Editing Chord (aeronautics)

{{short description|Imaginary straight line joining the leading and trailing edges of an aerofoil}}
{{distinguish|Wing chord (biology)}}
[[File:Wing profile nomenclature.svg|400px|thumb|Aerofoil nomenclature showing chord line]]
[[Image:Chord length definition (en).svg|right|thumb|400px|Chord line of a turbine aerofoil section.]]

In [[aeronautics]], the '''chord''' is an imaginary [[straight line segment]] joining the [[leading edge]] and [[trailing edge]] of an [[Airfoil|aerofoil]] cross section parallel to the direction of the airflow. The '''chord length''' is the distance between the trailing edge and the leading edge.<ref name=Clancy5.2>[[L. J. Clancy]] (1975), ''Aerodynamics'', Section 5.2, Pitman Publishing Limited, London. {{ISBN|0-273-01120-0}}</ref><ref name="houghton&carpenter"/> The point on the leading edge used to define the main chord may be the surface point of minimum radius.<ref name="houghton&carpenter">{{cite book | title=Aerodynamics for Engineering Students |author1=Houghton, E. L. |author2=Carpenter, P.W. | edition=5th | year=2003 |publisher=Butterworth-Heinemann | editor=Butterworth Heinmann | isbn=0-7506-5111-3}} p.18</ref> For a turbine aerofoil, the chord may be defined by the line between points where the front and rear of a 2-dimensional blade section would touch a flat surface when laid convex-side up.<ref>https://www.abbottaerospace.com/downloads/nasa-sp-290-turbine-design-and-application/, p.66 {{Dead link|date=February 2022}}</ref>

The [[wing]], [[horizontal stabilizer]], [[vertical stabilizer]] and [[Propeller (aircraft)|propeller]]/rotor blades of an aircraft are all based on aerofoil sections, and the term ''chord'' or ''chord length'' is also used to describe their width.  The chord of a wing, stabilizer and propeller is determined by measuring the distance between leading and trailing edges in the direction of the airflow.  (If a wing has a rectangular [[planform (aeronautics)|planform]], rather than tapered or swept, then the chord is simply the width of the wing measured in the direction of airflow.)  The term ''chord'' is also applied to the width of [[Flap (aircraft)|wing flaps]], [[ailerons]] and [[rudder]] on an aircraft.

Many wings are not rectangular, so they have different chords at different positions. Usually, the chord length is greatest where the wing joins the aircraft's [[fuselage]] (called the '''root chord''') and decreases along the wing toward the wing's tip (the '''tip chord'''). Most jet aircraft use a [[Tapering (mathematics)|tapered]] [[swept wing]] design. To provide a characteristic figure that can be compared among various wing shapes, the '''[[Chord (aeronautics)#Mean aerodynamic chord|mean aerodynamic chord]]''' (abbreviated '''MAC''') is used, although it is complex to calculate. The mean aerodynamic chord is used for calculating pitching moments.<ref>The Design Of The Aeroplane, Darrol Stinton 1984,{{ISBN|0 632 01877 1}}, p.26</ref>

A chord may also be defined for compressor and turbine aerofoils in [[gas turbine]] engines such as [[turbojet]], [[turboprop]], or [[turbofan]] engines for aircraft propulsion.

==Standard mean chord==
Standard mean chord (SMC) is defined as wing area divided by wing span:<ref>{{Cite book|title=Flight dynamics principles : a linear systems approach to aircraft stability and control|last=V.|first=Cook, M.|date=2013|publisher=Butterworth-Heinemann|isbn=9780080982427|edition=3rd|location=Waltham, MA|oclc=818173505}}</ref>

:<math>\mbox{SMC} = \frac{S}{b},</math>

where ''S'' is the wing area and ''b'' is the span of the wing. Thus, the SMC is the chord of a rectangular wing with the same area and span as those of the given wing. This is a purely geometric figure and is rarely used in [[aerodynamics]].

==Mean aerodynamic chord==
[[Image:Aircraft chord.svg|right|thumb|400px|Chords on a swept-wing. Note that the MAC occurring at a point where the trailing edge sweep changes in this image is just a coincidence for this particular wing. In general, this is not the case and any shape other than a simple trapezoid requires evaluation of the integral discussed in this section.]]

Mean aerodynamic chord (MAC) is defined as:<ref>Abbott, I.H., and Von Doenhoff, A.E. (1959), ''Theory of Wing Sections'', Section 1.4 (page 27), Dover Publications Inc., New York, Standard Book Number 486-60586-8</ref>

:<math>\mbox{MAC} = \frac{2}{S}</math><math>\int_{0}^{\frac{b}{2}}c(y)^2 dy,</math>

where ''y'' is the coordinate along the wing span and ''c'' is the chord at the coordinate ''y''. Other terms are as for SMC.

The MAC is a two-dimensional representation of the whole wing. The pressure distribution over the entire wing can be reduced to a single lift force on and a moment around the [[aerodynamic center]] of the MAC. Therefore, not only the length but also the position of MAC is often important. In particular, the position of [[center of gravity]] (CG) of an aircraft is usually measured relative to the MAC, as the percentage of the distance from the leading edge of MAC to CG with respect to MAC itself.

The ratio of the length (or ''span'') of a rectangular-planform wing to its chord is known as the [[aspect ratio (wing)|aspect ratio]], an important indicator of the [[lift-induced drag]] the wing will create.<ref>Kermode, A.C. (1972), ''Mechanics of Flight'', Chapter 3, (p.103, eighth edition), Pitman Publishing Limited, London {{ISBN|0-273-31623-0}}</ref> (For wings with planforms that are not rectangular, the aspect ratio is calculated as the square of the span divided by the wing planform area.) Wings with higher aspect ratios will have less induced drag than wings with lower aspect ratios. Induced drag is most significant at low airspeeds. This is why [[Glider aircraft|glider]]s have long slender wings.

==Tapered wing==
{{redirect|Taper ratio|taper ratio in space elevator construction|Space_elevator#Cable_materials}}
Knowing the area (S<sub>w</sub>), taper ratio (<math>\lambda</math>) and the span (b) of the wing, the chord at any position on the span can be calculated by the formula:<ref>Ruggeri, M.C., (2009), ''Aerodinámica Teórica'', Apuntes de la materia, UTN-FRH, Haedo, Buenos Aires</ref>

:<math>c(y)=\frac{2\,S_w}{(1+\lambda)b}\left[1-\frac{1-\lambda}{b}|2 y|\right].</math>
where

<math>\lambda=\frac{C_{\rm Tip}}{C_{\rm Root}}</math>

==References==
{{reflist}}

==External links==
* [http://www.ae.su.oz.au/aero/contents.html Aerodynamics for Students] 
** wayback machine:[https://web.archive.org/web/20041031075800/http://www.ae.su.oz.au:80/aero/contents.html]
* [https://web.archive.org/web/20180703141301/http://airfieldmodels.com/information_source/math_and_science_of_model_aircraft/formulas/mean_aerodynamic_chord.htm Finding the Mean Aerodynamic Chord (MAC)]
* [https://web.archive.org/web/20150626103336/http://www.aviarus-21.com/cg-calc?lang=en Image based Mean Aerodynamic Chord (MAC) calculator]

[[Category:Aeronautics]]
[[Category:Aircraft aerodynamics]]
[[Category:Aircraft wing design]]