# Is it possible to make an analogy between a lever and an airplane wing in terms of force applied over distance?

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?

• While this may not answer directly, indeed "lever effect" is used on an airplane. The reason the tail (elevators and rudder) and the ailerons are located far from the aerodynamic center is to have a larger torque, and generate control forces with as little lift as possible (because generating lift also creates fuel-expensive induced drag in proportion).
– mins
Dec 19 '18 at 14:31

Well, they call them air PLANES for some reason. Maybe not a lever, how about a ramp?

How does 1/4th the thrust lift a given weight? One consideration that is very important for aviators is to realize the best way to use thrust is to create speed. Speed creates lift.

It is indeed a minor miracle that the airflow over a wing at flying speed creates so much upward force. One way to see how this works is to look at the back of a boat while it is travelling slowly. See the swirls and eddies of the water in the wake. Now speed up and the water separates from the stern and forms a wave behind the boat. The lack of water at the stern is the same as air being deflected away from the top of the wing at sufficient speed. This area of lower pressure near the wing is lift. How much to lift a one ton Cessna? The wing is roughly 5 x 40 = 200 square feet. 200 square feet x 144 square inches/square feet = 28800 square inches. 2000 pounds/28800 square inches = 0.07 psi. Not much, but it works!

Slow down and the wave collapses back to the boat. This is a stall on a wing. So lift is INDIRECTLY produced from thrust by forward motion (and angle of attack).

• I will note deflection of air off the bottom of the wing also contributes to lift. Dec 18 '18 at 1:44

A lever is a very poor analogy to a wing. And so is a ramp.

A lever used to lift a heavy load exchanges a small force over a large distance for a large force over a small distance. In both cases the work done (force x distance) is the same. Ignoring friction, a lever is 100% efficient, because the work out is the same as the work put in.

A ramp lifts a weight a short distance against gravity while moving it a large horizontal distance.

However the thing to note about a wing is that (at least in horizontal flight) it's doing no work against gravity at all - because the airplane isn't going up or down.

The wing is doing the same amount of work as my chair (as I sit in it) and a hook while it holds my coat off the floor, neither of which require any energy input - that is, zero work.

A wing is effective at providing a vertical FORCE in exchange for a horizontal amount of WORK. Since no actual work is being done in the vertical direction in level flight the wing has an efficiency of zero %.

It would be nice to understand a wing as a kind of lever, but I'm afraid that's not what it is.

• This is the fallacy of work = force x distance/time. These definitions were made at a time when work was defined as moving from point A to B. This would be better defined as Sum of Forces (3 dimensionally to determine direction, average velocity to determine distance). Much easier to consider forces. The wing DOES require energy input, in straight and level flight it is in EQUILIBRIUM with GRAVITY (two opposing forces cancel). Dec 17 '18 at 23:26
• @RobertDiGiovanni Work is defined the same way it always has been, which is work = force x distance. The quantity (force x distance)/time is power, and the "sum of forces" is the net force. All Capt. Aerodynamics is doing is explaining that work is perhaps not the right quantity to be focusing on. Dec 18 '18 at 1:47

I don't think you can make a really useful comparison because the lever is applying force to one fixed object, pivoting around another fixed object, with a fixed mass and a fixed force and you can repeat the same result over and over. The airplane is applying force to a fluid (gas), which imparts a gazillion variables to an action/reaction situation.

On top of that, the airplane is accelerating a gas rearward to create the forward momentum, and then the wing is taking the same gas and accelerating it downward to create the lifting force, so you have a gazillion variables multiplied by a gazillion variables, which results, if my math is correct, in a jazillion variables. You get the idea.