- Lift-to-drag ratio
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 wingor 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
airspeedby 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.
Induced dragis 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 dragis 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 speedfor 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 attackand a gentle stall are also important.
As the aircraft
fuselageand 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.
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.
Mathematically, the maximum lift-to-drag ratio can be estimated as:
: [cite web|author=Loftin, LK, Jr.|title=Quest for performance: The evolution of modern aircraft. NASA SP-468|url=http://www.hq.nasa.gov/pao/History/SP-468/cover.htm|accessdate=2006-04-22] ,
where "A" is the aspect ratio, is the aircraft's efficiency factor, and is the
zero-lift drag coefficient.
upersonic/hypersonic lift to drag ratios
At very high speeds, lift to drag ratios tend to be lower.
Concordehad a lift/drag ratio of around 7 at Mach 2, whereas a 747 is around 17 at about mach 0.85. Dietrich Küchemanndeveloped an empirical relationship for predicting L/D ratio for high Mach: [ [http://www.aerospaceweb.org/design/waverider/design.shtml Aerospaceweb.org Hypersonic Vehicle Design] ]
Windtunnel tests have shown this to be roughly accurate.
The following table includes some representative L/D ratios.
Specific fuel consumptionthe 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
Inductrack maglevhas a higher lift/drag ratio than aircraft at sufficient speeds
Gravity drag rockets can have an effective lift to drag ratio while maintaining altitude
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