A mathematical solution to a biological puzzle that may not really exist might prove useful for designing hopping rovers for space exploration.
Alberto Vailati at the University of Milan, Italy, normally researches the physics of fluid dynamics. However, about 10 years ago, after noticing jumping insects on a holiday, he was intrigued to read some lab studies in which insects, including fruit fly larvae, gall midge larvae and froghoppers, had all been seen leaping with an average take-off angle of about 60 degrees.
The idea that many different types of insects should have independently evolved to leap at this take-off angle seemed odd to Vailati: for insects wanting to escape predators, or simply move efficiently from A to B, a 45-degree take-off angle is the natural choice, as this maximises the range of a jump.
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For several years, Vailati mentioned the insects to his first-year students, in the hope that it would pique their curiosity too. After a recent lecture, one student, Samuele Spini, came back with two pages of hand calculations and the idea that a 60-degree take-off angle may help the insects avoid obstacles mid-jump.
Vailati, Spini and their colleagues then built a mathematical model to investigate the idea. They considered the trajectory an insect would take depending on the take-off angle and explored which aerial path would give the insect the best chance of avoiding step-like or fence-like obstacles of random size and position lying ahead. The researchers also factored in wind and air resistance to make their calculations more applicable to the real world.
Defining a successful jump as one in which the insect leaps over or lands on top of an obstacle, they found that a take-off angle of 60 degrees minimised the probability of striking the side of an obstacle, while maintaining a long jump range.
鈥淚nsect jumping is an interesting thing,鈥� says Malcolm Burrows at the University of Cambridge, but he is confused by the biological puzzle that Vailati and Spini鈥檚 team has solved. Burrows has spent much of his career studying insect neurobiology, including jumping behaviour, and is unaware of any research indicating that a wide range of insects typically leap with a take-off angle of 60 degrees. He says insects vary their take-off angle from jump to jump, depending on what they can see in front of them.
The new study might nonetheless prove useful for engineers designing hopping rovers to explore astronomical bodies. Gareth Meirion-Griffith at NASA鈥檚 Jet Propulsion Laboratory in Caifornia is exploring this concept. He says this derivation of an optimum take-off angle of 60 degrees could be helpful for exploration robots jumping in places with very rough surfaces and low gravitational pull, or jumping in subsurface structures we can鈥檛 map with satellites, like lava tubes on the moon.
Insects may not always jump with a 60-degree take-off angle, but it is just possible that space rovers in the future might.
Reference: arXiv,
