Matt:

Not necessarily. This took me a while to understand in USAF pilot training; maybe my explanation will help.

L/D max is most 'bang for the buck.' It does give the most speed for an amount of fuel flow. Analogy: You're in your car, in 5th gear, driving 45 mph. Car is burning about 1.5 gallons an hour, or 30 mpg. L/D max is best mpg.

Max endurance is the lowest possible power setting where you can stay airborne. It's not costing you much gas, but you aren't making much distance, either. Analogy: you start your car, put it in 1st gear, and leave it there, idling your way down the street at 5 mph. You can't go any slower (ie, reduce fuel-flow) without stalling the engine. In idle, you're burning 0.5 gallon an hour, which is only 33% of what you were burning before. Sounds good...car will run 3 times longer before flaming-out.

But, at 5 mph, you are only getting 10 mpg.

There is usually a sizable difference between L/D max and Max Endure in swept-wing jets as induced drag becomes huge (due to tip vortices and the resultant losses/drag) at high angles of attack.

In a maneuvering fighter, this could be because you put "g" on the jet (once took an F-4 from 500 kts, in Afterburner, to 230 kts, in about 9 seconds, by pulling 8.3 g). In a civil jet, the angle of attack would equal getting slow.

It happens in straight-wing jets and props, but I don't recall it being as a significant difference.

I should add that in jets, where fuel is a significant portion of your total weight, the speed varies with weight. As you burn it off, it usually decreases the best speed. I haven't touched on best altitude, wind, etc.

As to the engine-out questions: L/D varies a little in engine-out situations, as the remaining engine(s) may not be capable of achieving the original "best fuel economy" speed. That is, they may not have enough thrust to hit that speed. Example: the T-38's best range speed is pretty close to 320 kts (no-wind). With one engine, it will be closer to 275 kts, depending on altitude, because one engine can't make it go 320. To use the car analogy again: if one of your spark plugs was bad, you'd probably still get the best mileage in 5th gear, but it might not be able to go faster than 40 mph.

In 4-engine jets, the question would be 1) how many engines are out; 2) do I have symmetrical engines remaining, as asymmetric yaw and resultant rudder trim would affect the total drag on the airplane. (In the 747 [sim-only; thankfully!] two engines-out on one side was a handful, requiring full rudder AND full rudder trim...and I still got a 'Charlie Horse' from holding the pedal to the floor!