Tuesday, August 31, 2010

This One Rings a Bell (8)

Oh yes, I was writing a blog - now it all comes back to me. Where'd all those days go? No, in case you are wondering, I did not win an all-expenses paid holiday to some island in the Caribbean. I have however moved house, joy of joys, and that cut three days or so off my drawing time. It also gave me some wicked asthma, which is how my body has decided to react to the Ragweed (Goldenrod) currently in maximum pollen release mode. I'm recovering well enough now that I'm staying (for a little while) down in Connecticut, where such noxious pests are not so widespread. There are other pests, like the drivers around these parts, but I'll save that diatribe for another occasion.

So, on the days where I haven't been preoccupied with other matters, which is most of the past 10 days, I have been drawing full time. Progress has been won at the end, but an epic struggle was endured with things looking dire at certain junctures. I'll spare you most of the details.

I've been working exclusively on the upper roof, focusing on getting the common and hip rafters established before I begin working on the other structural members. One of the advantages of the Japanese double roof system is that it allows one greater latitude in where the supporting elements can be placed. All that should become clear soon enough in the days ahead, but today's post looks at those pesky common rafters and those irksome hip rafters.

These were the toughest rafters I've ever laid out, more onerous than the fanning rafters in the exposed eave. The intense difficulty is due to the fact that the upper roof's shape is not only irregular-plan but also of double curvature - and the whole works is perched atop a curvilinear base in the fukiji and other perimeter fascia build up layers.

Let's see, trying to draw something curved in two directions and placed on top of a curved plan... Result? Near insanity, let me tell you (not that I have far to go to reach that condition!).

It was a tough nut to crack, and the process was hindered considerably by the fact that SketchUp is rather poor at dealing with curvilinear objects in general. Several parts were re-drawn multiple times until I could obtain a satisfactory result.

It all began, early one morning, with the seemingly innocuous task of establishing the curvature of the high pitched (7.5/10) common rafter:

Then the other parts, namely the low pitch (5.5/10) common and the hip rafter profile, are developed from that rafter's profile. Sounds easy enough, what could go wrong?

Initially I followed a drawing shown in one of my layout books- with the aid of a magnifying glass - and here's how that drawing looked when it was complete:

That little sketch took me 4 full days to complete. If I pull the traces out of the development, you can see more clearly the principal players:

The high pitch common is on top, the low pitch common to the right, and the two faces of the curved irregular hip are splayed out on each side of the irregular hip's plan, in green.

Another view:

Clicking on the above images will make them more legible, if you're feeling brave enough to look what may appear as little more than a mass of tangled wiring.

Here's a zoom into the tip of the irregular hip:

The brightly colored bits are cross-sectional views of the eave build-up components, both at the face of the hip and at the centerline:

Did I mention that I spent 4 days on that friggin' drawing? I was about as nervous at the end of it all when it came time to 'raise' the 3-d parts off the 2D developments as I would be after having cut a stick of wood when a bit uncertain in the layout.

And you know what? The layout didn't quite work! I am absolutely sure I followed the book very closely, and yet things just didn't quite come out right at the hip - nor did the high and low pitch curves correspond properly. There was a bit of teeth gnashing at that point.When there isn't much hair left to pull, you grind your teeth - that's how it was explained to me.

So, back to the drawing board. After several mock ups and re-draws I was finally able to iron out all the wrinkles and produce a high pitch side and low pitch side that had perfect correspondence with each others curvature where they met at the irregular hip. Here's a view of the underside of the mock up:

The light blue piece in the middle represents the plane of the centerline of the irregular hip rafter. A click on that image will make it all come clear I hope.

With the rafters sorted out, I could then commence building up the roof underlayers atop the rafters, which will comprise 2 layers of 3/8" ply and some peel and stick and ice & water shield, yada, yada:

The hip rafter is not developed yet. Well, it was, incorrectly, at least three times so far, but that was then and this is now. Round 11 and I'm a little punch drunk. It should come out fine this time, knock on wood.

I placed the roof parts up in the main sketch to see how things were shaping up. Wanna see? Here's a look into the gable end with the shallower pitch:

Now, the gable end rafters will not be running up into the middle of the roof and meeting each other, as it appears in the picture - I've left them long for the time being as I have yet to sort out the details in the gable opening.

Here's a view looking at the face of the steeply pitched side:

A corner perspective:

One of the consequences of having the eave curve begin right in the middle of the eave edge is that the ridge and purlins are curved as well. It's one option among many, and the one I went with this time.

Lots to do yet, but the worst appears to be over. Ha-ha, where have I heard that before!

I can complete the hips tomorrow and sort out the gable detailing including minoko. Once the overall form is looking right, then I can locate the fanning cantilevers and the rest of the supporting cast, and as none of that work is double curvilinear, it might almost go quickly. Well, I'll hold off on the optimistic time projections for the time being.

Thanks for coming by the Carpentry Way today. Comments most welcome. --> on to post 9

Wednesday, August 25, 2010

Fan of the Fan (V)

So far in this series I have taken an in-depth look at the issues inherent in laying out fan rafters, and have presented a couple (post III, post IV) of different traditional Japanese methods for spacing the rafters. Each of those methods has proven to be decent in one aspect of spacing (at the rafter tips), but not so good at the other (that being the view of the inter-rafter wedge-shaped spaces from directly underneath).

Today I will examine another traditional Japanese approach to the problem. This is one of the more commonly-described techniques in the layout texts: the infamous '2.7 slope' method.

Again we start with a 45˚ plan view, that is, a regular hip rafter corner:

This is a right triangle of course, labeled 'ABC'.

Now I drop a perpendicular down from the eave edge, line AB, measuring 2.7 in length. The end of this line is marked 'D', and a line is connected from it back over to 'B':

Next, the hypotenuse of this 2.7/10 triangle, line BD, is subdivided into the desired number of rafter spaces - again we choose 8 divisions, just as we had with the preceding examples:

The next step should be predictable enough by now - we connect lines from the origin of the fan, point 'A', through to the division marks on line BD:

It's time to analyze the results. First we look at the eave edge, line AB:

Clicking on the above picture will render it larger and more readable. While 10/8 gives an average 'ideal' spacing of 1.25, when using the 2.7/10 method it can be seen that the spacing of our rafter tips along the eave edge follows a pattern of gradually increasing value:


Whats nice about this pattern is its smooth progression. In fact, each rafter tip space is roughly 1.06 times larger than the one preceding it. Our average 'ideal' value of 1.25 for the spacing falls in the middle of the series of values (more accurately: it would be a median value if placed into the series). That gives a pleasing look for the rafter tip spaces it seems to me.

Next, let's see what this method does for the pattern of wedge-shaped spaces - the view from under the eave:

An even division of 45˚ into 8 equal angles would be 5.625˚. As you can see, with the 2.7/10 method, the angular values start out in excess of that with 5.7736˚, and then proceed as follows:

5.7736˚... 5.9708˚ ... 6.0446˚ ...

The spaces are climbing steadily for the first three intervals, however we started out somewhat over the 5.625˚ value, so something will have to give soon - and it does with space #4:

5.7736˚... 5.9708˚ ... 6.0446˚ ... 5.9857˚ ... 5.8016˚ ... 5.5144˚ ... 5.1547˚... and 4.7543˚

So, this fan pattern exhibits a similar behavior to the previous method in post IV: the spaces between rafters climb up from the start, then drop back down as we sweep over to the hip. In fact, this 2/7/10 method gives a greater extreme in the range of values for these wedge-shaped spaces than the post IV method. The only advantage this method has over the method in post IV is that the eave rafter tip spacing is on a more regular progression and does not exhibit the same extremes. This method is the simplest really in terms of the steps of layout, so that is a point in its favor. Still, it's not ideal. Choosing between this method and that in the previous post is a bit of a toss-up if you ask me. Therefore, the search continues.

Is there any solution to this conundrum? The three methods we have looked at so far all have their shortcomings. Well, the answer to the rhetorical question is, 'yes', and we'll be looking at what is undoubtedly the penultimate method for spacing fan rafters in this thread's next post. I hope you'll return for that installment.

Thanks for your visit to the Carpentry Way today. --> on to post 6

Saturday, August 21, 2010

This One Rings a Bell (7)

Welcome to post 7 in this design and build thread for a Japanese bell tower, or shōrō. When I last left off, I had completed the eave build up for the lower roof, which consisted of a square-section kaya-oi, a rectangular uragō above that, in turn surmounted by the upper piece, the kami-uragō. I had completed all that, yet, as things turned out, I was not in fact done. Design and re-design was the reality, and as I mentioned in the last post there were a few things to figure out with that eave edge yet before I could proceed with the structural upper roof.

Some of you may be wondering why there are all these pieces at the eave edge. After all, in Western carpentry, it is typical to overlay the rafters directly with planking (or plywood in modern times) and then apply the roofing to that substrate. The eave edge is thin, to say the least, unless a covering fascia is applied and a gutter (which blocks the view of the fascia, does it not?).

While there are several important differences architecturally between Japanese and the western vernacular architecture, one of the most primary is that of where the emphasis is placed. In Western architecture, the house is essentially a decorated box, as a certain F.L. Wright said some years back. That elaboration and ornament of the building revolves around the fenestration - how the facade of the building is configured, how the windows are placed/aligned, how the doors are visually framed, what pattern of window muntins are used, what paint or siding is to be specified, etcetera. The roof, particularly since the advent of modernism, has become reduced greatly in emphasis. It's just a lid on a pot so to speak.

As I understand it, the disillusionment that followed the first World War in Europe led to a certain ideological perspective in the influential design houses of the day. This perspective rejected hierarchy and authoritarian social structures in favor of more socialist ideas, design for the "common man" (= cheap) and so forth. The eave on the roof was considered by these designers to be symbolic of the crown, so, for that reason, the eave was eliminated as a design idea and the flat plane roof without eave came to be the favored choice. A case of ideology trumping reason once again. The eave helps the rain water avoid running down the walls after all. The roof does need to keep the weather out, or at least one would think so.

This affectation lingers on in the west, even in non-modern style structures. The roof is largely an irrelevant architectural feature. The eave, if there is one invariably features a monotonous white perforated metal soffit, and the only function to having a thicker eave edge might be for mounting gutters. Yes, I simplify the argument a bit here, for brevity's sake.

In Japan, the roof is everything, whether we are looking at a thatch-roofed farmhouse (minka), or an imposing temple. The word for roof in Japanese, ya-ne, (屋根), literally means the root () of the house (). In the Japanese traditional perspective, there can be no house without a roof. That may sound obvious enough, but it goes further than mere practicalities of keeping the rain off the insides of that box.

The various elements added to the eave edge of a Japanese traditional roof are rich in diversity of form and arrangement. Depending upon roof covering material (tile, thatch, wood shingles, asphalt shingles, bark shingles, slate, metal, etc.), and how the under eave space is to be decorated, the eave edge will vary in treatment. The pile up of structural elements at the edge of the roof serve structurally to tie the rafters together at their ends, provide a space between exposed and hidden roof components into which cantilevers or other eave strengthening elements may be easily added, and convey a certain aesthetic value in and of themselves. A thicker roof edge suggests a more robust and solid roof, even if the thickness is confined only to the last 20~50 cm of the eave edge and the main body of the roof has a much thinner actual build up of roof material. That edge thickness may be acquired by stacking shingles many layers deep at the edge, or by piling up layers of wood, as I have done in this bell tower, or by a combination of the two.

One point common to both tiled and metal shingled roofs, particularly on temples, is the use of an inclined board atop the build up of eave edge fascia. This inclined board is pitched differently to the lower support pieces like the kaya-oi or uragō. It's called a fuki-ji (葺地) - here's a view of a roof rafter with these parts laid on top:

The rafter is on bottom in orange, the kaya-oi is in green above it, and uragō is on top of that piece in a light brown color. The fukiji is the piece in red at the very top, along with the associated thinner support board below it in yellow. Notice how the front face of the fukiji is tilted away from the front faces of both the uragō and kaya-oi. The tilt of the fukiji, in fact, is 90˚ to the line of the upper roof rafters (not pictured). The fukiji, associated to the upper roof, serves as a transition piece between the lower roof, which includes the uragō and kaya-oi.

Here's how the fukiji is used in an application of copper roof shingling:

See how the roof shingles are continued down the face of the fukiji from the roof surface above. In fact, the copper continued right around the underside of the fukiji support board (in yellow in the first illustration) and ends at the junction with the uragō. Thus, any water that runs over the roof edge will travel down a protected surface and will drip off without having any opportunity to touch the woodwork. Another advantage to the fukiji is that it allows the field rafters to connect to it with simple square end cuts - with the kami-uragō employed instead of fukiji, the rafters need to be tapered out to a thin end to fit cleanly. It is also simpler to terminate the roof substrate onto a fukiji than onto an uragō or similar.

Here's another example of the fukiji treatment:

The fukiji transition can also be effected with shingles of another sort:

On a tile roof, the fukiji is typically scalloped out to receive the individual roof tiles (this one is only slightly tilted forward though):

So, that's the fukiji element. Looks straightforward enough, simple even, but, things ain't what they seem, particularly in the case of a roof with a curved eave edge towards the hip rafters. with those elements in the eave edge that tie to the lower roof, their surfaces are geometrically in plane with the rafters; thus, as the rafters rise, the fascia elements rise perpendicular to the rafter as well:

Now figuring out the curves and intersections for those parts is entertaining enough, but with the fukiji, given the fact that its face is along a different slope than the elements below it, we have the following effect when the roof edge curves up:

While the kaya-oi and uragō rise up in unison, the fukiji wants to fly south for the winter: as the roof rises, the fukiji moves further and further away from the pieces below, geometrically-speaking.

Here's the graphical depiction of the effect of a certain amount of rise on those elements:

Notice what happens to the distance 'A' in the drawing, which elongates to 'B' at the end of the rise. The point being, looking from below at the eave edge, one can observe the parallelism of the reveal at 'A'. If the fukiji is simply lifted up, then the gap increases, which is to say that parallelism is destroyed. This doesn't look so good - like the upper layer was put on crookedly to the layer below. The Japanese solution to the 'fukiji problem', as I term it, is to bend the fukiji piece back inward so as to maintain parallelism with the uragō's front edge .

Welcome to the curious and often very counter-intuitive world of compound layout my friends.

I first became aware of the fukiji issue on the Ellison project in 2003 or so when my co-worker Walter asked me about a section of a textbook, but one page, that mentions the matter. It has occupied my mind ever since as one of the curious layout issues that I didn't fully comprehend, and now that I have at last the opportunity to do a structure with a copper shingled and strongly curvilinear roof form I can at last face the demon.

It's been a struggle for the past few days getting to grips with the fukiji and learning how to correct the distortion. Here's a shot from the drawing showing the development of the 3D part from the 2D developed plan:

Here's a glance at the other side of the piece, where it is perhaps apparent how the front surface of the fukiji is somewhat curvilinear, just like the undersurface:

So, the fukiji is an example of the dreaded double curvilinear work, and it was a slice of delight let me tell you. I still have a few hairs left after the pulling and cursing! Actually, it wasn't so bad though I did draw it 4 times before I had the configuration and proportions I wanted.

Back in the bell tower, the kami-uragō was ditched and the new fukiji installed in its place - let's see how that turned out.

Before (with kami-uragō) on top:

After (with fukiji):

One very slight change engendered with the fukiji is hardly noticeable - a 0.5 cm extension of the hip nose.

Here's the look from up over the edge, staring at the innards:

Sighting right along in parallel with the face of the fukiji, a view no one will be able to readily have, the slight re-curve inwards is evident:

And from below, a seamless parallel line between fukiji and the uragō below:

Right then, the lower roof is officially done and I am moving on to the structural roof above, where the pitch will be 7.5/10. Danger, curves ahead.

Thanks for checking out the Carpentry Way today. Take care! --> on to post 8

Tuesday, August 17, 2010

This One Rings a Bell (6)

Well, another week or so has flown by, and I've been hard at work on the bell tower drawing. Today I will bring y'all up to speed with the most recent developments.

I have beefed up the exposed hip rafters for starters. This was accomplished by raising the hip section around the lower end so as to make the komai (battens) sit in housings along the hip, rather than atop the hip:

This added 1cm or so of height to the lower section, and makes for a better joint with the komai to the hip. Also, by having the komai sit in housings, the ceiling boards will attach cleanly to the hip without a gap between each successive set of komai. The upper section of the hip never needed to be backed, so I returned it to a rectilinear section and added about 5cm in height. Also visible in the above picture is the hiro-komai ('wide' komai) which sits at the top of the run of battens, and covers over the small boards - men-do-ita. These boards block the wind from passing in between the rafters, and deter birds from nesting in space like that too! Both the hiro-komai and the mendo-ita are curvilinear like the rest of the battens.

In other news, the fan rafters are finally completed. OMG! These took a long time to draw and stretched me to my limits in layout. These are tough and required lots of calculation and 12 separate descriptive drawings!

I've got lots of pictures to share - here's the first:

I've left the bell out of the drawing for the time being as it speeds up the rendering. One other detail added, visible in the above picture is at the eave edge, where the build up of fascia now features an added layer - the kami-uragō - or, 'upper carapace'. There may be yet another layer going on there, the fukiji, or something else, but I haven't decided yet on that matter.

An aerial view of the fan rafters:

Now from on down, crouching low and looking up:

In the above picture one can also see another small change I have made to the support structure. Notice that on the right side, on top of the lower beam, there are now two bottle-neck struts instead of the one as there used to be, and as remains on the left side. This change improves the strength and resistance to deformation in that section (and the one directly across from it), though it does mean that there are now two different arrangements in view. Now the step is done, I think it looks fine with that small amount of asymmetry, though I was uncertain about it when considering the matter initially.

I have also added the final layer to the decorative eave structure- the ceiling boards:

In this case I have made them to look like Eastern Red Cedar (actually a juniper), however that is just one possibility. The other leading candidate is Western Red Cedar (not a true cedar either). I am looking for something that is light, rot resistant and relatively easy to bend. Funny enough, I can obtain higher quality WRC here in Massachusetts than I could back in B.C. (in Canuckistan) from a lumber yard. That's what they mean by 'export markets' I guess. While some countries experience a brain drain, Canada seems to have a board drain.

Looking straight up, this is the view:

The section in the middle of the roof will have a ceiling fitted, but I am leaving off designing this part of the building until the rest is done. It is a standard in Japanese architectural drawing to provide a plan of the ceilings in a house or other structure, as they are an important design element and subject to considerable elaboration and differentiation. At this stage of the drawing I have left the ceiling boards as an overly-simplified 'mono-board', however in the actual structure they will be individually shaped pieces, just like the rafters that sit below them. Each ceiling board will be a section of the fan, and differentially curved.

The reverse view, looking straight down:

Interesting to note the optical effect of the fan rafters, making two of the beams below in the support structure look like they are curving outward like a pair of parentheses '()'. Take my word for it, those beams are dead straight!

A close up of the eave build up, with the square-section kaya-oi on the bottom, then the uragō, and then the kami-uragō:

Here's a look at the fan rafters with the komai and ceiling boards removed:

Next, a view of the rafter tips looking along the eave edge:

Notice how the rafter tips gradually project out further as they move along to the hip and their downward cuts, along with their top/bottom cuts, vary with each rafter. This treatment provides a very smooth visual flow along the eave edge, point to point along the rafter tips. I think the final one in the row, right next to the hip has a very slight error though in the down cut, which I will attend to shortly.

One for the road:

The exposed eave structure is now complete, and I can move on to the actual structural roof drawing. While I am deciding about how to cap off the eave edge, I can lay in the lower tier of support beams inside the roof and lay out the fanning cantilevers, or ōgi-ha-ne-gi. Are you drowning in the Japanese lingo yet? Sorry about that - just trying to be clear without recourse to such gems of concision as 'whatchamacallit', and 'thingamabob'....

Thanks for swinging by today. Comments most welcome. Take care on your travels, and hope to see you soon. --> on to post 7

Thursday, August 12, 2010

Fan of the Fan (IV)

Last time we looked at one method the Japanese use in traditional carpentry practice to space fan rafters. That method involves taking the run length and swinging it over to the hypotenuse length, after which the difference between those two lengths is divided and a new line snapped across. The aim was to split the difference between the extremes of spacing associating to both ends of the fan spectrum, moving from the common length to the hip length. The result of that method was that the spaces between rafter centerlines at the eave edge climbed steadily as the fan swung over to the hip, while the angular value of the wedge spaces between rafters climbed for a rafter or two, then fell off steadily. That method did not result in perfection, so we will consider other approaches to see if something better can be found.

Today we look at another traditional Japanese method which is fairly similar to that first one in that the difference between the extremes, namely the run of the hip rafter and the run of the common, will be related.

Here's our starting point, triangle a-b-c, 45˚ in plan:

Previously we swung the run length over to the hip run; in this case we do the opposite and will swing the hip length over to the common, creating point D:

In the previous method we then divided the difference in the two lengths in half - here we will not. A line is simply snapped across from B to D, forming, incidentally, a 22.5˚ angle to the eave line AB:

The triangle formed, B~C~D, is an isosceles ('iso-' means equal, and '~sceles' means scale). Notice that as with our previous method, we have also divided our new line segment, B~D, into eight equal divisions.

Next we extend rafter centerlines from the origin to the eave, passing though our line division marks:

Right, there we have the method for fanning the rafters along eave edge A~B.

Now let's see in depth what result devolves. First we will look at how the angular divisions work out. If we divide 45˚ into 8 even units, we obtain 5.625˚ as mean, or 'ideal'. Here's what we have produced with this second method in comparison:

Clicking on the image will make it more easily readable. The angular pattern is this, moving from common over to hip:

5.2421˚ - 5.5570˚ - 5.7888˚ - 5.9121˚ - 5.9121˚ - 5.7888˚ - 5.5570˚ - and 5.2421˚

This pattern grows steadily to the middle pair of rafters in the set, then falls steadily, in mirror image. Considering the 'ideal' of 5.625˚ as a mountain peak, say, we have climbed up to, slightly surpassed, and then dropped down around that mark. Not the smoothest pattern - the rafter angulation appears slightly congested at each end of the range.

Let's take a look now at the rafter tip spacing. If you divided the eave edge, a length of 10 in the drawing, into 8 equal parts, you would have rafters spaced 1.25 units apart as an 'ideal'. The result of this second method produces the following however:

Similar to the first method seen in the previous post, the arrangement of rafter tip spacing is on a gradually ascending order. That's not too bad. Like the first method we looked at, this one produces a decent pattern at the eave edge, however the arrangement of the angular spaces, such as would be seen viewing the fan rafters from below, is not so sweet. It seems like the perfect arrangement still eludes us. In the next post in this thread I'll take a look at a third Japanese traditional method for arranging fan rafters, one of the most popular, to see what it offers.

Thanks for dropping by the Carpentry Way today my friends. --> go to post V

Tuesday, August 10, 2010

This One Rings a Bell (5)

Today is a post about progress, the sort one makes by taking a step back and then two forward. Yes, another wormhole was discovered, and I surely fell on into it. I was trapped in there for a good while today.

Here's the problem - a little matter that all started with a couple of lines that weren't quite matched up:

You might be wondering what place in particular I am referring to, so I'll zoom in a little closer to the left-hand fan rafter:

Do you see it now? No? Well, how about we look a little closer yet:

Stands out like a sore thumb, no? Okay, okay, I'll move in closer yet, towards the spot where the middle horizontal line intersects the vertical line on the left side:

If you click on the picture, you'll see that just a hair to the side of the solid line is a little dashed line. Trouble is, that dashed line was the reference, and the solid line snapped slightly over to the side for some reason. A solid line I based a whole bunch of stuff on....

Damn that SketchUp - I shake my tiny fist...

That little kafuffle with the line had effects when I started placing one of the developed fan rafters into place on one of the purlins and things just weren't quite adding up. That's how I found it - tracking backward until I located the discrepancy. Unfortunately, in the end I realized that the repercussions of that line being just a hair wrong were going to have numerous down-stream effects, and more importantly, it meant that I had to re-draw all of the curvilinear parts. -gulp-!

Here's the thing - while the drawing will look absolutely fine upon inspection, unless you magnify in, way in, continuing on with the drawing when it is based on an error, no matter how slight, means I cannot rely upon the data points I have acquired so far in the drawing process. You see, once the drawings are completed, I will be spending quite a while re-drawing key portions of the 2D so as to make a whole bunch of templates with which to shape parts and check alignments. The 3D allows me to be absolutely sure of my results, but it absolutely punishes me if I don't have the 2D portion just perfect. Nothing painful mind you - I imagine some future version of the software might be configured to give the user little jolt of they make an error, who knows. Just kidding, I think...

By getting the 2D perfect, I can rely upon the drawing directly when I draw the templates in full scale, and I will be able to take off various heights and measures from the virtual into the actual with total confidence. So, it's worth taking on the error and fixing it now. That's my stand at least.

Questions of deciding whether to fix an error once discovered or to carry on and either build on top of it or try to compensate for it some way come up all the time in construction. It's all about the best laid plans of mice and men, and this mouse is trying hard to get the plans laid as right as he can.

So, 10 hours later at the drawing board, and I am only just managing to stave off going completely 'round the bend, but here we have it, the Mark II:

Yes, that back step was a royal pain in the you know what, but it paid truly handsome dividends in the end. You see, that little line problem wasn't the only discrepancy haunting me.

Though I had completed the hip rafter layout to the point where the fit between components was decent at the exterior intersection...

... in reality all was not totally fine as there were some problems with the peak of the backing cut on the hip:

That little gap above the hip arris where the kaya-oi meet on their lower surface had been bugging me, and I had decided after that previous trip down the wormhole that I would, you know, how do they say it? Oh, yes: 'deal with it later'.

Trouble was, I hadn't really found a solution for determining the backing cut on a gradually curving hip rafter with a curving purlin meeting it. I have virtually every Japanese layout book there is, and, strangely I might add, none of them seem to cover this matter of the backing on a curved hip rafter with curved kaya-oi. There is one illustration in one of Togashi-sensei's books that shows the hip nose layout including the backing cut, and I had followed it faithfully, several times over in fact, and the results were plain enough: it didn't come together right when the parts were assembled in 3D. The drawing above is proof of that, a product of that method, and when I drew the new hip rafter and kaya-oi, I had the same problem again. So much for the aforementioned 'later'.

I have other roof carpentry layout books in French, German, English, and even Yankee, but the topic of curved hips is really not covered in any semblance of detail. The few odd methods I have come across in those texts I have tried but they don't work when the eave purlin which lies atop the hip is also curving up. They only work for curved hips with with straight parts laying on top of them. A curved hip with flat strips or boards laid upon it is no big deal, but if the eave purlin, kaya-oi, is curved, the backing cut is a tough nut to crack. It has stymied me for a while now.

Well, was a tough nut to crack, for I managed to solve the layout on that today! By determining the correct method, through some reverse-engineering and a sudden flash of insight, I was able to also determine what exactly was wrong in the illustration in Togashi's book. That, my friends is the very first error I have ever discovered in the master's work. While I derive little satisfaction in finding his little mistake, I am tremendously pleased that I have at last solved a vexing puzzle. Maybe I'll write him - not sure if he is still alive though.

In the end, I had to construct new hip rafters, kaya-oi, and komai. So far I have placed the new hips (sumi-ki) and kaya-oi on the roof, and things are fitting just as they should:

I also had picked up a subtle little tip that I noticed discretely marked in one illustration of Togashi's book and from there re-sloped the hip nose cut and re-shaped the hip end slightly:

These slight changes decrease the amount of end grain of the hip sticking out, always a good thing to do.

Here's a look down that hip rafter, showing the curving and slightly twisting backing cut:

Well another adventure in layout-land my friends. Next I hope to take a few more steps forward.

Thanks for your visit and comments always welcome. --> on to post 6