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#26 Zorns Lemma

Zorns Lemma

    Sir Scrt

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Posted 14 May 2009 - 11:03 PM

Doom is correct, except for a small issue. For most applications where you choose between springs, your displacement is fixed, because your plunger stroke is fixed. If you can increase plunger stroke, you should do it, regardless of spring choice, because that optimizes energy, and therefore theoretical muzzle velocity (thus, range), more than stiffness, which depends on the characteristics you identified (#coils, WD, coil OD).

Let us then fix compression stroke x, plunger tube length d, and maximum compressed length d-x. If the segment of spring you use exceeds maximum compressed length (distance from plunger head to spring rest when plunger rod is at catch) then your gun won't prime.

Given x and d, you have two options:

- Maximum acceleration: optimize with regard to k. That is, find the spring with the highest k, such that the section you use will compress to a distance (solid length) less than or equal to d-x. Solid length is initial length * CPI * wire diameter.

- Maximize energy: this one is trickier, and most likely, requires you to use a weaker spring, and "precompress" it. The mathematical model is as follows

max k*(L-d+x)^2 - k*(L-d)^2
such that: L * CPI * WD <= d-x


If anyone cares, I'll actually crank out the optimization for that problem, but the answer will be quite meaningless, since the final optimization point is a function of both spring characteristics and the length you use. You still have to arbitrarily fix OD/WD before you can get any useable data.

The main point is that in maximizing acceleration, you can just fix L=d and maximize k subject to the compression constraint. In maximizing energy, L > d and varies with k.
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