# Airplane Thrust and Weight

Q:
Physics in schools teaches two contradictory and mutually exclusive things: (1) That the upward lift force on an airplane in flight equal its weight (Lift = Weight = mass x gravity). This is based on applying Newtons 2nd law of motion (F = ma) to the airplane in flight. (2) However, modern commercial airplane like the Boeing 747ï¿½400 can fly with thrust-to-weight ratio as low as 0.3. Here the engine thrust is only 0.3x the weight of the airplane, but this thrust is sufficient to push the airplane forward and generate enough lift to fly. Therefore the upward force required for lift and flight must be a lot less than 0.3x the weight of the Boeing 747-400. (Lift < Thrust < Weight). Both statements cannot be true. Which is correct? Thanks.
- Nicholas Landell-Mills (age 52)
Argentiere
A:

Statement one, that in level flight the lift equals the weight, has to be true.
It's also true the thrust to weight ratios of ~0.3 are common for modern passenger planes.

How can they both be true? Because it's not true that lift < thrust. Lift is less than thrust if the plane is taking off vertically. For a plane in uniform horizontal the thrust only needs to equal the frictional drag. The lift created by the airflow around the wings can be bigger than that drag.

The deep esson underlying this is that force, unlike energy, is not some conserved quantity. You don't have a certain absolute thrust force to divide up into different vector components. What is conserved is energy, ad that's what gives you that the thrust must equal the drag for uniform horizontal motion. For that motion, there's no vertical velocity, so the vertical forces aren't doing any work.

Mike W.

(published on 06/18/2019)

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