Hi Finn,
Its been a long time since I dove this deep into cooling
ducts/lip contours etc. But, here goes.
The duct (lip + diffuser) is suppose to convert air
velocity to air pressure with minimum loss/drag and
turbulence. However, like almost everything else involving
flight - there is no single best answer - only an optimization
or approximation to the best (that you are going to get with
the compromises you have to make). So in our case one set of
compromises might be between cooling effectivness and cooling
drag. As you know the larger your radiator the more heat you
are going to get rid of, but, the larger your core the more
cooling drag you are going to encounter.
Now at low speeds you might get away with sticking the
radiator out in the airstream without any ducting and get
adequate cooling, but it will have higher drag - now at
biplane/slow airspeed the drag might be acceptable, but at 200
mph quite unacceptable. Again, it depends on what you are
trying to achieve.
Its been quite a while, but Ill give it a shot on trying
to explain the charts. I presume that External refers to air
factors prior to the lip and Internal refers to air factors
after the lip of the diffuser (or internal to the duct). you
mention wanting a 100-20 mph slow down. That is a data point,
but as I recall that is the overall slow down which would
include the slow down across the lip of the duct and the
across the radiator combined. Also for a faster aircraft
where Vo is quite high, perhaps Vi/Vo = 0.40 makes for less
drag but gives you all the cooling needed as opposed to
selecting cooling as a Vi/Vo = 0.20.
Also the Positive CPs are all below the horizontal line for
Internal flow. With lower Vi/Vos resulting in higher positive
CPs. That makes sense because if we have Vi/Vo = 1.0 then
that would imply the least conversion of velocity to internal
pressure, and we get a negative ratio Cp = -0.6. Conversly
if Vi/Vo = 0 then that would imply all the velocity energy is
coverted to pressure Vi/Vo = 0 then Cp = max or approx
positive 1.0 which tends to jive with the graphs.
The Cp external magnitude tends to increase as A (lip
Curvature) becomes more pronounced (with A=40 being the most
pronounced and A=10 the less pronounced lip curvature).
External pressure would be considered a drag component in my
opinon, so you want the least of that possible consisten with
other objectives (such as cooling).
So I think A=20 was chosen as the best compromise of lesser
drag and adequate cooling. Also, other lip curvatures might
have had "Separation" or other problems at different angles of
attach (from 12 to -12 degrees). For example perhaps if A=40
was choose, separation may have occured at angles below 12
Degs and for that reason alone been unacceptable.
Best this old brain can do perhaps someone of the younger
generation can jump in and clarify.
Ed