In
aerodynamics, the lift-to-drag ratio (or L/D ratio) is the
lift generated by an aerodynamic body such as an
aerofoil
An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turb ...
or aircraft, divided by the
aerodynamic drag caused by moving through air. It describes the aerodynamic
efficiency under given flight conditions. The L/D ratio for any given body will vary according to these flight conditions.
For an aerofoil wing or powered aircraft, the L/D is specified when in straight and level flight. For a glider it determines the
glide ratio, of distance travelled against loss of height.
The term is calculated for any particular airspeed by measuring the lift generated, then dividing by the drag at that speed. These vary with speed, so the results are typically plotted on a 2-dimensional graph. In almost all cases the graph forms a U-shape, due to the two main components of drag. The L/D may be calculated using
computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate t ...
or
computer simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...
. It is measured empirically by testing in a
wind tunnel
Wind tunnels are large tubes with air blowing through them which are used to replicate the interaction between air and an object flying through the air or moving along the ground. Researchers use wind tunnels to learn more about how an aircraft ...
or in free
flight test.
The L/D ratio is affected by both the form drag of the body and by the induced drag associated with creating a lifting force. It depends principally on the lift and drag coefficients,
angle of attack to the airflow and the wing
aspect ratio.
The L/D ratio is inversely proportional to the
energy required for a given flightpath, so that doubling the L/D ratio will require only half of the energy for the same distance travelled. This results directly in better
fuel economy.
Lift and drag
Lift is created whenever an asymmetric body travels through a viscous fluid such as air. The asymmetry of an aerofoil is typically introduced by designing-in
camber and/or setting it at an
angle of attack to the airflow. The lift then increases as the square of the airspeed.
Whenever an aerodynamic body generates lift, this also creates induced, or
lift-induced drag. At low speeds an aircraft has to generate lift with a higher
angle of attack, which results in a greater induced drag. This term dominates the low-speed side of the graph of lift versus velocity.
Form drag is caused by movement of the body through air. This type of drag, known also as
air resistance or
profile drag varies with the square of speed (see
drag equation). For this reason profile drag is more pronounced at greater speeds, forming the right side of the lift/velocity graph's U shape. Profile drag is lowered primarily by streamlining and reducing cross section.
The
total drag on any aerodynamic body thus has two components, induced drag and form drag.
Lift and drag coefficients
The rates of change of lift and drag with angle of attack (AoA) are called respectively the
lift and
drag coefficients C
L and C
D. The varying ratio of lift to drag with AoA is often plotted in terms of these coefficients.
For any given value of lift, the AoA varies with speed. Graphs of C
L and C
D vs. speed are referred to as
drag curves. Speed is show increasing from left to right. The lift/drag ratio is given by the slope from the origin to some point on the curve and so the maximum L/D ratio does not occur at the point of least drag, the leftmost point. Instead it occurs at a slightly greater speed. Designers will typically select a wing design which produces an L/D peak at the chosen
cruising speed for a powered fixed-wing aircraft, thereby maximizing economy. Like all things in
aeronautical engineering
Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is sim ...
, the lift-to-drag ratio is not the only consideration for wing design. Performance at a high angle of attack and a gentle
stall are also important.
Glide ratio
As the aircraft
fuselage and control surfaces will also add drag and possibly some lift, it is fair to consider the L/D of the aircraft as a whole. As it turns out, the
glide ratio, which is the ratio of an (unpowered) aircraft's forward motion to its descent, is (when flown at constant speed) numerically equal to the aircraft's L/D. This is especially of interest in the design and operation of high performance
sailplanes, which can have glide ratios almost 60 to 1 (60 units of distance forward for each unit of descent) in the best cases, but with 30:1 being considered good performance for general recreational use. Achieving a glider's best L/D in practice requires precise control of airspeed and smooth and restrained operation of the controls to reduce drag from deflected control surfaces. In zero wind conditions, L/D will equal distance traveled divided by altitude lost. Achieving the maximum distance for altitude lost in wind conditions requires further modification of the best airspeed, as does alternating cruising and thermaling. To achieve high speed across country, glider pilots anticipating strong thermals often load their gliders (sailplanes) with
water ballast: the increased
wing loading means optimum glide ratio at greater airspeed, but at the cost of climbing more slowly in thermals. As noted below, the maximum L/D is not dependent on weight or wing loading, but with greater wing loading the maximum L/D occurs at a faster airspeed. Also, the faster airspeed means the aircraft will fly at greater
Reynolds number and this will usually bring about a lower
zero-lift drag coefficient.
Theory
Subsonic
Mathematically, the maximum lift-to-drag ratio can be estimated as:
:
where ''AR'' is the
aspect ratio,
the
span efficiency factor
The Oswald efficiency, similar to the span efficiency, is a correction factor that represents the change in drag with lift of a three-dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio and an elliptical lift ...
, a number less than but close to unity for long, straight edged wings, and
the
zero-lift drag coefficient.
Most importantly, the maximum lift-to-drag ratio is independent of the weight of the aircraft, the area of the wing, or the wing loading.
It can be shown that two main drivers of maximum lift-to-drag ratio for a fixed wing aircraft are wingspan and total
wetted area. One method for estimating the zero-lift drag coefficient of an aircraft is the equivalent skin-friction method. For a well designed aircraft, zero-lift drag (or parasite drag) is mostly made up of skin friction drag plus a small percentage of pressure drag caused by flow separation. The method uses the equation:
:
where
is the equivalent skin friction coefficient,
is the wetted area and
is the wing reference area. The equivalent skin friction coefficient accounts for both separation drag and skin friction drag and is a fairly consistent value for aircraft types of the same class. Substituting this into the equation for maximum lift-to-drag ratio, along with the equation for aspect ratio (
), yields the equation:
:
where ''b'' is wingspan. The term
is known as the wetted aspect ratio. The equation demonstrates the importance of wetted aspect ratio in achieving an aerodynamically efficient design.
Supersonic
At very great speeds, lift to drag ratios tend to be lower.
Concorde
The Aérospatiale/BAC Concorde () is a retired Franco-British supersonic airliner jointly developed and manufactured by Sud Aviation (later Aérospatiale) and the British Aircraft Corporation (BAC).
Studies started in 1954, and France and t ...
had a lift/drag ratio of about 7 at Mach 2, whereas a 747 is about 17 at about mach 0.85.
Dietrich Küchemann developed an empirical relationship for predicting L/D ratio for high Mach:
:
where ''M'' is the Mach number. Windtunnel tests have shown this to be approximately accurate.
Examples of L/D ratios
*
House sparrow: 4:1
*
Herring gull 10:1
*
Common tern
The common tern (''Sterna hirundo'') is a seabird in the family Laridae. This bird has a circumpolar distribution, its four subspecies breeding in temperate and subarctic regions of Europe, Asia and North America. It is strongly migrat ...
12:1
*
Albatross 20:1
*
Wright Flyer
The ''Wright Flyer'' (also known as the ''Kitty Hawk'', ''Flyer'' I or the 1903 ''Flyer'') made the first sustained flight by a manned heavier-than-air powered and controlled aircraft—an airplane—on December 17, 1903. Invented and flown ...
8.3:1
*
Boeing 747 in cruise 17.7:1.
* Cruising
Airbus A380 20:1
*
Concorde
The Aérospatiale/BAC Concorde () is a retired Franco-British supersonic airliner jointly developed and manufactured by Sud Aviation (later Aérospatiale) and the British Aircraft Corporation (BAC).
Studies started in 1954, and France and t ...
at takeoff and landing 4:1, increasing to 12:1 at Mach 0.95 and 7.5:1 at Mach 2
*
Helicopter
A helicopter is a type of rotorcraft in which lift and thrust are supplied by horizontally spinning rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forward, backward and laterally. These attribut ...
at 4.5:1
*
Cessna 172
The Cessna 172 Skyhawk is an American four-seat, single-engine, Monoplane#High, high wing, fixed-wing aircraft made by the Cessna Aircraft Company. gliding 10.9:1
[
* Cruising ]Lockheed U-2
The Lockheed U-2, nicknamed "''Dragon Lady''", is an American single-jet engine, high altitude reconnaissance aircraft operated by the United States Air Force (USAF) and previously flown by the Central Intelligence Agency (CIA). It provides da ...
25.6:1[
*]
* Rutan Voyager
The Rutan Model 76 Voyager was the first aircraft to fly around the world without stopping or refueling. It was piloted by Dick Rutan and Jeana Yeager. The flight took off from Edwards Air Force Base's 15,000 foot (4,600 m) runway in the Mo ...
27:1
* Virgin Atlantic GlobalFlyer 37:1
See also
*Gravity drag
In astrodynamics and rocketry, gravity loss is a measure of the loss in the net performance of a rocket while it is thrusting in a gravitational field
In physics, a gravitational field is a model used to explain the influences that a massive ...
rocket
A rocket (from it, rocchetto, , bobbin/spool) is a vehicle that uses jet propulsion to accelerate without using the surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entire ...
s can have an effective lift to drag ratio while maintaining altitude.
* Inductrack maglev
* Lift coefficient
* Range (aeronautics) range depends on the lift/drag ratio.
* Thrust specific fuel consumption the lift to drag determines the required thrust to maintain altitude (given the aircraft weight), and the SFC permits calculation of the fuel burn rate.
* Thrust-to-weight ratio
References
[Cessna Skyhawk II Performance Assessment http://temporal.com.au/c172.pdf]
External links
Lift-to-drag ratio calculator
{{Maglev
Aerodynamics
Aircraft performance
Aircraft wing design
Drag (physics)
Engineering ratios
Gliding technology
Wind power