Zenos Paradox resolved

The stem of my boat was not moving and yet I have been having trouble reaching it.





Finally I remembered Marks solution to the paradox.


I got as close as I could to the stem, then I bridged the gap with some epoxy thickened with wood flour.








Voila!


The hull planking is complete at last.


Next the boat needs to be rolled over so that the temporary forms can be removed and the interior finished.

Zenos paradox

Or why it is taking so long for me to finish the hull of the boat.



Zeno was a 5th century B.C. philosopher.
Achilles was trying to catch a tortoise. No matter how fast Achilles would run, by the time he reached where the tortoise was the tortoise had moved a little further. Thus Achilles could never catch the tortoise.

To paraphrase the paradox.

On the first day you complete one half of the distance to your goal.

On the second day and each subsequent day you complete one half of the remaining distance.

You will never be able to reach your goal because there will always remain at least a small distance between you and your goal.







The first plywood hull panels went on fairly quickly. They were pretty big and pretty flat. Before long I was working towards the bow.





As the hull developed more and more curve the panels had to be made shorter and shorter so they could be bent to the shape. Because the panels are curving the straight edges of the plywood could no longer simply be butted together.

To fit nicely each edge had to be gently curved.


The closer I got to the bow.

The more difficult the fit and the slower my progress.





The piece in the foreground is dark because I have soaked it to make it take the shape more easily.

There is more than one way to scarf a cut

The plywood pieces that make up the hull need to be fastened together.


You can butt the ends together and reinforce with epoxy fiberglass.


Or there is the hard way.





When you cut through plywood at an angle the layers of wood form an interesting pattern.


In a previous post What Knot I described cutting a scarf joint in the 1x4 by 24 foot board that was to become the keelson.


Here I am cutting a scarf joint in the 1/4 inch plywood that is to become the sides of the hull.



I have been too chicken to try to get the circular saw to cut the slope down to a feather edge so I finish the job with a plane.




Here are some of the panels forming the side of the hull.

Hull

The bottom hull panels of an EC 22 are two layers of 4mm plywood.





Here the first layer is being glued down.






After the first layer is on, a second layer is glued on top.

The joints are staggered.







I used a notched spreader to apply a thin coat of thickened epoxy.





Additives are used to thicken the epoxy to a consistency tailored for each job.


There are at least a half dozen additives that can be used. Phenolic microballons give the mixture I am using the brick red color.





The second layer needs to be held down firmly and evenly to make a nice epoxy sandwich.





Staples, clamps, screws, weights, whatever can hold the sandwich together.












The reason for using two layers of plywood is that up near the bow the bottom panels begin to bend quite sharply.

A single thicker layer of ply would not be able to make the bend. Even the 4mm plywood takes a good deal of force to take the bends near the bow.

Keel, keelson, keel batton, all have specific boat building definitions. We do not need to shave too closely here. I am just talking about the backbone of the boat.





The keel batton for Skorpa is 1 inch by 3.5 inches and 20 feet long. It runs from the stem to the transom.



Skorpa's bottom has a shallow V at the stern that steepens sharply as you near the bow.



The keel batton must have a bevel that matches this angle shallow at the stern gradually at first than quickly getting steeper at the bow.


To creat this bevel I first cut notches every 2 feet along the keel that matched the bottom of the hull at that point.











Next I used a batton to draw a fair line that connected all the notches.


I then made saw cuts down to the line and knocked the wood out with a chisel.











The idea is to get rid of the bulk of the unecessary wood without going below the line.


Then a sharp plane eases the wood down to the line.

More or less.




Here the keel has been mounted back on the jig.


Way in the background you can see the first hull panel in place.


They are next up.

Back to the Stem

The stem is this L shaped piece of wood, rectangular in cross section.




Way back in April I laminated the stem and mounted it on the jig.







I put so much work into laminating the stem I was a little reluctant to start hacking into it, but sooner or later you just have to do it.






The stem needs to be beveled to a point at an angle that varies all along its length.




The stem is more pointy in the middle and a little flatter at its ends.




How you shape the stem to this angle is one of the mysteries of boatbuilding.





Battens are used to attempt to find the bearding line.




A lot of this you just have to figure out on your own.









Notches are cut into the stem from the bearding line to a center line drawn down the face of the stem.



The inwale and side stringer are set into notches cut in the side of the stem.








I think building a stem is a little like singing on key. You do not know for sure that you have done it correctly until after the note is sung.


Fortunately we have music editing software and epoxy.


The stem is attached to the keelson. The keelson needs to be faired as well.


The keelson is longer, but it is much less painful.










The stem looks pretty good but I won't know for sure until I try to fit the plywood hull panels.






Next I will fair the keelson.


Then it is on to attaching the plywood hull panels.

Transom on the Tangent of 3 Degrees

Here you can see the transom hanging on to the jig and the keel coming in at more or less a right angle.




The tangent is equal to the ratio of the opposite side over the adjacent side of a right triangle.

Right now we are at 2 inches divided by 39 inches or about 2.9 degrees which is probably way close enough.

The tangent of 3 degrees equals 0.0524077793.





In the plans the designer specifies that the transom should be raked forward 3 degrees. Now I have a suspicion that when Graham was building the first EC 22 Southern Skimmer that he just tilted the transom in a wee bit and let it go at that. He could not really write that on the plans so he put down 3 degrees. Now I am going to spend an hour or two trying to set the transom within a couple of minutes of 3 degrees.










I know the stem of a boat can be difficult. The stem is often curved, it has rabbits, and bearding lines and plank landings. The stem can be complicated but a transom that is pretty much just a flat board stuck on the back of the boat. Right?


Well not quite!


Checking to see how the matched halves of the transom fit the pattern.


Here I am separating the halves and laying them out on the full size drawings. Hmmm any differences between the plywood and the drawings are due to humidity induced paper distortions.







Checking to make sure that I am keeping the edges of the transom square as I plane them down to the lines.






I clamped two pieces of plywood together and cut out both halves of the transom at the same time. I cut just outside the line using the circular saw set to a very shallow cut. Then I used a sharp plane to bring the pieces just down to the line.










I transferred the curve of the transom from the plans to a 2x8 that will support the transom on the jig and maintain the specified arc.