## Principles of Yacht Design

Fig 7.9 Influence of camber on driving force

### Fig 7.10 Influence of camber on side force

For the upwind case, at 30° and below, there is a very small difference in driving force between the two deepest sails, but the deepest one has a slight advantage. The difference in side force is somewhat larger: approximately 10%. Which sail is the best is hard to say. since it depends on the ability of the underwater body to balance the side force

Sails sheeted at more than 90 degrees

120 150 180

J1'

/7

V

1/1 o A

\

1/

'20-

\

-

\

without producing too much induced resistance. The problem can be resolved in a complete equilibrium calculation for the yacht, such as in a VPP program (see Chapter 16), but the result is not obvious without such a calculation, unless heeling is a problem. In stronger winds the 10% smaller side force of the l/w sail has to be compensated by reefing of the \/i sail. Considering the fact that the centre of effort of the sails is then lowered, the area has to be reduced some 7%. which would reduce the driving force by an equal amount. This force would then be smaller than the Vm sail. It is thus better to flatten the sail than to reef it to reduce heeling, a fact well known by most sailors.

From Figures 7.9 and 7.10 it is obvious that for larger apparent wind angles the full sail is the best. At the maximum driving force around 100° there is a difference of about 10% between the Vi and l/io sails, while the side force is zero. An interesting feature of the measured results is that it is advantageous to develop a negative side force, ie to windward, for angles in the range 100 to 150°. The sails should thus be sheeted at more than 90° giving an angle of incidence of the sail small enough to avoid separation on the leeward side. The total force developed is then so large that, although it points somewhat to windward, the driving component is larger than if the sail is sheeted in the normal way. This possibility does not normally exist in practice, due to the shrouds, but it could be of interest for dinghies.

The effect of the position of the maximum camber is shown in Figs 7.11 and 7.12. These figures are based on wind-tunnel measurements for sails with a mast, and arc thus applicable to the mainsail. It can be seen that this effect is much smaller than that of the camber size. Interesting

Fig 7.11 Influence of maximum camber position on driving force

Fig 7.12 Influence of maximum camber position on side force cs A

 2/ 2-- v S \ differences, however, are noted in the figures, which show results for three sails with the maximum camber at '/3, Vi and 2A of the chord. At small angles the ]/i sail develops the largest driving force, followed by the lA and 2A sails. Around 55° they are all equal, while at the maximum driving force around 100° the 2A sail is the best, followed by the lA and Vi sails. The side force is smallest for the Vi sail and largest for the 2A sail in the range of angles up to maximum thrust. The results indicate that the sail with the maximum camber at mid-chord is the best upwind, while on broad reaches the maximum camber should be further aft. Note that these conclusions arc for the mainsail. A more forward position of the camber is likely to be better for the foresail. The aft position should be avoided, since the flow approaching the mainsail might then be too disturbed. Mast interference The flow around a sail behind a mast in upwind sailing is shown schematically in Fig.7.13. As can be seen in the figure the flow is not attached to the sail all the way. Three zones of separation can often be distinguished. Two are immediately behind the mast, to windward and leeward, respectively, while the third zone is on the aft part of the leeward side. The separation behind the mast can be minimized by proper shaping of the mast section and by introducing turbulence stimulators. The aft separation zone depends, in fact, to some extent on the forward one, since a massive separation forward causes a thick boundary layer to develop in the attached part of the flow. This layer separates more easily than a thin one. To a large extent the aft separation depends also on the loading of the sail. By proper sheeting and a good mast design this zone can be very small or even eliminated.