# Thread: Airspeed and Lifting Force Relationships

1. ## Airspeed and Lifting Force Relationships

The lifting force exerted by the atmosphere on the wing of an airplane is proportional to the square of the plane’s airspeed. Determine the relationship between the relative change in the airspeed and the relative change in the lifting force.

Does this have to do with related rates? Any advice on how to proceed?

Thanks,
Kristina

2. Originally Posted by kristinac
The lifting force exerted by the atmosphere on the wing of an airplane is proportional to the square of the plane’s airspeed. Determine the relationship between the relative change in the airspeed and the relative change in the lifting force.

Does this have to do with related rates? Any advice on how to proceed?

Thanks,
Kristina
You have:

$\displaystyle f=kv^2$

Then a small change in $\displaystyle \delta v$ in $\displaystyle v$ gives a change $\displaystyle \delta f$ in $\displaystyle f$:

$\displaystyle \delta f \approx \frac{df}{dv}\delta v$

So:

$\displaystyle \frac{\delta f}{f}=\frac{df}{dv} \frac{\delta v}{kv^2}=2kv \frac{\delta v}{kv^2}$

etc.

CB