Question

Describe the "behavior" of F_air: in Rocket Dynamics , why might it first increase with height, and then decrease with even greater height. Dissect the equation like a physicist: what terms in the equation for F_air are more important and when?

The air force = -(.5cAd0e^-ky)v^2/m.

Answer 1

The air drag force equation has two parts

where

where y is the height

and

where v is the velocity.

At first when the rocket is launched, the velocity of the rocket increases because of the thrust and the height, y is still small

Therefore the air drag force increases because of the term

After the rocket has reached considerable height, the term dominates and this term decreases as y increases. Hence the drag force decreases at greater height.

The drag force's schematic graph (F vs y ) looks as follows

where the increase in F in the first part is due to the term

and the decrease in F in the later part is due to the term