Can the Plane Take-Off?
 

there's a 988 post arguement going on in this other forum... im pretty positive about the answer... (there is technically no true answer till someone experiments... and many people will argue that they need proof. only proof possible would be by experiment... and so far i know of noone who has done an experiment)
and please dont turn this into a flame war.... as has happened in the other forum. i mean for this to be amusing. ill post what i think a bit later after a couple posts have been made so i wont give any ideas from the 988 post wisdom i have lol. or you can pm me and ill answer what i think.

have fun!

Re: stolen from another forum
 

The answer most certainly can be determined by the laws of physics.

All planes move by reacting with the air, either through propellers or jet engines. The speed of the ground under the wheels has almost nothing to do with the speed of the plane down the runway.

In this case, the plane would accelerate down the runway, and the 'runway' would accelerate in the other direction. The plane would still take off more or less normally, the only effect being the wheels will be spinning twice as fast as they normally would when it leaves the ground.

Hey that was easy, we settled the argument on CD in one post! :^)

Re: stolen from another forum
 

As Ken said, whether a plane can take off or not depends only on how fast the air is moving in relation to the plane's wings.

It's for this reason that airplanes take off facing into the wind whenever possible: the plane's ground speed at takeoff is not as high as it would be if there were no wind, so a smaller length of runway is needed.

Re: stolen from another forum
 

yes.... except one thing.
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).

so. laws of wear and tear and motor output of either engine(plane or conveyor) ignored, but friction not ignored, the conveyor belt spins fast enough that the friction of the wheel bearings keep the plane from accelerating. so if the conveyor really can turn exactly the same speed(but in the opposite direction) of the plane, the plane would not be accelerating. relative to the conveyor belt it may as well be going almost the speed of light but since the conveyor belt is going the opposite way at almst the speed of light, the plane doesnt move.... im redundant arent i?
well anyways. so the plane wont fly then? i unno
but my thoughts are that a conveyor belt would fail before an airplane engine or landing gear so the plane would fly... eventually... but only after the conveyor belt fails.


-edit- addition-..... oh. and i should just say this.. you both completely ignored the way the conveyor belt works. its not a normal treadmill you see...

Re: stolen from another forum
 

Wow, that other forum must not be full of really bright people. :D Easy question. As mentioned previously, a plane's flight is based on it's relation to the air, not to the ground. Thrust comes from engines pushing on the air, not from wheels pushing on the runway.

Re: stolen from another forum
 

you are adding conditions to the question that are not in the question.

The runway moves in the opposite direction of the plane, at the same speed. Nowhere does it say the runway moves to keep the plane in the exact same spot. That is your mistaken conclusion of what will happen.

A jet plane is able to produce thousands of pounds of thrust. Lets say its an F15, able to generate 30,000 lbs of thrust.

The wheels, with the brakes off, will have a very low coeffecient of friction. So lets start at zero mph.

The plane speeds up to 10mph, putting out 30,000 lbs of thrust. The runway matches this speed in the opposite direction. The wheels are putting maybe 5 or 10 POUNDS of force in the reverse direction due to the runways backward movement.

The resulting net force on the plane is 30,000 pounds forward minus 10 pounds backwards = 29,990 pounds of thrust (force) in the forward direction

and the plane is moving forward with a 10mph airspeed and its wheels are spinning at 20mph. The runway is moving backwards at 10mph (ground speed)

as the plane continues to accelerate (due to the thrust from its engines) the runway speeds up, but the force the spinning wheels apply to the airframe will never match the force of the engines, unless the pilot does something stupid like stand on the brakes.

Re: stolen from another forum
 

Lift actually acts on the wings and is completely independent of a plane's engines. The engines provide thrust to move the plane through the air fast enough so as to create sufficient lift against the wings.

If the aircraft is not moving in relation to the air, as seems to be the case in this example, it would remain on the ground -- no matter how powerful its engines.

The debate rages on...

Re: stolen from another forum
 

Think of it this way:
If I have a balsa glider in my hand and I run down the sidewalk, there will be lift on the glider due to the moving air. If I run on a tredmill, the glider doesn't have any lift.

The situation at hand is the same. The airplane is on a tredmill, so it can't go anywhere.

Re: stolen from another forum
 

true. but some are quite smart. and well...most are the normal "ur stupid" flaming.... but you gotta have an open mind to understand why both opinions are valid. everyone agrees that the plane must be moving forwards relative to the air to fly... but the plane isnt moving forwards relative to the air.. because the wheels are mounted to bearings which are on the axles... and to my knowledge there are no true frictionless bearings... and because of that friction, the conveyorbelt can keep the airplane from moving forwards relative to the air completely. ok. now shake your brains around and give them a nice stretch... and think slowly... at first the plane is sitting still. now the pilot turns on the enignes. afterburners are fine too. just no vtol technology allowed. so the plane should move forwards... but no, the plane CANT move forwards because the conveyorbelt tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). ... so the plane does not move. because if the plane moves 1mm forwards that would mean the conveyorbelt is not turning the belt at EXACTLY the same speed as the plane.(but in the opposite direction)..
so simply put, the plane DOES NOT MOVE. but in which case where does the air being pushed by the plane's engines go? backwards. but since air molecules have inertia too, the plane should move forwards now. but it doesnt.. so in this problem, because of an improbable conveyorbelt control system, some parts of physics must be ignored... or looked into detail... depending on how you look at it.

Re: stolen from another forum
 

Yeah.. so most people know that I am a student who absloutely hates the book work of physics, but gets what is going on in the experiements.

I'm gonna switch to common sense, or lack their of in this analogy, and say that since Plane (A) is "accelerating" in a positive direction, and Conveyer belt (B) is "accelerating" in a negative direction based on Plane (A) then in all essence the plane is not moving (linearly) at all on this conveyer belt and the plane will not take off.

A = +X speed
B = -X speed

They cancel each other out, and there is no linear displacement.

And my physics training will say that distance (or the X amount of miles the plane is racking up spinning it's wheels on the conveyor belt, does not equal the displacement required to take off.

For example:
What would happen if you put a car on a dyno machine.. It accelerates, and adds up milage, but it's not going anywhere.. (as long as your dyno doesn't fail and freeze up) lol

And yes, I know cars and airplanes are not created equally, but I'm just sayin' - It's the same kind of setup.

Re: stolen from another forum
 

oh no, Madison! Its late sunday night so I forgive you! :^)

look at it another way - an F15 comes in at 200mph for a touch and go landing pass. It flies down on the runway, but maintains its airspeed, so the wheels touch the ground, then it throttles up and flys away.

Ok, so add your moving runway to the picture. The plane comes it at 200mph again, the wheels hit the runway, which is going backwards at 200 mph, so what happens? does the plane instantly stop, ignoring the laws of momentum?!

no, the wheels go BRIRP! and spin up to 400mph, the pilot hits the throttle again and does his 'touch and go', just as before.

The engines on a plane do not react off the runway. If they did, then how do planes in alaska with skis instead of wheels get off the ground?!

Re: stolen from another forum
 

nuhhuh.. its been there all along. you say it yourself.
same speed as in...... ZERO mph? which means its not moving?

wait a second.... the plane does not get to 10 mph.... it does not move
again, IT DOESNT! :D




yes,, arguements are finally starting.. :p i have succeeded in starting a big arguement! yay!!


ps. please rememebr to be nice to everyone. even i get excited and then agitated by seemingly nonunderstanding members of the opposing group.. but then again the other side thinks the same about me.

Re: stolen from another forum
 

That's why I initially edited my post and added, "That said, Ken's right," but subsequently removed it. I understand your explanation completely and it makes sense, but I don't fully comprehend why -- so I removed my edit. When I can completely describe what's happening mathematically as I know it to be happening anecdotally, I'll be happy.

This is, in a lot of ways, quite similar to confusion about whether its Bernoulli or Newton who've got the proper theories about what causes lift -- when in reality, neither theory fully explains things.

Re: stolen from another forum
 

ok, now you got me laughing :^)

if the plane cannot move then the conveyor belt cannot move either. When the planes 'speed' is zero the conveyor belt speed is also zero !

Re: stolen from another forum
 

Ah, I now see the error in my thinking..

Let's say we drop a missile from an airplane. Better yet, from a helicopter that is hovering in place. The missile will still go forward even if it has no contact with the ground. So, the ground has nothing to do with the airplane's ability to take off.

Re: stolen from another forum
 

whoa i had completely forgotten about those.... i had to actually look at the problem again.... and i found :D
so you cannot use that as an example. ;)

Re: stolen from another forum
 

The coefficient of friction of the air speed pushing back wards, overcomes the static coefficient of the snow, and lets the ski's move forward, and the snow stays put..

(ignoring sticky snow of course)

For the plane not to move in the snow, then the coefficient of the air speed friction, will have to be equal, or less than the coefficient of the snow/ski's relation.

Also, it has to actually be greater, since there is a funky term (which name escapes me now :( ) that overcomes the coefficient and let's it move freely..
(it's basically the force necessary to overcome the friction (break the grip between surfaces so to speak) and get it rolling, but it is not equal to a "rolling start" coefficient of frictional speed.

Re: stolen from another forum
 

Or, to mix metaphors, strap the missile to Elgin's dyno. :) The missile isn't going to make the dyno spin.

Re: stolen from another forum
 

exactly... which is why this problem is so confusing.. and fun!

Re: stolen from another forum
 

static and kinetic friction

Re: stolen from another forum
 

Define "move".

The wheels may counteract and spin in the opposite axial direction and thus they will "move" but my thoughts are since they cancel each others linear "move"ment out, then technically this is a trick question, cause the plane is not "moving" as most people think of as moving.

When I think of a car "moving" it's displacement is constantly changing. Down the highway. But who's to say that same car on my dyno is not "moving". It's not moving linearly, but the wheels are moving axially.

Thanks. I should of know that. lol



Oh, and does anyone foresee an episode of mythbusters coming on about this???? :D

Re: stolen from another forum
 

Ok, I gotta fess up here and admit that when I took physics 101 in college I had to first unlearn 'roadrunner physics'

our thinking gets so ingrained to the things we experience personally, like driving a car or running on a treadmill, that we have a hard time doing thought experiments on things we are not familiar with (like flying a jet plane).

The question here makes you think the plane will not move at all, because our minds jump to something familiar - like a car on a dyno, or a person running on a treadmill.

Go back to the initial conditions: the plane is at rest, the runway is not moving.

The pilot hits the throttle and the plane has 30,000 pounds of thrust on its airframe. How on earth is the runway going to apply 30,000 pounds of thrust in the opposite direction to STOP the plane from moving? Through 3 wheels with greased roller bearings?

Lets say the plane gets up to 10mph like I said before. The runway is only allowed to move backwards at 10mph - to match the forward speed of the plane. There is no way the wheel bearings are going to have 30,000 pounds of friction while spinning at 20mph net speed! the wheels will have a few pounds of friction at the most, and the plane will continue to accelerate

and take off, pretty much like normal.

Picture the tablecloth trick, you yank the tablecloth out from under the dishes, and there is not enough force to pull them off the table.

'yanking the runway' out from under the plane is not going to have enough friction to overcome 30,000 pounds of thrust from the jet engines.

Re: stolen from another forum
 

the engines on all types of planes have no connection or effect on the wheels. The engines do not rotate the wheels. Therefore, on an aircraft, the only thing that can 'move' is the aircraft relative to the air

in fact, when you are flying it is impossible to measure your ground speed, unless you know the wind speed and direction. Aircraft do not have speedometers attached to their wheels :^)

Re: stolen from another forum
 

Until I read KenWittlief's post (one above mine) I was pretty sure about this reasoning:

The plane will not take off.

In order for a plane to lift off the ground, the air above the wings needs to be of lower pressure, which happens when it is moving faster, than the air beneath the wings. (The reason that the wings are curved.) In order for the air above to be moving faster than the air underneath, the plane needs to be moving relative to the air. Due to the conveyer belt, the plane DOES NOT MOVE in relation to the air. Thus it does not take off.

But now I'm confused as to whether to plane actually moves... And intuition says the plane will take off...

~Stephanie :confused:

EDIT:
ABSOLUTELY!!

Re: Can the Plane Take-Off?
 

You all are driving me insane. The plane will take off just the same as it would on a traditional runway. There will be no episode of mythbusters because this is a stupid myth that requires no experiment whatsoever to disprove. Please, everyone, reread Ken's posts. Other than extremely negligible friction, the runway exerts no force whatsoever on the airplane. Yet the airplane is exerting tremedous force on the air. The airplane will proceed to move forward and take off. You really need to analyze what forces are being applied where and then you'll "get it."

(Don't make me put my RC plane on my treadmill :mad: :D )

Are you guys just being sillyto make this thread go on forever or do you really still not "get it"?

EDIT: I meant the runway exerts virtually no force on the plane in the horizontal direction. In the vertical direction, it exerts a great deal of force until the plane gets some lift.

Re: Can the Plane Take-Off?
 

Hmm.. well.. LIke I said before, I suck at the math and equations behind physics.. but if I recall correctly we have a minimum of 4 forces at work here. (horray for using force digrams in Physics class over and over again :rolleyes: )

Fn - Force of Conveyer pushing up at the plane (+Y) (the force comes from the contact of the conveyor to the plane's wheels) and it it is a staple in every force equation which you have apparently forgot about and left out. Also known as Normal Force.
Fg - Force by gravity holding the plane down (-Y) on the conveyer
Ft - For this case, thrust of airplanes jets going in the reverse direction (+X) of:
Fcb - Force being countered by the conveyer belt (via really wicked cool sensors - which I would like to see in the kit next year :p ) in the equal and opposite direction of the airplane's thrust. (-X)

So.. in this equation.. and using Newton's third law, which states "For every action, there is an equal and opposite reaction."

Fn + -Fg = 0 = no movement in Y direction
Ft + -Fcb = 0 = no movement in X direction

Care to tell me what I am missing and how this hypothetical plane lifts?

The only thing I can think if is since I am not an aerospace engineer, or a hyphothetical physicist (or even a real one), is the combination to add positive force to both Ft and Fn to make the plane raise up which may come from the wings and their relation to the non linear movement of the airplane??? :confused:

Is that enough analyzing?

Did I miss something? If I did, I guess I am stupid or rather just uninformed.

Care to inform me?


Oh, and please refain from using words such as stupid on these forums. We're all here to learn and help each other, not to call each other names.. Thank you!

Re: Can the Plane Take-Off?
 

ok, looking at this from a relative velocity standpoint, if we analyze just the plane and treadmill in relation to the runway, ken is right; the plane can't be sitting still and moving at an equal but opposite velocity. physics prevents this. i know you've said that some physics rules need to be bent to solve this problem, but i refuse to accept that; if you get to bend the rules that manage relative velocity, then i'm going to bend the rules that manage gravity, and float the plane off the ground.

now, if we take the linear velocity of the wheel at a point 180 degrees from it's contact patch (instead of the velocity of the stationary plane), and the velocity of the treadmill, both relative to the ground, then we can satisfy both the 'equal but opposite treadmill' and the 'stationary plane' requirements, assuming that the wheels generate enough of a drag force (the pilot left the parking brake on?).

Re: Can the Plane Take-Off?
 

Ken is right. The airplane will take off. The only thing that is different than a "normal" take off is that the wheels will be freewheeling at twice the lift-off speed.

The problem is that you have to remember that the wheels are free spinning, and DO NOT provide motive force (other than the minute amount of drag due to bearing friction, also accounted for by Ken). The acceleration forces for the airplane are due to the thrust of the engines against the surrounding atmosphere - NOT by the wheels transmitting force to the ground.
In Elgin's analysis, the assumption is made that Ft is equal to Fcb. This is where the mistake creeps in. The problem statement does NOT state that the counter-rotating conveyor belt is applying a force to the airplane that is equal and opposite to the engine thrust. It simply states that the conveyor runs at a velocity inverse to the (ground) speed of the plane. The actual force transmitted to the airplane is limited to the relatively minute amount of drag due to friction in the wheel bearings (under the presumption that the pilot is not standing on the brakes). This drag force is a very tiny fraction of the forward thrust force applied by the airplane engines. In other words, Fcb is defined as the wheel bearing drag, and Ft >Fcb. And since Ft >Fcb, then Ft +-Fcb>0 => movement in X direction.

If you still think that the plane will not take off, then think through this: imagine exactly the same stating conditions. The airplane engines ramp up to full thrust. If you are assuming that the airplane (relative to an off-conveyor observing position) is "standing still" the explain the following: the pilot quickly retracts the landing gear, so the airplane is no longer in contact with the conveyor belt, the engines are still at full thrust, and the airplane is at zero velocity relative to the ground. What happens next? When you try to reconcile this self-conflicting condition, you will realize that in the original problem, the airplane takes off.

-dave

Re: Can the Plane Take-Off?
 

I just have one question about the treadmill: is the runway moving itself (to match the plane's forward speed) via motors, or is it the plane's force against the runway causing it to move?

Re: Can the Plane Take-Off?
 

The plane would not be able to move the runway in the opposite direction unless the wheels were driven (like an automobile). So, I'm assuming the runway has some really freaking huge motor driving it in a continuous loop like a treadmill.

Now, for anyone else who doesn't get why the plane does take off, draw your free body diagrams You are mingling your separate forces into two different systems that have very little to do with each other. Isolate the system, and then determine the forces.

Re: Can the Plane Take-Off?
 

Ah, but the plane still has to deal with gravity, which the plane's engines aren't going to overcome automatically. So the plane is still putting the same force against the ground as the ground is putting on it, and if the wheels are touching the ground, they'll move.

My next question would be if there's a limit to the plane's engine output.

Re: Can the Plane Take-Off?
 

Ok.. I'm not gonna give in on my answer, but I see the way it could potentially work now.. Still kind of mind boggling.

So.. this leads to the real world applications and possibilities:

Why not build this huge conveyer belt system as an alternative to making short runways on a mountain where real estate is a prime commodity??? :yikes: ;)

Think of the potential a system like that could have if it worked.
This way larger planes could take off in a small space, and cargo can be brought in by air to these reletively remote places.

Uh oh though.. will this same problem work in reverse, yet be to my thought advantage this time, and make the plane land and stay still so as not to leave the area of the huge conveyer belt and still use that same small real estate???

Or will the speeds (plane and treadmill type device) have to be non equal and perfectly harmonized for this to work, and this is just a pipe dream???

Yeah..

-------> ( Me - "Outside of box") :p
BOX

Re: Can the Plane Take-Off?
 

The opposite of this is done every day -almost - on aircraft carriers

the catapult on aircraft carriers acts as if the runway suddenly accelerates forward under the plane. It pulls the plane up to 200 mph in a matter of seconds, and flings it off the deck of the ship. The aircraft engines then take over and the plane continues to accelerate

but heres the difference: the catapult captures the front wheel of the plane until it takes off. Imagine what would happen if the catapult was accidentally left unconnected? nothing.

and if the aircraft carrier launch system were just like this question, but the belt moves forward rapidly, and the pilot was not standing on the brakes with both feet, then when the belt suddenly moves forward the wheels on the plane will spin like crazy, but instead of being flung off the ship at 200mph, it will barely move

like yanking a tablecloth out from under dinner plates

the runway would have to be able to apply a tremendous amount of force horizontally to the plane to either fling it off the aircraft carrier, or to keep the plane from moving on the backward treadmill. That force simply cannot be applied to the aircraft through free-wheeling landing gear.

Re: Can the Plane Take-Off?
 

You're forgetting the coefficient of friction (mu, but I'm going to use u because I don't want to spend the time to figure out how to type mu) in there. The force exerted on the plane by the tredmill will be at the bearings between the wheels and the axles. (We're assuming that the wheels have infinite traction on the ground) So, your Fcb term has to have u.

Fcb = umg or uFg

Where m is the mass of the plane and g is the acceleration due to gravity. If we take the extreme case and say that we have ideal bearings, u will be 0. That would cancel out the Fcb term. Even if we go to the other extreme and say that u is some thing absurdly high, like 1, we still get that Fcb = Fg. I'm not really sure what a plane weighs, but there's a plane that produces more thurst than it weighs (I think the F16).

Re: Can the Plane Take-Off?
 

OK i think that i can explain this but i want everyone to break out an RC car or a vex bot and follow along with my reasoning and finish ready my post before yelling at me,

Heres what happens when snow makes me stay home from physics:

1) The plane will not stay on the conveyor! :ahh:

The force of the engines will push against the air an accelerate the plane forward off the conveyor at its normal slow begining of takeoff speed the wheels will just be spinning 2x as fast, when it leaves the conveyor the wheels will slow to the same speed as they hit ground and the plane will continue taking off as normal since the forces are plane pushes the air, the air pushes the plane, the belt spins the wheels the wheels spin the belt(not exact but its just the logic, if on the other hand the pilot applied the breaks or something the plane would not take off

2) put your RC car on a treadmill, turn on the treadmill so that the car when going full forward stays in place now strap a rocket engine to the car and light it, the car will go forward because it is being pushed by the rocket(you could even use a non motorized car more like the plane and put the rocket on that and no matter how fast you send the treadmill the car still goes forward)
-The alternate and safer methode is push the car with your hand to represent the interaction with the thrusters and the air


Now read kens posts for background and facts then apply it to mine and i think we have decided it will take off,
Cuog

Re: Can the Plane Take-Off?
 

the other thing that is counter-intuitive in this problem is this: the rolling friction of wheels is independant of the speed at which they are rolling

so no matter how fast the runway is moving backwards under the plane, the force that it applies to the airframe through the free-spinning wheels is a constant.

Its hard to imagine this, because we have never been in a situation where the rolling friction of a wheel is the only force stopping our motion. When you ride a bike, as you go faster the wind resistance increases exponentially with your speed, and thats what you feel in the pedals. But if you could ride a bike in a vacuum once you accelerated up to ANY speed, the force required to maintain that speed would be the same (the same at all speeds)

because all you are doing at that point is keeping those super low resistance bearings spinning.

Same with the jet plane - if you landed a jet plane on a runway at 200mph, in a vacuum, and did not apply the brakes to stop it, it would probabally coast for 3 or 4 hours until the rolling resistance of the wheels alone brought it to a stop.

And in the question posted, the only force that is trying to stop the plane from accelerating to takeoff speed is that same (small) rolling resistance of the wheels.

Re: Can the Plane Take-Off?
 

rememebr, that doesnt work because your treadmill will not match the airplane's velocity. not relative to the treadmill but to the .... well we'll say a far person's point of view.
[quote=sanddrag]
Are you guys just being sillyto make this thread go on forever or do you really still not "get it"?
well, im trying the best i can to keep this discussion going.... if thats what you mean. i completely understand both sides. and i just support the seemingly weaker side right now.


the people who say it will fly are completely ignoring that the conveyorbelt will match the planes speed. of course common sense says that it is impossible for a conveyorbelt to do what the problem says, but WHAT IF.
and someone said the limit of the plane's output.... well then what is the limit of the conveyorbelt's speed (or power)... if that reaches infiniti for the lack of a better term, what then? if the conveyorblet has the power to do exactly what the problem says, what happens?
a HUGE fan blowing air towards the plane would be easier.

okay... the aircraft carrier catapult.... waht if the catapult extended forever and the plane was mounted backwards... and the speed of the catapult was varaiable? (improbable... maybe impossibel... but a concept) .... then what?(oh btw the catapult is not mounted to the plane itself but has a plate that also continues forever underneath the tires of the plane) :D


oh. since so many people are saying sumthing about the wheels spinning twice the speed of takeoff, thats not right. only if the treadmill was matching the speed of the plane... not matching the speed of the plane instantaneously... which means it doesnt matter how fast the wheels spin, the belt spins faster and faster so the friction of the bearings are enough to keep the plane from moving forwards.... and since the problem does not say there is a limit on how fast the conveyorbelt can go before failure, we must say it doesnt fail EVER.

BADDDD example. the treadmill must speed up when the car speeds up due to the rocket.... the conveyor belt matches the speed. not just once but continuously.
correct. which is why you can say either side is correct. if you ignore conveyorbelt limits

Re: Can the Plane Take-Off?
 

PS... although everyone is repeating the same things over and over, see how this can expand to an almost 1000 post thread? less than 24 hours and we've reached 36. and the other forum has flamers and postwhores and idiots, and well. almost 40k people

Re: stolen from another forum
 

It has been discussed on the Mythbusters website forums since early November. So far it looks like they're not into testing it.
Now if I could only convince them.............too bad I'm not dating Kari. ;)

Re: Can the Plane Take-Off?
 

I don't understand your basis for that. Let's go back to Elgin's equations that I've been working with:

Fy = Fl + (-Fg) - Fl is lift force, Fg is force of gravity
Fx = Ft + (-Fc) - Ft is force of thrust (engines), Fc is force of conveyor

and some I'm adding:
F = ma <- solve for a
a = F/m <- integrate with respect to t
V = (F*t)/m
Vx = [(Ft - Fc)*t]/m
Fc = umg = uFg - u is coefficient of friction

Vx is a function of Fx. And we know Fy is a function of Vx. So, the only thing we really care about is Vx. If Vx > 0, we'll have Fl > 0. If Fl > Fg, Fy > 0.

So, how do we get Vx > 0? Well, Fx has to be >0. This is true as long as Ft > Fc. We know that u << 1. With this, we'd only have to provide some Ft that is some small fraction of Fg.

As you can see, the speed of the conveyor never comes into play.

Re: Can the Plane Take-Off?
 

I fear adding even more 'bad physics' to the discussion, so instead I'll simply pose a different question.

If the conveyor belt was capable of not only matching, but exceeding the velocity of the aircraft, could you stop it from becoming airborne? If so, theoretically, what speed must the conveyor travel to achieve that result?

I think I know the answers, but again -- I'm scared of 'bad physics'.

Re: Can the Plane Take-Off?
 

You'd have to move the runway fast enough to move the wheels fast enough where the friction generated in the wheel bearings is so much that it heats up the wheel to so hot that it blows the tire and the airplane landing gear collapses and it falls on it's belly where there is large friction between it and the belt and then it is swept away backward.

Of course by the time the belt got moving that fast, the airplane would already be flying. :)

Re: Can the Plane Take-Off?
 

NO.

force of engine thrust is not equal to force of conveyor. Ft<Fc
Ft+Ffriction of bearings=-Fc i think... gotta go... think about it slowly later...

Re: stolen from another forum
 

Ahh, I see where the confusion is here. The problem states that the speed of the conveyor is exactly the same as the speed of the plane. If this is the case, the plane will take off with no problems. However, you are interpreting the problem as saying that the conveyor is moving at exactly the same speed as the surface of the wheels (relative to the plane).

In a car, where the interaction between the wheels and the road provide the forward motion, these two are equal. However, in the case of an airplane, these aren't necessarily the same.

If the conveyor moved as the same speed as the surface of the wheels, the plane would probably not take off because as soon as the plane started moving, the speed of the wheels would always be larger than speed of the conveyor, and you would get the belt up to an infinite speed, and the friction would be providing an infinite force backwards (this is all assuming, of course, that the wheels don't slip at all, which they would far before the force equalled infinity ;)).

However, since the problem clearly states that the speed of the plane is being matched, Ken (and the others on that side) are correct.

Re: Can the Plane Take-Off?
 

Ken and all the others are correct. If you want proof, see this video clip. They mounted a fan on top of a skateboard, and as the skateboard began to gain velocity, the paper underneath the skateboard was pulled backwards at the same velocity in the other direction. The skateboard continued to accelerate, just as normal.

Here is another good way to think of this problem, as it was posted by an unregistered user on another forum:

Re: Can the Plane Take-Off?
 

As Ken said, I'm pretty sure this would be the opposite of what you want. An airplane, unless you do something like manipulate the speed of the earth/atmosphere, needs to have a certain space of air to fly through to achieve a certain velocity through the air. So, the x-distance traveled, if the plane's speed is constant, can also only be constant. The conveyer would only be limiting the velocity of the plane ( not by much, but still). The only practical way to shorten takeoff is to increase the acceleration of the plane via a catapult device.

Or you could turn the atmosphere's rotation speed in relation to the plane...:D

Re: Can the Plane Take-Off?
 

One thing you could do (theoretically) to shorten a takeoff or landing distance is to create a nice strong headwind along the runway. The airplane would maintain enough of a speed difference with relation to the air to maintain lift, but you could theoretically have it with zero speed in relation to the ground. You could takeoff and land while not moving in relation to the ground. You could even do it going backwards in relation to the ground. (I've done this on my RC flight simulator program and it is great fun).

However, flying a plane in any sort of strong wind is tricky and it would be difficult to construct an apparatus to move such a large volume of air at such a high velocity to create this artificial headwind.

Re: Can the Plane Take-Off?
 

hmm.. well although this wont mean anything, there is no proof that the paper was moving at the same speed... actually, it wasnt.

i have no idea how i should word this, but well...
you are all saying that the belt is moving at the same speed as the plane but the plane moves forwards. wheels or not, if Vplane=-Vground(in this case belt), Vplane+Vground=0. which means the plane does not move. ignore the wheels completely. the plane is on blocks attached to the plane.. the plane has unlimited thrutst so this does not affect anything.. (the belt also has unlimited thrust... or torque, if its a conventional conveyorbelt. so that also doesnt change anything)
so at first the plane is standing still. so Vplane=0.... which means Vbelt=0 also

now the throttle is pushed on the plane.
so Vplane relative to the air = 1
except since Vplane =1, Vbelt=-1... except the blocks and belt have enough friction ............................
or waaaaaaaaaait a second...... Friction is changed only by normal force...(since the coefficients dont change)....
Crap.. a BIG point everyone including me has failed to point out.... Force of Kinetic friction is always constant no matter how fast the two planes are rubbing right?darn.... so basically the wheel's bearings.... no matter if they are spinning at 1rpm or 287346821736498723649876rpm, the force of friction is the same right?... so the conveyor belt... no matter how fast it spins, it can not stop the plane...
aha. and no, noone mentioned that before, yes people have said that the friction was negligible but noone backed that up. i think im not the only one that was under the impression that the faster you......
or.... darn it. lost it.... anyone continue on that proof?
till then..

but yea. well i guess this shouldnt be called a physics problem cuz so much is ignored.... and yea. the plane does go up i guess. or does it..
all these people have examples of experiments.... even the video.. but noone has created a "true" conveyor belt... so those experiments are flawed. SO confusing... but this problem is a neverending pit of trying to prove the other wrong.

Re: Can the Plane Take-Off?
 

Woah, I just realized that this problem is a whole lot more interesting than I originally thought.

We can all agree that the real question here is "does the plane move forwards?". There is a lot of talk about how planes are different from cars, but let's look closely at what would happen if we put a car on the conveyor. I will restate the problem thusly:

A car is standing on a street that can move (some sort of band conveyer). The car moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the car speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).

The question is:

Will the car move or not?

I am going to argue that it does!

Imagine that you are in the car on the conveyor. You start the car moving forwards at 1mph, and the belt begins to move backwards at 1mph. However, when the belt reaches 1mph, your car is now essentially going at zero speed, so the belt stops. With the belt stopped, you are now going at 1mph, so the belt goes to 1mph, and so on. If you take the average speed of the belt and your car, you will see that each is half the time going 1mph and half the time stopped, so the average of each is .5mph.

Of course, you have to take acceleration into account here, since the belt cannot start and stop instantly. If you do, you will see that between the belt speeding up and the car slowing down as a result, you will soon reach the point where, as stated above, the belt's speed is 0.5mph and your car's speed is 1mph-0.5mph=0.5mph. That means that with everything working, you will always move forward at half the speed showing on your spedometer.

Therefore, my conclusion is that this is a poorly worded question since it fails to identify how speed is measured (speed of the wheel's rotation, speed of the plane relative to the ground, or speed of the plane relative to the belt).

One of my pet peeves about physics education is that teachers make sweeping generalizations about things like friction, which people (myself included) take to be fact.

What you said about friction is only true for dry friction. However, when you have lubricated bearings, you must take viscosity into account. When you have "friction" against a fluid, the resisting force is actually a function of the speed you are moving through that fluid. This is why falling objects reach a terminal velocity: as the speed increases, the resisting force increases until it is equal to the force of gravity, and which point the object stops accelerating since the net force on it is zero. However, as Ken below me pointed out, this effect is very small compared to the rolling friction in the wheel itself.

Re: Can the Plane Take-Off?
 

um... no. Kinetic friction being a constant has been brought up - go back and read the thread again

you simply ignored what we have been saying until now, because you jumped to your conclusion first, then tried to backfill your reasoning. *

This is a common debug problem that engineers face everyday: we think we know the answer, but then when things dont work out we cant figure out why. Its always something you assumed to be correct, and very often its stareing you right in the face.

This plus the logical error that planes spin their wheels the same way cars do. If the plane is not moving forward relative to the earth, then what is making the wheels rotate? Nothing. If the wheels are not spinning, and the conveyer is not moving, then what is stopping the plane from moving? Nothing!

and BTW, the rolling friction of a wheel is not fluid friction. The bearings are oiled or greased but they roll over the races, they do not slide through a pool of oil or grease. The major component of rolling friction on a tire is the compression of the rubber. This is what causes a tire to heat up on straight and level pavement, the rubber is constantly flexing. But this amount of energy dissapation is small.

I have to say, this problem does demonstrate how difficult it can be to convey the laws of physics into a frame of reference that the average person can grasp. I was so temped to draw detailed vector force diagrams, but keeping this discussion in text made it more challenging.

* wanted to add: this is human nature. When we get an idea in our heads it becomes 'our idea' and for some reason we feel the need to defend it. Part of it is ego and part is pride. Its something we have to deal with as engineers all the time: jumping to a conclusion, then feeling like you have to stand behind it, no matter what.

In fact, this is a very interesting aspect of engineering. A Jeckel and Hyde situation. In the early stages of the engineering design cycle we try to figure out everything, and avoid mistakes at all costs. We dont want to design something that will have bugs.

But when you reach the point where something is fabricated, or manufactured, or code is written, then you WANT to find the errors - then errors are golden, you have to discover your errors and embrace them, discover the root cause of every mistake in the design.

The reason is, if you dont find the errors in your system (through testing and debug) then your customers will! Once you start shipping product or delivering systems its very expensive to recall them and make updates or corrections.

So at first mistakes and errors are a bad thing and you shun them, then they are golden and you must embrace them and understand them. Engineers very often cant make the jump to the second part. When errors or bugs show up in a product, some want to sweep them under the rug, or patch them up as quickly as possible, instead of understanding how they happened, how to fix them correctly, and how to keep them from happening on your next project.

Re: Can the Plane Take-Off?
 

whoops. sorry. mustve missed that. posts pile up so fast i cant keep up.
wait a second. from the moment i posted this problem up i said i agree with both sides. i just kept trying to find ways to unbalance the arguements. kinda ran out of ideas tho,..
good point. didnt notice that detail.
i totally agree. i just hope you arent directing that towards me.

Re: Can the Plane Take-Off?
 

I tried to look at this as simply as possible. When a person is running on a tread mill, the only reason you dont move forward or backward is because you are moving at a constant speed with the treadmill. If the treadmill sped up, you would fly backwards. If you sped up, you would run into the control panel. But if the treadmill could read how fast you were increasing your speed, as you did it, then you would remain still. Because the speeds would be constant. And you say you need wind for an airplane to take off, if you were running on a treadmill at 10 mph, then you increased to 100mph, if the control system kept up with you, you wouldnt feel wind hitting your face because in essance, your not moving. therefore I feel the plane will not take off.

Granted people are saying that the enignes are producing thrust against air and therefore you dont need the wheels, yet in this case, the engine is producing X amount of thrust and is in turn causing movement, which, when pushed against something that is not moving(a paved runway) it causes motion which can be read in MPH. So the engine thrust is causing motion(MPH) So if the runway can match the MPH of the plane, no matter what air the engines are pushing against, the planes "movement" is still in MPH and that can be matched by this runway so the runway would cancel the thrust by the engine and the plane would remain still. Granted the engines would be in full throttle and the runway would by whipping underneath but the plane would be motionless.

When all esle fails, read my orignal paragraph

Re: Can the Plane Take-Off?
 

What you're missing is that thrust is a force, not a velocity. Go back to Newton's 2nd Law: F=ma. Velocity is the result of a force acting on a mass. Actually, I think that if thrust was a velocity, it still wouldn't matter.

Let's assume an ideal case: infinite traction between the wheels and the tredmill, 0 friction between the wheels and the axles (through the bearings). In this situation, how does the tredmill stop the plane from moving?

Now let's assume a practical case: some finite but large amount of traction, some very small but non-zero friction in the bearings. What effect does this have on the plane's movement?

Re: Can the Plane Take-Off?
 

Now I see what your saying. The wheels have no connection with the engine so if they are forced backwards,theres not enough friction reated to act against the power of the engine. I think this should have a poll attatched with it. Be intersting to see where everyone stands

The Debate Rages on

Re: Can the Plane Take-Off?
 

The plane would most certainly take off.
What are we not getting here?
If the plane was in a wind tunnel, then it would not take off, but since it is on the ground, and the wheels aren't powered, it will.Thats for the same reason that a car can drive into a stiff wind, because while the wind is pressing against the car with force, its not enough to overcome the power of the wheels.

Think of a toy car on a treadmill, the treadmill could be going 100mph, and if you were holding the car on the treadmill, the wheels would be spinnng at that speed, but the car would be still. Now imagine that you pushed the car foward on the treadmill at 5mph. The body of the car would be moving foward at 5mph, and the wheels would be moving at 105mph. The planes engines would be like your hand, not efected by the treadmill because it's not touching the treadmill.

If that didn't help you visualize it, I'm sorry, that was the best I could do and I tried :)

Re: Can the Plane Take-Off?
 

Well I don't want to muddy this debate with my lack of appropriate formulas, but I think the plane would still take off in a wind tunnel.

A plane is not a big brick wall, it is aerodynamic to reduce wind friction. Therefore in a wind tunnel it would still take off if the wind was blowing at the same speed as the plane was moving, because the wind is slipping around the plane, not pressing against it.

Re: Can the Plane Take-Off?
 

yes. in a windtunnel it will take off. technically not because the wind is "slipping" around the plane but because the plane's aerodynamics do not choose how fast the plane is moving to the ground but only with how fast the air over and under the wings are flowing.

Re: stolen from another forum
 

NO! This is not possible because the speed of the trake and wheels (which usually are not powered, it's the engine that pulls the plane if I am not wrong. But lets go with the example) will cancel out and the airplane will stay in place. Airplanes have airfoils, where high pressure builds on the bottom and low pressure on the top as air passes by. This creates lift, but how can the airplane lift if there is no air moving across the wings? The answer is it can't! In this sitution it can't.

Re: Can the Plane Take-Off?
 

As many people have said, there is no connection between engines and wheels in an airplane. The treadmill could be going backward at lightspeed, but if that plane's engine(s) is (are) going full blast forwards, or close to it, then the plane will move forward, thus getting the lift it needs. Wheel drag will not be enough to stop the plane from taking off unless the pilot is standing on the brakes, in which case he wouldn't take off anyway.

Now, people have used an F-18 as an example, but I'll try a Harrier for an example. Harrier won't go forward at all, but it will take off in its VTOL manner (that's Vertical TakeOff and Landing) and take off. No question about that, right? (Yeah, I'm cheating a bit, but if it's any airplane, I'll just go with a VTOL and take off without the debate. ;) )

Re: Can the Plane Take-Off?
 

:D
vtol is not allowed. the plane's thrust is angled down so the conveyor belt can't move in the opposite direction anymore. illegal move :p

Re: Can the Plane Take-Off?
 

I was thinking outside the box. And if the conveyor belt isn't supported well enough, it will move--downwards--until it can't stretch anymore--and then it won't move anymore.:p

If someone has a powered model airplane with landing gear (improvised or included), they should put it on a treadmill (in a big open area), run both, take a video, and post it here. I think that's the only sure way to answer the question.

Re: Can the Plane Take-Off?
 

That wont work, you will never ever get the type of precision that you would need to get a computer to say okay plane is moving 60mph make conveyor move 60mph even a nano-second delay means that the plane will move forward, and with a treadmill that makes things that much more difficult because there is no way to get close to the syncronization needed for this to work

Re: stolen from another forum
 

In jumps a beautiful aircraft device we like to call theDME .

Watches your change in distance from a VOR point, and gives you your airspeed. It only works when the pilot is flying directly too or from the VOR (though that is fairly common).

Re: Can the Plane Take-Off?
 

I guess I should have been more specific. In an aircraft its impossible to measure your ground speed directly. GPS also reports ground speed, but that is measured relative to satellites in orbit, with known positions and velocities - its not measured relative to the ground. If the satellites fail (or if your VOR points on the ground fail) then the aircraft cannot know its ground speed.

There is no instrument you can put in a aircraft that can directly measure the speed vector of the groud under the plane by itself.

By contrast, a car measure ground speed directly, by the rotation of its wheels.

Re: Can the Plane Take-Off?
 

It would be an interesting test. With the plane at a fixed throttle position you could measure the airspeed of the plane, with the treadmill still, and with it running, and see what effect it has on the planes airspeed.

It doesnt match the original problem/question, but you shoud be able to calculate the force the moving threadmill is applying to the plane (by the amount its airspeed is reduced) and extrapolate from there.

I think the answer you will get will be the same we have been saying since post #2 on page 1. The plane will take slightly longer to lift off than normal.

Re: Can the Plane Take-Off?
 

It wouldn't take off and go FORWARD, sorry for the muddy-ness :D


EDIT: foreward relative to the ground, not the surrounding air, Yet more muddyness, sorry.:o

Re: Can the Plane Take-Off?
 

this has been going on for a while since my last post but i will venture to hypothesize that the treadmill's speed makes almost no difference to the way the plan behaves, as long as it is still pointed so that the wheels can freespin.

Now i will attempt to explain myself again since i am so terrible at explanations:

The planes engines while create thrust pushing on the AIR the AIR will then follow Newton's third law and push the plane FORWARD

Now the wheels in contact with the ground will spin at whatever speed they need to because the ground is just there, when the ground accelerates BACKWARD the wheels will spin faster and faster until the plane has TAKEN OFF then, the wheels will slow to a stop in the AIR,

OK i think i got it this time,
Cuog

Re: Can the Plane Take-Off?
 

I sent this thread to a team 237 Mentor who is a Aeronautical Engineer by Degree, and this is what he sent me back.

It's a doozy.

Sorry about the bad formatting of the text. I tried to fix it up as much as possible.

Elgin

Re: Can the Plane Take-Off?
 

thats cool! Even an aerospace engineer was confused by the question.

its really a trick question. If you think the airplane will stay in one place, because the treadmill is 'matching its speed' - thats impossble.

If the plane is staying in one place then its speed is zero. If the planes speed is zero then the treadmill speed is zero. So whats stopping the plane from taking off? where does the force come from?

The only way the treadmill CAN move is if the plane is moving - and if the plane IS moving the treadmill is not holding it in one place.

The only logical (possible) answer is that the plane takes off normally, with the wheels spinning twice as fast. Any other model of the systems behavior is self-contradictory, and therefore cannot possibly happen.

Re: Can the Plane Take-Off?
 

Ok, here's my two cents:

The treadmill control is measuring the plane's speed relative to the rest of the world (stationary objects like trees), right? so when the plane begins to move, at say, 1 MPH, the treadmill will move in the opposite direction at 1 MPH. As stated above, a plane is propelled by it's engines reacting with the air. The wheels are completely free-rolling, except for a braking system. Therefore, except for a little increased drag from the wheels spinning twice as fast as normal, the treadmill would have no effect on the plane.
My conclusion: the plane might have to use a few extra HP to compensate for the extra drag from the wheels, but it would definitely take off.

Re: Can the Plane Take-Off?
 

Not to make too fine a point of it, but that is incorrect. A car measures the rotational rate of the wheels and from that determines the surface velocity of the tires. It does not measure ground speed, ever. We rely unpon the presumption that as long as the tires are firmly in contact with the ground, the tire surface velocity and the true ground speed of the vehicle will usualy be the same. For most cases, this is a safe presumption, but it is not always true. E.g. drive slowly on a slick road and hit the gas hard. The wheels spin, the speedometer will slam the needle around to the right, but your actual ground speed will remain unchanged.

The distinction becomes important if we try to put details on the original problem statement. Depnding on how the "plane speed" is determined (e.g. speed relative to the ground as determined by a ground-based observer, speed relative to the belt as determine by a belt-based observer, speed relative to the belt as determined by an airplane-based observer, speed relative to the ground as determined by an airplane-based observer, etc etc etc), you are going to come up with a different answer to the question.

-dave

Re: Can the Plane Take-Off?
 

but there is no equipment on any aircraft that measures ground speed through the tires - they dont use the same speedometers that a car uses.

so if you ADD one to an aircraft for the purpose of this experiment, then you are altering the way that aircraft measure their ground speed, and you are rigging the test to get the answer you want.

Re: Can the Plane Take-Off?
 

Apologies for resurrecting this ancient thread, but THIS JUST IN:

The Mythbusters will be going for this one next week at 10 E/P!

Re: Can the Plane Take-Off?
 

On wednesday? I am going to see that.

Re: Can the Plane Take-Off?
 

Isn't Mythbusters usually on at 9 PM Eastern? I saw the ad, and thought of this thread, but I didn't notice the different time.

Re: Can the Plane Take-Off?
 

Yeah, I got Mythbusters confused with Smash Lab, so 9 EST/Pacific.

Re: stolen from another forum
 

Yes.

Re: Can the Plane Take-Off?
 

The plane could take off. Planes do not put any force into the wheels when it taxis. It moves the same way it does in the air, prop or jet. Due to inertia you could say the plane would stay in the same position relative a third stationary observer. the conveyer belt could move back and forth rapidly and the plane would still stay still. All the wheels do is just keep the plane from falling and give it support when it has 0 lift. If you turn on the prop the plane would move foward, it doesnt matter at all what the conveyer belt does, the only force it can put on the plane is up. If you had a converyer belt long enought he plane would take off for it would be moving compared to the 3rd stationary oberserver. The only way it would not work is if the conveyer belt was not long enough or there was a strong tail wind. but a plane can not take off without a conveyer belt in thos conditions.

Re: Can the Plane Take-Off?
 

Here we go again.
The key to this puzzle is the statement in the initial conditions "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)."
As soon as the thrust of the engine pushes the plane forward some small distance (thus it has some speed), the conveyer moves at whatever speed necessary to counteract that speed. It can move at any speed!

So, the force on the plane from the belt is limited by the friction of the wheel bearings. Move that belt at a high enough speed (a fraction of lightspeed, for example) and the force transmitted to the aircraft through the freely rolling wheels will be enough to counteract the force of the engine.

By definition, the plane cannot move because the belt is free to move at any speed, and while the rolling wheels don't transmit a lot of force to the airframe, the force is nonzero and therefore you must account for it.

Oh, in a real, practical world, you are correct: The plane will move before the belt can reach 0.1c. But, that wasn't the puzzle question...

Don

Re: stolen from another forum
 

ok, before I read ken's post, I assumed that if they went canceling speeds then (like running on a treadmill) then the plane would stand still and Bernoulli's principle would have no effect. Now I see that the run way moving would have no effect whatsoever on the plane except making its wheels spin faster.

Cool, this would make for a very fun team debate ;)

thanks, Vivek

Re: Can the Plane Take-Off?
 

Ummm... Don, I don't see how you can say that the belt can move at any speed.
The condition says that the speed of the conveyor is (effectively) the negative of the speed of the airplane. It does not say that the conveyor goes fast enough to stop the plane with friction. It does not say that the conveyor is attached to the wings or tail (which would be necessary to stop the plane from taking off unless the brakes were on).

All it says is that the conveyor moves at the same speed as the plane in the opposite direction.

That said, guess who's going to be watching Mythbusters next Wednesday if at all possible?

Re: Can the Plane Take-Off?
 

This argument reminds me of that trouble-making ancient Greek philosopher, Zeno. To paraphrase him tremendously, he argued that motion is impossible.
Take the example (as he did) of an arrow shot from a bow. It is understood that the arrow exists, and takes up space, and at every infinitessimal instant, has a known position. Since positions are absolute and immobile (as measured from your frame of reference, i.e. the earth's rotation), the arrow does not move because at any given freeze-frame moment it is in a given position & orientation and therefore it is still.
We all know this is not true, otherwise Robin Hood would have been out of a job. But, as Zeno endeavored to prove, it does show the fallability of human logic. There are many more instances that recall this notion (Heraclitus saying one can never step in the same river twice, and the completely ridiculous "if a tree falls...." nonargument) that show that logic can be used to prove (or disprove) nearly anything.

To discuss the notion of a giant fan producing lift (or "suck") to the plane, this would be a colossal mistake. As soon as the plane leaves the wind chute provided by the fan, it would enter the (relatively) still airmass and fall back down, either tilting back each time and eventually reaching a stall or resulting in a nosedive.

Re: Can the Plane Take-Off?
 

The plane can take off. The thrust is not relative to the speed of the wheels turning. The plane will move forward regardless of how fast its wheels are turning, the thrust is not going into the wheels. The question is basically flawed in making you think that because the conveyor belt is moving at the same speed as the wheels that the conveyor could hold back the thrust/forward movement of the plane. To believe that the plane can not take off, you would also have to believe that if the conveyor belt was moving the wheels at the same speed the plane needs for take off, the plane would fly without its engine on. In order for the conveyor belt to stay under the plane once the thrust is enough for take off, the conveyor had better be moving pretty fast in relation to the ground if it wants to stay underneath the plane. The conveyor can not put enough force into free spining wheels to hold back the thrust of the planes engine.

EDIT: The plane does not move forward and take off because the wheels are turning, the wheels turn because the plane is moving and the wheels turning do not make the plane take off. The question is flawed.

Re: Can the Plane Take-Off?
 

I love this question.

See attached Image.

-Oris-

Re: Can the Plane Take-Off?
 

I see that both sides have good reasons, however in theory I believe that it would not take off. IF the conditions were exactly as stated, then it would be impossible for the plane to move relative to the air. And that relativity is the important part. Oh well, I guess we will all see come Wednesday. However, I guarantee you that no matter how MythBusters recreates this somebody will not agree with their conditions and will therefore claim the results void.

Re: Can the Plane Take-Off?
 

I ask how would it be impossible?

For the record, if I had a long enough conveyor belt, I would probably be able to test it. The rig would be the problem, but I can almost guarantee you I could get a plane off the ground under the experiment conditions.

Re: Can the Plane Take-Off?
 

Don't you see the problem in this debate? It is the "experiment conditions". The way many of you are reading it, it suggests that the plane can move just because the wheels don't give any propulsion. The way that I am reading it, the plane can't move(relative to the air) period. That is what is critical here. It is not that they can't take off if the plane can move relative to the air. In fact, with the conditions that you specify I agree, It could take off. The point I disagree with you is the conditions that you interpret from the original statement.

The original post:
"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).

The question is:

Will the plane take off or not? Will it be able to run up and take off?"

The formula:

The vest way to track the speed of the plane would be to find the
C=circumference of the wheels
R=# of rotations of the wheel
T=time the wheel takes to rotate that # of times
S=Speed of plane=Speed of conveyer belt

S=(C X R)/T

Now, let's take this one step at a time. The plane is stopped. The conveyer belt is stopped. The plane starts to move and the conveyer belt INSTANTANEOUSLY starts to move in the opposite direction. (remember this is all in theory with ideal conditions) As the plane speeds up to the speed necessary to take off, the conveyer belt does the same in the opposite direction. Now, with these conditions, it is impossible.

To truly put this to rest, the conditions would have to be more clearly stated in the question. For instance, how does it track the planes speed? That is rather critical. Do we ignore friction? As some have posted in the past, what about wear and tear? I think that interpretation is the true decider on this one. I am positive that with the conditions in my mind, I am right. I am positive that with the conditions in your head, you are right. The thing is that the conditions were not clearly stated to the original post and thus we have no choice to say that either outcome is possible depending on how it is interpreted.

P.S. I hope that if you do not understand my statement on the interpretation of the problem, then we can just agree to disagree.

Also, sorry for the long post.

Re: Can the Plane Take-Off?
 

The key to this problem, which has been established by some pretty intelligent aerospace engineers earlier in this thread, is that the wheels' rotation have ABSOLUTELY NOTHING to do with the speed of the plane.
It took me a while to get my head wrapped around that notion, but once I did, this problem became very simple.

Re: Can the Plane Take-Off?
 

I'm sorry, but I still do not understand. You haven't done any work to prove the equation. Under the experiment conditions, I could probably get at least an R/C aircraft off the ground. The only condition is that the conveyor is moving at the airplane's speed in the other direction. And the fact of the matter is, an airplane's wheels give NO propulsion. (If you want to argue this point, come on over to SDSMT, and I will take you into the CAMP area to where the Aero Design team is and show you on R/C aircraft. Or, find your local model-aircraft store.) The only factors here are friction and thrust. Friction of the wheels--probably negligible. Thrust of the motor/engine--plenty to overcome friction.

Re: Can the Plane Take-Off?
 

If you theoretically create a huge fan at the end of a runway, that will shorten the ground roll of the aircraft. However, the aircraft will not have enough speed to fly if it immediately leaves this stream of moving air. Thus you can have a shorter runway but the aircraft will need to remain in the accelerated air for some time.

Again, not to beat a dead horse, but the fact that rolling frition and static friction both depend on normal force makes this question possible to answer. Regardless of the speed that the airplane moves [and thus the conveyor belt] the force exerted by the wheels on the aircraft is constant (Except that it will be marginally higher initially to go from static to kinetic friction). Unless this constant is so large that the aircraft cannot take off under normal circumstances, the aircraft will take off.

Now to argue the other extreme:

As mentioned earlier in this thread, assuming the experiment conditions make it such that the aircraft cannot move, due to viscosity effects in the air immediately above the treadmill, the treadmill drags some of the air along with it. This boundary layer increases in thickness with increasing velocity, and so at some speed of the treadmill, the wing will experience enough relative air velocity to produce lift. At this point, it will lift the aircraft off of the ground. Now it may be argued that the treadmill now stops, the aircraft drops to the gound, repeat ad infinitum, or that the aircraft will then gain enough airspeed to then transition to full forward flight. In either case, the airplane has lifted off the ground, technically a takeoff.

Thus the aircraft will lift off regardless of any of the conditions in the problem statement.

Re: Can the Plane Take-Off?
 

I dunno...on a simulator, I've been able to take off at about half the speed I'd otherwise need. I finished accelerating in the air. There are these tricks known as high-lift devices. Specifically, flaps on the wing's trailing edge. Once in the air, I'd pull them in.

Edit: Lemon1324, I know how to fly. The flaps would get retracted once I was at a decent speed, and only when I was at a flying speed. I might not even use them until I cleared the accelerated air, an then use them only until I got a better speed.

Re: Can the Plane Take-Off?
 

Flaps and other high-lift devices will only make the problem worse--when you retract the flaps, your coefficient of lift drops, and so you get less lift at that particular point in the envelope. Now after you lift off (at half the ground speed, presumably) when you leave the accelerated air, the airspeed of the aircraft drops suddenly. If you also retract flaps, the aircraft will most likely stall and come crashing back down.

Re: Can the Plane Take-Off?
 

The answer is yes; the belt tracks and recreates the planes speed in the opposing direction, yet if the plane isn't moving and just standing still, then neither is the belt. The problem never states it is moving in such a speed that it would cause the plane to not move forward, it only says it would go in the opposite direction at the same speed of the airplane.
Under experiment conditions... it works perfectly fine, even at take off the belt is only moving as fast as the plane is forward, this just means the wheels are rotating at twice their normal take off speed...

Re: Can the Plane Take-Off?
 

The reason I did not source the formula is because it has been around for long enough that it does not need a source. It is common knowledge. Also, the wheels can still be used to measure speed despite the fact that they are not used for propulsion. Furthermore, I am not discussing this anymore until I have seen Mythbusters. I hope that I did a reasonable job explaining some of the misinterpretations of my words. Until then, Good day.

Re: Can the Plane Take-Off?
 

I didn't ask for the source, I asked for a proof. Also, how does it tie in? You did not explain that part. The equation is there with no tie-in.

I don't disagree that the wheels can be used to measure speed, but there is a chance (I've done it in a simulator) that one or more wheels will be off the ground at any given instant, so which wheel do you measure? How do you determine which wheel's data is correct, if you do all of them?

And the conditions are clearly stated in the problem. What conditions did you have in mind? For anyone to analyze your conditions, you have to state them. You don't. Therefore, I cannot fully answer you because my mind-reader is on the blink (and has been for 19 years at this time). If I know what conditions you use, I can either agree or disagree with the conditions. I may or may not agree with you, but not knowing what conditions you have in mind prevents my doing either. I disagree based on the given conditions. You have other conditions. Very well, let's hear them.

Re: Can the Plane Take-Off?
 

The Mythbusters have conclusively proven that a plane on a treadmill can take off! (When comparing airspeed vs. conveyor speed)

Warning! Science Content!;)
This can be explained by comparing the means of propulsion of a plane vs. a car. A car uses the powered spin of its wheels to propel it forward.

Now a plane uses it's propeller to push against the air, while the wheels are left to free spin. And a plane depends on the speed of the air passing over its wings to generate lift to take off. With enough headwind, a plane can take off while not moving relative to the ground. Thus, a plane will pull itself through the air, no matter if it's wheels are spinning (or how fast they are spinning) or even if they are not spinning at all.

There is a corollary to this.
And I'm not sure if I will be explaining it right.
You have to be measuring the plane's airspeed for the experiment to work. If the speed of the wheels was monitored, and you were only trying to match the speed of the conveyor belt to the rotation of the wheels, assuming no friction in the system other than that between the wheels and the conveyor, the plane wouldn't have to exert any propulsion of any kind to remain stationary (Newton's First Law of Motion). However, in real life, the plane would be pulled backwards along with the conveyor, relative to the ground due to the friction of the wheels and their bearings. So to counter this, the plane would have to be pushing some air with its propeller to remain stationary to the ground for the wheels to match the speed of the conveyor.
In this case, the plane would not take off, as the speed being measured was the speed of the wheels matching speed of the conveyor, not the airspeed vs speed of the conveyor. To sum it up, the plane would remain stationary to the ground and thus have zero airspeed (assuming no wind) and not be able to take off.

Re: Can the Plane Take-Off?
 

I will have to disagree. Engines at full power means nothing. If you retract the landing gear you will crash the plane because your air speed is 0. Many people are confusing ground speed with air speed. If air is not going over the wings you can not lift a plane off the ground plain and simple.

Re: Can the Plane Take-Off?
 

The air speed is ONLY zero if:

1. the wind is directly from one side, or
2. the wind is from dead aft at the same speed as the plane (and a wind that fast would ground half the planes in the area anyway).

The airplane moves forward on the ground. Ground speed is approximately airspeed, in a calm. If the aircraft is moving on the ground, it will have airspeed, unless one or both of the conditions above is met. The airplane will also be able to move fast enough to beat the wind.

Oh, and I have heard of a fighter pilot on a conventional runway who pulled his gear up to take off. No rising of the plane. If you can do the same on a moving runway, you can take off.

This besides the point that Dave was making: Same conditions apply, but the pilot simply pulls up the landing gear and is no longer in contact with the belt. IF you are assuming that the plane will stand still, THEN the plane will not take off.

However, the Mythbusters have shown that the plane CAN take off, especially because it moves, so this discussion is moot, unless you have a problem with their methods.

Re: Can the Plane Take-Off?
 

I normally don't post in these kind of threads, yet i feel the need to in this one.

There is an airspeed/ground speed issue here.

Think about the problem in terms of the horizontal forces -- You have the thrust of the aircraft pushing the body of the plane forwards, you have the force of the treadmill being pushed opposite the engine thrust on the wheels.

F=M*A tells us that if these two forces do not equal each other, the plane will accelerate with the direction of the greater force.

As for the force being applied by the treadmill, onto the wheels -- If you think about where that force is being applied, and in what direction, you'll see that it's acting tangent to the wheel, so all (well nearly all) of that force goes into rotational motion on the wheel. I say nearly all because of any wheel bearing friction. So that force goes to almost zero.

Since there is still a force being applied to the aircraft frame by the propeller or jet engine, the plane will accelerate (f=ma)

When the plane reaches normal takeoff speed, the wheels will be spinning at twice normal takeoff speed (due to the treadmill below), but because they are free-spinning and not powered wheels, there is almost no difference between this and a normal takeoff.

my $.02

Re: Can the Plane Take-Off?
 

Yes. The trust generated by the plane is no match for anything else