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Math Help - Airspeed and Lifting Force Relationships

  1. #1
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    Question 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
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kristinac View Post
    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:

     <br />
f=kv^2<br />

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

     <br />
\delta f \approx \frac{df}{dv}\delta v <br />

    So:

     <br />
\frac{\delta f}{f}=\frac{df}{dv} \frac{\delta v}{kv^2}=2kv \frac{\delta v}{kv^2}<br />

    etc.

    CB
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