Definitions

# Lift-to-drag ratio

In aerodynamics, the lift-to-drag ratio, or L/D ratio ("ell-over-dee" in the US, "ell-dee" in the UK), is the amount of lift generated by a wing or vehicle, divided by the 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 needed 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.

## Drag

Induced drag is caused by the generation of lift by the wing. Lift generated by a wing is perpendicular to the wing, but since wings typically fly at some small angle of attack, this means that a component of the force is directed to the rear. The rearward component of this force is seen as drag. 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.

Profile drag is caused by air hitting the wing, and other parts of the aircraft. This form of drag, also known as wind resistance, 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.

It is the lowest point of the graph, the point where the combined drag is at its lowest, that the wing or aircraft is performing at its best L/D. For this reason 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 descent to its forward motion, is numerically equal to the aircraft's L/D. This is especially of interest in the design and operation of high performance gliders (called 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 sailplane'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 altitude lost divided by distance traveled. 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, gliders are often loaded with water ballast to increase the airspeed (allowing better penetration against a headwind). As noted below, to first order the L/D is not dependent on speed, although the faster speed means the airplane will fly at higher Reynold's number.

## Maximum endurance

For maximum endurance, one should fly at the point on the graph with minimum drag. Since the lift on an aircraft must equal the weight, this point is equal to the maximum L/D point. Max endurance is achieved when the engines are using the smallest amount needed to overcome drag, and therefore the fuelflow is at the lowest at L/D max, causing the airplane to stay in the air the longest.

## Theory

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

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

where A is the aspect ratio, $epsilon$ is the aircraft's efficiency factor, and $C_\left\{D,0\right\}$ is the zero-lift drag coefficient.

## 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:

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

Windtunnel tests have shown this to be roughly accurate.

## Examples

The following table includes some representative L/D ratios.