Small quest for the bored...

[SNAFU]

A small quest for the smara$$es of this forum... ;)

 

An airplane is standing on 2km long treadmill, exactly as long and wide as a runway.

The speed governor of the treadmill is setting the speed of the treadmill to the same, but opposite speed of the rotational speed of the airplane`s wheels, as soon as the wheels start turning.

The airplanes tries to take off.

What is happening? Will it take off under this circumstances? :pilotfly:

[asparagin]

Is it a jet or does it have propeller?

 

A:

It won't take off. Except if it is the F-35B.

Edited November 22, 2010 by asparagin

[SNAFU]

Well ok, lets say it is no vertical takeoff, propeller or jet, well I prefer propeller, but wheatever...

 

You say it won´t takeoff, ok, not enough lift will be produced to takeoff, but why?

[Lixma 06]

No airflow over wings.

[G3]

the treadmill itself might be travelling just below takeoff speed :D

then it's conceivable you might take off when the plane starts to move.

 

alternatively the plane is crushed under a huge overweight lady in lycra

[asparagin]

You say it won´t takeoff, ok, not enough lift will be produced to takeoff, but why?

 

Because the airplane will be stationary?

[SNAFU]

Mmmh, I would say the thrust comes from the propeller or jet, not from the wheels, but lets hear some more opinions?

[2IAE-CrashBG]

The plane will be stationary and no lift will be generated by the wings. And the question is not put correctly, anything about the engine?

Edited November 22, 2010 by 2IAE-CrashBG

[SNAFU]

What is not put correctly? Please give me a hint, english is not my mother tongue. ;)

[2IAE-CrashBG]

Nevermind, I'm really confused about the question at the moment :D :D

[MasterZelgadis]

Er sagt es ist ein Fehler in der Fragestellung

 

Just translated the term he didn't get.

 

Airplane will not take off. Lift is generated by airflow over th wings, not by speed over the ground. If the plane is moving over a still ground the air causes lift on the wings.

 

If the ground moves below the aircraft, the wings don't move in the air, so no airflow and no lift. That's it ;)

[asparagin]

Mmmh, I would say the thrust comes from the propeller or jet, not from the wheels, but lets hear some more opinions?

 

That's the tricky point: If thrust comes from wheels than it can't take off. But if thrust comes from the jet then it should make no difference if its on the treadmill (like a rocket), so it can take off.. right?

[2IAE-CrashBG]

There we go :) I was thinking the same, but couldn't explain it. Thank you MasterZelgadis!

[mvsgas]

YORCk1BN7QY&feature

 

They tested this a year or two ago. The only thing that could happen in larger, faster jets is the tires may fail before takeoff. But wheel speed has noting to do with aircraft speed, and treadmill would only affect wheel speed.

Edited November 22, 2010 by mvsgas

[SNAFU]

Er sagt es ist ein Fehler in der Fragestellung

Ja, das habe ich schon verstanden, nur nicht wo der Fehler ist... ;)

 

I am at office and the vids are blocked, so I cant answer on that one.

 

But I say that under the given conditions, that the rotational speed of the wheels has to be the same as the treadmill`s surface speed, the plane must not move a bit, other wise the conditions are not obeyed.

 

As soon as the plane moves, the wheels have the speed of the treadmill and additionally the speed of the plane, so the planes speed must be zero, to keep the conditions, or not?

[asparagin]

But wheel speed has noting to do with aircraft speed, and treadmill would only affect wheel speed.

 

Nice found.

 

But I say that under the given conditions, that the rotational speed of the wheels has to be the same as the treadmill`s surface speed, the plane must not move a bit, other wise the conditions are not obeyed.

As soon as the plane moves, the wheels have the speed of the treadmill and additionally the speed of the plane, so the planes speed must be zero, to keep the conditions, or not?

 

The speed of the wheels is correlated to the speed of the treadmill surface but not proportional to the aircraft speed.

The only option for the aircraft not to take off (or to remain stationary) would be if the thrusters would induce motion through wheels. (which is not the case, but we are tempted to think that at first sight :smilewink:)

[MTFDarkEagle]

Wont take off, no airflow. If it were to be a car, the engine drives the wheels, matching the speed of the treadmill, so it would stay stationary. But the engine in a aircraft don't power the wheels (as they are independant), so the engine would push the aircraft forward, resulting in take-off

+1 mythbusters

[SNAFU]

Nice found.

The only option for the aircraft not to take off (or to remain stationary) would be if the thrusters would induce motion through wheels. (which is not the case, but we are tempted to think that at first sight :smilewink:)

 

I don´t know mythbuster, as stated, but I am sure mythbuster used other general conditions or broke the given conditions.:joystick:

 

The plane will only move on the threadmill, if the wheels turn faster than the threadmill, but given the condition, that the speed of threadmill and wheels are always the same, so the planes speed must be zero. :smartass:

 

Uwheel = Uthreadmill + (Planespeed / wheel diameter)

 

The condition is Uwheel = Uthreadmill, this is only possible if

 

Planespeed = 0, therefore the plane will not takeoff... :book::P

[Mugenjin]

The plane will only move on the threadmill, if the wheels turn faster than the threadmill, but given the condition, that the speed of threadmill and wheels are always the same, so the planes speed must be zero. :smartass:

 

That condition is not realistic though. The propeller propels (duh ^^) the plane, the wheels would just spin faster.

[MTFDarkEagle]

I don´t know mythbuster, as stated, but I am sure mythbuster used other general conditions or broke the given conditions.:joystick:

 

The plane will only move on the threadmill, if the wheels turn faster than the threadmill, but given the condition, that the speed of threadmill and wheels are always the same, so the planes speed must be zero. :smartass:

 

Uwheel = Uthreadmill + (Planespeed / wheel diameter)

 

The condition is Uwheel = Uthreadmill, this is only possible if

 

Planespeed = 0, therefore the plane will not takeoff... :book::P

 

The propellor doesn't power the wheels now does it ;)

[SNAFU]

No, but if the wheels speed the same as the threadmill, the plane won´t move, you could even tie a Apollorocket on the back and fire it. ;)

 

Ok, I admit that is mathematical, but in the given conditions, it is not possible for the plane to move, theoretical. ;)

 

Practical the threadmill would blow itself to the moon,trying to maintain the same speed as the wheels, which it will never be able to, because the plane will surly move, and therefore the wheels will turn faster than the threadmill, which it will try to compensate by speeding up to the infinite. ;)

 

PS: The trap is the way the question is defined. At first you think, yepp it won t move, because you are used to cars, then you think about it and say, of course will it move and take off, but then this would break the general conditions and base of the question, wouldnt it? ;)

So finally, the answer is, the plane will not move and therefore not takeoff.

Edited November 22, 2010 by SNAFU

[egorter]

is the treadmill stationary?

[Shaman]

That condition is not realistic though. The propeller propels (duh ^^) the plane, the wheels would just spin faster.

 

And that's correct:smartass:

[MTFDarkEagle]

SNAFU: how difficult is it to get your head around it? The wheels can turn freely meaning they can spin at 48865745863256 kmh, it doesn't matter! The prop pushes the aircraft forward, the tyres just spin an awfull lot faster.

[SNAFU]

No, DarkEagle, you ignore the condition that the speed of the wheels must be the same as the speed of the threadmill, but the opposite direction of turn. ;)

 

Try it your self in the fittnes centre. As long as the condition is valid, that boths speeds are the same, the plane speed must be zero, thats simple maths. ;) Sure the thrust moves the plane, but as soon as the planes moves over the fixed threadmill, the wheels turn faster, than the threadmill, which does not comply with the conditions, stated in the quest.

 

If you skip this condition, sure then, but no cheating, huh? ;)

 

For example look at a gear with pinion and wheel of the same modulus and tooth number (here replacing the wheel and the threadmill). As soon as the wheel turns faster as the pinion, the shaft is moving and you have a planetory gear, but as long as the condition is given, both speeds are the same, the shafts wont move. ;)

Edited November 22, 2010 by SNAFU