To find the center of radius for a given crown—
(a) Connect the endpoints and the center of crown with straight lines, or chords.
ing a height of 85A inches in 7 feet 1 V2 inches length. You can lay off this line on the floor and swing arcs of experimental radii until your knees and patience have both given out and you've achieved a curve that comes very close to hitting all those points. Or you can attack the problem as in the accompanying drawing (Figure 15-2, steps a,b, and c), which is self-explanatory and uses up what little I remember from my high school geometry lessons.
Then there's the textbook method, known to all students of naval architecture, whereby you drawr a doughnut (which sits on a line like the sun on the horizon) and carve it into strange sections whose heights are spaced at ordained intervals along the lines. Spring a batten to these marks, and there you have it—the almost-perfect. arc, flawed minutely, if at all, by the irresponsibilities of a less-than-perfect homogeneous batten. My head aches when I think of it.
Then there's the right way, which deserves a paragraph in itself.
You draw a line, the length of the beam. At each end of the line, stand a rubbing post in the form of an eightpenny nail (or any other size you have handy—I don't want to be too damned didactic), and halfway between these nails, measure up, from the line, the height of the crown you want in the beam. Find two straight-edged boards, each slightly longer than the longest arc you expect to need (4 inches sliced off the edge of an 8-foot sheet of plywood come straight and handy). Snip off a corner on each so that you can butt the points together at the mid-crown mark while the edges are pushed against the nails (see Figure 15-3). Tack some laths across to keep the two straightedges touching at the point and at. a constant angle to each other. Now, if you slide the point from the
(c) These intersect at the circle's center from which the arc of crown may be drawn.
(b) Draw perpendicular bisectors with compass or trammels.
renter mark to one nail and then to the other, keeping the straightedges against the respective nails while sliding, the path of the point will be a perfect, flawless arc reaching from nail to nail, and the arc will be exactly the right height in the middle. Run a pencil point, of course, at the end of the tip, to mark the pattern you want to cut. This truth machine can be readjusted in moments to fit any beam whose length and height of crown are within its scope. (Soon we'll be equipped to determine the length and crown of any beam in a tortured housetop, and we'll be happy we have this quick-and-dirty way to mark it out.)
Now, in sweet charity, let's assume that the design calls for constant crown, and that, about six days from now, you will need 16 beams, identical (except for length) in every respect.
If you have on hand some clear, sweeping planks that grew in a curve to match your pattern, then you may rest serene and go on to the next step, knowing that you can saw them out when they're needed. But beware—such sweeps have been known to change shape after sawing. Don't plan to saw your beams out of straight-grained stock, because they'll be likely to check open and break where the grain runs across the curve. You could steam-bend the stock over a form built to a tighter curve, precisely calculated to produce the arc you want when the beams straighten out—ever so slightly, indeed, but inevitably, and not all to the same amount. In view of these difficulties, you'd perhaps best plan to make them of glued laminations, thus:
Build a gluing form (or two, or three, if you have the strength) by sawing out a 2- by 2-inch rainbow and mounting it on a backboard like a prize fish (see Figure 15-4). The radius of the top edge of the two-by-two should theoretically be shorter (by the depth of the beam) than the radius of the finished beam.
Saw out and smooth the stock for the laminations. The strips are too rough as they come from the saw and should be planed before glu-
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