## Jim Michalak's Boat Designs

118 E Randall, Lebanon, IL 62254

## A page of boat designs and essays.

(1March2013) This issue will continue the old "drawing a boat" essays that first ran in 2005, in particular the preliminary displacement calculations. The 15 March issue will continue the topic.

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.

## FIGURING DISPLACEMENT

THE VERY BASICS...

One of the real basic errors in boat design is to not match the capacity of the hull to the weight it needs to carry. It's actually pretty easily done. Let's take an example: a fellow wants a 12' skiff to handle two adults. He figures the empty boat will weigh 120 pounds and the adults together at 350 pounds. So he has to float a total weight of 470 pounds.

One thing is for sure: no matter what the shape of the hull, it will sink into the water until it pushes aside, or displaces, 470 pounds of water. (The way I heard it was that ancient Greek mathematician Archimedes figured out the basics while sitting in the bath tub.) Fresh water weighs about 62 pounds per cubic foot and salt water usually about 65 pounds per cubic foot. So the volume of fresh water displaced by the 470 pound boat is 470/62 = 7.6 cubic feet. That was easy!

Next the problem becomes one of shaping the underwater part of the hull such that it displaces 7.6 cubic feet with good flow lines.

METHOD 1: THE PRISMATIC COEFFICIENT...

We talked about the prismatic coefficent a long time ago and you should be able to look it up in the way back issues index. Basically we construct a prism with the same length as the waterline length and the same cross section as that of the boat's maximum beam. The hull will fit neatly into the prism. Divide the volume of the underwater hull by the volume of that prism and you have the prismatic coefficient.

What is interesting to me is that the prismatic coefficient doesn't vary much from one displacement hull to another, as far as normal small boats are concerned. Jewelbox, with a flat bottom and squared off ends, has a prismatic coefficient of about .60

And Toto, with very pointy ends and multichine cross section, has a prismatic coefficient of about .50

So I figure if you were to assume a halfway normal displacement hull has a prismatic coefficient of .55 then you would always be within 10% which is actually pretty good.

So without drawing a line I might say that the 470 pound weight will need a "prism" with a volume of 7.6/.55 = 13.8 cubic feet. The prism could have any combination of cross section and length that will have that 13.8 cubic feet total volume.

Remember that the prism has the same length as the hull's waterline length and underwater cross section as the boat's maximum cross section. Remember we want a 12' boat, but the waterline will be shorter if we want some rake to the ends (for looks) and maybe enough rocker to make sure the stem and stern don't drag the water (for low drag). We might guess that the waterline length will really be about 10'. Then the maximum cross section would have to have 13.8/10 = 1.38 square feet of area below the waterline. If we wanted a flat bottom 3' wide (wide enough to have sailing stability and narrow enough for reasonable rowing) we would have a draft of approximately 1.38/3 = .46' or 5.5".

If we wanted a different cross section than the simple box shape I'm assuming here, we would have to tinker a bit. Draw up a cross section with the 1.38 square foot cross section and see if we like it. Actually in this case I'm going to flare the sides out to 4' at the top of the wale at the cross section. But that won't affect the area under the waterline much. We might sketch out something like this:

METHOD 2: THE CURVE OF AREAS...

This method of the "curve of areas" is an accurate and flexible way of determining the volume of almost any oddly shaped thing. It's actually pretty easy to do but first you need a drawing of the proposed boat (unlike the prismatic coefficient which just needs a general idea of the boat).

Let's take our proposed boat and draw a line on it that represents 5.5" draft, our guess at what is needed to float 470 pounds. Every now and then along the length of the hull we take cross sectional cuts of the hull and measure the area at each cut below the 5.5" waterline. The cuts can be taken anywhere but there must be enough to get a good definition fo the hull. Actually for a normal boat about five cuts will do. The more you take the more accurate your work but five will get you really close. Our example boat might be like this:

The dimensions of the underwater sections are measured right off the paper drawings and the area of each is calculated like this:

Next we graph those underwater areas spacing them the same distance apart as they are on the real hull to get the "curve of areas" like this:

The area enclosed under the curve of areas is a volume and is indeed the volume of the underwater hull - it's what we are looking for. In the old days you would measure the areas with a planimeter, a clever and expensive gadget. But you can do well by just breaking down the curve into triangles and trapezoids, figuring the area in each trapezoid, and adding them all up. In the example, second trapezoid from the left is figured by 1/2(175+209)X12 = 2304. Adding the sections together gives us a total of 12500 at 5.5" draft. That equates to 450 pounds of water. So the first guess was off by 20 pounds or about 4%. By the way, the drawing showed a waterline length of 9'5" instead of the first guess 10'.

As mentioned before this method can be used to figure the volume of almost anything. Let's say we wanted to find the weight of a mast. Say the mast is 24' long, 3.5" in diameter at the base and 1.5" in diameter at the top, with a curved taper between. The figuring of the volume might look like this:

1920 cubic inches equals 1.1 cubic feet. Wood usually weighs 25 to 35 pounds per cubic foot. At 30 pounds per cubic foot the mast would weigh 33 pounds.

You can also use the area of curves to find the CG of the object, too. For real simplicity I've seen designers in the aircraft industry draw the curve on cardboard, cut it out and balance the thing on a knife edge. The item's CG will lie on that balance line.

THE COMPUTER METHOD...

Finally you can use your computer to figure it all out. I'm sure all of you know that getting the computer to spit out the right answer might take a lot longer than doing it by hand. The program I used to get the drawings above was Hullform6s which can be downloaded from the links shown at the end of this page. What were the answers that Hullform6s predicts for the 12' skiff with 470 pounds displacement? 5.5 " draft, waterline length of 9'4", and prismatic coefficient of .55! So the first guesses were quite good. But the area of curves method was also excellent, within 4%. It showed the same waterline as Hullforms. Perhaps with more data points to flesh out the curve the hand method would get the same answer as hullforms but I wouldn't bother. You will never guess the weight of the finished boat within 4%.

NEXT TIME...

We'll apply this to the new Bobsboat design.

## Paddleplank

PADDLEPLANK, PADDLE BOARD, 14' X 32", 70 POUNDS EMPTY

Can you walk this plank? Actually the request was for a stand up paddle board, sort of like a surf board that is paddled while you stand up like on a real surf board shooting the big waves in Hawaii.

I had all sorts of reasons for not designing it, the first being that I could never stand up on such a thing myself for more than a second or two. As a starting point I decided to take the bottom of a light dory, which is usually about this length and about 2' wide. It is generally held that you should never stand up in a light dory and my experiences confirm that. But it looks like the surfers are well ahead of us mortals in that respect and besides they expect to get dumped regularly and maybe the long double paddle offers a bit of stability, sort of like the poles the tightrope walkers use.

So I started with that bottom and added a little top, maybe 4" of freeboard which will not keep you very dry. I put just enough rocker to support 470 pounds before the bow and stern start dragging, enough for two people plus the weight of the hull usually. I can't see two people standing up on this at once but if they both sit it might be a fun wet boat for warm waters. The deck is supposed to be totally watertight, of course, so it will shed water like a duck and be low enough in the water for a swimmer to reboard.

I knew from the start it would not be light, at least not light enough to carry under one arm as they did in "The Endless Summer". Bolger had warned all of us long ago that decks weigh a lot, more than the bottom he said because they must be strong enough to take your weight with no water underneath pushing upward. So Paddleplank will indeed weigh about the same as a light dory. I figure 75 pounds if made with the usual 1/4" plywood, maybe 15 pounds lighter if the topsides are made with 1/8" ply. You can't really go thinner than 1/4" on the bottom and you need some thicker area where you stand, so it is hard to make it much lighter.

I wondered a bit about how Bruce Brown carried his surfboard around under one arm. Sure, he's a big hunk but even so there were expensive tricks involved. Let's say you need to float a 180 pound man on a board. Light wood weighs over 20 pounds per cubic foot, so if you totally immerse a cubic foot of that wood it will have about 40 pounds extra buoyancy, given that water weighs about 60 something pounds per cubic foot depending on where it is from. So you would need about 5 cubic feet of wood to float the man, or at least 100 pounds of solid wood. But then he would be just awash, so to give an inch or two of freeboard to go surfing would require even more. I suppose that is the situation with old time historic surfboards.

I googled around some surfboard history. The first hollow boards were made about 90 years ago and they first broke the 100 pound barrier, so my guess was pretty close. Then they went to balsa cored boards (Hey! Balsa is really a hardwood!) and got down to 60 pounds or so. Then post WW2 they went to fiberglass and foam, etc.

Anyway, after the google, I stopped feeling guilty about the weight of Paddleplank.

I'm thinking Paddleplank is too wide for a real surfer dude but would be a good plaything for the rest of us.

Three sheets of 1/4" plywood with the chines done with taped seams. I have it drawn for jigless construction but you might not get away with that since the sides will be so thin and limber. Thus I have also shown some dimensions to a "base line" so you could set up the initial construction on a ladder frame to hold it all true until the bottom is on.

Prototype Paddleplank 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.

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

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.

Hullforms Download (archived copy)

Brian builds Roar2 (archived copy)

Herb builds AF3 (archived copy)

Herb builds RB42 (archived copy)