View source for Lift-to-drag ratio

{{Short description|Measure of aerodynamic efficiency}}

[[File:Airfoil lift and drag.svg|thumb|upright=1.2|[[Lift (force)|Lift]] and [[aerodynamic drag|drag]] are the two components of the total [[aerodynamic force]] acting on an aerofoil or aircraft.]]

In [[aerodynamics]], the '''lift-to-drag ratio''' (or '''L/D ratio''') is the [[Lift (force)|lift]] generated by an aerodynamic body such as an [[aerofoil]] or aircraft, divided by the [[aerodynamic drag]] caused by moving through air. It describes the aerodynamic [[efficiency]] 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 the [[Lift-to-drag ratio#Glide ratio|glide 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 using [[computational fluid dynamics]] or [[computer simulation]]. It is measured empirically by testing in a [[wind tunnel]] or in free [[flight test]].<ref>{{cite journal | doi=10.1177/1729881418766190 | title=Accurate calculation of aerodynamic coefficients of parafoil airdrop system based on computational fluid dynamic | date=2018 | last1=Wu | first1=Wannan | last2=Sun | first2=Qinglin | last3=Luo | first3=Shuzhen | last4=Sun | first4=Mingwei | last5=Chen | first5=Zengqiang | last6=Sun | first6=Hao | journal=International Journal of Advanced Robotic Systems | volume=15 | issue=2 | doi-access=free }}</ref><ref>[https://www.diva-portal.org/smash/get/diva2:342732/fulltext01.pdf Validation of software for the calculation of aerodynamic coefficients] Ramón López Pereira, Linköpings Universitet</ref><ref>[https://www.mdpi.com/2226-4310/8/2/43/pdf In-flight Lift and Drag Estimation of an Unmanned Propeller-Driven Aircraft] Dominique Paul Bergmann, Jan Denzel, Ole Pfeifle, Stefan Notter, Walter Fichter and Andreas Strohmayer</ref>

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 wing [[Aspect ratio (aeronautics)|aspect ratio]].

The L/D ratio is inversely proportional to the [[Dissipation|energy 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 better [[fuel economy in aircraft|fuel 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 and drag==
[[File:DragvsSpeed.jpg|thumb|upright=1.2|Drag vs Speed. L/DMAX occurs at minimum Total Drag (e.g. Parasite plus Induced)]]
[[File:Coefficients of Drag and Lift vs AOA.jpg|thumb|upright=1.2|[[Drag coefficient|Coefficients of drag]] C<sub>D</sub> and [[Lift coefficient|lift]] C<sub>L</sub> vs [[angle of attack]].]]
[[File:Polar Curve 2.png|thumb|upright=1.2|Polar curve showing glide angle for the best glide speed (best L/D).  It is the flattest possible glide angle through calm air, which will maximize the distance flown.  This airspeed (vertical line) corresponds to the tangent point of a line starting from the origin of the graph.  A glider flying faster or slower than this airspeed will cover less distance before landing.<ref name="bw">{{cite book |last1=Wander |first1=Bob |title=Glider Polars and Speed-To-Fly...Made Easy! |date=2003 |publisher=Bob Wander's Soaring Books & Supplies |location=Minneapolis |pages=7–10}}</ref><ref name=faa>{{cite book |title=Glider Flying Handbook, FAA-H-8083-13 |date=2003 |publisher=U.S. Department of Transportation, FAA |isbn=9780160514197 |page=5-6 to 5-9}}</ref>]]
Lift can be created when an aerofoil-shaped body travels through a viscous fluid such as air. The aerofoil is often [[camber (aerodynamics)|cambered]] and/or set at an [[angle of attack]] to the airflow. The lift then increases as the square of the airspeed.

Whenever an aerodynamic body generates lift, this also creates [[lift-induced drag]] or induced drag. At low speeds an aircraft has to generate lift with a higher [[angle of attack]], which results in a greater induced drag. This term dominates the low-speed side of the graph of lift versus velocity.
[[File:DargPolarAL.png|thumb|upright=1.2|right|[[Drag curve]] for light aircraft. The tangent gives the maximum {{math|L/D}} point.]]
[[Form drag]] is caused by movement of the body through air. This type of drag, known also as [[air resistance]] or [[profile drag]] varies with the square of speed (see [[drag 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.

The [[Drag (aerodynamics)|total drag]] on any aerodynamic body thus has two components, induced drag and form drag.

===Lift and drag coefficients===
The rates of change of lift and drag with angle of attack (AoA) are called respectively the [[lift coefficient|lift]] and [[drag coefficient]]s C<sub>L</sub> and C<sub>D</sub>. 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 C<sub>L</sub> and C<sub>D</sub> vs. speed are referred to as [[drag curve]]s. 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 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 a high angle of attack and a gentle [[Stall (flight)|stall]] are also important.

==Glide ratio==
{{see also|Gliding flight#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. The [[Gliding (flight)#Glide ratio|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 [[sailplane]]s, 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) with [[Gliding competitions#Water ballast|water ballast]]: the increased [[wing 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 greater [[Reynolds number]] and this will usually bring about a lower [[zero-lift drag coefficient]].

==Theory==
===Subsonic===
Mathematically, the maximum lift-to-drag ratio can be estimated as<ref>{{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|access-date=2006-04-22}}</ref>
: <math>(L/D)_\text{max} = \frac{1}{2} \sqrt{\frac{\pi \varepsilon \text{AR}}{C_{D,0}}},</math>
where AR is the [[aspect ratio (wing)|aspect ratio]], <math>\varepsilon</math> the [[span efficiency factor]], a number less than but close to unity for long, straight-edged wings, and <math>C_{D,0}</math> 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 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. 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<ref>{{cite book|last1=Raymer|first1=Daniel|title=Aircraft Design: A Conceptual Approach|date=2012|publisher=AIAA|location=New York|edition=5th}}</ref>
: <math>C_{D,0} = C_\text{fe} \frac{S_\text{wet}}{S_\text{ref}},</math>
where <math>C_\text{fe}</math> is the equivalent skin friction coefficient, <math>S_\text{wet}</math> is the wetted area and <math>S_\text{ref}</math> 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 (<math>b^2/S_\text{ref}</math>), yields the equation
<math display=block>
 (L/D)_\text{max} = \frac{1}{2} \sqrt{\frac{\pi \varepsilon}{C_\text{fe}} \frac{b^2}{S_\text{wet}}},</math>
where ''b'' is wingspan. The term <math>b^2/S_\text{wet}</math> is known as the wetted aspect ratio. The equation demonstrates the importance of wetted aspect ratio in achieving an aerodynamically efficient design.

===Supersonic===
At supersonic speeds L/D values are lower. [[Concorde]] had a lift/drag ratio of about 7 at Mach&nbsp;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:<ref>[http://www.aerospaceweb.org/design/waverider/design.shtml Aerospaceweb.org Hypersonic Vehicle Design]</ref>
: <math>L/D_\text{max} = \frac{4(M + 3)}{M},</math>
where ''M'' is the Mach number. Windtunnel tests have shown this to be approximately accurate.

==Examples of L/D ratios==
[[File:Bruno Gantenbrink Nimeta D-KGYY.jpg|thumb|The [[Eta (glider)|eta]] has the best glide ratio for a sailplane]]

{{div col|colwidth=25em}}
* [[House sparrow]]: 4:1
* [[European herring gull|Herring gull]] 10:1
* [[Common tern]] 12:1
* [[Albatross]] 20:1
* [[Wright Flyer]] 8.3:1
* [[Boeing 747]] in cruise 17.7:1.<ref name=fili>{{cite web|url=http://aerodyn.org/HighLift/ld-tables.html |author=Antonio Filippone |work=Advanced topics in aerodynamics |title=Lift-to-Drag Ratios |url-status=dead |archive-url=https://web.archive.org/web/20080328133906/http://aerodyn.org/HighLift/ld-tables.html |archive-date=March 28, 2008 }}</ref>
* Cruising [[Airbus A380]] 20:1<ref>{{Cite book|title=Jet Propulsion|last=Cumpsty|first=Nicholas|publisher=Cambridge University Press|year=2003|pages=4}}</ref>
* [[Concorde]] at takeoff and landing 4:1, increasing to 12:1 at Mach 0.95 and 7.5:1 at Mach 2<ref name=concorde>{{cite book |url= https://books.google.com/books?id=VzNUJlX7CXoC|title= The Concorde Story |author= Christopher Orlebar |page= 116 |publisher= Osprey Publishing |date= 1997 |isbn= 9781855326675 }}{{dead link|date=January 2018 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>
* [[Helicopter]] at {{cvt|100|knots|km/h}}  4.5:1<ref name=leish>{{cite book |author= Leishman, J. Gordon |url= https://books.google.com/books?id=nMV-TkaX-9cC&pg=PA230|title= Principles of helicopter aerodynamics |page=230 |publisher= Cambridge University Press |date= 24 April 2006 |isbn= 0521858607 |quote= The maximum lift-to-drag ratio of the complete helicopter is about 4.5}}</ref>
* [[Cessna 172]] gliding 10.9:1<ref name=c172/>
* Cruising [[Lockheed U-2]] 25.6:1<ref>{{cite AV media |url= https://www.youtube.com/watch?v=nQnBJrj_-l8 |title= U2 Developments transcript |publisher= [[Central Intelligence Agency]] |date= 1960 |via= YouTube |access-date= 2016-03-05 |archive-date= 2022-06-19 |archive-url= https://web.archive.org/web/20220619041725/https://www.youtube.com/watch?v=nQnBJrj_-l8 |url-status= dead }}
*{{cite web |date=June 4, 2013 |title=U2 Developments |url=https://www.cia.gov/library/video-center/video-transcripts/u2-developments.html |archive-url=https://web.archive.org/web/20130816051125/https://www.cia.gov/library/video-center/video-transcripts/u2-developments.html |archive-date=2013-08-16 |website=Central Intelligence Agency }}</ref>
* [[Rutan Voyager]] 27:1
* [[Virgin Atlantic GlobalFlyer]] 37:1<ref name=noland>{{cite magazine |author= David Noland |title= The Ultimate Solo |magazine= Popular Mechanics |date= February 2005 |url= https://books.google.com/books?id=984DAAAAMBAJ&pg=PA79}}</ref>
{{div col end}}

{| class="wikitable sortable" 
|+ Computed aerodynamic characteristics<ref>{{cite journal |url= https://download.docslide.com.br/getdownload/document/?id=7IJToCKFQw1H4bxRVjAQc53PeU0CJKL04f4MFQhIRbSW%2F98TIdrs5xeyro9No7gOgevKjxbS9apqzxEm7avV1Q%3D%3D |title= Historical evolution of air transport productivity and efficiency |author= Rodrigo Martínez-Val|display-authors=etal|doi= 10.2514/6.2005-121 |date= January 2005 |journal= 43rd AIAA Aerospace Sciences Meeting and Exhibit |url-access= subscription }}{{Dead link|date=January 2019 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>
! Jetliner !! cruise L/D !! data-sort-type="date" | 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
|}

==See also==
*[[Gravity drag]]—[[rocket]]s can have an effective lift to drag ratio while maintaining altitude.
*[[Inductrack|Inductrack maglev]]
*[[Lift coefficient]]
*[[Range (aeronautics)]] range depends on the lift/drag ratio.
*[[Thrust specific fuel consumption]] the 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]]

==References==
<!--See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for an explanation of how to generate footnotes using the <ref(erences/)> tags-->
<ref name=c172>Cessna Skyhawk II Performance Assessment http://temporal.com.au/c172.pdf</ref>
<references/>

==External links==
* [https://www.fxsolver.com/browse/formulas/Lift-to-Drag+Ratio Lift-to-drag ratio calculator]

{{Maglev}}

[[Category:Aircraft aerodynamics]]
[[Category:Aircraft performance]]
[[Category:Aircraft wing design]]
[[Category:Drag (physics)]]
[[Category:Engineering ratios]]
[[Category:Gliding technology]]
[[Category:Wind power]]