Survey of Blunt Body Dynamic Stability in Supersonic Flow <s> A. Semi-Empirical Impact Methods <s> An analysis is presented which extends the previously developed unsteady embedded Newtonian theory down to finite supersonic Mach numbers. It is found that Mach number can have a very large influence on the stability characteristics of slender blunted cones, and that there exist cone angle-nose bluntness combinations for which these Mach number effects are minimized. The computed effects of nose bluntness on static and dynamic stability derivatives are in excellent agreement with available experimental data. This also holds true for the highly nonlinear effects of angle of attack. <s> BIB001 </s> Survey of Blunt Body Dynamic Stability in Supersonic Flow <s> A. Semi-Empirical Impact Methods <s> An unsteady, embedded Newton-Busemann flow theory is developed by extending the unsteady NewtonBusemann flow theory of Hui and Tobak to blunt bodies, incorporating the embedded Newtonian flow concept of Seiff and Ericsson. In this theory the unsteady surface pressure includes the Newtonian impact part plus Busemann's centrifugal correction. Applications to dynamic stability of blunt bodies of revolution show that 1) the centrifugal pressure is just as important as the impact part and must not be neglected and 2) with its inclusion the complete theory is in good agreement with existing experiments for high Mach number flow. <s> BIB002 </s> Survey of Blunt Body Dynamic Stability in Supersonic Flow <s> A. Semi-Empirical Impact Methods <s> The stability of oscillatory motions of vehicles flying at hypersonic Mach numbers is of considerable relevance to their initial design. Methods are needed for quick and accurate predictions of stability and control that are applicable over a wide range of body shapes, angles of attack, and flow conditions without the need to resort to computationally time-consuming numerical flowfield calculation methods. The purpose of this paper is to present experimental and theoretical data concerning the static and dynamic pitching stability of pointed and blunted 10 deg semiangle cones and a double-flared hyperballistic shape. Although Newtonian theory gives inadequate accuracy of prediction, inviscid embedded Newtonian theory, which accounts for the reduced dynamic pressure and lower flow velocity in the embedded flow downstream of the strong bow shock, is shown to provide surprisingly good agreement with experimental data over a wide range of conditions. Comparisons with experimental results show that the broad flow features associated with nose bluntness, angle of attack, and center of gravity position and their effect on static and dynamic stability are well described in regimes not containing flow structural change. However, in some cases discrepancies exist between the predictions and experimental observations, and these have been attributed to a variety of viscous-flow phenomena involving boundary-layer transition and flow separation, including complex lee-surface vortical flows. <s> BIB003
There is great motivation for the development of adequate prediction methods using numerical techniques. To obtain the aerodynamic characteristics, accurate prediction of the time varying pressure field acting on the body is required. For the static case at hypersonic Mach numbers, Newtownian impact methods are used to approximate the lift, drag, and moment coefficients as well as their derivatives. In order to apply impact techniques to the dynamic case, modified methods have been developed. One of these methods, known as embedded Newtonian, "accounts for the reduced dynamic pressure and lower flow velocity in the embedded flow downstream of the strong bow shock" BIB003 . This semi-emprical inviscid technique was first introduced and developed by Seiff  -  and extended to the unsteady case by Ericsson  for infinite Mach numbers. Further development by Ericsson BIB001 generalized this theory to finite Mach numbers, with good agreement for sharp slender cones down to M=3 (see Fig. 12 ). In this method, as Mach number increases, the approximation approaches the experimental results. Ericsson notes, however, that the effect of cone angle in these results is inconsistent. Although he applies this method to sharp blunted cones, the method is not developed for application to the high drag, blunt bodies generally used in planetary entry missions. The method of Ericsson BIB001 was extended by Tong and Hui BIB002 with the addition of the Busemann correction for the centrifugal forces within the shock layer. Their work improved results for blunt bodies relative to the underpredicting method of BIB001 , although demonstration of this improvement was limited to low hypersonic Mach numbers. The results of BIB002 were examined by East and Hutt BIB003 for sharp and blunt 10 o cones as well as a slender, flared blunt cylinder, demonstrating that with proper empirical Mach number relations, the centrifugal force correction of the Busemann theory would overpredict damping and suggesting that the theory developed by BIB002 be applied only in the cases where M→∞ and γ → 1 . Predictions from both methods are demonstrated for relatively sharp bodies with results that differ substantially from the available experimental data under certain conditions due to the complexities in the flow environment BIB003 .