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# Lift-to-drag ratio

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 Title: Lift-to-drag ratio Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Lift-to-drag ratio The Wright brothers testing their gliders in 1901 (left) and 1902 (right). The angle of the tether reflects the dramatic improvement in the lift-to-drag ratio

In aerodynamics, the lift-to-drag ratio, or L/D ratio, is the amount of lift generated by a wing or vehicle, divided by the aerodynamic drag 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 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 can be determined by flight test, by calculation or by testing in a wind tunnel.

## Contents

• Drag 1
• Glide ratio 2
• Theory 3
• Supersonic/hypersonic lift to drag ratios 4
• Examples 5
• References 7

## Drag

Lift-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 air resistance or profile drag varies with the square of speed (see drag equation). 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 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 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 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:

(L/D)_{max} = \frac{1}{2} \sqrt{\frac{\pi A \epsilon}{C_{D,0}}},

where A is the aspect ratio, \epsilon the span efficiency factor, a number less than but close to unity for long, straight edged wings, and C_{D,0} 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 the 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, which makes use of the fact that 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:

C_{D,0}=C_{fe}\frac{S_{wet}}{S_{ref}},

where C_{fe} is the equivalent skin friction coefficient, S_{wet} is the wetted area and S_{ref} is the wing reference area. The equivalent skin friction coefficient accounts for the 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 (b^2/S_{ref}), yields the equation:

(L/D)_{max}=\frac{1}{2} \sqrt{\frac{\pi \epsilon}{C_{fe}}\frac{b^2}{S_{wet}}}

where b is wingspan. The term b^2/S_{wet} is known as the wetted aspect ratio. The equation demonstrates the importance of wetted aspect ratio in achieving an aerodynamically efficient design.

## Supersonic/hypersonic lift to drag ratios

At very high speeds, lift to drag ratios tend to be lower. Concorde had a lift/drag ratio of around 7 at Mach 2, whereas a 747 is around 17 at about mach 0.85.

Dietrich Küchemann developed an empirical relationship for predicting L/D ratio for high Mach:

L/D_{max}=\frac{4(M+3)}{M}

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.

Flight article Scenario L/D ratio
Virgin Atlantic GlobalFlyer Cruise 37
Lockheed U-2 Cruise ~28
Rutan Voyager Cruise 27
Albatross 20
Boeing 747 Cruise 17
Common tern 12
Herring gull 10
Concorde M2 Cruise 7.14
Cessna 150 Cruise 7
Helicopter 100 kts speed 4.5
Concorde Approach 4.35
House sparrow 4

In gliding flight, the L/D ratios are equal to the glide ratio (when flown at constant speed).

Flight article Scenario L/D ratio/
glide ratio
Modern sailplane Gliding 40–60 (depending on span)
Hang glider 15
Gimli Glider Boeing 767-200 with fuel exhaustion ~12
Paraglider High performance model 11
Helicopter Autorotation 4
Powered parachute Rectangular/elliptical parachute 3.6/5.6
Space Shuttle Approach 4.5
Wingsuit Gliding 2.5
Northern flying squirrel Gliding 1.98
Space Shuttle Hypersonic 1
Apollo CM Reentry 0.368