Dynamic Similarity in the Analysis of Animal Movement

Summary

Dynamic similarity is a concept from physical science, related to the more familiar concept of geometric similarity. Two motions are dynamically similar if one could be made identical to the other by uniform changes of the scales of length, time and force. This chapter asks whether different-sized animals move in dynamically similar fashion.

When gravitational forces are important (as in running), dynamic similarity is possible only if the motions being compared have equal Froude numbers (v²/gl, where v is velocity, g is gravitational acceleration and 1 is a length — leg length in studies of running). Studies of running show that mammals ranging from small rodents to rhinoceros generally move in approximately dynamically similar fashion, when their speeds are such as to make their Froude numbers equal.

When elastic or viscous forces are important, dynamic similarity requires equal Strouhal numbers or Reynolds numbers, respectively.

The concept of dynamic similarity has proved valuable in studies of running but has not so far contributed much to studies of swimming or flight.