The maximal total range is the maximum distance an aircraft can fly between takeoff and landing, as limited by fuel capacity in powered aircraft, or cross-country speed and environmental conditions in unpowered aircraft. The range can be seen as the cross-country ground speed multiplied by the maximum time in the air. The fuel time limit for powered aircraft is fixed by the fuel load and rate of consumption. When all fuel is consumed, the engines stop and the aircraft will lose its propulsion.
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Ferry range means the maximum range the aircraft can fly. This usually means maximum fuel load, optionally with extra fuel tanks and minimum equipment. It refers to transport of aircraft for use on remote location without any passengers or cargo. Combat range is the maximum range the aircraft can fly when carrying ordnance. Combat radius is a related measure based on the maximum distance a warplane can travel from its base of operations, accomplish some objective, and return to its original airfield with minimal reserves.
Derivation
For most unpowered aircraft, the maximum flight time is variable, limited by available daylight hours, aircraft design (performance), weather conditions, aircraft potential energy, and pilot endurance. Therefore, the range equation can only exactly calculated and will be derived for propeller and jet aircraft. If the total weight of the aircraft at a particular time
where
The rate of change of aircraft weight with distance
where
It follows that the range is obtained from the definite integral below, with
The term
Propeller aircraft
With propeller driven propulsion, the level flight speed at a number of airplane weights from the equilibrium condition
The corresponding fuel weight flow rates can be computed now:
Thrust power, is the speed multiplied by the drag, is obtained from the lift-to-drag ratio:
The range integral, assuming flight at constant lift to drag ratio, becomes
To obtain an analytic expression for range, it has to be noted that specific range and fuel weight flow rate can be related to the characteristics of the airplane and propulsion system; if these are constant:
Jet propulsion
The range of jet aircraft can be derived likewise. Now, quasi-steady level flight is assumed. The relationship
Jet engines are characterized by a thrust specific fuel consumption, so that rate of fuel flow is proportional to drag, rather than power.
Using the lift equation,
where
the specific range is found equal to:
Therefore, the range becomes:
When cruising at a fixed height, a fixed angle of attack and a constant specific fuel consumption, the range becomes:
where the compressibility on the aerodynamic characteristics of the airplane are neglected as the flight speed reduces during the flight.
Cruise/climb
For long range jet operating in the stratosphere, the speed of sound is constant, hence flying at fixed angle of attack and constant Mach number causes the aircraft to climb, without changing the value of the local speed of sound. In this case:
where
Or