Fig 6.14 Forward and ah because the hull has a leeway angle and the rudders are far apart the rudder configuration distance between the trailing vortex systems may be significant, if not large (see the bottom part of Fig 6.14). A leeway angle of 4° with the rudders separated 15 metres would result in a trailing vortex separation of approximately 1 metre, which is about 40% of the draft. This should be enough for a noticeable drag reduction.

Fig 6.14 illustrates another interesting effect of the positioning of the rudders at the ends of the relatively deep hull. The trailing vortex systems are influenced by the flow around the hull, as can be seen in the top figure. The ultimate location in the wake will be further down than for an ordinary keel positioned approximately at the maximum draft of the canoe body. Since it is the location of the vortex far behind that determines the effective draft, the rudder arrangement is better, given the maximum geometric draft of the configuration.

A third possible advantage of the forward and aft rudder configuration is the effect on the wave system. While an ordinary keel has an unfavourable effect on the waves, the opposite may be true for the rudders. When the hull sails upwind at full speed, the Froude number is around 0.35 and the wavelength is slightly smaller than the waterline length. There is thus a wave trough at midship. Tf the hull heels significantly the suction side of the keel will be close to the water surface, thus deepening the trough. The rudders, on the other hand, will apply their suction in regions where there are wave crests, which should reduce their height.

There are several practical aspects of the forward and aft rudder configuration. In principle manoeuvrability will be increased, but that requires a good control system for the co-operation between the rudders. Another aspect is the risk of ventilation when the rudders are lifted due to the heeling of the yacht. Beamy yachts may lift the rudders too much to be effective. In any case, the forward and aft rudder configuration is interesting and will probably appear more frequently on fast racing yachts in the future.

Tandem keels As for the forward and aft rudders, the side force on a tandem keel is split on two foils, but much closer together. Normally they are also linked through a horizontal fin or a bulb-«(see Fis 6.15, where there is also a trim tab on the aft foil). There is now a strong interaction between the two foils in much the same way as between the jib and the mainsail, which will be described in the next chapter. The reader is referred to the theoretical explanation given there.

Fig 6.15 Tandem keel with trim tab

The two major positive effects of the tandem configuration are the increased maximum lift coefficient obtainable before stall, and the possibility of obtaining laminar flow over a larger area. The latter may seem surprising, but according to experiments the turbulence in the wake of the forward foil is swept sidewards fast enough not to disturb the aft foil, so laminar flow may be exploited even there. The increased maximum lift coefficient means that a smaller lateral area is required, so both effects mean smaller friction. A further step in this direction might be taken by dropping the rudder altogether and steering the yacht with the trim tab.

Evaluation of some An evaluation of seven different keel concepts was made at the Delft planform concepts University of Technology in the early 1980s. All keels were tested on the same hull, a 3.2 m model of a 63 ft fast cruising yacht. To isolate the hydrodynamic effects from the stability, which varied somewhat between the keels, all evaluations were made with the same righting moment of the yacht.

The seven keels are shown in Fig 6.16. Since the emphasis was placed on minimizing the draft of the yacht without compromising performance too much, most of the keels had a very small span: only 1.39 m. This was true for nos 2, 3, 4, 5 and 6, while 1 and 7 had a more

Kee/ span ■ sha!,ow kee/s (2, 3t 4, 5, 6): 1.38 [m]

1. Plain deep keel n i i

4. Scheei keel

2. Keel—centre board

5. Wingiet keel

6. Wingiet keel

3. Plain restricted draught keel

Fig 6.16 Keels tested by normal span of 2.29 m. No 1 was a standard trapezoidal keel, with Prof.Gerritsmaetal which to compare all the others, and no 7 was elliptic. Among the shallow draft keels, no 3 was just a trapezoidal reference case, while the others exploited some kind of device at the tip. No 2 had a centreboard, which increased the draft by 1.41 m, no 4 was a so-called Scheel keel and nos 5 and 6 had wings of different spans. A Scheel keel has very thick sections near the tip, as can be seen from the figure. This is to try to reduce the overflow by means of the 'comers' seen in the front view near the bottom of the keel.

Tests were made and evaluated using a Velocity Prediction Program (VPP), as explained in Chapter 16. Sailing speeds at all wind speeds and directions of interest were thus obtained, and Table 6.1 presents the final outcome, namely the elapsed time on an Olympic course at two wind speeds. It may be seen that the elliptic and the basic trapezoidal keels are the best, and virtually identical. The fact that they are the best is not, of course, surprising, sincc they have the largest draft. More interesting perhaps is the fact that keel no 6, which is much shallower, is almost equally good in the strong wind. It is thus possible to reduce the draft by introducing wings without much loss in performance. In fact, if the draft difference had been smaller the winged keel might have been equal, or even better. The wingiet keel with the small span, the Scheel keel and the shallow trapezoidal keel were 2%, 3.5% and 5%, respectively, slower than the best on the Olympic course. A somewhat disappointing result is the performance of the centreboard keel, which had the largest draft including the board, but was 2% slower than the best. It should be noted, however, that the board was left down under all conditions, while in reality it would have been raised downwind.

wm lip ----- ■••• |
• - A',. -V, *------J -.. > ..-' .1 |
Elapsed time (hours, with decimals) on an Olympic course for the Delft keels | |

Wind speed (knots) i 2 |
Keel no 03 4 |
ftMg^ag^WliiNM llHIJA1'1!? Ife : | |

15 3.96 4.06 25 3.52 3.60 |
.v-',.'/!\ ^.'.Z s. 1 Z jl; IS I '.1 Z'.Z M'I'iVAVv< yl : ^ * •! :» ;: i:: : ii^V^o. |
S,v>// ivXv' «.%-xci cox >I*M |
4.01 3.96 3.53 3.52 |

Definition of the section

The sectional shape of the keel does not have such a significant effect on its characteristics as the planform, but on the other hand the most important planform parameter, the aspect ratio, is fixed in most class rules and heavily penalized in rating rules. A study of the influence of the sectional characteristics may therefore be worthwhile.

In Fig 6.17 the geometrical parameters defining a foil section are presented. The section of the figure is asymmetric, ie the mean line, defined as the line midway between the upper and lower surface contours, is bent. As pointed out above, asymmetric sections are rarely used for sailing yachts, since they have to perform equally well on both tacks. We will limit most of the following discussion to symmetric

Fig 6.17 Definition of section shape

C — chord length t = thickness r• — nose radius

Mean line

Mean line

Thickness ratio = t /C

max sections, where the mean line is straight. The thickness t is measured at right angles to the mean line, and the maximum thickness is denoted tmax. The thickness ratio of the section is tmax/C, where C is the chord length. An important parameter for the section characteristics is the nose radius, rl5 which is defined as the radius of curvature at the leading edge. This definition is not very practical, but as a rule of thumb the nose radius defines a circle, which follows the nose contour upwards and downwards about 45°.

Three useful NACA Unfortunately, many sailing yachts use foil sections that are not well sections designed. As a general rule the designer should not attempt to develop his own section, unless he is an experienced fluid dynamicist. There are several books listing useful sections available, and these can be used in most cases. The most well-known publication in this area is Abbott & von DoenhofPs Theory of Wing Sections. This book contains not only theories of wings and wing sections, but also an extensive presentation of the geometry and characteristics of a large number of sections.

In Table 6.2 the geometries of three useful sections are presented. The first belongs to the so-called four digit series, where the last two digits represent the thickness ratio and the first two give information about the mean line. For a symmetric section only the last two digits are of interest. The other two sections belong to the six-series, which may be considered more modern, even though it was designed in the 1940s. The six-series contains five different groups, denoted 63, 64, 65, 66 and 67, where the second digit gives the position of minimum pressure along the chord. The 63-series thus has its minimum at 30% of the chord from the leading edge, the 64-series at 40%, etc. This information is quite important, as we will see. After the dash in the number the first digit concerns the mean line, while the last two give the thickness ratio in per cent. All three sections of Table 6.2 have a thickness ratio of 10%. The

Fig 6.18 Nose radius

nose radius

Ellipse

Table 6.2

Three useful NACA sections y y y

0010 63-010 65-010

OOöCO - • CvjyCt- "■ "*•' " 1 ' ii'I''"- "!v ■ a <i'- -» IvMw. 1 a * »^/o * ~ A*- r - ..

10 3.902 3.362 3.040

15 4.455 3.994 3.666

20 4.782 4.445 4.143

25 4.952 4.753 4.503

30 5.002 4.938 4.760

35 5.000 4.924

40 4.837 4.938 4.996

45 4.766 4.963

50 4.412 4.496 4.812

55 4.140 4.530

60 3.803 3.715 4.146

65 3.234 3.682

70 3.053 2.712 3.156

75 2.166 2.584

80 2.187 1.618 1.987

85 1.088 1.385

90 1.207 0.604 0.810

95 0.672 0.214 0.306

four-digit series can be scaled to any other thickness by multiplying all y-values by the thickness desired divided by the given 10%. This is not precisely true for the six-series, but it is a good approximation if the thickness ratios are not too far from 10%.

The sections are specified in the table by a set of x-y values, where x is along the chord, measured from the nose and y is at right angles to x. Note that both coordinates are given in per cent of the chord length and that only one half of the (symmetric) section is defined. To be able to describe the most important part of the section, namely the nose region, the nose radius is required. This varies quadratically with the thickness ratio, as appears from Fig 6.18, which gives the radius, not only for the two series, but also for an ellipse. Il is seen that the six-series is relatively close to the ellipse, while the nose radius for the four-digit series is much larger.

Influence of shape on In order to understand the influence of the shape of the section on its section characteristics performance, reference should be made to Fig 5.5, which shows the boundary layer around a hull. In principle, the same picture may represent the flow around an airfoil section. There ^ is a laminar boundary layer developing backwards from the leading edge. After a certain distance the flow becomes unstable, and shortly thereafter the boundary layer undergoes transition to the turbulent state. Under certain conditions the flow may separate and recirculation may occur. When compared to the case of Fig 5.5, which is symmetric, one difference is that for an airfoil at an angle of attack the flow picture is not the same on the two sides. We recall from the discussion in Chapter 5 that the boundary layer development is determined from the pressure distribution, which in turn depends on the shape. A favourable pressure distribution with diminishing pressure stabilizes the flow, which is then sucked backwards. An increasing pressure works in the opposite direction and destabilizes the flow in such a way that transition moves upstream and separation occurs more easily.

Writh these considerations in mind it is of interest to examine the pressure distribution on the three typical sections shown in Fig 6.19. The first is a conventional four digit NACA section with a thickness ratio of 9%, while the other two belong to the 65-series, with 9% and 21% thickness ratios, respectively. As before, negative pressure is upwards on the vertical scale. It may be seen that the four-digit section has its pressure minimum very far forward, close to 10%> of the chord from the leading edge. This means that a favourable pressure distribution exists on only 10%) of the chord, and that transition is likely to occur far forward. On the two other sections the maximum thickness and hence the pressure minimum, occurs further back, and a much larger laminar zone can be anticipated, resulting in a considerable drag reduction.

For the 65-series two extra pressure distributions are given. These show the pressure on the upper and lower sides of the section at the maximum angle (ie maximum lift coefficient) for which it works properly. It can be seen that a favourable pressure distribution is maintained even on the suction side up to a lift coefficient of 0.06 for the thin section and 0.44 for the thick one. At higher lifts, ie larger angles of attack, the suction peak moves very far forward on the suction side, transition occurs close to the leading edge and the drag increases. A typical lift coefficient sailing upwind is 0.2, while it is almost zero downwind. The differences between the three sections may now be summarized as follows:

• the four-digit series has its pressure minimum further forward and has consequently a smaller region of laminar flow as compared to the 65-series;

• the thin section works well only in a small range of angles of attack, while the thick section accepts larger angles.

Fig 6.19 Influence of shape on pressure distribution

We will now turn to a more quantitative discussion of the differences in lift and drag. First the difference between the series will be presented. In Fig 6.20 two sections of the same thickness (9%). are shown, together with the corresponding drag curves. The four-digit and 63-series arc compared, since the 65-series, shown in Fig 6.19, is rarely used for such small

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