Range (aeronautics)

The maximal total range is the maximum distance an aircraft can fly between takeoff and landing.

[1] Unpowered aircraft range depends on factors such as cross-country speed and environmental conditions.

The range can be seen as the cross-country ground speed multiplied by the maximum time in the air.

Some aircraft can gain energy while airborne through the environment (e.g. collecting solar energy or through rising air currents from mechanical or thermal lifting) or from in-flight refueling.

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.

With propeller-driven propulsion, the level flight speed at a number of airplane weights from the equilibrium condition

Thrust power is the speed multiplied by the drag, is obtained from the lift-to-drag ratio:

here Wg is the weight (force in newtons, if W is the mass in kilograms); g is standard gravity (its exact value varies, but it averages 9.81 m/s2).

The range integral, assuming flight at a constant lift to drag ratio, becomes

To obtain an analytic expression for range, a specific range and fuel weight flow rate can be related to the characteristics of the airplane and propulsion system; if these are constant:

An electric aircraft with battery power only will have the same mass at takeoff and landing.

the total efficiency (typically 0.7-0.8 for batteries, motor, gearbox and propeller),

here W is a force in newtons Jet engines are characterized by a thrust specific fuel consumption, so that rate of fuel flow is proportional to drag, rather than power.

is the air density, and S the wing area, the specific range is found equal to:

During World War I, René Devillers, engineer at the Ecole Supérieure D'Aéronautique, developed methods to calculate radius of action and range for bombing missions.

After their declassification they were published in 1921 by the French aviation pioneer, Louis Charles Breguet, and got misattributed to him.

[3] For jet aircraft operating in the stratosphere (altitude approximately between 11 and 20 km), the speed of sound is approximately constant, hence flying at a fixed angle of attack and constant Mach number requires the aircraft to climb (as weight decreases due to fuel burn), without changing the value of the local speed of sound.

is the specific heat constant of air 287.16 J/kg K (based on aviation standards) and

It is possible to improve the accuracy of the Breguet range equation by recognizing the limitations of the conventionally used relationships for fuel flow:

In the Breguet range equation, it is assumed that the thrust specific fuel consumption is constant as the aircraft weight decreases.

This is generally not a good approximation because a significant portion (e.g. 5% to 10%) of the fuel flow does not produce thrust and is instead required for engine "accessories" such as hydraulic pumps, electrical generators, and bleed air powered cabin pressurization systems.

This can be accounted for by extending the assumed fuel flow formula in a simple way where an "adjusted" virtual aircraft gross weight

Here, the thrust specific fuel consumption has been adjusted down and the virtual aircraft weight has been adjusted up to maintain the proper fuel flow while making the adjusted thrust specific fuel consumption truly constant (not a function of virtual weight).

The above equation combines the energy characteristics of the fuel with the efficiency of the jet engine.

Doing so completes the nondimensionalization of the range equation into fundamental design disciplines of aeronautics.

where giving the final form of the theoretical range equation (not including operational factors such as wind and routing)

A physical interpretation is a height that a quantity of fuel could lift itself in the Earth's gravity field (assumed constant) by converting its chemical energy into potential energy.

for kerosene jet fuel is 2,376 nautical miles (4,400 km) or about 69% of the Earth's radius.

While the peak value of a specific range would provide maximum range operation, long-range cruise operation is generally recommended at a slightly higher airspeed.

Most long-range cruise operations are conducted at the flight condition that provides 99 percent of the absolute maximum specific range.

Maximum Endurance and Range versus airspeed. The maximum endurance condition would be obtained at the point of minimum power required since this would require the lowest fuel flow to keep the airplane in a steady, level flight. Maximum range condition would occur where the ratio of speed to power required is greatest. The maximum range condition is obtained at maximum lift/drag ratio (L/DMAX)