does the treadmill's speed (let's call the runway a treadmill) equal the airplane's forward airspeed, or the speed determined by seeing how fast the wheels turn?

(2) If the treadmill's speed is determined by the airplane's forward airspeed there is no problem. At, say, TAS=100 knots [for you ground-pounders, TAS is True AirSpeed] (let's say north), the treadmill goes 100 kt south, and the wheels roll at 200 kt. The airplane takes off when it reaches its normal Vr (rotation speed).

(3) If the treadmill's speed is determined by how fast the wheels are rolling, the question is inherently self-contradictory. Proof: assume the wheels are going at speed Vw, the airplane is going at speed Vp, and the treadmill is going at speed -Vt.

Then, Vw = Vp + Vt because the wheels are assumed not to skid.

Also, Vt = Vw

Then, Vw = Vp + Vw, from which Vp = 0. This means the plane does not move, but the statement of the problem inherently assumes that it DOES move. Contradiction! Another way of saying it is that, if the plane moves, the treadmill cannot behave the way the problem statement says it does. Reductio ad absurdum!

My goodness, these are simple problems.

Incidentally a Harrier is, by definition, not an airplane when taking off vertically. It's a hovercraft, and becomes an airplane only when it gaines airspeed enough to support its weight by aerodynamic lift instead of thrust.

What do you fly, Sharyn? I fly only small taildraggers.

-- Carl

I've read the entire post, gotten a migraine because math was used by someone, took my medication, and have reached the following conclusion:

If I go to the airport to catch my flight and my 747 is on a big treadmill, I'm going to get back in my car and drive to my location. I really hate running on my treadmill, and the plane probably doesn't like it, either - I DO NOT want to piss off the plane.

Since we're talking about planes: Now that Amtrak has received however many zillion dollars to upgrade their system, it begs the question:

If Train A and Train B are on the same track 400 miles apart, and Train A is travelling 60mph while Train B is travelling 80mph, how long will it be before Amtrak is broke again?

(3) If the treadmill's speed is determined by how fast the wheels are rolling, the question is inherently self-contradictory. Proof: assume the wheels are going at speed Vw, the airplane is going at speed Vp, and the treadmill is going at speed -Vt.

Then, Vw = Vp + Vt because the wheels are assumed not to skid.

Also, Vt = Vw

Then, Vw = Vp + Vw, from which Vp = 0. This means the plane does not move, but the statement of the problem inherently assumes that it DOES move. Contradiction! Another way of saying it is that, if the plane moves, the treadmill cannot behave the way the problem statement says it does. Reductio ad absurdum!

-- Carl

Almost spot on except the part about the case where the plane doesn't move being absurd. It is a valid solution to the problem.

What if you replace the plane with a car like on Mythbusters?

Their reasoning for why the car won't move is incorrect. If you measure 'speed' for the car as Vp (speed with respect to the air) then it will drive off of the tread mill with the tires spinning twice as fast as the car drives off the belt, Vp (airspeed).

It's just a vector problem. 'Speed' is an ambiguous term in the problem and depending on what you define it as you either get an object moving off of the belt or you do not. The matter of propulsion doesn't matter.

This is an entirely different thing...based on the initial question on this forum, most likely the plane would not fly simply due to the plane being stationary in relation to an Earth observer.

Based on the wheel speed, we need not even talking :)

While I didn't bring anything new, my initial assessment was that the plane would not fly, based on the initial formulation. The, reading through the thread I see all these contradictions to an obvious thing (for me)...thus, reading all and seems Mr. John Miller (#155) spotted the formulation issue.

Anyway...heh :) Long thread, thanks for confirming I am still sane though :)