daggerboard horizontal lift force

i am trying to figure out the chord and length of a straight daggerboard that i am designing, to reduce the leeway on 30-45ft displacement monohulls. i have already picked an asymmetrical foil based on Cl, Cd, Cm etc...

my question is how much of a horizontal lift force must a daggerboard generate to work against the leeway when going upwind? typical speeds of 6-9 knots.

100 lbs ?
200 lbs ?
300 lbs ?

is there an easy way to calculate this?

thank you.
Oz.

 

The daggerboard horizontal force equals the side force applied by the sail rig and topsides. This is true regardless of the design of the daggerboard. The leeway angle adjusts to maintain this equilibrium.

You can drive the leeway angle as low as you want by making the daggerboard large enough. But an excessively large daggerboard will be draggy. You can also make the leeway angle, measured from the hull centerline, any value you want by changing the incidence or camber of the daggerboard. You can think of this as being like having the daggerboard moving through the water on its own, and mounting the hull on top of the daggerboard while pointed in the desired direction. So minimizing leeway, in itself, is not a very useful design criterion.

What you really want to do is to provide the necessary side force with minimum drag. And you need to balance the size of daggerboard that minimizes the drag at high speed with the size of daggerboard that is needed when tacking and accelerating from low speed. The two biggest sources of drag on the daggerboard come from skin friction on the board and from the side force developed by the board.

You can reduce the skin friction by cutting the chord, making the board more narrow. This will also increase the leeway angle. You can reduce the drag due to the side load by making the board deeper. If you combine these two approaches, you end up with a board with a high aspect ratio, making it both deep and narrow.

If you don't know the aerodynamic loads, then probably the best thing to do is to make the area of the board a percentage of the sail area, based on successful designs of similar boats. You probably have some idea of the maximum depth that is acceptable for the intended cruising grounds, and this can be used to set the length of the daggerboards.

 

Tom,
the idea of percentage of the sail area sounds good however which boat is an example of a displacement monohull with daggerboards? they tend to be race boats, which have less hull in the water and are not a good replica of what i am trying to do.

I am looking for a ball park number for a say 40ft disp. mono. what kind of lateral force do i need to generate with the DB for a 5 degree less leeway?
Cheers.
Oz.

 

People think about leeway in completely the wrong way. Its not really the boat slipping sideways in a parasitic way, its the necessary angle of attack that the boat must make to the water to provide the necessary lift.

Lets make a very over simplified example by ignoring the hull.

Consider a centreboard boat that makes, say, a course made good of 45 degrees to the wind, and in order to do it has the bow pointing at 40 degrees to the wind, which we call 5 degrees of leeway.

Now rotate the centreboard 5 degrees to the hull. The boat now makes zero degrees of leeway. Does it sail at 40 degrees to the wind? It does not. It still makes good a course of 45 degrees, but now the bow is pointing at 45 degrees, not 40. Your actual performance on the water is unchanged. Rotate the board another 5 degrees and you'll make 5 degrees of negative leeway - the bow will be pointing at 50 degrees to the wind, but the boat will still make good a course of 45 degrees.

So, as Tom Speer says, you are really asking the wrong question. The amount of lift from the hull/foil combination will be the same no matter what leeway angle. All else being equal, the bigger the daggerboard you have the less leeway you will make. If you have an asymmetric section daggerboard mounted at an appropriate angle it could even go negative. But much of the effect will be on the angle of the hull to the wind and not on the course made good through the water.

I don't think you're going to get a quick rule of thumb for what size daggerboard will give the greatest improvement in the actual performance of this boat through the water, which is what you should care about. Whether that's with 5 degrees of leeway, 2 degrees of leeway or even -5 degrees really doesn't matter. Its going to depend on dozens of variable to do with rig, hull shape and goodness knows what else. You may also find that in the end the biggest design factors are not to do with performance. How much room are you prepared to sacrifice in the boat for daggerboard cases? How much draft can you have without hitting rocks all the time? But any reasonable size, well profiled daggerboard is going to make an improvement because daggerboards are so much more efficient at generating lift than hulls are.