Jet engine takeoff?

Question

This is a theoretical question,if a jet airplane is sitting on a giant conveyor belt that travels backwards, matching the thrust of the engine or engines will the aircraft sit there or take off ?

Answer 1

I'm assuming you mean matches the speed of the belt to the acceleration of the aircraft. The fallacy in your hypothetical no-takeoff is that the wheels have no connection to the engine. If you're speaking purely theoretically, without friction, the wheels would spin freely at the same speed as the conveyor belt, and the plane would still propel itself forward and take off.

The jet engine propels the mass through the air. Once the initial friction on the gear was broken, allowing the plane to start rolling forward on the conveyor belt, the resistance to rolling drops rapidly. In practice, if it were possible to place it on a conveyor belt large enough to hold a plane, the belt could not possibly counteract the force of the engine by spinning the wheels. The entire system would fail in countless places, from the belt to the actual gear if this were attempted.

Ultimately, the jet engine acts on the aircraft and airmass, not the ground, so a conveyor belt would lose all influence at higher speeds where friction reduces to near zero, and the plane would still build airspeed and lift. (If friction didn't reduce to zero, the gear could overheat and cause other systemic problems, but the belt doesn't prevent the plane from taking off.) This is somewhat related to why planes can take off from an icy runway but not safely land... Great question though!

EDIT: To the respondent, if you really are a "physicist", then you should know better... unless you simply have no practical knowledge of how an airplane works... If you need another way to think about it, consider a man bicycling on a treadmill, to get the wheels rolling while he doesn't move. Then strap a rocket engine to his back as he lifts his feet off the pedals and the bike coasts in place for a second. He's not going to stay in one place. The speed of the treadmill and bike tires could increase as much as you like, but once that jet engine or rocket engine lights up, the physical mass (your body) will move in respect to the airmass (the air around you).

Answer 2

The aircraft will accelerate and roll forward because the only horizontal forces acting on it are the thrusts of its engines. A constant velocity conveyor belt does not cause a force on the aircraft because of f = ma, there has to be acceleration for a force to be generated.

Eventually the aircraft would take off because its acceleration would likely bring it up to airspeed...relative to the air, not to the conveyor belt. So we would need to take the conveyor speed into account when calculating the airspeed. Thus v = u - c; where v is the velocity through air, u is the velocity of the aircraft over the conveyor belt, and c is the velocity of the conveyor belt.

For example, if the aircraft VR (velocity at which it rotates for takeoff) = 200 kt and the conveyor belt were traveling 100 kt in the backward directions, then it would need to accelerate to 300 kt = u = v + c = 200 + 100 to have 200 kt airspeed for that safe rotation. Clearly, there would be a backward speed of a conveyor belt where the aircraft just could not get to VR, but it would have to be a very fast conveyor belt.

There is another issue, however...the relative velocity of the air acting against the thrusts of the engines. As the conveyor moves backwards, a relative air velocity moves forward over the aircraft.. That velocity pushes against the thrusts of the engines. At some point, design dependent, such counteracting air velocity will cause a flame out. It's like blowing out a candle. In which case, the aircraft isn't going anywhere.

Answer 3

Since what makes the aircraft take off is its relative speed with respect to the air it would not take off since the air speed would be zero in the experiment. Relative air speed is required to provide the lifting forces on the fuselage and wings of the aircraft.

Answer 4

It will sit there. It needs airspeed to lift off.