Trans RINA, Vol 152, Part B1, Intl J Small Craft Tech, 2010 Jan-Jun
Figure 5 shows the calculated CD plotted against CD measured in the wind tunnel with the Real-Time VPP for sails
at different de-powering levels
effective wind angles. Figure 5(a) shows CD calculated without the twist parameter. For small βeff of 25° and 30° the CD is under predicted and by introducing the twist parameter in its original form in Figure 5(b) and with the t0 expression in Figure 5(c) the
agreement is
consecutively improved. At larger βeff the CD is however still over predicted when de-powering the sails.
7.3 PARASITIC DRAG DEPENDENCY ON REDUCTION IN LIFT
The current trim parameter model assumes that CDp is independent of sail trim as long as reef is not optimised. Figure 6 shows CDp plotted against (CL/CLopt)2, which is equivalent to ease squared and reduces as the sails are depowered, to assess whether CDp is independent of de- powering. CDp in Figure 6 does not include the windage and has a constant component of 0.0289, which can be approximated as the skin friction of the sails, subtracted
so that CDpOpt at βeff of 20° and 25° is close to zero. At βeff of 20° and 25° the CDp seems independent of the sail trim, but at 60° and 90°, and to some extent also at 30° and 40°, CDp reduces when the sails are de-powered. CDpOpt increases with βeff and the reduction at βeff of 60° and 90° is significant. The concept of a dependency of CDp on the reduction in lift is not completely new as CDp is defined as a function of reef squared and flat for upwind sailing cases by van Oossanen [16] but no explanation of the reasons behind it is given. The wind tunnel data shown in Figure 6 however indicate a squared relationship with the reduction in lift.
CDp can be seen as a form of pressure drag which is caused by an obstruction to the flow and leads to separation.
Therefore CDp
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-0.1 0
0 Figure 6: 0.2 0.4 (CL /CLopt )2 [-] 0.6 0.8 1 Parasitic drag coefficient (CDp) excluding
windage calculated from Real-Time VPP measurements plotted against (CL/CLopt)2 for different βeff
B-16
EWA 20° EWA 25° EWA 30° EWA 40° EWA 60° EWA 90° EWA 30° modelled EWA 40° modelled EWA 60° modelled EWA 90° modelled
usually increases monotonically up to βeff of 180°. Although this drag for a range of
component is also caused by separation, it cannot be seen as the separation drag coefficient (CDs), derived from wing aerodynamics for small angles of attack, as a function of CL and CL
2 because CL decreases toward zero
at βeff of 180°. When de-powering by easing the sails the projected area obstructing the flow is reduced and so the consequential reduction in parasitic drag may be modelled by making it proportional to flat, as suggested by van Oossanen [16]. However experimental data shows that the reduction in parasitic drag is approximately proportional to the reduction in lift squared. In the new model the reduction in lift is modelled as ease (ε) and equation (13) can be rewritten to include the dependency of CDp on ε2 as
C CDpOptε2 + S Lopt 2
D = c C ε2 +C Di . (25)
Figure 5(d) shows that modelling CDp as a function of ε2 significantly improves the agreement for βeff from 30° to 90°. At βeff of 90° some errors are still present but considering that CD can vary significantly when trimming the sails, because the flow is partially separated, and that CD has a very small influence on the performance of the yacht at larger βeff, the model can be considered to give very good results.
7.4 REDUCTION IN LIFT DUE TO TWIST
One of the fundamental assumptions of Jones [12] and therefore also Jackson [8] when defining the increase in CDi with the twist parameter is that CL remains constant. It is assumed that, as the angle of attack at the head of the sail is reduced, the angle of attack at the foot of the sail is increased so that the twisted sail produces the same CL with a lower zCoE and an increased CDi. This is feasible for aerofoils at small angles of attack (α) by varying the washout since CL changes linearly with α. An optimally trimmed sail at larger βeff operates at α close to or above the maximum CL so that the sectional CL at the foot of the sail cannot be increased by increasing α and CL cannot be kept constant. Even at small βeff where CL could be kept constant by further sheeting in the foot of the sail this would reduce CFx since the fully powered-up sail is trimmed to have the best lift to drag ratio. In reality a reduction in CL due to twisting off the sails is therefore likely.
The conditions that the sectional lift coefficient at the bottom of the sails cannot increase when applying twist and that CL is not affected by twist can be satisfied if CL is lowered ‘before’ twist is applied by reducing α or the camber along the whole span so that
the loading
distribution remains approximately constant. Applying twist then increases the sectional lift coefficient at the bottom of the sails back to the maximum while keeping CL constant. The relationship between the reduction in zCoE and the increase in sectional lift coefficient at the bottom of the sails is investigated using lifting-line theory assuming an initially semi-elliptic load distribution with the water surface as the symmetry
©2010: The Royal Institution of Naval Architects
CDp - (CDwindage+0.0289) [-]
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