Page 204 - The Complete Rigger’s Apprentice

Start by establishing Working Circumference—
π X (Mast Diameter + Wire Diameter)—and multi-
ply this by .75. This gives you enough wire to get
three-quarters of the way around the mast (Figure
6-10). Now we can decide how much extra wire to
allow for a nice, fair lead to the throat of the splice
or seizing at, say, an angle of 45 degrees. To do this,
measure straight across at three-quarters of the way
around. This chord is the hypotenuse of a right tri-
angle (Figure 6-10B), so it’s easy to find its length by
the good old “sum of the squares of the two sides”
2
2
method. In this case that’s 6 (inches) + 6 (inches)
1
= 72. The square root of this—8 ⁄2—is the length
of our chord. Divide this distance by 2, and then by
sin 22.5 degrees. The result will be the length of one
of the legs from the three-quarters-circumference
point to the throat.
Why does this work? Because each leg of the
eye is also part of a right triangle (Figure 6-10C),
and half our chord’s length for the base for each
leg’s triangle. That’s only one side, and we have to Figure 6-10. Arriving at the Ideal Soft Eye circum-
know the length of two sides for the “sum of the ference.
square method” to work. That’s where that “sin
22.5 degrees” comes in: Long ago mathematicians
worked out the proportions of right triangles. Their dummy mast to see how far it drops, and calculate
successors managed to cram all these proportions the rest of the shroud length from the point where
into the program of any calculator equipped with the seizing or splice touches the mast. If this wire is a
trig functions. Among other things, these functions shroud, its mate will fit over it, thereby losing a little
enable us to start with the length of just one side and length. To compensate for this, make the second eye
one of the two acute angles in a triangle, and find circumference longer than the first by twice the wire
the length of the other two sides. diameter, including service and leather.
In Figure 6-10C we have the length of the base
of our triangle: 4 ⁄4 inches—and we know the angle Measuring for a New Rig
1
we’ll use is 22.5 degrees—half the desired conver- If you skipped over all that trigonometric hoo-haw,
gence angle of 45 degrees. What we need is the figuring you’d just eyeball eye size, you’re in big
length of the hypotenuse (the longest side of a right trouble now. That was a way of showing you a use-
triangle). The sine of any right triangle is the ratio ful procedure while introducing some mathematics
you get by dividing the length of the base by the that are central to what follows. When you don’t
length of the hypotenuse: B ÷ H = sin T. The sine of have an old rig to base measurements on but you
22.5 degrees is .3827. To find “H,” transpose a bit still want to turn up both ends in the loft, trigonom-
1
to 4 ÷ .3827 = H. This works out to 11 ⁄8 inches. etry can be a very good friend to know.
1
The two legs together equal 22 ⁄4 inches. Add- The measurements we’ll make in this section are
ing this to our three-quarter circumference of 2 feet for a new gang of rigging for Katy, my 16-foot cat-
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4 ⁄32 inches will give us an eye of 4 feet 2 ⁄16 inches. boat, designed by Sam Crocker in about 1933. The
9
(Figure 6-10D) Put an eye this size on the mast or old rig design wasn’t quite what I wanted, so sailor
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