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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 $\ C_{L}$ = C_{L} \approx 1.54$.  The solution to the second problem is beyond the scope of simple geometric arguments. To solve for the air flow over ocean swells, a good method is to introduce an ensatz, or in other words, a guess. As a first step, I approximated an ocean swell as a sinusoidal wave of amplitude$\ h$. From there I required that at a large height above the wave the wind would feel no effects from the wave, and would travel with$\ v_{x}$ = constant =$\ v_{o}$, the undisturbed wind speed. Both$\ v_{x}$ and$\ v_{z}$ decay at equal rates with additional altitude$\ z$ and therefore obey the same exponential decay factor, exp[-($\alpha$)($\ z$)] Since at this point I do not have any intuition for what this factor is, I introduced the undetermined constant $\alpha$.  
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In fact, This top speed introduces a new constraint in the system: my equation will only return a real value for the cos($\phi$), assuming wind blowing in the opposite direction of the wave, for$\ v_{pelican}$ $\geq (v_{ph} = v_{o})$, and the$\ v_{z}$ no longer holds when there are large waves, because the pelican is unable to catch up with a top speed of $\approx 16m/s$. To avoid imaginary solutions, where the deep water approximation describes $\omega$ I will consider $\hat v_{o} = \hat v_{ph}$. As I plan on evaluating the typical trade wind wave, intuitively it makes sense that the wind would be blowing with the wind, since after all the wind is generating the waves in the deep ocean. Furthermore, winds that blow against the propagation of the waves are called "offshore winds": even the name of this phenomenon leads one to believe it will occur near shore. Therefore where the shallow water approximation describes $\omega$, I will assume $\hat v_{o} = -\hat v_{ph}$  The density of air is a known constant, roughly 1.2 kilograms per meter cubed. g is the gravitational accelleration constant which is exactly 9.8 meters per second squared. I was unable to find any information on In researching  the coefficients coefficient  of dragand lift but for the purpose  ofgetting some numbers on  the board I am going to approximate$\ brown pelican, Iosilevskii's article in the Society of Open Science gave $\  C_{D} = 0.1$ \approx 0.5$  and$\ C_{L} C_{L}$ was calculated to be$\  = 1$.$\ k$, 1.54$.$\ k$.  the wave number, is defined as$\ 2pi$/$\lambda$. Two meters of swell ($\ h = 1$meter)at a period$\ T$ of eight seconds describes the common tradewind based ocean swell; such a swell would have a wavelength given by $\lambda$ =$\ v_{ph}T$ =$\ gT^2/(2pi)$ $\approx$ 100 meters and speed$\ v_{ph}$ $\approx$ 12.7 m/s, with$\ k = pi/50$. Primarily we'll use a low wind speed, 2 m/s in $\hat v_{ph}$. This will make calculations easier and will give us something to compare to if we want to plug in a higher wind speed (still within the domain of the work function, obviously) to see which gives the pelican more benefit. I'm sure some math could be done to find the optimal wind speed for compression surfing. Regardless, back to our problem: plug in these numbers and it is easy to see that under the deep water dispersion relation an upper bound on the work done. done, by the wind, as a function of distance.  $\ W_{w, max}(d_{trav}$ =  Under the deep water dispersion relation my values gave the work done by wind to be roughly one Joule per kilometer of compressions surfing. The upper bound case is the same in both deep and shallow water as$\ v_{ph}$ is only present in the exponential factor, as flight heighth This clearly is unrealistic. At this point I can safely say that I will have to reevaluate my ensatz as I have overlooked some factor. Perhaps as the bird is flying so low, the funnelling of air between the wing and the wave could accellerate the air and, by bernoulli's principle, provide additional lift to that I did not consider. Furthermore in approximating the component wind speeds I threw out the pressure gradients, assuming pressure differences to be negligible. Perhaps this is not the case, and accounts for the failure of my ensatz. Despite my answer not adequately describing the physical situation, I feel that I now have a good basis with whcih to reconsider the problem and adjust my ensatz. Every time I have had to do this so far due to some contradiction my approximation has come out stronger as result, so hey, this setback is not the worst thing ever. First I am going to look into the funnelling possibility. If this fix does not provide a reasonable answer I will consider pressure gradients in the continuity equation and Bernoulli's relation. One thing is certain though--I have come too far to simply give up now! 
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Burton, R. (1990). Bird Flight, Facts on File. New York.  Schnell, Gary D.; Hellack, Jenna J. “Flight Speeds of Brown Pelicans, Chimney Swifts, Hainsworth, F Reed. pg (431-444). "Induced Drag Savings from Ground Effect  and Other Birds.” \textit{Bird-Banding} - Spring 1978 - Vol. 49, No. 2. Pg(108-112): Formation Flight in Brown Pelicans." Department of Biology, Syracuse University, Syracuse, AT, USA. Accepted 21 October, 1987 into \textit{J. exp. Biology}: Printed in Great Britain © The Company of Biologists Limited 1988.  Wei Shyy, Hikaru Aono, Chang-kwon Kang, Hao Liu. \textit{Cambridge Aerospace Series}: An introduction to flapping wing aerodynamics. ch 1. pg(1-40). Cambridge University Press. Avenue Iosilevskii, G. 2014. Forward Flight  of the Americas, New York, USA. Published 2013. Birds, Revisited. Part2: Short-Term Dynamic Stability and Trim. Royal Society for Open Science.  Prepared by: Department of the Interior - U.S. Fish and Wildlife Service. “Brown Pelican; Pelecanus occidentalis”. (entire article). U. S. Fish and Wildlife Service Endangered Species Program. 4401 N. Fairfax Drive, Room 420, Arlington, VA, USA. January 2008.  Prepared by: Department of the Interior - U.S. Fish and Wildlife Service. “Brown Pelican Proposed Delisting Questions and Answers”. (entire article). U. S. Fish and Wildlife Service Endangered Species Program. 4401 N. Fairfax Drive, Room 420, Arlington, VA, USA.   Schnell, Gary D.; Hellack, Jenna J. “Flight Speeds of Brown Pelicans, Chimney Swifts, and Other Birds.” \textit{Bird-Banding} - Spring 1978 - Vol. 49, No. 2. Pg(108-112):  United States. National Park Service. "California Brown Pelican." National Parks Service. U.S. Department of the Interior, 16 Dec. 2014. Web. 16 Dec. 2014.  \textit{J. exp. Biology}: pg (431-444). Hainsworth, F Reed. Induced Drag Savings from Ground Effect and Formation Flight in Brown Pelicans. Department Wei Shyy, Hikaru Aono, Chang-kwon Kang, Hao Liu. \textit{Cambridge Aerospace Series}: An introduction to flapping wing aerodynamics. ch 1. pg(1-40). Cambridge University Press. Avenue  of Biology, Syracuse University, Syracuse, AT, the Americas, New York,  USA. Accepted 21 October, 1987. Printed in Great Britain © The Company of Biologists Limited 1988. Published 2013.