Hypersonic aircraft has become the trend of international and domestic research. In order to meet the requirements of thermal protection, the shape of hypersonic aircraft is typically highly streamlined with few control surfaces. To meet the requirements of controllability, the stability of the aerodynamic layout must be considered in the initial layout design. Currently, most research on hypersonic stability focuses on static stability, while research on dynamic stability is relatively limited. However, the mechanism of dynamic instability is more complex, and its effect is also more challenging to evaluate.  Furthermore, posterior design methods can result in high iteration costs and cannot provide specific guidance for dynamic stability aerodynamic design. In this context, this paper investigates the relationship between the hypersonic lifting-body's shape parameters and its dynamic stability. The main work is arranged as follows:

(1)Combining the hypersonic simplified geometrical model and hypersonic Newtonian theory, an analytical model for the relationship between two main shape parameters, the center of gravity position and overall dynamic stability derivatives has been constructed through theoretical derivation. The model has been validated by combining dynamic derivative results from unsteady CFD numerical simulation and forced-vibration method, which demonstrates that the analytical model can reveal the quantitative relationship between the layout shape parameters and dynamic derivatives effectively. The relationships revealed include: increasing the deflection angle can increase the overall dynamic stability, while increasing the dihedral angle will enhance the directional dynamic stability, but reduces the lateral and longitudinal dynamic stability.

(2)The influence of viscosity on the dynamic derivatives of hypersonic aircraft is evaluated through unsteady numerical simulations. The mechanism behind the influence of viscosity is also revealed by introducing the concept of ‘Effective Shape’. The research finds that viscosity enhances directional dynamic stability while slightly reducing lateral and longitudinal stability. The influence of shear stress mainly enhances yaw stability, while the viscous interaction effects are more significant. During the movement, the effective shape changed by the viscous interaction effects provides a buffering influence on the surrounding flow, resulting in a lower induced pressure increment and thus ultimately reducing overall dynamic stability.

(3)The dynamic derivatives of the hypersonic waverider shape are further investigated through unsteady numerical simulations. A comparison of the results for different deflection angle features shows that the directional dynamic stability is higher for the shape with a bigger equivalent dihedral angle. In comparison, lateral and longitudinal dynamic stability is lower, which is consistent with the principles revealed by the theoretical analytical model. In addition, the effects of the upper surface and blunted leading edge are also evaluated, and it is found that the upper surface has a minor effect. In contrast, the blunting effect generally enhances lateral and directional dynamic stability and reduces longitudinal dynamic stability.