With a common center at point D the radius of the lower breadth arcs is 7½ ft, which is equal to ½ the beam (DC = DC' = 7½ ft = 1/2 the beam). If a larger radius were chosen the midship section would be fuller, while a smaller radius would result in a finer section. From the maximum beam points the lower breadth arcs (with point D as the center and a radius of 7½ ft) are swung with a compass downwards to points G and G' that lie on the diagonals DB and DB' (Figure 27b). These diagonals, unlike the surmark diagonals, are simply temporary construction lines created as a preliminary step to aid in drawing the midship section (Figure 27a).
A few additional preliminary steps have to be taken before being able to draw the floor arc. First, it is necessary to divide each of the rectangles, ABCD and AB'C'D, on either side of the centerline, AD, in half with the vertical lines HI and H'I'. Note that the distances AH and AH' are equal to 1/4 the total beam and the distance from point H to H' is equal to half the beam (Figure 27c). Next, a parallel line, FF', is drawn 3 inches up from the baseline BB'. This line crosses the centerline AD at point E, thus BF = AE = B'F' = 3 inches (Figure 27c). The line FF' intersects the lines HI and H'I' at points J and J'. The width between JJ' is the same as that between HH', which as was noted above equals ½ the beam. In this particular case this distance is the width of the floor at the midship frame.
Finally, in order to draw the floor arcs, using a compass successively set to various widths one must "discover", through trial and error, points K and K' on the diagonals DB and DB' that will serve as center points for arcs, with a radius of KG = K'G', that will intersect line FF' at points J and J'. There will be only one radius measurement that will allow the drawing of arcs GJ and G'J' (Figure 27d). The center of the floor arc, K, is located on the same line, DG, as the center for the breadth arc, D. Therefore these arcs are tangent where they touch at point G. Only with the center point at K, "discovered" by trial and error, would an arc drawn from point G intersect line IH at point J. This procedure of "discovering" a center point for a tangent arc given another predetermined point off that line is common in French ship design (e.g., Duhamel 1758:209).
To complete the lower midship section, the floor arcs must be joined to the edges of the centerline timbers. Once again, a few preparatory steps are needed. The vertical lines LM and L'M' are drawn 4 inches to either side of the centerline AD (Figure 27e). These lines represent the sides of the centerline timbers—the stem, keel, and sternpost. Then from points L and L' the straight lines LN and L'N' are drawn tangent to the arcs GJ and G'J' (Figure 27e). Since the floor arcs are joined to points L and L' with tangent lines, on the actual frame contour these arcs only extend to points N and N', which are slightly higher up on the arcs than the points J and J' (Figure 27e). NEXT
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