After I put the back on the pot I took a look at it and decided that the 1/2" standoff represents a rather huge hole in the system, far too large for the resonance that I want. I decided to calculate exactly how big that hole is.
The area of the gap is the distance that the back is from the bottom of the pot times the circumference of the pot. The circumference of the pot is 2 times π times the radius, R.
Area = 1/2 * 2 * π * R
The 1/2 and the 2 cancel out, so the area of the hole is equal to π times R, and R is about 7 inches.
3.14159265359 * 7 = 21.9911485751 square inches.
If we made a hole in the back with the same square inch area, how big would the hole be? Let's calculate it.
Area of a circle = π * R2
so
Sqrt(Area / π) = R
Sqrt(21.9911485751 / 3.14159265359)= 2.64575131106
Diameter = 2 * R, so
Diameter = 5.29150262213
So the space between the back and the pot is the same size as a hole in the back that is over 5" across. That is much too large for the acoustic resonance I am looking for. I decided to cut the notch down to 1/8" and make the hole 1/4 of its current size.
Sqrt(5.49778714377 / 3.14159265359)= 1.32287565553
Diameter is 2 * 1.32287565553 = 2.64575131106
Now we have a gap that is the same size as a hole that is about 2 1/2 inches across. That should be better.
OK. Enough of that. I also decided to trim off the backs of the standoffs to take care of the problem that the range of the screw adjustment would not allow me to turn the standoffs around and mount the back flat against the pot. I decided to cut 1/4" off the back of the blocks.
Cut Off 1/4" from the Back
Here is another problem that I ran into. The slanted edges of the slots are very rough, so the heads of the screws fall into the holes and are not smoothly adjustable.
This Surface Needs to be Smooth
The chisel made quick work of that problem.
Use the Chisel to Straighten the Side
I marked the blocks to cut 1/4" off the back and to cut down the size of the standoff to 1/8".
Remove Some of the Wood
I cut one of them down and put it next to another one with the original standoff.
Original versus New Design
The panel saw made quick work of the job.
Cutting a Block
It only took a few minutes to make them all the same.
All the Blocks are the Same
I screwed them back onto the back, but this time with the standoffs facing inward. That will allow the back to sit directly onto the bottom of the pot.
This Configuration is for No Gap
Here is the banjo with the back installed.
Installed on the Pot
Here it is from the bottom.
A View from the Bottom
That is all I did today. It looks pretty good. Now I need to put some finish on it and then see how it plays.
