Can the Plane Take-Off?

[EddieMcD]

Originally Posted by sanddrag

The plane would not be able to move the runway in the opposite direction unless the wheels were driven (like an automobile).

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.

[Elgin Clock]

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???

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")
BOX

[KenWittlief]

Originally Posted by Elgin Clock

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???

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.

[sciguy125]

Originally Posted by Elgin Clock

Fn - Force of Conveyer pushing up at the plane (+Y) ...known as Normal Force.
Fg - Force by gravity...
Ft - For this case, thrust of airplanes jets...
Fcb - Force being countered by the conveyer belt...

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

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).

[Cuog]

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!

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

[KenWittlief]

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.

[greencactus3]

Originally Posted by sanddrag

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

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?

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???

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)


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.

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)

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.

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.

correct. which is why you can say either side is correct. if you ignore conveyorbelt limits

[greencactus3]

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

[Jay H 237]

Originally Posted by Elgin Clock

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

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.

[sciguy125]

Originally Posted by greencactus3

correct. which is why you can say either side is correct. if you ignore conveyorbelt limits

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.

[Madison]

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'.

[sanddrag]

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.

[greencactus3]

Originally Posted by sciguy125

Fx = Ft + (-Fc) - Ft is force of thrust (engines), Fc is force of conveyor

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...

[ahecht]

Originally Posted by greencactus3

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....

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.

[artdutra04]

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:

If you still don't get it - imagine you are wearing a pair or rollerskates and you're standing still on a conveyer belt which isn't moving and you are holding a rope tied to a distant tree. You start to pull on the rope with sufficient force to pull you forward at 5mph. The conveyer belt instantly moves at 5mph in the opposite direction. Does that stop you moving closer to the tree? NO. You continue to move at 5mph and the wheels rotate at the equivalent of 10mph.