People make spine calculation much harder than it needs to be. I have a 1x4 mounted on the wall with nails at 26" apart. Centerline is marked on the board with marker, and I then put a piece of masking tape over the centerline mark. Hang my arrow on the nails, draw a line from the top of the shaft on the tape, hang a 2lb weight from the shaft, and then mark the new position on the tape. I only use a 1/32nds ruler to measure the difference. 1/32 is accurate enough for me, and easy to see, but you could use a set of calipers if you need the .0001 or however close you need your tolerances... Anywho, spine is 26/deflection. So if the space between my two marks = 9/16ths, then 26/.5625 (.5625 is 9 divided by 16)=46.2lbs
If that is just too simple for you engineer types, then this is about as easy as it gets with mechanical(ish) action
http://www.youtube.com/watch?v=DhxYuzwDyVM