Jim Michalak's Boat Designs
118 E Randall, Lebanon, IL 62254
A page of boat designs and essays.
(1 December 2014) This essay is about sail area math. The 15 December issue will present an essay by David Gray about advances in polytarp.
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.
Greg with his new Piccup Squared on the Columbia River near Portland.
118 E Randall,
Lebanon, IL 62254
Send $1 for info on 20 boats.
SAIL AREA MATH
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.
LADYBUG, SAILBOAT, 14' X 5,5', 250 POUNDS EMPTY
Ladybug is a lot like Woobo which was one of my first designs. There was a Woobo near here for a while. I never got to sail it but was told it would really fly. (That boat was made of Lauan plywood from Home Depot which fell to pieces after rainwater filled the boat over the winter.) Ladybug is a bit shorter and wider and deeper and has bench seating, much more suited for older legs. Both boats have a small motor well. The best motor for something like this is the 2hp Johnson/Evinrude which weighs 25 pounds. Even that is overkill since 1hp will push this hull at top speed, anything more just makes bigger waves. Here Sandra Leinweber pushes into a stiff breeze with a 2hp Honda.
This shape of hull with multichines and a plumb bow seems to be a good all around thing with rough water abilities. I think if there is a problem it is that it has almost no lateral drag and unless the boat has a big skeg or keelson or something like a leeboard or daggerboard or centerboard it would just as soon go sideways as straight. I've given Ladybug a keelson and when using power you should keep the leeboard down just enough so its tip drags the water.
Ladybug's hull has the layout I like the best - a 6-1/2' cockpit between two storage/buoyancy boxes. It would be a great solo camping boat. The buoyant wooden spars prevent it from turning turtle. You bring it upright with weight on the lowered leeboard. Then you must climb back on board and a slot in the rudder seems to be the best boarding ladder around, bringing your weight back on board where it least affects the boat. You will have to bail some water.
I've kept the same sail as with Woobo, a 75 square foot balanced lugsail. It hoists on a 13' mast with 11' yand and boom. All very low tech built with common materials.
Chuck Leinweber of Duckworksmagazine.com built the prototype and brought it to our Rend Lake messabout so I had a chance to go for a long ride in it. One thing that impressed me was how large it was for a 14' boat. In the opening photo you see it sail with three men on board, all comfortably sitting to windward on the bench seat, and I'm told it has sailed with four men with no effort. I do think it would be quite suitable for a family of four say with lots of room for all and storage space for all their junk. Here Sandra Leinweber sets things up at a recent campout on the Texas coast:
Here is the same campout from a distance with the mast folded to support a tent. I'm told the tent is not done yet. Chuck has modified the bench seats so that his expand towards the center and meet in the center thus making a 6' x 5' sleeping platform. Turns out a small commercial camping tent can be set up on that platform and that is what they are using for now.
Ladybug uses taped seam construction. Six sheets of 1/4" plywood, one sheet of 3/8" plywood and two sheets of 1/2' plywood.
Plans for Ladybug are $40.
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.
I think David Hahn's Out West Picara is the winner of the Picara race. Shown here on its first sail except there was no wind. Hopefully more later. (Not sure if a polytarp sail is suitable for a boat this heavy.
Here is a Musicbox2 out West.
This is Ted Arkey's Jukebox2 down in Sydney. Shown with the "ketchooner" rig, featuring his own polytarp sails, that is shown on the plans. Should have a sailing report soon.
And the Vole in New York is Garth Battista's of www.breakawaybooks.com, printer of my book and Max's old outboard book and many other fine sports books. Beautiful job! Garth is using a small lug rig for sail, not the sharpie sprit sail shown on the plans, so I will continue to carry the design as a prototype boat. But he has used it extensively on his Bahamas trip towed behind his Cormorant. Sort of like having a compact car towed behind an RV.
And a Deansbox seen in Texas:
Another prototype Twister is well along:
And the first D'arcy Bryn is to the point the builder can sit and relax in it and imagine boating. You can follow the builder's progress at http://moffitt1.wordpress.com/ ....
The first Jukebox3 is on the (cold) water. The mast is a bit too short - always make your mast too long. A bit more testing will be nice...
AN INDEX OF PAST ISSUES
THE WAY BACK ISSUES RETURN!
MANY THANKS TO CANADIAN READER GAETAN JETTE WHO NOT ONLY SAVED THEM FROM THE 1997 BEGINNING BUT ALSO PUT TOGETHER AN EXCELLENT INDEX PAGE TO SORT THEM OUT....
THE WAY BACK ISSUES
15dec13, Trailering, Sportdory
1jan14, Cartopping, OliveOyl
15jan14, Width/Stability, HC Skiff
1feb14, Hiking, Shanteuse
15feb14, Dory Stability, IMB
1mar14, Scram Capsize, Scrampram
15mar14, Bulkhead Bevels, Frolic2
1apr14, Capsize Lessons, RiverRunner
15apr14, AF3 Capsize, Sneakerbox
1may14, Paper Capsize, Blobster
15may14, Prismatic Coefficient, Roar2
1Jun14, Roar2 Repair, Piragua
15jun14, Rend Lake 2014, Toto
1jul14, Mast Tabernacles, Musicbox3
15jul14, Sandell Tabernacle, Mikesboat
1aug14, Taped Seams, Cormorant
15aug14, Plywood Butt Joints, Paulsboat
1sep14, Rowing 1, Vireo
15sep14, Rowing 2, Philsboat
1oct14, Guessing Weight, Larsboat
15oct14, SailOK2014, Jonsboat
1nov14, Chine Runners, Piccup Pram
15nov14, Lugsail Rigging, Caprice
Mother of All Boat Links
The Boatbuilding Community
Kilburn's Power Skiff
Bruce Builds Roar
Rich builds AF2
JB Builds AF4
JB Builds Sportdory
Puddle Duck Website
Brian builds Roar2
Herb builds AF3
Herb builds RB42
Barry Builds Toto
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