# THE 21 st CHESAPEAKE SAILING YACHT SYMPOSIUM ANNAPOLIS, MARYLAND, MARCH 2013

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4 Figure 3 Modified Balance Geometry, #2 Genoa, 100%. Figure 3, based on the same boat and sail plan as Figure 2, proposes a geometric method for doing this. First, it requires that the generic foretriangle be abandoned, and that the actual proposed headsails be worked with instead. On the drawing, indicate a given sail's sheet and where it meets the deck (the sheet position). (Authorities vary as to the exact angle the sheet should travel from the sail. Some say to bisect the angle at the clew, others to split the difference between this bisector and the line from the sail's CEg to the clew, still others say to start at a point on the luff 40% of the hoist up from the tack and draw a line from that to the clew, the extension of which is the sheet. The right answer for a given sail is generally somewhere in between these variations, which will more closely coincide with higher clews and lower aspect ratios.) Once the sheeting position is located, draw a triangle the corners of which are the head and tack of the sail and the sheet position (ignoring the clew). Find the geometric center of this triangle in the normal fashion. This now becomes that sail's CEg, which will more closely approximate its actual influence on the boat. When coupling this sail with the rest of the sail plan (main, etc.) to establish the overall CEg, continue to use the sail's actual area, but with this modified position of its center of effort.

5 APPLICATION TO EXISTING VESSELS Figures 5 represents a fairly close approximation of the arrangements described in the anecdotes above. In this arrangement, the helm stayed slightly lee until about 18 knots of wind, above which it went weather. What becomes apparent is that this sailing vessel example, which showed a traditionally derived lead of 18%, now, with its #1 genoa, and accounting for the inclusion of the sheet's influence on the boat, shows a lead in Figure 4 of 14.3%. If the same modified process is applied to Figure 5, with the smaller headsail, then a lead of 14.9% is arrived at as shown. This is contrary to the virtually unchanged lead when using only the sails themselves to determine the lead. Figure 4 Sail Plan of the boat described in the anecdotal example, in this case with her #1 genoa.

6 Figure 5 Modified Balance Geometry, small working Jib It is perhaps now becoming apparent as to why, in the experiences described above, the smaller headsail induced a lee helm. Simply put, the sheet position for the smaller headsail was too far forward, creating a balance lead that differed significantly and detrimentally from that derived from the genoa. The correction for this vessel then, if it is assumed that the balance was correct for the genoa (i.e., the full sail plan), is that any smaller headsails should have profiles which, with their sheet positions included, would generate a similar or lesser lead. In this case, this would be accomplished by reshaping the smaller headsails with higher clews in order to move their sheet positions aft. Figure 6 shows how this might take shape, in that a small working jib of an area similar to the small jib in Figure 5 is reshaped with a higher clew so as to move the sheet position aft significantly. The resulting balance lead is 12.6%, less than the genoa's 14.3%, resulting in a reduced sail plan that continues to maintain acceptable balance, such that, while the helm still stays lee in light air, it becomes weather at a more useful lower wind speed of about 14 knots, or about when you'd want to reduce sail.

7 Figure 6 Reshaped small working jib to correct lead and helm. As a further illustration of how this approach might be applied to correcting an existing boat's performance, let's look at the case of a 31' fractionally rigged racer-cruiser whose weather helm with her 160+% genoa was annoyingly excessive. The clew of this sail was not particularly high, but high enough to put the sheet position quite far aft, at about the.8lod position. The owner of the boat, however, was particularly enamored of this sail, most likely due to the magnitude of the financial investment therein. After being the last boat at the windward mark with discouraging consistency, the crew rebelled, and insisted that the #2 jib be tried next time out. Next race (wind about 10kt), first to the mark, first to the finish line! In addition to quicker, more efficient tacking, this 110%, fairly low clewed, full hoist sail put its sheet position quite a bit farther forward at about the.5lod position. Applying the modified geometry described above, this sail increased the boat's balance lead and lessened the weather helm significantly. The foot came off the brake and the boat was allowed to sail as intended. Of course, lessening the heel helped as well, while still keeping plenty of power. The big genoa was still useful as an off-the-wind sail, so the owner was not entirely bereft. But the #2 became his #1 windward sail.

9 Figure 8 Cal 40, full main, #2 jib, moderate air, showing the Leads.

10 Figure 9 Determining the Lead dimension and the Transverse Offset dimension of the sail plan shown in Figure 8. The concept of solving for rudder angle to determine the final balance condition will require that the two competing balancing moments, Lead (Falling Off) and Luffing (Rounding Up), which can also be thought of as torques, be determined beforehand. First, for the arm components of these moments, the positions of the CEg and the CLRg relative to each other must be determined both horizontally and vertically, including accounting for the heel of the boat. Referring to Figures 8 & 9, the fore and aft Lead dimension between CEg and CLRg is shown in the normal fashion on Figure 8 and on the plan view of Figure 9. Also required is the total transverse offset of the sail plan, or the distance that the CEg is moved laterally off of the centerline due to both the camber/sheeting offset and the angle of heel. The range of these offsets, and the force components of the two moments in question will then be determined by the... S/V BEHAVIOR PREDICTION (S/VBP) TOOL With a few additional assumptions, sufficient and proper information is now available to utilize Figure 11 below, the S/V Behavior Prediction Tool spreadsheet, developed by the author for this paper. A typical condition calculated for is shown in Figures 8 and 9 above, and demonstrates the derivation of certain of the pre-entries required prior to final calculation, such as the lead dimension, the vertical distance between CLRg and CEg (VDC), and the initial camber offset sheeted closehauled. Additional foundation information required includes displacement, metacentric height (GM) derived from previously established stability information, sail area, beam, and main foot length (E). Also required will be rudder area and rudder arm, taken from the rudder's CEd to the CLRg. A plot of various curves, an example of which is shown below in Figure 12, will be created based on the output of these calculations. These curves will be plotted against a range of true wind speeds at a given apparent wind angle, in this case 30º. The assumptions for the specific Figure 11 calculation are a) apparent wind is 30º; b) AR-related lift and drag

12 pressure at the given AWS times the heeled SA times the heeled VDC is essentially the same as the HM = HM0º x Cos² This construct is presently under review (Johnson, et al, 2013), especially for higher heel angles (>GZ max ). This S/VBP tool may need to be modified accordingly as this research progresses. Second, that this sail plan has been calculated up through winds much stronger than would normally be carried by this plan, as shown in the graph in Figure 12. A by-product of this S/VBP Tool may then in the future be the ability to also predict behavior when the boat is in extremis, not only in terms of both heel and helm response, but also downflooding. However, since neither lines nor stability information are available in this case, the effects of heel angles beyond GZ max have not yet been incorporated into the S/VBP Tool. GM in this case has been parametrically estimated. Figure 10 Performance data for the Cal 40 sailing to windward, assuming 30º apparent wind. Figure 10a Performance data obtained from showing estimated adjustments for 50% ± reduced sail, and sailing with 45 degrees of apparent wind.

13 Figure 11 - Construction of the Rounding Up (Fig. A) and Falling Off (Fig. B) Moments (Torques), in addition to the calculations to determine her Residual Steering Moment, and, finally, the rudder angle needed to hold a steady course. See also the Appendix for additional Rounding Up & Falling Off Moment/Torque constructions for other upwind points of sail.

14 Figure 12 Graphic Results derived from the S/VBP calculation procedures in Figure 11, Sail Plan #1, the reference plan. Figure 13 shows the Cal 40's S/VBP curves with her genoa. Applying the modified balance geometry shown above and the balance/helm calculations now results in very light to moderate weather helm up to about 10 knots of wind, becoming heavier to handle in the knot range, as one would expect for full sail. Experience has taught that weather helm in light air is generally very minimal, and occasionally becomes a tolerable lee helm. This condition is confirmed here. In extremis situations also now become more apparent. Figure 13 S/VBP results, Sail Plan #2, Full Sail.

15 As the wind freshens, shortened sail configurations at 45º apparent wind are shown in Figures 14 and 15. It is interesting to compare these two configurations, as they have somewhat similar sail areas, but Figure 14, Plan #6, is showing a double reefed main with a working jib, while Figure 15, Plan #8, has a single-reefed main with a storm jib. Their balance leads are 3.34' (11%) and 0.04' (0%) respectively, a significant difference. As might be expected, the weather helm for Plan #8 starts to get heavy fairly early at around knots of wind. Plan #6, on the other hand, is keeping a reasonable helm until about knots of wind, which most would consider preferable in these conditions, even at the expense of a lee helm at winds less than 12 knots. Figure 14 S/VBP results, Sail Plan #6, double-reefed main & working jib. Figure 15 S/VBP results, Sail Plan #8, single-reefed main & storm jib.

17 higher to begin with, with their commensurate well-aft sheeting positions. A common sight, especially on bareboats in the Caribbean Christmas winds, is for those sailors, perhaps a bit spooked by handling a strange boat in those hefty winds, to simply roll out the genoa and sail under that alone. Yes, sail has been reduced, and the boat is more or less in control. The quality of seamanship thus displayed is perhaps best left for another discussion, although one aspect does stand out they seem to be sailing in reasonably good balance (and which they seem to like to brag about at the bar at the end of the day). Figures 18 and 19 may provide some insight as to why this can happen. This is the Cal 40 again, this time rigged for cruising with a typical big roller-furling genoa, sailing to windward (30º apparent wind) in "bareboat" mode. Applying the modified lead approach, it can be seen that, in normal Christmas winds, her helm becomes weather at a little over 14 knots of wind. This is one case where extra heel may work to advantage to a point! In stronger Christmas winds, weather helm can actually become a handful at about 24 knots of wind. Light air, lee helm as would be expected. And at broader apparent wind angles starting at about 45º, the helm becomes weather even in light winds. Figure 18 Cal 40 rigged for cruising, sailing with genoa only. S/VBP results: Figure 19 S/VBP curves for the Cal 40 sailing in "Bareboat Mode."

19 Skene, N., "Elements of Yacht Design," Sheridan House, Dobbs Ferry, NY, website, "Swedish Sailing and Racing," APPENDIX:

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