# Aerodynamic Study of the NASA's X-43A Hypersonic Aircraft
## 5 Conclusions  
A 2D aerodynamic study of the NASA's X-43A hypersonic aircraft has been performed using two approaches. The first one (analytical) neglects the effects of the scramjet and is based on the resolution of the oblique shock wave and Prandtl-Meyer expansion wave theories, while the second one (computational) considers the real shape of the aircraft and involves the use of a CFD package. On the one hand, in the analytical model, only one single case whose design angles allowed the aircraft to fly with the nose optimised configuration for \(AoA=0^{\circ}\) has been strictly studied for \(M_{\infty}=7\) and \(z=30\) km. The lift coefficient, drag coefficient, aerodynamic efficiency and pitching moment coefficient in terms of the angle of attack with \(AoA\in\left[-4,\ 14\right]^{\circ}\) have been depicted. The linearity of the lift coefficient, the second order polynomial dependence of the drag coefficient, the increase and decrease of the aerodynamic efficiency with \(E_{max}=4.02\) for \(AoA=4.94^{\circ}\) and the longitudinal instability of the aircraft have been observed. Afterwards, the study of the pitching moment and Vertical Force Balance conditions have been defined. For the zero pitching moment condition, the lift coefficient has resulted in being negative and, consequently, a negative aerodynamic efficiency has been obtained. Contrary to that, for the Vertical Force Balance condition, the aircraft has reached its maximum aerodynamic efficiency. In both conditions, the aircraft has been analysed to be flying with the nose optimised configuration. The discussion of the analytical model has been closed by the changes of the aerodynamic parameters (lift and drag coefficients, aerodynamic efficiency and pitching moment coefficient) with the design angles. The changes of these parameters have been far more significant with the manipulation of \(\alpha_{1}\). Furthermore, it has been observed that the aerodynamic efficiency of the aircraft increased with the decrease in the design angles \(\alpha_{1}\) and \(\alpha_{4}\). On the other hand, in the CFD model, three different cases with different design angles have been analysed for \(M_{\infty}=7\), \(z=30\) km and \(AoA=\left[-4,\ -2,\ 0,\ 2,\ 4,\ 6,\ 8,\ 10,\ 12,\ 14\right]^{\circ}\). The pressure, density, temperature and Mach fields of case 1 have been shown for \(AoA=0^{\circ}\) and \(AoA=14^{\circ}\) as well as the pressure field for the other cases at a zero angle of attack. Firstly, the oblique shock and Prandtl-Meyer expansion waves along the physical domain have been visualised as well as an attachment condition at the leading edge for all situations. Case 1 has appeared to be flying with the nose optimised configuration for \(AoA=4^{\circ}\) (different from the \(0^{\circ}\) of the analytical study) as well as case 3, while for case 2 it has been imposed to be for \(AoA=0^{\circ}\). Secondly, the shock diamond inside the scramjet with two reflection waves causing high pressure gradients has been confirmed. Thirdly, an expected flow disturbance caused by the drastic flow expansion at the trailing edge has been detected and, finally, the boundary layer could have been visualised in those regions with low \(y^{+}\) values. In addition, the same aerodynamic parameters as in the analytical study and the mass flow rate throughout the scramjet in terms of the angle of attack have also been presented. The study highlights the importance of properly choosing the aircraft nose design angles in order to generate oblique shock waves meeting at the scramjet inlet lower edge. The analysis of the zero pitching moment and Vertical Force Balance conditions has also been carried out. Once again, \(AoA_{(VFB)}\) and \(AoA_{(C_{M_{CG}}=0)}\) have been calculated since a single angle of attack could not allow both conditions. Cases 2 and 3 have resulted in a better aerodynamic performance, but case 1 generated a higher mass flow rate for both operating conditions.