Humans are pretty good problem solvers, but we've still got a long way to go before we better evolution's ingenuity; which is why engineers turn to biology for inspiration. Self-cleaning glass and gecko sticky tape are just two examples of biologically inspired inventions. When it comes to moving under water, fish and cetaceans have a lot to teach us. Which is why Qiang Zhu and Kourosh Shoele have been investigating the propulsive properties of fish fins. Far from being rigid like the fins on submersible vehicles, most fish fins are flexible skeleton-strengthened membranes. Curious to know how fish fins function, Zhu decided to mathematically model a simulated fish tail(p. 2087).

Developing the algorithm to simulate fish tail function was a lengthy process. Zhu had to integrate fluid dynamics simulations while modelling the fin's strengthening rays as beams that could be stretched, twisted and bent. Modelling the tail as a membrane with nine embedded skeletal rays, he simulated the membrane in two ways: as springs connecting adjacent rays and as panels that push against the water. Having built his computational tail, Zhu was able to run thousands of simulations where he controlled the movements of all nine tail rays independently, just like the muscles that control fin movements, computationally reproducing real tail movements and calculating the tail forces and efficiency as it wove from side to side.

According to Zhu, many of the simulations weren't very fish-like, but after months of calculation he had collected several dozen simulations that reproduced realistic tail beats. One of the first things that Zhu noticed was the flexible fin's efficiency; it was 20–30% more efficient than a rigid fin. More importantly,' says Zhu the performance is not sensitive to kinematic parameters': the tail does not have to be controlled as precisely as a rigid fin to produce the same performance. The flexible fin also wastes less energy, by generating sideways force, than a rigid fin, and reduces the waste even more when the top half of the tail beats out of synch with the bottom half. Zhu's calculations also showed that flexible tail fins generate some lift as the fish swims forward, as well as reproducing many of the fluid flow features that experimental biomechanists have seen when visualising the flows around swimming fish tails.

Zhu admits that he was surprised that the mechanical performance of flexible tails is so much less sensitive to the way they move than rigid tails, and suspects that this could be an important discovery for engineers designing propeller systems; `it simplifies the control system' he explains. What is more, flexible fins are easily folded, doing away with bulky fins on modern submersible vehicles.

Having modelled how flexible tails propel fish through water, Zhu is keen to model how fish actively control the curvature of reinforcing fin rays to produce more complex fin shapes and movements.

Zhu, Q. and Shoele, K. (
2008
). Propulsion performance of a skeleton-strengthened fin.
J. Exp. Biol.
211
,
2087
-2100.