Physics Question for you.....

[Kristofor]

Guys.... Think back to your basic high school physics/mechanics and draw up a force diagram.

Force = Mass x Acceleration (F=MA)

Lets assume the wheels are the famous massless frictionless bearing surface (these come from the same catalog as massless inextensible strings, frictionless blocks, pulleys, and surfaces, etc.)

In our thought experiment the airplane is sitting quietly on the conveyer with nothing moving. Now without turning on the engines, start the treadmill. The wheels will start spining, but plane STILL won't be moving because you have not exerted any lateral force on it F=MA, with no force, you have no acceleration.

In a world (like ours) with friction, the plane will in fact start moving back due to friction on the wheels, but not at the same speed as the treadmill, and the smoother the bearings, the less movement there will be. So, there would be a small force vector pointing toward the back of the plane (a small amount of force in the negative direction).

Now lets look at the props or the jet engine. It's forcing mass (air) toward the back of the plane. Thanks to convervation of momentum and our buddy Newton's laws of motion we know that an equal and opposite force will be pushing the plane forward at whatever amount of thrust the engine generates. So now we have a large amount of thrust (the normal takeoff thrust) in the positive direction.

F=MA if the sum of the small amount of negative force and the large amount of positive force is positive then we have a net positive force and MUST have the airplane accelerating.

Since veloctiy = acceleration * time, and we've just shown that the plane is accellerating its velocity is increasing when it reaches takeoff speed, the plane will in fact take off.

The reason these aren't used on aircraft carriers is because as you just saw above it takes just as long (time and distance) to reach that velocity, the tredmill only serves to put extra mileage on the landing gear.

Kristofor.

[backpacker85]

OK, now that I've changed my mind three times, I'm ready to commit: the plane WILL take off, and it will be in a shorter distance than if on a normal runway.

If you were walking on a treadmill, or driving a car on a conveyor, your motion relative to the air around you would be zero. The conveyor belt/treadmill would in effect be providing a frictionless surface, and no progress would be made (think of running or spinning your wheels on ice). But this only applies where forward motion is dependent upon the friction between the wheels and the ground.

In the case of an airplane (or jet), forward progress is based on the backward thrust from the propeller or engine (equal and opposite reaction) relative to the surrounding air, not the ground. The plane WILL move forward, and because of the conveyor belt (no friction between wheels and ground), the plane will reach takeoff speed in a shorter distance (IMHO).

Please don't make me change my mind again....

[mmgross144]

Wings need thrust

In response to:

"THRUST does NOT make the plane fly! The PURPOSE of Thrust is to get enough speed up so that there is a fast flowing of wind/air OVER the WINGS. It is WIND Speed over the Wings that create lift for flying.

Thrust will not make it "fly" until there is enough airspeed (wind) over the wings.

Think - Generate Lift, Generate Lift, Generate Lift, - then the plane will fly. Generateing lift is what Wings are for. If you think you will fly before you have "180 MPH wind speed" over the wings of a 747 then you will not need wings at all. So take the wings off.

For those who think it would fly once 200 mph treadmill speed is reached are thinking in terms of Star Trek space travel where Thurst is what drives it and wings are not needed."

Of course, but wings without thrust are just nifty sun-shades. Wings cannot lift off by themselves without an outside force, Wind. Wings, properly balanced can glide if given sufficient airspeed to generate lift, but they won't do it from the ground by themselves.

Since the natural winds are hardly controlable, nor convenient to our flight requirements, artificial wind must be generated, BY THRUST, to acheive sufficient airspeed.

OK, sorry to belabor the subject. Have a wonderful holiday season!

[leehljp]

Thurst has NOTHING to do with it FLYING in our earth atmosphere!
Runway/treadmill Speed has NOTHING to do with it FLYING in our earth atmosphere.

Thrust in this case only keeps it in the same place as the treadmill runway moves.

(HINT: Think - What are WINGS for? What is the purpose of wings? Wings lift. Wings need wind speed. Not wheels, not thrust, wind speed!)

THRUST does NOT make the plane fly! The PURPOSE of Thrust is to get enough speed up so that there is a fast flowing of wind/air OVER the WINGS. It is WIND Speed over the Wings that create lift for flying.

Thrust will not make it "fly" until there is enough airspeed (wind) over the wings.

Think - Generate Lift, Generate Lift, Generate Lift, - then the plane will fly. Generateing lift is what Wings are for. If you think you will fly before you have "180 MPH wind speed" over the wings of a 747 then you will not need wings at all. So take the wings off.

For those who think it would fly once 200 mph treadmill speed is reached are thinking in terms of Star Trek space travel where Thurst is what drives it and wings are not needed.

[mmgross144]

Overestimating thrust.

let me explain it one other way for you doubters:
The treadmil examples the feet are coupled by friction to the treadmill.

In the airplane/conveyor its a different problem. The airplane is not coupled to the conveyor at all, except by low, assumed zero friction of the wheel bearings. THerefore when the engines fire, the plane will accelerate w.r.t the air and eventually take off when it reaches sufficient air velocity. The conveyor is completely a red herring. The conveyor, by definition of the problem, must move in an equal and opposite direction to the plane, but it cannot hold the plane back, or motionless w.r.t. the air that supports the airplane's flight.

Loring,
1. An aircrafts thrust builds slowly, unless catapulted (aircraft carrier). As a former jet engine mechanic I used to run up near mach capable jets (A-7's) to full thrust (called "military") while the front landing gear was tethered to the ground by a single cable (yes it was 3 inches thick) and with the wheels chocked. The small landing gear had NO problem handling the strain BECAUSE the thrust was not instantaneous. Pilots do not increase thrust as they travel the runway in order to increase speed, they hit full thrust very quickly and it takes the length of the runway (the larger the aircraft the longer the runway needed) to gain the necessary airspeed to acheive lift...NO LIFT - NO FLIGHT. THis is also why aircraft carriers will wheel around to face into the wind in order to aid in acheiving lift sooner.
2.) The problem states that the aircraft's forward motion is being equally countered by the conveyor belt. If the conditions are as stated, and conveyor belt friction does not disable the mechanism and the aircraft wheels and bearings (though only casting will still build up heat via friction, it would take some amazingly impossible engineering!), the aircraft will NEVER acheive the necessary airspeed for lift-off...in fact it will run out of fuel and roll backwards.
3.) Your statement "airplane is not coupled to the conveyor at all" is in error, as ALL objects on this planet are "coupled" to the planet's surface by gravity, and will remain so until acted upon with sufficient force to defeat gravity.
4.) To settle this definitively, my wife works for Boeing for a senior Vice-President who has a degree in physics/aeronautics and she has agreed to present this question to him. I will post his answer. Now, don't we all have Christmas/Hannakah(spelling?) presents to either make or buy?

[LCHIEN]

let me explain it one other way for you doubters:
The treadmil examples the feet are coupled by friction to the treadmill.

In the airplane/conveyor its a different problem. The airplane is not coupled to the conveyor at all, except by low, assumed zero friction of the wheel bearings. THerefore when the engines fire, the plane will accelerate w.r.t the air and eventually take off when it reaches sufficient air velocity. The conveyor is completely a red herring. The conveyor, by definition of the problem, must move in an equal and opposite direction to the plane, but it cannot hold the plane back, or motionless w.r.t. the air that supports the airplane's flight.

[Stytooner]

What is it about equal speed in the opposite direction that is confusing?
The experiment is exactly like a tread mill. When you try to run faster and faster forward, the conveyer runs just as fast the other way to effectively keep you stationary with absolutely no wind in your hair. Why do you guys still imply that the plane keeps on moving forward. Its stated in the beginning that its forward speed is negated by the conveyor. It really ain't going anywhere.

[niki]

I just copied the question to have it in front of me

"A plane is standing on runway that can move (some sort of band conveyer).

The plane moves in one direction, while the conveyer moves in the opposite direction.

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 opposite direction)."


Let's make an experiment.
Instead of the airplane put your car on the conveyer and just for the experiment lets stick a pole near by. Take your hand out of the window and hold the pole.

Now, "step on it", the car will accelerate to 100mph, but the conveyer will also accelerate to 100mph to the opposite direction at the same time. The relative velocity to the ground and to the air is - zero. your hand will still hold the pole.

Second experiment
Go to the gim and stand on the conveyer and start to walk on it.
Slowly slowly increase the conveyer speed until you run at your maximum running speed.
Are you advancing relatively to the ground? - no, you are running at the same place.
Do you feel any wind on your face (which indicates relative velocity between you and the air)? - I don't think so, you are not advancing relative to the air around you.

niki

[bigfoot]

OK, this is what I get for not reading it all.

I change my answer, plane DOES take off, due to the fact that thrust is not pushing against the ground (conveyor belt), but rather thrust is pushing against the air. This is an interesting picture to wrap the brain around.

[Tom Miller]

The orignal problem states the plane moves. And that the
conveyor belt moves equal speed in the opposite direction.

Those who say the plane stay motionless w.r.t. the ground are seriously in error.

Yeah, I think Loring's interpretation most closely matches the original problem, after re-reading it. I.e. if the plane is moving 100mph forward, relative to the ground, then the conveyor is only moving 100mph in the opposite direction, not as fast as it takes to keep the plane motionless wrt the ground.

The landing gear moving at 100mph (freewheeling, essentially) will not provide enough force to counter the jet engines, and the plane will continue to pick up speed relative to the ground (and air), until it has enough airspeed to take off.

Regards,
Tom

[LarryG]

Nope, sorry Loring, you're forgetting gravity, and the weight of the plane.

The OP does indeed stipulate that "The plane moves in one direction ..." however I think it is plain that the point of the problem is that the plane is attempting to move in one direction but is being frustrated by the conveyor beneath it which is moving in the opposite direction.

Until the plane's wings are moving fast enough through the air to allow the wings to develop sufficient lift for it to take off, the plane's weight is being supported by the conveyor belt ... and since the conveyor belt is moving backwards, it will carry the plane with it. Since the conveyor belt is able to match whatever speed at which the plane attempts to move forward, it will be like a hamster in a wheel: running mightily but never getting anywhere.

For a (conventional) plane in flight at a steady speed and constant altitude, thrust = drag and lift = weight. If thrust > drag, the plane accelerates, and vice-versa; if lift > weight the plane climbs, and vice-versa. Take-off cannot occur until the amount of lift being generated just slightly exceeds the plane's weight. Until that moment is reached, the plane's weight is being supported by the ground. In this case the ground is moving backwards, and it will ... it must ... carry the plane along with it. This defeats the wings' attempt to generate lift. And with no lift, no flight.

[LCHIEN]

All you who say there is no air speed are seriously miscontruing the situation. The orignal problem states the plane moves. And that the
conveyor belt moves equal speed in the opposite direction.

Those who say the plane stay motionless w.r.t. the ground are seriously in error.
The whole problem is relative motion.
As one person said, put a stake in the ground. THe plane moves away from the stake due to the thrust of its engines against air. The conveyor belt moves in the opposite direction relative to the stake because that's the behavior the problems states. They're both moving V but the vectors are 180° out. The wheels will roll twice as far as normal.
Plane takes off, period.

[Stytooner]

No air passing under and over the WINGS, no flight. This statement is true of winged aircraft. Not true of missles and Harrier type jets. They overcome with shear thrust. All they have to overtake is gravity. Winged craft need airflow under and over the wings, not merely through the engines.
Jump jets and copters are different. They both have elements that rotate to direct the airflow once gravity is overcome, to forward motion, thus creating airflow under and over the wings.
Consider a common towed glider plane. If it were hooked up to the aircraft in discussion, it would never move. They keep these anchored down when parked because a simple wind gust can pick them up. If there is no wind, a plane would NOT fly under the given scenario.

[bigfoot]

Lacking time to read the whole thread, I am surely repeating an already posted answer, but, here goes anyway.

Plane never leaves the ground.

Land speed is more than high enough
AIR SPEED = 0

no lift=no fly

[LarryG]

The force that's countering the jet engines is mostly the friction force in the bearings of the landing gear.

No -- there's also gravity; the weight of the plane. What you say would only be true, I think, if the plane's weight were being supported by something other than the conveyor belt. Take-off cannot occur until the amount of lift being produced is sufficient to support the plane's weight. As long as the plane's wings are stationary relative to the air, no lift is being produced, and the full weight of the plane is being supported by the conveyor. That would provide considerably more friction than the wheel bearings alone.

Also, the instant the wings begin to move forward through the air, drag is being produced. Drag will slow the plane's rate of acceleration, and the conveyor's speed-tracking mechanism could reduce its setting accordingly.