Jim Islip goes for a sail.
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Jim Michalak
118 E Randall,
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(15Mar04) This issue will start an essay about figuring how much sail area your boat needs. The 1Apr04 issue will continue the topic.
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BOATBUILDING FOR BEGINNERS (AND BEYOND)
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Left:
Jim Islip goes for a sail.
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FIGURING SAIL AREA 1
SAIL SIZING
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....
HORIZONTAL FORCES...
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?
RIGHTING MOMENT...
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.
NEXT TIME...
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.
PICCUP PRAM
PICCUP PRAM, SAIL/ROW PRAM, 11' X 4.5', 90 POUNDS EMPTY
Piccup Pram was the first boat of my design to get built, back in 1990, I think. I still have the prototype and use it regularly. I designed it to be the best sail/row boat I could put in the back of my short bed pick up truck. But I found it to be a good cartopper, too. It has capacity and abilities I had previously thought impossible in a 90 pound cartopper. The photo above shows the original 55 square foot sail on Pensacola bay a long time ago. Piccup is a taped seam multichine hull which can take a fair amount of rough water.
Piccup continues to be one of my most popular designs and I get nice photos from builders. Here is one of Richard Donovan hoping for more wind up in Massachusetts.
Richard's Piccup has the larger 70 square foot sail that prefer myself. It's the same as the original but is 2' taller. This balanced lug sail sets on a 12' mast and rolls up easily for storage on its 9' yard and boom. The idea was to be able to store the rig easily in the boat during rowing and it works. There is a pivoting leeboard and kickup rudder on the boat and they can be left in place raised while rowing. Converting to full sail takes a couple of minutes as you step the short mast, clip on the halyard and tack lines, hoist the sail, lower the boards, and off you go. And the balanced lug sail reefs very well although reefing any small boat is best done on shore.
Here is a Piccup by Vince Mansolillo in Rhode Island, a nice father/son project. Piccup will be large enough to hold both of them. You can see the large open frameless cockpit, large enough for sleeping. And you see the buoyancy/storage boxes on the end.
But Piccup will take two adults as seen in the photo of Jim Hudson's boat. Jim's boat has a polytarp sail as does my own Piccup.
These boats have proven to be good for sail rig tinkerers (be sure to read and apply the Sail Area Math essay before starting). Here I am in Piccup with a polytarp sharpie sprit sail. The rig is different from the originals but the hull here is totally unchanged (except for paint) from the original shown on the beach at Pensacola.
I think my own Piccup has had about six rigs of different sorts and was always the test bed for the polytarp sail experiments. But, hey!, that's nothing compared to the tinkering Reed Smith did with his out in California. Here is his Piccup rigged as a sharpie sprit yawl!
Here is Rob Rhode-Szudy's yawl rig Piccup that was featured in his essays about building Piccup that you can access through the old issue links.
Here is another by Doug Bell:
This one is by Jim Islip:
And this one by Ty Homer:
Piccup Pram uses taped seam construction from five sheets of 1/4" plywood.
Plans for Piccup are still $20.
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 Texas Ladybug is getting details (Toto in background):
Out West the Picara project gets its bottom. Winter shifts work to sailmaking indoors:
The Deep South Skat is getting its brightwork:
Another Picara, this one with a 1' stretch in the middle, going together in Arkansas. Sailmaking right now.
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)