Can a Plane on a Treadmill Take Off?

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.

Yes.
The problem states '..moves in the opposite direction at exactly the speed
that the airplane is moving
forward..' So the plane is moving forward, thus it will fly. The wheels
are just spinning at 120mph instead of the usual 60mph.

"pilot" wrote in message
oups.com...

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.

Exactly right.

In the end we'd have to say it's a nicely phrased question. My first
instinct was to say the ariplane had zero speed relative to the ground
the moving belt is on, but that is NOT the condition the problem
stated.

So, under the usual circumstances (not having a significant tail wind,
for example) you'd lift off assuming the wheels are not going to self
distruct turning at twice their usual takeoff speed.

"Tony" wrote in message
oups.com...
Exactly right.

In the end we'd have to say it's a nicely phrased question. My first
instinct was to say the ariplane had zero speed relative to the ground
the moving belt is on, but that is NOT the condition the problem
stated.

So, under the usual circumstances (not having a significant tail wind,
for example) you'd lift off assuming the wheels are not going to self
distruct turning at twice their usual takeoff speed.

The plane would take off from the treadmill even if there were a tail wind
equal to Vr (though in that case, the wheels would be turning at *four*
times their usual speed).

--Gary

Gary Drescher wrote:
The plane would take off from the treadmill even if there were a tail wind
equal to Vr (though in that case, the wheels would be turning at *four*
times their usual speed).

SMALL corrections:
*First of all, a plane doesn't take off at Vr but at Vlof (lift off
speed). Vr is the speed at which you lift the nosewheel from the ground
and this speed is smaller than Vlof which is the speed at which the
plane lifts off the ground. So: "The plane would take off from the
treadmill even if there were a tail wind equal to Vlof". But you
probably meant it right.
*Second, in the case of a tailwind equal to Vlof, when the plane leaves
the ground, the wheels would spin at a speed 3 times their usual speed
and not 4. Actually this entire question and solution is about adding
and substracting velocity vectors and a perfect example of Einstein's
relativity theory. It all depends on what you take as a reference (the
ground, the tredmill or the air). As some other folks said here, the
question was not clear enough and there was not enough info! So
obviously we were dealing with a communication problem here. Anyway,
since that is solved now, let me get into adding and substracting
velocity vectors to explain you the case of a tailwind.

----------(4) ----------(2) ----------(1) vectors in
reference to the conveyor belt
----------(1a) vector in ref
to the airplane
_____________________________conveyor belt

the plane moves from right to left in the above drawing and the
conveyor belt from left to right.
(1a) is the speed (let's call it "x MPH") at which the conveyor belt
moves

NO WIND CONDITION:
*Engines not running:
Assuming perfectly frictionless wheels, the plane's speed relative to
the surrounding ground (Ground Speed or GS) will be zero. Since there
is no wind, the speed relative to the air (True Air Speed or TAS) is
also 0. However, the conveyor belt moves at a speed x in reference to
the plane (vector 1a) and the wheels will spin at a speed x (vector 1)
and this is also the speed at which the plane moves forward in ref to
the belt.
Briefly:
GS=0 TAS=0
Tire speed=x not taking off!

*At takeoff thrust and the plane has reached Vlof=x MPH:
The engine thrust is pushing the aircraft away from the air behind it
to put it in simple words. In other words, we are now moving at an
airspeed (TAS) of x MPH=Vlof and since there is still no wind,
groundspeed is also x MPH BUT the plane is now moving at a speed equal
to 2x in ref to the conveyor belt. Twice the usual speed.
Briefly:
GS=x TAS=x
Tirespeed= 2x Plane lifts off!

I'll have to make an additional post since I reached max number of
characters . To be continued...

....continue my previous post
TAILWIND equal to x MPH:
*Assume a tailwind has suddenly come up! Suddenly means that the plane
didn't have time to react to it and since the tailwind equals Vlof this
means that your entire true airspeed drops away! So airspeed now is 0!
But your groundspeed for the moment remains x MPH as in previous case
and so does the tirespeed/tredmill speed which is 2x.
Briefly:
GS=x TAS=0!
Tirespeed=2x plane would not anymore takeoff!! WINDSHEAR,
WINDSHEAR!! Dangerous condition which can happen in real life!

*Now assume the plane has overcome the tailwind and the airspeed has
recovered and is again equal to x MPH. Good! Now the groundspeed will
be 2x and the tirespeed 3x! Because vector 2 is counteracted by an
opposite and equal in magnitude wind vector, there is now a new vector
4 (see drawing previous post). Oh God, maybe I should have drawn that
sketch a little differently! I'm not going to go through all this
again. Anyway, would you now do me a favor and CLOSE THE DISCUSSION
PLEASE!!

In short, the article from the first post is correct! End discussion,
"point final", over and out!!

PS:If you would like to know, I'm an engineer and an airline pilot!
Jeeeeezus!

Kpi$LyLcEhRo wrote:
/snip/

PS:If you would like to know, I'm an engineer and an airline pilot!
Jeeeeezus!


Q: How do you know if there is an (airline pilot/engineer) at a party?

A: Oh, he'll tell you!

Happy Flying!
Scott Skylane

"Kpi$LyLcEhRo" wrote in message
oups.com...

Gary Drescher wrote:
The plane would take off from the treadmill even if there were a tail
wind
equal to Vr (though in that case, the wheels would be turning at *four*
times their usual speed).

in the case of a tailwind equal to Vlof, when the plane leaves
the ground, the wheels would spin at a speed 3 times their usual speed
and not 4.

Suppose the plane lifts of at an airspeed of 30 knots, and suppose a 30 knot
tailwind. At takeoff, the plane then has a 60 knot ground speed. By
stipulation, the treadmill moves backward as fast as the plane moves
forward, hence at 60 knots too. Thus, the wheels are turning at 120
knots--four times the usual speed.

Actually this entire question and solution is about adding
and substracting velocity vectors and a perfect example of Einstein's
relativity theory.

No, this is strictly Galilean relativity (from four centuries ago);
Einstein's relativity has no bearing on this discussion.

--Gary

My dear Gary, how could I forget that in post number1 there is a line
saying "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..." so in other words, the belt adapts it's speed to the
forward motion of the plane?? Another communication problem I guess.
I'm not surprised though, after 55 freakin' posts this topic is
becoming off limits in my personal opinion! But I do hope that now
everyone agrees that the explanation on that website is correct. It's
just a matter of explaining the question properly with all details and
eliminating possible communication problems, right?

No, this is strictly Galilean relativity (from four centuries ago);
Einstein's relativity has no bearing on this discussion.

I don't agree completely. But your right that Galilean blabla has to do
with this but then saying that it's all about Newton's laws would also
be correct. So does Einstein! May I remind you of one of Einstein's
many mind experiments... The one about a train moving at a certain
speed, an observer inside the train walking to the front of the train
and an observer outside the train, standing still... As I said, it all
depends on what reference you take! To the observer outside the train,
the train may be traveling at 100km/h and the guy inside the train will
be walking at 105km/h! But to the guy inside, the train seems
stationary, while he himself is going at 5km/h and the guy outside to
him appears to be going backwards at 100km/h! It all sounds very
complicated and silly but relativity (and communication problems) is
all this topic is about! Now why don't y'all go and get a nice cup of
coffee and then start another topic.
No hard feelings I hope!

Actually, it is Newtonian relativity, but I'm not here to pick the flyspecks
out of the pepper.

Jim



No, this is strictly Galilean relativity (from four centuries ago);
Einstein's relativity has no bearing on this discussion.

--Gary