Math question

[Dave Bagwill]

Suppose you have already sanded the back rim to a 15' radius.
If the red box is the block, and the black is the rim, what would the calculation for angle A be?

Measured, it's about 84.2*

[John Parchem]

I think the angle you are measuring is the opposite angle as the one you are showing is bigger than 90. So my guess that your A is 95.8. What I show will give you the 5.8 part

To calculate the angle is complicated because the back is generally sloped relative to the heal and tail block. you can calculate the angle first assuming there was no slope; the arc sitting on two blocks the same height. But you really need to include more information because it is an arc and there are an infinite number of tangents.

What I would do is to use the calculator at http://www.liutaiomottola.com/formulae/sag.htm to calculate the sagitta of the arc for your back. Using the same units (inches or feet) fill in half the length of your guitar and the 15' radius and get a saggitta.

Then go to the bottom calculator in http://www.liutaiomottola.com/formulae/sag.htm Calculating Height of an Arc at Any Point, and calculate the rise at the end of your heel block. For X you would use half the length of your back minus the thickness of the block.

You can use this height to get an approximate angle of the block by calculating the tangent using the height you calculated above and the thickness of the heel block. The tangent of an angle is tan(θ) = Opposite / Adjacent of the sides of a right triangle. In this case opposite is the height you calculated just above and the adjacent is the thickness of the block. Divide the opposite by the adjacent and use an arctan calculator for the angle, just make sure you are getting degrees not radians. http://rapidtables.com/calc/math/Arctan_Calculator.htm

Now you have an angle representing just the contribution of the sanded radius that you can add or subtract to the angle of your block that is based on the slope of the back.

[Dave Bagwill]

Excellent, thank you John! I'll head over to Mattola's site and proceed apace.

[John Parchem]

For me having said all of that. I think I would draw out using my 15' sanding stick and measure it with a protractor.

[ken cierp]

Many makers and factories no long bother with sanding the correct angle on the tail block, simply shaving a reverse angle to allow clearance so the plate does not even touch the block -- I may incorporate this design.

[Hans Mattes]

I've been beveling the tail block, both top and bottom, so that the ends that glue to the soundboard and the back are the same thickness as the kerfing. And then I "taper" both ends while driving the bus. My intent was to keep the surface glued to the top and back constant around the lower bout, both to facilitate vibration of the top and back and also to minimize "print thru" of the tail block as the top and back might "evolve" over time. It's certainly easy; does anyone see a problem with this?

[John Link]

My two cents goes along with Ken and Hans. If the extra area of glue-down presented by the heel block is actually used it effectively eliminates part of the top (and/or back) from vibrating.

With respect to John's observation, I agree that going obtuse with a 90 degree angle adds degrees, not deletes them. 5 or 6 seems about right, without considering anything except the definition of obtuse angle and looking at the drawing and thinking (vaguely) about a 15 foot radius.

In the end, if it can't move it can't sing.