Jim Michalak's Boat Designs
118 E Randall, Lebanon, IL 62254
A page of boat designs and essays.
(15May 2014) This issue will look at some hull coefficients. In the 1 June issue I hope to breath new life into my old Roar2.
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:
Well, maybe it is starting to thaw by now. 

PRISMATIC COEFFICIENT
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) Wavemaking. 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 "speedlength ratio" which is equal to speed (in knots) divided by the square root of the waterline length (in feet). Usually a reasonable maximum speedlength 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 wavemaking 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 speedlength 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 belowthewater 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 in a future 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 after the scow had to go home.
To me the importance of the prismatic coefficient is in using it to get a quick idea of the size of a boat. For example a fellow wants to float 1000 pounds, a flat bottomed sailing hull with no flare but with pointed bow. And he wants it 4'wide and wants to draw no more than 4" of water. So his max cross section will be 4 x .33 = 1.32 sq ft.. And he will displace 1000/62 = 16 cubic feet of water. I would assume he has a prismatic coefficient of about .55 and expect that to be correct within 10%, probably a closer guess than his weight guess. So his waterline length would have to be 16/(1.32x.55)=22' to float the weight. It's a 5 minute calculation that you need to do before drawing anything on paper. It is very basic and reliable.
Roar2
ROAR2, ROWBOAT, 14' X 42", 75 POUNDS EMPTY
Roar2 is a modification of the original Roar which had a plumb stem. After I had designed, built, and paddled Toto with its V entry bow I went back and cut the lower plumb bow off my Roar and converted it to a Totolike bow. So Roar2 has a deep V entry which is carried well aft. About two feet of the sharp bow is immersed and provides a skeg action forward. As a result Roar2 behaves well in all aspects of wind and waves and is more capable in rough going.
The new shape makes a different sound  a "swish, gurgle" as it cleaves the water, where the original Roar has a "tap, tap" sound typical of boats that go over the water instead of through it. I suspect the original shape is slightly faster in smooth water but the new bow has the edge everywhere else. She'll row at 41/2 mph with medium effort using the 7 foot oars detailed in the plans. Adding a passenger to either version will hardly slow her, although acceleration and deceleration are affected.
Walter Kahlhammer built a clipper version of Roar2 without the bracing shown across the wales and reports his boat was still rigid. But the aft cross brace is almost mandatory for use as a passenger's back rest. Without it the passenger will soon tire and lean to one side or slide aft to rest against the transom, throwing off the trim in a way that will drive the oarsman crazy. (Walter uses a removable passenger seat.)
These are excellent camping boats, light enough to solo cartop, large enough for much gear and with a flat bottom plank long enough to sleep on while the whole rig sits upright. Kevin Garber took a Roar2 on a three day row of the Big Bend region of the Rio Grand, seeing no humans from putin to takeout. He brought a folding chair, a barbacue, and a tent fly with poles. In camp he set up the fly over the hull and slept in the boat. Here is a photo of me in my old prototype (still use it) demonstrating proper nap position:
I have found some more photos builders have sent. I'm sure I've forgotten where I've stored others. Here is Charlie Ballou rowing off into the Massachusetts sunset:
Here is Greg Rinaca in Texas:
Another by Lincoln Ross:
And Brian Walker in Canada:
Plans for Roar2 are still $15. Taped seam construction from four sheets of 1/4" plywood. No lofting or building jigs.
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.
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 taped and bottom painted. You can follow the builder's progress at http://moffitt1.wordpress.com/ ....
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....
1jun13, Drawing Boats 8, Polepunt
1jul13, Drawing Boats 9, AF4 Grande
15jul13, Taped Seams, Mikesboat
1aug13, Plywood Butt Joints, Paulsboat
15aug13, Sink Weights, Cormorant
1sep13, Lugsail Rigging, Hapscut
15sep13, Sharpie Spritsail Rigging, Philsboat
1oct13, Modifying Boats 1, Larsboat
15oct13, Modifying Boats 2, Jonsboat
1nov13, Modifying Boats 3, Piccup Pram
15nov13, Sail Area Math, Caprice
1dec13, Stretched Stability, Ladybug
15dec13, Trailering, Sportdory
15jan14, Width/Stability, HC Skiff
1mar14, Scram Capsize, Scrampram
15mar14, Bulkhead Bevels, Frolic2
1apr14, Capsize Lessons, RiverRunner
15apr14, AF3 Capsize, Sneakerbox
1may14, Paper Capsize, Blobster
Table of Contents