# Aerodynamic Characteristics of Supersonic Rocket-Sled Involving Waverider Geometry
## 3 Results and Discussion
### Force Characteristics  
Shockwave oscillation has a strong unsteady property, so it is necessary to investigate the time domain characteristics of shockwave oscillation. Figure 13 shows the pressure distributions of the ASRS at the symmetrical interface at four different moments. To compare the position on the rocket-sled, we take the origin of the nose of the rocket-sled as \(\Delta y=0\). In the front part of the rocket-sled, the pressure distribution on the upper and lower surfaces is almost identical, which indicates that the front part of the rocket-sled is not affected by head shockwaves and reflected shockwaves. Furthermore, the pressure distributions at four different moments are also identical; this implies that the shockwave structure at the front of the ASRS is quasi-steady in both time and space domains. However, there are discrepancies in the middle and rear of the ASRS. In Figure 13a, we find that, at \(t_{1}=0.0180\) s, the pressure on the lower surface reaches a local maximum value at \(\Delta y=1.385\) m, which is the central position of the reflected shockwave action at this time. Then in Figure 13b, the local maximum pressure point is located at \(\Delta y=1.322\) m. Compared with Figure 13a, the local maximum pressure point (LMPP) shifts forward. However, at \(t_{3}=0.0192\) s, not only does the position of the LMPP change, but the pressure  
Figure 11: Distribution of \(\partial\rho/\partial y\) in ASRS flow field at \(t_{1}=0.0180\) s: (**a**) front section, (**b**) middle section, (**c**) rear section. Figure 12: Distribution of \(\partial\rho/\partial y\) in RWRRS flow field at \(t_{1}=0.0180\) s: (**a**) front section, (**b**) middle section, (**c**) rear section. distribution in its vicinity is also very different. In the space domain, the pressure changes more dramatically; thus, pressure increases rapidly from about 1 atm to LMPP and then rapidly recovers to about 1 atm. Similar to the common ground effect problem, the pressure distribution on the rocket-sled surface should be almost constant over time if there are no additional disturbances on the ground. Therefore, the change in the LMPP can be inferred to be caused by the fastener. By comparing Figure 13a-d, we can make a reasonable inference that the time interval of the relative maximum pressure point changes in the four moments may be related to the shockwave oscillation frequency caused by the fastener. The pressure distribution for the RWRRS is quite different from that of the ASRS. As shown in Figures 14a-d, the upper and lower surfaces of RWRRS are separated by leading edge lines. The pressure increases to more than 5 atm above the leading edge and then begins to fall back. In the region between \(\Delta y=0.5\) m and \(\Delta y=0.65\) m, the pressure drops to the lowest value of about 0.4 atm, which is consistent with the triangular region shown in Figure 8. The pressure then recovers to 1 atm in the region after \(\Delta y=1\) m. The pressure on the lower surface is always around 1 atm with very little fluctuation, which indicates that there is little aerodynamic interference to the lower surface. More importantly, by comparing Figures 14a-d, there is hardly any change observed in the pressure distribution at different times. The ability of RWRRS to reduce shock oscillations is thus demonstrated. The properties of lift and drag are important results in many aircraft studies as they reflect the aerodynamic performance of a certain configuration. As shown in Figure 15, we extracted the lift and drag vibration curves of two rocket-sleds for comparative analysis. \(\Delta_{max}\) represents the difference between the maximum value and the minimum value. The average lift of the ASRS is 0.361 kN, which means the ASRS has an upward trend in vertical direction. The instantaneous lift varies greatly from \(-0.734\) kN to 1.319 kN and the fluctuation range is over 2.063 kN. It can be inferred that the dramatic change in lift will cause the sled to oscillate vertically.