David,
I think we are approaching something useful now. I looked up in my latest version of the “Arne’s Chain Calculator”. This has mainly dealt with the very large round needed along the battens to get enough bagginess. I have touched the matter of horizontal stretch in the cloth as well, but never quantified it.
Look at the very fresh photo below left. Today I have done some practical “camber measurements” on my garden fence: I fastened two screws at a horizontal distance of 4.9m (= B on Ingeborg). Then I hung a Dyneema line on the one to the left and put a 4.9m mark on it with tape in the right end. Mid between the two screws, I measured up marks, 30, 40 and 50cm down from the horizontal screw-to-screw line. These points represent the 6, 8 and 10% camber. Then I moved the tape mark in an out from the right screw, horizontally, until the line sunk to the 30, 40, and 50cm marks.
The first thing I noted was that it takes very little horizontal movement (slackening) of the line until the bight sinks to 2, 3 and 4% “camber”. For this reason, one needs not bother with slackening the sail along the yard and upper 2-3 battens, where the sail is planned with little camber.
The result of today’s measurement was that it took...
· 5.0 cm (= 1.0% of 4.9m) slack to reach about 30cm or 6% camber,
· 9.5 cm (= 1.9% of 4.9m) slack to reach about 40cm or 8% camber and
· 15cm (= 3.1% of 4.9m) slack to reach about 50cm or 10% camber
Those 9,5cm to get 8% camber coincides well with the 8.7cm I got when measuring the length of the 8% curve in the CAD-drawing, below (there I used a number of 100mm radius circles along the curve to measure it).
Practical use of my findings.
Sooo, theoretically I should shorten the sail of Ingeborg’s dimensions 9.5cm in from the B=4.9m mark on the batten (foreward end). That is a shortening of 1.9% of B. However, with the look of Johanna’s blue sail in mind, with her D-shaped vertical panel curves, I think I would only slacken the sail with 70% of what my measurements above suggests.
Then, to get...
· 6% camber, I would shorten the sail 0.71% of the batten length B along the batten,
· 8% camber, I would shorten the sail 1.4% of B (6.9cm in Ingeborg’s case)
· 10% camber, I would shorten the sail 2.1% of the batten length, B.
One has a choice on what to do about the excess cloth along the battens:
One may leave it as it is, where it will show as wrinkles (less than on Johanna, more like on Frøken Sørensen), or one may shorten the sail the same length by inserting 2-3 tucks along the rounded batten panel edges before assembling the panels.
I think that by using these numbers, the sail will inflate well in light winds and hit quite close to the planned camber. The vertical curve should end up closer to the box section in Frøken Sørensen’s sail than the D-section in Johanna’s sail.
Arne