What bank angle creates the least energy loss in an emergency engine out 180 degree turn? A situation we all hope to never have:  engine quits at a low distance AGL.

What bank angle will produce the least altitude loss for a 180 degree turn?
Is this common for all aircraft?

Readings have shown the elevator/wing to be more efficient at turning the aircraft
than the rudder alone.

It would seem better not to try to hold altitude on the turn, but one still must avoid stalling
the wing.  Airspeed is also a factor in gliding efficiency.

What is the best way to turn 180 degrees with least loss of altitude?

Some good references provided.  Curious about rudder technique in a steeper bank. At 45 degrees, rudder is pitching nose down some, but should be there to "follow" the wing around the turn (lowest drag).  Some elevator, some rudder to swing the tail through the yaw plane, giving up some altitude, so as not to load the wing as much (like an emergency descent)?
Asked and answered, since a any plane without a functioning engine is basicly a glider:
What is the optimal bank angle to accomplish a given turn in a glide?

Assuming the question refers to an engine failure after takeoff, there is a lot more to the stunt than just turning with the least amount of altitude loss. In any case, before attempting "the impossible turn" you must be above the safe altitude for the maneuver. If you have not yet reached safe altitude, you make an emergency landing in the front sector. The safe altitude varies heavily with different plane makes and models, but for example a C 172 needs about 500ft and rather aggressive (yet skilfull) handling according to tests made for AOPA Pilot 2002 july article.

To make an efficient 45 degree turn while maintaining a steady speed is not exctly a walk in the park if you have just lost an engine. Attempts to return to the runway after an engine failure during initial climb have a strong tendency to end in tragedy.