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

If the brakes are locked then the wheel speed is zero and the treadmill
speed (as specified in the problem) must also immediately go to zero.

.... until the propeller starts to pull the airplane (with its locked
wheels) forward.

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.

Travis Marlatte wrote:

Why isn't there forward motion on the treadmill? The pressure differential
around the prop or the thrust from a jet will propel the plane forward to
takeoff speed on glare ice (wheels don't have to spin at all) or the
treadmill (wheels spin at twice the speed).

The Original Question said that the treadmill speed was such as
to counter wheel speed so that the airplane stood still. That's what I
was thinking. Somewhere along this thread the assumption must have
changed and I'm arguing apples against oranges.
No airspeed, no lift. Period. Propeller or jet blast is not going
to lift the airplane. We need forward motion relative to the
atmosphere, or a really strong headwind.

The tires used on light aircraft are Type III and are rated for
120 MPH max. They'd probably explode before 150 MPH, seeing that the
forces increase by the square of the rotational velocity. Or. more
likely, the average lighplane tire being as out-of-round and imbalanced
as it is, the vibration would shake the airplane apart by the time we
got to 120.

Dan

wrote in message
ups.com...


The Original Question said that the treadmill speed was such as
to counter wheel speed so that the airplane stood still. That's what I
was thinking.

That's where you fell into the trap. The statement was that the treadmill
moves backwards at the same speed as the airplane is moving forward - it
didn't say that the airplane stood still (but that's the conclusion it
wanted you to reach). But, since the propeller and not the wheels is
driving the plane forward it doesn't matter how fast the belt on the
treadmill runs backwards, the plane will still move forward.

No airspeed, no lift. Period. Propeller or jet blast is not going
to lift the airplane. We need forward motion relative to the
atmosphere, or a really strong headwind.

wrote in message
ups.com...

Travis Marlatte wrote:

Why isn't there forward motion on the treadmill? The pressure
differential
around the prop or the thrust from a jet will propel the plane forward
to
takeoff speed on glare ice (wheels don't have to spin at all) or the
treadmill (wheels spin at twice the speed).

The Original Question said that the treadmill speed was such as
to counter wheel speed so that the airplane stood still. That's what I
was thinking. Somewhere along this thread the assumption must have
changed and I'm arguing apples against oranges.
No airspeed, no lift. Period. Propeller or jet blast is not going
to lift the airplane. We need forward motion relative to the
atmosphere, or a really strong headwind.

The tires used on light aircraft are Type III and are rated for
120 MPH max. They'd probably explode before 150 MPH, seeing that the
forces increase by the square of the rotational velocity. Or. more
likely, the average lighplane tire being as out-of-round and imbalanced
as it is, the vibration would shake the airplane apart by the time we
got to 120.

Dan

I am not sure what sort of perversity is causing me to continue reading this
insane thread, much less respond to it.

Here is a copy of the text, lifted from the New York Times web site as
linked; except that I have edited out the special characters which appeared
as a result of the text conversion:

-----------begin NY Times excerpt---------

December 11, 2006, 4:37 pm
The Airplane-Treadmill Conundrum
OK, this 's driving me crazy. This brain-teaser is ripping around the
Internet, plus I actually overheard it THREE TIMES in airport conversations
on a recent trip to Canada.'s how I found it presented at
http://boards.straightdope.com/sdmb/...d.php?t=348452 Imagine a plane
is sitting on a massive conveyor belt, as wide and as long as a runway. The
conveyer belt is designed to exactly match the speed of the wheels, moving
in the opposite direction. Can the plane take off? I say no, because the
plane will not move relative the the ground and air, and thus, very little
air will flow over the wings. However, other people are convinced that since
the wheels of a plane are free spinning, and not powered by the engines, and
the engines provide
thrust against the air, that somehow that makes a difference and air will
flow over the wing. The guy behind me at the airport told his buddy that,
in fact, the plane WOULD take off, and his buddy seemed to agree. Do we have
any physicists in the audience?

---------end NY Times excerpt-------

Please note that the embedded link still works.
Please note also that nothing new can be added.

I submit that there are really only two logical presumptions, both of which
have been explored:
1. The aircraft will take off normally.
2. The magic treadmill has no inertia and no limiting speed; and, by some
unexplained means, can sense the rotation of the wheels. Therefore, if the
aircraft is placed very near the departure end of the runway and connected
to an airport tug which is placed on solid ground; then, as the tug begins
to slowly pull the aircraft forward, the magic treadmill will quickly
accelerate until the wheels and tires of the airplane have catastrophically
failed.

I further submit that the second presumption is ridiculous.

Peter

In article Ueegh.387$Iz.365@bigfe9, "Peter Dohm"
wrote:

What keeps the wheels in contact with the treadmill when the treadmill
(and wheels) are going supersonic?

In the original problem statement; nothing except gravity causes contact of
the wheels, or any other part of the airplane, to the treadmill at any
speed.

so, eventually, the treadmill won't have the ability to apply drag to the
airplane.

--
Bob Noel
Looking for a sig the
lawyers will hate

"Bob Noel" wrote in message
...
In article Ueegh.387$Iz.365@bigfe9, "Peter Dohm"

wrote:

What keeps the wheels in contact with the treadmill when the treadmill
(and wheels) are going supersonic?

In the original problem statement; nothing except gravity causes contact
of
the wheels, or any other part of the airplane, to the treadmill at any
speed.

so, eventually, the treadmill won't have the ability to apply drag to the
airplane.

That has been my position.

However, my position has been based upon the presumption that the word
problem was only intended to test whether a respondent understood that there
is no connection between the wheels and the engine(s) of a typical airplane,
and my position was further based upon the idea that the word problem was
originally intended to be solved by the airplane taking off normally.

I must admit that the most precise parsing of the language in the problem
statement does suggest that the wheels will be quickly spun to failure as
soon as the airplane begins to move. No limit speed was stated in the
problem, so the possibility of infinite speed and instantaneous response
would be linguistically correct--one of the other contributors used the
analogy of "division by zero."

Peter

On Thu, 14 Dec 2006 00:32:09 -0800, in 11660851
If the brakes are locked then the wheel speed is zero and the treadmill
speed (as specified in the problem) must also immediately go to zero.

Depends upon the definition of "wheel speed" then...

Either the treadmill moves to the rear and the wheel rotation increases
significantly and the plane manages to take off because takeoff is
determined by air speed, not the rotational speed of the tires

OR

the treadmill is set to keep the wheels from rotating in which case you
manage to takeoff with no rotational movement on the wheels...

Several of you are debating two different kinds of wheels speeds. I happen
to believe that the original question was of a simple nature and meant that
the treadmill speed matched the forward motion of the plane (or forward
motion of the wheel). Those who want the wheels to explode before the
treadmill reaches an infinite speed assume that the original question meant
that the treadmill speed somehow stops forward motion by matching a wheel
speed I haven't seen you define.
--
-------------------------------
Travis
Lake N3094P
PWK
"Jose" wrote in message
et...
If the brakes are locked then the wheel speed is zero and the treadmill
speed (as specified in the problem) must also immediately go to zero.

... until the propeller starts to pull the airplane (with its locked
wheels) forward.

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.

Unbelievable."Montblack" wrote in
message ...
("peter" wrote)
If it were given to me as an engineering question then I'd immediately
point out that the treadmill being requested can't possibly be built
since it requires instant acceleration of a massive structure and would
request that the project be modified to come up with something
feasible. But as a puzzle question having a gigantic treadmill that
can instantly accelerate to thousands of miles per hour is perfectly
legitimate - just don't ask me to build one.


The treadmill need only be (approx) 6-ft wide x 8-ft long.
(If it needs to be any longer, your answer is wrong)

The object (the plane) isn't THAT heavy.

Our GIGANTIC treadmill only needs to average both accelerations - not have
instant acceleration. (Kind of like your home's thermostat keeping the
room
at 68F. It has a 3 or 4 degree temp spread so it isn't "popping" on all
the
time. BTDT)

When the plane roles forward two inches, the electric motors speed up
...until the 'curb feeler' sensors detect the axle has returned to point
X.

Then, with basic computing, the treadmill readjusts its speed. It might be
only an inch for the "forward" or "back" tolerances ...or it might be a
foot.

It's a small Cessna/Piper/Cri-Cri we're dealing with, here. NOT an F-18
off
a carrier deck!

If you can't slap one of these puppies together in an afternoon... :-)


Montblack-to-the-drawing-board




You'd better make it a little bigger 'cause the plane is going to roll many
hundreds of feet and take off.

-------------------------------
Travis
Lake N3094P
PWK

"peter" wrote in message
oups.com...
Montblack wrote:
("peter" wrote)
If it were given to me as an engineering question then I'd immediately
point out that the treadmill being requested can't possibly be built
since it requires instant acceleration of a massive structure and would
request that the project be modified to come up with something
feasible. But as a puzzle question having a gigantic treadmill that
can instantly accelerate to thousands of miles per hour is perfectly
legitimate - just don't ask me to build one.


The treadmill need only be (approx) 6-ft wide x 8-ft long.
(If it needs to be any longer, your answer is wrong)

Unlike other responders here, I'm trying to go by what the problem
actually states, not what they think it should state instead. In
particular, the problem says "Imagine a plane is sitting on a massive
conveyor belt, as wide and as long as a runway." So it needs to be as
wide and long as a real runway to be in agreement with the problem
statement - that's much bigger than 6' x 8' - at least based on the
real runways I've come across. (But I commend you on your short field
landing and take off skills.)

The object (the plane) isn't THAT heavy.

Our GIGANTIC treadmill only needs to average both accelerations - not
have
instant acceleration. (Kind of like your home's thermostat keeping the
room
at 68F. It has a 3 or 4 degree temp spread so it isn't "popping" on all
the
time. BTDT)

Your home heating system is in a negative feedback, well-controlled
situation as opposed to the treadmill which is in a positive feedback,
runaway and out-of-control situation. In the first case the action
taken in response to the stimulus (turning on the furnace when it gets
too cold) acts to reduce the stimulus. But in the second case,
speeding up the treadmill when the wheels speed up, only acts to make
the stimulus worse. So the faster the treadmill goes, the more it
pulls the wheels of the plane around and makes them spin even faster.
I've experienced that kind of positive feedback in miswired electronic
control circuits and it results in rapid escalation out of the physical
bounds of the devices - i.e. as soon as it was turned on there was a
sudden flash, a puff of smoke, and generation of lots of heat.

When the plane rolls forward two inches, the electric motors speed up
...until the 'curb feeler' sensors detect the axle has returned to point
X.

But that won't happen easily since the plane is being pushed forward by
the thrust of its motor (a substantial force) and the only thing
pushing it back to point X is the slight frictional drag of the
spinning wheels. So until the treadmill reaches a really high speed
where that frictional drag becomes significant (probably when either
the wheel bearings start to overheat or the tire starts to fail) the
plane will keep moving forward and triggering the treadmill to go ever
faster.

Then, with basic computing, the treadmill readjusts its speed. It might
be
only an inch for the "forward" or "back" tolerances ...or it might be a
foot.

Let's give it your maximum tolerance of a foot. That means that in the
time it takes your Cessna 150/whatever to move forward just one foot
the treadmill needs to speed up to the point where the wheel drag is
enough to equal the thrust from propellor. A 150 may not have a whole
lot of thrust, but it's still large compared to the drag of the wheels
turning at say 100 mph. I'd call an acceleration from 0 to 100mph in
the time it takes the plane to move a foot pretty impressive for a
treadmill the size of a runway - and that wouldn't even be enough since
the thrust is still larger than the 100 mph drag force. So the
treadmill has to go still faster until something in the plane's landing
gear (tires/bearings/etc.) breaks and results in a greater frictional
drag force which can counter the propellor thrust.

It's a small Cessna/Piper/Cri-Cri we're dealing with, here. NOT an F-18
off
a carrier deck!

If you can't slap one of these puppies together in an afternoon... :-)

I think you're seriously underestimating the difficulty of the design,
but you're welcome to prove me wrong with a working model.



A couple of good arguements but the treadmill doesn't have to go that fast.
What type of matching wheel speed would cause that? The only reason that the
treadmill would need to accelerate to inifinity is if the question had posed
that the treadmill acted to stop forward motion. Then, I agree that the
treadmill would have to accelerate to a point where the friction was enough
to counteract thrust. However, the question posed only that the treadmill
matched the wheel speed. I take that to mean the forward motion of the
wheels which is the same as the forward motion of the plane.
-------------------------------
Travis
Lake N3094P
PWK