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

"Richard Riley" wrote in message
...
On Mon, 11 Dec 2006 21:27:16 -0500, "Morgans"
wrote:


"Ray" wrote in message
...
Looks like airplane treadmill problem, regularly a spark for flame wars
on
R.A.P., has made it into the mainstream.

http://pogue.blogs.nytimes.com/

Let the arguing begin!

It is truly amazing how many clueless people have commented on the
problem. MX
should go hang out there. He would look like a rocket scientist.

Quite by coincidence, last week I visited a wind tunnel with a
treadmill in it.

http://www.swiftengineering.com/06Ot...Windtunnel.htm

A "rolling road" gets rid of the boundry layer, and better simulates
what a race car will see on the track.

There was a lot of talk 30+ years ago about what a nice thing this would be;
mainly to test the effectiveness of anti-lift devices for sports car racing.

Peter

Darkwing wrote:



Nope the plane won't take off.


You'd better not just be trolling...

Friction generated by wheels is almost negligible. Even for very large aircraft like a
747, wheel friction is nearly constant, regardless of speed (at least at sane speeds). It
only depends on the amount of force pushing down on the wheel.

So let's look at all of the forces acting on this airplane. In the horizontal direction,
we have:
Thrust from the engine (nearly constant at these speeds)
Aerodynamic drag (goes up as the square of speed)
Wheel friction (again, nearly constant)

For any object to accelerate in a given direction, the total force acting on it in that
direction must not be equal to zero. For a normal airplane, on a normal runway takeoff,
thrust must obviously be greater than the other two forces, since we see airplanes take
off every day. Even at the moment of takeoff, aerodynamic drag may have increased, but
the airplane still has a fair bit of excess thrust, and (assuming you don't pull up too
steeply) will continue to accelerate.

So now, let's put the plane on the treadmill. Once again, the ONLY forces acting on it
are thrust (which stays the same), drag (which still increases as speed squared, and wheel
friction (which, again, IS CONSTANT! no matter how fast the treadmill runs, until we start
talking about silly cases like 5000mph treadmills). Sticking to sane, airplane-like
speeds for the treadmill (80-160mph or so) We see that, once again, thrust is greater than
the other two. Therefore, the plane MUST accelerate.

I'd like to also point out that I have tried this on an actual treadmill with a small
model airplane. It takes right off, no problem. Now I just need to go fin

Peter Duniho wrote:
"Ray" wrote in message
...
Looks like airplane treadmill problem, regularly a spark for flame wars on
R.A.P., has made it into the mainstream.

http://pogue.blogs.nytimes.com/

And handled with every bit as much intelligence and consideration as we've
seen here. Which is to say, there's no shortage of people convinced that
the airplane won't take off, even though it will.


The problem is that as it is stated, the scenario is not one that could
ever be created with a real treadmill subject to normal engineering
constraints.

Let's imagine that the plane gets started in a slow roll down the
runway at a steady 10 mph relative to the calm air & earth. Now the
treadmill has to speed up to 10 mph, but that makes the plane's tires
start spinning at 20 mph. Therefore the treadmill has to speed up to
20 mph which makes the tires spin at 30 mph, which makes the treadmill
speed up to 40 mph, etc.
Even though the plane is only moving slowly relative to the earth, the
tires and treadmill speeds are in an infinite loop to ever higher
speeds.

As soon as the plane starts moving at all relative to the earth, the
tires and treadmill will start their endless positive feedback loop to
try and reach an infinite speed. If the treadmill has a fast enough
response mechanism to keep up with the increasing tire speed the system
will reach some kind of physical limit before the plane can get any
appreciable speed relative to the air. The tires might explode, the
wheel bearings may fail, the treadmill propulsion system may run out of
power, but you can't satisfy the conditions as stated and have the
plane get up to takeoff speed.

Of course the above is based on a particular interpretation of "speed
of the wheels" i.e. that it is measured based on the speed of rotation
and therefore measures show fast they are rolling on the treadmill
surface. If instead the "speed of the wheels" is measured by seeing
how fast the wheel hub is moving forward relative to the earth then the
above infinite feedback loop doesn't arise and the plane can take off
fairly normally although the wheels will be spinning twice as fast as
normal at takeoff.

But that second interpretation of wheel speed doesn't strike me as
consistent with normal usage - i.e. when a bicyclist is on a stationary
trainer we would normally measure the speed of his rear wheel based on
rotation rate, not say that it's zero since the hub is just spinning
but not moving forward.

Actually the question makes sense, at least to the non-aviation public,
because the normal use of a treadmill suggests the opposite, ie a
person walking on the treadmill remains stationary, yet he burns energy
as if he were walking on solid ground. The same would be true if it
were a car, except it would burn slightly less fuel because of the lack
of wind resistance (same is true for a person walking too, but the wind
resistance is even more negligible for walking).

A better way to pose the airplane question would be " what would
happen if the airplane is landing on a treadmill that is moving in the
opposite direction and speed?"






Peter Duniho wrote:
"Ray" wrote in message
...
Looks like airplane treadmill problem, regularly a spark for flame wars on
R.A.P., has made it into the mainstream.

http://pogue.blogs.nytimes.com/

And handled with every bit as much intelligence and consideration as we've
seen here. Which is to say, there's no shortage of people convinced that
the airplane won't take off, even though it will.

Let the arguing begin!

Why? Haven't you had enough by now?

A better way to pose the airplane question would be " what would
happen if the airplane is landing on a treadmill that is moving in the
opposite direction and speed?"

How about dispensing with the treadmill entirely. What would happen if
the airplane were on a frictionless surface? The wheels couldn't push
on anything, so how would the airplane take off?

Jose
--
"There are 3 secrets to the perfect landing. Unfortunately, nobody knows
what they are." - (mike).
for Email, make the obvious change in the address.

"peter" wrote in message
oups.com...
The problem is that as it is stated, the scenario is not one that could
ever be created with a real treadmill subject to normal engineering
constraints. [...]

You can interpret the question in that way of course. However, the intent
of the "puzzler" is clear, and the fact that it is poorly stated should not
interfere with making a reasonable, good faith effort to address the
intended question.

It's well and good to nitpick about physically impossible situations, but
rest assured if you started doing so in a true interactive situation in
which the person stating the puzzle had the opportunity to restate it, you
would quickly get past the nitpicking and get to the intended question.

It's a waste of time to do the nitpicking in the first place. It's easy
enough to infer what the interesting question really is. And the
interesting question doesn't have the treadmill blowing up.

Pete

"Andrew Sarangan" wrote in message
ps.com...
Actually the question makes sense, at least to the non-aviation public,
because the normal use of a treadmill suggests the opposite, ie a
person walking on the treadmill remains stationary, yet he burns energy
as if he were walking on solid ground.

Who says the question doesn't make sense?

The problem that the people who don't "get it" have is that a typical
treadmill is used in a situation where propulsion is via the interface with
the ground, whereas airplanes get their propulsion via other means. (And I
don't think this has anything to do with aviation public vs non-aviation
public...plenty of pilots don't understand the physics either, as has been
amply demonstrated here).

[...]
A better way to pose the airplane question would be " what would
happen if the airplane is landing on a treadmill that is moving in the
opposite direction and speed?"

That's not a better way at all. That asks an entirely different question
and takes advantage of a completely different prejudice the answerer might
have.

Pete

"Darkwing" theducksmailATyahoo.com wrote in message
...
This looks like a job for the MythBusters!!!

*Yawn*

That would be a boring show. Either they'd have to fill 19 minutes with the
construction of the treadmill itself, or they'd have the airplane taking off
in the first 30 seconds, leaving them with 19 minutes of filler at the end.

You don't need MythBusters. You just need a little knowledge of physics and
some common sense.

Pete

"Bob Martin" wrote in message
...
Darkwing wrote:



Nope the plane won't take off.


You'd better not just be trolling...

Friction generated by wheels is almost negligible. Even for very large
aircraft like a 747, wheel friction is nearly constant, regardless of
speed (at least at sane speeds). It only depends on the amount of force
pushing down on the wheel.

So let's look at all of the forces acting on this airplane. In the
horizontal direction, we have:
Thrust from the engine (nearly constant at these speeds)
Aerodynamic drag (goes up as the square of speed)
Wheel friction (again, nearly constant)

For any object to accelerate in a given direction, the total force acting
on it in that direction must not be equal to zero. For a normal airplane,
on a normal runway takeoff, thrust must obviously be greater than the
other two forces, since we see airplanes take off every day. Even at the
moment of takeoff, aerodynamic drag may have increased, but the airplane
still has a fair bit of excess thrust, and (assuming you don't pull up too
steeply) will continue to accelerate.

So now, let's put the plane on the treadmill. Once again, the ONLY forces
acting on it are thrust (which stays the same), drag (which still
increases as speed squared, and wheel friction (which, again, IS CONSTANT!
no matter how fast the treadmill runs, until we start talking about silly
cases like 5000mph treadmills). Sticking to sane, airplane-like speeds
for the treadmill (80-160mph or so) We see that, once again, thrust is
greater than the other two. Therefore, the plane MUST accelerate.

I'd like to also point out that I have tried this on an actual treadmill
with a small model airplane. It takes right off, no problem. Now I just
need to go fin

I am a regular on RAP, not a troll.

Show me video and I will believe it, if the plane is not moving relative to
the wind then the wing isn't making lift. I have ran on treadmills and I
never felt a "wind" blowing in my face.

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

Peter Duniho wrote:
"peter" wrote in message
oups.com...
The problem is that as it is stated, the scenario is not one that could
ever be created with a real treadmill subject to normal engineering
constraints. [...]

You can interpret the question in that way of course. However, the intent
of the "puzzler" is clear, and the fact that it is poorly stated should not
interfere with making a reasonable, good faith effort to address the
intended question.

It's well and good to nitpick about physically impossible situations, but
rest assured if you started doing so in a true interactive situation in
which the person stating the puzzle had the opportunity to restate it, you
would quickly get past the nitpicking and get to the intended question.

It's a waste of time to do the nitpicking in the first place. It's easy
enough to infer what the interesting question really is.

My view was that it was exactly the infinite feedback mechanism that
made the problem as stated interesting. Otherwise it's trivial and
boring.