## 1 Introduction  
An air-breathing hypersonic vehicle generally refers to an aircraft powered by air-breathing engines and flying at a Mach number above 5 [1]. It has a series of advantages, such as high altitude, fast speed, and strong penetrability, which has a far-reaching impact on the future development of the aerospace field [2, 3]. Therefore, the research of hypersonic technology has received extensive attention from researchers all over the world. In the cruise phase of a hypersonic vehicle, steady-state cruise refers to the cruise mode whose altitude and speed remain constant [4]. Steady-state cruise is simple and direct and has high stability for a hypersonic vehicle [5]. In order to save fuel and increase the range of the aircraft, the fuel consumption averaged by the range is an important indicator that many studies of trajectory optimization focus on. Research has shown that, when the aircraft performs steady-state cruise at different altitudes or Mach numbers, the fuel consumption is different [6, 7, 8, 9]. Under a determined aircraft model, there is an optimal steady-state cruise point composed of the optimal cruise Mach number and the optimal cruise altitude. When the aircraft performs steady-state cruise at the Mach number and altitude of the optimal point, the fuel consumption averaged by the range is lowest [10]. To obtain the optimal cruise point, a great deal of research is carried out. Based on a parametric model of HL-20, a hypersonic vehicle widely used in trajectory optimization research, [PERSON] et al. [11] developed a two-level optimization algorithm combining particle swarm optimization and sequential quadratic programming to solve the optimal steady-state cruise point; [PERSON] et al. [12] employed the fmincon function in MATLAB to determine the position of the optimal cruise point. In [13], it was pointed out that a higher altitude was beneficial to reduce drag, but, at the same time, it would reduce the specific impulse. Therefore, the optimal cruise point was a combined result of these two aspects. Most of this research is based on the HL-20 aircraft model. However, the parametric model of HL-20 is an ideal model whose specific impulse is independent from the equivalence ratio, while it has been found that the specific impulse should be negatively correlated with the equivalent ratio in the ramjet engine [14]. As a hypersonic vehicle enters the stage of engineering practice, to better develop the hypersonic vehicle, it is significant to clarify the cruise characteristics based on a more practical aircraft model. In addition, for different aircraft models, the positions of the optimal cruise points are also different, which reveals the position of the optimal cruise point is closely related to the aircraft parameters. Even though some methods have been developed to solve the optimal cruise point, there is little research about how the aircraft parameters influence the optimal cruise point. In the aircraft design process, when the aircraft parameters are determined, there is a corresponding optimal steady-state cruise point. However, if the subjectively desired cruise Mach number and altitude deviate from the objective Mach number and altitude of the optimal cruise point, the fuel consumption cannot be reduced fully. Then, the optimal cruise point can be taken into account in the aircraft design to guide the optimization of the aircraft parameters. The optimal cruise point can be changed after aircraft parameters optimization and then coincide with the subjective desired cruise point, which is of great benefit to save fuel. Therefore, exploring the influence law of aircraft parameters on the optimal cruise point and carrying out the research on aircraft parameter optimization is of great significance to provide a new perspective for aircraft design. Regarding the analysis and optimization of aircraft parameters, a great deal of research has been carried out.