Saturday, October 1, 2011

Lucarne Et Nolet Sur Un Comble Moins Élevé

The titles keep getting longer it seems, as does the length of the post. Today's piece is about the final dormer drawing shown, in detail, in Louis Mazerolle's work Traité Théorique Et Pratique De Chapente. This dormer differs from the preceding dormers - lucarnes - I have written about in several respects. This is the first dormer to have a form of king piece truss, and the first dormer to have the rafters overhang the eave. Thus there is no molding to worry about. The most significant difference however is that the main roof in this case is lower - moins levé - than the dormer roof. Thus, a portion of the back side of the main roof has to climb up to meet the peak of the dormer, creating a situation where there are 'hip' pieces resting atop valley pieces at the intersection of the two roof planes. So, like the other dormers to be studied in this text, the main problem to solve is that of the shapes and dimensions of the valley/hip pieces which enable the roofs to connect seamlessly.

It occurred to me that for those readers not especially familiar with the geometrical issues which come up in roofs with hips and valleys, namely the places on a roof where differing roof planes come together, a few pictures might help to better explain the situation, particularly in respect to this dormer.

Here's the basic set-up: we have a dormer at right angles to the main roof, and a simplified truss on the dormer which (for this example) I have made to look just like a capital 'A':

 Next, I have placed a couple of planes on top of the dormer so the intersection of the dormer's roof planes with the main roof plane can be more obvious:

Note the horizontal traces associated to both truss and roof planes (one at the ridge, and another line each tied to the tips of the rafters) which extend from the dormer roof on back and through the main roof. On the main roof I've connected these upper and lower traces to match the tipi-like shape of the dormer roof meeting the main roof.

So, at the spot where the dormer roof meets the main roof it would be jolly nice to have some sticks of wood in there to connect things together. In the next drawing I have taken the 'A'-shaped roof truss and moved a copy over and laid it on angle to rest against the main roof plane:

Slight problem here Houston, as it is obvious that the roof truss, when laid over to slope of the main roof, is not tall enough to meet the ridgeline from the vertically-oriented truss on the dormer. While the width of the dormer, as measured at the bottom end of the truss rafters, remains the same at the main roof, we have a longer distance to climb up that roof plane - the truss needs to be put in a medieval torture device and stretched some. In the following picture, I have worked some magic and s-t-r-e-t-c-h-ed the truss laying against the main roof so that it meets the dormer's theoretical ridge height:

Can we sit back and bask in glory, another tricky problem solved? Well, not quite yet. You see, while the stretched truss portion does now reach all the guidelines established by the traces at ridge and rafter tips, if we put the roof planes back in place we can see another issue cropping up:

It would appear that the laid-over truss bits, which are square in section sticks just like the vertical truss, poke out from the roof plane. Here's a view from the other side:

If we left those sticks protruding like that the finished roof surface wouldn't look too good.
There are two solutions for this - the, uh, cheesy one, called in some parts of North America a 'California' valley, would be to move those sticks of wood on the main roof in and down so that  they touch the dormer roof plane along just an arris - the upper outside arris on the sticks. Then over goes your sheathing, and wham-bam with a bunch of nail-gunning fun and it is all tick-tacked together. As the song goes,  Little boxes, little boxes, on the hillside...

A better solution, except in terms of getting it done as fast as possible, would be to re-shape the sticks of wood laying against the main roof so that they met the planes from the dormer perfectly. This is the French solution, although they also employ what we might more usually call a 'valley' rafter; that is, a stick of wood cut so that it has a vee-shaped trench running down its top surface, one half of which is in plane with the dormer and one half of which is in plane with the main roof. Those are a lot of work to make, and not the sort of solution we are looking at today.

These re-shaped valley pieces used in these dormer examples from Mazerolle's book take a while to learn how to draw but are tidy, strong, and efficient solutions to connecting the dormer roof planes to the main roof. Here's a look at how that original 'A'-shaped truss would be re-shaped to conform to the width, height, and surface planes of both dormer and main roof:

I next apply the roof planes again so you can see clearly that the valley pieces, laying flat against the main roof also fit flush to the dormer's roof planes:

And a look from the other side showing how the folded-back upper portion of the 'A' conforms to the reverse side of the main roof:

Now, to produce these pieces requires a bit of developed drawing work - all the dormers in Mazzy's book are showing applications of the same method to produce these curiously-shaped valley pieces. The developed drawing work is presented for you in the book:

This drawing is deceptive however for several reasons. For one thing, only a small portion of the actual lines required to do the 2D drawing, to completion, are shown. For another, and as regular readers of this blog will have heard from me in the past, one can expect to find 'mistakes', 'misdraws', omitted labels and other such vexations. I now expect to find these problems in the book, with every single drawing, so it does not put me off like it used to. I'm now battle-hardened. Ah, the good old days, when I had a naive belief that an illustration in a layout book would be accurate....

In terms of the text associated to this particular lucarne drawing, in the final paragraph Mazerolle remarks (my best translation at least):

"...but in order to not unnecessarily complicate the text a lot of operations are described only once so readers should pay close attention to the explanations and refer to them as needed."

Yes, my friends, pay close attention. This reminds me of of a certain tradition you will see in the martial arts world, where the master will walk out onto the floor and, without so much as a "how do ya do?", will throw a few people around for a while then make an exit, stage left. No explanation was offered for how the techniques shown are to be done or were done, or why those ones were done and not others. The keen student who experiences this just once will realize, hopefully, that the next time the master shows up he/she had better keep their eyes pinned like laser beams upon the moves of the master to have any hope of gleaning some useful information. In the West, this approach doesn't tend to sell so well, as students are habituated, it would seem, to not paying close attention when the moves are done and expect to be able to ask many detailed questions afterward, "why...?", "how come...?", "what if...?", and, "could you do that again, slowly?". The real answer to all those questions, in that context, is simply this: train more.

Mazerolle is a bit like that, except a terse explanation is offered, and then the moves shown sometimes are entirely misleading. And, it must be said, a certain intellectual apprehension of the material is most helpful. It's a special kind of challenge, and since he's long dead I have no opportunity to question anybody about the hows and whys. You have to take it as it comes and be prepared for some struggle. At least I do - struggle, that is. There are undoubtedly more gifted and insightful individuals out there who would see the solutions and grasp the essential points far more quickly than I. But then this is hardly a race, and the tortoise did do rather well in the end against that rabbit, no?

So, back to the 2D part where all the secrets may be revealed, if you know where to look. Here's what the drawing looks like when most of the lines are in place:

The method being shown is the same method I have run through several times already with this text, and involves figuring out footprints of sticks and the planes which associate to them.

Here's a bit more focused view of the portion of the drawing in which the valley pieces are worked out:

I'm not going to delve into a detailed look at the how and why aspect here, but in the following drawing (with some layers stripped away for clarity), with another zoom-in, you can see the white footprints that are produced by way of the developed drawing technique shown:

Notice how all the footprints are rhomboids. The two at the left side are for the 'hips' which climb up above the main roof, while the footprints at the right are for the valleys laying against the main roof.

I was surprised by the shapes obtained since in all previous drawings the sections of noulet (valley rafters) were trapezoids, not rhomboids. Still, with every new drawing in the book, something new and different is shown, something to which I must pay close attention, so I tend to accept at face value what is shown  - until later. 'Later' is the point where I construct in 3D parts from the 2D floor sketch. And then new things come to light....

First off, the book shows both a footprint for the 'hip' pieces which climb up above the main roof, along with a side elevation view which shows the shape of those hip pieces and where their lines are located. Following this faithfully, I produced the following 'hips':

Notice how they only meet the main roof's surface along an arris? It's like a 'California' version, with all due apologies to the fine people of that state.

Here's another sketch where I have placed a semi-transparent plane in there on top of the hip pieces, a plane aligned perfectly to the back side of the main roof:

This solution is not workmanlike, in my humble opinion. Those small white triangles at the bottom are, in effect, the footprint  of the missing bits of these hip rafters - if the hip pieces had these bits fleshed in, the result would be as follows:

The hips are now shaped so as to fit the backside of the main roof flush. Looks/works better, no?

And the valley pieces had a similar problem. Refer back to the drawing above showing the plan of the footprints and you will see that the valleys on the right side of the drawing also have rhombus-shaped footprints. If we make the valleys in a shape which conforms to that rhomboidal footprint, we obtain the following result:

You can see clearly that the horizontal slice in white at the top of the valley produces that desired rhombus print, however the problem is that a portion of the valley piece is now occluding into the body of the main roof. That won't fly. The solution is the reverse of what I did for the hip pieces - instead of adding material, with the valleys I must subtract a bit so that the back surface of the noulet is flat against the main roof.

Once those shape adjustments have been accomplished, the footprint plan looks like this:

You can see that the footprints are not rhomboids, but trapezoids, as they should be.

In regards to the footprints though, there was an even more significant problem with the drawing in the book. If you examine the foregoing drawing carefully (click to enlarge), you will see that the lines which govern the footprints are labeled 'D.P.', which stands for devers de pas. The D.P. lines for the valley footprints are developed in a similar manner as to those for the hip section footprints to the left of the drawing, however the points they connect to, and the places that they originate from in other sections of the drawing, are of course different from one another. Trouble is, if you follow the drawing in the book exactly, you will produce footprints which are not angled quite correctly. I was able to prove this by way of constructing 3D pieces from the 2D. This 3D also enabled me to solve the problem - I re-configured the 3D parts so they were shaped correctly, and then took horizontal slices (ie., 'footprints') of those sections and placed them back down in the plan view. From there, I projected traces off of those footprints to see where they led. A bit of reverse-engineering that would make modern China proud.

What I discovered by the reverse-engineering was that the text had swapped the connection points for the foot development D.P. lines with one another. That was a first for Mazerolle, as the 'foot-printing method', as such, is, I do believe, his special and unique technique. His claim to fame as it were. The how and why of this particular error cropped up in the text is unknown to me, but I was glad to have the 3D for solving such a problem.

The result is a valley and hip piece combo that serve to tie all the colliding roof planes together - with what must be said to be a bit of an ungainly arrangement where the hip and valley pieces connect to one another:

You can see that the hip and valley pieces do not meet each other with their inside faces. Now, they could be made to meet on their inside faces, however another stick of wood governs the desired outcome here, a stick I have colored blue in the next sketch:

The French love to have everything aligned in a particular way, and with the pieces colored blue, the desired outcome is that the cuts on each end of that blue stick are done with a simple bevel cut, not a compound bevel cut. So, if one reshaped the hip and valley pieces so that their inside faces met seamlessly, then the cuts on the end of the blue-colored pieces would have to have compound cuts to fit correctly. In this case, that (the compound cut) is something I would choose to do, as I really don't care much for the 'stock' arrangement here (excuse the pun).

One of the aspects to the love of alignment I just mentioned relates to the decorative rafter tails - the valley pieces have their tails cut so that they are perfectly co-planer to the other dormer rafters:

In that case, alignment, as a desired outcome, is all good.

A few final pics showing the placement of the new dormer in with the other ones I have studied thus far:

I haven't fully integrated this dormer framing in with the other parts of the conglomerate - not quite sure yet where the whole drawing is going. A view from inside:

'Standing at street level' and looking up:

A front elevation:

 Quite a motley collection of lucarnes, each a scarring and traumatic memory (just kidding, sorta...):

All for today. There's more Mazerolle drawing stuff to come down the pike, though at this point I'm not entirely sure which drawing I will tackle next. I'll probably take a break for a short while to recharge.

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