# Thread: Advanced questions regarding CoE - CLR balance of small boats

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## Advanced questions regarding CoE - CLR balance of small boats

When it comes to balancing the sail plan to the hull of a sailboat, we all know the basics: Center of Effort, the force on the sail, must be in line with Center of Lateral Resistance, or be somewhat forward of it, creating the so called "lead". Boats, especially small ones that are designed to be sailed flat, usually have little or zero lead, while those that are expected to heel, have a larger lead, 5-10%, to account for the turning moment.

For round-bottomed hulls, and hard-chine boats that are still reasonably round, the hull shape is usually neglected, and the CLR is estimated to be at the center of the area of the centerboard/daggerboard. Some say that rudder should be taken into account too, but only calculating 1/3 of it's area. I always disregarded rudder in my designs, and it worked out well.

It is also known that for the boat to have negligible drift, the area of the board must be at least 3.5-4% of the sail area.

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These are the premises that I always took for granted, and it worked out fine for me. Correct me if you see a principal mistake there.
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However, there are some situations where I'm convinced there are more, significant factors to account for when designing a well-balanced sailboat. I will describe each of them.

1) In a boomless-rigged boat, the lack of boom results in a much greater force on the sheet.

People seem to disagree on this, so here's a quote from Philip C. Bolger's book "100 Small Boat Rigs", page 11-12:

In the boomless rigs, all the force that drives the boat is delivered along the line of the sheet. The effect is as though the boat were being towed by a tug with a the towline attached at the sheet block. Such a towline would tend to swing the boat around. When towed by the sheet to the sail, the turning effect produces weather helm. The pull of the luff of the sail on the mast is to leeward and somewhat aft. This partly compensates for the off-center towline, but the boats setting boomless sails will normally carry more weather helm than boats with booms and should have their rigs stepped farther ahead on the hull.

The question is, how much extra lead is needed to compensate for it, compared to an identical boat and rig, only with a boom? How does one estimate it?

2) Next, the question of additional appendages with very low aspect ratio, like a skeg:

While a centerboard or a daggerboard is usually long and thin, developing lift and working like a wing, the skeg only provides brute lateral resistance due to it's low aspect ratio. And yet, it's effect is measurable, which is very evident from added directional stability when rowing.
So, if a boat has both the skeg and a board, how does one calculate the net effect of the two? The centroid of sum of areas of the two can't be right, because a board is more effective, especially in higher speeds. So, how much does the skeg move the CLR aft? How much can it be utilized to move the CLR into the desired position?

3) Then, what about hulls that have steep sections that contribute to the lateral resistance? GIS, for example, has very little flare throughout it's length:

Which could possible mean that the lateral resistance is more or less consistent throughout the length of the boat. Not so simple in a hull of a racer like a National 12 (at least in this specific example), which can have a significantly variable flare:

Obviously, the bow section is steep, meaning it will provide a lot of lateral resistance, but as it goes aft, the profile becomes more round, offering less lateral resistance. Therefore, this kind of hull will move CLR forward - question is, how much?

While it's safer to neglect it's effect on the amount of lateral resistance, relying solely on the 3.5-4% rule of the board, it might be dangerous to neglect the change of location of the lateral resistance of such a hull - it could change the balance in an unexpected way, not always correctable by sitting more forward or aft or raking the mast.
So, the question is, when does the hull shape start to matter on the location of the CLR? What flare angles, how does beam curve come into play? How strong is this lateral resistance, compared to the lateral resistance provided by the centerboard/daggerboard?

I know that making a accurate, complete analysis of all these variables is next to impossible and impractical in small boats, short of performing tests in wind and water tunnels, or asking the America's Cup boat designers to "lend" their supercomputers to run these incredibly complex simulations.

But I would not rather eyeball it either. Say I am designing a flat-bottomed skiff with variable flare, a skeg and a boomless sail. While any one of these characteristics might not do too much damage on the balance of the boat, the net effect of the three might turn the boat into a steering nightmare.

What I am asking here is some rules of thumb, general estimations and assumptions that would allow me to make a reasonably accurate guess of how these characteristics play together, and to build a boat that doesn't run from the wind on it's own, nor spends most of it's time in irons.

Thank you in advance. Hopefully whatever information you can provide will prove useful to other sailors and builders as well.

2. ## Re: Advanced questions regarding CoE - CLR balance of small boats

Then, what about hulls that have steep sections that contribute to the lateral resistance?
More experienced designers may correct me here, but I believe that on a traditional built-down hull (such as my near-Friendship sloop), those "steep sections" are refered to as "salient keel". And yes, from my experience, the difference in form does make considerable difference to helm balance:

My 19' sloop drew 3'3". A couple years ago I modified her underwater profile when I notched her keel and shifted about 35% of her ballast outside --I gave her 1" more draft in order to get a bigger chunk of lead down there. The increase to 3'4" was entirely salient keel: a rectangular-sectioned lead ballast keel, with a wood "wormshoe" added aft, and a wood filler piece directly ahead of the ballast keel to fair the straight run of the keel into the stem. The sides of all the additions were 90° to the flat underside of the keel; in keeping with the original shape, I did not round them at all. Most of the increase in surface area was located abaft her CLR.

When I next launched her, much to my surprise her significant weather helm had decreased substantially. I had hoped for maybe a little bit of improvement, but just 1" of draft, about 9' long --so 108 square inches-- changed her enormously. The change is stunning. Her helm is only about half as heavy as it was, her speed has increased accordingly, and she now tracks well enough to heave-to. Yes, some of that helm change is the increased moment arm of the lower ballast keeping her more upright, but even at a given angle of heel, her helm is markedly lighter.

I don't know a thing about how to calculate it, but I'm about ready to "shim" my sloop's keel down, year by year, giving her another 1/2" per year until her helm balances out perfectly!

Alex

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