The two Borelli laws for jumping animals

Meeting Abstract

S3-10  Friday, Jan. 4 14:30 – 15:00  The two Borelli laws for jumping animals SUTTON, GP; University of Lincoln

Borelli’s law is 500 year-old constraint on how high an animal can jump. The argument is simple, as animals get larger, their ability to generate mechanical energy and their mass both go up at the same rate. Consequently, the net height of the jump (related to the energy divided by the mass) is independent of size. We will show that the available energy density per mass, however, is different depending on the underlying biomechanics of the jump – animals that generate a jump with muscle contractions approach a different energy density limit than animals that power their jumps with spring loaded power amplification systems. There are thus two ‘Borelli’s laws’, one for muscle powered jumpers and one for spring driven jumpers. Which of these two laws an animal follows is a consequence of its size, with it being much more energy efficient for large animals (mass greater than 1 kilogram) to power their jumps with direct muscle contraction, while it is more energy efficient for small animals (mass smaller than 1 gram) to power their jumps with springs. I will show where these two energy limits are, the underlying principles that cause these limits, and how these limits constrain the jumping heights of various sized animals. Excitingly, frogs (which exist in the mass range between 1 gram and 1 kilogram) exist in a ‘half way’ zone between these two biomechanical size limits, providing an intermediate kind of jumping mechanism: ‘direct muscle contraction enhanced by a power amplifying spring’.

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