deletions | additions       diff --git a/k.tex b/k.tex  index 3f0a64f..a790322 100644  --- a/k.tex  +++ b/k.tex 
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$\ W_{w}$($\ d_{trav}$)=(($\rho_{air}$)$\ d_{t}A_{wings}/2)arctan(C_{D}/C_{L})[ghk^2/(gh - 2v^2_{o})]^2exp[(2h/k)(gh/v_{o} - 2v_{o})cos((kl/2)(sqrt(v^2_{pelican} - (v_{ph} + v_{o})^2)/v_{pelican}))]$  Where, for deep water$\ v_{ph}$ = $\sqrt(g/k)$ and shallow water$\ v_{ph}$ = $\sqrt(gH)$. Evaluating the work equation with a complete set of values relevant to pelicans in standard international (SI) units, this equation can be interpretted as the energy in Joules saved by the pelican during compression surfing as a function of distance.This expression makes it simple to gain intuition for,  despite its foreboding mathematical appearance. appearance, from here on out we know all of the remaining variables as predetermined constants, and we know the domain which our expression makes sense in, so now we can make qualitative conclusions.    An ancient creature, estimates have it that this majestic bird has been cruising the skies for at least thirty million years. Historical geologists would call this period of time the "Oligocene epoch" of the "Paleogene period," but to the rest of us these implications can be put in much simpler terms--Pelicans are dinosaurs! Perhaps it is to this that the Brown Pelican owes its aerial expertise. Thirty million years has allowed evolution to take its course, and over the generations the pelican has been able to develop the artform of "compression surfing."