The lift paradox.

[Nick]

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? 

 

[Nova]

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

[harey]

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...

[plasmid]

I'm not sure I agree with harey. While it's true that if a plane's power is lost it will drop more slowly than a ballistic due to the drag of air against the wings keeping it from accelerating too quickly, while it's flying straight and level and the net vertical velocity is zero I would imagine that it shouldn't have an impact.

I'm also puzzled by the fact that a plane can stay aloft when the force of gravity is greater than the thrust of the engine. It probably has something to do with the fact that a plane can only stay aloft when the airflow across its wings is laminar, and that if the airflow becomes turbulent (for example if the pilot pulls the nose up too much and the plane goes into a stall) then it can no longer maintain enough lift and starts falling. But I don't know how to account for that with equations and account for balancing out the force of gravity.

[harey]

I did some research...

At first, the drawing Nick made is somewhat confusing. What he calls "forward force" should be "thrust" and what he calls "thrust" should be "drag". Just google "drag thrust weight lift".

If thrust=drag and lift=weight, the plane will fly at constant speed at constant height (plenty of pages).

Now, the question is how much thrust we need to generate lift=weight (or a little better).

On the end of the article https://en.wikipedia.org/wiki/Lift-to-drag_ratio, there is a table: latest air-crafts have a coefficient over 19.