Plane on a Treadmill

[FlyTiger77]

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..

Again, I beg to differ. About the only thing in common a person walking on a treadmill has with the original question is that a treadmill is present in both.

In order to move forward by walking, your feet, aided by friction, push against the ground to generate motive power. This is why walking on a nearly frictionless ice surface is so difficult. However, an airplane generates motive force by moving a column of air generally independent of the ground.

Although still imperfect, a better analogy would be to have the person on the treadmill reach forward on the hand rails and pull himself forward while dragging his feet lightly on the treadmill. In this case, the person's arms will replicate the action of the propeller and the hand rails will stand in for the surrounding air mass, both of which are unaffected by either the action of the treadmill or his lightly dragging feet. This person will move forward, both relative to the treadmill and, most importantly, relative to the ground.

The notion that an airplane needs its wheels to act against the ground to produce forward motion can be seen to be false by the fact that, if an airplane is in a steady-state flying condition at an altitude greater than 0' AGL (straight and level and constant airspeed in a still air mass of consistent temperature) and the throttle is advanced, the aircraft will accelerate without any interaction with ground. This same fact can be seen by watching ski planes and float planes accelerate and take off from the surface where the landing gear can only provide support for the weight of the aircraft prior to the wings taking the weight.

In my mind the only question is whether or not the aircraft will be stationary relative to the treadmill or moving at 2 times the flying speed when the airplane takes off, and that answer is wholly dependent on how you interpret the arguably ambiguous wording of the original poster's proposal. In both cases, the airplane will be accelerating relative to the earth (to include the airmass) and reach a speed sufficient to sustain flight, assuming it could fly if the treadmill were not present.

v/r

[lordmonar]

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 disagree that the treadmill will produce enough rolling resistance to counter the thrust.

[NIN]

This reminds me of a discussion we had many, many years ago on the USENET group rec.skydiving about spotting, exit order and separation for skydivers jumping from an aircraft in flight.  The two basic camps were "ground speed matters more than airspeed" and "airspeed is key, ground speed is not" and there was tons of handwaving around the descriptions of the subjects and conditions.   (Very similar to what I've read here so far, BTW) 

The entire idea was to find the most effective and safe solution that would naturally and logically deconflict differing groups of jumpers (both in terms of size and fall rate) such that there was sufficient horizontal separation and also induced time and vertical separation that was helpful versus harmful to the overall equation.  Nobody liked the idea of tracking off a skydive to find someone from the previous group deploying in your face, or having someone from a following group come burning thru yours at breakoff...  usually results in what NASA commonly understates as a "bad day."

There was always this "well, the wind at 12,000 ft is this, and the airspeed of the plane is this, so it makes the ground speed this, but the wind at 8,000 ft is this.." and then there would be wildly divergent offshoots talking about ground speed versus airspeed, the jumper's forward throw after exit, the effect of body position on terminal velocity, the tendency for freeflyers to carve around the sky rather than describe a substantially vertical path, a column of air moving at xspeed, etc, etc. 

Someone would always say "Imagine that you're jumping from a balloon tethered to the ground and the wind doing y knots..."  and all these hypotheticals and variables.  One description, as I recall, using the balloon and wind analogy involved "hooking the DZ up to a tractor and dragging it along the earth.." to simulate ground speed.   Thereafter, every time this would come up again, I'd always say "I'm not getting into this again, I just volunteer to drive the tractor."

Finally, two kind gents named Winsor Naugler and John Kallend got together and did a couple presentations at the World Freefall Convention in Qunicy, IL on the subject and John, being a PhD in something, really put together a number of cool simulations to graphically explain the whole thing.  Finally, everybody "got" what was being posited and several years of heated discussions sort of evaporated.   Maybe someone smart/skilled can do the same here?

BTW, you can check out John Kallend's trajectory simulations right here: http://mypages.iit.edu/~kallend/skydive/

[davidsinn]

This reminds me of a discussion we had many, many years ago on the USENET group rec.skydiving about spotting, exit order and separation for skydivers jumping from an aircraft in flight.  The two basic camps were "ground speed matters more than airspeed" and "airspeed is key, ground speed is not" and there was tons of handwaving around the descriptions of the subjects and conditions.   (Very similar to what I've read here so far, BTW) 

The entire idea was to find the most effective and safe solution that would naturally and logically deconflict differing groups of jumpers (both in terms of size and fall rate) such that there was sufficient horizontal separation and also induced time and vertical separation that was helpful versus harmful to the overall equation.  Nobody liked the idea of tracking off a skydive to find someone from the previous group deploying in your face, or having someone from a following group come burning thru yours at breakoff...  usually results in what NASA commonly understates as a "bad day."

There was always this "well, the wind at 12,000 ft is this, and the airspeed of the plane is this, so it makes the ground speed this, but the wind at 8,000 ft is this.." and then there would be wildly divergent offshoots talking about ground speed versus airspeed, the jumper's forward throw after exit, the effect of body position on terminal velocity, the tendency for freeflyers to carve around the sky rather than describe a substantially vertical path, a column of air moving at xspeed, etc, etc. 

Someone would always say "Imagine that you're jumping from a balloon tethered to the ground and the wind doing y knots..."  and all these hypotheticals and variables.  One description, as I recall, using the balloon and wind analogy involved "hooking the DZ up to a tractor and dragging it along the earth.." to simulate ground speed.   Thereafter, every time this would come up again, I'd always say "I'm not getting into this again, I just volunteer to drive the tractor."

Finally, two kind gents named Winsor Naugler and John Kallend got together and did a couple presentations at the World Freefall Convention in Qunicy, IL on the subject and John, being a PhD in something, really put together a number of cool simulations to graphically explain the whole thing.  Finally, everybody "got" what was being posited and several years of heated discussions sort of evaporated.   Maybe someone smart/skilled can do the same here?

BTW, you can check out John Kallend's trajectory simulations right here: http://mypages.iit.edu/~kallend/skydive/

I already did pictures. What more can we do? I'll do equations next I guess.

[NIN]

I already did pictures. What more can we do? I'll do equations next I guess.

My bad. I read pages 1, 11 & 12.  All that middle stuff? "Too long, did not read."

[davidsinn]

I already did pictures. What more can we do? I'll do equations next I guess.

My bad. I read pages 1, 11 & 12.  All that middle stuff? "Too long, did not read."

Back at post #147 It kind of feels like an argument with moon landing deniers.

[CadetProgramGuy]

Guess I will have to go get a model airplane and a treadmill.....

My point is somehow getting complicated.  I agree if the wheels on the airplane were not in motion, the treadmill would pull the aircraft backwards.

I also agree that to keep the wheels of the aircraft moving at 60kts IAS, without the treadmill, the airplane will have to move forward.

Now if the treadmill was moving at 60kts, IAS, and the airplane was matching the 60kts IAS under power, the aircraft is not moving forward, or the ground speed is 0, and the airspeed indicator reading through the pitot tube would also be 0, would it not?

I realize and agree with the premise that the airplane would have to be moving forward to counteract the treadmill, but if equal speeds are present, then you are on a highway to nowhere.

[lordmonar]

Guess I will have to go get a model airplane and a treadmill.....

My point is somehow getting complicated.  I agree if the wheels on the airplane were not in motion, the treadmill would pull the aircraft backwards.

I also agree that to keep the wheels of the aircraft moving at 60kts IAS, without the treadmill, the airplane will have to move forward.

Now if the treadmill was moving at 60kts, IAS, and the airplane was matching the 60kts IAS under power, the aircraft is not moving forward, or the ground speed is 0, and the airspeed indicator reading through the pitot tube would also be 0, would it not?

I realize and agree with the premise that the airplane would have to be moving forward to counteract the treadmill, but if equal speeds are present, then you are on a highway to nowhere.

No....you are supposing that the treadmill is pulling back at some rate that would resist the thrust of the propeller at an RPM that should be propelling the aircraft at 60 Kts.

This is possible.....but not within the parameters set by the original premis.

Here is why.

The plane's throttle is set at say 2000 RPM....enough that it normally would give you 60 Kts IAS in still winds on an asphalt runway.

If the treadmill was only going 60 Kts it would not induce enough drag to stop the aircraft.

Here is the proof.

If the treadmill was stationary and the plane accellerated to 60 kts there is NOT ENOUGH DRAG to stop the aircraft.

So....the treadmill MUST move at a significantly higher speed....much higher then the top speed of the aircraft.

So.....it is possible to build a machine to do this.....they are called chocks and breaks  .

So you would have to build a treadmill that moved at a speed high enough that it induced the same amount of resistance as the brakes or chocks do.....and that speed would have to be very high....not the "same speed as the wheels" that the original premise stipulates.

[Al Sayre]

Guess I will have to go get a model airplane and a treadmill.....

My point is somehow getting complicated.  I agree if the wheels on the airplane were not in motion, the treadmill would pull the aircraft backwards.

I also agree that to keep the wheels of the aircraft moving at 60kts IAS, without the treadmill, the airplane will have to move forward.

Now if the treadmill was moving at 60kts, IAS, and the airplane was matching the 60kts IAS under power, the aircraft is not moving forward, or the ground speed is 0, and the airspeed indicator reading through the pitot tube would also be 0, would it not?

I realize and agree with the premise that the airplane would have to be moving forward to counteract the treadmill, but if equal speeds are present, then you are on a highway to nowhere.

Using your 60 Kts treadmill speed:

If the wheels are moving in contact with the treadmill BUT the aircraft has no forward motion relative to the earth then:

     The wheels are moving at 60 kts rotational velocity (Vww), 0kts ground velocity(Vg), and 0 kts
          Indicated Air Speed(IAS). 
     The aircraft wing is moving at 0 + Vv (Wind Velocity vector * calibration factor) Calibrated Air Speed   
     The treadmill is moving at -60kts Vwt and 0kts Vg

If the wheels are in contact with the treadmill, AND the aircraft has motion relative to the earth, then:

     The wheels are moving at (60+X) Kts Vww  and X kts Vg.  Where X=Vectoral Sum of Vv + Calibrated Air Speed (CAS). 
     The aircraft wing is moving at X Vg and CAS
     The treadmill is moving at -(60+X) Vwt and 0 Vg

When the CAS exceeds Vr (rotation velocity of the wing)  (CAS>Vr) the aircraft will become airborne.


The point of all this is that Vwt and CAS are independent variables and the problem cannot be solved with the information given

If the treadmill is moving at 60 Kts IAS, it is airborne attached to the aircraft, hence Vwt and Vww are moot since the aircraft is airborne.