The first idea is to have the Cunningham line running through two reeving points, either side of the mast at the level of the boom.
The second, simplest idea, is to have a single the line running through just one reeving point *on the mast*. Note that the spreadsheet does *not* model the situation where the reeving point is on the *boom*. Maybe in version 3...
In both cases, the interesting question is what happens when we change, amongst other things, the distance between the reeving points and the gooseneck pivot axis.
I've now developed a second spreadsheet (version 2.1, around 61 kb) to estimate the amount of easing. This version goes a little further than the previous version, since it now also models what happens to the Cunningham (or downhaul) line from the tack of the mainsail to the reeving point on the mast. In this sense, it models the complete run of the line, and not just the part that runs between the boom and the mast.
The spreadsheet makes some simplifying assumptions. One is that the tack point is the same offset distance from the mast as the reeving point; this is fine for 'normal' situations. Two is that the wrap around the mast of the line, illustrated by the green thick line in the above diagrams, can be approximated by the hypotenuse of two triangles; that is, I've not modelled the wrap as a helix, although the second page of the spreadsheet gives you the relevant formulae if you'd like to do that. Three is that the reeving points are in the same horizontal plane as the gather point on the boom.
But most importantly, fourthly, the spreadsheet assumes that the tack rotates around the mast in synchrony with the boom. This means that, if the spreadsheet shows the Cunningham line with, say, zero release or ease, that's fine -- it means the tack has just enough line which allows it, in theory, to rotate as needed.
The following graph illustrates the situation with a 11 mm dia mast, a gooseneck whose pivot is 5 mm aft of the mast (hence giving a 10.5 mm pivot offset), reeving points which are just 1 mm proud of the mast (hence 6.5 mm reeve point offset), a tack which is 15 mm above the reeving points, and a gather point 20 mm aft of the gooseneck pivot.
You can see that the downhaul line eases substantially, somewhere between 2 mm and 15 mm when the boom is right over at 90 degrees, depending upon the reeving point angle (how the points are arranged around the mast).
The special case when the reeving point angle is 0, is illustrated by the second graph. This graph shows what happens when the gather point is positioned closer to the gooseneck pivot point.
You can see that the line eases very slightly (around 0.8 mm), and this might be an ideal outcome -- this means that the tack has just enough line to rotate with the boom, but not so much that the line is flapping around too loose and allowing the luff to creep up the mast and belly out in a blow...
©2011 Lester Gilbert