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

© 2014 TARAS PEVNY

REF: tangencypress.com/essay/1/page/19

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