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Thanks for that, I still need to play with this equation a bit more.
I've been reading a variety of things from Semi-Truck aero through to Belbouth design for engine air intakes, but one thing that struck a chord was rocket nozzle theory.
A perfect rocket nozzle will have maximum efficiency when gass departing is at the same pressure as the surrounding atmosphere, if it is higher it is wasted energy, when it is lower pressure it creates drag.
From this, in an abstract way I started to look at template theory as an inverted rocket nozzle, the ultimate goal is to leave the air behind the vehicle completely stationary, as if the vehicle had never been there.
This equation with the kick in the tail may well be in the vicinity, the rate of change in angle is ever decreasing and then reverses at the end so departure angle at the tail tip is 0, this goes in line with having 0 velocity and ambient pressure at that point.
Although most of us will never build a full perfect boattail, but understanding what one is will help us to build an effective Kammback or trailer canopy.
We know that perfection lies in the vicinity of the paramaters aerohead has provided, 2.5:1 total ratio, 1.78:1 tail ratio, 22-23° max angle etc., this has been proven experimentally numerous times, so this is the ballpark we need to play in. I think the final equation will incorporate natural constants of growth and decay and be completly logical when we find out what it is, till then keep discussing and debating to get ourselves closer.
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