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


The error is calculated relative to the fully powered-up trim at each βeff.


The description in equation (8) is used in FS-Equilibrium to produce the benchmark results, against which the generic trim parameter models


are assessed,


4. TRADITIONAL ‘REEF AND FLAT’ MODEL The traditional de-powering method introduced


Kerwin [1] uses the trim parameters reef and flat


optimising power to maximise the speed of the yacht for every sailing condition.


by to


describe mathematically the changes in CL , CD and zCoE compared to the aerodynamically optimal value. In the original model reefrepresented a linear reduction in span and chord of the sails. The sail area is therefore reduced by r2. Although reef was originally intended as a geometric, rather than an aerodynamic, factor which models the physical reefing of a sail, it has become thought of as representing any change to the sail trim that reduces the centre of effort height. However the formulas used in the traditional model are essentially based on the original geometric ideas. The trim parameter flat (f) conceptually describes a reduction in camber, but can also represent any change in sail trim which reduces lift without affecting the centre of effort height. CL can hence be related to the optimal fully powered-up lift coefficient


(CLopt) through the reef


parameter squared and the flat parameter so that []


C C r f L = 2 Lopt , r f ∈ 0,1 , , where CLopt is a function of βeff.


Following standard aerodynamic theory the induced drag is a function of the lift coefficient based on actual area, the efficiency (e) and the aspect ratio (AR), which is calculated from AS and the mast height (zmast) with


AR z2 =


mast AS


. Di =


⎝ ⎛


⎜ ⎜


Di =


q r A L


2 eff s


C C r f Lopt


2 πeAR


⎠ ⎞


2 2 2


⎟ π ⎟


.


eAR q r A . 2


1 eff S (11)


Substitution of equation (9) gives the induced drag coefficient (CDi) as


(12)


The total drag is then modelled as a sum of parasitic drag (CDp), separation drag (CDs) and induced drag


C CDpOptr + c C r f C Di D = 2 2 S Lopt 2 2 + , (13)


where CDpOpt is the parasitic drag of the fully powered-up sail modelled as a function of βeff and cs is the separation constant usually taken as 0.0016 for upwind sailing conditions and 0.0019 for downwind cases following Kerwin [1].


(10)


Hence, with the area reduced to r2As, the induced drag (Di) becomes


(9) by


In the traditional reef and flat model the centre of effort height (zCoE) is reduced only by reef, so that r


zCoE = zboom + z( CoEopt − zboom ) , powered-up condition modelled as a function of βeff .


In 1999 Claughton [11] acknowledged the problem that the centre of effort height is not description until the sails begin to


reduced in this reef


while


experimental results show that the centre of effort height is reduced by flattening and twisting the sails before they are reefed. It is suggested that the ‘twist’ effect could be incorporated by linking the centre of effort reduction also to the trim parameter flat, but no further details on how to implement this are given.


5. JACKSON’S ‘TWIST’ MODEL


Two years later Jackson [8] introduced a third trim parameter twist which accounts for the twisting-off of the sail. Assessment of the trim parameter models against the wind tunnel measurements showed that the addition of the twist parameter, in its original implementation, unfortunately reduces the accuracy of the model. The traditional reef and flat model is therefore employed in the comparison to follow but the original implementation of the twist parameter is still introduced here because it forms the basis of the improved model introduced later. Twist models the twisting-off of the sail which makes the lift distribution along the span of the sail less efficient and hence increases the induced drag, although the original idea was that it should not change the lift coefficient. With the inclusion of twist equation (9) remains the same, but the induced drag coefficient is:


eAR C C r f


2 Di = π Lopt 2 2 (1+ c t t 2 ) , (15)


where t is the trim parameter twist and ct is the twist weight constant which in the idealised case of constant downwash is 8 as shown by Jones [12] and discussed further by Hansen [13]. With this model the other drag terms were unaltered.


The other alteration introduced affected the centre of effort calculation. In the traditional reef and flat model the centre of effort height (zCoE) is reduced only by reef, but in this model the twist parameter also has an effect so that


zCoE = zboom + z( CoEopt − zboom r) (1 ),−t t∈ [] , 0,1 (16)


and so the centre of effort height is reduced as twist is increased. It should be noted that in the fully powered- up situation t=0, whereas both reef and flat are equal to 1.


6. TWO STAGE REEFING MODEL


In 2008 Claughton et al. [14] introduced a new two stage reefing model based on wind tunnel data for different rig plans investigated by Fossati et al. [7]. During this study


©2010: The Royal Institution of Naval Architects B-13 (14)


where zboom is the boom height above the water and zCoEopt is the optimal centre of effort height


for the fully


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