Most efficient bank in takeoff engine failure

[rookie1255]

Out of curiosity, does anyone know the most efficient bank angle to return to the airport if one has an engine failure on takeoff?

I know the best answer is almost always to find a landing spot straight ahead. I also know that the actual turn is a lot more than 180 degrees. After factoring in aligning with the runway and corrections it can be about 270 degrees.

So if you try to make it back with a shallow bank, your turn rate is slower but your descent rate is slower also. A steep bank will get you there sooner, but you will lose altitude faster.

Is there an optimum bank angle (maybe standard turn rate?) where you lose the least amount of altitude for the turn rate? For the sake of this argument we're going to say you're at a high enough altitude to make it back.

 

[Jim Logajan]

For gliders, if the tow rope breaks at between about 200 and 400 feet, a bank angle of 45 degrees is suggested as being optimum when doing a 180 turn-back. [http://www.gliderbooks.com/downloads/M_Ch8.pdf] I do not know whether this is applicable to aircraft with lower L/D. Possibly a link to the relevant computation appears in the impossible turn thread.

 

[Jim Logajan]

It does, and the calculation showed 45 degrees to produce the least altitude loss.

http://www.pilotsofamerica.com/forum/showpost.php?p=1908446&postcount=35

Ah, thanks. I recall running across the computation once upon a time but couldn't recall the initial assumptions.