Here's a specific reference saying that endurance is independent of altitude even for jets
Adam, I'm afraid he is incorrect as he has not taken into account the efficiency of turbine engines with respect to altitude. The higher the altitude the more efficient they are in terms of fuel burnt for the thrust produced. Higher means colder air for consumption, and the rotor/s are operating at higher RPM, both elements increasing efficiency. Theoretically a jet will have its greatest endurance at or near the tropopause. (As taught by the USN and USAF)
What is taught by the RAF and RAAF
Principles
1. Broadly, since fuel flow is proportional to thrust, fuel flow is least when thrust is least; therefore maximum level flight endurance is obtained when the aircraft is flying at the IAS for minimum drag (VIMD), because in level flight thrust is equal to drag.
2. Maximum endurance is obtained at an altitude which is governed by engine considerations. Although for a given set of conditions the IAS for minimum drag remains virtually constant at all altitudes, the engine efficiency varies with altitude and is lowest at the lowest altitudes where rpm must be severely reduced to provide the low thrust required.
3. To obtain the required amount of thrust most economically, the engine must be run at maximum continuous rpm. Therefore maximum endurance is obtained by flying at such an altitude that, with the engine(s) running at or near optimum cruising rpm, just enough thrust is provided to realize the speed for minimum drag, or MCRIT, whichever is the lower. Above the optimum altitude little, if any, additional benefit is obtained, and in some cases there may be a slight reduction because burner efficiency decreases at or about the highest altitude at which level flight is possible at VIMD. In general, optimum endurance is obtained by remaining between 20,000 ft and the tropopause at the recommended IAS and appropriate rpm. The greater the power/weight ratio of the aircraft, the greater will be the optimum height. With aircraft having high power/weight ratios, maximum endurance is obtained at the tropopause.
4. Altitude should only be changed to that for maximum endurance if the aircraft is above or near the endurance ceiling, otherwise if the aircraft is climbed from a much lower altitude, a considerably higher fuel flow will be required on the climb thereby reducing overall endurance.
5. On engines having variable swirl vanes, the consumption increases markedly if the rpm are so low that the swirl vanes are closed. If the altitude is low enough to cause the swirl vanes to close at the rpm required for VIMD, the aircraft should either be climbed to the lowest altitude at which VIMD can be obtained with the swirl vanes open, or the rpm increased to the point at which the vanes open, accepting the higher IAS.
Effect of Weight
6. Drag and thrust at the optimum IAS are functions of the all-up weight; the lower the weight the lower the thrust and fuel flow. Endurance varies inversely as the weight and not as the square root of the weight as in range flying because in pure endurance flying the TAS has no importance.
Effect of Temperature
7. In general, the lower the ambient air temperature, the higher the endurance, due to increased thermal efficiency, and vice versa. However, the effect is not marked unless the temperature differs considerably from the standard temperature for the altitude. In any case, the captain can do nothing but accept the difference, since any set of circumstances requiring flying for endurance usually ties the aircraft to a particular area and height band.
Twin and Multi-Engine Aircraft
8. When flying for endurance in twin or multi-engine aircraft at medium and low altitude, endurance can be improved by shutting down one or more engines. In this way the live engine(s) can be run at rpm closer to the optimum for the thrust required to fly at VIMD, thus improving GFC. Provided that the correct number of engines are used for the height, altitude has virtually no effect on the endurance achieved.
Use of the Fuel Flowmeter
9. The fuel flowmeter is a useful aid when flying for endurance. If the endurance speed is unknown, the throttle(s) should be set at the rpm which give the lowest indicated rate of fuel flow in level flight for the particular altitude.
10. Whenever reporting aircraft endurance, the time for which the aircraft can remain airborne should be given. It is confusing and dangerous to report endurance in terms of amount of fuel remaining because of the possibility of mis-interpretation.
Conclusions
11. Maximum endurance is achieved by flying at an altitude where optimum rpm give the minimum drag speed. It will rarely pay to climb to a higher altitude unless the commencing altitude is very low; in any event, the instruction or need to fly for endurance may preclude this. At the lower altitudes, maximum endurance may be obtained either by flaming-out engines to use optimum rpm on the remainder, or by using near-optimum rpm to give VIMD. It should be remembered that:
a. The importance of flying at VIMD outweighs engine considerations, always assuming that an engine, or engines, will be stopped in the low level case.
b. At lower altitudes there will be a slight decrease in endurance due to the higher ambient temperature reducing engine thermal efficiency.