Abstract: In order to investigate the optimum ascent trajectory of an air-breathing vehicle，a strategy is identified to find out the optimal trajectory required for the ascent phase of a general supersonic vehicle propelled by a ramjet. The accelerator vehicle operates approximately from Mach 2.7 to 6.0 (altitude 19km to 25km). The system model is established with an ideal ramjet model and a vehicle dynamic model in the vertical plane. Considering with two different objective functions and also unstartprotection constraint，minimum-fuel and minimum-time trajectory problems are formulated，and then solved via Gauss Pseudospectral Method. The results show that the essence of trajectory optimization problem is match engine performances with atmosphere characteristics. Compared with that along the minimum-time trajectory，a vehicle with 1000 kg weight operating along the minimum-fuel trajectory can reduce fuel consumption by 4.7% but requires 30.3% more time. It is also found that the take-off weight has an obvious influence on optimum trajectories，and a heavier vehicle needs more dynamic pressure before climbing.

Key words: Ramjet；Trajectory optimization；Gauss pseudospectral method；Minimum-time trajectory；Minimum-fuel trajectory

摘要： 为了研究吸气式飞行器加速过程的最优轨迹，针对一个以冲压发动机为动力的超声速飞行器，由起始状态19km(约2.7马赫)至终点状态25km(约6.0马赫)的加速爬升过程，提出了一种考虑发动机推进机理的加速过程轨迹最优化方法。将理想的冲压发动机模型与竖直平面飞行器动力学模型相结合，考虑不启动保护约束，分别定义了最小油耗和最小时间两种轨迹最优化问题，并应用高斯伪谱法进行求解。结果表明，轨迹最优化问题的实质是将发动机比冲和推力性能与飞行器动力学性能进行最优化匹配。最小油耗轨迹较最小时间轨迹增加了30.3%的加速时间，节约了4.7%的燃油消耗。不同的起飞重量对最小油耗轨迹有一定的影响，较大的起飞重量需要飞行器在爬升前获得更大的动压。

关键词: 冲压发动机；轨迹优化；高斯伪谱法；最小时间轨迹；最小油耗轨迹