by Dean Beeman
Phi comes into play when you consider the calculus formula for the natural curve of a piece of wood versus trying to duplicate it any other way- the curve cannot be achieved other than by allowing it to appear naturally. You could try to beat this proposition if you have a micron-level machine or a laser cutting tool, but the resulting piece of wood will break if you touch it.
Equifinality rears its not-so-ugly head because there are many ways to bend the wood, but there is only one result- an artistically pleasant curve. Not to mention the fact that it is aerodynamically perfect.
Such is the tyranny of nature and history- fight these if it suits you.
Lets get on with these two sections of the boat.
I’m using 4 scraps of 1/16 x ¼ basswood for each section. After steaming, these are placed in the bending frame:
It isn’t obvious, but I have shielded the strips from the pegs using scrap shims. This will prevent denting of the strips- they should emerge as very clean curved pieces. (This is the bow pulpit- I’m planning on bending the stern somewhat differently. ) Allow at least a few inches of excess material at each end- the longer end will be incorporated into the keel plank and the shorter into the papyriform crown.
In case you wound up here before building the whaleboat, the bending form is covered in that book, or trace the shape from the drawing below and build one using oriental tool picks and 3/16th plywood scraps.
The sweeps will change as the hull and assemblies are fitted, but the drawing should be enough to convey where we’re headed.
After the pulpit strips have been in the bending form for a few hours, (still slightly damp), mark a line straight across all of them as a reference point. Remove them and apply release (beeswax) to all of the form surfaces. Then apply a thin bead of wood glue between the strips from the start of the curve to whichever end is going to point upward. Re-clamp and let dry overnight. The laminated assembly should be flat to the form’s base, and protected from the pegs by strips of (released) scrap.
After steaming, bending and gluing, a pulpit should look like this:
In the above photo the next pulpit is in the bending press, a formed pulpit is behind it, and I have laid a cutout from the drawing at the bow of the boat. Whether the formed pulpit or the cutout is the bow or stern has yet to be determined, since they should each fit either end of the boat. If you look very closely at the end of the curved portion of the formed pulpit you can seen my pencil marking that was used to line up the pieces before they were glued at one end, and to define an unglued area on the other end that could be cut and fitted to the hull. Since the photo was shot at an angle it also isn’t obvious that the formed pulpit is a pretty accurate 90-degree shape. ( Given the many variations adopted by the Egyptians, a perfect 90-degree angle here seems preferable, but close-enough was acceptable, too.)
Trim both ends of one pulpit, cut off both ends of the ceiling (about 1/2 inch or so) and mark the keel stringers so that the pulpit will fit to the keel plank at what will become the bow. Cut and chip out or remove the waste section of the stringers. Trial-fit the pulpit to the keel plank. I have adjusted the fit so that what is now the bow blends into to the overall sweep of the hull. In my case the bow section does not conform perfectly with the scaled photo, but it looks harmonious so that’s where I’m going with it.
Remove the ceiling, and glue and clamp the pulpit to the keel plank. Don’t glue the strakes to the pulpit- some of the strake area has yet to be removed.
The stern assembly is more complex, and in many other models, is just not done pleasantly, or as artistically as the ancient Egyptians, which amounts to the same thing. So it requires a little precision, patience and your judgment of what looks right. My opinion in the matter counts for my model but not for yours.
Recall phi- it is an infinite number. In this case, like phi, there is no amount of physical measuring that will make the balance of the model, and the bow and stern profiles mathematically perfect, or even correct, (if correct is even the right term). Like quite a few things in life you’ll have to know it when you see it.
Trim off about 3/8 of an inch at the stern, cutting through the strakes and keel stringers, but not the keel plank. Like the bow section, mark the stringers, cut them on the mark, chip out or otherwise remove the waste sections. The stern pulpit will rise about and trial-fit the stern pulpit (either end) to the keel plank.
Document the angle of the bow pulpit by leveling the boat (I’m using a cardboard shim). Using the bending template and a piece of cardboard or paper, trace the elevation and angle of the bow pulpit onto the paper. My paper gauge looks like this:
The papyriform capital at the top of the pulpit at the stern will have the same angle as its cousin at the bow. It will be slightly higher- both the Tut model and the Cheops actual are identical- the stern is 1.07 the height of the bow at their highest point. Any other difference is probably the width of the pencil line that I used as a guide. Why or if the angles and the heights matter is probably another subject of lively but pointless debate- I’m sticking with the what not the why.
To achieve the proper elevation and angle the stern pulpit will have to rise about 4mm, or 3/32nd , and I have sanded 2 more lengths of 1/32nd strip into gently-sloped chisels- these will provide additional strength to the pulpit, and provide a more robust sanding base. The stern assembly now looks like this:
Most of what appears to the left of the curve in the photo will be cut off and discarded.
If you place this assembly on top of the bow and stern pulpit drawing (the stern, bottom drawing ), the cut lines basically extend from the notch (facing the bow on the drawing, on the right, above ), straight down and off. Then the remaining base should be cut at about a 12-degree angle starting about an 1/8th of an inch in back of the notch and ending about 1 inch from the notch on the top.
If this all sounds too much like a geometry problem, cut a piece of card stock or cardboard, fit it into place and trim it until you‘re comfortable with the cut pattern. Then trace and cut the wooden piece.
Glue and clamp the stern pulpit to the keel plank.
I leveled the boat on the board and marked a line around the bow pulpit that is 62mm from the board, then I cut off the bow pulpit at 70mm. In the stern I marked the pulpit at 65mm and cut it off at 73mm. I cut the keel plank off at an angle at the bow to blend it into the pulpit base, and at the stern I trimmed about ½ inch off the aft (rear) section of the plank and the pulpit.
I cut off the strake braces and gave both ends and the strakes a light pass with the 150-grit sanding wand. The boat now looks like this:
Compared to both originals, the lines of the model are now pretty clear, and it is more or less true to its heritage. That probably depends on the eye of the beholder and which aspect(s) of which original(s) should dominate.
Let’s keep going.
Inner Ceiling (Sides)
In the case of Khufu’s boat, what could be called ribs were lashed to the ceiling, and formed a platform for the thwart beams that in turn supported a main truss that ran stem-stern. The forces on the main truss were transferred to the ribs by way of stanchions that supported the thwart beams.
Harking back to the discussion of the steamboats, you’ll recall the hogging frames that were built to accommodate the weight of the massive engines- the Egyptians built exact forerunners of these frames during at least the Eighteenth Dynasty, giving ship builders another 3,000 years to get it right.
The lashing of the rib-stanchion-beam-truss structural system on Khufu’s boat was clearly secured by using some variation of the twist-rope vise, and it is likely that as the boat was being tightened, wedges were used to keep the lashings very tightly held. The modern equivalent would have been the tuning pegs on a grand piano.
With that in mind we can begin to tune the boat.
I have steamed a 1/16 x 1 x 8 inch strip of basswood that will become the apparent inner surface of the strakes. I’m using the same fixture and pattern that was used to bend t
he strakes:
The length is about the shortest 1/16th that will bend to the pattern without breaking. If you use something like 1/32nd or 3/64th material you can make the blank shorter.
Once the blank has dried, use the strake pattern to trace a line on the blank. Cut the blank on the line, and then adjust the length of the blank to the length of the lashed ceiling:
Trace the curve from the strake pattern onto the lower level of the blank, and cut the blank along that line. Sand a slight bevel into the lower edge of the blank (sharp edge inward). Then, using the drilling template, drill a companion set of holes through the blank, lining up the “T“ with the top edge of the blank.
Repeat this steaming-bending-drilling step for the other side.
Now let’s fit the side ceilings to the deck. Starting at the center and working for and aft, thread sets of lashings, one at a time, through the first row of corresponding holes in the side blanks (probably the first 2 or 3 in each direction) until the distance between the threads and the edge of the deck is less than 1/16th (the thickness of the sides). Leave slack between the deck and each side, and bring these thread back through the second set of holes.
A each end, loosely thread the last set of threads through the 3rd holes. The threads are ready for the first batten. Loosely thread the lashings center through the 3rd holes in the same row, and slide a 1/16th square strip across the side and between the 2nd and 3rd holes. Lightly snug the threads to hold the batten, and then work your way across the row.
As in the above photo, the side batten should extend past each end of the side, and the threads should be dangling out of the outboard side. At each end there will probably be a set of threads that won’t fit neatly into the side- these will prevent the side from forming onto the ceiling. These should be re-threaded through themselves underneath the deck, and the side hole left empty.
Working from the center, snug the threads. The deck should now start to conform to the shape of the sides. Working your way back and forth, keep tightening the thread until the sides fit onto the top of the deck and the deck conforms to the shape of the sides.
As you are tightening it will become apparent that these sets of weak individual lashings are, in fact, becoming incredibly strong as a group. If you want to test their strength, try pulling the batten back out- it can’t be done (or at least in one piece). We might have been able to apply glue to achieve a similar strength, but when it came to building a ship, this threading-lashing format is the forerunner of the planking rivet, and achieves the same result- the wood will be destroyed before the joint fails( assuming you could make the joint fail at all). This fact will make an interesting discussion topic with an unsuspecting student of marine architecture.
Let’s get back to the boat. Apply dots of clear nail polish to each set of threads at the holes. When it is dry, trim off the threads and apply a coat of nail polish along the trimmed row. Trim off any excess batten on the ends. The side should look like this:
Complete the other side. As you go you may want to reposition the ceiling in the boat to insure that it still fits, but it will.
When both sides are finished, replace the ceiling in the boat and firmly hold (clamp) it in place. Trace the top of the third strakes onto the sides of the ceiling- this will be the cut line. Remove the ceiling and cut and sand the ceiling sides level with the top of the third strake. As usual, cut on the outside of the line and then sand the line off.
On Khufu’s boat the ribs were lashed to the ceiling bottom, stanchions were lashed to the ribs, and the main fore-aft truss sat on the stanchions. The thwarts (beams) were mortised into and rested on notches on the main truss and were stabilized with port and starboard lashings. The main deck rested on this truss- beam structure.
With a minor risk of any viewer noting that the ribs weren’t, in fact, solid, you can probably combine the entire lower structure into one piece and call it a frame. I was tempted, but it would have looked too much like a kit, so let’s get on with the structure.
I’ve cut 5 ribs, each 1 inch long from a 1/16 x 1/8 strip. Using the fine saw blade and knife, I’ve chipped out notches to clear the battens, and tacked these in place with white glue. On the actual these would have been lashed using a crisscross pattern between mid-plank tunnels, but due to our restricted real estate I’ve drilled new holes on either side of each rib and lashed them to the keel plank with a single thread.
The ceiling now looks like this:
Pulpit Capitals
To achieve the symmetrical rounding of the forward edges of the pulpits I’m using a 1 in. strip of 150-grit sandpaper. The hull is clamped to the table, and to avoid any side motion I’ve drilled a hole in the worktable for a holding dog that fits through the centering hole in the keel plank. This is not as complicated as it sounds:
First, begin to shape the pulpit by working the sandpaper up and down the pulpit, maintaining pressure (symmetry) as you go, and try to achieve a slight forward taper. I plan to cut the top of the pulpit later, so precision at that end is not all-important. Once the pulpit is rounded on the forward edge, use a sanding wand to sand a slight upward taper on both sharpened edges, and sand it half-round again. (The holding fixture can be as simple as your lap.)
This as good a time as any to glue the ceiling in place. At both ends, cut off about 1 inch, down through the battens and ceiling planks. Apply glue lines along the keel stringers and the middle brace in the ceiling, clamp it securely and let it dry. Then cut off (if you used one) the centering post.
The round papyriform capitals will be weak if a single piece of wood is used for a blanks, so I’m going to make 2 capitals out of sets of circles cut out of a scrap of 1/16th basswood. I have a pattern template, but any series of round holes will work fine.
First, trace the circles:
The exact diameter is not important, but the capital is going to flow into the pulpit, so the smallest circle should be the width of the pulpit (¼ inch or so). In my case I’m starting at ¼ and building up to 3/8. If you want to make the curve in the capital more severe, change the diameter more abruptly and use fewer blank circles. I rough-cut these away from the blank and then rocked the knife around each perimeter. Glue 2 sets, stacked like pyramids of 3-4 blanks each. When the glue dries, drill pilot holes close to each center from the bottom up, but not penetrating the top (largest) circle. Drill a final hole to the diameter of whatever wooden post ( toothpicks, etc.)you have on hand, ( I’m using some 1/16th dowels) and glue these in place. The rough assemblies should look something like this:
In this case I’m going to cut the pegs midway, and chuck them into a rotary tool ( a cordless drill). The first sanding step is to round/square the top layer using a square sanding wand. I want the curve to blend, so I have wrapped 100 grit sandpaper around a standard 5/16th pencil. This is how mine looked after milling the first one:
I’m going to sand these to approximately the same size. I’m not going to try and achieve the delicate reed and ring pattern on the Tut’s boat, since that is a good deal more whimsical than the straight rounded capital found on Khufu’s boat. Looking at all the variations in the many originals, that detail ranges from non-existent to elaborate, so my vote is simplicity. If you disagree, have at it.
The size and angle of the capital, the rake of the pulpits, the size of the fore and aft deck platforms and other details that we’ll explore all imply that the ancients probably had a wry sense of humor. Nothing else would explain their exact adherence to details that were so widely mixed and matched. This also leads to the conclusion that any model builder worth his salt might as well go along with the joke and laugh at least once or twice when a modern attempt to match them goes to hell.
( I bring this up because my first attempt to bring phi into the picture with the pulpits and capitals resulted in what can only be described as a kluge. Throwing phi to the winds resulted in a much more pleasant but mathematically-incorrect bow and stern.)
Drill a shallow set of holes down into
the center of the bow pulpit and trial-fit the capital. If it is off-center, saw off the pulpit‘s head to the depth of the hole and re-drill. There is no fixed or proportionate rule for the height of the pulpit, but try not to deviate too much from the scaled photo‘s proportions. When everything seats well, drill a slightly deeper hole, trim off some of the peg, and glue the peg and capital into the pulpit. R
epeat at the stern pulpit.
I’m going to call the forward section the forward section. Using the keel plank pattern, trace the forward end onto a piece of 1/16th basswood. Much of this will be sanded away, so 1/16th is about the best thickness. Lay this out so that the deck piece is cut cross-grain: cutting in this direction allows flexibility so the deck can climb up the pulpit. This piece should be about ½ inch long- I’ve rounded the front edge but that is probably not necessary.