Wednesday, March 17, 2010

Following Mazerolle: "Théorie Des Devers De Pas" (II)

In part I of this post, I introduced the first drawing in this thread, the "Théorie Des Devers De Pas", or 'theory of the various leg inclinations and their diverse footprints'.

I showed the drawing as it is found in the book. Like most studies, the investigation first proceeds by duplicating the master's work, digesting it's content, and then repeating as necessary until you have it down. Pattern is first and foremost. Then, the next step is that one tries to apply the method to some variation to really see if it has been understood in its entirety and can be manipulated freely with related examples. After drawing the example in the book about 3 times, I felt confident about it, and curious to experiment further, I ventured out into a drawing of my own creation. I wanted to see if could make the techniques work for me - if I couldn't make it work, or ran into some snag, then it would mean that it was time to study the pattern some more. The Mark II, in other words, is on today's menu.

This time, I started with an irregular hexagonal plan, with the ridge slightly off center:

Above the plan, the common rafter elevation can be seen - this I made a steeper pitch than the text's study example. I chose this shape of plan for no other reason than it would allow me to work a variety of examples, and the hexagon was the final frontier, so to speak in the text's drawing, so I decided to spring forward from there.

In this illustration I left off doing the common rafters, regular or askew, as they are simple enough to do and the focus is on getting the hips sorted out. The plan, ABCDEF has the center G; the first hip to be dealt with is G~A:

This G~A hip takes the form of a regular pentagon. The dark shadowed pentagon is the section view of the rafter, and the grey-infilled irregular pentagon is the footprint of the rafter on slope, the point of the rafters intersection with the ground - that is, any horizontal reference surface.

Next, hip G~B, which is a regular (actually, it's irregular) old hip rafter, backed on top, and with sides plumb to the floor:

Notice that the hip rafter is not symmetrical about the centerline of the hip - this is one of the interesting aspects to French carpentry layout. The asymmetry gives the sides of the hip rafter different heights. Since the roof slopes on each side of the hip centerline are different, the jack rafters will have different lengths along their plumb cut lines. The converting of the hip to an asymmetrical section allows the jacks on each side to meet perfectly to bottom arris and backing cut line. If the hip were 45˚, then it would be symmetrical about the centerline. The drawback to this technique is that you can end up with a backing cut on one side of the hip with very little material to land the roofing onto, and if the asymmetry is too great the rafter might look a bit odd if it were visible to view. In any case, it is an interesting way of dealing with this particular issue in irregular hip layout, but by no means the only solution.

Here's hip rafter G~C, which is a regular heptagon:

The heptagon nearly meets the floor at both sides of the plan, however it is actually flush only on one arris. Near the letter 'D' you can see a line moving off to the right -that is the line which gives the front edge of the footprint and you can see it is not aligned with the plan.

Next up, hip G~D:

In this case, in contrast to the previous hip described, I have made the leg section an irregular hexagon so that it will meet the plan at 'D' with both forward faces flush to the plan - a backed hexagonal hip rafter in other words.

The last two hips are legs G~E and G~F, which are square sections, one rotated to one side, and the other rotated the opposite way:

With all the various hip plans, along with their section and footprint views in place, you have the makings of what might be called a spaghetti, Western:

Step my friends, into the vortex....

Next step is to draw in the hips, along with a hexagonal king piece:

I might have improved it by making the king piece an irregular hexagon like the plan, but it doesn't really matter. It's definitely a bit goofy looking as a 'roof' goes, and not something I would design as a structure, but it is after all a drawing exercise to explore the possibilities of hip rafters, or compound splayed posts, as the case may be.

Another view, with the heptagonal hip closest to view, the regular style backed hip to the right, the pentagonal hip at the rear right side, and the backed hexagonal hip to the left:

And if this crazy thing were to be roofed over, the form would look like this:

The cool thing about the method is the possibilities it opens up. It is satisfying to be able to manipulate pretty much any polygonal section of wood into a hip rafter. These hips can be made to be backed so as to fit flush to the plan, or to meet just one side of the plan, or neither, just touching along the arris only. The king piece can be a wide variety of shapes, centered or not. The plan can be any polygon, regular or irregular in form.

I've been thinking it would be neat to do a series of stools of different polygonal shapes and matching legs. A triangular stool with backed triangular legs, a hexagonal stool with backed hexagonal legs, etc. I feel my understanding of splayed post structures has deepened as a result of this study, and the cross-fertilization of the French methods with the Japanese techniques for these forms should yield some interesting offspring.

Well, I feel like I have the method (theory) fairly solidly down at this point (we'll see - I can always return to this drawing if I get stuck later), and will thus press on to the next drawings in the book, which are dormers. Stay tuned, and thanks for coming by today.


  1. After studying the "X Marks the Spot" blog series from Chris (from Nov 2010 onwards), I thought I had from-cross-section-to-footprint under the belt.

    Returning to this series, I see something rather (?) different: the edges of the cross-sections and the footprints are joined by converging construction lines,
    going off in all directions - even off the page ! Chris, could you give some idea how these construction lines are developed, please ?

    Later comment: Looking again at the 3rd figure, I do see a familiar arc and what looks like part on an elevation. May be this is a variation on the "X Marks ..." method ?

  2. Rob,

    thanks for your comment, and your work in studying this topic is to be congratulated.

    Yes, the third figure above shows the very same method as seen in the 'X Marks the Spot' series for determining the actual cross section of the stick required to produce the correct meeting with the floor (or plan view): one takes the line of the stick at slope, imagines a cross-section of that stick, and then swings it down onto the ground. in the 'X Marks the Spot' series we took it as a given that the two sticks are to be square in section - in the above method, we presume that the sticks will be shaped so as to fit against the irregular hexagonal cone, in both roof surface and floor plan, that we have established.

    The method of swinging a perpendicular to the slope line of the stick down so as to establish the cross-section of the stick is common to the layout of regular hip roofs and even sawhorses as well.

    In some cases you will know ahead of time which cross section of piece you want to employ for that hip rafter, or sawhorse leg, and need to figure out how that meets the ground (or, say, the wall plate), and in other cases you know what sort of roof surface and wall plate configuration you are working with and need to establish the correct section of stick which will conform to that.

    The same drawing method essentially serves for both objectives, though when you are needing to obtain the hip section (and don't know quite what it will look like) some added projection lines are required to produce it. If you study post 1 in the above series I deal with that projection a bit more in detail.


  3. Rob,

    actually, looking at the first post in the series, I see I didn't spend much time at all explaining that hip development. I'll take up that issue in some future drawing series I imagine, so the above two posts will have to suffice for now.

    In post 1 of this series, careful study of picture 1, leg K~D, will perhaps prove informative. Not all the lines are present on that drawing for all members, in the interest of clarity, but leg K~D shows the method well enough I think.


  4. Chris,
    Thanks, that was good advice. I studied leg K-D and managed to reproduce your drawing of that part. First using pure "X Marks..." and then as you have done it. The difference being that in "X Marks..." the elevation triangle is shifted out of the way of the stick, whereas here the base line of the triange lies along the "radial" line of the leg. The latter method requires very careful work to get the perpendicular projections right !
    I started from the cross-section which I twisted a guessed amount. This meant my footprint did not line up with the eave. So another execise is in store.

  5. Rob,

    good work. The fun never really ends with layout. Look more closely at how the footprints and the cross-section relate - you will see a projection line or two that relate individual faces to/from the footprint.



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