Comparison of m. a. Chord and m. a. Center for. Basic Planforms and Loading Distributions

In Table C. l taken from (Yates, 1952), values of m. a. chord and у are given for some basic planforms and loading distributions.

In the general case the additional loading distribution and the spanwise center-of – pressure position can be obtained by methods such as those of De Young and Harper (1948), Weissinger (1947), and Stanton-Jones (1950). Fora trapezoidal wing with the local aerodynamic centers on the nth-chord line, the chordwise location of the mean aerodynamic center from the leading edge of the m. a. chord expressed as a fraction of the m. a. chord /i„ r is given by

Table C. l

Planform

Additional

Loading

Distribution

М. Л.С.

c

у

Constant taper and sweep

Any

2cr 1 + A + Л2

r?, „ ‘

b

(trapezoidal)

3 1 + A

2

Constant taper and sweep

Proportional

2 cr 1 + A + A2

b 1

+ 2k

(trapezoidal)

to wing chord (uniform C, J

3 1 + A

2 3(1 + A)

Constant taper and sweep

Elliptic

2 cr 1 + Л + A2

b

4

(trapezoidal)

3 1 + A

2

3 7T

Elliptic (with straight

Any

c, 8

VcP’

b

sweep of line of local a. c.)

3 7Г

~~2

Elliptic (with straight

Elliptic (uniform

cr 8

b

4

sweep of line of local a. c.)

c,„)

3 7Г

2

3 7Г

Any (with straight sweep of

Elliptic

2 fW2

b

4

line of local a. c.)

T dy

S J о

У ’

Зтг

where A = aspect ratio, b2/S

A = taper ratio, cjcr c, = wing-tip chord

The length of the chord through the centroid of area of a trapezoidal half-wing is equal to c. For the same wing with uniform spanwise lift distribution (i. e., Cla = const) and local aerodynamic centers on the nth-chord line, the m. a. center also lies on the chord through the centroid of area. The chord through the centroid of area of a wing having an elliptic planform is not the same as c, but the m. a. center for elliptic loading and the centroid of area both lie on the same chord (see Yates, 1952).

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