For an aircraft in a glide, what—if any—is the optimal bank angle to make a given turn while maximizing glide distance and maintaining published best glide speed?
In other words, at a constant airspeed, which bank angle will produce the greatest turn rate with the smallest loss in altitude. Assume a constant airspeed turn that is already established. I am not asking which bank angle will produce the least reduction in the vertical component of lift.
In envisioning this scenario, I specifically have in mind a single engine aircraft experiencing an engine failure at low altitude. However, the aerodynamic theory may apply to any fixed wing scenario.
Edit: let me emphasize that this question assumes the pilot is maintaining the aircraft's nominal published best glide speed throughout the turn, not adjusting airspeed to some variable theoretical best glide speed. Airspeed should not be a variable.