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The lift paradox.



I'd appreciate any answers to this logic conundrum. Thanks.  

Engineers are confronted with two apparently true but contradictory statements: 

a)    To fly, lift must equal the weight of the airplane (Lift = Weight). 

b)    Commercial airliners such as Boeing 747-400 and Airbus 320 have thrust-to-weight ratios of about 0.3.  i.e.  Thrust / Weight  =   0.3

If the engine thrust (Thrust) is 3N, then the weight must be 10 N, and the Lift must be 10 N as well. 

But there is a significant problem: According to this logic, 10 N of Lift is 7 N greater than the 3 N of Thrust. This is impossible as 3 N of Thrust cannot produce the Lift of 10 N.  

Hence a paradox arises, as equations (a) and (b) appear true when stated individually. But combined they produce equation (c) ‘Thrust / Lift = 0.3’ that is false (i.e. impossible).

Therefore, one of the equations (a) or (b) must also be false.  But which one? 


lift paradox.png

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This is what I got from it:

First of all, lift should balance out weight for it to fly ( since there is no motion in that direction) 

Secondly, I am not sure why you are subtracting lift and thrust when they are in different directions. And also why lift being greater than Thrust is a problem? for the plane to fly, the lift and weight should be equal and therefore the lift would be greater than the thrust in this case

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You forget the lift by air depression on the wings.

When the space shuttle (which is basically a plane) takes off vertically, as long as the thrust is less than 10 [N/kg], it does not move. When the thrust exceeds this value, it moves up. [If you then cut the engines, it slows down, stops and falls like a stone.] That's what your equations describe.

When a plane flies horizontally at a constant speed, the gravitation is compensated by depression on wings - if you cut the engines, the plane glides. You still can keep it at constant horizontal speed, it slowly loses potential energy, but does not vertically fall like a stone. This implies that on constant speed/height, you need to furnish less energy than by a vertical takeoff and therefore less thrust.

Another approach: The energy of a cruising plane is constant, so the furnished energy must be equal to the energy lost. As the lost energy is partly transformed to lift on the wings...

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