Capt. Stable
You raise several interesting points.
I wasn't suggesting that max coefficient of lift / rate of turn ratio is a constant, merely that for a given aircraft in a given situation, minimum height loss per unit angle turned is achieved at max coefficient of lift.
I can well imagine that the optimum manoeuvre involves a changing angle of bank, but the point is that by rolling on 45 degrees of bank, a la Rogers, you achieve a result considerably better than the one given in the article that HugMonster cites. I can see that, particularly in larger aircraft, roll rate can be an issue. What's the maximum rate of roll to 45 degrees in WWW's 737?
I have no issue with the views that the turn-back manoeuvre is not usually worth the risk of getting it wrong and is also difficult to practise safely. But I do feel that the risk management should be based on proper physics rather than needlessly pessimistic data.
arcniz
The Rogers article indeed does assume a constant angle of bank, and it may be possible to do better. But I'm not convinced that your argument for increasing speed holds water. The rate of turn is very sensitive to speed, and I think Rogers shows in his paper that the trade-off you suggest is not a good one.
One further point: the state is not unaccelerated, and the assertion that maximum lift coefficient is optimal means flying an AOA rather than a speed. Thus you're absolutely right that the optimum is not going to be at constant airspeed.
Finally I don't doubt that given a few hundred feet more than the absolute minimum, your method may be a much safer and more effective option.