Hi Ike and everyone,
Excellent, excellent discussion. Many of your conclusions match what I got when I took F = ma = -kx, turned it into a = -kx/m and found x(t) and v(t) using hypothetical values of m and k. If all we care is the velocity of the kicker and momentum at the end of the swing, having smaller spring rate and longer draw do indeed create a higher velocity and momentum in the end. Same with increasing the kicker's mass (it reaches a peak after a while).
So, I started looking for the actual spring rate of springs 115 used on the robot this year, and ended up digging around the spring manufacturer's site as well as through Shigley's Mechanical Engineering Design textbook. I found a nice pdf in Century Spring's website (our springs' manufacturer) that talks about spring rate and various other considerations:
http://www.centuryspring.com/pdfs/230-289.pdf, and I found the mechanical property of Hard-drawn wire from Shigley's. I obtained a theoretical spring rate that matches closely with what's listed in the catalog specs (We used 0.563 in OD, 8.5 in length, and 0.054 in wire diameter springs).
Then I took one of our springs home, hang it up with a coat hanger, tried to put weight on it, and tried to calculate the actual spring rate. To my surprise, the rate is different at different load (5 lbs, 10 lbs, 15 lbs). It's much higher at lower load and approaches the theoretical value as load increases (the highest suggested load for this spring is 9.2 lbs).
Then I pulled up a spreadsheet I made about a week ago when I was messing around with kicker/cable/pneumatic geometry, and tried to calculate effective cable tensions at different kicker angle.
Long story short, I will be posting a white paper on spring loaded, pneumatic drawn kicker systems in the near future.
-Ken L