麻豆传媒

鈥淭HIS,鈥� says Michael Triantafyllou reverently, 鈥渋s a tuna.鈥� He thrusts an
object the size of a four-year-old child into the arms of a visitor to his lab.
It isn鈥檛 a real tuna, just a fibreglass cast, but Triantafyllou鈥檚 enthusiasm for
its streamlined form almost brings it to life.

He conducts a nose-to-tail tour of the fish that most biologists nominate as
nature鈥檚 most efficient swimmer. He points out the shallow depressions in the
tuna鈥檚 body into which it can fold its pectoral fins to reduce drag. He explains
the way that the long, serrated fin that runs from its belly to its tail can
subtly direct water flow to ease the fish forward. 鈥淣ature has spent millions of
years perfecting this design,鈥� he says. And if it鈥檚 good enough for nature, it鈥檚
good enough for Triantafyllou.

Since 1992, this naval architect and professor of ocean engineering at the
Massachusetts Institute of Technology has been trying to teach machines to swim
like fish. He envisions fleets of tuna-shaped robots criss-crossing the oceans
for days or weeks at a time, mapping nutrient concentrations or temperature
gradients. Meanwhile, robotic pike鈥攎odelled on the fish famous for its
astounding acceleration鈥攃ould reconnoitre dangerous spots around volcanic
vents or chemical spills. And Triantafyllou imagines a mechanical muskellunge,
based on the agile North American gamefish, twisting and turning among
underwater wreckage while human observers watch from the safety of a support
vessel via an on-board camera.

As Triantafyllou and his colleagues have been transforming these dreams into
reality, they have also been busy using their robots to solve the mystery of how
fish swim so efficiently. What they have learnt is remarkable. It seems fish
manipulate the water around them, drawing energy from whirling vortices not just
to turn on a sixpence, but also to swim faster than their muscles alone could
propel them.

Triantafyllou鈥檚 mission grew out of controversial research by physiologist
James Gray. In 1936, Gray calculated that fish shouldn鈥檛 be able to
swim鈥攁t least not nearly as well as they do. At that time, dolphins were
thought to swim at speeds of up to 10 metres per second, but Gray鈥檚 experiments
suggested that their muscles couldn鈥檛 move them this fast. Fish, Gray concluded,
must somehow manipulate water to ease their passage through it. Although
scientists now believe that Gray鈥檚 calculation was flawed, his belief that fish
can control the flow of water around them has continued to intrigue
(麻豆传媒, 20 November 1999, p 28).

Fish and ships

It was this question that first caught the attention of Triantafyllou and his
brother George, who is also a naval engineer. They were hoping to find new ways
to make ships more efficient, and began by pondering a fish鈥檚 chief source of
power鈥攊ts tail. They reasoned that the tail had to be particularly good at
moving water, and that something similar attached to a boat should boost speed
and save fuel. However, when they tested simple foils that swished like
fishtails, the models squandered energy.

So the brothers began to look at one of the basic principles of fluid
dynamics. Any object in a flow鈥攁 rock in a stream, an airplane wing in
air, or a fish in water鈥攍eaves trails of eddies or 鈥渧ortices鈥� behind it. A
rigid object like a sailing boat obstructs the flow and leaves a swirling wake
as it cuts through the water, but when a fish swishes its tail it actively
pushes water backwards. The result isn鈥檛 a simple wake but a jet of moving
water. The researchers had a hunch that the vortices inside this jet somehow
generate thrust. If they were right, then the key to boosting the efficiency of
their foils should be to manage these vortices deftly.

In earlier studies of vortices, the brothers had encountered something called
the Strouhal number. By multiplying the width of an object鈥檚 wake by the
frequency with which vortices form inside it, then dividing the result by the
speed of the flow, the Strouhal number gives a measure of how fast vortices are
being created and how close together they are.

Working with Mark Grosenbaugh, a marine engineer at the Woods Hole
Oceanographic Institution in Massachusetts, the researchers decided to apply the
equation to swimming fish. They adapted the Strouhal number to express the
frequency of tail swishes multiplied by the width of the jet, with the product
divided by the fish鈥檚 forward speed. Then they retreated to their lab and
flapped their foils at a range of speeds and amplitudes. Measuring the results
and refining the combinations, they found that the foils moved the most water
using the least amount of energy when the Strouhal number was between 0.25 and
0.35. In that range, their fabricated fishtails delivered efficiencies of up to
86 per cent, compared with a maximum of about 80 per cent for the peak
efficiency of ships鈥� propellers. Later, they discovered that most fish swim
within that same range鈥攆ar above the 0.1 or less that the Triantafyllous鈥�
earlier foils had struggled to achieve.

They decided that the only way to learn how these creatures accomplish this
apparently impossible task was to build their own aquatic robot. So over the
next two years, the Triantafyllous and Grosenbaugh worked with graduate student
David Barrett to meticulously copy the external physiology of the bluefin tuna,
the creature that many zoologists believe is the most efficient swimmer in the
oceans.

To do this, they built a body with eight jointed sections and an intricate
system of pulleys and strings鈥攖he mechanical equivalent of muscles and
tendons鈥攖o make it move on command. In 1994, the RoboTuna was finally
baptised in the MIT test tank (麻豆传媒, 1 October 1994, p 22).

All the robot鈥檚 movements are programmed into an external computer and
effected via cables in a rigid mast attached to the top of RoboTuna鈥檚 head. As
the mast tows the automaton through the water, the computer moves the body
sections in predetermined ways and the sensors transmit water-pressure data back
to the computer. As the apparatus moves, Michael Triantafyllou and his team
watch to see what happens to the water around the fish using a technique called
digital particle imaging velocimetry.

To set up the experiment, tiny fluorescent particles that are neutrally
buoyant are added to the water in the test tank. The lab is darkened and the
robot begins to swim the length of the tank. As it moves, two laser
beams鈥攅ach spread into a two-dimensional sheet of light with a special
lens鈥攆lash alternately. These horizontal sheets of laser light slice
through the water in the plane in which the robot is swimming, lighting up the
fluorescent particles. A video camera looking down into the tank takes a picture
every time a laser flashes and the researchers use these images to track the
luminescent particles. From this, they can work out the movement of water around
the fish.

The researchers then analyse those patterns and combine them with water
pressure readings to determine which combination of body
movements鈥攖ail-flapping frequencies, flapping amplitude and body
flexing鈥攜ield the smoothest flow of water and, therefore, the greatest
efficiency.

However, there is an almost infinite number of ways to combine the frequency
and amplitude of tail movement with the positions of eight body sections. To
sort through those permutations relatively quickly, the team used a genetic
algorithm鈥攁 sort of digital breeding programme.

RoboTuna would test 10 combinations of these properties in succession. Then a
computer sorted through the data to rank the patterns of body and tail motions
according to their efficiency. Trials ranked in the bottom five were discarded.
Then those that remained were 鈥渃ross-bred鈥� and retested. Again, the least
efficient were discarded and the survivors cross-bred. In total, about 2000
digital offspring were produced, speeding up鈥攑erhaps by years鈥攖he
work of discovering the most efficient combination of motions.

After this programme, the researchers believe they have a pretty good idea of
how fish swim so efficiently. It鈥檚 not just a fish鈥檚 tail that matters: the role
played by the rest of its body turns out to be far more important than almost
anyone suspected.

Hints that this might be the case first surfaced in 1973. In a strange
experiment, a biologist called Paul Webb who was working at the University of
Michigan at Ann Arbor amputated the tails of young salmon, threw them back in
the water and found that they still delivered about 80 per cent of their
swimming efficiency. No one really understood how this could be, and the finding
was forgotten.

Until recently, that is. In September 1999, in a paper published in The
Journal of Experimental Biology, Grosenbaugh and Triantafyllou not only
confirmed Webb鈥檚 result, they also explained what was behind it: they found that
it is the body of a fish, rather than its tail, that creates the strongest
vortices in the water.

In a spin

As a fish swims, undulations in its body create differences in water pressure
that help to pull the fish forward, much as the curves on the surfaces of an
airplane鈥檚 wing create a difference in air pressure that allows the plane to
rise into the air. But these movements also stir the water around the fish,
whipping up a series of large vortices, one after another. Depending on the way
the fish wiggles, some of the vortices rotate clockwise, others anticlockwise.
As the fish moves forward, these vortices roll along the fish鈥檚 body and into
the path of its tail.

That could spell trouble. Depending on their direction of spin, some of the
vortices throw water back toward the fish. That might seem useful, like having a
tailwind.

In reality, it creates chaos. If these vortices simply fell directly behind
the fish, they鈥檇 send water crashing into the wake that the fish is creating
with its tail. The result would be a drag-inducing backwash.

However, the researchers have shown that fish have evolved a clever trick to
avoid this. As the vortices trail off the body at the tail, they roll up into
bundles. 鈥淭he vortices swirl around each other and wrap up together,鈥� says
Grosenbaugh. The fish seems to sense the direction in which each is spinning.
With flicks of its tail, it sweeps each bundle of vortices spinning clockwise
towards the left and anticlockwise ones to the right. When these vortices meet
behind the fish, they form a jet that sends water away from the fish, boosting
thrust just as a jet engine sends hot gases backward to propel an airplane
forward (see Diagram).

Fish exhibit a similar level of control when it comes to changing direction.
Just as some jet aircraft can use thrust vectoring to manoeuvre quickly, the
body and tail of a fish combine to create a sudden, directed spurt of water from
a pair of counter-rotating vortices which spins the fish around on the spot.
Remarkably, the researchers found that the fish sheds no uncontrolled vortices
as it turns. 鈥淲e were the first to show this large vortex structure around the
fish body,鈥� says Grosenbaugh, 鈥渁nd to explain how the body uses it to perform so
well on its own.鈥�

Triantafyllou believes that a fish does a similar trick with smaller vortices
formed along its sides by its forward motion. As a fish swims, the water
molecules that it touches are dragged along with it. This sets up microscopic
vortices in a thin layer of water along the fish鈥檚 body. These tiny eddies
create friction or drag that should slow the fish down. But Triantafyllou has a
hunch that fish may even be able to recapture this small stream of lost
energy.

The fish鈥檚 tail could never move fast enough to swish this continuous stream
of tiny whirlpools from one side to the other. So Triantafyllou suspects that as
these vortices roll off the fish, they, too, tangle together to form large
vortices that the fish can control easily. If he鈥檚 right, the fish could
recapture much of the energy that its body loses as friction. 鈥淚t鈥檚 possible
that the fish does something with these microscopic vortices,鈥� Grosenbaugh
admits. 鈥淲e need to do more work.鈥�

While Grosenbaugh pursues those basic questions, Triantafyllou is awaiting
further funding that will send his creations into the open sea. His group has
crafted a free-swimming robotic pike and muskie, whose movements are
preprogrammed to keep their efficiency in the optimal range
(麻豆传媒, 28 February 1998, p 11).
At the same time, the team is building
a second-generation RoboTuna to include a feedback system that will continually
adjust body and tail motion to maximise efficiency as water conditions change.
And as the feedback system evolves, its adaptations will be built into the pike
and muskie.

Descendants of Triantafyllou鈥檚 robofish with the ability to think for
themselves could survey the seabed in hazardous zones such as thermal vents, or
monitor the condition of underwater equipment such as oil and gas rig structures
and optical fibre cables. At least that鈥檚 the vision of William Sandberg, deputy
director of the Laboratory for Computational Physics and Fluid Dynamics at the
Naval Research Laboratory in Washington DC. Robotic fish could even conduct
underwater damage assessment for ships at sea. 鈥淭here are many inherently
dangerous missions they could perform that now require sending down expensive,
multipurpose vehicles鈥攊f the vehicles are even available鈥攐r risking
the safety of humans,鈥� says Sandberg.

Even though they鈥檙e still only swimming around in tanks, Triantafyllou鈥檚
current generation of robots have turned out to be more useful than anyone
expected. 鈥淭his is the first work I know of that models the comprehensive motion
of fish,鈥� says Mory Gharib, a specialist in biofluid mechanics at the California
Institute of Technology in Pasadena. 鈥淚t鈥檚 almost impossible to create a
computer model鈥攖here are just too many possible combinations. The only way
to figure it out is to build a physical model or run experiments. Their project
does both, which is best because that way you learn directly from nature.鈥�