Tuesday, September 14, 2010

This One Rings a Bell (10)

I'm having some extraordinary troubles moving ahead in the drawing. Sure, part of that is my perfectionist nature, but really the drawing is now taking me longer, I feel, to complete, than is even remotely sane. Well, who's to say how long this should take, given it's extreme complexity?

The aspect that is slowing me down has nothing to do with being able to 'figure out' how to draw the parts. At times, as I've noted I've been baffled with certain aspects, and re-drawn and re-drawn, gaining new insights. The fukiji shape, for instance, proved to be slightly wrong, so I corrected it and then went to move on.

Last post I felt I had finally sorted out the irregular hip rafter shapes. I was wrong. Later checking and analysis revealed there were problems.

Now here's the thing: I am actually producing the shapes correctly as per the Japanese drawing techniques, it's just that the shape produced doesn't quite come out as I would expect, and furthermore, based on the hip profile, specifically it's curve, I am unable to develop the jack rafters from that hip. If I can't develop the jacks, then developing a roof surface above that isn't going to happen either.

Allow me to explain. In a regular non-curvilinear hipped roof, the rafters are straight along their length, right? Well, in a 'basic' Japanese curved hip, both the eave build up and the hip rafter curve in tandem with one another and once again the rafters are straight along their length. In order to accommodate themselves to the curved parts, the upper and lower surfaces of the rafters must be progressively slanted to meet the surfaces - each rafter as it moves along up the curve becomes therefore a slightly more exaggerated parallelogram in section than the one that precedes it. While it might seem like another route would be to bend each successive rafter up to meet the curve, this produces a twisting in the roof surface and the eave edge and it's parts would be curled inward progressively as the curve progressed. Thus they would be twisted as well. Though this occurs in Chinese and Korean roofs, this is not what the Japanese do.

So, I take it as a given that whatever the rafter profile is, that curve remains a constant shape along its length as the roof curves and the rafters move along toward the eave corner.

Consider the following example, the corner of my irregular hip upper roof:

You can see the two fukiji assemblies, in a pine color, and the irregular hip meeting them at the corner. The hip has been developed according to the method shown in my layout texts. At the left side is the high pitch common rafter along with a section of the roof underlayment.

A close up of the meeting of the hip nose and the inner corner of the fukiji shows a decently close correspondence in how the hip backing cut meets the line:

I know that the center of the backing does not meet the inside corner exactly, but there is a reason for that, and that detail does not affect any of what I have to say today.

Now, removing the hip rafter for a moment, I will place an angled plane vertically in place of the hip, and run that rafter section along, repetitively, until it meets the corner of the fukiji:

On the plane of the hip, I have then connected the intersections of the top of the rafter sections to form a curve. It looks, to my eye at least a fair curve, though it is segmented somewhat. That's a Sketchup issue. I'll have more to say on that soon enough.

Now, another way I might consider creating the roof profile would be to take the line formed along the upper outer arris of the fukiji and copy out that line repeatedly, running it up the common rafter, like so:

The points formed where that fukiji line intersects the hip plane at various spots can be connected to form a reasonably fair curve. As a matter of fact, it forms the same curve as did the preceding method.

Now, SketchUp has a tool called 'follow me' which you can use to extrude a surface along a curve. Let's see what that looks like if I make use of that tool, taking the very upper surface (the rubber membrane under the roofing itself) along the fukiji for a ride:

Again this forms a fair curve, and it turns out to be the same curve which the previous two methods yielded.

Now see what happens when I put that hip back in to see how it compares to the extruded surface:

Not so well. As you can see, the hip is formed in a less deep curve than the roof surface. That can only mean that the common rafter's curve is gradually eased as it moves along. That is, the common rafter's profile along its length does not remain constant.

'Okay, so what?' you might say. "Go with whichever one you like."

Well, I don't actually have a preference for one curve over the other. It's not about which one I like better. The problem with the hip's curve, as developed by the descriptive geometrical techniques, is that it is a different curve produced by the methods shown above directly from the the common rafters and fukiji. Moreover, I cannot find a way to 'build' a fair surface using SketchUp and that hip. I can see that the common rafter curve must slacken a bit to fit on the hip, but by how much and in which spots?

Here's the thing: in Japanese construction practice, the hidden or field rafters are of a section which allows them to be bent to conform to the supporting parts. In no layout book will you find a section describing anything to do with geometry or curvature of the field rafters. They just bend them to fit and fair it out. That's fine, and is a common approach to both wooden boatbuilding and Japanese curved roof work. However, I need to produce a drawing with a roof surface so I can develop those jack rafters and then locate the rest of the parts in the structure. The client is waiting to see a 3D drawing, and I have been stuck, for two weeks now, on this particular aspect. Each time I solve one portion of it, learn some new detail, find another layout error either in the text or in my own drawing, I keep thinking that at least I will be able to move forward. But no!

For the longest time I have been thinking that I have somehow erred and developed the field hip rafter in an incorrect shape. I got so frustrated with it yesterday that I decided to hell with the irregular hip. I set out to draw a version with a regular 45˚ plan curved hip, which compared to an irregular hip is easy peasy. Well, when I finished developing that hip and placed it into the drawing, I found the same exact problem: the developed hip was of a slacker curvature than the points left on the hip panel by the common rafter traces (or by extruding the surface, or by running the fukiji line up the common). I realized then that I was in all likelihood producing an accurate hip profile by the conventions of Japanese drawing, for both regular and irregular hips. A part which would not allow me to figure out anything from there. There is no SketchUp tool to take a rafter, say, and 'bend it to fit'.

I've been losing sleep over this stuff and getting very stressed out. It's weird when it is far harder to draw a thing than to make it, but I really do have to produce an accurate drawing for both the client and the structural engineer. I decided when I woke up this morning that the only way forward is to reverse-engineer from the high common rafter using SketchUp. I will set aside the method I have been using to produce the hip via descriptive geometry, something I have been very adverse to doing, feeling 'it must be right'. I'm desperate though. This reverse-engineering is how I had produced the roof shapes previously, as shown several posts back. I can obtain outlines of the hip rafter and low-pitch common from this method, and those outlines can be mapped so as to produce parts. It's all geometry, after all, regardless of how the parts are produced. I am puzzled still as to the shape the descriptive drawing produces, for it either the rafter profile must vary or the method is wrong, or??

So, that reverse-engineering is what I set out to do this morning, and again I ran into a roadblock - an old and familiar one: SketchUp sucks at curves! It's pathetic really. My old MacDraft 2D program was much better in this regard. Crikey, all I'm taking about here is producing the same sort of curve obtained by bending a wooden batten around some nails. That is what I would do to make the templates for the parts. But can I equal that in SketchUp? No!!

If the rafter section, and the fukiji, are both composed of chunky segments, then when you project them over and onto the hip plane, you can end up with some funny effects, like undulations in the roof surface, kinks and dips, etc.:

The hip plane profile, when used to develop the low pitch common rafter, gives an even more pronounced effect. The low pitch common is on its way to becoming serpentine. This is massively frustrating for me. Drawing is all about the point to point connections, and if things don't mesh it just takes forever to sort out. I realized today that this SketchUp shortcoming was really getting the way of progressing with the design.

One tool I had in MacDraft that was perfect for curves of the nature such as I need to form in this project is a Bézier curve spline tool. SketchUp does not have such a tool. A few months back there was such a tool available as a plug in for SketchUp, but it was pretty poor in function and didn't allow me to do what I wanted. I rarely use it. Then a better version came along, but of course Google updated to a version 8 with SketchUp and the tool wouldn't work in version 8.

I checked again today and found that the tool had been recently updated to work with version 8, so awesome! I downloaded the plug in and, once again, returned to that drawing board. I am getting oh so good at taking back steps perhaps I should invent a new dance.

I decided that I may as well reform all the eave build up layers into smoother curves. Here's the result of the uragō and kaya-oi being redrawn with greater smoothness:

Here I am at work on the fukiji, and note how many segments the upper curved surface (the piece is however rolled on its side in the picture) has - far, far more than before:

Any curve done on a computer is going to be composed of segments. The more the better, but if there are too many segments the data becomes onerously large and the drawing will become slow to process information and more crash-prone.

So far, this afternoon's 5 hours of work has got me to the point where I have manged to redraw all the eave parts:

I hope you'll agree that the eave looks better now with that fattened up fukiji. I am now ready to re-draw the common rafter and move from there back to the hip and on to the low pitch common rafter, etcetera.

Fingers are crossed here that I will be able to move forward now. I'll let you know what unfolds (er, unfurls, actually!).

Thanks for coming by the Carpentry Way today. --> on to post 11


  1. Hi Chris,

    With respect to the topic on "geometric techniques" used to produce curves on Japanese roofs. From my inventory of books, I am able to extract two methods:

    1.) The technique that produces the curve at the eave edge. (kayaoi & fukiji etc)
    2.) The technique that produces the curve of the high pitched hidden rafter.

    The books I have, however, did not mention how to generate the curves for the gable barge board. Is it safe to assume that I can use technique #2 to generate the curve for the hafu-ita?

    Also, other areas that have curves, such as the decorative rafters as well as the bottom outline of the hijiki of the brackets. Is there specific techniques to generate curves for these pieces? Or is it acceptable to use any of the method above. It would be great if I can get recommendations on book(s) that cover these problems.


    1. Frank,

      thanks for the question. Yes, there are specific methods to derive the proportions and curvature of the hafu-ita, the shape of the bottom of hijiki, curved decorative rafters, and so forth. These methods are varied, just as proportioning systems are varied. Bargeboards curve and they also swell and shrink along different parts of their length. The methods for deriving eave edge curve or field rafter curve should not be applied to other areas.

      I am away from my desk right now so I can no lay my hands on any specific book titles for you from memory alone. A lot of the stuff I have is either out of print now, or photocopied from books which are out of print, so I´m not sure how helpful the titles would be anyhow.


    2. Hi Chris,

      Thanks for the quick response. I am planning on ordering more books from Japan starting next week or so to add to my collection. I am very excited to hear your recommendations as soon as you are back (fingers crossed that they are not out of print yet :) )


  2. Hi Chris,

    In addition to the my questions posted above, there is another layout problem regarding two tier rafter work that has been on and off my mind for the past year or so. It involves the slope of the flying rafters. From Togashi's book, he gives specific slopes that can be written using whole numbers; something like 3/10 etc. However, a paper that I read, specifically the diagram on page 233 (page 245 if using Adobe Acrobat's page system) of the following:


    The author of the paper classified the 2 tier rafter layouts into 3 categories; A, B, and C. It seems that in those layouts, a horizontal line is marked out to denote the elevation of the kayaoi. This, in turn, invariably determines the slope of the flying rafters. From my observations, and also when I tried implementing those layouts in my drawings, the slope of the flying rafter needs decimal numbers in order for the kayaoi to intersect the aforementioned horizontal lines. As mentioned earlier, Togashi uses whole numbers for slopes and as such, none of his diagrams match any of the 3 categories from the paper above. Can slopes of flying rafters contain decimals instead of whole numbers? Does the 3 categories listed in the paper exists in other Japanese texts so I can confirm its authenticity?

    Still waiting for the book recommendations from earlier ;).


    1. Frank,

      I don't know if you realize it but I have a newborn and my time and mental energy is rather limited at present.

      Slopes for rafter can be more refined decimals, like 2.65/10, 3.05/10, etc.


  3. Hi Chris,

    In regards to the question I asked earlier, I realized it may have been phrased a little confusing. As an example, in the case of the hijiki arms, Togashi-san's temple pattern book already gives direct proportions for me to reference. Thus I have all the proportions marked and the curve's 2 endpoints calculated already in my drawings; the only thing left is to connect the 2 endpoints by a curve. The hilarious part is I'm reluctant to connect those two points because I'm thinking there may be a specific method to actually draw the curve itself given two endpoints. At the same time, I'm also thinking maybe its just common sense; connect the two points with just an arc. This reluctance to connect the two endpoints of a curve also exists in other parts of my drawings such as the hafu-ita, curved decorative rafters, the curves on the bottom of pillow blocks etc; all involves that I already have the proportions and guidelines drawn, only connecting 2 dots with the curve is missing.

    I am sure that you are still very busy. My intention is not to be pushy; I just wanted to let you know I'm still interested in hearing the titles to the books that may answer my questions about these curvatures. I am totally fine in waiting and giving gentle reminders periodically. I am not designing these buildings for any client anyways, rather its a serious hobby and as such, I have no deadlines to follow. I am thinking will it be ok if I contact you via email? It seems pointless to fill the comment sections with reminders in my view.

    On a side note, a new edition of Togashi's Roof Layout book came to my attention a few weeks back (木造建築 屋根工法墨付け図解). I ordered it since the book was supposed to be out of print as I understood. The interesting thing is I found an error in one of his sumigi drawing (I think it might be the same error you found that you mentioned in one of you blog post). Apparently the problem is that one of the markings for an intersection point between guidelines is placed incorrectly. I would have thought that the error would have been corrected for a new edition to be out? Besides that minor error, the book is a solid resource on drawing roofs.

    Hope you have a speedy recovery.


    1. Frank,

      thanks for the comment. I also have the new expanded edition of Togashi's roof layout book. The first edition effectively went out of print when the publisher Rikogakusha went out of business. He found another publisher., Ohmsha.

      In regards to drawing curves for part, in no case that I am aware of is a simple circular arc used. If you send me an email I'll illustrate a few methods - when I get a spare moment.



All comments are moderated, so if you're planning to spam this, know now that your clicking and pasting is in vain. I do read the comments before posting, so your mission is doomed from the outset. All this time and effort trying to put your inane spam onto blogs -- is this how you want to spend your time on earth?

Please do me the courtesy of appending your name to your comment, even if posting under the 'anonymous' option. No name = deleted.

Comments NOT accepted include:

-those containing links unrelated to blog content
-spam of any kind, or ham for that matter
-did I mention that attempted spam postings will be non-starters?