On the calculation of static and dynamic stability derivatives for bodies of revolution at subsonic and transonic speeds

Unsteady local linearization solution for pitching bodies of revolution at freestream Mach numbers = 1 - Stability derivative analysis

“…The parabolic-arc results for the second-order distributions of normal force (dC Nd /dx) 2 and damping-in-pitch normal force (dC N^/ dx) 2 presented here agree in trend but differ somewhat in magnitude with those determined by the "parabolic" method. 3 Those results would correspond to using the sonic results of the present method over the entire body with the additional provision that the surface acceleration [see Eq. (24)] is held constant at some representative value.…”

“…where d 0 is the maximum displacement, RP signifies the real part of a complex quantity, k is the reduced frequency defined by k -wf/ £/oo, and </> satisfies (3) In Eq. (3) (4) where </>/ is the axisymmetric steady perturbation potential, which satisfies Eq.…”

“…The approach generalizes the results of Landahl, ! Liu, 2 Liu et al, 3 and Ruo and Liu, 4 both in the sense of encompassing the entire low-frequency range, including £ = 0, and also in eliminating the "parabolic" assumption, 3 ' 4 thereby properly accounting for local regions of subsonic, 3onic, and supersonic flow. Applications are made to various parabolic-arc half-bodies and cones at M^ = 1, and results are presented for unsteady force and moment distributions and static and dynamic stability derivatives.…”

Unsteady linearized transonic flow analysis for slender bodies

“…However, for the unsteady flow problems, apart from the work appearing in Ref . 4, which is an extension of the earlier work of Liu et al, 5 little advance has been made for the slender bodies in transonic flow. The purpose of this paper therefore is to develop an efficient, analytical method for deriving the approximate near-field solution for bodies in unsteady transonic flow.…”

“…Examination of recent results given by Stahara and Spreiter,4 however, reveals that, in most cases, little difference exists between the stability derivatives obtained by the local linearization method, and by the parabolic method. 5 - 6 On the other hand, the present approach consists of the preliminary steps toward a future development of a shock-inclusion method such as Hosokawa's nonlinear correction procedure (e.g., Ref. 5).…”