Wood Boat Plans And Kits | Math is Hard Calculating a Waterline

Wood Boat Plans And Kits

Who would have thought boatbuilding would involve so much math?

I was reading Glen L. Witts Boatbuilding With Plywood and realized what should have been obvious to me:  The waterline of a boat is calculated beforehand.  I guess it makes sense that boatbuilders dont guesstimate their designs only to drop their boats into the water and see what happens. On top of that, many of the handling characteristics of a boat are built into the design, including balance.

With our cabin shifted back from the center, this would shift the balance toward the back.  Add to that the weight of the motor and fuel and we have a potential problem.  So far, Ive been assuming symmetrical bow and stern as many barge boats feature, but in order to increase buoyancy in back and shift the center of buoyancy forward, I can reduce the rake in back to get more of the hull in the water there.  This explains some of the barge boat that did feature a smaller stern rake.  How would I go about calculating that?  That is something I will have to think about.

But as an interesting exercise, I can calculate the waterline height as a function of the rake angles, length and width of the boat, and overall loaded weight of the boat.

I had to go back to my algebra and trigonometry reference books to look up how tangent and the quadratic equation worked.  The last equation gives us the waterline height h_w as a function of

w = overall width/beam
l = overall length
h = height from bottom to deck (or to the top of the rake)
?b = angle of bow rake
?s = angle of stern rake
Vw = volume at waterline (= the weight of the displacement of loaded boat)

Simply put, the total volume of water displaced is equal to the sum of the water displaced by the bow, stern, and center.  The volume of each of these can be calculated geometrically as a function of our unknown, the height of the waterline.

We then solve for the unknown and get an equation in a quadratic form (the forth one from the bottom).  So we use the quadradic equation (which Ive always hated) to solve for h_w.

Taking our equation for a spin

Lets say the total weight of the boat plus gear plus people plus 25% safety margin is 7000 lbs.  Then the calculated volume of the boat at the waterline is 193,846 cu in.

Well say the boat is 8 foot (96 inches) wide, the length is 20 foot (240 inches), and the height from the bottom to the deck is 2 feet (24 inches).  The bow rake angle is 45° and the stern rake is a modest 10°. 

So plugging in the numbers, and taking the plus-or-minus of the quadratic formula into account, I get:

hw = 370 inches or -9.28 inches

So either my boat will have a waterline 31 feet above the keel (that is to say, the boat will be underwater), or it will float 9 inches out of the water. No wonder I always dreaded the math part of a real-world problem.

Checking my math... ah I forgot a negative sign!  New solutions:

hw = 9.28 inches or -370 inches

Thats much better.  If we throw out the negative solution, we have a waterline 9 and a quarter inches above the keel.  Cool.

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Small Boat Plans And Kits | Karaoke Doodles

Small Boat Plans And Kits

So far, Ive ignored the inside cabin layout, thinking that it would sort itself out eventually.  But I got thinking, and with a few beers started doodling.  I went to the normally quiet Trout Farm on Zayante Road (the same road on which we will build the shantyboat).  Unbeknownst to me, it was karaoke night at the Trout Farm and so I did my sketches and drank beer while people sang Bonnie Raitt and Sam Cooke. 

As you can see, the beer was liberally applied, and not just to me.

First thing I noticed was that in all my previous drawings I forget the head. Then I had to figure out a good place for it.  We will bump it out on to the deck a bit and bump it into the room a bit for a 3 x 3 foot head.  Probably better on the back deck, just because the bump out looks a little funny in front.

So there are three things that need to be located in a corner:  the head, the galley, and the woodstove.  Actually, the woodstove could go in the middle of a side wall, but it might be in the way.

I have the front door swing out because swinging in on a step down is weird and dangerous.  The back door swings in (despite the step) because otherwise it would interfere to much with whatevers happening on the back deck.

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Boat Plans Arch Davis | Destruction and Creation

Boat Plans Arch Davis

Sometimes the treasure hunt of creating something from salvaged materials is half the fun.  Okay,  Okay. Ill admit it, more than half the fun.  Ive been making art out of bullshit found in junkpiles and on dump runs for more than a decade. 

But when you want to create a barn or a shed or a shantyboat out of old barn wood and rusty sheet metal, you got to do some searching.  If you live in a less-than-rural area, good luck.  On my country drives, the amount of rusty weathered junk in the yard of every farm we pass sets me drooling.  To find materials I have to get more creative.

This weekend we went out to the deep country of Hollister (made famous by Marlon Brando in The Wild One) to tear down an old chicken coop.  It was beautiful.  Beautiful country, beautiful weather, and beautiful 80 year old redwood lumber and rusty sheet metal.

Salvaging a building, involves deconstructing a building in the reverse order it was constructed.  We remove the shingles, then the roof battens, then the roof beams, and so on.  It is an interesting way to understand how a building is constructed. 

The chicken coop featured "single wall" construction.  That is, no stud framing, just siding that holds up the roof.  When we were done, we had a huge pile of beautiful old redwood 1x12s and a handful of redwood beams.  It was rough-cut "dimensional lumber," meaning a 2x4 actually measures 2 inches by 4 inches.

Jen and Kai helped disassemble the chicken coop, and then Alex helped disassemble a nearby outhouse the next weekend.  This lumber will be used to construct the cabin on our shantyboat.  The corrugated metal will form the roofs over the cabin and porches. 

Walking out into the nearby fields we found an old shack with gorgeous peeling paint patterns.  Hard not to joink this door as our shantyboat door.

I get hot just looking at old weathered textures.  In some ways, for better or worse, it is my love of this aesthetic which guides a lot of the decisions about the shantyboat.

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