The aircraft will not fly. Wheels don't make an aircraft fly, nor does thrust (look at a glider). The force that makes an aircraft fly is the air that passes over the wings creating lift (air moves at more velocity over the top of the wing than the lower surface, creating a low pressure area - therefore, lift).
The treadmill always moves at the same speed as the aircraft - so the aircraft can never gain forward momentum in relation to the static (unmoving) neighboring air, therefore the wings can not create lift. In effect, the treadmill, the wheels and the engines don't even matter in the 'problem' - if the aircraft can not move in relation to the air (and create lift) they might not as well even be moving. Even an aircraft using very heavily 'blown' wings and flaps (using engine bleed air) require at least a small amount of forward motion to create the extra lift which is used for very low speed takeoffs. (Search the NASA site for more details...)
Simply put it's not an aircraft's engines that make it fly, it's the result of the movement of the air over the wings (the engines simply move the aircraft forward, creating that movement.) No movement no lift. No lift, no fly.
There IS such a thing as a variable speed treadmill - an automotive dynomometer. Somebody have an airplane we could use?
Mike Kopack
FAA Airframe and Powerplant Technician
EX USAF F-16A/B/C/D Crew Chief
http://www.lucky-devils.net
Comments
Sir, with all due respect,
Sir, with all due respect, that's why (thank God!) you will never be a pilot.
I suggest you either go back to school and deserve your job position, otherwise FAA will find out that you are not capable and fire you on the spot.
Wow Mike. You're a
Wow Mike. You're a powerplant technician? Please explain to me why a plane doesn't slow down and fall from the sky once airborne, since clearly the powerplant is transmitting the energy required for flight to the plane's wheels.
So you are saying the plane
So you are saying the plane cannot move forward on the treadmill?
What is preventing the plane from moving forward?
your mom
Your mom is preventing the plane from moving forward.
Calculations
The plane will take off!
Here is the proof: http://img183.imageshack.us/img183/3369/plane5qm5.jpg
Sorry, No Flight
Impressive graphics and calculations, but the fact of the matter is this:
the wheels can spin at 10 million rpm, but the treadmill will neutralize the force transmitted to the wheels.
no force = no groundspeed.
no groundspeed = no airflow across wings.
no airflow across wings = no lift.
no lift = no flight.
You, sir, are wrong.
"...the treadmill will neutralize the force transmitted to the wheels..."
...sigh...a plane does not transmit force to its wheels, you are wrong. I have been patient with people like you thus far. I can't hack it any more. IT IS NOT A CAR FOR CHRISTS SAKE.
a C-A-R would remain stationary, spell it after me now: C...A...R, because it transmits force to its wheels.
Lets follow your logic to its conclusion: A plane, landing at a speed of around 200 mph, could in fact just land on a treadmill and come to an immediate halt because the treadmill would absorb all of the forward momentum?
At thought, you fail.
Sorry, Mike and "no flight"
The problem clearly states that the treadmill moves in the other direction - at the speed of the plane.
At the speed of the plane, not at a speed that will hold the airplane still. Neither does the treadmill move at the speed of the wheels.
The ground speed would be twice the airspeed (should it be a still day with no wind), but the plane would still take off due to its airspeed. The undercarriage would probably be stressed by quite a bit.
If the above does not make sense, but Mike's answer does, a good night's rest should help. Think it over again in the morning with a cup of coffee and a scratchpad :)
I agree with Mike
I don't see how the plane can fly. If the conveyer belt is nullifying the forward movement caused by the thrust of the engine and propeller, there isn't going to be any air flowing over the wings. How is the Bernoulli effect going to be generated? I just don't see the plane taking off.
Guess I'll find out tonight on Mythbusters.
The Plane Will Fly
Think about this as a thought experiment.
In order to compare apples to apples - a car on a treadmill is the equivalent to a plane in a wind tunnel. Or thought another way, an Amphibious Aircraft, on sleds or skis, will take off on a reasonable calmed river, regardless the current so long as it's flying into a headwind.
Oh, and I crewed F-16s also. Back in the 80's.
- rick
On second thought...
Damn, I can't believe that people are still arguing about this. Ok, yes, I am Mike who wrote the above comments. It was something that I through together after looking at the question for a couple of minutes - ten minutes later I'd forgotten the whole thing.
It looks as though my first look at the problem has touched on some raw nerves - sorry. As I look at the problem again, I'm not so sure about my answer. Everyone can learn new things if they keep an open mind. On the other hand, I don't really care enough about the theoretical problem to put any more effort into it.
If you need an aircraft maintained, come and talk to me. If you want to talk about impossible treadmills and their effect on aircraft, keep on going.
Mike
It is all about airspeed
If the conveyor belt generates sufficient airflow over the plane's lifting surfaces, then lift will be generated and the aircraft will rise. It has nothing to do with the speed of the conveyor belt or the thrust from the engines. Airflow is king here. However the higher the plane rises above the airflow generating surface (i.e. the conveyor belt) the less the airflow will be, so at a certain point equilibrium would be achieved.
I would be surprised if the belt did generate enough air motion in the appropriate direction, but it is possible. You might as well leave the engines off and tether the plane though.
That's half right, air flow
That's half right, air flow is the important variable in getting the plane to fly, and the treadmill isn't what is giving the plane airflow, it's the fact that the plane is moving forward, (in respect to both the ground the air and the treadmill) What I'm saying is that the treadmill wouldn't actually keep the plane "still."
This is where thrust is important, because the engines are creating thrust on the air, and not the treadmill the plane would still move forward, even though the treadmill is running the other way at the same speed. I'm pretty sure to keep the plane still you would have to have not a treadmill, but a massive air treadmill (wind probably?) that is acting to cancel out the thrust from the engines on the air, not the wheels from the ground. All the wheels were ever doing in the first place was to keep the plane from scraping the runway, and creating a bit of frictional force.