___________________________________________ FIVE



5- 1-1 Geometry of the Fuselage

Whereas the main function of the airplane wing is the formation of lift, it is the main function of the fuselage to provide space for the net load (payload). It is required, therefore, that the wing at given lift and the fuselage at given volume have the least possible drag. Consequently, the fuselage has, in general, the geometric shape of a long, spindle-shaped body, of which one dimension (length) is very large in comparison with the other two (height and width). The latter two dimensions are of the same order of magnitude. In Fig. 5-1, a number of idealized fuselage shapes are compared. In general, the plane of symmetry of the fuselage coincides with that of the airplane. The cross sections of the fuselage in the plane of symmetry and normal to the plane of symmetry (planform) have slender, profilelike shapes. The most important geometric parameters of the fuselage that are of significance for aerodynamic performance will now be discussed.

In analogy to the description of wing geometry, a fuselage-fixed rectangular coordinate system as in Fig. 5-1 will be used, with

x axis: fuselage longitudinal axis, positive in rearward direction у axis: fuselage lateral axis, positive toward the right when looking in flight direction

z axis: fuselage vertical axis, positive in upward direction

Figure 5-1 Geometric nomenclature for fuselages, (a) General fuselage shape, (b), (c) Fuselage teardrop with noncircular cross sections, (d) Fuselage teardrop with circular cross sections (axisymmetric fuselage). (<?) Fuselage mean camber (skeleton) line.

In general, it is expedient to place the origin of the coordinates on the fuselage nose. For axisymmetric fuselages, utilization of cylinder coordinates as in Fig. 5-Id is frequently preferable, where r stands for the radius and # for the polar angle.

— 8p

— bp

_ s**

— Op

The main dimensions of the fuselage are the fuselage length lF, the maximum fuselage width bFmax, and the maximum fuselage height hFmax (Fig. 5-1). The fuselage cross sections in the yz plane are usually oval-shaped (Fig. 5-lb and c). The simplest case is the fuselage with circular cross sections as in Fig. 5-1 d, with ^Fmax = ^Fmax=^FmMJ where dFmzx is the maximum fuselage diameter. From these four main dimensions, the following relative quantities can be formed:

The first three quantities are measures of the slenderness or fineness ratio of the fuselage. For the fuselage of circular cross section, 8F = 8p = 8p* and p = 1.

A more detailed description of fuselage geometry can be given by introducing the fuselage mean camber line. As shown in Fig. 5-1 a, this line is defined as the connection of the centers of gravity of the cross-sectional areas Ap{x). The line connecting the front and rear endpoints of the skeleton line is designated as the fuselage axis; it should coincide with the x axis. The fuselage skeleton line zF(x) as shown in Fig. 5-1 e lies in the fuselage symmetry plane. The largest distance of the skeleton line from the fuselage axis is designated as fp.

In analogy to the wing shape, Sec. 2-1, a general fuselage shape as shown in Fig. 5-Ій can be thought of as being composed of a skeleton line zF(x) on which cross sections Л^(х) are distributed. The body with this cross-section distribution is also termed a fuselage teardrop. In the case of noncircular cross sections of the fuselage, fuselage teardrops are characterized by the distributions hp{x) and bF(x) as in Fig. 5-1 b and c. In the case of circular fuselage cross sections, the fuselage teardrop is determined uniquely by the distribution of the radii R(x) (Fig. 5-1 d). The geometric parameters of a wing (teardrop and skeleton) can be selected first for the required aerodynamic performance. For fuselages this procedure is possible only to a very limited degree, because the fuselages must satisfy important requirements that may not be compatible with the aerodynamic considerations. For theoretical investigations on the aerodynamic properties of fuselages, the profile teardrops discussed in Sec. 2-1 are well suited.

The ellipsoid of revolution of Fig. 5-2a is a simple fuselage configuration for subsonic velocities. Another simple fuselage of axial symmetry that is used particularly for supersonic flight velocities is the paraboloid of revolution with a pointed nose as shown in Fig. 5-2b* To accommodate jet engines, fuselage configurations with blunt tails may be chosen. Among the design parameters not only fuselage length and diameter play an important role, but also fuselage volume and surface area. Volume and surface area of axisymmetric fuselages are given by


Figure 5-2 Special axisymmetric fuselages, (a) Ellipsoid of revolution. (b) Paraboloid of revolution.


SF = 2n J R(x) ds (5-1 b)


where s is the path length along the fuselage contour and Ip is the associated length of a meridional section measured on the fuselage contour.

Finally, a few data are given here for the volume of the ellipsoid of rotation and the paraboloid of rotation (Ip = !p0) of Fig. 5-2, respectively:

VF=llFAFmax (ellipsoid) (5-2 a)

Vp-Ysh^Fxmx (paraboloid) (5-26)

Here, lF is the fuselage length and Apm^x is the maximum fuselage cross-sectional area, also called the frontal area.

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