Monday, September 12, 2011

Following Mazerolle: Lucarne Biaise À Fronton. Nolet Biais (II)



In March of 2010 I was on the second dormer problem in the Mazerolle text from the 1860's (modern reprint). It's an innocuous looking number this dormer, and acknowledged as an unusual thing by the author in fact - a gabled dormer on a biased angle in relation to the line of the roof. Here's what I'm talking about:


In that post (<<-- please take a look if you haven't seen it before) I concluded that, 

"If you follow the lines of development, you will see that most of them do not coincide with the actual climbing molding. The drawing in the text is, once again, completely misleading and shows a result which is impossible or unusable. C'est merde.
WTF is up with this book? It's becoming sorta humorous now. How can it be that example after example is basically un-buildable as shown? Somebody help me out here, as I think I'm going to have to turn to hard liquor."

Yep, I was a little ticked off after my attempts to solve the puzzle. I did manage to avoid a significant bout of liquoring up, but the result of that investigation, along with the subsequent dormer in the book, led me to put the book down in frustration and annoyance.

Several weeks ago a fellow in France contacted me named Tim Moore. He's not a compagnon, a carpenter or a woodworker, however he is interested in geometrical drawing, and had, after reading my blog posts, obtained the Mazerolle book and started delving into the drawings. Kudos for that. Welcome to my nightmare and all. Tim sorted out some issues with the first dormer drawing in the book and let me know his solutions. He seemed to think, at that point, that the book wasn't deliberately misleading as the compagnons are highly ethical people and wouldn't do such things. I'm sure they are highly ethical people, but still, there are so many errors to be found in virtually every drawing that something weird is/was definitely going on.

Anyway, be that as it may, Tim's contact, work on the book's drawings, and general enthusiasm fired up my interest in the book again and I suggested we work collaboratively on trying to solve the biased dormer problem. The crux of that problem (and this may not have been the intention) is the molding, it seems to me, a molding which wraps around the lower edge of the gabled roof and surmounts a tympanum molding on the front of the gable itself.

Just to review a little to start...

The plan view of the dormer shows however that the miter on the peak of the molding is not aligned in the same manner as the common rafters (in line with the theoretical ridge line of the roof) - rather it is supposed to be square in plan to the front line of the gable:


 You can see a line springing off the miter of the molding in the plan view, circle over to the right and project vertically up. It goes to a frontal elevation view, meeting the peak where the miters join - note the vertical trace to the right of the picture:


The above drawing also reveals certain other apparent requirements for the molding which climbs the gable - in the side elevation view (left side of the drawing), the top surface of the molding, as seen at the peak, is in plane with the roof surface and the rafters. As it should be.

The trouble is that if you try to satisfy those various requirements, a molding that is both in plane with the dormer roof surface and a molding that meets at the peak so that its top cut moves squarely across the stick in plan, you end up with something non-constructable or which leads to problems in the resulting roof surface. I tried to convince myself otherwise several times, through several rounds of drawing, to no avail.

The book's drawing shows, in fig. 5, a method for developing the molding which climbs the gable:


That method is some sort of cruel joke as it doesn't work at all. It indicates, for one thing, that the top surface of the climbing molding is square in section to the rear face and front face - if it were square in section like that, the top of the molding could not be in plane with the roof surface. The sketch does make it appear though that determining the profile for the molding, referred to correctly as an obtuse raking molding, is some sort of simple affair. It isn't. The dormer looks simple enough, but that, as they say, is a bit deceptive. Well, it's hair-pulling material at times frankly.

So I reviewed the problems that cropped up in past attempts and decided to try the problem again, taking a different tack this time from the outset. I dispensed with the molding section altogether and had a look to see if I could make a rectangular stick of wood follow the edge of the roof along, up, down and back around. Some period of sketching later, I determined that I could actually get sticks of wood to do just that:


The key point the came with the above drawing, for me, was the realization that the climbing moldings have to come from a section of wood that is a parallelogram in section. A parallelogram section allows the stick to have a back and front face which is plumb, and a top face which is in plane with the dormer's roof. The climbing moldings are, in fact, a similar problem in certain respects to this one with askew rafters:


In the above picture, both of the rafters which angle to the left and right side of the common one in the middle are parallelogram in section - that allows the entire roof plane to be flat across all the rafters.

Later on in drawing the biased dormer I discovered that the molding sections on this biased dormer, if they are to be obtained from parallelograms, are in fact reversed parallelogram sections to one another on each side of the gable. One of the raking moldings distorts upwards into a parallelogram, while the other one distorts downward into a parallelogram. They meet at the ridge with a compound miter to boot.

If sticks of wood could be worked around the roof edge, than a profiled section taken from those sticks could do the same thing. The key issue was obtaining the profile of the raked section, both left and right sides. I tried lots of things including some quite complicated developments involving the cross section changing shape some half a dozen times as it worked its way around and through.

Recently I was at McGill library in Montreal, Quebec, and came across a book by George Collings on the topic of roof carpentry. One of the pages there showed a graphical development for working out a miter for an obtuse raking molding. Just what I was looking for!!

Now, a typical obtuse raking molding is traveling along the join between wall and ceiling or soffit. Here's one such example - a molding (in blue) traveling along a wall and climbing up along a 45˚ intermediate wall before returning to horizontal:



Here's another view in in case the transition between planes isn't apparent enough from the foregoing picture:


Another view:


With this form of raking molding, each section of molding lies in plane with the ceiling above it, and connect to one another with a miter. The climbing section of molding is milled from a larger section of stock than the horizontal moldings - you can't use the same molding stock all the way around.

In the lucarne biaise, the situation is a little different in that the molding which climbs the gable has to keep its top surface in plane with the roof itself, which is aligned to the horizontal molding sections. I played around with the Collings development method and got it to work for this particular condition. Here's the drawing I did to develop the raking molding sections:


Click on the image to see a bigger version. The raking molding sections are dark blue.

A closer view of one side of the development:


 With the moldings worked out, I could construct the entire molding along the edge of the dormer. I was pretty psyched when it all came together at last:


A view more to the right:


Looking up from 'street level':


 Side elevation - note that peak of moldings where they meets at the miter is horizontal:


Plan view - the molding miter at the peak is aligned to the ridge line of the dormer roof:

As I wrote to Tim, getting the molding sorted at last was, for me, akin to how one might feel after having worked a while to decipher some Egyptian hieroglyphics, discovering along the way that someone has carved in a few spelling errors. I was elated and battle-scarred.

My solution for this molding is not identical to what is drawn in the book in all respects, but having tried in every way to put together a roof which does follow the book's illustrations with no success, I am feeling that I have solved the problem in the cleanest possible manner. The drawings in the book are wrong in several key respects, plain and simple.

I prefer the moldings meeting at a miter which is aligned to the ridge of the dormer, and have kept the surfaces of all the moldings in proper alignment to the roof planes.

Tim has completed the work developing the rafters and the other complicated pieces in this puzzle - the noulets. I'll delve into that in a follow up post,and flesh out the rest of the dormer. Thanks for visiting the Carpentry Way.  --> Next post <--

4 comments:

  1. I was pushing for a solution where the front moldings were independent of the roof planes and the moldings were significantly higher than the roof, in order to hide the skewed roof behind. In some ways that idea is more consistent with the front view of the lucarne given in Mazerolle. This is still tricky to work out, but easier than the skewed parallelogram construction. Chris persuaded me that this would not be practical. However, this morning I saw such a façade on a dormer in a house in Bordeaux. The critical difference is that it is made of stone. So, I still wonder whether that was what Mazerolle, or his illustrator, had in mind.

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  2. Tim,

    thanks for your comment. I can see, for stylistic reasons, cases where having the top edge of the gable protruding up above the plane of the roof, and with the construction I have come up with, it would be simple to extend the molding up to achieve that. Your solution however had the molding on one side sticking up in an angular fashion from the roof plane, while the other molding, also tilted out from the roof plane, only met that plane along one arris. Clean carpentry work would have the top of the molding on the gable, regardless of whether it protruded up beyond the dormer roof planes, to be co-planer with those roof planes. It would look weird otherwise. Also, I never have liked the look of the dormer gable moldings meeting so that their miter edge, in plan, is running at a different angle than the ridge. Such an arrangement could only work with a gable molding which stuck up above the roof surface planes - otherwise the roof surface would be awkward where it converged with the top surface of the gable molding.

    Yes, figuring out what Mazerolle, or whoever illustrated that book, had in mind is a significant chunk of the battle. Still whatever results when the drawing is complete needs to conform to good carpentry practice and with a roof, the most important thing is keeping the weather out, so one wants to avoid constructions that are problematic to make weather-tight.

    ~Chris

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  3. Since Tim Moore is a new introduction here I followed his link and came across Stereotomy - a word I had not heard of before. It obviously has a modern usage but in the period, say, 1860 - 1920 it seems to be used exclusively(?) in the stone cutting industry. I found a digital book with Stereotomy in its title:
    "Stereotomy: Problems in Stone Cutting in four classes" by St. Edward Warren, published in 1890. Here's a link:
    http://babel.hathitrust.org/cgi/pt?id=mdp.39015021297430;page=root;seq=1;view=1up;size=100;orient=0

    I am no historian, but I can image that the period 1860-1920 was the time in which all that amazing stuff learnt during the earlier 1800's is being written up for propagation to a wider, technical audience. It is instructive to look at page 5, Problem II of class 1: I thought, page 5, that should be do-able. Think again; it is incredibly complex for a problem II ! (Not helped by the accompanying "Plate I" not having been scanned correctly.)

    Perhaps we are pampered now, but I cannot imagine anyone being able to crawl through these long and complicated prose descriptions of problems (and solutions). Also, the book is written for engineers and architects but its style seems to be addressing stonemasons themselves - the stonemasons must have had Ph.D's then. This book is not alone. One of the revealing things about the old textbooks now made easily available by Google Books, and similar projects, is what I call their "density", and their rather discursive style, as if they had been dictated. Of course, this was early days for writing textbooks, there were few if any models of good practice to follow.

    I think Chris's struggles with Mazerolle are related to this (although an even earlier period). Louis Mazerolle clearly expected much more from his readers/students than we do today !
    But I am pleased this material has, as it were, re-surfaced - its fascinating.

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  4. Rob,

    very interesting comment. Stereotomy, ala Gaspard Mongé, was where this form of desciptive geometry started, and that was, as you note, for stonecutting. Castle fortifications had evolved to the use of battered polygonal walls and other such complex shapes, and a system for determining the geometry of efficiently laying out and cutting the blocks was worked out by Mongé, an army Lieutenant in the early 1700's. It was a state secret for many years. When introduced at west Point in the early 1800's it was also a US state secret.

    I was startled to see the Fourneau text at Laval University as it must be the first to show the complex stereotomy for carpentry problems, and it is very similar to Mazerolle's work. It re-set my sense of the timing for these developments. I'm trying hard to keep this knowledge alive, as it is in some danger of being lost in carpentry, given current building practices.

    Yes, the texts are difficult to work through, the language archaic and hard to follow in places, however the geometry is going to work once you crack the code. I'm getting closer to that all the time, but it takes a lot of work.

    ~C

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