Originally Posted by Anderson, Introduction to Flight, Section 1.16.2
Maximum endurance for a propellor-driven airplane occurs when the airplane is flying at a velocity such that (C_L)^(3/2)/C_D is at its maximum
Anderson apparently makes the simplifying assumption that power-specific fuel consumption is constant, which in practice it is not. Also thrust-specific fuel consumption for a jet engine is not constant. It typically has a minimum, and increases from there towards idle and towards max. thrust.
Actually only max L/D is defined only by the lift and drag characteristics of the airplane. Both Endurance and Range involve the propulsion system fuel efficiency, and strictly speaking the optimum speed cannot be defined by reference to cL and cD alone. For a jet transport airplane with an engine perfectly matched to the airframe at optimum weight/altitude/speed, the speed at which the engine operates at its minimum sfc point will be close to the airplane max L/D speed, and hence max range speed will be close to max L/D speed.
regards,
HN39