Math is Hard Calculating a Waterline

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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Hogfish Maximus is ashore for hurricane Danny and TS Erica

Today as I write this post we are sitting on land in the boat yard in Jolly Harbour in Antigua. Tropical storm Erica is making its way past us blowing at least 50 plus knots or more with rain. The Hogfish shakes a bit in the bigger gusts. It could be blowing more but we are hiding behind and a bit below a bunch of bigger deep draft sailboats. The wind is howling through all their rigging. Antigua has been experiencing  its worst drought in recorded history. The rain is very welcome.

We hauled out a few days ago because of the threat of Hurricane Danny that was projected to go over Antigua. 

We are uninsured. Normally we find a good mangrove creek to go up and put out all our 7 anchors and tie as many lines as we can to the shoreline. This we have done for the past five hurricanes we have weathered In Grenada, the Exumas, Abaco,Florida and back home in Spainish Wells in the Bahamas.

In Antigua where I am redoing the deck on Wild Bird there are no soft shorelines. Lots of concrete and expensive boats and docks about. The only good creek to go up is 9 miles away to weather in a very remote place. We would normally go there but we want to be near Wild Bird to look after her. So we have spent a few dollars to come ashore and be 100 away from Wild Bird. She has her masts out and is in a full cradle with boats that are stored the same way. A very secure way of surviving a hurricane.

Being self insured means that since launching Hogfish in 1999 we have put our money in anchor

rodes, chain and anchors. We also have gone to great lengths to stay away from all other boats. Its other peoples boats that normally wreck your well placed and secured boat. Having a shoal draft boat enables us to get away to be by our shelves.

If we had been paying for insurance since 1999 we would have shelled out at least $22,000.00 US to date. So far this is the first time we have gone ashore to avoid being next to boats we would have no control over as to how their owners would tie up. The Yard here is very professional. When I picked it to do the Wild Bird deck Project I made sure they would be able to haul us out too in the event of a storm.

So here we sit. The yard crew loves our boat as all they had to do was to lift us out and place us on the ground. We did not spend the money to power wash off the bottom as we will be back in the water on Friday. The growth here is non stop.

No keel !

Anyone who thinks they can sail a shoal draft boat off shore with a shallow horizontal rudder is foolish.

You need a good deep rudder at sea.

The straps are mandatory. We have sat on the bottom with the tide out for several hurricanes of catagory 1-2 with out moving.

The prop strut is made out of fiberglass. I took this time to take the prop off and grease the shaft so it will be easy to remove under water as I will be getting a new feathering prop next week.

Being off set we get very good prop drive but the drag from this fixed bladed prop is about 1/2 a knot in speed loss. The small keel skeg with its flat end plate is made of solid fiberglass.

The Scheel keel idea

Looks like a Chinese take out box hull shape

Detail of bow anchor set up. We have three different headsails we can set. The 110% roller furling jib.

The staysail behind it set on its removable stay or a large Genoa on the forestay.

The 75lb. Fisherman hangs on this simple piece of hardware.

That little bit of Scheel keel really does wonders

Nice and flat. When the boat is heeled over going to windward that chine becomes a vee shape so no pounding. A vee bottom bow when heeled becomes flat so lots of pounding.

 Gayle with our new Bruntons Auto prop that is coming from England. Tim Bought it on EBay for us for $783.00 and will bring it over next week when he visits. Will let you know how it performs against the old three blade fixed prop. This prop self feathers to engine revs so is supposed to be very efficient under power. I also hope to get back that 1/2 knt. Speed loss under sail.

Would post pictures of the wind if it would really show anything. Todays been a good layday for writing blogs. 

The bad thing about hurricanes is you always wish them to go somewhere else. Somebodys going to end up with them. Tropical storm Erica will be gone by tonight but its heading for the Bahamas and is projected to go over our house in Spanish Wells. Such is life when living and sailing in the bowling alley.

When growing up in California we had to worry about Forrest fires and earth quakes. Not much you can do about them. But you can build a house to go through a hurricane and you can do a lot to save and protect your boat in a hurricane if you are aboard to plan ahead.

Once you have set your anchors and tied your lines then you have to decide to stay aboard or go ashore to a safer place. Once the wind is up over 35 knts there is nothing you can do but sit back and hope for the best. We have stayed aboard for most hurricanes being alone and only in 2-3 of water so we felt the risk was acceptable. Rachel and the kids have stayed ashore when they had a very good place to stay. That hurricane in Grenada was quite exciting for me anchored when the gusts would come across the small bay at over 100 miles an hour. With 7 anchors out Hogfish really did not move around but leaned over at times to 20 degrees in these gusts.

So now we will watch Erica on its path to the Bahamas.

Fortunately we have good people that will close up our house for our old renter. Our place is built to go through storms. We just hope for the best with our plants. 

Will let you know how it all turns out in a week.

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Epoxy is Stressful

You know the scene at the end of any action movie where the hero has minutes to disarm the bomb, cutting the wires in just the right sequence or he blows up the 747 full of schoolkids?  Working with epoxy is just like that.

In short, using epoxy involves mixing two dangerous chemicals together to make a viscous adhesive so powerful it permanently bonds anything it touches.  You have minutes before it reaches critical temperatures and kicks off like a bomb.  And if you do it wrong, at best, you completely ruin your work, and at worst it burst into a violent conflagration.

Okay, thats overstated, but isnt really too far from the truth.

Back in the day there were a few waterproof adhesives that were used for boat building.  Ive never used them, so for me, they are largely mythical.  Some came in powder that you mixed with water.  Some had multiple parts you mixed together. But for the last several decades, epoxy is king.

Until I started researching boat building methods, I really didnt understand epoxy.  Epoxy was just something I squirted out of tiny twin tubes now and then to fix something that wouldnt stay together with a liberal coating of Elmers.  Who would have thought Id be brushing epoxy on to 2x4s and plywood with a paintbrush by the bucketful?

After wading through books on fiberglass boat building, Im wise to its ways.  Epoxy is simply a hard plastic that comes in (generally) two parts that you mix together and apply as a viscous liquid.  The formulation contains a resin and a hardener -- and several other things including stabilizers, thinners, accelerators, decelerators, fillers, and sometimes waxes -- that together make a polymerized plastic goo.  When hardened, it is much stronger than the wood it is adhering together.  Two pieces of wood epoxied together are for all practical purposes one piece of wood.

Epoxy is commonly the stuff that is used with woven glass cloth to make fiberglass.  Together, the two make a super tough, resilient compound material.

The reaction of the resin and hardener is exothermic and sets up hard as the result of the heat generated by rapid oxidation.  What that means, is that from the moment you pour the hardener into your resin, the clock is ticking.

Chemicals in epoxy are varying degrees of poisonous.  It is recommended that you wear eye, skin, and respiratory protection.  In practice, we regularly only used skin protection in the form of a release cream for our hands and latex gloves.  Principally because the epoxy is uncomfortably sticky and once stuck to your skin, more or less permanent.

Kai had some experience with epoxy (she helped her dad fiberglass his submarine!), so that helped take the edge of terrible uncertainly that was epoxy for me.  Still, it is stressful.  Preparation, planning, and timing are everything.

We had the "slow" epoxy formulation that under ideal conditions (70-80 degrees Ferenheit, medium humidity) takes an hour to set.  What were ideal conditions for us, a sunny barnyard, were less than ideal conditions for epoxy.  We had about 20 to 40 minutes to work with the epoxy before it rapidly started turning hard as a rock.  Despite all of our planning, we had a few containers of epoxy kick off faster than we could use them, resulting in a few hard plastic hockey pucks.

Before any complicated assembly we carefully discussed our game plan before we committed with the epoxy hardener. A simple plan might look like this:

1. Set up the epoxy station, level the surface (for volume measurements).
2. Get the drill ready with the extension cord, correct star bit, and screws.
3. Put wax paper under everything.
4. Turn the pieces adhesive-side up, mark places to epoxy.
5. Measure out single batch of  resin, do a final check.
6. Add hardener and stir for at least one minute, scraping the sides.
7. Apply first coat to all surfaces to be adhered.
8. Measure out 2nd single batch of resin, final check.
9. Add hardener and stir for one minute.
10. Add filler (silica) to thicken.
11. Apply 2nd coat of thickened goo to one surface.
12. Assemble pieces, screwing as you go.
13. Smooth out excess goo that may have squished out

 

As recommended on the Glen-L Waterlodge plans, we used epoxy to adhere every single joint and piece of plywood together.  We used it to "encapsulate" piece of wood, that is, seal them completely in epoxy so they are waterproof and rot-proof.  And later we will use it to cover the hull of the boat in fiberglass.

So when you see in future build days that we say something like "assembled side stringer," understand that this means cutting all the pieces, assembling them for fit, and epoxying and screwing every single joint.

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Portuguese bridge is painted

I took half a day off yesterday and finished the painting the Portuguese bridge. Before I put all the paint gear away, I think Ill paint the aft deck bulwark and the two door jambs in that area. This way, all the off white painting will be finished until I have her at the launch site and install the wheel house and salon. Ill be able to get a good leg up on some detail work while shes in the barn and all the good tools are close at hand.

I had blasted and primed the Portuguese bridge, then faired grinder marks, the deck:PB joint, and seam sealed the frame to sheathing joint. Once I was happy with how the fairing looked, I spot primed those areas with two coats of primer to seal the porous fairing compound, which will help the top coat look more even. If I didnt seal the fairing compound, it would suck up the top coat paint, and make a pretty decent looking job look like crap.

Because of other things I had going on, I had to wait more than 72 hours to top coat the PB. If you wait longer than 72 hours, a chemical bond between the top coat and the primer will not happen, so you have to scuff the primer to get the top coat to bond to it. I use the red 3M scuff pads for this job, and they are made for just this application. I have a hook and loop dual action air sander, and I cut the scuff pads into a six inch diameter circles, they will now hook on to the sander and make quick work of a tedious job. Once the scuffing is completed, I blow the work off with my air compressor then tape and paper the area I dont want paint. I bought a tape/paper applicator at Lowes the other week, and I have to say that while the tool was fairly inexpensive, it did a nice job. It did such a nice job and made taping so much quicker, I have to recommend it as a tool one might want to consider purchasing for any paint work. That $17.00 tool paid for itself in no time on what I had just done.

The scribe line marking the wheel house layout was starting to get a little faint, so I decide to paint the wheelhouse deck using the wheel house scribe line as my layout. You can now see how the wheel house will fit in the scheme of things. The wheel house floor is going to be cork, so Ill use some less expensive metal primer and paint, and apply that will a roller. Ill glue down 1/4" plywood as a substrate, and apply the cork to that. Spraying the cheaper paints is not such a good idea as the paint tends to stay wet while its floating around the shop. Whatever it lands on it sticks to it. Because of the quick evaporating reducers Im using with the high dollar paint, the over spray acts like heavy dust when it lands in the barn. I still protect my new shiny paint from over spray, and if I do get some on a good finish, a little rubbing compound will take it quickly off. Not so with paint such as Rustoleum.

Now that this painting is finished, Im going to spend the rest of April getting some detail work completed. I have a some sand blasting guys stopping over so I can get an idea of what the cost of blasting below the water line will be. The sooner I get the bottom blasted the sooner I can barrier finish painting the hull. Getting the boat on a dolly is a big deal for me and I want it done well in advance of moving her to the launch site. Youll probably start to notice a consistent theme in my future posts, and that theme is going to be " getting her to the launch site".

One thing Im starting to realize is that this is a big boat. On deck shes 44, and over all she is 48. The living spaces and machinery spaces seem to go on forever, and the wheel house is huge. Once the wheel house and salon are in place, the displacement will begin to be felt. With the hydraulic bow thruster, I feel shell be able to be single handed, but I do feel shes close to needing an admiral.

So, heres to getting her to the launch site and seeing more shiny paint.

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Super structure metal work is finished

Tomorrow morning, before I take off for work, Im going to spend an hour or two so I can clean and organize the shop now that the metal work is completed. Im ready to prep the super structure for paint so I need to put away all the tools Ive been using to do battle.

Im a little blown away with how long it took to get the metal work completed. I did have a major set back in that the rough openings for the windows were cut for a four inch radius, and the windows are built using a six inch radius. There are 17 windows in the super structure and the repair consisted of me using my plasma cutter to cut out the 68 corners out of the existing rough openings. I then cut 68 new radius corners and welded them back in to the openings. The windows in the salon were easy as they were all square. The windows in the pilot house were a bit more of a challenges as they are all parallelograms, and required a little bit of noggin work to get the angles along with the radiuss correct. But, the window openings are now correct and all the widows fit the way theyre supposed to. Along with repairing the window openings, I added 60 or 70 more tabs to the window openings to bolt framing lumber to. 

 

 

 

 

 

Another job I got finished was fabricating the Tabernacle for the mast. After some indecision and talking with some other builders, I decided to go with a six inch mast. The primary function of the mast is going to be used to hoist my skiff to the roof of the salon. I am also going to have my radar mounted on the mast, and some lights and antennas. My long term plan regarding the mast is to be able to use it for a future para vane rig, and at a minimum, a flopper stopper rig. The Tabernacle is built out of 1/2" stainless steel. The pins used to hold the mast to the tabernacle are 1.25". The tabernacle is centered on frame #13. The tabernacle also has a doubler plate that it sits on and by doing some additional framing and reinforcing, I am spreading the load of the tabernacle to two additional frames, #14 @ # 12 . The bracket that will hold the para vane pole is also connected to frame #13 with solid 1/2" plates. I increased the flange thickness on # 13 to 5/16, and all is a continuous weld  were the reinforcing occurs. Two frames aft of the main para vane bracket, sits another bracket for another pole that will act as a brace for the main pole. The bracket for the brace is also connected to the frame with 1/2" plates. To connect the stays and shrouds, I welded 1/2" stainless pad eyes to frames.  I have two shrouds on each side, and one fore stay. I dont know if Ill ever use a para vane rig, but I do know Ill use flopper stoppers while at anchor. I had an engineering friend of mine give me some advice with beefing up the structure, and I feel good that I have things beefy enough. A fair amount of time and fabricating went in to this part of the boat. Because I will have electric winches for the mast/boom, radar, and some lights, I welded a 1.5" stainless nipple next to the tabernacle to run the mechanicals. I positioned the nipple so that  I can bolt a 6"x6" splice box to the tabernacle gusset, and use a grommet to make a water tight seal to the nipple. Ill use good quality cord grips to bring the various feeds out of the splice box.

The other job I  did was increase the width of the door at the salon to 32". Ill be fabricating the aluminum door, so I feel OK with the increased size. I plan on  having at least two dogs in the door to help hold it fast. Along with being weather tight, I want a door that will keep the thieves out.

Im using composting toilets on board and each one of those requires an 1.5" vent. I made those vents out of sch. 40 stainless. One is welded in to the soffit above the salon, and the below deck vent is welded in to the front of the wheel house.  Ill use PVC to connect the toilets to the stainless stubs I welded in the hull.

We have a shower for the cabins below deck, but due to the size of my posse, I felt it best if we had another shower on board. The easiest place to do this was on the aft deck in the port side corner of deck on the salon bulkhead. This will be a hot/cold shower. I fabricated a stainless shelf with a lip on it to retain soap, and a bar for wash rags and to hold back shampoo bottles.

I installed a 4" stainless vent for our 230volt clothes dryer.

On the aft salon bulkhead on the aft deck the fuel fills and vents reside. There is a two inch fill on both the port and starboard side. Next to each fill are the vents for the two port side tanks and two starboard tanks. The fill and vent pipes are welded in place. I really need a box around each set of pipes, similar to what Peter did on Koala ( now Kame Hele... not sure of the spelling). I have a little bit of time left where I can fabricated these boxs, and I might try braking them over the work bench. If not, my neighbor will do it on his press brake.

Outboard of the fill and vents are the two three inch vents for the lazzarette. These are weld in place.

I welded the six inch vent intakes for the master cabin. These vents are in the foreword wall of the wheel house.

To get up on the the roof of the salon, Im going to gain access via the wheel house side deck. Because of the raised pilot house, a five foot tall ladder is all that is needed to get on to the roof. I fabricated and welded some brackets to the salon wall to pin the removable ladder to. Its hard to describe it now, but because of the bulwark, and how I plan on working the salon roof hand rail, this will be a safe, secure way to get up on to the roof. I was going to get fancy and use a torsion spring to have the ladder self stow up on the roof, but my short time frame killed that idea and I decide to stow the ladder on  stainless post welded to the front of the wheel house. The forward  rake of the wheel house windows along with the almost 5 distance to the Portuguese bridge will allow all to pass by this area without bumping the ladder. It will make more sense once the super structure is welded to the hull.

Because I moved the aft salon wall, I had to cut the panel that extends down the salon line towards the aft deck. One of the boarding doors conflicts with this panel, so I cut it to fit. I gave this cut a nice looking radius where it meets the aft deck roof. It was important to me to keep some protection of the aft salon wall at this area, so we still have an inside corner where I cut the panel to accommodate the boarding door. Because both the port and starboard side panel are 3/16 material, I decided to treat each edge with a 1/2" stainless round bar. The round bar treatment should come in handy on the side where the boarding door is as this area will get some abuse. Hopefully, the stainless round bar helps with decreasing my  maintenance painting. Every exposed, exterior edge on board, has a 1/2" stainless round bar welded to it.  

I used 70 lbs of .035 welding wire to build the super structure. Im not for sure, but I think I drilled darn near 500 5/16 holes for bolting framing lumber to the steel frames. I might have drilled more holes, but Im going to order 500 2"x1/4" carriage bolts, nylock nuts and washers and see how that works out. 

As of today, my paint schedule is going to be blast the metal followed by two coats of epoxy primer. The inside of the super structure will get two more coats of Alkyd Enamel, then the framing lumber gets bolted on followed by spray foam. The roof of the super structure will get blasted followed by two coats of epoxy primer then three or four coats of Acrylic Urethane. Ill probably put a non skid on the roof, but that wont happen until after launch. The outside of the super structure will get blasted, two coats of primer, two coats of high build primer, fair ed, more primer to seal the high build, then top coat with three or four coats of Acrylic Urethane.

The last job I did to get the super structure ready to begin paint prep was to have my daughter and her friend Olivia walk around on the roof so I could fix the six or seven areas that were "oil canning". All that was required of that job was to find the offending areas, then weld a 1.5" flat bar between the longs and pull the roof sheathing down and weld it to the flat bar. Pretty easy job, but it still took us about three hours to wrap it up.

As anyone can imagine, Im glad to have this part of the job behind me. Paint and paint prep is going to be nasty, but I can now see the bitter end. Maybe by early October, Ill be able to post some sort of smiley face as I should be starting to take the front of the barn off.

 

 

 

 

 

 

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