Plane on a Treadmill

[davidsinn]

IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

Please explain how the prop has anything to do with the wheels?

[lordmonar]

IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

No....

Plane is at rest.....prop at 1200 RPM brakes set....Wheel speed is 0 treadmill speed is 0.
Release the brakes, advance the throttle....wheels move at say 10 Kts threadmill moves at 10Kts in opposite direction.....the wheels will rotate twice as fast.

Speed picks up to 60 Kts the treadmill is moving at 60 Kts....wheels are rotating as if they were moving at 120 Kts.

Plane speeds up to 100 Kts.......treadmill is moving at 100 kts.....wheels are rotating as if the were moving at 200 kts.....plane lifts off.

This is counter inutitive to what we experince walking on a treadmill or driving a car on test stand....because the thrust in walking or driving a car comes THROUGH the axel to the wheels....so as you thrust forward the ground moves away you do not generate any friction and the car/or person goes no where.

On a plane the thrust is from the power propeller.  It pushes on the air and nothing else.  It does not matter what the ground is doing.

[davidsinn]

IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

No....

Plane is at rest.....prop at 1200 RPM brakes set....Wheel speed is 0 treadmill speed is 0.
Release the brakes, advance the throttle....wheels move at say 10 Kts threadmill moves at 10Kts in opposite direction.....the wheels will roate twice as fast.

Speed picks up to 60 Kts the treadmill is moving at 60 Kts....wheels are rotating as if they were moving at 120 Kts.

Plane speeds up to 100 Kts.......treadmill is moving at 100 kts.....wheels are rotating as if the were moving at 200 kts.....plane lifts off.

This is counter inutitive to what we experince walking on a treadmill or driving a car on test stand....because the thrust in walking or driving a car comes THROUGH the axel to the wheels....so as you trust forward the ground moves away you do not generate any friction and the car/or person goes no where.

On a plane the thrust is from the power propeller.  It pushes on the air and nothing else.  It does not matter what the ground is doing.

I drew what the major is explaining. It's a few pages back.

[ßτε]

Once the wheels start moving faster than the treadmill, you have broken the premise of the problem. Remember that the premise of the problem is that the treadmill is moving at the same speed as the wheels. As I interpret it, it means the edge of the tire is moving at the same speed as the treadmill. If this is the case, then the airplane will not move relative to the stationary airport. It will not fly.

Once the airplane does move forward, the wheels and the treadmill are no longer moving at the same speed, so even if the airplane does fly, it doesn't contradict the statement of the problem since the premise is no longer in play.

The problem with the question is really if there is any possible way for the treadmill to prevent the airplane from moving forward if the airplane is under full power. My contention is that there is not.

[NC Hokie]

On a plane the thrust is from the power propeller.  It pushes on the air and nothing else.  It does not matter what the ground is doing.

Yes, but what the wheels are doing does matter, as they indirectly transfer the propeller's thrust to the ground.  What happens when you lock the wheel brakes and run the engine up to full throttle?  The aircraft wants to move forward, but the thrust is unable to overcome the resistance generated by the brakes.  You have plenty of thrust, but your ground speed is zero.  As long as that remains true, you're going to remain grounded and stationary.

Put that same plane on the postulated treadmill and it will act the same way.  The thrust of the aircraft is negated by the opposing motion of the treadmill, leaving you with an effective ground speed of zero.

[FlyTiger77]

Yes, but what the wheels are doing does matter, as they indirectly transfer the propeller's thrust to the ground. 

I beg to differ. The wheels merely provide a way to reduce friction between the aircraft and the ground with some limited cushioning being provided by the wheels themselves.

Wheels are not required in order to transfer propeller thrust to the ground, as there is no need for the thrust to work against the ground (cf. the Wright Flyer of 1903 which was on skids, or the myriad float and ski planes). Sir Isaac Newton said famously, "For every action, there is an equal and opposite reaction." The propeller accelerating a column of air rearward is sufficient to impart forward motion to the aircraft. This can also be seen by increasing the throttle on an airplane at 10,000 feet and noting, all other things being equal, the acceleration of the aircraft, even though the ground is nearly 2 miles away.

I would submit, that in the original question, the aircraft would fly away from the treadmill even as the wheels have no rotation. The airplane will be stationary relative to the treadmill, but at flying speed relative to the earth and surrounding air.

Agreed, however, that if you lock the brakes and don't have sufficient thrust to overcome the huge increase in friction, the airplane will remain stationary.


v/r

[Major Lord]

Once the wheels start moving faster than the treadmill, you have broken the premise of the problem. Remember that the premise of the problem is that the treadmill is moving at the same speed as the wheels. As I interpret it, it means the edge of the tire is moving at the same speed as the treadmill. If this is the case, then the airplane will not move relative to the stationary airport. It will not fly.

Once the airplane does move forward, the wheels and the treadmill are no longer moving at the same speed, so even if the airplane does fly, it doesn't contradict the statement of the problem since the premise is no longer in play.

The problem with the question is really if there is any possible way for the treadmill to prevent the airplane from moving forward if the airplane is under full power. My contention is that there is not.

Its clear though that you have misinterpreted the premise of the question. The premise stated that the treadmill will travel in a direction opposite, but directionally proportionate to, the aircraft wheels.  The premise tells us that the Treadmill MATCHES the speed of the WHEEL. The treadmill will always be either at the fixed velocity of the wheels, or increasing or decreasing in velocity to accommodate the speed of the aircraft wheel.

The mental image generated by an incomplete reading of the premise implies in some minds, the idea of a man walking against an escalator, If them man walks faster, and the escalator speeds up at the same rate and absolute velocity, the man stays stationary, like an hamster in a wheel. These models are not what the original premise tendered. The forces used to accelerate the airplane are not a function in any significant fashion of the rotational velocity of the wheels, but only of the true forward motion of the aircraft. The wheel velocity according to the premise will always be 2X the forward velocity of the aircraft. The idea that the treadmill's opposing force is sufficient to decelerate the aircraft to a static position is a red herring.

If we restate the problem as making the wheels match the treadmills speed, instead of vice-versa, you might be able to create a static airplane on a treadmill, but there is no way on Gods' green earth you could make it happen the other way around.

Major Lord

[CadetProgramGuy]

IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

EXACTLY!!!!!!

[FlyTiger77]

IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

EXACTLY!!!!!!

Please see my post at #205 above. The wing of the airplane cares not a whit about the speed that the wheels are rotating (either at 0 knots or 2xFlying Speed, depending on how you interpret the ambiguous wording of the original question). The airplane will accelerate forward (relative to the earth, even while remaining stationary [or moving 2x flying speed, again based on your interpretation of the original question] relative to the treadmill). To posit that wheels are necessary for takeoff, regardless of their rotational velocity, does a great disservice to aircraft that have skids, floats and skis for landing gear and to flying boats with no landing gear at all.

v/r

[SSIAJ]

Are you people really still perplexed by this??? When the air speed reaches 60......somethin' funny is gonna happen.  Reguardless how fast the little wheels turn, how fast the snow is moving under the ski or how fast the current is moving under the float. Something funny is gonna happen. 

[CadetProgramGuy]

What airspeed?  The airplane is not moving........

[lordmonar]

Once the wheels start moving faster than the treadmill, you have broken the premise of the problem. Remember that the premise of the problem is that the treadmill is moving at the same speed as the wheels. As I interpret it, it means the edge of the tire is moving at the same speed as the treadmill. If this is the case, then the airplane will not move relative to the stationary airport. It will not fly.

I addressed this earlier......the only way that the treadmill can move that would make the wheels NOT move (that is rotate) is to move in the same direction that the plane is moving.....in which case the plane still has forward motion, AKA air speed, and will fly.

Once the airplane does move forward, the wheels and the treadmill are no longer moving at the same speed, so even if the airplane does fly, it doesn't contradict the statement of the problem since the premise is no longer in play.

I brought that up also.....depending on the lag between the wheels gaining speed and the treadmill matching that speed......if you assume a ZERO time lag the only states (mathmatically) of the wheels are zero and infinity!

The problem with the question is really if there is any possible way for the treadmill to prevent the airplane from moving forward if the airplane is under full power. My contention is that there is not.

The answer is yes...there is a way for the treadmill to move that would induce enough drag that would prevent the plane from gaining lift off speed....but that speed would be much greater then the foward speed of the aircraft, and the wheels which the original question stated was not the case.

[lordmonar]

Yes, but what the wheels are doing does matter, as they indirectly transfer the propeller's thrust to the ground.

No they don't.  The wheels and the ground induce drag that fight against the thrust of the aircraft.  Thrust is NOT transferred to the ground via the wheel in an aircraft.

What happens when you lock the wheel brakes and run the engine up to full throttle?  The aircraft wants to move forward, but the thrust is unable to overcome the resistance generated by the brakes.  You have plenty of thrust, but your ground speed is zero.  As long as that remains true, you're going to remain grounded and stationary.

Absolutely true....but once you release the breaks and it moves forward and the treadmill moves backward you no longer have that resistance because you have removed the brakes from the equation.

Put that same plane on the postulated treadmill and it will act the same way.  The thrust of the aircraft is negated by the opposing motion of the treadmill, leaving you with an effective ground speed of zero.

Not necessarily true.  IF the treadmill was moving at a very high rate of speed then it would induce enough drag into the equation to prevent flight.....but that speed would be much higher then the speed of the wheels.....which is the upper limit of the original premise.

[lordmonar]

What airspeed?  The airplane is not moving........
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Again...what is preventing the air craft from moving.

There are only two possiblities of the premise.

a) The definition of "the speed of the wheels" is the speed of the surface of the wheel as it turns which can be expressed as RPM.

b) The dfinition of "the speed of the wheels" is the speed of the axle or hub as it is moved foward by the propeller.

If it is case a....then the onlly outcome is that the as the plane moves forward and the treadmill moves backward the speed of the wheel induces a positive feed back loop that quickly spins the wheel (and the treadmill) to something close to the speed of ligh and a black hole is created (assuming indestructable wheel and treadmill).

If it is case b....then the wheel just spins twice as fast as it would normally spin as the plane accelerated down the run way.

The treadmill could move in a way to induce enough drag to stop the plane from moving forward but that would be greater then the speed of the wheels (by either definition) and a violation of the premis.

The only way the treadmill could move that would negate the movement of the wheel (as in case a) would be to move in the same direction of as the moving aircraft....again a violation of the original premis.

[lordmonar]

What airspeed?  The airplane is not moving........

It must move.

The premise clearly states that the treadmill matches the speed of the wheels.  The only way for the wheels to move is for the whole aircraft to move.  The only way for the treadmill to keep the aircraft from moving forward is if it was moing in such a way to induce the same amount of drag as a set of chocks or the break....and that would require the treadmill to move at significantly higher speeds then the the whees are moving.

[N Harmon]

The only way for the wheels to move is for the whole aircraft to move.  The only way for the treadmill to keep the aircraft from moving forward is if it was moing in such a way to induce the same amount of drag as a set of chocks or the break....and that would require the treadmill to move at significantly higher speeds then the the whees are moving.

So it seems like there isn't a whole lot of disagreement between us, except for our interpretation of "the speed of the wheels". You take it as meaning the distance displacement of the whole wheel in some time, which makes the wheel speed the same as the aircraft speed in all situations. In that case the problem is exactly the same as your conventional "plane on a treadmill" problem, and the aircraft flies.

However, some of us took "the speed of the wheels" as meaning the wheel's circumference multiplied by its angular velocity (RPMs). Basically, what a speedometer attached to the wheels would measure. If the treadmill matches this speed exactly, it will produce enough rolling resistance to counter the power output of the power plant, and prevent the aircraft from flying.

I think it is probably a waste of time arguing which interpretation is correct, since the problem itself is ambiguous. But the details of the problem are interesting to discuss as they provide a good refresher of basic mechanics.

[ßτε]

The only way for the wheels to move is for the whole aircraft to move.  The only way for the treadmill to keep the aircraft from moving forward is if it was moing in such a way to induce the same amount of drag as a set of chocks or the break....and that would require the treadmill to move at significantly higher speeds then the the whees are moving.

So it seems like there isn't a whole lot of disagreement between us, except for our interpretation of "the speed of the wheels". You take it as meaning the distance displacement of the whole wheel in some time, which makes the wheel speed the same as the aircraft speed in all situations. In that case the problem is exactly the same as your conventional "plane on a treadmill" problem, and the aircraft flies.

However, some of us took "the speed of the wheels" as meaning the wheel's circumference multiplied by its angular velocity (RPMs). Basically, what a speedometer attached to the wheels would measure. If the treadmill matches this speed exactly, it will produce enough rolling resistance to counter the power output of the power plant, and prevent the aircraft from flying.

I think it is probably a waste of time arguing which interpretation is correct, since the problem itself is ambiguous. But the details of the problem are interesting to discuss as they provide a good refresher of basic mechanics.

Nathan, you beat me to it. I was about to post a similar post. We finally agree on something in this thread.

We probably still disagree on whether or not the treadmill can in fact prevent the airplane from accelerating, but we do not need to discuss it further.

[N Harmon]

We probably still disagree on whether or not the treadmill can in fact prevent the airplane from accelerating, but we do not need to discuss it further.

Nah, who needs to discuss anything on here?   But it is a good refresher for basic physics understanding.

I'm curious how you see the airplane still accelerating.

[AirAux]

The wheels go round and round..They are moving, but only in relationship to the treadmill and not to the ground.  As long as the wheels and treadmill are moving in opposite directions at the same speed, there will be no movement of the AC on the treadmill.  No movement of the AC, no lift..  It is, as was mentioned above, but somehow misconstrued, the same as a person walking on a treadmill.  the person is not moving in relationship to the ground and has no ground speed..  The AC is the same..it has no ground speed, it has no airspeed, it has no lift, it has no way possible to fly..  But, the wheels go round and round..

[ßτε]

The wheels on the bus go round and round.
round and round.
round and round.
The wheels on the bus go round and round,
all through the town!

The people on the bus go up and down.
up and down.
up and down.
The people on the bus go up and down,
all through the town!

The horn on the bus goes beep, beep, beep.
beep, beep beep.
beep, beep, beep.
The horn on the bus goes beep, beep, beep.
all through the town!

The wipers on the bus go swish, swish, swish.
swish, swish, swish.
swish, swish, swish.
The wipers on the bus go swish, swish, swish,
all through the town!

The signals on the bus go blink, blink, blink.
blink, blink, blink.
blink, blink, blink.
The signals on the bus go blink, blink, blink,
all through the town!

The motor on the bus goes zoom, zoom, zoom.
zoom, zoom, zoom.
zoom, zoom, zoom.
The motor on the bus goes zoom, zoom, zoom,
all through the town!

The babies on the bus go waa, waa, waa.
waa, waa, waa.
waa, waa, waa.
The babies on the bus go waa, waa, waa,
all through the town!

The parents on the bus go shh, shh, shh.
shh, shh, shh.
shh, shh, shh.
The parents on the bus go shh, shh, shh,
all through the town!

The mommy on the bus says, I love you.
I love you, I love you
The daddy on the bus says, I love you, too.
All through the town.



For some reason I couldn't resist.