Lift-to-drag ratio
Overview
 
In aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...

, the lift-to-drag ratio, or L/D ratio, is the amount of lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...

 generated by a wing
Wing
A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...

 or vehicle, divided by the drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

 it creates by moving through the air. A higher or more favorable L/D ratio is typically one of the major goals in aircraft design; since a particular aircraft's required lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy, climb performance, and glide ratio.

The term is calculated for any particular airspeed
Airspeed
Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: indicated airspeed , calibrated airspeed , true airspeed , equivalent airspeed and density airspeed....

 by measuring the lift generated, then dividing by the drag at that speed.
Encyclopedia
In aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...

, the lift-to-drag ratio, or L/D ratio, is the amount of lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...

 generated by a wing
Wing
A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...

 or vehicle, divided by the drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

 it creates by moving through the air. A higher or more favorable L/D ratio is typically one of the major goals in aircraft design; since a particular aircraft's required lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy, climb performance, and glide ratio.

The term is calculated for any particular airspeed
Airspeed
Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: indicated airspeed , calibrated airspeed , true airspeed , equivalent airspeed and density 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 2D graph. In almost all cases the graph forms a U-shape, due to the two main components of drag.

Lift-to-drag ratios are usually found using a wind tunnel
Wind tunnel
A wind tunnel is a research tool used in aerodynamic research to study the effects of air moving past solid objects.-Theory of operation:Wind tunnels were first proposed as a means of studying vehicles in free flight...

.

Drag

Induced drag is a component of total drag that arises whenever a three-dimensional wing generates lift. At low speeds an aircraft has to generate lift with a higher angle of attack, thereby leading to greater induced drag. This term dominates the low-speed side of the L/D graph, the left side of the U.

Form drag is caused by movement of the aircraft through the air. This type of drag, also known as wind resistance or profile drag varies with the square of speed (see drag equation
Drag equation
In fluid dynamics, the drag equation is a practical formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid....

). For this reason profile drag is more pronounced at higher speeds, forming the right side of the L/D graph's U shape. Profile drag is lowered primarily by reducing cross section and streamlining.

The peak L/D ratio doesn't necessarily occur at the point of least total drag, as the lift produced at that speed is not high, hence a bad L/D ratio. Similarly, the speed at which the highest lift occurs does not have a good L/D ratio, as the drag produced at that speed is too high. The best L/D ratio occurs at a speed somewhere in between (usually slightly above the point of lowest drag). 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, the lift-to-drag ratio is not the only consideration for wing design. Performance at high angle of attack
Angle of attack
Angle of attack is a term used in fluid dynamics to describe the angle between a reference line on a lifting body and the vector representing the relative motion between the lifting body and the fluid through which it is moving...

 and a gentle stall
Stall (flight)
In fluid dynamics, a stall is a reduction in the lift coefficient generated by a foil as angle of attack increases. This occurs when the critical angle of attack of the foil is exceeded...

 are also important.

Glide ratio

As the aircraft fuselage
Fuselage
The fuselage is an aircraft's main body section that holds crew and passengers or cargo. In single-engine aircraft it will usually contain an engine, although in some amphibious aircraft the single engine is mounted on a pylon attached to the fuselage which in turn is used as a floating hull...

 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 approaching 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
Wing loading
In aerodynamics, wing loading is the loaded weight of the aircraft divided by the area of the wing. The faster an aircraft flies, the more lift is produced by each unit area of wing, so a smaller wing can carry the same weight in level flight, operating at a higher wing loading. Correspondingly,...

 means optimum glide ratio at higher 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 higher wing loading the maximum L/D occurs at a faster airspeed. Also, the faster airspeed means the aircraft will fly at higher Reynolds number and this will usually bring about a lower zero-lift drag coefficient.

Theory

Mathematically, the maximum lift-to-drag ratio can be estimated as:
,

where A is the aspect ratio
Aspect ratio (wing)
In aerodynamics, the aspect ratio of a wing is essentially the ratio of its length to its breadth . A high aspect ratio indicates long, narrow wings, whereas a low aspect ratio indicates short, stubby wings....

, the span efficiency factor, 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.

Supersonic/hypersonic lift to drag ratios

At very high speeds, lift to drag ratios tend to be lower. Concorde
Concorde
Aérospatiale-BAC Concorde was a turbojet-powered supersonic passenger airliner, a supersonic transport . It was a product of an Anglo-French government treaty, combining the manufacturing efforts of Aérospatiale and the British Aircraft Corporation...

 had a lift/drag ratio of around 7 at Mach 2, whereas a 747 is around 17 at about mach 0.85.

Dietrich Küchemann
Dietrich Küchemann
Dietrich Küchemann CBE FRS FRAeS was a German aerodynamicist who made several important contributions to the advancement of high-speed flight...

 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 roughly accurate.

Examples

The following table includes some representative L/D ratios.
In gliding flight, the L/D ratios are equal to the glide ratio (when flown at constant speed).

See also

  • 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
  • Range (aircraft)
    Range (aircraft)
    The maximal total range is the distance an aircraft can fly between takeoff and landing, as limited by fuel capacity in powered aircraft, or cross-country speed and environmental conditions in unpowered aircraft....

     range depends on the lift/drag ratio
  • Inductrack maglev
    Inductrack
    Inductrack is a passive, fail-safe electrodynamic magnetic levitation system, using only unpowered loops of wire in the track and permanent magnets on the vehicle to achieve magnetic levitation. The track can be in one of two configurations, a "ladder track" and a "laminated track"...

     has a higher lift/drag ratio than aircraft at sufficient speeds
  • Gravity drag
    Gravity drag
    In astrodynamics and rocketry, gravity drag is a measure of the loss in the net performance of a rocket while it is thrusting in a gravitational field...

     rocket
    Rocket
    A rocket is a missile, spacecraft, aircraft or other vehicle which obtains thrust from a rocket engine. In all rockets, the exhaust is formed entirely from propellants carried within the rocket before use. Rocket engines work by action and reaction...

    s can have an effective lift to drag ratio while maintaining altitude
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