The required rig parameters are as shown in the following diagram. (Note that the spreaders are ignored in these calculations, and that the spreadsheet assumes the mast is vertical. As far as I can see, none of these simplifications has a significant effect.) Importantly, the spreadsheet also assumes that the jib boom is always set close up against the mast. That is, if the pivot offset changes, the jib boom is moved so that the clew just brushes past the mast. Otherwise, a considerable gap can open up between jib and mast, with consequences for rig tensions that the spreadsheet does not handle.
The spreadsheet calculates the angles made by the backstay, the shrouds, and the jibstay. It takes the tensions specified in the backstay and the shrouds, resolves them into vertical and horizontal components, and then calculates the resulting tension "felt" by the jib. For the IOM, this tension is taken in part by the jibstay, and in part by the topping lift, in proportion to the size of the jib pivot offset along the boom. Finally, it calculates the total mast compression load.
It is interesting to play with the spreadsheet to see what makes a difference, and what doesn't seem to matter much. The spreadsheet has macros which populate rows of data for the graphs. One graph shows the jibstay and topping lift tensions versus the pivot offset for a default wind speed (called the "Pivot" macro), and another graph shows these tensions versus wind speed for a default pivot offset (called the "Wind" macro). The example graphs were calculated for a backstay tension of 3.5 lb, shroud offset of 20 mm, and a shroud tension of 8 lb. The pivot offset graph assumes the boat is sailing in 14.5 ft/s wind speed, while the wind speed graph assumes a pivot offset of 72.5 mm. Notice that the graphs illustrate the dynamic rig tensions calculated in the second part of the spreadsheet and described on the jib luff sag page. In the "Tensions vs wind speed" graph, it is interesting to see how the jibstay tension rises with the wind, and of course how the topping lift tension decreases.(1) The shroud height doesn't affect the jibstay tension much. What happens is that, as the shroud height -- ie the attachment point of the shrouds on the mast -- varies, so does the angle the shrouds make. Lower height, greater angle, and so about the same amount of shroud tension is transmitted to the jibstay, regardless. Interesting and unexpected. (Please remember that this is one of those "other things being equal" ideas. In fact, mast stiffness comes into play if we vary shroud height greatly. The principle is only accurate for modest changes in shroud height, say somewhere between the hounds and no more than about 400 mm below the hounds.)
(2) The amount of shroud tension transmitted to the jib is pretty much dependent upon the shroud offset -- the distance between the chainplate (shroud attachment point at the gunwale or inwale) and the mast step. As the offset increases, increasing shroud tension is applied to the jibstay and topping lift. The spreadsheet estimates the lost ability of the main boom to set square on the run with significant aft chainplate offset. On a hull with 280 mm beam, a chainplate offset of 50 mm will bring the main boom to rest at an angle of about 70 degrees rather than 90 degrees. This is not very significant provided you are careful to gybe as needed to keep the main at the right angle to the wind. If you do not take such care, then this is significant and you will notice the loss of drive as the others come past you on the run.
(3) I was interested to see how much the jibstay tension rises dynamically. Although its static value is a modest 5.3 lb, it rises quite dramatically to around 11 lb when the wind speed is 14 or 15 ft/sec.
(4) Rather than backstay tension, it seems that varying the shroud tension and the shroud offset could be the major way of changing jibstay tension. An 11.1 mm mast can't take more than about 1.5 lb backstay tension if it is not pre-bent (and can take about 3.5 with pre-bend). This tension contributes about 2.1 lb (4.8) to the jibstay tension, assuming a 75 mm pivot offset. Putting, say, 8 lb tension into the shrouds and having a shroud offset of 50 mm, causes the jibstay tension to rise to about 4.4 lb (7.1), a very significant increase. So having juggled the backstay tension to set the required mast bend, the shroud tension can now control jibstay sag quite adequately.
This is good news for skippers who don't like using mast pre-bend; it is also good news for skippers who use mast pre-bend but would like to do without it. The bad news is that you'll have to handle much higher mast compression loads, as below.
(5) The pivot offset determines how much of the general jib tension feeds into the topping lift specifically. It is the topping lift which maintains the twist in the jib, and it would be very useful to be able to keep the jib shape until a certain point, after which you want the jib to twist off in a gust. The spreadsheet plots a graph of topping lift tension versus pivot offset, allowing you to determine what pivot offset gives you what topping lift tension for a given set of shroud and backstay tensions and shroud offsets. This is explored in more detail in the third Web page.
(6) I was surprised to see that the jibstay tension stays the same, more or less regardless of pivot offset. The graph shows an essentially horizontal line for jibstay tension at a given wind speed no matter what the pivot offset. This makes life a whole lot easier -- the pivot offset only changes the topping lift tension, leaving the jibstay tension wherever you want it, having set it with your shroud and backstay tensions and shroud offset.
To use the spreadsheet, start with the "Tensions" worksheet and enter the number of the rig you want to play with: 1=A rig, 2=B rig, and 3=C rig. The spreadsheet then looks up the various default rig parameters from a table, such as backstay height, boom length, and so on. The three major parameters you set in the spreadsheet are the backstay tension, the shroud tension, and the shroud (chainplate) offset. From these, the spreadsheet calculates the static tensions. If you want to change any of the default rig parameters, go ahead.
So far, these ideas mean(1) A highly adjustable pivot offset, with concomitant adjustable sheet attachment points on the boom and sheet reeving points on deck to maintain the required jib sheeting radius, and adjustable deck attachment point for the pivot.
(2) Adjustable chainplate offsets.
(3) Reinforced hull, around the mast step and around the chainplates, to accommodate the considerably increased compression load. The spreadsheet calculates the mast compression. For the sorts of figures we've been using, it comes out at between 30 lb and 45 lb! That is pretty high! This calculation is useful if you are thinking of getting serious about your shroud tension, and using these tensions to control jibstay sag while keeping a relatively light backstay.
(4) More care needed when you set your correct gybe on the run.
The static tension calculations are straightforward applications of trigonometry upon the rig geometry. The shroud tension that feeds in to the jibstay is adjusted for the hull beam. It doesn't make that much difference, but more accurately models what happens.
©2011 Lester Gilbert