Surfaces Of Double Curvature

Surfaces of double curvature (domes, etc.) cannot be developed with complete accuracy, nevertheless the method illustrated in 347 is sufficiently accurate for most practical purposes. Assuming that a hemisphere has to be developed to provide the exact shapes of the constructional ribs and of the covering veneers, first draw the elevation and divide horizontally into any number of zones A, B, C, D, E, F, etc. The outer circumference of the dome is then drawn on plan, and the zones in elevation projected downwards to the corresponding circles on the plan B, C, D, E, and F. The circle on plan is then divided into any number of equal parts 1, 2, 3, 4, 5, etc., and the radii drawn in. To develop any one zone in the elevation, for instance the zone contained within the horizontal lines C and D shaded on the drawing,

ELEVATION

SIDE

ly end yj

CD

346 Developments (1)

draw a straight line CD through C and D from point O to meet the central axis R extended, and with centre R and radii RD and RC describe arcs. These arcs are then plotted off to correspond with the division of the appropriate circles D and C on plan and numbered similarly (the drawing shows part of the development only and 12 divisions will be required to plot the exact circumferential length of the zone).

To plot the shapes of the individual gores or lunes draw verticals from the points of intersection of each individual circle on plan with any two adjacent radii, and where these verticals intersect the horizontal limits of each zone will lie points through which smooth curves will define the gore. The true approximate shape of

347 Developments (2)

the gore can be developed by bisecting one sector on plan 2-3, plotting off the distances from A to F in elevation along the bisecting line 2-3, and with radii equal to the corresponding circles on plan describing arcs through the plotted points. If parallel lines (radiates) to the bisecting line are then produced from the appropriate arcs of the sector to contact the arcs already drawn in the development, the intersections will provide points through which smooth curves can be drawn to yield the outline of the gore. As already mentioned the development can only be approximate because the distances measured off to provide the arcs A, B, C, D, E, Fin the development are in reality chords of the true arcs of each zone, therefore, in cutting veneers for gores, an allowance must be made for trimming in position.

GEOMETRIC DECORATION Volutes and spirals

Classical architecture made considerable use of volutes and spirals as decorative elements. The former conforms to the convolution or twist of the spiral shell of certain molluscs (snails, etc.), and 348:1 gives the method of construction in

347 Developments (2)

348 Volutes and spirals, etc.

348 Volutes and spirals, etc.

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