Wikipedia / Range (aeronautics)
Wikipedia / Range (aeronautics)
The maximal total range is the maximum distance an aircraft can fly between takeoff and landing. Powered aircraft range is limited by the aviation fuel energy storage capacity (chemical or electrical) considering both weight and volume limits. 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. The fuel time limit for powered aircraft is fixed by the available fuel (considering reserve fuel requirements) and rate of consumption.
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. These aircraft could theoretically have an infinite range.
Ferry range means the maximum range that an aircraft engaged in ferry flying can achieve. This usually means maximum fuel load, optionally with extra fuel tanks and minimum equipment. It refers to the transport of aircraft without any passengers or cargo.
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
the initial and final aircraft masses
Specific range
is the fuel consumption rate, is called the specific range (= range per unit mass 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.
Propeller aircraft
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 9.81m/s2).
To obtain an analytic expression
Electric aircraft
An electric aircraft typically around 0.3.
Jet propulsion
The range of jet aircraft is used. The thrust here W is mass, as before, and Wg is a force in consistent units, e.g. newtons
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 is the air density, and S the wing area
Inserting this into (
When cruising at a fixed height, a fixed angle of attack is the initial flight speed: the flight speed reduces during the flight. (The effect this may have on the aerodynamic characteristics of the airplane is neglected).
Cruise/climb (Breguet range equation)
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 were misattributed to him.
For aircraft operating in the stratosphere (altitude approximately between 11 and 20km), the speed of sound is approximately constant, hence flying at a fixed angle of attack and constant Mach number the speed of sound which is known as the Breguet range equation.
Modified Breguet range equation
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. It is often useful to separate these terms. Doing so completes the nondimensionalization of the range equation into fundamental design disciplines of aeronautics.
where
is the geopotential energy height of the fuel (km)
is the overall propulsive efficiency (nondimensional
The geopotential energy height of the fuel is an intensive property for kerosene jet fuel is or about 69% of the Earth's radius.
As an example, with an overall engine efficiency of 40%, a lift-to-drag ratio of 18:1, and a structural efficiency of 50%, the cruise range would be
Operational considerations
The range equation may be further extended to consider operational factors by including an operational efficiency
may be expressed as the product of individual operational efficiency terms. For example, average wind may be accounted for using the relationship between average ground speed (GS), true airspeed (TAS, assumed constant), and average headwind (HW) component.
Routing efficiency may be defined as the great-circle distance
(e.g. 99% at 10 deg C above International Standard Atmosphere (ISA) temperature).
Practice
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. The advantage of such operation is that one percent of the range is traded for three to five percent higher cruise speed.
See also
References
External links
Anderson, David W. & Scott Eberhardt (2010). Understanding Flight, Second Edition. McGraw-Hill. (eBook) (print)
Marchman, James, III (2021). Blacksburg: VA: University Libraries at Virginia Tech. CC BY 4.0.
Martinez, Isidoro.
Ruijgrok, G. J. J. Elements of Airplane Performance. Delft University Press. .