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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. In researching the coefficient of drag of the brown pelican, Iosilevskii's article in the Society of Open Science gave $\ C_{D} \approx 0.5$ and$\ C_{L}$ was calculated to be$\ = 1.54$.$\ k$. 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, 1 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, by the wind, as a function of distance.  $\ W_{w, max}(d_{trav} = (20 J)d_{trav} J)d_{trav}$  This uppper bound estimate is the same in both the deep and shallow water cases. Comparing this to the work done by a pelican in flying without compression surfing, which is roughly 15 Joules per meter traveled, we can see that the brown Pelican is able to effectively compression surf without inputting any energy at all! Notice though the upper bound work is greater than than the work expended by the pelican in the first place. This is because the upper bound is the work that would be done by the wind if the bird could fly, literally touching the surface of the wave. We know that this is impossible, and that birds actually fly in the air. From the equations I have derived we can now find the height at which a pelican can glide with no additional energy input for any given wave. All we need to do is plug in the numbers and do a little algebra! The upper bound simply shows us that for the old wizened pelican who has been compression surfing his whole life, This guy could potentially go on flying forever with no additional energy input, in the idealized case where the wave never dissipates or changes shape.