By Paul Austin Jr.- Irving, Texas - USA

This article will deal with the balance of boats—masts, sails, and lateral resistance. The basic concept is that when the wind is caught by the sails, its force is transferred to the center of the boat. If, say, you put the sail all the way forward with no board or rudder, the boat would spin around like some teenager doing a wheelie in a Bonneville while he listens to the Beach Boys. If you want to irritate the older generation or sling off the stern the chucklehead who’s dating your daughter, fine. Boat spinning has a certain shameless, mindless fun to it.

But if you want to get anywhere, the sail and the boat will have to work together. Joshua Slocum often said he spent many hours away from the rudder because Spray was so perfectly balanced. What this means in a general sense is that the sail is directly over the deepest part of the hull, and both of them are in the middle of the boat.

This is Philip Bolger’s Elegant Punt. It’s easy to see the leeboard directly below the sail. If there were no rudder the boat would sail at its fastest, and in theory, straight. In order to get to that point, you need fasting, prayer, and perfect balance.

The problem is, as the crusty old guy with the beard and pipe on the waterfront says, there ain’t no formula in the sand for getting perfect balance. In the past, designers just starting out copied previous boats. Some learned more from this than others, but somewhere laying in the bilge were the good guidelines.

If you take a lawn chair with a mint julep in one hand, put the lawn chair in the river and sit down, you’re going to go floating down the river along with the water. But what if you want to float to the other side of the river? Then you’ll have to stick your other hand down in the water, to resist it in order to go sideways across to the other bank.

If you hold an umbrella with one hand while your other hand is in the water, to get across the river, the wind in the umbrella will push you against the water. With your hand resisting that water, you’ll get across the river at an angle. This is the principle of wind into a sail while the shape of the boat resists the water.

Throughout the centuries we’ve learned if the resistence to the water is at the bow, the stern just swings around to smash other boats. Fun, sure, but you pay while the judge laughs. Now if you put the resistence at the stern, things get better. The boat steers some, but not enough to get anywhere before dark. So back ages ago, some genius put the resistence in the center of the boat, and voila, he got his boat across the river.

Moses in the bushel basket floating down the Nile is one thing. Christopher Columbus waiting for a favorable wind is better, but what’s best is when your hand is directly below the umbrella.

As a result, designers have figured out how to get the resistance of the boat directly below the center of the sail. These things are not perfect, since a sail catching the wind fills out, changing its shape. And when the boat leans over, it changes the shape of the hull in the water. This stuff isn’t exact but it’s close enough.

The lean of the wind on the umbrella is called, center of effort. The pressure of the water on the lawn chair is called center of lateral resistance. When one is directly above the other, fill the glass with another julep because life is good.

What designers do is draw the sail as a triangle. Then they find the midway point along any one of the three sides. From this point they draw a straight line to the angle opposite that side. The measure 1/3 of the way from the side used. That will be the center of the triangle, reasonably close to the actual center of effort. So far this is pretty simple, and fairly accurate.

But now for the hull. The center of lateral resistence is the midpoint of the waterline length. This, however, is not so exact. Boats differ in shape, some have
keels while some have centerboards.

Probably the easiest way to get the general point of lateral resistence is to draw the profile of the hull on a flat piece of paper and then balance it with a pin through the mid point. Where it balances is the point of lateral resistence.

Below is an illustration of the pinned paper technique. It probably works well enough with small boats, especially flatbottomed boats with one topside panel.

In Skene’s Elements of Boat Design, Mr. Skene gives the mathematical formulas for finding balance exactly. It amounts to creating squares of wetted surface and adding them together. When you get a grand total, you divide it. I don’t do that, since I can’t even balance my checkbook.

What is relevant is that the center of effort should be forward of the center of lateral resistance. This is called lead, pronounced, leed. Flat-bottomed boats often have lead of 15 % of their waterline length.

Usually designers will either not consider the rudder as lateral plane, put it in, or put the forward third of the rudden in. Ted Brewer says he uses the forward third of the rudder as part of the lateral plane.

But what if you have more than one sail? You’ll have to put your spectacles on and crunch numbers. Now if you want to know how to add, subtract or divide, don’t be sending me any emails. I was an English major, I know how to stick pins in cardboard.

Think of your two sails as a chubby boy and a skinny boy on the see-saw. That skinny little blister will have to be further away from the pivot point to balance out the chubmeister. So it is with the sails. The bigger sail is given a sail area called ‘weight.’ The distance from its center of effort to an axis we’ll choose is called its ‘arm.’ So weight times arm equals a number called ‘moment.’

These terms are our booklearning. You know stuff now. So let’s draw two sails and crunch some numbers on them to figure the cente of effort for a main and jib daysailor.

  • The main will be 100 square feet of sail.
  • The jib will be 25 square feet of sail.

The axis is at the main’s center of effort, so the distance between the CE of the main and the CE of the jib is 10 feet.

Where the two blue lines intersect the red line are the two CE.

If we take the sail area times the arm, we get the moment. So since the SA of the main is 100, and the axis is its own CE, then it is 100 times 0=0. Nothing from nothing leaves nothing, as the song says. This much I can get.

Now if we take the sail area of the jib— 25 square feet—and multiply it by its arm, which is 10 feet, we get 250. So with the total sail area, 125 feet, divided it by our 250, we get the answer as 2 inches. Here we measure forward from the main CE along the red line 2 inches and that is our lead. If the boat is 20 feet long, 2” is a lead of 12 %.

If there were no lead at all, the boat would want to head toward the wind, hard. This is called ‘weather helm.’ Some is good, more is less good. If the boat wants to head away from the wind this is ‘lee helm.’ This is not good, and at times with big ships in storms has led to capsizing.

Lee helm means the adjusted CE is too far forward of the center of lateral resistance. Weather helm means the adjusted CE is aft of the lateral resistance. For the sake of clarity I have not shown the CLR, which would presumably be between the adjusted CE and the mast. In any case, the rudder must be designed with lead in mind.

From the designer’s point of view, there is a great deal more to this than a flat sheet of paper. How the topsides curve, how many panels, is it carvel, and the center of gravity—all these things go into a balanced boat.

I have to admit I admire those old ship designers who could get all this right on clipper ships, schooners, brigantines. That’s plenty of addition. Or maybe the addition was the rum.


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