Carbide Saw Blades

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Stave Construction

If you have ever looked at a barrel to see how it is assembled, you will have noticed that it is constructed of segments. These are called “staves”, and the principle is used in any application where the end product is to be rounded or connected end to end in a circular fashion.

Columns, lamp bodies, bowls and turned boxes are all examples of stave construction that this article will cover.

When staves are put together in this way, a polygon is formed, with each facet or side of the polygon being a stave. Laying out polygons is not the mystery a lot of people believe it to be. Squares and triangles are easy, but when you get into pentagons, hexagons, octagons etc., things get a little trickier, but a little geometry will rescue your project.

In any polygon except a triangle, the included angles add up to 360 degrees. Once you decide on how many sides or segments your polygon will have, simply divide 360 degrees by the number of segments. Each segment and it's radial lines form a triangle whose included angles equal 180 degrees.

Divide 360 degrees by the number of segments desired, to find the included angle of the radial lines. Subtract this number from 180 degrees. Divide the result by two to find the miter angle to be cut on each end of a segment, or each side of a stave. This holds true for any number of segments.

Let us assume a pentagon, which, of course, has 5 sides. Divide 360 by 5, and you get 72 degrees. This is the included angle of the radial lines, and since a triangle has 180 degrees, the angles at each end of the segment are half of the difference between 180 degrees and 72 degrees. (360/5=72. 180-72=108. 108/2= 54) The angle at each end of the segment is 54 degrees, which is the miter angle at which you will cut each segment.

When building columns, whether turned or facetted, I like to join the staves together with splines, and I use 1/8” plywood, or door skins, for the splines. The carbide saw blades that I use cut a kerf just the right size for the plywood, and the splines add tremendous strength to the joint through additional gluing surfaces area, and they keep the staves in perfect alignment in the gluing and clamping process. If you are a biscuit joinery devotee, by all means use biscuits. They serve the same purpose, and they have the added advantage that the groove doesn’t show at the end of the stave. In either case, make sure that they are deep enough not to interfere with turning, if you intend to turn your project on a lathe.

Segments or staves can be of contrasting woods for added interest, and can be glued up in a myriad of designs like checkerboards, book matched grain patterns, or maybe a strip between staves. If using a strip between staves, you needn’t cut a miter angle on the strip, because the strip will be parallel to the miter cuts on the stave. You do, however, have to shorten the width of the stave by the width of the strip to maintain the desired overall size.

To form a base for a bowl, it is customary to cut wedge shaped segments, which, when glued together may be turned or bandsawed to form a circle that will fit a recess cut into one end of the glue-up. These segments may be the same angle as the staves, or any angle that is esthetically pleasing to you, the designer.

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trigonometry help !!!!!!!!?

The length of an arc intercepted by a central angle of θ radians in a circle of radius r is rθ . The length of the chord,c, joining the endpoints of that arc is given by c= r √(2 - 2cosθ). Find the actual distance between the tips of two adjacent teeth on a 12 in. diameter carbide tipped circular saw blade with 22 equally spaced teeth. Compare your answer with the length of circular arc joining two adjacent teeth o a circle 12 in. in diameter.

The length of chord C is found using

C = r(sqrt{2}) - 2 cos(theta)

We are given that the diameter is 12 inches. This tells me that the radius is 6 inches.

The angle theta = n degrees/22, where n = 360 degrees (the total measure of a circle in degrees).

We are searching for C.

C = 6(sqrt{2}) - 2cos(360/22)

C = 6(sqrt{2}) - 1.918985947

C = 8.485281374 - 1.918985947

C = 6.566295427, which can be rounded off to two decimal places becoming 6.57 inches.

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