Jim Michalak's Boat Designs
118 E Randall, Lebanon, IL 62254
A page of boat designs and essays.
(1October 2012) This issue will start a series about calculating sail area, originally presented in 2004. I hope the 15 October issue will review Sail OK 2012, then we return later to the sail area 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.
Mark Albanese's Jewelbox Jr is pulled up for the night for a campout. Looks like an excellent cabin slot cover!
Figuring Sail Area 1
I've really never seen any essay on how large the sail area should be for a given boat. Modern sailing boats often assume a small basic sail plan with a bevy of light wind sails that can be added if needed. That idea won't work well for the boats I design which are supposed to be simple to build and operate and inexpensive. I guess the experienced designers would build upon patterns with previous boats and guess at the sail size for new designs. Maybe I'm starting to do that more and more as I get more experience. But I think there is a more precise way to figure the size of the sail area to go on a given boat.
THE BASIC EQUATION....
Here is an end view of a boat sailing along in conditions that don't change. By that I mean it is a "static" view which is not to say the boat is sitting still, only that the forces on the boat are not changing as they would in a "dynamic" analysis. So this boat is in a steady wind and in smooth water! I suppose if you went sailing every day of the year you might get to sail in that situation once or twice a year. So it is not totally realistic but is better than nothing when doing the analysis. I don't know how to do a dynamic analysis which would include the effects of rolling and pitching in waves and of gusting winds. I've never seen that sort of study done and doubt if it was ever done in a serious way by a single designer. Perhaps in an America's Cup effort worth millions of dollars a few brains use a super computer to get a dynamic analysis, but not here.
Anyway, in a static analysis all the forces on the object will total to zero and the boat won't be accelerating in any way. It is in equilibrium. There are four forces shown and we'll look at them one at a time.
The weight W is the total weight of everything, the hull, rig, crew, food, stowaways, etc., etc.. As simple as this may sound, weighing a boat is rarely done and the designer can only guess at it in the beginning design stages. And if ten boats are built by ten different builders using identical drawings the weights of the boats will vary a lot no doubt! The weight points downward trough a mythical point call the "center of gravity", basically the point where the boat would balance on say a knife edge.
The buoyancy B is the same as the weight but points upward. The boat will sink down in the water until the weight of the water displaced (pushed aside) by the hull equals the weight of the boat. It can be thought of as acting at a "center of buoyancy" which is essentially the center of the blob of water that is displaced by the boat.
So in the vertical direction the total of W + B equals zero.
Now, if the boat were sitting straight up and down and if all the weights were centered (say like a rowboat or canoe might be) then all would be in balance rotation wise too. But as shown in the example the boat is heeled a bit and the buoyancy has moved off to the side that is deepest in the water while the weight remains centered. Now the two forces are offset by the amount L. And the result is a torque equal to WxL (or BxL since W=B). If there were no other forces on the boat that torque would rotate the boat back to vertical and bring the two forces back in line. But something else is going on here that won't allow that....
Looking at forces in the horizontal direction we have the side force S on the sail pushing sideways. Why sideways? Because when a boat is close hauled sailing into the wind almost all of the sail force is sideways. Only a small portion of the total sail force then is pushing forward on the boat and moving it forward. The lion's share in this situation is pushing sideways, so much so that we might as well assume here that all of the sail's force is sideways (as it indeed will be at times).
The boat would slide sideways under that sail force if it were not for the equal and opposite side force generated by the boat's underwater fin (or keel or centerboard or leeboard or daggerboard, etc.). The fin force, F, equals the side force of the sail and is generated by the flow of water over the fin which is at an angle of attack to the motion of the boat (looks like leeway to the skipper). So if the fin is too small or the water flow is not sufficient for it to equal the sail's force then something will happen to make them equal, most likely the boat will start to head more downwind which both increase the fin force and decrease the sail's side force. So if you want to sail to windward well you need a good sized and efficient fin. So F=S when equilibrium is finally established.
But, you say, the sail's force S is way up yonder and the fin's force F is way down below. Let's say the forces are apart by a distance of D. And another torque is established by the offset in the forces equal to SxD (or FxD since S=F).
BALANCE OF TORQUES...
Most engineering involves just figuring out balances like these. It's really simple! For the boat to be in equilibrium all of the forces and all of the torques will total zero (if they aren't the boat will be accellerating in some way). We have already balanced the vertical forces with W=B. And we've balanced the horizontal forces with S=F.
Now we need to balance the two torques on the hull to total to zero. So SxD = WxL. Let's rewrite that to be S = WxL/D. So for the hull to be in equilibrium the force on the sail will be equal to the boat's weight times the offset between the boat's center of weight and it's center of buoyancy all divided by the the offset between the boat's center of sail area and its center of fin area.
What happens if the force S exceeds that amount say as in a gust of wind? The boat will roll to try to increase the distance L if it can. But there is a limit to that distance on any given boat. If the the force S is strong enough the boat will continue to roll right on its side and over. It capsizes!
So my idea is that the sail force S can be controlled by calculating the sail area needed to capsize the boat in a given wind. How do we do that?
The value WxL is usually called the "Righting Moment". To an engineer the "moment" is the same thing as a "torque", that is a force times a distance, and I don't know the source of the names. So it will be measured in some units like foot-pounds or inch-pounds in the old English units that we old timers still use.
But for a given hull the value of WxL varies as the boat is rolled. How to figure it? 'Tain't all that easy! It's so tedious that I think it was seldom done exactly in the old days except for major ships. But computers don't mind tedium at all and you can download the free program Hullforms by clicking in the links section of this page. Hullforms will do the calculation in a second or two, something that might takes weeks by hand. Only thing is that you need to "model" your design into the program for Hullforms to do its job. Essentially you will be plugging in hull offsets to define the shape of your hull. Here is a picture of such a model that I did a while back. This one is for Picara:
And you have to tell Hullforms the weight of your boat and tell it where that weight is centered. There might be a lot of combinations of weight and cg's that should be checked. It needs all the information that you would need to do the job by hand. Then Hullforms will roll your hull a few degrees at a time, as you instruct it, and figure the righting moment at each angle of heel and plot it all out for you. Here is an example of such a plot for Picara at 2000 pounds with cg 2' above the baseline:
When I look at one of these there are a few things that I note. The maximum righting moment, WxL by my nomenclature, is what we are looking for as far as sail sizing goes. If you know the maximum value of WxL from the program, and you know the value of L (by measuring the distance between the sail center and the fin center on the drawing of your proposed boat) then you can calculate the maximum value of S, the sail's force. If your sail's force exceeds that value, the boat will continue to roll until it capsizes if that force is not reduced quickly. In the above graphic Hullforms has presented the value Gz which is his nomenclature for my L, the "righting arm". That times the weight gives WxL, the righting moment. So with Picara in this weight and cg location the maximum value of Gz is .84' and that times the 2000 pound weight would give a maximum righting moment of 1680 foot-pounds.
As an aside I like to also take note of what angle of heel that maximum righting moment occurs at. Usually for small flat bottomed shallow boats it seems to occur quickly at maybe 15 degrees of heel. That tells me that when sailing such a boat you will get the max sail force and maybe max speed at that angle of heel. Exceed that angle of heel and you can't carry as much sail force and still keep the boat upright. Deeper ballasted boats seem to have the max righting moment at maybe 30 degrees or more, Picara shows to max at 25 degrees of heel.
And I take note of when the righting moment goes to zero, which is when the boat will capsize and turtle (or maybe float on its side if the sail rig is buoyant as with a wooden rig). It is sort of a point of no return. For a shallow unballasted boat it might be around 45 degrees. Heel more than that and you will go for a swim. Hopefully for a ballasted boat the righting moment goes to zero around 90 degrees of heel. At that point the wind force on the sail should be greatly reduced (the sails are now going into the water) and the boat should self right although it might be in slow motion at first.
You can see all the guesswork involved, especially involving weights and their locations. On small boats the weight of the crew is such a large proportion of the total that it greatly influences the results in the program and in real life. Hullforms assumes the weight is centered but if you place your weight to windward by "hiking" you can greatly increase your righting moment and carry a lot more sail, like this:
On a small boat where the crew weight is large compared to the total the effect of hiking can be huge. Here the man has about doubled the value of L and he can carry about double the sail force than in the original case.
On the other hand if your weight is to leeward you greatly decrease it. So the skipper is something of a tightrope walker. If you hike to windward in shifting gusty winds you may find your "windward" weight suddenly becomes a "leeward" weight and you can capsize backwards!
Lots of tricks have been used over the years to multiply this hiking effect. Sailing canoes use long hiking boards across the hull with the skipper sitting way beyond his boat's hull. In the old days they shifted sandbags from side to side as they sailed to get more weight to windward. Today they pump water to windward ballast tanks. All of these schemes have the same problem though in shifting winds of the backwards capsize.
Making the boat wider allows for more extreme hiking, thus the shallow sandbaggers of old were also very wide. But narrow hulls have less drag than wide boats, thus the modern "winged" hulls with narrow bottoms and very wide extended side decks.
Catamarans of course take full advantage of the idea. Long narrow hulls that cut the water a lot faster than any normal calculation of "hull speed", and a wide platform atop that allows the skipper to put his weight maybe 8' outward of the leeward hull providing all the buoyancy as the windward hull flies totally out of the water. Then his crew grabs a line and sits in a trapeze seat even farther to windward! Well, that is fast sailing.
Weight alone will make a boat more stable although it almost always also slows the boat.
The length of a hull has no effect on stability other than perhaps the extra weight in a longer hull. And when you think about how large a sail rig should be you might as well not be looking at the side view.
Beam on the other hand has a huge effect on stability. And when you think about how large a sail rig should be you should be looking at the end view of the hull to see its beam.
Now that we can put a number on the righting moment, we'll look at the elements that make up the force on the sail.
LARSBOAT, DOUBLE PADDLE CANOE, 15.5' X 30", 65 POUNDS EMPTY
Larsboat was built by Lars Hasselgren to replace a Folboat that had finally met its end. Lars wanted capacity for two, plus decking, as with his old boat.
I took Toto and lengthened it with a 30" plug in the middle to gain capacity. But lengthening a hull with a straight plug like this usually improves a boat in almost every way and Larsboat should be faster than Toto in good conditions. In this case the plug meant I didn't have to refigure the shape of the twisted bow panels as I would if I'd lengthened Toto with an overall stretch. (I can figure twisted panels pretty reliably now, but not back when Toto and Larsboat were drawn.)
The decking was quite simple because even the original Toto could take a forward deck of flat sheets with a center peak. I should add that I feel the decking is very optional. This prototype weighs 61 pounds and deleting the deck might cut another 10 pounds or so. The undecked boat also would have a better cartopping shape. I'd keep the stern chamber. It will ease your mind about taking a big wave over the stern.
This would be a preferred project for someonw who intends to do a lot of cruising and camping. In the Toto camping I've done the sleeping room has been OK, but the storage is limited. Larsboat would be better both because of increased capacity and because there is dry storage under the bow deck.
The basic hull is taped seam construction needing four sheets of 1/4" plywood for the decked version and three sheets for the undecked version. No jigs or lofting required. Plans are two blueprints with keyed instructions for $20.
The photo above is of Bob Smithson's Larsboat. He customized the decking a bit. I think he also built the boat of 1/8" ply to save weight. I've forgotten what his boat weighed but he did say it was sufficiently rigid for him.
Bob Hoyle built this one without a deck down in Florida:
Paul Moffitt built this one. You can see this is a much better two person boat than the shorter Toto:
And remember Garth Battista's vertical Larsboat?
And the old outboard motor guru Max Wawrzniak often goes for a paddle in his Larsboat:
Larsboat plans are $20.
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 ready for taping. You can follow the builder's progress at http://moffitt1.wordpress.com/ ....
AN INDEX OF PAST ISSUES
A NOTE ABOUT THE OLD WAY BACK ISSUES (BACK TO 1997!). SOMEONE MORE CAREFUL THAN I HAS SAVED THEM. TRY CLICKING ON...
which should give you a saving of the original Chuck Leinweber archives from 1997 through 2004. They seem to be about 90 percent complete.
15oct11, Sail Area Math, Jonsboat
1nov11, Sail Oklahoma 2011a, Piccup Pram
15nov11, Sail Oklahoma 2011b, Caprice
1dec11, Taped Seams, Trilars
15dec11, Bulkhead Bevels, Sportdory
1jan12, H14 Rig, Olive Oyl
15jan12, Knockdown Recovery 1, DarcyBryn
1feb12, Knockdown Recovery 2, Caroline
15feb12, Underwater Board Size, IMB
1mar12, Underwater Board Shape, Paddleplank
15mar12, Underwater Board Shape2, Frolic2
1apr12, Underwater Board Shape3, Marksbark
15apr12, Rowboat Setup, Toon2
1may12, Electric Boats 1, Blobster
15may12, Electric Boats 2, Electron
1jun12, Messin With Motors, AF4
15jun12, Rend Lake 2012, Toto
1jul12, Prop Thrust, Brucesboat
15jul12, Making A Hull1, Mikesboat
1aug12, Making A Hull2, Paulsboat
15aug12, Olympic Thoughts, Cormorant
1sep12, Making A Hull3, Hapscut
15sep12, Making A Hull4, Philsboat
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
Table of Contents