INFLUENCE OF FUSELAGE ON ROLLING MOMENT

Although conventional fuselage shapes do not produce a significant rolling moment, their interference effects upon the wing moments are large and cannot be disregarded. Such effects are particularly evident in regard to the rolling moment when sideslipping.

(11) Analysis of rolling moments due to fuselage:

(a) Jacobs, Analysis, YearbkP Lufo 1941 p 1-165.

(b) Braun, Rotational Body, Ybk D Lufo 1942 p 1-246.

(c) Maruhn, Rectangular Shapes, Ybk D Lufo 1942 p 1-263.

Analysis. Evaluation of the two-dimensional cross flow field as in (11 ,a) of a fuselage with an equivalent infinitely long cylinder then yields a flow-angle distribution along the lateral axis (beam) and a corresponding lift distribu­tion. The resultant rolling moment is essentially independ­ent of the wing’s lift coefficient and is a function of the geometry of the wing-fuselage combination. As an exam­ple, numerical results for a specific configuration taken from (12,a) are given in figure 19. Experimental results confirm the theoretical prediction with reasonable accu­racy. In the two extreme positions, at h/r = plus and minus 1.0, the rolling moment derivative produced by the fuselage is the equivalent of plus/minus 3.5 dihedral, i. e. for the configurations as tested having b/d in the order of

8.

Fuselage/Wing Size. The influence of the fuselage de­scribed above was analytically studied (11 ,a) for a number of configurations with the following results:

1) The effect of a body with Л/d = 7 is up to 10% smaller than that of a long cylinder.

2) The influence of wing shape (rectangular or elliptical) is small.

3) The rolling moment is for practical purposes independ­ent of the wing’s aspect ratio, meaning that the incre­ment of the coefficient ДС^ ~ 1 />Га for constant wing area.

4) The increment of the rolling-moment coefficient deriv­ative is proportional to (d/b)2 and it reduces in pro­portion to 1/b for a given fuselage. The moment is proportional to (d2 c) where c = average wing chord; therefore, “L”/(q d2 c) = constant for a given body shape.

Shape of Fuselage. Various cross-sectional shapes (circu­lar, elliptical, square, rectangular) have analytically been investigated (11). For practical purposes, it can be de­duced from the results:

a) A square fuselage shape (with rounded edges) has approximately the same effect as a circular shape (as in figure 19) provided that the fuselage volume (rather than the d/b ratio) is kept constant.

b) In the case of fuselages with elliptical or rectangular cross-section shapes the rolling moment induced by them increases approximately in proportion to the height/width ratio, again provided that volume or cross-sectional area is kept constant. [127]

Dihedral. As noted above, the effect of the fuselage upon rolling moment is the equivalent of a certain wing di­hedral. It is also stated that the derivative of the coeffi­cient (indicating rolling moment in relation to wing lift) varies in proportion to (d/b) . Any small-span (small – aspect ratio) and high-wing airplane configuration is there­fore liable to have too much rolling moment due to yaw. An example of such a configuration is the Lockheed F-104 high-speed fighter airplane. Rolling moments are reduced by giving the wing a few degrees of negative dihedral. All low-wing airplanes have, on the other hand, appreciable amounts of positive dihedral (between 5 and 10°), (a) to counter-act the “negative” effect of their fuselage and (b) to provide the magnitude of rolling mo­ment desirable for optimum handling and for lateral sta­bility.

Influence of Wing Flaps. Conventional landing flaps are of the part-span and inboard type. They may also be used (at a moderate angle of deflection) during take-off and while climbing. Their influence upon the characteristics of wings is basically similar to that of tapered plan form and/or wing twist.