Jim Michalak's Boat Designs
118 E Randall, Lebanon, IL 62254
A page of boat designs and essays.
(15Jul05) This issue will repeat the sailboat math essay. The 1 August issue will continue the Bobsboat series.
THE BOOK IS OUT!
BOATBUILDING FOR BEGINNERS (AND BEYOND)
is out now, written by me and edited by Garth Battista of Breakaway Books. You might find it at your bookstore. If not check it out at the....ON LINE CATALOG OF MY PLANS...
...which can now be found at Duckworks Magazine. You order with a shopping cart set up and pay with credit cards or by Paypal. Then Duckworks sends me an email about the order and then I send the plans right from me to you.
Left:
Garth pushed the big Cormorant project to completion, and added a water slide. 



Sail Area Math
BACKGROUND...I have to rerun this essay every year. This subject is the most common area where tinkerers of designs get in trouble. It always has been and always will be. Anytime you modify the sail rig you need to keep this math in mind.
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...
...We'll delve into Bobsboat's bevels.
Mayfly16
MAYFLY16, SAILBOAT, 15.5' X 5.5', 350 POUNDS EMPTY
Mayfly16 is large enough to swallow up three men or maybe a family with two kids. She has two benches that are 7' long and there should be plenty of room for all. I would say that her fully loaded maximum weight might be 900 pounds and her empty weight about 350 pounds, leaving 550 pounds for the captain and crew and gear.
At the same time the Mayfly16 can easily be handled solo, although with just the weight of her skipper she will not be as stable as when heavily loaded. The boat also has two large chambers for buoyancy/storage and I can see her used as a solo beach cruiser because the floor space is large enough for a sleep spot. I've made her deep with lots of freeboard.
Mary and George Fulk built the prototype and passed by here with the prototype on their annual migration north for the summer and I had a chance to see and sail in Mayfly16 for a short bit. Weather was hot and the wind light and steady, perfect for testing. She sailed quite well I thought and everything worked as planned. It certainly was roomy and easy to rig and use.
The balanced lug rig sets on short spars and sails very well reefed, in fact can be set up with jiffy reefing. The spars are all easily made and stowed, the mast being but 14' long setting 91 square feet of sail. In addition there are oar ports for those with lots of time and little money and a motor well for those with lots of money and no time. Two horsepower is all that a boat like this can absorb without going crazy.
The motor well is an open self draining well that uses the full width and depth of the stern. It will come in handy for storing wet muddy things you don't want inside the boat, like boots and anchors. I've suggested in the plans that the rudder can be offset to one side a bit to give more room for the motor. We did not use George's little Evinrude since the boat sailed easily in all directions, but George says the sidebyside sharing on the stern of the motor and rudder works fine. There was no interference with the rudder. (As with any outboard on any sailboat, the motor has a desire to grab the sheet with each tack so you usually have to tend the sheet a bit.)
Mayfly16 uses conventional nail and glue construction needing six sheets of 1/4" plywood and two sheets of 1/2" ply.
Plans for Mayfly16 are $35.
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.
The AF4G is done and launched. Writeup after testing:
Garth has the big Cormorant done and has spent a family vacation with it. Report in a few issues:
The out West Picara has its roof and some major sail rig bits done:
The down South Picara is getting its innards done.
This long and lean project is a 19' version of Toon2. I'm told this one is more or less complete, left with the 15 % of the work that takes 85% of the time.
This is a slightly modified Veep14. I'm told the sheer is raised a bit and the stern given a bit of flare but the bottom is per the plans. Waiting for a test:
A Vector builder is keeping a website of the project at http://www.geocities.com/michsand@sbcglobal.net/ but in the meantime I got photos of a Vector completed by Pete Mohylsky in Florida. Here he is fussing with his sail. Hopefully a report soon:
And the Polish Polepunt is complete and water has been added. Report next issue:
AN INDEX OF PAST ISSUES
Hullforms Download (archived copy)
Plyboats Demo Download (archived copy)
Brokeboats (archived copy)
Brian builds Roar2 (archived copy)
Herb builds AF3 (archived copy)
Herb builds RB42 (archived copy)