The
Wright brothers testing their gliders in 1901 (left) and 1902 (right). The angle of the tether reflects the dramatic improvement in the lifttodrag ratio
In aerodynamics, the lifttodrag 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 Ushape, due to the two main components of drag.
Lifttodrag 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

See also 6

References 7
Drag
Liftinduced drag is a component of total drag that arises whenever a threedimensional 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 lowspeed 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 drag curve
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 fixedwing aircraft, thereby maximizing economy. Like all things in aeronautical engineering, the lifttodrag 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 zerolift drag coefficient.
Theory
Mathematically, the maximum lifttodrag ratio can be estimated as:

(L/D)_{max} = \frac{1}{2} \sqrt{\frac{\pi A \epsilon}{C_{D,0}}},^{[1]}
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 zerolift drag coefficient.
Most importantly, the maximum lifttodrag 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 lifttodrag ratio for a fixed wing aircraft are wingspan and total wetted area. One method for estimating the zerolift drag coefficient of an aircraft is the equivalent skinfriction method, which makes use of the fact that for a well designed aircraft, zerolift 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}},^{[2]}
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 lifttodrag 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:^{[3]}

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

^ Loftin, LK, Jr. "Quest for performance: The evolution of modern aircraft. NASA SP468". Retrieved 20060422.

^ Raymer, Daniel (2012). Aircraft Design: A Conceptual Approach (5th ed.). New York: AIAA.

^ Aerospaceweb.org Hypersonic Vehicle Design

^ ^{a} ^{b} David Noland, "Steve Fossett and Burt Rutan's Ultimate Solo: Behind the Scenes", Popular Mechanics, Feb. 2005 (web version)

^ ^{a} ^{b} ^{c} ^{d} Fillipone

^ Leishman, J. Gordon. Principles of helicopter aerodynamics p230, Cambridge University Press, 24 April 2006. Accessed: 27 February 2012. ISBN 0521858607. Quote: The maximum lifttodrag ratio of the complete helicopter is about 4.5

^ ^{a} ^{b} Space Shuttle Technical Conference pg 258

^ Hillje, Ernest R., "Entry Aerodynamics at Lunar Return Conditions Obtained from the Flight of Apollo 4 (AS501)," NASA TN D5399, (1969).


Technologies



Transport



Transport Accidents



Proposals in italics


This article was sourced from Creative Commons AttributionShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, EGovernment Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a nonprofit organization.