lift formula

[height & heading]

In the Lift formula can anybody inform me as to why we use ½ Rho and not all of Rho and why is Velocity squared?

[The Greaser]

The lift equation really only has the use of telling us that lift varies directly with density (rho) and directly with the square of the airspeed.
Cl (lift coefficient) is a non-dimensional coefficent obtained by dividing lift force by 0.5 rho V squared.

[Tinstaafl]

When talking about 'Lift' we're really referring to a reaction that occurs as the result of a force applied to air molecules being accelerated in a new (direction/speed) ie the molecule's Kinetic Energy (Ke) is changed.

Ke = 1/2 mass v^2

The scale of this force is related to the amount of Ke that is changed per molecuel and how many molecules are affected.

'Surface area' effects how many molecules are effected (bigger wing ==> more molecules affected at any instant)

'Coefficient of Lift' combines Angle of Attack & Camber into a single factor that applies a measured scale to the effect of eacho of these two things.

So,

Lift = CL 1/2 rho v^2 s ;where

CL= Coefficient of Lift ( the combined effects of angle of attack AND Camber.

v = velocity

rho = density (think 'mass')

S = surface area

Substitute 'mass' for 'rho' (same thing in this context)

and '1/2 rho v^2'

is the same as

'1/2 mass v^2'

which in turn is just 'Kinetic energy'.


Ke = 1/2 'mass' v^2


so Lift = CL Ke S


In a nutshell, the more the Kinetic energy that is changed, and the greater the amount of available energy available to start with (the Ke), the greater the force (or reaction to it) that must have occured.

CL affects the acceleration (speed & direction) that happens,

S multiplies the whole effect by how much air gets affected

Ke the Kinetic Energy contained within the body of air that gets accelerated.

-------------
Written in inebriation so any grammatical/spelling/meaning errors are entirely the fault of Arthur Guinness