Inaerodynamics, thelift-to-drag ratio (orL/D ratio) is thelift generated by an aerodynamic body such as anaerofoil or aircraft, divided by theaerodynamic drag caused by moving through air. It describes the aerodynamicefficiency 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 theglide 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 usingcomputational fluid dynamics orcomputer simulation. It is measured empirically by testing in awind tunnel or in freeflight test.[1][2][3]
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 wingaspect ratio.
The L/D ratio is inversely proportional to theenergy 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 betterfuel economy.
The L/D ratio can also be used for water craft and land vehicles. The L/D ratios for hydrofoil boats and displacement craft are determined similarly to aircraft.
Lift can be created when an aerofoil-shaped body travels through a viscous fluid such as air. The aerofoil is oftencambered and/or set at anangle of attack to the airflow. The lift then increases as the square of the airspeed.
Whenever an aerodynamic body generates lift, this also createslift-induced drag or induced drag. At low speeds an aircraft has to generate lift with a higherangle 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 asair resistance orprofile drag varies with the square of speed (seedrag 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.
Thetotal drag on any aerodynamic body thus has two components, induced drag and form drag.
The rates of change of lift and drag with angle of attack (AoA) are called respectively thelift anddrag coefficients CL and CD. 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 CL and CD vs. speed are referred to asdrag curves. Speed is shown 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 coefficient, 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 chosencruising speed for a powered fixed-wing aircraft, thereby maximizing economy. Like all things inaeronautical engineering, the lift-to-drag ratio is not the only consideration for wing design. Performance at a high angle of attack and a gentlestall are also important.
As the aircraftfuselage 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. Theglide 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 performancesailplanes, 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) withwater ballast: the increasedwing 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 greaterReynolds number and this will usually bring about a lowerzero-lift drag coefficient.
Mathematically, the maximum lift-to-drag ratio can be estimated as[6]
where AR is theaspect ratio, thespan efficiency factor, a number less than but close to unity for long, straight-edged wings, and thezero-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 totalwetted 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[7]
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 equationwhereb 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.
At supersonic speeds L/D values are lower.Concorde had a lift/drag ratio of about 7 at Mach 2, whereas a 747 has about 17 at about mach 0.85.
Dietrich Küchemann developed an empirical relationship for predicting L/D ratio for high Mach numbers:[8]
whereM is the Mach number. Windtunnel tests have shown this to be approximately accurate.
| Jetliner | cruise L/D | First flight |
|---|---|---|
| Lockheed L1011-100 | 14.5 | Nov 16, 1970 |
| McDonnell Douglas DC-10-40 | 13.8 | Aug 29, 1970 |
| Airbus A300-600 | 15.2 | Oct 28, 1972 |
| McDonnell Douglas MD-11 | 16.1 | Jan 10, 1990 |
| Boeing 767-200ER | 16.1 | Sep 26, 1981 |
| Airbus A310-300 | 15.3 | Apr 3, 1982 |
| Boeing 747-200 | 15.3 | Feb 9, 1969 |
| Boeing 747-400 | 15.5 | Apr 29, 1988 |
| Boeing 757-200 | 15.0 | Feb 19, 1982 |
| Airbus A320-200 | 16.3 | Feb 22, 1987 |
| Airbus A310-300 | 18.1 | Nov 2, 1992 |
| Airbus A340-200 | 19.2 | Apr 1, 1992 |
| Airbus A340-300 | 19.1 | Oct 25, 1991 |
| Boeing 777-200 | 19.3 | Jun 12, 1994 |
The maximum lift-to-drag ratio of the complete helicopter is about 4.5