We may consider the buoy, shown in Fig. 301, as being constructed of a cone and a hemisphere. It will be seen from the position of the joints that the girth of the buoy is divided up into six plates.
Four patterns will be required, and these are all shown set out in Fig. 302. The patterns for the conical part will be laid out as explained in the earlier chapters; the radii for the bottom tier of plates being c b and c d, and for the top tier c d and c e. The arc B F on the large plate will equal in length the arc b f, this being one-twelfth the circumference of the cone base. The length of the arcs, marked D D, at the small end of the large pattern, and the large end of the small pattern, should be the same length; or, if the thickness be taken into account (which it always should), the arc D D on the small pattern - seeing this plate is one of the inner tier - will be the thickness of the plate less in length than on the large pattern. Two corners on each of these plates will need thinning, and, of course, the rivet-holes can be put in before the plates are rolled.
The hemisphere is made up in seven pieces: six sectors and a circular centre plate. First let us mark out the shape of plate for one of the gores, or sectors. A quarter-circle, b o a, is drawn, and the lines o f, o s set along to make angles of 30° with o b and o a respectively; the arc b s will then give one-sixth the circumference of the hemisphere. Next draw L k square to o f, and, using L as centre, run around the arc k M. Now lay down the line L B in any convenient position, and draw B P square to it, and equal in length to the arc f b; then run down P N parallel to B L, cutting the arc k M in N. Next mark B M equal to B N. The points F, S, and T are then determined by making B F equal to the chord b f, F S equal in length to the arc f s, and S T equal to s t; the latter line being drawn square to o s. Using T as centre, and T S as radius, an arc is now drawn through S and cut off equal in length, on each side of S, to the arc g h; that is, S H equals g h. The point g, it will be noticed, is determined by dropping a perpendicular from s on to the line o b. The line f r is next drawn square to o b, and the arc r q run around. Now, using L as centre and L F as radius, the arc R R is drawn, the lengths F R on each side being measured off equal in length to the arc, r q. Choosing a suitable radius (one that will give an arc to pass through the points H, R, M) the side curves are now drawn. Allowances for laps are afterwards added as shown.
In work of this character, where the operator has had little experience, it is always best to experiment on a model pattern, this being marked out for a similar article drawn to a small scale. Such a pattern is shown marked out at the bottom of Fig. 304. The model pattern can be cut out of sheet iron or other metal, and before working into shape, its surface should be firmly marked with crossed lines, as shown, these being 1/8 in. or 1/4 in. apart. When this pattern has been worked up to the proper curvature, it can then be examined, and by measuring between the lines on its surface it can be ascertained which part has been extended or contracted. If it does not work up to the exact size required, then, by careful examination and measurement, the deficiency can be determined, and this allowed for when striking out the pattern for the full-size articles.
The dimension of disc for the spherical segment will be found by using a u as the radius to mark it out.
By the exercise of some thought and careful experiment the pattern for any other kind of gore for an egg-ended boiler, still, or other vessel can be struck out with a good degree of approximation.