# Forces and Moments on the Fuselage

The following sections will be devoted to a detailed discussion of fuselage aerodynamics. To give a feeling for the magnitudes of the forces and moments acting on the fuselage, a typical measurement on a fuselage will be presented first. In Fig. 5-3, some results of a three-component measurement on an axisymmetric fuselage by Truckenbrodt and Gersten [50] are plotted. Here, the following dimensionless coefficients have been introduced for the components of the resultant force (lift and drag) and for the pitching moment:

Lift: Lp — Cip Ур! г q ж

Drag: DF = cDFV^qco (5-3)*

Pitching moment: MF = cMFVFqoo

where =(p/2)i/i is the dynamic pressure of the incident-flow velocity £/«, and

VF is the fuselage volume. Figure 5-3 shows the lift coefficient cLF, the drag

coefficient CjjF, and the pitching-moment coefficient c^f plotted against the angle of attack a. The position of the axis of reference for the pitching moment is indicated in Fig. 5-3. In the range near a = 0, the lift coefficient changes linearly with angle of attack a. At larger angles of attack, cLF grows more than linearly. This lift characteristic cL(a) is very similar to that of a wing of very small aspect ratio (see Fig. 3-49). The drag coefficient cDF is approximately proportional to the square of the angle of attack, similar to that of the wing. In the range of large angles of attack, the pitching-moment coefficient depends almost linearly on the angle of attack.

Forces and moments, in addition to those discussed above, act on the fuselage

Fuselage volume is introduced in this case as a quantity of reference in compliance with the theory of fuselages (see Sec. 5-2-3). The drag coefficient is frequently referred to the surface SF or the frontal area Apmax of the fuselage.

Figure 5-3 Three-component mea­surements Cip, Cdf, an^ CMF vs. angle of attack on an axisymmetric fuselage. Reynolds number Re = 3 • 106. Theory for cj/fp from Eq. (5-34).

as a result of the turning and sideslip motions of the airplane, as has been discussed for the wing in Sec. 3-5.

The summary reports of Munk [41], Wieselsberger [58], Goldstein [14], Thwaites [47], Howarth [22], Heaslet and Lomax [17], Brown [5], Ashley and Landahl [4], Hess and Smith [18], and Krasnov [28] deal with the questions of flow over a fuselage in incompressible, and, to some extent also in compressible flow. Also, the survey of Adams and Sears [1] must be mentioned. Furthermore, the comprehensive compilations of experimental data on the aerodynamics of drag and lift of fuselages of Hoerner [19] and Hoerner and Borst [20] should be pointed out.