# Equation for drag force

## Homework Statement

I know that standard formula is, FD = 1/2 CD *ApV^2

FD = Drag Force. SI: N
CD = Drag Coefficient. SI: Dimensionless (Typical Values)
A = Coss-sectional Area perpendicular to the flow. SI: m2
r = Density of the medium. SI: kg/m3
v = Velocity of the body relative to the medium. SI: m/s

But our prof also said theres another formula for drag force,

FD = 1/4 AV^2

(Its is not supposed to be equal but approximately)

So the question is when is the equation above false, whats the error in the equation that makes it approximate.

## Homework Equations

FD = 1/4 AV^2

FD = 1/2 CD *ApV^2

## The Attempt at a Solution

I searched everywhere on wikipedia and NASA site and no luck and I dont know integration yet so can't follow the complicated math. Please anyone can help me.

Look closely at the second equation. It is a private case of the first.

The factor of $$\tfrac{1}{2}$$ is pretty weird too.

All you need to remember is what the drag force is proportional to, and that's fairly simple:
The higher the area perpendicular to the flow - the greater the drag.
The greater the density of the medium - the greater the drag.
The greater the square of the velocity of the object wrt the medium - the greater the drag
And then there's just some constant.

Thanks for your reply. But it was like a bonus question kind of thing, why 1/4 AV^2 instead of the other equation, he said the 1/4 will work for any speed less than speed of sound and uses normal air and something. And he said 1/4 is not the error that # is precise, so the problems got to be in the AV^2.hmm.