Why a Dolphin Swims Faster Than It Mathematically Should - Experiment to Support (or Otherwise) a Theoretical Computer Model

“It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.”

Richard Feynman, Cornell University Lecture 1964

My background is in engineering both in Industry and Academia. In 1993 I went back to University to work with a team, who themselves were working on theoretical and computer modelling for a concept, first postulated by Aristotle over 2000 years ago. However, it was only in the 1950s that any type of experimental investigation into the drag reducing properties of simulated dolphin skin was undertaken. The team were looking for a research engineer, with an academic and industrial background, who could, from the ground up, design and carry out a physical experiment in a water tank within a laboratory setting. The goal being to finally prove or disprove the theory of the dolphin's seeming ability to control turbulence. This proposal would also form the nucleus for both a PhD¹ and further post doctoral research.

¹A. J. Colley, “An experimental investigation of the flow in the boundary layer above a rotating disk, with compliant characteristics, in water,” 1997.

This was the first question I was asked. The second being '...and how deep?'

For example, the two major previous experiments had been undertaken in:

1. The Pacific Ocean - a very big tank, (Kramer, 1957)

2. A towing-tank, one quarter of a mile long. (Gaster, 1987)

Thus the first consideration with my experiment was a calculation, in other words I had to scale down from the Pacific.

Often experimentation starts with really simple questions such as the above and in this case, we can use fundamental fluid dynamics equations to solve these seemingly abstract concepts, so as to be able to create the specification for the apparatus. Using the calculations obtained, led to the essential initial design parameters and the material requirements for the equipment and the type of transducers required to measure the all important phenomena.

Involved in the above consideration was the undertaking of the stress calculations to support the apparatus, its volume of water and that the support structure for the instrumentation was rigid enough for its payload, whether static or dynamic.

Also involved in the process was several months spent reading up on the previous literature and this continued throughout my research as new articles were published in related fields. This was also due to the buzz around the topic as it had potential commercial application as a coating. Thus reducing drag could reduce both time and energy consumption.

Once I had the design parameters it was then necessary, as in all builds, to provide drawings for the University workshop. I created all the drawings using Autodesk's AutoCad® versions 12, 13 & 14.

This was done because the Departmental draughtsman was snowed under with work and the leadtime to even start to produce drawings would have delayed the experiment by at least a year.

In undertaking this, I learned a huge amount about the machine I was making, simple but true and that helped in being able to communicate my requirements to the technicians involved in the process.

In Industry I would not have gained this experience, as this role would have been carried out by the Drawing Office.

Experiments within an academic environment can often highlight the disconnect between it and the commercial world. One of the first ways in which my background in industry helped to cut both leadtime and costs, was in my knowledge of 'how to find stuff that already exists'. In this case it was the mechanical seal to the tank, which the team had considered designing and fabricating on site but could be externally sourced and acquired at a fraction of the cost and delivered within 48 hours.

There was also the question of specialist instrumentation, such as probes and data acquisition equipment, which coming from industry, I was perhaps more aware of the 'cut-and-thrust' behaviour when tenders were submitted. This in particular when Universities are often viewed as having a bottomless purse.

Once all the components had been made to my satisfaction, they were all transported to the lab for assembly and whilst this was going on I was writing the control software for testing the equipment.

My investigations were to study the development of instabilities within the boundary layer that existed above the surface of a rotating disc and I needed to use transducers called 'hot film anemometer probes'.

An important consideration was that as these cost around $600 each, were the size of a fountain pen nib and extremely fragile, it was imperative that the control software could move the probe holder with an accuracy of 5µm ± 0.5µm and for calibration purposes could accelerate the probe to a speed up to 3m/s and back to 0m/s within the diameter of the tank.

The rest of the software had to control the main motor rotational speed and to furnish a trigger signal for data acquisition.

As with any experiment, it is essential to be able to prove that the apparatus works satisfactorily and fortunately there was previous work, in air, with which to compare my results (Wilkinson and Malik, 1985).

These resulted in a confirmation that the equipment was working correctly and that we could progress to the real purpose of the research.

In order to complete the experiment it was necessary to fabricate a flexible surface, which our computer models had indicated would behave in a similar fashion to that of the dolphin skin.

The suggestion was that this should be less dense than water according to the model but no such material would or could have been practically poured and then tested.under water.

The analogy of this situation could be compared to using 'sky hooks', where the computer model is working within an abstract environment, unrelated to the real World. However, this does not mean that the hypothesis is wrong, it's simply that the material as suggested by the model is merely a number or parameter that couldn't be practically used in a physical experiment.

In this part of the experiment it was therefore necessary to compromise and initially test a much more 'rigid' material. This was a silicone rubber, which could be modified by the addition of silicone oil prior to curing. This actually felt like skin, it was soft and elastic.

As with all experimentation the fabrication of this surface had many complications in the real World, not least of which was to produce a flat surface of minimum roughness, comparable to the commissioning surface which was a glass disc. Thus we would not be introducing too many variables to the experiment.

Above you can see the skin after pouring. It contains a few bubbles at the very edge but as the probe will be taking the samples from nearer the centre, this is unimportant.

The other two images are of an elastic modulus testing machine, the creation of which was also part of the experiment.

After analysing the results form the first series of experiments, it was evident that the phenomena we were searching for existed but a majority of the signals were very 'noisy', thus not as valid a series of results as was initially hoped for.

To this end I decided on two major improvements:

The first was to the arrangement of the apparatus by means of creating a shroud instead of the lid (image above) in the tank to divert extraneous 'noisy' flow into the region under investigation

...and the second was the means of undertaking the experiment, which was to only acquire the data over the weekend, when no other machinery was running in the building. this meant working all night on Saturdays and Sundays.

The above show a comparison between before the modifications and after the modifications on both the rigid (glass) and the compliant disc (silicone) at the same rotational speed.

The compelling red area on the compliant disc is a low frequency disturbance that was predicted from the computer model and had never been previously observed.

The experiment related here shows a very brief summary of seven years doctoral and post doctoral work and was a step in achieving the validation of the previous thousands of years work of many scientists, going all the way back to Aristotle. Experimentation in this area is still ongoing and each of us over the centuries has made an individual contribution. That maybe is the true nature of Scientific research, it is a collaboration, where each brings their specific skills to the Whole.

I learned a lot doing this research and not just about fluid dynamics and the knowledge I gained and the process used to gain that knowledge is still of immeasurable benefit to me today.

Hope you enjoyed it too!

Cheers, Andy