## Range (aeronautics) |

The maximal total **range** is the maximum distance an

**
Ferry range** means the maximum range the aircraft can fly. This usually means maximum

- derivation
- see also
- references

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 is

= ,

where is the zero-fuel weight and the weight of the fuel (both in kg), the fuel consumption rate per unit time flow (in kg/s) is equal to

.

The rate of change of aircraft weight with distance (in meters) is

,

where is the speed (in m/s), so that

It follows that the range is obtained from the definite integral below, with and the start and finish times respectively and and the initial and final aircraft weights

.

The term is called the specific range (= range per unit weight of fuel; S.I. units: m/kg). 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.

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

The corresponding fuel weight flow rates can be computed now:

Thrust power, is the speed multiplied by the drag, is obtained from the

; here Weight is a force in Newton

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

; here Weight is mass in kilograms therefor the gravityconstant g is added. Depending on the distance to the centre of gravity of earth but in average terms g = 9,81 m/s².

To obtain an

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:

; here Weight is a force in Newton

Jet engines are characterized by a

Using the

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

the specific range is found equal to:

Therefore, the range (in meters) becomes:

; here Weight is again mass in kilograms therefor the gravityconstant g is added, an average of g = 9,81 m/s².

When cruising at a fixed height, a fixed

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

where is the cruise Mach number and the

where ; here is the specific heat constant of air 287.16 (based on aviation standards) and (derived from and ). en are the specific

Or , also known as the *Breguet range equation* after the French aviation pioneer,

Other Languages

العربية: مدى (طائرة)

čeština: Dolet letadla

Deutsch: Breguet’sche Reichweitenformel

español: Alcance (aeronáutica)

français: Distance franchissable

한국어: 항속 거리

Bahasa Indonesia: Jarak jangkau

italiano: Autonomia (meccanica)

қазақша: Ұшу алыстығы

Nederlands: Actieradius

日本語: 航続距離

polski: Zasięg pojazdu

slovenčina: Dolet (letecká technika)

slovenščina: Dolet

suomi: Lentomatka

اردو: حد (طیرانیات)

中文: 航程 (航空)