Most of the volutes I have drawn in the accompanying plates have been set out in the form described by Gibbs.19 This is a comparatively easy method to set out, but produces somewhat abrupt changes of curvature at the junctions between adjacent arcs.
The method recommended by Chambers20 gives a smoother curve and a more regular diminution of the width of the fillet. (Indeed, Chambers castigates Gibbs for the treatment of the fillet in his method, which involves short straight lines joining some of the component curves.)
However, Gibbs and Chambers agree that the breadth of the curved fillet should be one sixteenth of the total height of the volute.
To set out the volute proceed as follows:
1. Draw a vertical line FCB, F being the crown of the volute where it touches the abacus tangentially, C the centre and B the lowest limit of the eye. FC is 0.225 in length and CB 0.025.
2. With centre C and radius CB draw the circular eye (0.05 in diameter). Point A is the uppermost limit of the eye, where its circle intersects FC. Draw the horizontal diameter DCE.
3. Bisect the vertical radii CA, CB to give points i and 4.
4. With side 1,4 construct a square 1,2,3,4. Side 2,3 is bisected by point E. Draw oblique lines C2, C3 .
5. Divide side 1,4 of the square into six equal parts, numbering the points thus established in the following sequence: i, 5, 6, C, 12, 8, 4.
6. Draw horizontal lines through these numbered points to cut oblique lines C2, C3 at further numbered points 6, 10, ii and 7. This arrangement is shown clearly in enlarged figure (a). A complete sequence of numbered points from i to i2 has now been established.
7. With centre i, radius iF draw the quadrant of a circle to intersect line i,2 produced at G.
8. With centre 2, radius 2G draw the quadrant of a circle to intersect line 2,3 produced at H.
9. Continue in this manner drawing quadrants centred on the numbered points in sequence, each quadrant in turn determining the radius of the next, finishing with a quadrant centre i2, radius i2R, which merges with the eye at A.
The volute thus produced changes its radius at every 90° of rotation, giving a smooth enough curve for practical purposes.
In order to produce the inner edge of the fillet similarly curved and steadily diminishing in width, the process is repeated using a second, slightly offset series of numbered points:
10. As shown in figure (b), draw CF horizontally, measured from the main drawing, and draw VF vertically, equal in length to C i. Join VC.
11. Draw FS equal to the greatest desired width of the fillet. Draw a line vertically from S cutting VC at T.
12. Take the length ST as equivalent to C1 to construct on line FB a slightly smaller square in the same manner as before, to establish the twelve numbered points for drawing the diminishing quadrants forming the fillet. The radii for this second series of quadrants are shown on the main drawing in broken line.
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