Daggerboards basically opposes to the leeway generated by the
sails, there are few elements that defines the design of a daggerboard: sail
area, boat target speed, lift to heel ratio wanted. Obiouvsly it's of main
interest the center of effort of the sail as the center of all anti leeway
surfaces (submerged hull, daggerboards and rudders) are to exactly match
in order to make the boat as much neutral as possible under wind action. Since
daggerboards are the most important of all these surfaces, they have to be
positioned with great accuracy along the hulls.
Usually as the sail center of effort changes following the trim of the sail, it is really hard to find a position that goes exactly well for these variation, so designer prefers to put the center of leeway a bit ahead the sail's center of effort in order to obtain a very safe and usefoul tendency of the boat to turn naturaly upwind (slowing first then stopping by this way a boat that loses control).
Sail area, wind conditions and boat speed defines al together the daggerboard area. All starts from the Lift coefficient Cl of a given airfoil at a certain Reynolds number Rn at a given angle of attack.
Cl= where L is lift in Newton, in our case is equal to about 3500N, rho is the density and is about 1000, v stands for speed in m/s and we put equal to 8m/s (about 18 Kn), S is our variable that we are looking for. Always consider that we have to have Cl for Rn of 2807040. Rn= where V is speed in m/s and L is length of the section ( practically our profile's chord).
So if we would know our Cl at a given angle of attack ( in our case i guestimate between 3°-5°) at a given Rn (2.8*10^6) it would be easy to deduct the S area we need. I don't have such a table , and since little variation of Rn especially in the water gives spectacular changes in these curves, i am not able to deduct our daggerboard area, if out there is someone who has a Cl table for section NACA 63-012 at Rn of 2800000, Let me know, however in this wonderfoul website there is a foil calculator that gives out what we are looking for, the problem is that one should define the sections with at least 50 coordinates, is a litle tricky, so i wait for further aknowdlegments.
Here you are a table where different naca sections (NACA 0006, 0009, 0012, 0015, 0018) are compared at 3000000 Rn.C stands for Lift, Cp stands for lift coefficient, R stands for drag, Cr stands for drog coefficient.
It is sure that C.A. Marchaj in his aerao-hydrodynamic of the sail give 4% as optimum percentage of daggerboard area respect to the sail area. Furthermore he analyze mmany daggerboard and he finds that all these dagerboards are statistically always bigger than that obtained from simple hydrodynamic calculations like that we have talked before, his conclusions are that those calculation doesn't take count of the many changes of a boat under sail condition as pitching, rolling etc..
However my A Class cat has a percentage of 1.25%, with an effective aspect ratio of 2.8 where : .
I would like to refer to these measures, i will refer also to the side area of my rudders as a percentage of my A Class cat daggerboard respect to that of rudder.
Regarding the aspect ratio of our foil : taller foils have more lift, less drag but also generates greater heeling moment than lower ones and viceversa. A common high performance daggerboard has a value of 2.8 and more for the aspect ratio, even if i think more extreme AR can be used well, this means that a 110 cm daggerboard is wide about 34cm (heigth is intented from the tip to the lowest point of daggerboard case). This daggerboardhas a area of 0.375m^2 with a percentage %SA of 1.25% and with an aspect ratio of 3.2. These seems good numbers to me, tell me if you would do it different.
I'm sure you are asking yourself " but ?... what about this centerboard section?".
Well, first of all we have to say that a catamaran sailing upwind has very small angle of leeway ( this is due to the high speeds achieved and to the long and thin shape of the hulls), so we can choose thin section obtaining by this way less drag. Usual section used are the 4-digit NACA series,
even if more extreme foils can ( and to me should )be used, i'm talking of the 6-digit series ( 63, 64 and 65 series). These foils can work only in a restricted range of angles of attack AOA, but ensures less drag while keeping the same lift coefficient. This is opposed to foil needed on the rudders as these ones work under a greater range of AOA than daggerboards.
I have to say that asimmetrical foils can be used in order to reduce that drag given by the leeway angle of the hull and daggerboard. This implies naturally that only the leeward foil is pull all way dawn in its case, as the other foil would work in the opposite direction. The same result is reached even with simmetrical foil on simmetrical hulls, becouse a cat hull moving with a heel angle of 5-7 degrees generates a true asimmetrical hull shape that help keeping the leeway angle very low. (see picture demonstrating this concept )
Regarding the thickness/chord ratio is about 0,09.So a common foil wide 44 cm is thick 3,96 cm. This means that we are going to use sections as NACA 63-012.
Let's talk about our foil planform. Somewhere i have red that for a foil working near to another surface (water level in this case) the ideal tip is not rounded as believed before but squared. This should reduce drag vortex on the tip and the heeling moment. It follows further treading on this interesting aspect.
The rudder gantry is a point of main interest since it has to
insure a rigid platform to substain the rudder but also a easy retract system in
order to avoid failures in case of precarious landig on beach or whatsoever. But
we will talk about this later.