Regarding the strength of the internal bridge force balancing leaf spring apparatus.
If I can calculate my string tension, and then the downforce based on my bridge height and build the top to withstand the static force without deflection, what percentage of that downforce would be a decent starting point for the spring’s deflection point? I would assume the stronger I make it, the less sustain the top will have.
is there a way to estimate these forces before the trial and error period starts?
@Bruce Johnson do you recall what the percentage of the downforce your spring was?
Banjozilla’s top probably had less contribution than an archtop will, but how much?
There are a few projects that really need to get done before I can start on this (without my wife killing me), but I’m getting twitchy with anticipation.
The downforce on the feet of the bridge will depend on the amount of break angle of the strings over the bridge. You can adjust the amount of downforce by adjusting the break angle; adjusting the height of the tailpiece in relation to the bridge.
Whatever amount of downforce you decide put down into the feet, the spring reaction system underneath needs to be adjusted to apply an equal amount of upforce to balance it. If you take the top out of the picture, the bridge should be able to sit there on top of the spring reaction system, with the strings up to tune. The force down pushing against an equal force up; an equal balance of the strings (being springs) against the opposing springs underneath.
At that balance point, the vertical position of the bridge should be right for the string action height over the fingerboard. That's the other reason for needing an easy adjustment of the spring system. If the action is too low, and you raise the height of the bridge saddles, as normal on an electric bass, you'll just compress the springs a little more. And the strings won't raise up. You have to be able to raise up the bottom of the springs, in order to actually raise up the bridge. Banjozilla has a big brass knob on a threaded stud that I can use to crank the spring system up and down.
Note that tightening the knob doesn't change the
spring rate (in lbs/in) of the springs. It raises the bottom of the springs, compressing them in height, and increasing the force (lbs.) applied upward. But the spring rate remains the same. You have to change to different springs (unsprung length, wire size, etc.) to change the spring rate.
The spring rate becomes important, because it determines
how much the top will deflect when the strings are plucked. When you pluck a string about as hard as you would want to, you would like the bridge (and top and spring system) to bounce up and down about 1/8" from the neutral balanced position. That's the goal, and
how much it bounces is determined by the spring rate.
My earlier spring systems in Banjozilla didn't have enough travel; the spring rate was too high. Not enough movement of the head, and the sound volume was weak. I increased the length of the coil springs. That reduced their spring rate. The longer springs had to be compressed farther to reach the pounds of force needed to balance against the string load. But they still had a lower spring rate. That meant that head deflected farther with the same plucking on the strings. A big increase in the sound volume. More travel from the diaphragm.
Those are the mechanics that you need to think about. Your spring reaction system, whether steel or wood, needs to be able to apply enough force upward to balance the download from the strings. The springs also need to have enough travel and a low enough spring rate to allow the top to deflect 1/8" under heavy plucking. And the top has to be able to deflect 1/8" without exploding.
