- Range (aircraft)
The maximal total range is the distance an
aircraftcan fly between takeoffand landing, as limited by fuel capacity in powered aircraft, or cross-country speed and environmental conditions in unpowered aircraft.
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 t_max. The range equation will derived in this article for propeller and jet aircraft.
fuelconsumption 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.
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 . 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 expressionfor 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:
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 characteristed by a thrust specific fuel consumption, so that rate of fuel flow is proportional to drag, rather than power.
Using the lift equation,
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 negelected 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 M is the cruise Mach number and a the speed of sound. The range equation reduces to:
Or , also known as the Breguet range equation.
* G.J.J. Ruigrok, Elements of airplane performance, Delft University Press
Wikimedia Foundation. 2010.
Look at other dictionaries:
Range — Contents 1 Mathematics, science, and technology 1.1 In mathematics 1 … Wikipedia
Aircraft diesel engine — Thielert Centurion aircraft diesel engine. The aircraft diesel engine or aero diesel has not been widely used as an aircraft engine. Diesel engines were used in airships and were tried in aircraft in the late 1920s … Wikipedia
Range Regional Airport — IATA: HIB – ICAO: KHIB – FAA LID: HIB … Wikipedia
Aircraft Communication Addressing and Reporting System — Aircraft Communications Addressing and Reporting System (or ACARS) is a digital datalink system for transmission of small messages between aircraft and ground stations via radio or satellite. The protocol, which was designed by ARINC to replace… … Wikipedia
Aircraft registration — A Van s Aircraft RV 7 displaying registration G KELS. The G prefix denotes a civil aircraft registered in the United Kingdom An aircraft registration is a unique alphanumeric string that identifies a civil aircraft, in similar fashion to a… … Wikipedia
Aircraft spotting — or Plane spotting is the observation and logging registration numbers of aircraft: gliders, powered aircraft, large balloons, airships, helicopters, and microlights. When spotting aircraft or planes , observers notice the key attributes of an… … Wikipedia
Aircraft type club — Aircraft type clubs are organizations that provide information and support to a single aircraft type or a group of aircraft types from the same manufacturer or family of aircraft.Canadian Owners and Pilots Association: The COPA Guide To Buying an … Wikipedia
Aircraft of the Battle of Britain — The Battle of Britain (German: [http://de.wikipedia.org/wiki/Luftschlacht um England Luftschlacht um England ] ) was an effort by the German Luftwaffe during during the summer and autumn, 1940 to gain air superiority over the United Kingdom in… … Wikipedia
Aircraft carrier — From bottom to top: Principe de Asturias, amphibious assault ship USS Wasp, USS Forrestal and light V/STOL carrier HMS Invincible, showing size differences of late 20th century carriers An aircraft … Wikipedia
Aircraft — An aircraft is a vehicle which is able to fly through the Earth s atmosphere or through any other atmosphere. Rocket vehicles are not aircraft if they are not supported by the surrounding air. All the human activity which surrounds aircraft is… … Wikipedia