Use of an Angle & Taper Calculator in everyday woodworking

[Woodman]

The other day Gene Howe asked about my process for obtaining the correct angle for stave cuts.  He probably envisioned reams of scribbled figures and diagrams, coffee-stained napkins with intense isometric sketches, and the like.  No, I used a free Stave Calculator posted by a guy who makes and sells his own drums.  A modern day Galileo. https://uniontownlabs.org/tools/stave/

 

Our exchange reminded me of an equally useful calculator link I was gifted by a luthier in Tatamagouche, the village in Nova Scotia.  An online Taper and Angle Calculation application hosted by Magafor (I think they make and sell specialty boring bits).  http://www.magafor.com/841/uk.htm

 

At some point a gent asked me to procure a 'good' violin for his daughter.  Jeff, of Little Deer Isle, Maine let a late 1800s copy of a famous 1813 violin go.  He warned me that the pegs were of the old 1:20 taper.  While I could shave new pegs, a reaming tool to 'touch up' the old pegbox would be costly, hard to procure, and perpetuate the problem:  When a new peg is needed, will an inattentive technician jam in the peg of a different taper?

 

After careful consideration, I modified the centenarian pegbox doing the unthinkable.  Removing wood.  Some haughty luthiers scoff, but is their scorn manufactured?  A sixth-generation European-taught technician was straightforward:  Yes, it is fine, to a certain point.  Based on rarity, age, value.

 

Break time!  I'll pick this story up in a bit.  How I used the angle calculator to turn this pile into a fiddle. 

 

 

 

 

 

 

 

 

 

[lew]

Looks like my grandfathers of violin.

 

I found some neat formulae here-

 

https://www.blocklayer.com/

[Woodman]

39 minutes ago, lew said:

I found some neat formulae here-

 

Thanks!  I'll use this on my first effort!  https://www.blocklayer.com/woodjoints/dovetaileng.aspx

 

When I put in steps 20+ years ago I did it the old fashioned way, drawing out rise/run ... times have changed!  Your link has several formulas which would work for staves. 

 

I used the angle calculator to determine exact angle of a 14" run (the length of a violin's strings) to rise 29.5mm (bridge height).  When that failed, what I had to do to reduce my rise by 10mm ... A collection of successes which led to a super fiddle crafted a few decades after the French Revolution being returned to playability.

 

(Failures x 20) + (Finally getting it right x 1) = Success

 

[kmealy]

Along a related line, here is a calculator to determine compound miter for staves, tapered side totes, etc.   If you don't have MS Excel, you can download, then import into Google "Sheets" that is a free clone.  Hidden inside is some trig, but you can just keep your eyes closed and enter the values. https://cdn.popularwoodworking.com/wp-content/uploads/calc.xls

[Woodman]

20 minutes ago, kmealy said:

Hidden inside is some trig, but you can just keep your eyes closed

How did you know? I've (actually) piped boilers in steel and copper with no tape measure. 

[Grandpadave52]

I think I had some trig for breakfast when I was in the hospital?

[frenchwwr]

I tried to teach myself trig in an Home Study Engineering Course back in the '80s. 

 

That was the end of the course

[Woodman]

On 3/5/2022 at 8:34 AM, Dovetail said:

 I'll pick this story up in a bit

As promised, I've posted the entire image series with recollections in Free For All (hobby luthiery) under the title:

 

Restoring an old fiddle

[kmealy]

Don't even get me started talking about trigonometry.

I always go off on a tangent.

 

[kmealy]

One technique I learned many years ago for setting an angle.  To verify, I made a 37 sided segmented section.  (an odd number so you can't just do two haves and plane out the middle). 

• Compute the angle that you need to cut. 
• Take the tangent function of that angle. 
• On a piece of scrap something measure over 1000 mm (slightly longer than a yard) and up the tangent of the angle. (tangent is side opposite over side adjacent of a right triangle) in mm. Scrap picture frame mat works well for this because it's 40"
• Draw a line between 0 and the tangent value point.
• Carefully cut along that line a few inches (or cm).
• Cut of the piece and use that to set your saw bevel or miter angle.

[Grandpadave52]

Must've been what the surgeon used to figure out where to stab me in the back? I suspect trig wasn't his strong suit in college.

[Gerald]

43 minutes ago, Grandpadave52 said:

Must've been what the surgeon used to figure out where to stab me in the back? I suspect trig wasn't his strong suit in college.

That would be a sight to see"a trig suite"