Have just realised that I didn't write anything about rudder design.
Two or three year's ago, I designed a rudder which I had made by Simon Cox at Synergy Marine. The reason for going to him was that he forms the shapes on a CNC cutting machine. I sent him drawings and iges files of coordinate data from Javafoil; Simon created A CAD model from this information and used this to drive his machine.
Below is an extract from an email I sent to Simon explaining a little bit of the design
basis.
“Dear Simon,
I will have a go at explaining as follows:
Background
1) A Merlin sailing at 2 m/s has a total drag of about 35 Newtons force,
i.e about 3.5 Kgs. So quite a small force.
2) Of this drag more than 10% comes from the rudder under steady-state
conditions, and much more comes during strong steering actions.
3) The rudder drag has two main components, namely:
a) Form Drag, which is made up of viscous friction drag and drag due to
pressure changes front to back. This latter includes surface wave effects and the
drag from blunt trailing edges.
b) Induced Drag which comes from carrying a lateral (steering) force and is
directly linked to the flow of energy into the tip vortex at the bottom end and
extra wave generation at the free surface.
4) Working Area. A good starting point is to have the working area about
half that of the centreboard. So about 0.15 to 0.17 sq. m. This fits in with
current practice, and with my experience in an experiment I did with a specially small foil (at 0.11
sq. m). This was a disaster in terms of speed round a course, despite lots of calculations which showed that it would
be fine.
5) A 10% reduction in rudder drag will give a 1% reduction in total drag,
which means a 0.5% speed increase which means a gain of about 25 feet per mile.
So about 2 boat lengths per lap in a 4 lap race (at Tamesis).
6) So the idea was to look for a significant reduction in drag over the
current run of rudder designs, while maintaining the same level of steering
control.
Design
1) Aspect Ratio. I have stuck with the current practice for this (i.e.
about 800 mm immersed depth and 200 mm chord). Going deeper brings problems with
increased bending in the stock and more likelihood of contact with the bottom.
And it is not automatic that drag is reduced by going for a high aspect ratio;
true, induced drag will come down as the square of depth but frictional drag
will go up as more than half the frictional drag occurs in the first 15% of the
chord. Hence, for a given area, a deeper board has more form drag because it has both
more leading edge and more trailing edge. I suspect that total drag round a course is not much
affected by aspect ratio with limits.
2) Section. This is probably the crux of it. As background, NACA 4-digit
foils are commonly used for boat foils. And they work fine as they tend to work
well at low Reynolds Numbers, have high resistance to stall and have
trailing-edge stall which tends to be “soft” and recoverable. They were
developed by NACA in the 1930’s as good, state-or-the-art foils for general
aircraft design of the time, drawing on development work in the US, UK, France
and Germany. However, they are not low-drag foils; the shape of the nose section
triggers the transition from a laminar to turbulent boundary layer very close to
the leading edge. This gives high resistance to stall but high frictional drag.
Maybe early aircraft designers were more worried about stall at landing speeds
than anything else? Later, in WW2 NACA produced laminar flow foils in the 63, 64
and 65 series to reduce drag on military aircraft flying at 400 to 500 mph.
These foils are not generally suitable for boats as they are designed to work at
high Reynolds Numbers and are very prone to leading-edge stall.
So, I started to play with JavaFoil to find a low drag section with high
lift. I set the Reynolds Number at 400000, which corresponds to a 200 mm chord
moving at 2 m/s thru fresh water, and is the lower limit of accuracy for
JavaFoil, anyway. What I found was that a 15% section with the standard NACA
nose rad of 2.48%C and the point of max thickness between 35% and 37% back. This
section gives
Max Coefficient of Lift = 1.25
Coefficient of Drag at Zero Lift = 0.0076
A standard 10% NACA foil would have the following, for comparison:
Max Coefficient of Lift = 0.95 to 1.00
Coefficient of Drag at Zero Lift = 0.011.
Hence game set and match. The only potential problem is that the JavaFoil
results are calculated values rather than derived from tests and so may be utter
bollocks. Who knows? We shall soon see! (This was written before the new design had been used. With use, I cannot tell about the drag reduction but the resistance to stall is very high.)
3) Area. My original rudder has an area of 0.166 sq m. Hence, its
maximum steering force at any speed is proportional to the max lift coefficient
times the area, i.e 1 x 0.166 = 0.166. This is called the Lift Area. Similarly,
its Drag Area is 0.011 x 0.166 = 0.00183.
Now my new foil needs the same Lift Area, as far as I know. To get this
with the higher lift coefficient means I only need an area of 0.166/1.25 = 0.133
sq m.
And if I have an area of 0.133 sq m., the new Drag Area becomes 0.0076 x
0.133 = 0.0010 sq m.
Hence, the new frictional drag should be only 55% of the old.
4) Trailing Edge. I can send references on this but any trailing edge
thickness has a huge effect on form drag. It really is worth the effort to get
this down as small as possible. You never see thick edges on aircraft; 3 mm is a
DISASTER for a foil 25 mm thick. It will increase the form drag by 40%.
5) Plan Shape. Two things need to be done here, namely;
- have a shape which minimises the drag induced by load carrying
- have a shape which matches to distribution of local lift coefficient so
that all of the area is working as a piece and coming up to stall at the same
time.
This subject gets very complex, much more than the equivalent problem for a
centreboard. This is because the rudder is a surface-piercing foil and how it
behaves is very dependent on the Froude Number of the chord at the surface. In
the 1990’s considerable work was done by US research organisations under the
PACT scheme for collaboration in the design of one of the America’s Cup boats. I
have some of the papers published on this subject, and some of Tom Speer’s work.
To cut a long story short, the best rudder profile for normal speeds is full
ellipse with the top just touching the surface (this is an elliptical distribution of chord and not necessarily an elliptical shape), i.e. nothing protruding above
the surface. Clearly, this is not practical, but the effort should be to get as
close as possible to this ideal, and have the centroid of the area about 50%
down. The result is a somewhat "pot-bellied" foil with the maximum chord and maximum thickness about half way down the immersed depth."
