Trans RINA, Vol 152, Part B1, Intl J Small Craft Tech, 2010 Jan-Jun different sail trim that produces less heeling moment.


This argument is not confined to MX, similarly a sail trim that reduces the aerodynamic side force and consequently the leeway angle or one that reduces the yaw moment and hence rudder angle could result in a better boat speed even though the sails


are not trimmed to their


aerodynamically most efficient shape and produce less drive force. Departing from the aerodynamically most efficient sail shape is often called de-powering the sails. The de-powering needs to be modelled in VPPs to optimise the boat speed for different sailing conditions.


Due to the large number of variables that define the sail shape and the complex flow structure around sails an explicit description of the sail shape in VPPs is usually not feasible. Another approach is to explicitly model the sail trim rather than the shape by having the trim controls such as traveller, mainsheet, jib sheet etc. as variables. This has the advantage that the variables are physically meaningful and can readily be measured in full-scale or the wind tunnel, but the disadvantage being that they cannot easily be related to the sail shape and that the number of variables is still significant for carrying out an efficient optimisation in a VPP.


To overcome these limitations implicit measures of sail trim are most commonly used to describe the changes in the aerodynamic forces and moments when de-powering the sails. The fundamental difference to the direct methods is that no attempt is made to explicitly link the aerodynamics of the sails to their shapes. When developing the first VPP Kerwin [1] and Hazen [2] implemented this concept through the trim parameters reef and flat, which are optimised by the VPP to obtain the maximum boat speed for each sailing condition. Although many people agree that these parameters do not model


the physics of de-powering aerodynamic force models in VPPs very have


well, not


fundamentally changed over the past 30 years and the ‘reef and flat’ model is still the most readily used approach for general upwind VPP analysis.


Previously one of the main challenges in assessing how well the trim parameters model the physical behaviour of the sails is determining the best depowered trim without using trim parameters. Due to the almost infinite number of possible flying sail shapes it is extremely computational expensive to optimise the flying sail shape directly


with computational


methods. In the wind tunnel the aerodynamically most efficient sail shape can be obtained relatively efficiently by experienced sailors by maximising the measured drive force. Achieving the optimum depowered sail shape by simply looking at the forces when trimming the sails is however very complex. Campbell [3] and Ranzenbach and Teeters [4] suggest methods based on limiting the heeling moment and optimising the drive force to heeling moment ratio when trimming the sails in the wind tunnel but both methods do not


address the fundamental difference compared to full-scale where the sails are


trimmed to optimise the performance of the yacht. Better results can be achieved by systematically changing the sail controls, post-processing the results in a VPP, and selecting the trim that gives the best performance for each sailing condition. Due to the large number of possible sail controls this is however a difficult and time consuming task.


To make this process more efficient a Real-Time VPP has been developed by Hansen et al. [5], as described in section 3.1, so that the sails can be trimmed in the wind tunnel based on boat performance. In this way realistically depowered sail trims can be achieved in the wind tunnel effectively. As described by Hansen et al. [6] and outlined in section 3.3 these measurements can be used to develop much more detailed semi-empirical trim parameter models. One being that the de-powering is described as a function of wind angle and the trim parameter power, which is defined as the reduction in heeling moment.


This approach of utilising a Real-Time VPP to depower the sails realistically in the wind tunnel and to model the changes


due to de-powering semi-empirically as


functions of wind angle and the trim parameter power is also adopted by Fossati et al. [7] when investigating the effect of mainsail roach and jib overlap.


However, detailed wind tunnel studies investigating de- powering with a Real-Time VPP are not feasible for many designers and there is merit in also developing generic de-powering models


based on aerodynamic


principles, such as the ‘reef and flat’ model. This paper therefore uses the


realistically depowered sail trims


obtained with the Real-Time VPP to assess how well reef and flat model de-powering. From this comparison four improvements to the existing model, also based on aerodynamic principles, are introduced in the ‘twist and ease’ model which significantly improve agreement with wind tunnel data.


2. PRINCIPLES OF SAIL FORCE MODELLING fluid dynamics (CFD)


The most commonly used aerodynamic sail force model in semi-empirical VPPs, which is used as a bases for this study and was introduced by Kerwin [1] and Hazen [2], derives the sail forces and moments from the lift and drag produced by the sails and the centre of effort position. The lift and drag coefficient (CL and CD) and the centre of effort position are modelled based on the fully powered-up CL, CD and centre of effort position of the aerodynamically most efficient shape, which are modified by the trim parameters to account for the de- powering of the sails.


To approximate the force and moment changes due to heeling of the yacht the effective angle concept is employed, which combines the apparent wind angle (βA) and the heel angle (φ) into a single angle; the effective wind angle (βeff). Kerwin [1] assumes that the sails are


B-10 ©2010: The Royal Institution of Naval Architects


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