Ian Stokes edited k.tex  over 9 years ago

Commit id: a48baf444e4fe0431750a5683a52960633921cf6

deletions | additions      

       

$\tan$( $\theta$ ) =$\ C_{D}$/$\ C_{L}$.   I will refer to this as the glide angle equation. From this expression we can easily formulate an equation that gives the work done by a pelican flying at a constant altitude$\ W_{p}$ as a function of distance using the definition of potential energy,$\ U = mga$. If we label the altitude lost while gliding under constant velocity descent as$\ a_{l}$ and the distance travelled in the horizontal xy plane as$\ d_{trav}$, we obtain the work equation for a pelican (mass M_{p}) flying on its own. For a pelican flying at constant altitude (no wave yet) Work, which can be interpretted as the energy expended by the bird, in joules: independent of ocean swell.  $\ W_{p} = M_{p}a_{l}g = M_{p}g(d_{trav})[(C_{D}/C_{L})]$  Work done by the pelican in maintaing constant altitude flight, which can be interpretted as the energy expended by the bird, in joules is given by the expression above.  We can also solve for$\ C_{L}$ using the glide angle equation. From the relationship between weight and lift, we can determine that the \textit{minimum} gliding speed$\ v$ = $\sqrt(2mg$/($\rho_{air}A_{wings}C_{L}))$. From this we have $\ C_{L} = 2mg$/($\rho_{air}A_{wings}v^2$) which I will call the coefficient of lift equation. From Schnell and Hellack, we have a minimum gliding speed of $\approx$ $\ 6 m/s$. From the "Brown Pelican Fact Sheet" we have an average mass of $\approx 4kg$. This value gives $\ C_{L} \approx 1.54$.