Farr 3.7 Centreboard Design By Trent Cornwall
I started with a blank piece of paper and
tried to make no assumptions on any shapes, profile or cross section from what
other people were using.
Obviously the first thing to do was measure
the sizes that the centreboard had to fit into:
1) Class Rules - 9a: “Centreboard does not exceed 1370mm in length”
2) Centrecase opening 24mm x 300mm
With a centrecase opening width of 24mm this
means that for these foil thickness’ the chord length must be:
Chord Thickness Chord
Length
6% 400mm
8% 300mm
9% 267mm
10% 240mm
12% 200mm
Obviously the 6% foil woud be too long a
chord to fit down the case and the 12% may be marginal on area (unless possibly
you built a non-tapered parallel profile board).
Chord Thickness
In light days the 3.7 centreboard has to
generate lift at fairly low non-planing speeds and on windy days it must perform when we are planing upwind
and be able to take quite abrupt changes in direction due to the short length
of these boats.
“A 9-10% thick section with a small
leading edge radius followed by a fairing parabola over the forward 15% of the
chord gives the best blend of both low and high speed behaviour.”
- High Performance Sailing – Bethwaite
Turbulent or Laminar?
There are two types of cross sectional
profiles to choose from. The Turbulent flow profiles such as the NACA 0009 or
0010 which most people are familar with or more specific Laminar flow profiles.
Laminar flow profiles are generally finer entry with the maximum width further back.
Although Laminar profiles have the ability to
generate much less drag, they can operate only at small angles of attack which
Bethwaite found to be about 3 ½ degrees. On this basis I discarded using these
and stuck with the traditional NACA profiles which operate more effectively
over much wider angles of attack.
Fig 1. Drag Curves - Turbulent and Laminar – From High Performance Sailing – Bethwaite
Profile
It has been documented in many books that
“Elliptical Lift Distribution” is the most desirable for centreboards and
keels. This does not neccessarily mean an elliptical profile.
Fig 2. Elliptic
Planforms
“Elliptic Planforms are shapes that
give rise to an elliptic lift distribution. To do this the planform does not
have to be the shape of an ellipse (or semi-ellipse): a number of shapes could
give an elliptic lift distribution if the section shape is varied
appropriately. If one stays with a constant section shape, then an elliptic
lift distribution results if the chord lengths are related to their position
‘y’ from the root by the equation of an ellipse”
- Symmetry of Sailing – Garrett
A Trapezoidal shape as in the two lower
figures in Figure 2 approximates an Ellipse in profile and generates Elliptical
Lift Distribution.
Taper Ratio
The Board must be tapered in profile to
approximate the ellipse and give the “elliptical lift distribution” mentioned
above. The Taper Ratio of the trapezoid i.e. the width at the tip divided by
the width at the base is theoretically optimum at 0.4 although this does vary marginally
with aspect ratio.
Figure 3 which is a graph of drag increase for
different aspect ratios and tip widths shows that the tip width ratio has a reasonable
range of variation before any noticable drag is induced.
Figure 3 – Principles of Yacht Design – Larsson
Aspect Ratio
Theoretically a foil with an infinite aspect
ratio will generate the maximum possible lift for any profile.
In the real world the majority of vortex drag is generated at the tip of the
foil so it stands to reason that a higher aspect ratio foil will always be more
efficient for a fixed area as there is effectively less tip area.
Therefore the highest possible aspect ratio
within the class rules must have the highest lift potential.
With a class rule fixed maximum length of
1370mm there must be a trade off between maximum aspect ratio and minimum area to prevent leeway i.e. the
highest aspect ratio/smallest centreboard you can get away with to still create
enough lifting force and with the minimal drag component possible.
Sweepback Angle
How much if any rake or sweepback angle should the centreboard have
and what effect does this have?
Figure 4
“The effect of sweep angle on vortex drag when surface effects are
taken into account. The lift produced by leeway is the same in both cases. For
small boats which are sailed upright, zero sweepback is best. When heeled some
sweep is beneficial. The optimum amount of sweep decreases with increasing
aspect ratio and draft.”
- Symmetry of Sailing – Garrett
Figure 4 clearly
shows that a foil with a zero sweepback angle has the lowest vortex drag for a
yacht sailing dead upright.
Conclusions
To achieve the highest possible aspect ratio with fixed
overall length the chord length must be as short as possible.
I opted for the 10% section on this basis and also as the
easiest way to reduce drag is to reduce area.
Also the shorter the chord the less area that may operate
under turbulence once the flow had broken away.
This
makes my centreboard 240mm wide where it exits the centrecase.
Remember that with the 3.7 when you talk about decreasing
the foil % thickness to reduce drag you
are actually increasing the chord length which is increasing the area and with
this IS an increase in drag (as the maximum thickness is always the centrecase
width aprox 24mm).
This was also part of my reasoning for the maximum length
and highest possible aspect ratio as all the lift is generated in the leading
edge area. Regardless of which section was to be used I figured looking head on
at the centreboard you would be displacing 24mm wide x aprox. 1100 deep, so
best to cut down on the area by using a thicker % higher lift profile.
I used a taper ratio of about 50% so as not to reduce the
area too much. I actually chickened out while making it as I was originally
intending to use 40% but the overall area looked way too small.
There must be a minimum area required to generate the
right amount of lift for each particular 3.7 rig/sailor setup and anything more
must be just drag, anything less and too much leeway.
I feel I must be fairly close for my rig, as in certain
windstrengths upwind if I am pinching a bit much for the sail the boat feels
like it crabs a little, then if a drop off a couple of degrees it seems to
power up and generate a lot more lift.
With a
50% taper ratio this makes the tip of my centreboard 125mm
The Aspect Ratio of the centreboard is : (Length divided by average chord)
1310/((240 +125)/2)= 7.18
As there is about 1100mm below the boat I guess its
effectively:
1100/((240 + 125)/2)=6.03 which is still very high.
Compare with a full case length
Short and Non-Tapered Centreboard
(assume 100mm less than maximum
length)
1000/300 = 3.33 AR
Construction
I constructed the centreboard using 3 pieces of Kahikatea
laminated together for the core. After shaping I planed a trough on each side
to lay the carbon unidirectionals in, faired over and then glassed with “S’
Glass.
To get a thin trailing edge that would not deteriorate I
then machined a groove down the trailing edge and glued in a 1mm thick piece of
formica.
Note
Other people have used laminar flow foils which seem to
work fine.
They are like mentioned before much more critical for
angle of attack (max 3 ½ degrees) and also the surface finish must be
practically perfect to keep the flow attached so far back. If they are not then
the flow can not stay laminar and breaks away at which point the foils cease to
perform very well at all.
References
[1] Bethwaite, Frank; High Performance Sailing, 1993 Waterline
Books
[2] Garret, Ross; The Symmetry of Sailing, 1996 Sheridan
House
[3] Larsson, Lars & Rolf E Eliasson; Principles of
Yacht Design, 1994 Adlard Coles Nautical,