Range (aircraft)
The maximal total range is the distance an aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...

 can fly between takeoff
Takeoff is the phase of flight in which an aerospace vehicle goes from the ground to flying in the air.For horizontal takeoff aircraft this usually involves starting with a transition from moving along the ground on a runway. For balloons, helicopters and some specialized fixed-wing aircraft , no...

 and landing
thumb|A [[Mute Swan]] alighting. Note the ruffled feathers on top of the wings indicate that the swan is flying at the [[Stall |stall]]ing speed...

, as limited by fuel capacity in powered aircraft
Powered aircraft
A powered aircraft is an aircraft that uses onboard propulsion. This requires a power source, and some method of coupling the power to the air in order to create a forward force or thrust...

, or cross-country speed and environmental conditions in unpowered aircraft.

Ferry range means the maximum range the aircraft can fly. This usually means maximum fuel
Fuel is any material that stores energy that can later be extracted to perform mechanical work in a controlled manner. Most fuels used by humans undergo combustion, a redox reaction in which a combustible substance releases energy after it ignites and reacts with the oxygen in the air...

 load, optionally with extra fuel tanks and minimum equipment. It refers to transport of aircraft for use on remote location.

Combat range is the maximum range the aircraft can fly when carrying ordnance.

Combat radius
Combat radius
Combat radius refers to the distance from an airbase that a warplane can reach, patrol there for a set amount of time and return to base with minimal fuel left, thus completing a combat mission...

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.

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. For unpowered aircraft, the maximum flight time is variable, limited by available daylight hours, weather conditions, and pilot endurance.

The range can be seen as the cross-country ground speed multiplied by the maximum time in the air. The range equation will be derived in this article for propeller and jet aircraft.


The fuel
Fuel is any material that stores energy that can later be extracted to perform mechanical work in a controlled manner. Most fuels used by humans undergo combustion, a redox reaction in which a combustible substance releases energy after it ignites and reacts with the oxygen in the air...

 consumption per unit time is:

Where is the total fuel load.
Since , the fuel weight flow rate is related to the weight of the airplane by:

The rate of change of fuel weight with distance is, therefore:

where V is the speed.

It follows that the range is obtained from the following definite integral

the term V/F is called the specific range (=range per unit weight of fuel). The specific range can now be determined as though the airplane is in quasi steady state flight. Here, a difference between jet and propeller driven aircraft has to be noticed.

Propeller aircraft

With propeller driven propulsion, the level flight speed at a number of airplane weights from the equilibrium condition has to be noted. To each flight velocity, there corresponds a particular value of propulsive efficiency and specific fuel consumption
Brake specific fuel consumption
Brake Specific Fuel Consumption is a measure of fuel efficiency within a shaft reciprocating engine.It is the rate of fuel consumption divided by the power produced. It may also be thought of as power-specific fuel consumption, for this reason...

 . The successive engine powers can be found:

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 is used. The thrust can now be written as:

Jet engines are characterised by a thrust specific fuel consumption, so that rate of fuel flow is proportional to drag, rather than power.

Using the lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...


where is the air density, and S the wing area.

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.


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 is the cruise Mach number and the speed of sound. The range equation reduces to:

Or , also known as the Breguet
Louis Charles Breguet
Louis Charles Breguet was a French aircraft designer and builder, one of the early aviation pioneers.- Biography :...

range equation.
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