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post #29 of Old 09-24-2012
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Re: Moment curves

The question is what do area curves tell us about a boat's performance?
First off I had better define "area curves". Boats are laid out with a series of tranverse stations, i.e. station 0 at the cutwater and station 10 at the intersection of the counter or stern profile with the DWL. I call this the "buttwater" because I think it sounds funny and is kind of accutrate. Armed with a ten station breakdown and some calculus the designer can determine the volume and distribution of the volume of a new design. Today the computer does it all. Years ago we did it all by hand with a slide rule or a calculator. An area curve shows the distribution of volue in a hull by plotting the area of each station along a horizontal line, usually the plan view centerline of the lines drawing. The curve is only a graphic dislay of what the numbers tell you. You do not need the curve, but it is fun to look at and can help especially when you overlay them for similar length designs. You can heel the boat over, maintaining the LCB/VCG alignment and also look at what happens to the area curve. Now you have a "heeled area curve".

Take a tube. Cut it in half lengthwise and put identical points on each end. Call it, for argments sake, a long, very skinny boat hull. With points on both ends it's a "ouble ender". As you heel this hull over it will rotate around the center of the arc with the centerline of the half tube staying parallel to the DWL. But boat hulls are not tubes cut in half. Most boat hulls are complex, asymetrical fore and aft shapes, the bow is pointy the sten is wide.

The closest thing we have in a real boat to our tube is a double ender ,like the Westsail 32. It's fatter with a far more complex sectional shape but fore and aft it is almost symetrical, i.e. it's hard to tell the bow from the stern once you ignore the curved stem and the straight stern post. A curve of areas for this hull will almost be symetrical around station 5. Or, damn close to it.

You see the same thing in long, skinny boats like 12 meters or 6 meters. Fore and aft they are almost close to symetrical. So, as they heel over they alomost rotate around a line running parallel to the DWL. Keep in mind the LCB, Longitudinal Cneter of Bouynacy will always stay right above the LCG, Longitudinal Center of Gravity. Always. If it does not, then the hull will automatically alter the fore and aft trim so the LCB is right over the LCG.

This is where it gets tricky.

If you take a modern beamy boat with a big fat fanny and a really pointy bow then you have the antithesis of our "tube boat". The fore and aft distribution of volume is going to be scewed well aft with the LCB being around, say 54.5% of the LWL aft of Sta 0. As this very asymetrical beamy boat heels over the volume immersed forward will not be enough to keep the boat rotating parallel to the DWL. The bow will need to immerse more than the stern to pick up new volume and when the bow goes down the stern comes up. Always. I call his "rolling down". The result is the waterlines that stayed almost symetrical fore and aft in the Westsail now become very asymetrical and distorted. Our once almost syemtrical "heeled waterline" now has a big bulge to leeward and is almost straight on the weather side. We are shoving a very strange, asymetrical shape through the water.

Plotting heeled curves of areas can help the designer predict just how much the boat is going to roll down when heeled. If you had a boat with a really full bow and a picnhed stern the exact oppropite would happen. The bow would pitch up as the boat heeled and the stern would roll down. But today we don;t see boats like that.

If you were doing a gran prix race boat you may want to do a study on heeled conditions to determine changes in Cp, LCB movement and wetted surface. Distorted heeled waterlines can give a boat wild changes in personality as it heels. You've heard people say, "You have to sail it flat." The boat with distorted heeled waterlines is not the same shaped boat at 25 degrees of heel as it is a 5 degree of heel. While with a boat like the old Valiant 40 the boat loved to be driven hard and tipped on it's ear. The balanced hull shape of the V 40 means that the hull shape does not change much as the boat heels through 30 degrees. The bow does not roll down and the stern does not pitch up. This is why for a well behaved boat I like to start the design proces by determining just how skinny I can make the boat. Skinny boats have better manners, generally speaking.

I've probably over simplified this. And, no doubt diagrams and illustrations would be a huge help. Check out Steve Killing's book YACHT DESIGN EXPLAINED. It's the best.

Before you come back and attack me think twice. Do some extra research and if you still think I'm wrong bring it on. But I warn you, I didn't invent these relationships. I have only observed them. Hope this has helped a bit.

Time to walk the dogs.

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