Then, given the amount by which the jibstay has stretched, the worksheet calculates how much the aft end of the boom has lifted, and calculates the dynamic twist in the middle of the jib. The aft end of the jib boom only lifts when the jib forces overcome the topping lift tension, so the spreadsheet suppresses any movement of the boom until the topping lift tension reaches zero. In reality, as very small values of the topping lift tension are reached, the jib boom will move and the jib will twist off, so it isn't the "on/off" "light switch" that the spreadsheet supposes.
The various cells of the spreadsheet illustrated calculate a linear interpolation of the estimated twist, given upper and lower boundary estimates by lookup of the table in the worksheet.
In calculating the new twist of the jib, the spreadsheet notes that the sag of the jibstay has the effect of lessening twist. That is, the jibstay sag "moves" the jib luff to leeward, decreasing twist. The amount of this movement is deducted from the leech gap, and the new twist estimated.
The example illustrated shows the jibstay sag to have moved the jib luff about 8.17 mm to leeward, and the new twist in the middle of the jib is about 7.6 degrees, having started at about 9.95 degrees in the static condition.
The "JS sag" worksheet provides a button (labelled "Leech twist") to activate the macro which populates cells to show the leech twist as a function of wind speed. The following graph shows the jib twist for a pivot offset of 72.5 mm in No.1 rig, with backstay and shroud settings as previously. The graph illustrates that the topping lift "releases" at a wind speed of around 16 ft/s, and that thereafter the jib twist climbs -- the leech has bagged out. Note that the calculations are for the middle of the jib, so the head of the jib has twisted off even more, probably about 30% or 40% more. But note that, before the leech bagged out, the jib twist was systematically reducing as the jibstay sagged, down from around 10 degrees to around 7.5 degrees. Hmmm...
The second graph shows the cumulative effect of increasing jib draft and decreasing leech twist upon the entry angle of the jib. It estimates that, at very low wind speeds, the entry angle of the jib was about 26 degrees, being made up of about 16 degrees due to jib draft, and 10 degrees due to jib twist. Remember we are talking about the middle of the jib here. Then, at a wind speed of about 14 or 15 ft/sec -- top of A rig -- total entry angle is around 36 degrees, made up of about 30 degrees due to increased jib draft and 7 degrees of decreased jib twist.
The major use of the spreadsheet is to experiment with various tensions and pivot offsets, so as to retain the required jibstay sag while setting the point at which the topping lift will release and allow the jib leech to bag out in the gusts.
All of the graphs can be calculated at once by using the "Do all" button located on the "Tensions" worksheet, just below the rig parameters box. The spreadsheet is most effectively used by setting the various rig parameters as needed, and then clicking the "Do all" button to see the results. Good luck!
The remaining spreadsheet calculations take the estimated jibstay sag and topping lift "lift" and calculate the new draft in the jib and the new twist in the leech. The spreadsheet macros for sag and twist carry out some calculations which are not carried out on the spreadsheet by itself, because of the recursive nature of these calculations.
What happens is that, because of jibstay sag, jib draft and twist will change. The amount of change depends upon the draft and twist in the first place, since the change is in fact a function of the total entry angle (entry due to draft, plus more angle due to twist). The spreadsheet simply can't handle this by itself. The macros handle it by cheating a little -- they use the total entry angle from the previous windspeed. So when calculating draft change at a wind speed of, say, 10 ft/sec, the macro peeks at the total entry angle currently seen in the jib for a wind speed of 9, and uses the SIN and COS of that to decide what the new draft and twist will be, after allowing for the luff allowance cut into the jib originally.
The draft calculations are done on the "JS Draft" worksheet. The innovation here is to divide the sail section into two parts, and to use an arc of a circle of one radius to model the forward part of the sail section, and an arc of a circle of a different radius to model the aft part of the sail section. The model is approximate, and it turns out that the spreadsheet cannot get the two arcs to "join up" perfectly at the point of maximum draft. The error, though, is quite small, in the region of 2% or 3%. Nevertheless, the result is that a better approximation is made of how the shape of the sail changes as draft is pushed into it due to jibstay sag. More importantly, the spreadsheet does not model the changing position of maximum draft, but assumes that this position stays constant as the jibstay sags. This is of course unrealistic.
In modelling the twist, the spreadsheet assumes that the twist is reduced because of jibstay sag, and calculates this effect by reducing the gap between the leech and the topping lift vertical reference line by the amount of the SIN of the total entry angle. So the "Twist" worksheet has two tables for modelling twist, the top table without jibstay sag accounted for, the bottom table with.
©2011 Lester Gilbert