geometric CLR and relate this empirically to the sail plan. This is the standard rule of thumb used for centuries and there is considerable experience available.
Centre of effort of the When the wind is at 90° angle of attack to a sail the flow behind it is sails completely separated. The centre of effort (or CE, as it is normally denoted) is then at the geometric centre of gravity of the sail. This is what happens on a run. For other courses the angle of attack is usually considerably smaller and the CE further forward. As pointed out above, this centre is at the 25% chord for a plane wing of large aspect ratio. Now, the sail is not a plane, so even if it works ,like a wing at smaller angles of attack, the CE will not normally be located that far forward.
Fig 8.3 shows how the CE moves with the angle of attack for different sail cambers. This is for a sail of aspect ratio 5.0. It may be seen that the flattest sail with a camber ratio of 1/27 has its CE at about 30% of the chord at small angles, while this point has moved back to 37% for the full sail with the camber 1/7. A practical implication of this is the change in balance caused by changing from a flat to a full sail. More weather helm will be required for the latter.
Fig 8.3 Centre of effort for sails at varying angles of attack (Marchaj)
10 20 30 40 50 60 70 80 90 100
Angle of incidence a [deg]
Distance from leading edge In % of chord
Another implication of Fig 8.3 is that there is normally a considerable distance between the geometric CE (corresponding to 50% of the chord) and the aerodynamic CE. In principle, it should be possible to determine a centre of the total sail plan based on, for example, 35% of the chord, but this approach is not normally used. Instead, only the geometric centre is employed. Fig 8.4 shows how this is found for a sloop rig. The centre for each sail is found first, as the intersection between straight lines from two corners to the mid-point of the opposite side. The fore and main triangles are used in this method. Having found the individual centres they are connected by a straight
Fig 8.4 Definition of lead
line, and the total CE is obtained as a point on the line, located as shown in the figure. If the yacht has a mizzen, only 50% of its area should be counted (cf the rudder efficiency above). The common centre for the main and jib then has to be found as shown in the figure, and then the main plus jib area at this point is combined with the rcduccd mizzen area at the mizzen CE. in the same way.
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