Summer Scholarship Programme Project Summary

Interactive Computer Simulation of the Principles Behind How Fish Swim

Student

Supervisors

Stephen Breuer, EPCC

Students in Heriot-Watt Biology department have a first year mathematics course, but then most forget about mathematics until it suddenly becomes necessary for their fourth year project. In fact, Biology is a subject in which students all too frequently regard mathematics and computing as alien subjects of little use to them.

The specific goal of the project is to develop an online tutorial which would be used as part of a second year course on fish biology. The students are taught the basic mathematics behind the swimming of fish, but this can be rather dry, and it can be difficult for them to make a connection between equations and the real world. The finished online tutorial would enable students to vary various parameters associated with fish swimming through a medium, such as Reynold's number, fish shape, frequency of sinusoidal motion of fish's tail etc., to investigate the resultant velocity and power output of the fish.

The software would be developed from the simple starting point of the linear dynamics of rigid blocks of different shapes, looking at the force required to achieve a fixed velocity through a medium. Initially the medium could be treated as non-viscous, and then viscocity could be added in to the model. The next stage would be to consider the means by which fish can supply this force (i.e. a tail) and to incorporate this into the model. The tail would be represented by a "paddle" attached to the back of the fish, capable of side to side motion of a particular frequency. This would then allow an estimation of the power output (power supplied to the tail) required to bring about a resultant forward velocity. This could be applied to different body shapes and sizes, as well as different body:tail size ratios. At this point some real data on the power output of real fish muscle could be incorporated, to allow assessment of the trade off between achievable velocities, body size and body shape. This could lead to interactive data input leading from questions such as "why are large fish species rarely rhomboid?" , i.e. an introduction of scaling principles. The inclusion of the physical principles behind fish swimming should be in parallel to the development of an attractive and user friendly interface to the simulation software, allowing the input of parameters and having the output of results. It is hoped that the student would also develop their own ideas associated with the presentation aspects of the package, with visualisation of aspects of the simulations and the results.

If the student completes the project as described so far, with time left to incorporate other principles into the software, then some of the following additions could be worked on :

1. The incorporation of sinusoidal motion of the body into the model.
2. The modelling of "fast starts", i.e. predator escape and wait-&-see predation.
3. The inclusion of more sophisticated additions to the model obtained from reading through the more advanced literature on fish modelling supplied to the student.

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