Optimal leap angle of legged and legless insects in a landscape of uniformly-distributed random obstacles

TL;DR

This study shows that small insects and larvae maximize their jump success in obstacle-rich environments with a take-off angle of about 60°, which is optimal even considering air drag effects, informing design of jumping robots for exploration.

Contribution

The paper reveals that a 60° take-off angle optimizes jump success probability in obstacle-laden environments, accounting for air drag effects, which is a novel insight into animal and robot jumping strategies.

Findings

Maximum jump success occurs at approximately 60° take-off angle.

Air drag influences trajectory but does not significantly shift optimal angle.

Optimal angle remains consistent across various Reynolds and Froude numbers.

Abstract

We investigate theoretically the ballistic motion of small legged insects and legless larvae after a jump. Notwithstanding their completely different morphologies and jumping strategies, these legged and legless animals have convergently evolved to jump with a take-off angle of 60$^\circ$, which differs significantly from the leap angle of 45$^\circ$ 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$^\circ$. 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$^\circ$ 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.