Will it Fly??

The airplane will not fly.  While on the ground, the propeller has to overcome the rolling resistance of the wheels on the ground, and the acceleration of the treadmill insures that the airplane never moves forward. 

Approach the problem this way: The aircraft is stopped as is the treadmill.  Start the treadmill running, and the airplane moves backward.  Turn the propeller just fast enough to stop the backward motion and the aircraft is now stationary.  Repeat and the aircraft will not move from it's original location, and never attain any airspeed.

However if the treadmill is moving that fast then it's going to be "sucking air" along it and the plain will indeed take off

Plane One, Treadmill zero

Carson,

The belt is the runway - 3000feet. Somewhere along the belt the plane will lift and gain altitude.

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Let me propose a challenge. We'll set up a plane on the treadmill as per your original post, rev it up, wind it up, blow it out .... at the end of your 3000' pseudo runway (about 1 foot in front of the treadmill), you stand on the ground and I'll be suspended across the runway from a wire about 12' off the ground (takes into account the maximum height of the propeller and how far down my legs reach). Then we'll see who becomes tomorrow's hamburger! ;D

Chet18013 said:

Here's one for you to think about.

Let's say you have a single engine airplane sitting on a runway that is 3000 feet long, and through some great engineering the runway is actually a giant treadmill. It's engineered so that when the plane starts to move forward the runway moves in the opposite direction at exactly the same speed., i.e. as the airplane's wheels pick up speed the runway matches it.
Will the plane get airborne?

What do you think?

Chet18013

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Perhaps it is just a poorly worded problem, but IMO, as you've worded the problem here -- yes, the plane would normally get airborne.  

To me, you are saying that if the plane is moving at 20, 40, 60 mph in the forward direction relative to ground, then the runway is moving at 20, 40, 60 mph in the rearward direction relative to ground.  (That is, the plane MUST be moving in the forward direction in order for the treadmill to be moving in the rearward direction, according to your statement.)  

The runway is passing under the plane at a relative speed of 40, 80, 120 mph, but the plane's wings are moving through the air at 20, 40, 60 mph and when they get to normal takeoff speed, the plane will lift.  [Ground-layer effect of the moving runway is not included, but it might actually enable the plane to lift sooner since it would create a small artificial headwind.]  The increased drag on the landing gear of the tires/bearings having to rotate at twice normal speed should be relatively small compared to the normal aerodynamic drag forces at work.  

Sorry, Frank, but no.  If you're on a treadmill, you don't feel any air moving past you, and neither would the airplane.  Ergo, no lift.  Get on a treadmill, get running at a comfortable speed and stick your hands out and see if you feel any air pressure.

I think Frank nailed it correctly.  The treadmill is moving backward in relation to the plane but not to the adjacent landscape.  The plane accelerates normally and takes off.

Sorry guys, if I have to pick a pilot it's going to be Ned, if the belt is moving backwards at the same speed as the airplane is accelerating there will be no relative movement of the AC, therefore no lift and "it ain't gonna fly" Been flying for 42 years and never used a treadmill yet, just trusted in Bernoulli

Ned said:

Sorry, Frank, but no.  If you're on a treadmill, you don't feel any air moving past you, and neither would the airplane.  Ergo, no lift.  Get on a treadmill, get running at a comfortable speed and stick your hands out and see if you feel any air pressure.

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Ned, you missed what I was saying.  Please read my post again.  I didn't say the plane was running on the treadmill.  The problem statement says that the treadmill's backward motion is equal to the plane's forward motion.  That is, "B" equals "A".  The plane's forward motion has to be with respect to ground.  The plane is moving foward with respect to ground and air is flowing over the wings.

To say the treadmill has a rearward velocity equal to a plane that is stationary is non-sensical.  That is saying the treadmill has a velocity equal to zero, or at best, equal to its own velocity.  That is "B" equals "B" -- a trivial statement.

I think we can agree on this --
Let's set aside the poorly worded problem statement and look at it from a real-world engineering force-balance perspective.  The pilot releases the brakes and gives the engine full takeoff throttle.  The prop gets up to full speed, forcing air backwards.  The forces on the plane are forward thrust from the prop which is resisted by the inertia of the plane and vertical load from gravity which is resisted by vertical load on the tires at the ground.  The plane moves forward with respect to a fixed ground reference system.  Air starts to flow over the wings.  Lift starts to build, relieving the weight on the tires.

At that point it is a secondary matter whether the plane is on a treadmill or not.  Go ahead and turn on the treadmill.  As long as the thrust from the prop is greater than the rolling friction of the tires on the ground, there is a net forward load component accelerating the plane forward with respect to fixed ground reference.  In a normal plane, the ratio of available forward thrust to rolling friction is very high, so whether the treadmill is moving or not will make little difference in the plane achieving enough forward velocity to lift off.

Frank, you're correct.  After a few late night thought experiments , I have reversed myself.  The wheels on an airplane are not driven, and the only resistance they offer to the forward movement of the airplane is minimal, an airplane can taxi at idle power.  So what the wheels do is irrelevant to the forward motion of the airplane, it's being pulled through the air by the propeller and not driven along the runway.  The airplane will fly after a normal takeoff run.

My previous answer was after an evening of food and drink with the neighbors, and that's my excuse

KodiakRV said:

The problem statement says that the treadmill's backward motion is equal to the plane's forward motion.  That is, "B" equals "A".  The plane's forward motion has to be with respect to ground.  The plane is moving foward with respect to ground and air is flowing over the wings.

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As a retired Navy pilot with carrier landings and retired air line pilot I will say this.  This bird won't fly.  Why do you think aircraft carriers turn INTO the wind before launching aircraft.  It's to get more wind flowing over the wings.  If they turned downwind, there would be a lot less landings than takeoffs and they would soon run out of aircraft.   ;D Same principle as your treadmill.

Don

Don, even if the carrier was turned downwind, if there was enough deck the planes would fly.

Another thought...

"It's engineered so that when the plane starts to move forward the runway moves in the opposite direction at exactly the same speed."

Based on the precise wording of the original premise, when the plane moves forward at 5 mph, the runway is moving back at 5 mph, the relative speed is ten mph.  If the plane takes off at 50 mph, the relative speed is only 100 mph.  That is certainly doable.  The plane will fly.
Art

I don't think the guy on a treadmill analogy applies. The guy running on the treadmill is relying on the friction of his feet against the treadmill to propel him forward, so his feet slide back during the very act of forward movement. Net forward motion is zero if the treadmill moves fast enough.

As has already been stated, the plane does not rely on ground friction - the airscrew (propeller) moves it forward . It will move down this theoretical moving runway regardless of the rearward movement of the surface. As far as I can see, the only thing the moving runway does is make the wheels turn faster - it won't stop the plane from moving forward and gaining airspeed. If the propeller is strong enough, it will achieve air speed and lift off..

I think the treadmill runway never moves relative to the landscape around it, it only moves relative to the wheels of the airplane.  Therefore it is a normal takeoff.

Don, even if the carrier was turned downwind, if there was enough deck the planes would fly.

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Yes, but the carrier is still moving in the direction of take-off, not backwards like the treadmill.

Karl said:

Yes, but the carrier is still moving in the direction of take-off, not backwards like the treadmill.

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The only thing that counts is AIRSPEED and in the proper direction.  A treadmill IS like an aircraft carrier going downwind because the the air moving over the wings is going from rear to front.

The original question stated that the treadmill would increase in speed to match the speed of the wheels so would the airplane get airborne.  The answer still is NO because their is no airspeed because you are standing still.  Airplanes need airspeed to get airborne.  You don't need wheel speed.  In fact, wheel speed is a LIMITING parameter at high altitude airports.  You can exceed the tire rotation speed before you get the required airspeed to fly.  The other side of the coin is I can get an airplane airborne with no propeller providing power.  Give me a strong enough head wind, the airplane will fly.  Just check out airports after a hurricane.

Some in this discussion have changed the parameters of the issue.  That changes everything.  As Tim the Toolman Taylor used to say, power is everything.  Give me enough power and I can get anything to fly.

Don

The original question stated that the treadmill would increase in speed to match the speed of the wheels so would the airplane get airborne.  The answer still is NO because their is no airspeed because you are standing still

Some in this discussion have changed the parameters of the issue.  That changes everything.

If we stick to the original premise!

Amen Don

I think we should run a POLL, and/or

have a place to place bets (with big bucks)

carson FL

My $1 is on Don, the experienced pilot. His education, training and experience sure beat a WAG, SWAG or anything else I've read.

As for my own aviation experience, the only way I could get my folded paper planes to fly was to hurl them in a direction that created airflow over the wings. Somehow they refused to take off when I held them stationary on a calm day 

I'll raise you to $1...million. I'll go with Art (aka KING).

carson FL