Here’s a little esoteric ‘how-to’ for those times you can not buy the ‘round’ you need in the size or material you want. This is a basic spar or mast builder’s technique which works for making things round and long.
Almost all wooden masts have traditionally been built with a changing taper, diminishing towards the top. In ancient Grecian and Roman times, many of their architectural columns in their buildings were gracefully tapered from base to capital, and in fact often, the tapers began at the base in a particular diameter, then the diameter increased slightly for a distance before beginning a graceful, curving decrease in diameter towards the top. Some opinions say these changing curves are based on the human figure, and in particular on the female figure – the lovely taper in a woman’s legs in the eyes of a man for example. For whatever reason, the idea of long, graceful tapering columns has carried over for millenia into more recent times in mast and spar building, and many other things too. Tapers also just so happen to be very well suited for making long things like masts smaller (lighter) towards the top, with weight being a penalty against stability the higher it is carried. You even see this in many aluminum light poles along the highways today.
Mast and spar builders over time developed techniques for both rounding something from a square piece of stock, and tapering it towards the end. And, that’s where the two extra holes come in in the little Gee Whiz multi-tool presented in part one of “Centerlines – Finding, Marking and Using Them!” (http://lumberjocks.com/GnarlyErik/blog/33315)
The extra two holes on the Gee Whiz are for laying out the facets on square stock to plane to in order to make the piece octagonal, or ‘8-sided’. Once planed to eight-sided, the stock can then be accurately rounded from there (on larger rounds, say over 10 or 12 inches, the stock is often ’16-sided’ after being 8-sided, but the concept is the same, though not the proportions).
In use, the tool is employed exactly as for centering long stock, but the two outermost pencil holes are used in lieu of the center hole. And, no matter the length, or taper, the marks will provide the lines to plane to for the full length of the stock except for the last few inches at the end. Simple as that.
Now, as to how this is laid out, here’s how it is done. First, the stock is squared, obviously. Then, at any point along the length of the stock a square is constructed on the side of the stock, the same as the cross section of the stock at that point (or on a bit of scrap on the bench if you prefer). This is next bisected by diagonals to find the centers, and a circle is drawn to fit inside the square of the stock.
Next, tangents are draw at 45 degrees to the edge, where the diagonals bisect the circle. The point where this tangent intersects the edge of the circle marks the point of intersection of one of the facets of the octagon enclosing the circle – and so on around the circle. The fact is you have only to find two of these points to be able to lay out your work, and here is where the Gee Whiz comes in. These two points are proportional to the width, no matter how wide, and that is why the Gee Whiz works for all tapers, the full length of the stock. By keeping the pins against the sides of the square, you keep the same proportion anywhere along the length – not exactly precise at very steep angles, but generally close enough for ’government work’ as they say. This is done on all sides of the stock, providing all the meeting points of all eight facets. @
I have included a graphic below which demonstrates the laying out of the points, and which should be easier to understand:
Laying out 8-sides using graphical method
Further, since these proportions are always the same, you can use a ruler to do the same thing, albeit not quite as conveniently. A two-foot folding rule is particularly well suited for this, and to watch an old-timer laying out the facets for 8-siding a mast with his folding rule was like watching magic! Here is how that works:
A two-foot rule (or measurement) is laid out across the stock, so that each end touches an edge. Marks are made at the 7” point, and the 17” point. This is done down the length of the stock at convenient points, and then all the marks are connected with a straight edge or batten. Simple as that! (see sketch below)
Laying out 8-sides with two-foot rule
And, any multiples with the same proportions work just as well, for example, a 12” measurement, marked at the 3-1/2”points and 8-1/2” points! Who’d a-thunk it?
@ And, as my old daddy used to say, “Then, you plane off everything that doesn’t look like a mast!”
-- "Never let your dogma get run over by your karma!"