The stress calculation asks the question: if I make braces of various species, and I make them all the same size, which ones will break.
I want to ask a different question: if I make braces of various species, and I size them to take advantage of their properties and not break, which ones will be most efficient (produce the highest monopole mobility)?
So, much like the discussion of thicknessing top panels, I'd like to measure the properties of my pieces, and dimension them appropriately.
In addition, I'd like to use average properties for the various species, and find those species of which I'm most likely to find individual pieces that will produce a good soundboard when appropriately dimensioned. Is Sitka really best for braces? Probably not.
To do this, I used the stress calculations as performed in sections 4.4.3 and 4.4.7. Unfortunately, there is not sufficient information on these pages to do these calculations, and as the footnote on page 4-49 suggests, I consulted an engineering textbook.
Bending of Beams
With this, I re-created the results in Table 4.4-2. Spreadsheet
This calculation takes some dimensions and calculates stress. I want to go the other way--take 50% of maximum stress for the species, and calculate dimensions.
I suppose it's possible to invert the equations, but that seems really difficult. I decided to use the "Goal Seek" feature in Google sheets. You tell it: here's the input cell (dimensions), here's the output cell (% allowable stress), and the target is value 1 (100%). It manipulates the input cell until it hits the output target.
I set some assumptions for the dimensions of my braces. I decided on tall triangles (per discussion on page 5-51), with a height 4.5 times the base. I also decided the major braces would be 1.4 times the width of the minor braces. There would be two major and two minor braces.
I then took those dimensions and calculated the mass of the soundboard (top panel plus braces) and the stiffness, and used these to calculate the monopole mobility of the top. This of course is not an accurate modeling of MM (the curvature and gluing of edges stiffens things further), but it is, I think, a good way to compare species.
I did this calculation for 210 species, using average values for density, flexural modulus, and flexural strength from wood-database.com, and sorted by MM. I found some surprising results.
Sitka came in at position 180. Not great.
The winners, as you might expect, were Balsa+CF, Sitka+CF, and KBP+CF. Off the charts MM.
Amongst the pure wood set, the top 10 were:
- Madagascar Rosewood
- African Blackwood
- Curupay
- Osage Orange
- Pau Ferro
- Etimoe
- Western Juniper
- Pau Rosa
- Norway Maple
- Pacific Yew
Now, some of these braces came out so narrow you probably couldn't actually make them. There are physical limits. Still, it demonstrates, I think, that if you properly dimension them, the best braces might be built from some pretty dense species. Madagascar Rosewood has a density of 1270 kg/m^3. For comparison, Sitka is 425. So nearly three times the density!
The Madagascar Rosewood braces would be triangles 1.7x7.5 mm and 2.3x10.4 mm, weighing 12.1 g total, and a MM of 19.2.
The Sitka braces would be triangles 2.6x11.7 mm and 3.6x16.4 mm, weighing 13.5 g, and an MM of 10.7.
Has anyone else tried to dimension braces based on the wood's properties?
Has anyone tried to use a heavy species for braces? I can get Pau Ferro, Bubinga, Ziricote, and Macassar Ebony locally. Even East Indian Rosewood looks good. I'm wondering if anyone has had success making braces from these species?
Greg