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Figure 5

The first was its shape. A round tub has a constant curve. Thus, the
vertical boards, or staves, which form the sides can all be the same
width and still maintain a tight fit with the base. The varying shape of
an oval tub requires staves of differing widths. Because the curve becomes tighter at the "ends" of the oval, each stave must be sized for
its location on the curve. Fortunately, this problem is reduced if the
oval is regular-a true ellipse rather than an egg. On an ellipse, four
staves (one in each quadrant) will be similar in shape (Fig. 1).
Furthermore, on a round tub all of the staves will have the same
bevel since they are the same width and thus occupy equal portions of
the circumference: a round tub of any diameter built with sixty staves
will use staves beveled on each edge at an angle of 3 ° (or 87 0, if you
prefer). The same tub built with forty staves would use bevel angles of
4.5° (or 85.5°), and so on. However, an oval shape requires that
each stave have a different bevel on each edge in order to fit properly
against its neighbors, each of which it meets at a slightly different
angle. This means that the four similar staves mentioned above will
actually constitute two pairs. Staves 1 and 3 will share the same
shape and beveled edges; staves 2 and 4 will share the same shape
but will have bevels reversed from numbers 1 and 3.
The second problem was the sloping side. The 10° angle meant
that each stave had to be slightly wider at the top in order to create
the larger diameter of the upper oval. (Visualize one half of a wooden
cask or an old wooden bucket.) This top-bottom taper is proportional
regardless of stave width as long as the side slope is constant. Thus,
once this taper angle is determined it can be used to layout all staves.
A little advance planning can resolve both these problems fairly
easily. On the drawing board layout the intended oval in a fairly large
scale (1" or 1 y," = 1 '_0") using whatever method you prefer (parallelogram, concentric circles, pin and string, or trammel). Then begin
at the minor axis and using the scale rule, determine how wide a stave
can be and still remain in contact with the ellipse across most of the
stave width. (In theory, of course, the stave will only be tangent at one
point. In practice there is a much greater margin.) Mark this width on
the ellipse and using dividers transfer it to the three similar staves in
the other three quadrants. Proceed in this fashion until reaching the
major axis. The size and location of all staves will then be plotted and
a lumber estimate can be made. (For this production the staves were
31c" thick, and cut from =2 spruce.)
When recording the stave widths for later use in cutting the actual
boards, it is better to err towards narrower staves than wider. Staves
which are too wide will not fit snugly against the ellipse and may necessitate starting all over. Contrarily, narrower staves may not quite

total the tub circumference but it is a simple matter to add one more
narrow stave at the "end" of the oval.
The problem of the bevel can also be solved on the drawing board,
although it is simpler and more accurate to do so during construction:
The board method:
Consider the portion of the ellipse covered by a stave to be an arc
of a circle. The same can be thought of the portion covered by the
halves of two adjacent staves. To find the correct bevel angle to
match the two staves, perform the following steps:
1. Using a compass, bisect that portion of the total "arc" covered
by half of each stave (Fig. 2).
2. Extend these bisectors until they intersect locating the center of
the imaginary circle.
3. Draw a "radius" from this center through the point where the
two staves will meet.
4. Draw second and third radii through the center point of each
stave (the ends of the original "arc").
5. Construct tangents to the "arc" at these center points.
6. Measure the angle described by each tangent and the first
radius to find the bevel angle for each respective stave.
The construction method:
1. Hold or clamp the first stave in position against the plywood
base of the tub at the minor axis and mark its width on the
curve.
2. Do the same for the next stave and then remove both staves.
3. Using the jig illustrated (Fig. 3), draw on the plywood base the
"radius" of the imaginary circle through the point where the
two staves meet.
4. Hold the staves in position one at a time (as tangents to the arc)
and record the angle described by the stave and the "radius"
using a bevel set.
5. Set the joiner fence at the angle on the bevel set and bevel the
first stave.
6. Proceed to the first edge of the second stave and bevel it.
7. Install the first stave and mark the positions of staves 2 and 3 as
was done for staves 1 and 2.
8. Continue in this manner around the tub to the major axis.
NOTE: Since the beveled edges will reduce the effective width
of each stave, there will be a continuous shift toward the minor
axis. The consequent discrepancy between adjacent staves is
negligible and will not become cumulative since each stave is

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