Some basics
Fat foils generate higher lift at low speeds than thin foils. Fat foils generate higher drag at higher speeds than thin foils. Most foils are designed for aeroplanes that travel fast in air. Moths travel sedately in water. For a given foil and angle of attack, lift increases with speed. The popular NACA 0009 and 0012 date from 2nd World War aircraft sections.
The general nature of the system
Beating to windward at low speed the force generated by the sail pushing the boat sideways is small, so a small amount of lift is needed from the foil to balance it. As the wind increases to the point that the helm is fully hiked out then as long as the lift generated by the foil balances the sideways force of the sail there is no point in the foil being capable of producing more lift. In other words, a foil that too powerful is of no value.
Lift is not free and that cost is called drag, the real and only gain here is in how efficient the foil is in generating the required lift. If we split drag into skin friction and section (the airfoil shape) we can see the effects and how to improve the foils performance. Skin drag is proportional to area (and surface finish) so for a given section, a smaller foil will run faster. A proper foil section i.e., NACA0009 and 0012 sections will have less drag and a greater lift than a homemade “freeform” section. The fatter NACA0012 section will give more lift but greater drag than the 0009 section.
With the centreboard we are limited by the width of the slot i.e. 25mm, position of the pivot bolt and the geometry of the case. In general vertical boards are more efficient than swept. The ‘classic’ Moth board will suffer from water tending to flow down the board rather than across it increasing tip losses. High aspect ratio (long and narrow) will suffer less tip losses than short and fat. High aspect ratio boards will benefit from less interaction with the hull where the two meet. The plan form shape can go from rectangular (easy to make) through tapered (slightly harder to make) to quarter ellipse (very difficult) and onto the exotic. Alas, performance comes with difficulty!
Historically the most common sections are NACA i.e. 0009 or 0012. The advantage is that for most people they are readily available and compared with the section that some people produce with a chain saw in the garden shed, close to heaven. Ian Howlett I understand is rather keen on a modified Wortmann section; on Hawkmoth I have used a modified Eppler hydrofoil section.
Whatever section you go for the result will be only as good as the accuracy of manufacture. As you may remember from the last time I wrote on this subject I have a modified router with micrometer head adjustment to produce the section from a series of coordinates. If you have a three-axis CNC machine centre that would do the job! If you use templates, how accurate can you make and use it? I was in conversation with someone a few weeks ago who makes foils professionally when asked to make a copy of a foil replied; which side shall I take the section from?
Decision time
For the centreboard, which would typically run at an incidence angle of 3degrees, the reasonable option would be the NACA0009 section, which has a thickness 9% of the chord. So the chord (width) would be for a 25mm slot width, chord = 278mm. If the slot width were say 22mm then the board would only be 244mm wide. The section determines the width of the board as a function of slot width. If the board were tapered then both the thickness and the width would reduce in order to hold the section geometry.
I would keep the length of the board to the maximum that will go into the box to keep aspect ratio high. See the Moth web site, 2004 Nationals results/pictures second down on the left for a photo. The size of my hand will give a clue on how narrow the board is.
Rudders have a problem in that they have to steer the boat and so will at times be operated at angles where they will stall. In general thinner sections i.e. NACA0009 will stall sooner than say NACA0012 that has a fatter leading edge. The down side is that they produce more drag. Width is not such a limiting factor as there is no limit on stock width. If we take for example a NACA0009 running at 4knots it will generate lift cleanly up to 5 degrees of steering angle before jumping into a high drag mode where the NACA0012 at the same speed will run clean up to 8 degrees. The decision comes down to how aggressively you steer, I am running a 9% section in a 20mm wide stock so the rudder comes out at 180mm wide with some 600mm under water. I think this is too big and I am in the process of working out the best way to make a quarter ellipse version.
However don’t forget that altering the ratio between rudder and centreboard areas will alter the centre of resistance of the boat.
For those with web access the following has some 1550 different foils listed including the above families with coordinates and section drawings:
www.aae.uiuc.edu/m-selig/ads/coord_databaseAlso there are a number of free programmes on the web that calculate lift and drag curves for various sections. The one listed below lets you modify a section or create your own, a very interesting exercise! You can also observe how very small changes to the shape upset the lift and drag curves.
www.mh-aerotools.de/airfoils/javafoil.htmIf you run this you will need to change on the options page, Density from 1.221 kg/m3 for air, to 1000 kg/m3 for water and change Kinematic Viscosity from 0.000014607 m2/s for air to 0.0000013 m2/s for water (at 100C). You can cut and paste directly into javafoil from the coordinate database.
www.vacantisw.com/foil.htmThis is a demo version, which has a handy Reynolds number calculator.
Notes
Sooner or later you will come across Reynolds numbers. Which in its simplest form is about the relationship between inertia and viscosity forces of the working fluid, in our case water. If you wish to do any serious comparisons of foil sections will need to get to grips with this.
For a given foil section and chord I calculate the Reynolds number for a given hull speed say 4knots. I then use that number when using the javafoil program above to calculate the lift and drag curves.
However beware that at typical hull speeds and chord lengths the Reynolds numbers are well below one million, which is well below what the foils were designed for.