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Posted by: Girly Brains on 2010-08-21, 07:41:18
There are fairly precise calculations for determining sail plans (as well as the sail areas in the first place). You establish the 'common centre of effort' (C of E) of the entire plan and relate this to the 'centre of lateral resistance' (CLR) of the hull. The distance between the two is called the 'lead' of the vessel and is expressed as a percentage of the waterline length. Among other aspects, it is crucial in determining the extent of 'lee' or 'weather' helm of the vessel. A rough guide is: Lead: (12 - 16)% for sloops; (8 - 11)% for yawls, and (5 - 7)% for schooners (etc). Use straightforward formula for calculating the areas of the sail shapes (triangles, trapezoids etc) and geometry for finding their centres of effort a well as the common centre of them all together (common centre of effort). Draw a vertical line through this centre. Use Simpson's rule for calculating the area of the underwater profile of the vessel and moments calculations for its centre of effort. Draw a vertical line through this centre. The distance between the two, as a percentage of the waterline length is the 'lead'. But for a model ..... ? ..... trial and error based on what looks right, using intuitive design and 'nice' judgement would be sufficient I should have guessed. And if it is a working (sailing) model, as opposed to just display, then use very basic materials and 'test' rigs first, to obtain the desired shapes and areas, and positions of masts etc. before proceeding to the finish quality. (If I can find a good link to a diagram of these geometric procedures I will edit it in). __________________ Edit: This site is reasonable. But they have not shown the geometry! ! And you can see the lead - the small distance between these two points, in the lower diagram. myrc.org/ Library/ centeref.htm But anyway, see the diagram for C of E. Find 'C.E. Main' ('centroid'): draw line from tack to bisect leach. Draw line from clew to bisect luff. Find C. E. Main at intersection (and so on, for others). Find "Combined C.E " or Common centre of effort (C of E): Calculate areas of jib and main. Find position of centroid of each sail. (As above): 'Jib C of E' and 'Main C of E'. Connect the two points. Extend lines at right angles to this line at each centroid. Upwards at one end of it, downwards at the other. (The bit the diagram noted, doesn't show). Plot TO SCALE in linear units the areas of main and fore along resulting lines RELATIVE TO OPPOSITE SAILS to find points A and B. Connect the two points. Find common C of E at intersection of A - B with 'Jib C of E' - 'Main C of E'. (Shown as 'Combined CE' on the diagram). [For plans with multiple sail arrangements, find each of these 'combined' centres and perform a moments calculation to find the common C of E for the whole plan.] ________________________ If it were me, for a model, I would make card or thin plywood patterns of the total sail plan (one pattern) and the hull's profile (another pattern). Then find the vertical centres by balancing each in turn on a blunt edge such as a ruler, held in a vice. Draw these positions onto the patterns, place them (5 - 7)% of the profile's waterline length apart and 'presto!' |
