Here's some comments from a "smart guy" friend of mine. I asked him in an email what he thought of the original question:
Well...first thing is this: the plane would have to be moving, not standing to even attempt to take off. A plane doesn't lift off the ground due to speed. Speed is just what helps airflow come across the wings to provide lift. If it were moving forward allowing air to pass over the wings than lift could be acheived. If the ground speed is 100 mph forward but the conveyor is going 100 mph backwards, then the true ground speed would be 200 mph but no forward motion hence no airflow over the wings which is what is needed for lift. The only thing that has enough power to overocome ground speed creating flow over the wings is a jet engine ( huge jet engine) in a very small plane. F14, F15 that could power the plane forward (air speed) without needing wheels on the ground (ground speed). Most all planes are not powerfult enough to overcome the weight and drag on the plane by engine alone. I say if you consider the plane is a normal passenger plane... it's not going anywhere but the wheels will be seeing lots of mileage.
Stony, your "smart guy" friend needs a little help here. <img src="/forums/images/graemlins/wink.gif" alt="" />
Well...first thing is this: the plane would have to be moving, not standing to even attempt to take off.
Nope - if (as someone suggested) an unpowered plane was tethered and facing a 100mph wind, it would begin to fly in place. If at the moment of lift-off you brought the engine up to speed and released the tether - and if the engine was capable of moving the plane at 120mph (air speed), the plane would move forward into the wind at 20mph (ground speed) or 120mph (air speed). If the plane could fly as slowly as 80mph (air speed) and the engine set at that power rate, if faced with a 100mph headwind, the plane would still fly, but it would move backward (relative to the ground) at 20mph.... but would still be flying. The same is true of boats moving against a current. I once trolled for 3 hours at an indicated 7 knots in a southerly direction at the edge of the Gulf Stream (flows northerly - usually at a rate of ~3 knots), which unknownst to me was moving at a rapid clip that day... after 3 hours I looked at the Loran and found myself 8 miles further North than my starting point. <img src="/forums/images/graemlins/scared.gif" alt="" /> That sort of stuff makes you question your sanity until you understand the forces at work.
A plane doesn't lift off the ground due to speed.
Yes, it does..... but it's called "air speed" (ground speed is irrelevant).
Speed is just what helps airflow come across the wings to provide lift.
Yes, ground speed is used to achieve air flow over the wing, but is assisted by available wind speed... which is why airplanes take off into the wind..... and headwind speed is deducted from necessary ground speed required to achieve takeoff speed (always measured in air speed).
If the ground speed is 100 mph forward but the conveyor is going 100 mph backwards, then the true ground speed would be 200 mph but no forward motion hence no airflow over the wings which is what is needed for lift.
Wrong again..... "wheel speed" would be 200mph but "ground speed" relative to the fixed-earth (not the conveyor belt) would still be 100mph. Forward motion relative to the conveyor belt would be 200mph and "ground speed" relative to the frame of the conveyor and the earth would be 100mph. Assuming no wind, "air speed" would also be 100mph.
The only thing that has enough power to overocome ground speed creating flow over the wings is a jet engine ( huge jet engine) in a very small plane. F14, F15 that could power the plane forward (air speed) without needing wheels on the ground (ground speed). Most all planes are not powerfult enough to overcome the weight and drag on the plane by engine alone.
I wonder how those little Cessna 150s can fly without a jet engine? <img src="/forums/images/graemlins/lol.gif" alt="" />
it's not going anywhere but the wheels will be seeing lots of mileage.
Yes, the wheels will see a lot of mileage, but it dang sure will fly. <img src="/forums/images/graemlins/kewl.gif" alt="" />
Curtis gave the simplest answer - the plane moves at 100mph relative to the earth, the conveyor goes 100mph in the opposite direction and the wheels turn at 200mph.... it's as simple as that.
If the brakes are applied, the airplane goes where the conveyor takes it.... once the brakes are released and power is applied, the plane moves against the air - just like a boat propeller moves a boat through the water (assuming zero frictional losses in the wheel bearings).
If the conveyor had any bearing on the plane's motion, we could fly a plane at 100mph onto a conveyor belt which was moving at identical speed in the opposite direction and have it stop on a dime (if the occupants could stand the G forces). We could almost do that (except for momentum) if the brakes were locked, but that would be called a "crash" instead of a "landing". <img src="/forums/images/graemlins/lol.gif" alt="" /> Now, if we turned the conveyor belt in the same direction and at the same speed as the plane, we could land the plane without the wheels turning at all. <img src="/forums/images/graemlins/kewl.gif" alt="" />
During WWII - when rubber was scarce and tires were rationed - my father watched planes coming into some of the Phillipine Island landing strips and burn off much tread as the tires came up to rotational speed from zero. He wondered why he couldn't install an electric motor with a frictional or viscous drive to turn the wheels at landing speed, negating the rubber loss on each landing and greatly extend tire life. Unfortunately, when the war was over, he returned home to find the idea patented.
Anyway, the plane flies off the conveyor belt as pretty as you please - so long as the wheel bearings don't seize. <img src="/forums/images/graemlins/shiner.gif" alt="" />
Frank