1. Recently, a transonic kernel function method has been developed by Northrop (Ref. 8) under the AFFDL contract support (F33615-78-C-3202). In Reference 8, the basic formulation of the transonic acceleration potential equation was derived f i r s t and i t s basic solutions in two- and threedimensional subsonic/transonic/supersonic flow regimes were obtained. Next, the two-dimensional transonic/subsonic, transonic/supersonic, and sonic kernel functions were then established. To solve for the downwash integral equation, two discrete element methods were introduced; these are the Doublet Lattice method and the Linear Pressure Panel method. We realized that the former method is only restricted to the transonic/ subsonic (or subcritical and purely subsonic) flow regime, while the latter method has the unified feature, i f rhe control point i s properly chosen, for subsonic/transonic/supersonic flow calculalations, although the calculation scheme could be more time-consuming than for the former method. 11. The Transonic Kernel Functions
2. It should be noted that the sonic solution rquation (4) can also be derived as a limiting case of the transonic/supersonic basic solution, Equation (5), and that of the transonic/subsonic basic solution, Equation (6). When we l e t B: of mi approach zero, and meanwhile keeping x nonvanishing in the latter equations, it can be shown that both expressions lead t o the sonic solution by means of asymptotic expansions of the Bessel function and the Hankel function for the large argument OR. Also, we note that these basic solutions (Equations 4-6) contain the purely sonic/supersonic/subsonic basic solutions as special cases.
3. Several special cases can be reduced from Eqs. (11) (12) and (13). When we l e t a l l the transonic parameters A, r and u approach zero, Eqs. (11), (12) and (13) reduce to the purely subsonic, purely supersonic and purely sonic kernel functions previously given by Watkins, Runyan and Woolston (Eq. (B.18) Ref. lo), by Watkins and Berman (Eq. 49, Ref. 11) and by Watkins e t a1 (Eq. B23, Ref. lo), respectively. Furthermore, the sonic kernel function Eq. (13) can be derived from either Eq. (11) or Eq. (12). It can be shown that Eq. 111.2 The Irregular Elements (13) is the sonic limiting case of these subsonic and supersonic kernel functions. 0 Leading-Edge Element 111. The Linear Pressure Panel (LPP) Procedure