Advanced questions regarding CoE - CLR balance of small boats

Far as I know any rudder area will affect CLR, no matter of the rudder type, so the rudder has to be taken into account to determine CLR, I believe.

 

I don't know. Maybe. Some reputable authors say it doesn't have to be taken in account, some say that 1/3 of rudder area is to be taken in account. I have never been able to determine who is right. I never took rudder in account in my designs, despite the fact that I like big rudders. It always worked out as expected.

 

Balanced rudder need adequate area ahead the rotation axe , not necessarily under the hull. You can achieve this with
a constant chord daggerboard rudder (like you showed) by angling the cassette relating to the axis of rotation.

 

Angelique and Laukejas, you are both right
Balanced rudders are commonly used on racing catamarans. if you trim your boat (mast rake) so the COE corresponds to the CLR without
taking into account the rudders, you need no lateral force on the rudder to go straight , i.e. zero the angle of attack of the rudder relating to the flow
which corresponds to the helm a littlle to leeward (the angle corresponding to the drift). But if you have a good high aspect ratio rudder you can decrease the total induced
drag (rudder + center board) allowing the rudder to contribute to the lateral force. To do this you move your sail CoE aft ( e.g. by raking the mast aft). Now
to go straight you need a constant lateral force on the rudder, so a constant non zero angle of attack relating to the flow. In this case, you have to
account the rudder to determine the Total CLR. But the draw back is you need an effort on the tiller for an unbalaned rudder, which looks to weather helm :
so the racing catamaran rudders are balanced to get a lighter helm !

 

Thank you very much for this explanation, it makes a lot of sense. But still, it would be great is someone could help out with my initial questions.

 

On small boats like this I tend to follow some basic rules. Jim Michalak’s newsletter archives has a fair bit of information about this. Generally, place the CE over the deployed leading edge line of the centerboard (Michalak’s approach). I usually place it a tad aft of this on sloops, but it works well on cats. Balance the boat's trim with a normal crew load, so the bow can just kiss the LWL, not remain immersed as drawn, of course the stern should be clear as well, so you might need more rocker for the anticipated loading/trim. This will dramatically move lateral area aft. Use 4% area rule for the board. I'd shoot for a 10% - 12% lead, to be safe. Make the stick plumb, with the intent to have a bit of weather helm, the idea being you can rake the stick a degree or two aft, which looks good, but isn't excessive, if the helm is too heavy. Given the long, shallow skeg, you'll have a fair bit of freedom in this regard, as it helps dampen the weather/lee helm issue (assuming the bow is free/clear).

 

Well, thing is, since it is a very small boat, balancing trim can be very limited with the full load of two people. As you can see from the drawing, at full displacement, the forefoot is already submerged, and the transom is just above the water. Moving crew weight fore or aft will either drag the transom, or bury the bow. I don't want to build in any extra displacement, because the boat will ride too high with a single sailor. It's a compromise. Boat has to sail reasonably well with either two sailors, or one. With a single sailor, the forefoot is just touching the waterline as you said, but I can't make it happen with two sailors too.

Could you please elaborate on the 10-12% lead suggestion? How did you come up with that number? How did you include the characteristics of the boomless sail and the size of this specific skeg into it? When you suggested that number, did you assume the CLR to be at the leading edge of the board, or the combined center of area of the board and the skeg? Because if the former, that would place the centerboard awfully aft.

I'm sorry to be so persistent about this, but I really want to understand how all this works, exactly. I'll try to find Jim Michalak’s newsletter archives, hopefully they are available online.

 

Jim Michalak's Boat Plans.

Jim's twice monthly online newsletter, back issues at the bottom of the page.

Archive of Jim Michalak's Newsletters.

Jim Michalak builders discussion group at Yahoo.

 

Thank you very much, that's a load of good information.

I still hope some other experienced builders and designers will visit this topic and share their own expertise on these three questions in my initial post.

 

This document contains good information http://www.hiswasymposium.com/assets/files/pdf/2012/Claughton HISWA 2013.pdf .

 

Thank you for the link, I went through it all. There is good information, but except for Munk moment, I already knew most of it. Sadly, it doesn't really explain how to estimate the combined center of lateral resistance of appendages with distinctly different effectiveness (like centerboard + skeg)...

 

To answer your original question, which I can only boil down to "How does one estimate CLR?", the answer would be, in one word: roughly.

 

"Roughly" would be good enough for me, because right now, I'm clueless. For example, about skeg's effectiveness compared to the daggerboard. How less effective is it? 50% less effective? 75%? 10%? Frankly, I have no idea whatsoever. Same for how much a steep-side bow section would move the CLR to the front, and how much weather helm does a lack of boom add. I just want to get in the ballpark.

 

The formula for the CLR of two combined foils at same angle of attack is a simple barycenter formula
XCLR = (S1*CL1*xclr1+S2*CL2*xclr2)/(S1*CL1+S2*CL2)
where XCLr i are abscissa from a common origin, Si areas, and CLi lift coefficients.
You can assess the lift at 5° angle of attack, and account for the aspect ratio of the foils.
A skeg is a low aspect ratio delta shape wich develops very little lift at low angle of attack.
You can find the formula ror lift coefficient in any aerodynamic textbook !
You need to account for the mirror effect of the hull on Aspect ratio
,which is roughlly multiplyed by 2

 

Finally! Thank you very much, that is extremely useful bit of information. I think I understand it, except for the "mirror effect of the hull on aspect ratio". Could you please explain what it is? I don't seem to find much on google.