Jim Michalak's Boat Designs
1024 Merrill St, Lebanon, IL 62254
A page of boat designs and essays.
(1 October 2022) We cover some hull coefficients. The 1 October issue will calculate displacement.
ORDER NEWS
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.
ALSO...In addition to the Duckworks downloads I also now have access to a large format inkjet printer which is making very nice full sized prints on paper. So I can return to what I started 30 years ago, you order direct from me by snail mail using the address above only with cash or check in US funds with the prices shown on this website, and I mail you full sized 2'x 3' paper prints. The price includes first class mail to US and Canada.
Prismatic Coeffiecient
HISTORY...
Ship design got serious and scientific over 100 years ago when men like Froude started studying the elements of hull resistance through the water. Ships then were strictly "displacement" boats, with no "planing" involved. Resistance was broken into four main catagories. 1) Wave-making. 2) Frictional. 3) Pressure or Form. 4) Air resistance. I'll only discuss 1 and 3 now. Frictional resistance is from the water rubbing past the skin. Air resistance is of the wind against the above water boat.
Waves come mostly from the bow and again from the stern and from any abrupt changes in the hull along its length. All the waves combine in one way or another to make humps and hollows in a resistance curve as the various waves reinforce and cancel each other. Attempts to hang pedictable numbers on the event lead to the "Froude Number". Usually we see the calculation of the Froude Number more in the form of the "speed-length ratio" which is equal to speed (in knots) divided by the square root of the waterline length (in feet). Usually a reasonable maximum speed-length ratio of 1 would be expected from a normal displacement hull although it can be a bit higher. Thus a hull with a 16' waterline length might peak at about 4 knots. A 25' waterline hull would peak at about 5 knots, etc.. The longer the waterline the faster the boat.
It's just a rule of thumb with lots of exceptions. Those of us who row a lot know that there is a lot more involved. For one thing the above rule of thumb makes no allowance for hull shape. For example a fine 16' rowboat will row two or three time faster than a 16' jonboat designed for a gasoline engine.
The Pressure or Form resistance effect is supposed to allow for some of those other factors that separate the faster ones from the slow ones. The form of the hull affects the turbulence and eddying of the hull as the water moves aft.
The wave-making and form resistance elements are often joined together into the "residual resistance".
The idea behind all this was to design a ship, make a small model of the hull and test it in a tank, measuring drag. This to be done at the same speed-length ratio as intended for the full ship, so the model has the same wave pattern as the full sized ship. The frictional drag element of the model can be calculated and subtracted from the whole. Eventually the entire business can be scaled up to the full sized ship and performance or powering requirements determined from the small model tests. That was the whole idea behind the head scratching.
BLOCK COEFFICIENT...
As I said before, some shapes are faster than others. For big ships, where the studies originated, it was found that a rough measure of shape could be the "block coefficient". Figures 1 and 2 show the idea behind the block coefficient.
Here is how it's done. Let's say your boat has a waterline length of L, a maximum waterline beam of W and draft of D. Then you might imagine it fitting neatly into a rectangular block with length L, waterline width W and depth D. That block will have a volume of LxWxD. The block coefficient is calculated by dividing the actual volume of your below-the-water hull by the volume of the imaginary rectangular block.
So there are two parts to the puzzle here. The underwater hull volume is determined by the weight of the boat. Once you've defined the underwater hull the L,W, and D, you need to measure the block are easily found.
First you need to know the total weight of your boat and everything in it. Not always an easy number to come by.
The boat's total weight is equal to the amount of water it "displaces" or pushes aside. Fresh water weighs about 62 pounds per cubic foot and salt water at maybe 64 pounds per cubic foot. So if your boat's total weight were 620 pounds it would push aside, "displace", about 10 cubic feet of fresh water.
Next you must push your imaginary design down into the imaginary water until the volume of hull under the waterline equals the volume of water to be displaced at the given weight. This is usually a trial and error calculation that will be explained next issue. Once you find a suitable draft to balance your weight, you measure the waterline length and maximum waterline beam at that draft. Those are the L, W, and D used to size the "block" of the block coefficient. Multiply L times W times D to get the volume of the imaginary "block"
Lastly, you divide the actual displacement by the volume of that imaginary block. That is the Block Coeffiecient.
A hull like a barge which is totally squared off will have a block coefficient of 1, the maximum you could have. If you refined the ends of that square barge and make them pointy and smooth and round you reduce the block coefficient for the design maybe down to .5 and it would go through the water with a lot less waves than the totally rectangular boat, even though it's main cross section is still rectangular.
But let's say you left the ends squared off and got a .5 block coefficient by using a V cross section instead of refined ends?
To avoid that confusion, the concept was refined from the "block" coefficient into the "prismatic" coefficient.
PRISMATIC COEFFICIENT...
This is a refinement of the block coefficient. Imagine you have a V or round sectioned hull, or any section which deviates from a rectangular cross section common on big ships. Then you use the "Prismatic Coefficient". Figure 3 shows how that one is figured.
Essentially the prismatic coefficient is figured the same way as the block coefficient except the rectangular block that you figured in the block coefficient is replaced by a similar constant section prism which has the same length as the boat's waterline and a cross section identical to the actual boat cross section.
You can see that the prismatic coefficient sort of takes away the cross sectional element that might confuse the block coefficient calculation. For example you might have two boats with a block coefficient of .5, one with very fine ends and a square cross section, and another with totally square off ends and a V bottom. But if the two were figured using the prismatic coefficient, the first boat would still have a prismatic coefficient of .5 and the second would have a prismatic coefficient of 1!
Anyway, that's all it is.
WHY ALL THE FUSS...
The prismatic coefficient is a rough measure of the fineness of a hull. A square barge will have a prismatic coefficient of 1. If you streamline one end and leave the other end blunt, as with a modern planing powerboat, you might have a prismatic coefficient of .75. If you streamline both ends you might get down to a prismatic coefficient of .5.
But the experimenters tell us the "optimum" prismatic coefficient is about .6. I assume they are talking displacement hulls in fairly smooth water. A check of my old Mechanical Engineer's Handbook shows almost all modern big ships do indeed have a prismatic coefficient of about .6. Some boats like crude oil carriers are closer to .75, apparently the extra volume in the blunter hull being more important than the speed that might be gained from finer ends. The Edmund Fitzgerald came in above .85! (The edition of my book was written before the wreck.)
We see small boat designers pushing the lines of their designs around to get the optimum. Me, I don't think it is anywhere near that simple or worth chasing after for two reasons. First is that our little boats often operate in conditions that are comparativly rougher than those of a large ship. So I'm pretty sure ends finer than the usual optimum might be better for most of us. And the other reason is that if you design almost any normal looking displacement boat, you will almost always end up with a prismatic coefficient between .5 and .6. The .5 value might be for a fine lined rowing boat or sailing boat with nice pointy ends. The .6 is pretty typical of a sailing scow. Yes, the scow with the "ideal" prismatic coefficient should outsail the other boat in smooth water, but the fine ended boat might keep going in rough stuff long after the scow had to go home.
Larsboat
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.
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.
We have a Picara finished by Ken Giles, past Mayfly16 master, and into its trials. The hull was built by Vincent Lavender in Massachusetts. There have been other Picaras finished in the past but I never got a sailing report for them...
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:
A brave soul has started a Robbsboat. He has a builder's blog at http://tomsrobbsboat.blogspot.com. (OOPS! He found a mistake in the side bevels of bulkhead5, says 20 degrees but should be 10 degrees.) This boat has been sailed and is being tested. He has found the sail area a bit much for his area and is putting in serious reef points.
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
15oct21, Choosing A Design, Jonsboat
1nov21, Lugsail Jiffyreef, Mayfly14
15nov21, Sharpie Sprit Reef, Piccup Pram
1dec21, Junk Rig Test, Ladybug
15dec21, Taped Seams , Sportdory
1jan22, Rowboat Setup , Normsboat
15jan22, Sail Area Math , Robote
1feb22, Bulkhead Bevels , Toto
15feb22, Trailering Boats , IMB
1mar22, Small Boat Rudders , AF4Breve
15mar22, Rudder Sink Weights , Scram Pram
1apr22, Sail Rig Spars , RiverRunner
15apr22, Water Ballast, Mayfly16
1may22, AF3 Capsize, Blobster
15may22, Mast Tabernacles, Laguna
1jun22, Underwater Board Shape, QT Skiff
15jun22, Capsize Lessons, Mixer
1jul22, Scarfing Lumber, Vireo14
15jul22, Rigging Lugsails, Frolic2
1aug22, Horsepower, Oracle
15aug22, Sharpie Sprit Sails, Cormorant
1sep22, Measuring Prop Thrust, OliveOyl
