Maximum range flying is done so we can fly the maximum distance for the amount of fuel onboard. This can be set against distance covered through air or over ground. It is of interest to a pilot when he wants to fly with the least amount of fuel flow for a distance traveled to save fuel.
Maximum endurance flying is done when the pilot wants to remain airborne for the maximum time possible given an amount of fuel. Waiting for the weather to clear to be able to land is an example of this practice.
Flying for maximum range or endurance can take the aircraft and maybe the pilot to their limits, do this safely and wisely.
For maximum range flying you must operate the aircraft and engine in such a way that maximum efficiency is obtained over the distance to be flown. Do that by keeping the following factors in mind:
We have two ways of expressing specific range: as Specific Air Range, which is air nautical miles per fuel unit (SAR) or as Specific Ground Range, which is ground nautical miles per fuel unit (SGR). These two are interconnected because SGR is SAR influenced by wind velocity.
If we would include time (hour) in these definitions then we get the following: Nautical Miles / Time = TAS (kts) and Fuel / Time = Fuel Flow (USG).
To achieve the best possible SAR we need to get the best TAS / Fuel Flow ratio and as fuel flow relates to power we can also say TAS / Power ratio.
Engine gross fuel consumption or fuel flow (GFC) depends on how much power is requested related to its specific fuel consumption (SFC), thus GFC = SFC × Power. Combining these formula's results in: SAR = TAS / Power × 1 / SFC.
Thus, we need to fly the aircraft to its maximum airframe efficiency TAS / Power and engine efficiency 1 / SFC. Maximum airframe efficiency is at the speed for minimum drag or maximum L/D ratio. This is usually equal to the well known VY.
For piston aircraft the best range speed is about 10% higher, sometimes known as the 'long range cruise speed'.
As the minimum drag or maximum L/D ratio does not change with altitude (TAS and power required increase by the same amount) so therefore there is no effect on SAR. Even the IAS remains the same. Only tailwinds at altitude could mean a real advantage.
Weight does have its toll on SAR. As weight increases, the angle of attack for the best L/D ratio is at a higher IAS (thus TAS is higher), more speed means more drag and more power is required and it is out of proportion too because Power = Drag × TAS. Thus specific air range is lower with an increase of aircraft weight.
To take into account the distance covered over ground we need to apply the headwind component to the true airspeed (TAS) to arrive at groundspeed (GS). It is easy to see that a tailwind favors specific range resulting in a higher SGR. GS is used to find the best SGR, thus GS / Fuel Flow or GS / Power.