We investigate theoretically the ballistic motion of small legged insects and legless larvae after a jump. Notwithstanding their completely different morphologies and jumping strategies, some legged and legless animals have convergently evolved to jump with a take-off angle of 60°, which differs significantly from the leap angle of 45° that allows reaching maximum range. We show that in the presence of uniformly distributed random obstacles the probability of a successful jump is directly proportional to the area under the trajectory. In the presence of negligible air drag, the probability is maximized by a take-off angle of 60°. The numerical calculation of the trajectories shows that they are significantly affected by air drag, but the maximum probability of a successful jump still occurs for a take-off angle of 59–60° in a wide range of the dimensionless Reynolds and Froude numbers that control the process. We discuss the implications of our results for the exploration of unknown environments such as planets and disaster scenarios by using jumping robots.

我们从理论上研究跳跃后小腿虫和无腿幼虫的弹道运动。尽管它们的形态和跳跃策略完全不同，但一些有腿和无腿动物已聚合进化为以60°的起飞角跳跃，这与允许达到最大射程的45°跳跃角明显不同。我们表明，在存在均匀分布的随机障碍物的情况下，成功跳跃的概率与轨迹下的面积成正比。在空气阻力可忽略不计的情况下，通过60°的起飞角可最大程度地提高机率。轨迹的数值计算表明，它们受到空气阻力的显着影响，但是，在控制过程的无量纲雷诺数和弗洛德数的范围很广的情况下，对于59-60°的起飞角，成功跳跃的最大可能性仍然存在。我们讨论了我们的结果对于使用跳跃机器人探索未知环境（例如行星和灾难场景）的意义。