The balance of lateral and directional static stability plays an important role in the lateral-directional dynamics and vehicle design. The theory of geometric influence on the lateral and directional static stability is mature for conventional aircrafts. However, the distinct configuration characteristics and flow physics for hypersonic vehicles may lead to different design theory, which is absent now. In order to solve this problem, simplified analytical models of lateral-directional static derivatives are proposed based on the simplified geometry model. It's found that the lateral and directional stability both increase as the deflection angle, dihedral angle, or angle of attack increases, whereas the influence of sweep angle can be neglected. The difference lies in that the lateral stability is proportional to dihedral angle while the directional stability is proportional to the square of dihedral angle. The reasonable accuracy is validated in comparison with the inviscid numerical solutions. Furthermore, the influence mechanism of viscous effects on the lateral and directional stability is investigated in detail based on the numerical results. It's found that the strong viscous interaction can improve the lateral stability evidently, and both the strong viscous interaction and the shear stress can lead to the increase of the directional stability. In addition, the lateral stability is slightly reduced by the chemical nonequilibrium effects.

横向和方向静态稳定性的平衡在横向动力学和车辆设计中起着重要作用。几何影响横向和定向静稳定性的理论对于常规飞机来说已经成熟。然而，高超音速飞行器独特的配置特征和流动物理特性可能会导致不同的设计理论，而这在现在是不存在的。为了解决这个问题，在简化几何模型的基础上，提出了横向静力导数的简化解析模型。研究发现，随着偏转角、二面角或迎角的增加，横向稳定性和方向稳定性均增加，而后掠角的影响可以忽略不计。不同之处在于横向稳定性与二面角成正比，而方向稳定性与二面角的平方成正比。与非粘性数值解比较，验证了合理的精度。此外，基于数值结果详细研究了粘性效应对横向和方向稳定性的影响机制。研究发现，强粘性相互作用能明显提高横向稳定性，强粘性相互作用和剪应力均能导致方向稳定性的提高。此外，化学非平衡效应略微降低了横向稳定性。与非粘性数值解比较，验证了合理的精度。此外，基于数值结果详细研究了粘性效应对横向和方向稳定性的影响机制。研究发现，强粘性相互作用能明显提高横向稳定性，强粘性相互作用和剪应力均能导致方向稳定性的提高。此外，化学非平衡效应略微降低了横向稳定性。与非粘性数值解比较，验证了合理的精度。此外，基于数值结果详细研究了粘性效应对横向和方向稳定性的影响机制。研究发现，强粘性相互作用能明显提高横向稳定性，强粘性相互作用和剪应力均能导致方向稳定性的提高。此外，化学非平衡效应略微降低了横向稳定性。强粘性相互作用和剪切应力均能导致方向稳定性的增加。此外，化学非平衡效应略微降低了横向稳定性。强粘性相互作用和剪切应力均能导致方向稳定性的增加。此外，化学非平衡效应略微降低了横向稳定性。