Theatre Design & Technology - Spring 1981 - 33

marked and cut in order. If need be, an additional stave can be
cut to fill the final space at the tight end of the ellipse. Also note
that if the curve is a regular ellipse, one stave in each quadrant
can be beveled using the same selling thus saving considerable
measuring and set-up time.

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The required taper of each stave can be determined before construction by mathematical or drafting methods. The drafting system is
the simpler of the two.
The drafting method:
1. Draw an elevation of the tub in a large scale (1" or 1 Y,"
1'0") showing the sloping sides.
2. Project this shape into a plan view.
3. Using steps 1 through 3 in the board method of determining
bevel angles (above), draw a radius through the edge of each
stave at the base of the tub and continuing through the arc representing the top of the stave.
4. Project this information into an auxilary view in order to determine the true shape of the stave.
5. Using the protractor, measure the angle of taper between the
sides of the stave and use this angle to layout each stave.
The mathematical method:
This method uses basic trigonometry and requires that the portion
of the ellipse covered by each stave be considered as an arc of a
circle of known diameter. Also required are known height for the tub
and a known angle of slope for the sides.
First, plot the imaginary circle for each stave as previously described and measure the number of degrees included by each stave.
An angle of 6° would mean that sixty staves of that size would be necessary to build a circular tub of that diameter (360° + 6° = 60).
All other measurements can then be calculated by using trigonometric functions. Consider the following example:
Let:
n
r
2r
h
s
t
2t
I
2x
2y
a

= number of staves
= bollom radius
= bollom diameter
= height of tub
= slope angle
= top radius
= top diameter
= length of stave
= bollom stave width
= top stave width
= taper angle

then,

. (3600)
y = t'SIn
~

I

~----~
\'

= 60
2r = 2'-0"
h = 3'-0"

s = 10°

R

0

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.~d':'UE

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STAVE

n

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In specific, if it is given that:

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-2t~

I

2t = 2r + 2 (h . tan (s))
1= h
cos (s)
. (3600)
x = r' Sin
~

..CD

@

Then,
2t
1
2x
2y
a

=

3.058' or 3'-"/, 6"

= 3.046' or 3'-'%2"
= .105' or 1

v. "

= .16' or 1 2%2"
= .517° or about y,0

The bevel angle can be approximated by using 360° /2n. The
actual bevel will be slightly less due to the 10° slope but the
amount of error is insignificant for this project. This trigonometric method becomes cumbersome since the same sequence of
calculations is required for each stave in a quadrant.
Whichever method is used, select clear, straight wood which can
be cut accurately. The smallest error will be multiplied by the total
number of staves so it is important to set saws and CUlling jigs very
carefully.
At this point all that remains is the final assembly. With all staves

temporarily in place, locate the position of the metal hoops and measure the circumference of the tub at that point on the slope. Cut the
steel bands approximately 1" short to allow for compression of the
wood as the bands are tightened. Weld on or attach the appropriate
fittings and remove any burrs (Fig. 4). Drill several small holes in the
band on about 2'-0" centers. After the bands are installed, drive small
nails or screws through these holes to prevent the bands from slipping
down the slope of the sides.
(Because of the 10° taper of the sides, the metal bands will bite
into the wood at the top, but this is not a problem structurally or esthetically. True barrel st9ves, of course, would be dadoed to retain the
base, but soft spruce does not have the strength for an across-grain
dado near the end of the board the way oak barrel staves do. The remaining shoulder of wood would shear off under the stress of two actors jumping and falling on the tub floor, or it would break through the
rigors of touring. Also, by placing the plywood tub directly on the
stage floor, the shock is transmitted directly to the floor.)
Apply glue to all joints. Install the steel bands and tighten them until
they begin to compress the wood. Insert the retaining screws or nails.
Thoroughly wipe off any excess glue with a damp cloth or paper
towel. The staves are fastened to the base with 6d nails and white
glue.
When the glue has dried, trim the stave tops to shape. Sand the top
edges and all bevel joints to remove traces of glue. Stain the wood as
needed and touch up screw heads and bright metal with flat black
paint. The result should be an allractive and very durable property.
This principle can be applied to wooden buckets and other round
units and may be used to custom design and construct your own hot
tub. However, use cypress, teak, redwood, or pressure treated lumber instead of pine. Select clear 2" stock to withstand the water pressure and the live loads exerted on the tub. Tongue and groove the
floor planks before clamping them together to cut out the floor shape.
Carefully cut all staves and clamp them together for a test fit. When
every thing is right, disassemble and cut spline joints for all the
staves. (Tongue and groove joints are not practical due to the wood
lost during shaping and the consequent change in the stave size.) Fit
the splines and reassemble. Do not use glue. The wet wood will swell
and seal small ieaks between staves. Also the bands can be tightened
at the base to help seal leaks there. 0

Elbin L. Cleveland is an associate professor and technical director in the Department of Theatre and Speech, University of South Carolina.
Table of Contents for the Digital Edition of Theatre Design & Technology - Spring 1981
