On most aircraft the engine force (thrust) is lower than the weight. Since wings therefore are always capable of generating greater force (lift) than the engine, there is an analogy between an airplane and a lever.
Now, a lever produces greater force by doing the same work on a shorter path. How can we prove that wings enable the doing of work on a shorter path than the engine thrust? Is it reasonable to say the path on which the thrust does the work is the distance the aircraft needs to accelerate to takeoff speed, and the work/energy accumulated this way is used by the wings to exert greater force on a shorter path on the air? (And then this kinetic energy is constantly replenished by the engine keeping it constant, assuming no further acceleration?)
Is this the right Newtonian explanation of flight? How can I find the distance on which the force is doing work on the air?