Trans RINA, Vol 152, Part B1, Intl J Small Craft Tech, 2010 Jan-Jun


the effect of fractionality, mainsail roach and jib overlap on the aerodynamic characteristics were investigated and modelled by response surfaces using Bezier curves.


The two stage reefing model uses the newly defined trim parameter RED, which describes the reduction in sail area in two stages. For RED values between 2 and 1 the headsail area is reduced from the maximum to the minimum overlapping jib. For RED values below 1 the mainsail area is reduced while using the minimum overlapping jib. Based on the RED value the geometric characteristics of the sail plan are calculated and the aerodynamic characteristics are determined from the wind tunnel response surfaces.


This model describes the reduction in sail area much more realistically than the reef parameter but it does not model


the de-powering by changing the sail shape


without reducing the sail area. The ‘twist and ease’ model only models the de-powering due to changing the sail shape without reducing the sail area. The ‘twist and ease’ model proposed here is therefore compared to the traditional ‘reef and flat’ model in this work since flat and to some extend also reef, if seen as a aerodynamic trim parameter, model changes in sail shape as well.


7. IMPROVED ‘TWIST AND EASE’ MODEL


If the sails are not physically reefed a reduction of the centre of effort height (zCoE) is usually achieved by twisting off the sails. The trim parameter twist is therefore an important conceptual improvement to model the reduction of zCoE and should replace reef as an aerodynamic factor. Reef


could still be used as a


geometric trim parameter with incremental steps to describe the physical reefing of the sails, but it is omitted in the new model presented here. In its original implementation twist only provides sensible results for small βeff since it applies excessive twist at larger angles. Furthermore even at small βeff the optimisation routine tends to prefer to lower the centre of effort height by using the reef parameter, rather than twist, since the former results in a


reduction in both induced and


parasitic drag, whereas the latter increases induced drag. A number of improvements to the implementation of twist are introduced here to improve its accuracy.


In its original definition flatrepresents a linear reduction in lift due to the reduction of sail camber. The lift is however in reality not only reduced by the reduction in


camber but also, and probably more


normally, by a reduction in angle of attack, which can also be accounted for by flat so that the name is somewhat misleading and should perhaps be changed to ease (ε ).


If the angle of attack of a twisted sail is


changed by a uniform amount zCoE also reduces, so ease needs to be seen as a combination of trim changes resulting in an easing of the sail while keeping zCoE constant.


7.1 REDUCTION OF CENTRE OF EFFORT RELATIVE TO WATERLINE


In the traditional ‘reef and flat’ model reef is applied relative to the boom as it describes


primarily the


deduction in sail area of the mainsail. Krebber and Hochkirch [15] conducted Reynolds Avaraged Navier- Stokes Equations (RANSE) calculations on the rig of Dyna for an upwind sailing condition which showed that the loading distribution is of some shape between triangular and semi-elliptical. The assumption that the sails are semi-elliptically loaded with the water surface being a mirror plane seems therefore more justifiable so that twist should be applied relative to the waterline and equation (14) can be rewritten as .


zCoE = zCoEopt (1 )t − 7.2 INITIAL NON-ELLIPTIC LOADING


The original implementation of the twist parameter assumes that the fully powered-up sails have a loading distribution that induces constant


downwash and


minimises the induced drag. This might however not be the case so that the centre of effort height of the optimally trimmed fully powered-up sail (zCoEopt) does not


equal centre of effort height The total sail twist is therefore t = −1 z t 0 = −1


CoEopt CoE


, of the loading


distribution with minimum induced drag (zCoEminDi) and the twist is not zero when the sails are fully powered-up.


divided into two


components, the twist due to de-powering of the sails (t), which is defined as z


(18)


and the base twist when the sail is fully powered-up (t0), which is given by z


z


CoEminDi CoEopt


. (19)


The total twist is denoted here as t′ and by substituting zCoE and zCoEminDi with equations (18) and (19) can be written as


t′ = − 1 z


CoEminDi CoE


z = + − tt0 t t0 . (20)


The induced drag coefficient (CDi) definition in equation (15) can be rewritten to include the new definition for the total twist so that


C CLopt (β ε2 AR e′


Di = π () , 2


2 eff ) 1+c t + −tt0 ) t ( t0 (21)


where part of the efficiency (e) is now included in the t0 expression so that e′ is written in the denominator. 1/e for the fully powered-up sails (t=0) is the sum of 1/e′ due to the base twist (t0) and other factors so that 1


e


= ′ + ′ 1


e t c


t


2 0


e 2-2t2t0-2tt0 . (22)


When expanding the squared bracket in equation (21) the higher order terms t2t0


2 can be ignored since (17)


B-14


©2010: The Royal Institution of Naval Architects


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