Thesis calculations - math!

So I've sent emails to the director and assistant director of the band at MIT, and the head of the physics dept. to let them know I'm interested and ask a couple of questions.

I also found out about what kind of pressure I'm dealing with for the silk spinner. I derived the equation:

P = (2ΔXm)/(πr²t²) = 2ΔXmπ⁻¹r⁻²t⁻²

to find the pressure (P) that I will need.

a simplified version:

P = (ma)/(πr²)

So, if I want the silk to travel ~7.5 meters (~24.6 feet) in 1 second, the acceleration will be 15 m/s².
I said the mass of the silk is 1X10⁻³ kg (which is very generous), and the change is negligible as more silk is extruded. I also said the radius of the opening in the extruder is .5mm.

I came out with 19,098.593171 kgm⁻¹s⁻² or ~19.1 kPa, which is ~ 2.90075 psi. So, about 3 psi should be plenty, which is good, because I was worried about it being a dangerously high pressure. The small radius combined with the small mass allows a small pressure to be sufficient enough to accelerate it.

Of course, this could be wrong, but there's only one way to find out...

I've been looking at some glass capillaries and solenoid valves to build with. I still need to acquire the acidic buffers and the all-important dope.

Update: (I found out the density of typical spider silk)

P = 2ΔXρₛLt⁻²
P = aρₛL

ρₛ being the density of spider silk which is ~1.3 g/cm³ (= 1300kg/m³), L being the length of the silk which should be 7.5m, and a being the acceleration which should be 15 ms⁻². With this new knowledge of mass, the pressure should be 146.25 kPa or ~21.21 psi. So a little less than average tire pressure - not too dangerous. I will double check my math, and I can always change the variables to lower the pressure. For an actual presentation, I think 5 ft/s is sufficient, so I can cut down on length and acceleration. (psi should be ~.88 psi for 5ft/s) However, for experimental purposes, I will start with what I have specified and modify from there.

The only thing I need to check is the maximum rate of production of fibers to make sure that the polymerization process itself can keep up with the ejection speed.

All in a day's work

- Noah