So...about that plane on the treadmill...

"John T" wrote in message
...
"Darkwing" theducksmail"AT"yahoo.com wrote in message


This has NOT been adequately explained or there
would be no question about it. If the plane is not moving on the
treadmill but rather keeping up with the speed that the treadmill is
moving (yes planes DO have throttle controls) the thing is going to
takeoff with no air moving over the wings? NO WAY.

Assuming you're a pilot, I don't understand why you think no air would be
moving over the wings, but I'll give this one good "college try"...


Yes I am a pilot.


First, the question posed in the link by the OP of this thread is an
incorrect variation of the original. The original problem asks: "A plane
is standing on a giant treadmill. The plane moves in one direction, while
the treadmill moves in the opposite direction and at the same speed as the
plane. Can the plane take off?"

As has been explained, placing a car on the question's treadmill would
result in a stationary vehicle relative to the observer standing beside
the treadmill. The reason is the car derives its propulsion through the
wheels sitting on the treadmill and the speed of the car is measured by
how fast the wheels are turning. The faster the wheels turn, the "faster"
the car moves. However, this is only relative to the treadmill belt. To
the observer standing beside the treadmill, the car is motionless. If the
driver placed his hand out the window, he would feel no wind even though
his "speed" as indicated by the speedometer may be 100 miles per hour.

This is very similar to your example of running on the treadmill. You did
not feel a relative wind in your face because you were stationary relative
to the observer standing beside the treadmill. The reason you were
stationary is you generate your propulsion by moving your feet against the
ground (or belt, in this case) and the belt is moving in the opposite
direction and same speed of your "travel". Like the car, your speed is
measured by how fast your feet move from front to rear and they match the
speed of the belt to cancel out each other.

Now, replace the car and runner with an airplane. The airplane derives its
propulsion from its engine pushing air from front to back. None of this
energy is sent to the wheels to propel the airplane. The speed of the
airplane is measured by the flow of air past the airplane, not the turning
of its wheels. As the airplane's engine spools up to takeoff power, air is
forced from front to rear and the plane moves forward regardless how fast
its wheels are turning. The observer standing beside the treadmill would
notice the treadmill speed up, the airplane's wheels turn twice as fast as
normal, and the airplane move forward (not stationary).

Speed is relative and the key here is the means of propulsion. The
airplane's speed is measured by how fast the air is moving past it, not by
how fast its wheels are turning or how fast the ground is flashing by.
None of the airplane engine's energy is transmitted to the wheels to
generate speed. All of the airplane's propulsion is derived from moving
air (otherwise it would never stay in the air after takeoff). Since the
treadmill has very little effect on the air (and what little effect it
does have actually helps the airplane generate more lift), the airplane
will indeed takeoff in the same distance it normally would use without the
treadmill. However, the airplane wheels would be turning at twice their
normal speed at the time of takeoff.


Try this experiment:

Take a toy car and attach it to a string. Tie the other end of the string
to a small spring scale. Place the car on the treadmill belt and hold the
scale in front of the car while you turn on the treadmill. Observe nearly
zero (essentially 1G) force being exerted on the string/scale. Speed up
the treadmill (for simplicity, let's say you set it to a constant 10mph)
and you'll observe no significant difference in force exerted on the
string (the only additional force is the friction of the car's axles). Now
gently pull the string/scale forward. As long as you maintain a 1G force
on the string, the car will continue to accelerate.

Now, to the observer standing beside the treadmill, was the car stationary
or moving forward? It's speed was certainly not zero as the car most
definitely moved from rear to front of the belt. What was the speed of the
car relative to the "driver" sitting inside the toy? The wheels would be
turning faster than 10mph. If the "driver" were to put his hand out the
window, how fast would the air be moving? Much slower than his wheels
would say he's moving, but faster than the driver I mentioned at the
beginning of this post.

Replace the toy with the mythical airplane above, replace your arm with
the airplane's engine (and propeller, if appropriate), then replace the
string with the airplane engine mounts. You should now be able to
visualize why the airplane sitting on that giant treadmill would most
definitely takeoff.

If not, I wish you good luck and safe flight. You'll need it.

--
John T


Thank you for your reply. Here is my .02, it would seem that the plane never
actually moves in respect to the observer no matter how fast the treadmill
moves, the plane will just take off like it is hovering and then slowly
accelerate away?

I guess I'll have to set this up and try it, I do have a few RC planes
laying around and I have a treadmill so I guess I'll know one way or
another, unless Mythbusters beats me to the punch.

-------------------------------------------------------
DW