Can a Plane on a Treadmill Take Off?

Jim Macklin wrote:
If the treadmill is stationary and the belt speed is equal
to the required take-off speed, the airplane will have zero
airspeed if it is "moving" in relation to the belt, the
airplane is moving, the prop has thrust and is balancing the
rearward movement of the belt. The tires are rolling, but
the airplane is stationary and there is no airspeed or lift.

Let's take this to a logical extreme. The purpose of a wheel is to
reduce friction, right? (Well, excluding steering and braking, since we
aren't using the brakes here) Anyways, let's now assume that the
airplane is sitting on the conveyor belt, and there is no friction
between it and the belt. For all intents and purposes, you now have an
antigravity device as your landing gear. Now run the engine up. If
there is no friction between the airplane and the belt (and
consequently no way to transmit force), how is the belt going to keep it
stationary? Remember, sum of forces=mass*acceleration, and the sum of
the forces in the horizontal plane is now mass*acceleration=thrust-drag
(where drag is a function of airspeed squared). No force from the
conveyor belt.

Now let's put the wheels back on. Certainly, if a wheel's purpose is to
try and reduce friction as much as possible, you aren't going to
suddenly have some wheels that drag on you with as much thrust as your
prop exerts...

if it comes down to it, I'll write a Matlab simulation of this, and show
the results to everyone.

Taken to the extreme, it might be considered ambiguous but that is only
nit-picking the puzzle. The general answer to the riddle is: if the plane
has enough excess thrust to overcome the additional drag of friction of the
wheels turning at twice the liftoff speed, the plane will fly. It will
accelerate slower and require a longer run due to the excess friction, but
it will fly.
--
-------------------------------
Travis
"Doug" wrote in message
oups.com...
Taxi is just nomenclature for the airplane moving along the ground.
"Takeoff run" would be more correct I guess, but in this case things
are so weird, as it is ambiguous whether the plane is going to takeoff
or not.

Jim Logajan wrote:
"cjcampbell" wrote:

Saw this question on "The Straight Dope" and I thought it was amusing.

http://www.straightdope.com/columns/060203.html


Seems Cecil Adams is compounding the confusion by having the page's title
begin:

"An airplane taxies in one direction...."

So is the plane attempting to taxi or take off? The page's title says one
thing, the person posing the question is stating another. The hypothetical
pilot of the taxing plane would presumably not let the the airspeed go to
takeoff speed, while the pilot of the plane taking off would want to
accelerate to rotation speed. So on that basis alone, we can say a taxing
plane isn't going to take off!

;-)
The earth is a treadmill. Goes about about 900 knots (at equator). Does
that bother your takeoff? Suppore treadmill stopped (rotation stopped).
Takeoffs any different, assuming you aren't launching into orbit?

BillJ wrote
The earth is a treadmill. Goes about about 900 knots (at equator).
Does that bother your takeoff? Suppore treadmill stopped (rotation
stopped). Takeoffs any different?

You forgot one major difference....in the case of the earth, the
airmass is travelling at the same 900kts, ignoring any localized
wind effect....not so in the treadmill case.

Bob Moore

In article , rmoore16
@tampabay.rr.com says...
BillJ wrote
The earth is a treadmill. Goes about about 900 knots (at equator).
Does that bother your takeoff? Suppore treadmill stopped (rotation
stopped). Takeoffs any different?

You forgot one major difference....in the case of the earth, the
airmass is travelling at the same 900kts, ignoring any localized
wind effect....not so in the treadmill case.

So when a treadmill runs the wind starts blowing ? OK... wot are yer
saying then?

--
Duncan

cjcampbell wrote:
"An airplane on a runway sits on a conveyer belt that moves in the
opposite direction at exactly the speed that the airplane is moving
forward. Does the airplane take off?" (Assuming the tires hold out, of
course.)

Cecil Adams (world's smartest human being) says that it will take off
normally.

Here's my read...

The propeller or jet provides thrust to move the plane forward through
the air mass. The prop wash on a propeller aircraft will not itself
generate sufficient airflow over the wings to lift the plane. Nor will
a jet engine. The purpose of these devices is to accelerate the whole
aircraft into the air mass. Once the plane is moving forward through
the air the wings will begin to generate lift... but you need positive
airspeed, not just propeller wash.

So, IF the plane is stationary in the air mass it WILL NOT take off.


The complete problem description states that the treadmil's control
system tries to counteract forward movement of the plane by speeding up
the treadmil. It's a flawed idea as the plane's thrust is mostly
decoupled from its wheels. Unless the wheel bearings are superheating
with friction and actually providing a braking force the plane is going
to move forward into the air mass... regardless of the rolling ground.

So the plane will trivially overcome the treadmill, accelerate away and
WILL take off.

.... unless the wheels melt.


Finally...

If, as the plane's prop runs up, a headwind is encountered which
perfectly cancels out the thrust then the plane will be accelerating
into an oppositely accelerating air mass all the way up to take-off
speed. Neither the plane not the treadmill will never have moved
relative to the ground, but the wings are getting all the airflow they
need. The plane WILL take off (like an elevator until equilibrium is
lost).


Regards,
Paul.

If you restate the problem as follows the aircraft will obviously NOT
fly.

The aircraft is on a conveyor belt.

The conveyor is programmed to move in such a way as to maintain the
aircraft at an airspeed of zero as measured at the pitot.

propwash?

No - It's a Skymaster and the examiner cut the front engine.

Oh-wait - It's a jet...

a.


cjcampbell wrote:
Saw this question on "The Straight Dope" and I thought it was amusing.

http://www.straightdope.com/columns/060203.html

The question goes like this:

"An airplane on a runway sits on a conveyer belt that moves in the
opposite direction at exactly the speed that the airplane is moving
forward. Does the airplane take off?" (Assuming the tires hold out, of
course.)

Cecil Adams (world's smartest human being) says that it will take off
normally.

wrote:

If you restate the problem as follows the aircraft will obviously NOT
fly.

The aircraft is on a conveyor belt.

The conveyor is programmed to move in such a way as to maintain the
aircraft at an airspeed of zero as measured at the pitot.

Absolutely, if you CHANGED the problem, and restated it as above, then
it wouldn't fly. Another way to state your entirely different problem
is to say that the conveyor is set up to always move at a speed that
maintains the wheel speed of the plane as the same as the conveyor
speed.

Or to parallel the original problem, "a conveyer belt that moves in
the opposite direction to the way the plane is pointed, at exactly the
speed that the airplane' wheels are moving, so that the plane is not
moving"

This will require a VERY fast conveyor, since once power is applied
and the brakes are released, it will have to move fast enough that the
rolling friction of the tires and bearing friction in the wheels
offset any thrust provided by the plane's propulsion system. Sounds
about as possible as any other conveyor belt runway!

cjcampbell wrote:
Saw this question on "The Straight Dope" and I thought it was amusing.

http://www.straightdope.com/columns/060203.html

The question goes like this:

"An airplane on a runway sits on a conveyer belt that moves in the
opposite direction at exactly the speed that the airplane is moving
forward. Does the airplane take off?" (Assuming the tires hold out, of
course.)

Cecil Adams (world's smartest human being) says that it will take off
normally.

--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

Alexy,

The conveyor is programmed to move in such a way as to maintain the
aircraft at an airspeed of zero as measured at the pitot.

Absolutely, if you CHANGED the problem, and restated it as above, then
it wouldn't fly.


Actually, you couldn't do that - which is another point the question
makes.

--
Thomas Borchert (EDDH)

Actually conveyor belt would decrease the length of runways if operated
in the direction of take off???