Sunday, October 3, 2010

Spiderpunk

(Picture from here.)

I am not a steam punk writer. I enjoy it immensely. But it is a fantasy arena in which I do not participate. Partly this comes from my love of eighteenth and nineteenth century science and engineering, much of which is ignored or used as mere furniture in steampunk romances. My limitation, I suppose.

I work a great deal in systems and instrument control which is largely accomplished these days by the use of software and electronic mechanisms. The big advantage of software is you're instructing systems how to be have in a language.

In the nineteenth century this was done by mechanical means using hydraulic systems, and comprises the field of fluid mechanics and hydraulic engineering. This means that steam-- the nineteenth century's nuclear power-- was tamed and controlled by valves and whistles. The physical world was controlled by physical laws and physical mechanisms, not minute bits housed in silicon. Very different from what I do and, of course, therefore fascinating.

Hydrodynamics, from the view point of nineteenth engineering, was formalized by Blaise Pascal and canonized in Pascal's Law:
$\Delta P =\rho g (\Delta h)\,$
What this says is the hydrostatic pressure (the difference in pressure between two points in a fluid column: delta-P) is a function of the fluid density (p), the acceleration due to gravity (g) times the difference in height between the two points in the fluid column (delta-h). To reframe it, if you take a garden hose and hook it to a piece of four inch PVC pipe and fill them with water the difference in height of the two water columns is a function of the weight of the water between them.

Note that no additional pressure has to be attributed to get the difference in pressure. Therefore, one interpretation of Pascal's law is that any change in pressure applied to a point in a fluid is transmitted undiminished through the fluid. Similarly, since pressure is a function of the mass of the fluid (the pg part of the equation), if you apply pressure across a wide area it will be increased when the area is reduced. Like a lever where the mechanical advantage is a function of the difference between the lengths of the lever on either side of the fulcrum, you can achieve mechanical advantage by a difference between the difference in areas where pressure is being applied. (See here and here.) Area increases as a square function (πr2 in the case of a circle) where length increases linearly. A consequence of Pascal's law was the Age of Steam.

Pascal's law, like a lot of physical laws discovered by human beings, was already exploited in biological organisms. The vertebrate heart and circulatory system exploit Pascal's law in reverse; by increasing the total cross sectional area of the carrying tubes (arteries->arterioles->capillaries) they reduce the pressure in the blood vessels. Once blood reaches the actual cells the pressure is quite low.

But vertebrate circulatory physiology is a topic for another time. Now I want to talk about something more steampunk-ish.

Spiders.

Vertebrates and a large number of invertebrates have flexor muscles and extensor muscles. Flexors reduce the angle of a joint (flexion) and extensors increase it (extension.) Your biceps is a flexor and your triceps is an extensor. (See here.)

Spiders do not have extensor muscles.

This was discovered back in the early twentieth century but the thought was that there was resistance in the joint such that spider locomotion was a sort of pull-relax-pull mechanism. The relaxation of the flexors would allow the resistance to straighten the joint. Then, someone noticed that dead spiders curled up. If there had been a passive straightening force dead spiders would have spread out.

In 1959, Parry and Brown published The Hydraulic Mechanism of the Spider Leg, a lovely paper where they put house spiders in tiny harnesses and measured how much actual pressure was being created by the spiders. They came up with some fairly impressive numbers for such a tiny creature-- as much as 50 mm Hg-- about .06 atmospheres. Not bad for a creature that's about the weight of a paper clip, if that.

Spiders share the same phylum as insects and pillbugs: Arthropoda. They belong to the subphylum Chelicerata, which they share with horseshoe crabs and sea spiders. The class Arachnida contains scorpions, ticks and mites as well as spiders, which fill the order Araneae. The line that evolved into spiders began at least 400 million years ago. The first true spiders seem to appear about 300 million years ago.

Fluid pressures are generated by muscles in the abdomen and transmitted to the legs. It's likely a primitive condition since a similar mechanism has been shown in whip scorpions which diverged from true spiders prior to the Carboniferous period. (See here.) The heartbeat, however, does appear to have something to do with it since the heart rate changes under forced exercise. (See here.)

There are evolutionary problems with a hydraulic based system. An injury can reduce the effectiveness of the pressure by fluid loss. The animal can be prone to desiccation reducing the ability to move. In addition, use of a hydraulic system for locomotion and for the circulation of oxygen and food puts the two systems in competition. (Anderson and Prestwich discuss this at length in a paper here.) Not to mention there is the additional complexity of managing two separate systems for locomotion. But spiders are very successful. How come?

Wilson (mentioned in the Anderson and Prestwich paper) noticed that the spider mechanisms of predation using webs and poison were extremely efficient. He suggested that these mechanism were so successful that they were able to overcome the problems inherent in their design. Anderson and Prestwich suggested additionally and advantage to the hydraulic system itself. By using a power mechanism whose source resides in the abdomen rather than the legs, the legs were freed up to add more muscles for purposes of flexion, increasing power.

Spiderpunks, indeed.

More on spiders:
Space system based on spider locomotion and here
Ed Nieuwenhuys great articles on spiders of Europe and his microbook, The Spider
AMNH's World Spider Catalog
Wikipedia's Evolution of Spiders
Energy Storage in the Pedipalpal Joints