对空中加油问题的前两个问题进行了深入系统的研究,发现并证明了与最优解相关的若干事实,对后续的问题求解具有重要的意义.利用得出的结论,加以推导得出求解rn的递推公式,并由此设计了类似于动态规划的循环递推算法.引入“虚拟基地”和“一次性加油”的概念,通过推导得到rn的上界和下界,得出rn与n的渐进关系是对数关系.最后,又提出将问题转化成为二维平面问题,建立一个二叉树模型,通过求解线性规划得到最优解. The first two problems of air refueling in the air have been systematically and deeply researched, and some facts related to the optimal solution have been found and proved to be of great significance to the subsequent problem solving.According to the conclusion, rn and recursive algorithm similar to dynamic programming is designed.The concept of “virtual base” and “one-time refueling” are introduced, and the upper and lower bounds of rn are deduced to get rn and n Asymptotic relationship is a logarithmic relationship.Finally, it is proposed that the problem be transformed into a two-dimensional plane problem, a binary tree model is established, and the optimal solution is obtained by solving linear programming.