Wing Geometry Definitions


The wing geometry may be specified in several ways. This section defines a few commonly used terms and how to compute them.

Wing Areas

The definition of wing area is not obvious and different companies define the areas differently. Here, we always take the reference wing area to be that of the trapezoidal portion of the wing projected into the centerline. The leading and trailing edge chord extensions are not included in this definition and for some airplanes, such as Boeing's Blended Wing Body, the difference can be almost a factor of two between the "real" wing area and the "trap area". Some companies use reference wing areas that include portions of the chord extensions, and in some studies, even tail area is included as part of the reference area. For simplicity, we use the trapezoidal area in this text.

Reference Wing Area Exposed Wing Area Area Affected by Flaps

In addition to the reference area, we use the exposed planform area depicted above in the calculation of skin friction drag and the wetted area which is a bit more than twice the exposed planform area.

 

Wing Span and Aspect Ratio

Of all the parameters that might be defined without a footnote, span seems to be the most unambiguous; however, even this is not so clear. The small effect of wing bending on the geometric span can become very measurable when the wing includes winglets. We ignore the differences here, but suggest that a reference span should be measured on the ground with a prescribed fuel load since this is the only condition in which it may be conveniently verified.

Aspect ratio is often used in place of the dimensional span in many of the aerodynamic equations of interest. Aspect ratio, or AR, is roughly the ratio of span to average wing chord. It may be computed by: AR = b2 / Sref. It is important that the same definition of reference area be used in the definition of aspect ratio as is used in the definition of coefficients such as CL and CD.

 

Reference Lengths

Various wing reference lengths are used in aerodynamic computations. One of the most important of these is the mean aerodynamic chord, or M.A.C.. The M.A.C. is the chord-weighted average chord length of the wing, defined as:

For a linearly tapered (trapezoidal) wing, this integral is equal to:

M.A.C. = 2/3 (Croot + Ctip - Croot Ctip / (Croot+Ctip))

For wings with chord extensions, the MAC may be computed by evaluating the MAC of each linearly-tapered portion then taking an average, weighted by the area of each portion. In many cases, however, the MAC of the reference trapezoidal wing is used.

The M.A.C. is often used in the nondimensionalization of pitching moments. The M.A.C. of just the exposed area is also used to compute the reference length for calculation of Reynolds number as part of the wing drag estimation. The M.A.C. is chosen instead of the simpler mean geometric chord for quantities whose values are weighted more strongly by local chord that is reflected by their contribution to the area.