Originally posted by Chris Ritchey: I admit I didn't read all 52 pages, just 15, so maybe it was mentioned in the remaining pages, but I just want to add a few things.
[b]Definitions
wind speed: speed of the air relative to the plane, 100mph wind speed means the wind is moving 100mph across the wings.
Global Perspective: This is the perspective being observed from the outside world, an example would be some one not standing on the tread mill watching the plane try to take off
Scenario perspective: Perspective from the plane, relative to the treadmill
Relative speed: speed of the treadmill as observed from the Scenario perspective, aka the plane
Absolute speed: speed of the treadmill as observed from the Global perspective.
Assumptions
conveyor belt only moves the ground below the plane, not the air around the plane, and moves in the opposite direction the plane is trying to move.
weather is ideal and wind is calm (0MPH).
group speed = air speed since the plane is on the ground.
wheels are freewheeling, ie there is little if any rotational friction between the wheel and the object it is attached to.
plane would be able to take off if the tread mill was kept stationary.
Facts
lift if determined by the wind speed over the wings.
Thrust produced by the engines (prop or turbine) applies a force against the air.
Thrust is dependent on wind speed, the higher the wind speed the lower the thrust, and vice versa.
Force from the thrusters is what propels the plane and not the wheels.
air is a fluid
ProofThe tread mill doesn't effect the speed of the wind:Lets just say for the sake of argument that the tread mill does move the air around the plane at the same rate as the treadmill. If the plane is trying to go down the run way and is stationary from the global perspective the the wind will increase in speed as it passes over the wings. This equivalent wind speed will cause enough lift for the plane to take off, this scenario is essentially the same as if it was going down a normal run way. So we know that the tread mill does not effect the planes air speed because if it did it would be able to lift off.
If we look at a force diagram, the engines produces thrust forward by "throwing" air backwards and pushes against the air already present which produces a force pointing in the forward direction, this is because of newtons third law, equal and opposite reaction. So a force backwards produces a force forwards. The ONLY way for the plane to stand still from the global perspective is to have another force applied to the plane that would counter act this forward force, other wise the plane will move forward since F=ma (Force = mass X acceleration). Here are some possible options that could produce the required force to prevent:
Air resistance, which is determiend by surface area and wind speed
Excessive friction between the plane and the ground, for example Wheel Brakes are applied, or wheels are not present wheels.
Plane is chained to a solid anchor
As seen by the fact that a high enough wind speed would creates lift and allow the plane to take off we can rule out wind, as enough wind the keep the plane stationary would surely allow it to take off.
Now if we make the assumption that the plane would be able to take off if the treadmill is kept still like a normal run way we can safely assume that plane has little resistance relative to the force generated by the thrusters. And that there is nothing nothing else binding the plane such as it being anchored. So we are safe to assume the airplane is not held by any external constraints.
Plus we know the wheel brakes are not applied because otherwise the plane would not be able to move anyways and the question is a trick question
So without any kind of constraints it is impossible for a plane to not move from a global perspective when it is at full throttle because there is no resistance to the forward force and because thrust and wind speed are inversely proportional therefor there will be a force acting on the plane moving it forward increasing the wind speed over the wing allowing for take off.
... In summary The planes method of propulsion acts on the global perspective and not on the relative perspective allowing it to move in the global perspective as well, even if the wind was acted form a relative perspective it would be able to take off since it would have a high enough wind speed.
so yeah, the plane can take off regardless...[/b]
Quote:
Originally posted by porsche996: The plane takes off in approximately the same distance necessary on a conveyor belt as it does on a regular runway.
Since Blue-Sky is mentioning his 20 years "aviation" experience, I guess I'll throw mine into the hat, even though it too has no bearing on the problem... I'm an airport designer. Civil Engineer. I design Runways, Taxiways, Aprons, and all things associated except the electrical & navigational equipment. I've been doing this for 6 years, now.
I assure you, the friction of the wheel bearings does not matter to the plane taking off. How's that? Because different surfaces have different coefficients of friction already. Asphalt runways have different coeff. than concrete. Significantly different on paper; absolutely no difference in the real world. Why's that? Because both numbers are so small in relationship to the take-off thrust of any aircraft that it doesn't matter.
[b]READ BELOW COMPLETELY FOR AS SIMPLE AN EXPLANATION AS YOU CAN GET ON WHY THE AIRPLANE WILL TAKE OFF
An aircraft's engine PUSHES (jet) / PULLS (prop) the aircraft along the ground. This results in a horizontal force on the axles of the aircarft because they are fixed rigidly to the aircraft. The by-product of this force is it causes ROTATION of the tires around the axles. The tires do nothing more than rotate around the axle; they do not cause any horizontal movement.
If a conveyor belt were under the tires, it too would cause rotation of the tires around the axles. But, it can not cause any movement and/or restriction of movement of the axles, as the tires do nothing but free-spin around them. Again, the conveyor belt spins the tires, but does not exert any horizontal force on the axle. You can test this "theory" by jacking up your truck (get a whole axle up in the air), and spinning a free-wheeled tire from below. The tire will spin, but the truck will NOT move. This is not because you aren't spinning the tire fast enough; spin it as fast as you want, and the truck still will not move. The truck can't move, because all the force you apply goes into spinning the tire; none of it is a horizontal force on the axle.
Summing the forces in the horizontal direction gives you a positive force from the engines, and 0 negative force, as the conveyor belt can not move the axles of the plane regardless of how fast it spins.
From Newton, Force = Mass x Acceleration. So divide the sum of the Forces (the engine force only as shown in the above paragraph) and divide by the Mass of the plane. What you get is the Acceleration of the aircraft. The friction is negligable, as it is an extremely small number compared to the Force.
The net result is the aircraft accelerates down the runway, and eventually obtains flight once there's enough lift provided by the air passing over the wings.
END EXPLANATION
And, it will reach its takeoff speed at the same distance down the runway as it would without the conveyor belt. The additional friction of the tires as they spin twice as fast is not enough to make a significant difference. Dynamic friction levels off at a certain point, and for all practical purposes remains a constant level whether the tire spins at 150 mph or 300 mph.
Editorial Comments...: While this is a physics, it's also a Statics & Dynamics problem. A problem like this would be taught in a 200 level Engineering Dynamics course, and any Engineer that can't answer it with only a fleeting glance ought to take some continuing education classes in a hurry...[/b]
Quote:
Originally posted by JeffW: Relevant information:
A plane is standing on a runway that can move (like a giant conveyor belt). This conveyor has a control system that tracks the plane's speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction).
Will the plane be able to take off?
Let's agree on what assumptions are sensible then. All of the assumptions below apply to virtually all aircraft.
Plane is powered by engines that push air (props or jets) Plane's speed is measured by a windspeed meter as well as GPS Plane's wheels spin freely Wheel friction is negligible when compared to thrust Newtonian physics apply
Coefficient of dynamic friction:
Force of friction:
F(f) = -uN
(negative because it opposes motion)
u = coefficient of static friction
N = weight of plane
Notice velocity is not included!
That means that the velocity of the conveyor belt is irrelevant for all practical purposes.
F(t) is force of thrust
a = (F(t)+F(f))/m
You won't find a scenario where |F(f)| is greater than |F(t)|. Therefore, in ALL cases the plane moves with respect to the atmosphere, thus achieving lift.
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