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Induced Power

Induced power is the power required to maintain enough lift to overcome the force of gravity. One can view this as the force required to accelerate enough air downwards (at speed $v_i$) to push the bird upwards enough to counteract the force of gravity ($m g$). This force must be balanced by a change in the momentum of the air passing through the bird's wing disc (area=$A_{wd}$, mass/time=$A_{wd} \rho v$), which gives an equation for the induced velocity,

\begin{displaymath}
v_i = \frac{m g}{2 \ v \ \rho \ A_{wd}} .
\end{displaymath}

The actual power requirement is the product of the force necessary ($m g$) and the speed it is applied at ($v_i$),

\begin{displaymath}
P_{ind} = K_i \ v_i \ m \ g = K_i \ \frac{m^2 g^2}{2\ v \ \rho \ A_{wd}}.
\end{displaymath}

In the above expression $K_i$ is a correction coefficient to account for the difference between the size of the wing disc and the actual tube of air displaced by the bird's wings.



James Powell
2002-02-15