On Thu, 11 Mar 2004 14:47:43 GMT, Robert Moore
wrote in Message-Id:
:

There were two groups, one was the slow down and use flaps
with a shallow angle of bank and the other group (me) quoting
the aerodynamic textbook solution of flying at maneuver speed
and using about 75 degrees angle-of-bank.

On 4/21/2000 John T. Lowry, PhD (author of: Performance of Light
Aircraft ISBN 1-56347-330-5) said:

Message-ID:
Actually the best turnaround bank angle (least altitude lost per
degree turned) is slightly above 45 degrees. See Performance of
Light Aircraft p. 295. Rogers neglected the inclination of the
flight path angle. For GA aircraft the extra angle beyond 45
degrees is, admittedly, negligible. For a Cessna 172, flaps up, I
get 45.4 degrees for the best turnaround bank angle. Now for that
flamed-out jet fighter ...

And on 1 Nov 1999 07:11:02 -0700:
Message-ID:
Best turnaround bank angle phi (least altitude loss per angle
turned through) for a gliding airplane is given by:

cos(phi) = (sqrt(2)/2)*sqrt(1-k^2)

where k = CD0/CLmax + CLmax/(pi*e*A)

where CD0 is the parasite drag coefficient, CLmax is the maximum
lift coefficient for the airplane's flaps configuration, e is the
airplane efficiency factor, and A is the wing aspect ratio. I know
most ng readers hate those darned formulas, but that's the way the
world works.

For GA propeller-driven airplanes, k is a small number (0.116 for
a Cessna 172, flaps up) and so the best turnaround bank angle is
very closely the 45 degrees cited by Rogers and, much earlier, by
Langewiesche (Stick and Rudder, p. 358). For the above Cessna, for
instance, it's 45.4 degrees. For a flamed-out jet fighter,
however, things are considerably different.

The formulas above, along with formulas for the banked stall
speed, for banked gliding flight path angle, and for the minimum
altitude loss in a 180-degree turn, can all be found in my recent
book Performance of Light Aircraft, pp. 294-296. The following
seven pages then treat the return-to-airport maneuver, from start
of the takeoff roll to contact with the runway or terrain, in
excruciating detail. Including wind effects, the typical
four-second hesitation when the engine stops, etc.

See also:

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