Jim Michalak's Boat Designs
118 E Randall, Lebanon, IL 62254
A page of boat designs and essays.
(1Jun00) This issue reruns a most important issue about Sail Area Math. Next issue, 15Jun00, will give a method of jiffy reefing a balanced lug sail.
The 11th annual Midwest Homebuilt Boat Messabout will take place on June 10 and 11 at the Gun Creek Recreation Area at Rend Lake in Southern Illinois. Take exit 77W off I57, head towards the golf course and you will see the signs. Lots of people arrive on Friday and leave early on Sunday. The camping fee is $10 which includes the ramp fee at this Corps of Engineers facility. There is no schedule of events. We have a pitch in dinner on Saturday evening.
Left:
Bruce Given at work. 



SAIL AREA MATH
BACKGROUND...
If you look at the picture below of the sail rig of Mayfly12 you will see on the sail some (fuzzy) writing (that didn't scan well) that says "55 square feet" to the left of a small circle that represents the center of that area (honest).
The center of that area is often called a "centroid" and you will see it is placed more or less directly above the center of the leeboard's area. That is very important.
As you might imagine a shallow flat hull like this with a deep narrow leeboard wants to pivot around that leeboard. If the forces of the sail, which in a very general way can be centered at the sail's centroid, push sideways forward of the leeboard, the boat will tend to fall off away from the wind. You should be able to hold the boat on course with the rudder but in that case the rudder will have "lee helm" where you have to use the rudder to push the stern of the boat downwind. The load on the rudder will add to the load of the leeboard. Sort of a "two wrongs make a right" situation and generally very bad for performance and safety in that if you release the tiller as you fall overboard the boat will bear off down wind without you.
If the centroid is aft of the leeboard you will have "weather helm", a much better situation. The rudder must be deflected to push the stern towards the wind and the force on it is subtracted from the load on the leeboard. Not only that, but when you release the tiller as you fall overboard the boat should head up into the wind and stall and wait for you if you are lucky. It's a good deal but if you overdo it you can end up with too much load on the rudder.
This balance problem is actually one of the few things about sail rigs that is not arbitrary. The type of rig and its area are pretty arbitrary depending on how fast you want to go, how much you weigh, etc. But balance is quite important and is one of the areas where backyard boaters get into trouble, sometimes changing the boat or rig with no thought of balance. So before you go doing that you should do a little homework. This essay will tell you how to figure sail area and find the centroid.
One last item: the balance situation shown for Mayfly12 is what I have found to be best for this type of boats. Boats with large fin keels don't balance that way  usually the sail centroid is well forward of the keel centroid. That distance is called the "lead". That type of boat is not within my personal experience and I'm not going to get into that. But you still would have to figure the area and centroid.
THREE SIDED SAILS...
This one is really easy. The area is just the base time the height divided by 2. Any side can be the base and the height is aways at a right angle to the base.
So when you lay out the sail you draw it up on thin paper to the same scale as your hull drawing with the leeboard (or daggerboard or centerboard) lowered. Draw a line through the center of the board straight up. Now we're going to locate the scale sail on the boat such that it's centroid falls very close to that line.
Here's how you find the centroid of a triangular sail.
Find the midpoint of each side and and draw a line from that midpoint to the vertex opposite it. The three lines will intersect at the centroid. Actually you only need to find the intersection of two lines but the third line is a good check.
That's it! Now you can take you scale sail drawing and slide it around your hull drawing until the centroid is on that line drawn up from the hull's board. Move it up and down and tilt it until you like the way it looks. But don't cheat much forward or aft of that line.
FOUR SIDED SAILS...
To find the area of a four sided sail you just divide it into two triangles, find the area of each triangle as above, and add the two together.
Now to find the centroid of the four sider. Start by finding the centroids of the two triangles that make up the four sided sail as shown above. Now draw a line from one triangle centroid to the other. The centroid of the four sider is on that line somewhere.
To find exactly where the centroid is on that line, measure the length of that connecting line. You need not use the same scale as is used on the drawing. I prefer to use a millimeter scale for this measurement. Then get out the calculator and work the formula shown in the Figure 4. Let's say for example the length of the connecting line on the scale drawing measures 120 mm (that is measurement L). Let's say the example sail has a lower triangle area of 50 square feet (that is A1). The upper triangle is 35 square feet (that is A2). So the total sail area is 50 + 35 = 85 square feet. The length L1, which will exactly locate the sail's total centroid, is L1 = 120 x 35/85 = 49.4 mm. So you take that millimeter scale and measure up from A1 centroid on the connecting line 49.4 mm and make a tick mark on the connecting line. That is the centroid of the total sail.
Another way to find the centroid, especially of a really odd shaped sail, is to take the scale drawing of the sail and cut it out. Then balance the cutout on a knife edge and mark the balance line, rotate the cutout on the knife edge about 90 degrees and rebalance and mark the new balance line. The centroid lies at the intersection of the two line.
Another way is to dangle the cutout on a pin stuck through a corner and into a wall marked with a vertical line that passes through the pin point. Mark the line that passes through that pivot corner and a vertical. Then rotate the cutout to hang it from another corner, and mark a second line through the second pivot corner and a vertical. The centroid lies at the intersection of those two lines. Back at the missle factory the designers had a favorite place, complete with pivot pin socket hole and vertical line, to hang these cutouts and that place was known as the "weighing wall". Meanwhile the super computer cranked away next door but its answers weren't to be trusted unless they agreed with the cutout hanging at the weighing wall.
RIGS WITH MANY SAILS...
Figure 5 shows the rig for Viola22. It has a main gaff sail of 177 square feet, and a mizzen sail of 45square feet. Where is the centroid of the assembly?
It's done exactly as with Figure 4. Draw a line connecting the areas of the two sails. Measure the length of the connecting line. Then run through the same equation as in Figure 4. Nothing to it.
One thing I might point out about the Viola22 rig is that the total centroid falls near the aft edge of the leeboard. By my experience the mizzen is not as efficient as its area suggests so it needs to be a bit oversized by normal rules, fudging the total centroid aft. I think in general the aft sails operate in the scrambled flow of the forward sail, causing loss of force back there.
NEXT TIME...
I'll show how I reef a balanced lug sail.
AF4Breve
AF4Breve, POWER CUDDY SKIFF, 15.5' X 5', 350 POUNDS EMPTY
Bruce Given of Virginia Beach, Virginia, did a perfect job on the AF4B prototype shown above. He said he didn't have the shop space to build the 18' AF4 and when I saw the photo of him working I believed him. So I scrunched the 18' AF4 down to 15.5'. I took 1' out of the cabin shortening it to 7', 1' out of the cockpit shortening it to 5', and 6" out of the motor well. I'm pretty sure everything is still acceptable, although the longer AF4 might still be preferred if you can live with the length. The width and depth of the cabin and transom are tha same as AF4's.
To a certain extent you could build the shorter boat without new plans by scrunching up the length dimensions. That method would be a lot more reliable for a simple flat iron skiff like this one. For more complex shapes where all the panels are expansions, including sides, bottom and bilge panels, it would not be so reliable. Bill Wainright built the original Smoar rowboat by scrunching up the Roar2 drawings but he is a sculptor and did the job with a model. Later I drew Smoar from scratch. Also the bevels shown on the long boat drawings will not be correct. That might be no problem with a taped seam hull.
So AF4B is a totally new set of drawings. There are two changes made besides the scrunching. I made the bottom 1/2" thick instead of 3/8" as I built into my AF4. Most folks would prefer the extra stiffness. On AF4 I think of the bottom flexing only when running hard into chop. The extra thickness finds its way into a lot of other parts since they are made from the off fall of the bottom panels. You could make the bottom from 3/8" ply and save about 50 pounds on the total weight. The second change adds a bottom to the bow well which lifts the well bottom up about 18". It is more complex to build but the original deeper well is hard to reach all the way into. The area below the new well is accessible from the cabin for an iota more storage.
Still suggesting 10 horse power max.
AF4B is simple nail and glue construction with four sheets of 1/4" plywood and four sheets of 1/2" plywood.
Plans for AF4B are $30.
Prototype News
Some of you may know that in addition to the one buck catalog which now contains 20 "done" boats, I offer another catalog of 20 unbuilt prototypes. The buck catalog has on its last page a list and brief description of the boats currently in the Catalog of Prototypes. That catalog also contains some articles that I wrote for Messing About In Boats and Boatbuilder magazines. The Catalog of Prototypes costs $3. The both together amount to 50 pages for $4, an offer you may have seen in Woodenboat ads. Payment must be in US funds. The banks here won't accept anything else. (I've got a little stash of foreign currency that I can admire but not spend.) I'm way too small for credit cards.
Here are the prototypes abuilding that I know of:
Jonsboat: Jonsboats by Greg Rinaca and Chuck Leinweber showed up at the Lake Conroe, Texas, messabout last month. Here is Greg's with a trolling motor. Full report next issue.
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We also have the start of a Jon Jr, a 12' x 3' personal sized jonboat, down in Texas. Here is the latest photo with the bottom going on.
IMB: Also at the lake Conroe messabout Jerry Scott's prototype IMB got into the water. A full report when I receive one.
Mayfly12: A Mayfly12 is going together up in Minnesota. It is now complete except for painting. Here is a construction photo from last summer.
Robote: Robote is supposed to be a fast somewhat extreme rowing boat based on my old WeeVee design, thus it has a deep V bottom but is stretched out to 14' long with a very pointy bow. It was drawn as a custom job but if it works out I'll put it in the catalog. The boat is now complete and launched but waiting for final photos and test results.
Herb builds AF3 (archived copy)
Hullforms Download (archived copy)
Plyboats Demo Download (archived copy)
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