I just skimmed through all 7 pages of this thread to take the intellectual pulse, so to speak. I've seen a lot of arguments with a lot of concepts and rationalization used in an attempt to support them. I've seen a lot of stupidity, too. But what I
haven't see is any real analysis of the problem.
What would a physicist do?
The first thing he'd do is draw a free body diagram and label the forces acting on the plane.
I'm not going to draw a free-body diagram, but I will use the picture below as a substitution:
The forces acting on the plane, in the horizontal (or x) direction are:
T (thrust - positive x direction)
R (rolling friction - negative x direction)
D (drag - negative x direction)
The TOTAL force is given by summing these up:
F=T-R-D
Everybody knows that F=ma, so we can calculate the acceleration of the plane:
F=ma=T-R-D
a=(T-R-D)/m
The acceleration of a plane is pretty high, therefore we can conclude that T is much much greater than R and D.
Now a quick word about rolling friction:
A spinning tire has rolling friction, due to the bearings, air, etc... This friction is constant. So a tire spinning at 10 rpm has the same amount of friction as a tire spinning at 100 rpm, or 1000 rpm. But the diagram shows that rolling friction
decreases as the plane's velocity increases. How can this be? This is because friction is a function of force, or weight. As the plane picks up speed, lift is generated due to the wings, the force due to weight reduces, and so does the friction.
Now if you consider a plane sitting on a treadmill. The brakes are off and the engines are off. The plane is free to roll in the +/- x direction.
If you turn the treadmill on such that it's surface is moving in the -x direction and speed it to 100 mph, what happens to the plane? What forces are acting on it?
The only force acting on it is rolling friction. The plane will begin to accelerate in the -x direction at a rate given by the amount of friction. And we know that the rolling friction is pretty small. So the plane will not instantly move at 100 mph in the -x direction. It will slowly accelerate to 100 mph in the -x direction. And when I say "slowly", I mean
slowly. Rolling friction is approximately equivalent to a coefficient of 0.003. At that rate of acceleration, it would take approximately 25 minutes to "catch up" to the speed of the treadmill of 100 mph.
However, since rolling friction is constant, this is the same acceleration working against the plane during a normal runway takeoff.
So let's now look at the forces acting on a plane under the treadmill scenario, where the treadmill matches the speed of the plane.
The forces are:
T (thrust - positive x direction)
R (rolling friction - negative x direction)
D (drag - negative x direction)
The TOTAL force is given by summing these up:
F=T-R-D
the acceleration of the plane on the treadmill is found by:
F=ma=T-R-D
a=(T-R-D)/m
Are any of these forces different from the runway condition?
Thrust from the engines T is the same, regardless of runway or treadmill.
Rolling friction R is the same, regardless of runway of treadmill.
Drag D is the same, regardless of runway or treadmill.
So a plane will take off from a treadmill just the same as it would take off on a runway. Therefore,
The treadmill is irrelevant
The treadmill is irrelevant
The treadmill is irrelevant
The treadmill is irrelevant
The treadmill is irrelevant
The treadmill is irrelevant
The treadmill is irrelevant
Well while u guys bicker over this tredmill thing I am going to sand the paint off the 82 regal limited body (now on sawhorses all gutted out :biggrin:
