Monday, August 30, 2010

1830's cottage north of Boston, Part 1

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A family with a small c. 1830 story-and-a-half house asked me for advice - how to expand their home in keeping with its character.
We talked about their needs, the house constraints, the land. I suggested that a variation of "big house, little house, back house, barn" might be work. (The old jump rope rhyme refers to the massing of early New England farms. There is a book of that name describing the phenomenon.)
Back on my drafting board - after I had drawn up a sketch for the family and their contractor which reflected our discussion - I played a bit with the form. Here's what came out of it:


The floor plan provided to me was at 1/8" = 1'-0", very
small. However I later
 measured the house. The plan is accurate. See my post in May, 2013, for the elevations. I am happy to discuss the date of the house, if asked.

The first floor plan and a sketch of the house is here. The red line shows the outline of the original c. 1830 house plan.

The second drawing shows the original floor plan with - in red - the length of the side used as a radius for a circle.


The third drawing shows that a circle whose radius is the length of the
wall touches the 4 corners of the main house.The rectangle of the house
is determined by the circle. An arc using the same radius defines the
length of the wing, but not quite the width. The interior arcs of the
daisy wheel also define the small front entry. The 6 points of the 'daisy wheel' are shown, only 2 of the 6 'daisy petals' are drawn.

The house is simply built, perhaps by a farmer, not a joiner. Whoever he was, whatever education he had in construction, he knew circle geometry and used it to layout this house.
















Tuesday, April 20, 2010

Regulating Lines - Asher Benjamin


Asher Benjamin's first book, published in 1797, gives proportions on every plate except those of buildings: Plates 25, 26, 27; and Plate 23 which shows how to place newel posts on a stair.

The photograph is of Plate 18, a fireplace mantle. He notes: "B, Cornice, half size; C, Architrave, half size; A, Moulding round tablet full size for practice." All the numbers on the drawing refer to parts. B, the shelf of the mantle - drawn in the fireplace opening - states "17 parts" on the left side, and the divisions are ticked off on the right side. Across the mantle base are tick marks to scale the mantle itself, and then the note on the right: "8 parts". A is that little piece of moulding beside the mantle in the upper left corner.

The next photograph is of Plate 29. The top figure is how to size a arched ceiling over a room. The lower figures show roof frames - the bottom one is intended for a meeting house. The proportions to use are shown marked off and in notation: Figure D is 7 parts long and 2 parts high.
Here too the compass arc is shown. The 2 intertwined circles on the right of the top figure determine the arch for the ceiling. Note that the circles themselves are based on the size of the room. In the roof frames the arc of the circle - with its center at the center of the lower chord - determines the placement of the trusses.

So, was the use of the compass and geometric design so common that Asher Benjamin simply needs to allude to it? If so, why didn't that knowledge get passed on?






Saturday, April 17, 2010

Regulating Lines #3 - Architecture



In November, 2009, Laurie Smith gave a workshop and a lecture at The Timber Framers Guild Eastern Conference in Saratoga Springs, NY.
Laurie Smith is a designer and a historic design researcher from Wales who is investigating the use of geometrical design in medieval Britain, documenting the use of circles and 'daisy wheel' geometry in the design of houses, tithe barns, and cathedrals. Ely Cathedral is pictured here.
His work is thorough, fascinating and thought provoking. Some of what he has written has been published in Timber Framing, the Journal of the Timber Framers Guild, www.tfguild.org.

My professors in architectural history had been in Europe after WWII. They told us about cathedrals in which the 'mark' (similar to a signature) of the stone mason could be seen on the parts of the columns. The marks were derived from the Golden Section.

Vitruvius, the Roman architect and engineer who wrote De Architectura, (On Architecture) in 10 books, writes about geometry and proportion, including the description of man as the basis for design that Leonardo da Vinci drew as the outstretched man in the circle. (I use a print by Cesare di Lorenzo Cesariano, c.1521, here.)

Peter Tompkins' Secrets of the Great Pyramid spends several chapters explaining how the pyramids are designed using the golden section. His book has much information about ancient Egyptian astronomy and
mathematics.
I didn't know about this book until a friend put his copy in the mail to me. Thanks, Bill. You'll get it back!

Arthur J. Lawton, and some others, researched the use of the square and its diagonal in Pennsylvania Dutch construction. It was published by the magazine, Pennsylvania Folklife, in the 1970's.
Section, its permutations, and the resulting regulating lines.





Monday, April 12, 2010

Regulating Lines - an Introduction

The feed-back from my post on the regulating lines of Lorenzo has been considerable. So I am putting forward for your consideration what I know about geometry and pre-Industrial Revolution design. Mainly:

Regulating lines are not mystical or mythical. They are not magic.They are simply geometry applied to design and construction.

They began as an accurate way to measure and layout design when people had only simple tools: a point, a line, and something to mark with. The line could have been string, a rope, a chain. The marker could have been chalk, charcoal, a stylus on wax or wet clay.

Find some wet sand, a beach perhaps. Make a knot in a length of string. Tie a stick to the other end. Use your thumb on the knot to hold the end of the string on the sand. With your other hand pull the string taut and trace an arc in the sand with the stick. You have begun to use geometry to design.

Geometry can be read by 'illiterate' people, or rather: People can be literate in geometry without knowing numbers or letters. It is a separate language which, like music, does not need translation.

I will list the sources I know of in art and architecture. I hope there is more I just haven't found, yet.








Wednesday, March 31, 2010

regulating lines #2 - Dynamic Symmetry and the Golden Section


'Dynamic symmetry' is the name Jay Hambridge (1867-1924) applied to his study of the use by the Greeks of mathematical and natural growth forms of nature in their design. His book explains his theories and gives 'Lessons' for the reader. The figures are taken from the his introduction and Lesson 2. (In figure 4, the ratio between the square and the rectangle derived from the radius of the diagonal of half the square is the golden section.)

The ratio of the Fibonacci Series was known in the Renaissance as the Golden Section or Ratio now called 'phi' (the Greek letter) or 6.18... It "... cannot be worked out arithmetically; but it can easily be obtained with nothing more than a compass and a straightedge." Peter Tompkins, Secrets of the Great Pyramid, p.190.

Artists tend to know about these ideas:

*About 10 years ago an art teacher casually mentioned the golden section, telling me it is a common organizing tool for artists. I have now heard this several times.

*On a tour of the Saint Gaudens National Historic Site, Cornish, NH, a guide mentioned that Maxwell Parrish, who often painted there, used the golden section. I can find no references to verify that memory. (Maybe I need to lay out regulating lines on his paintings!)

*Karyl M. Knee wrote a phd.thesis in 1966 on Byzantine icons which examines the use and history of dynamic symmetry from its development by the Egyptians to its use in Russian iconography. The thesis is on line.

*Luca Pacioli, author of the first book on accounting, was a mathematician. He taught Leonardo da Vinci. In 15o9, da Vinci illustrated Pacioli's book, De Divina Proportione, describing the 'golden ratio'. Leonardo da Vinci's painting, The Last Supper, uses the golden ratio as its organizing principle.

* French historian Charles Funck-Hellet analyzed the golden section in Renaissance paintings, unfortunately for me, in French. I have not found a translation.

Sunday, March 28, 2010

Regulating lines #1 - Le Corbusier

This is a post on my knowledge about 'regulating lines'.

Le Corbusier (1887- 1965) was one of the best known 20th C. modern architects.
As an architectural student I was so aware of him that I remember where I was when he died.
He wrote a book, The Modular, about visual relationships - a study on where to put what and why. Among other things he postulated a series of interlocking dimensions based on human scale, the Fibonacci Series, and the Golden Section.

In the book Corbu mentioned an associate, Jerzy Soltan, who was in my time, Dean of the Harvard School of Design. With amazing bravery for me, I, a student at MIT, called Professor Soltan to ask for a private reading class. He agreed. The first book he assigned was Dynamic Symmetry, by Jay Hambridge, an investigation of the Golden Section.

That year at MIT we had a series of visiting professors. I asked each of them privately if they used the Golden Section. Although they told me they did, they never mentioned it in lectures. It was considered a kind of magic.

I have Corbu's numbers posted beside my drafting board. I use them. I also use the Golden Section. When a client asks for a wing on an old house, I explore the existing pattern of the house - using the square, the diagonal, the permutations of the Golden Section - to help me read the regulating lines of the house so my design can be sympathetic to what is already there.
A note on the Fibonacci Series: any 2 numbers if added to each other will, within 6 calculations, become the same ratio:
1+2= 3, 2+3= 5, 3+5=8, 5+8=13, 8+13 = 21, 13+21=34 21/34 =0.617
1234 + 789=2023, 789+2023=2812, 2023+2812=4835, 2812+4835=7647, 4835+7647= 12,482
7,647+12,482 = 20129 12,482/20,129 = 0.620

Try it yourself.

Saturday, March 20, 2010

carpenter squares

In 1815, Silas Hawes in S. Shaftsbury, VT, joined 2 legs of steel together to make a stable, true 90* angle carpenter square. Hawes patented his idea in 1819 and began manufacturing. (Iron squares did exist before this. Illustrations of them can be found in the pyramids and in medieval English carvings. There was one recorded in Plymouth in the 1620's, and another in New Haven, CT, before 1700.)

I became curious about these steel squares when I realized that there were several factories producing steel squares on Paran Creek, which runs from Shaftsbury, through N. Bennington to the Walloomsac River. Lots of factories because of lots of demand - one factory, swept away in a flood in 1852, was immediately rebuilt.

At the same time Asher Benjamin is publishing his pattern books.
And post and beam framing systems are evolving from scribe rule to square rule. This is a change from each tendon fitting only one mortise, to the parts being interchangeable. For example, a brace could fit between the post and beam (sill and stud in the illustration) at the front of a barn or at the back.

Do these facts have anything in common?

A joiner needs to know the angle he uses will be the same each time, dependable, before he can make the same part to be used many places. He needs to own a carpenter square even if it is expensive, and it was - at least a week's pay.

Does the manufacturer of many, many carpenter squares in Vermont a play a role in the evolution away from design using 'regulating lines'?

The Eagle Square sign comes from The Shires of Bennington, published by the Bennington Museum in 1975. The illustrations were drawn by Edwin Tunis for his book, Colonial Craftsmen, the World Publishing Company, 1965.















Thursday, March 11, 2010

glass for Show and Tell

These items were part of the 'Show and Tell' we assembled for the forum on windows at the Dorset Historical Society in February. Choosing the pieces made me look more carefully.

The first is the piece left over from blowing glass. Today we call it a bulls-eye. It can sometimes be seen in the transoms over front doors in old houses. In the center is the closed-in hole where the molten glass was attached to the pontil - the tube the glass maker blows through. The swirls were caused by twirling the soft glass to thin it out to a plate about 5 ft. across which could then be cut into window panes. This was how glass was made before 1800. This center part was basically waste that someone found a use for.


The second is a reproduction Sandwich glass tumbler c. 1830, made with a 3 piece mold. I tried to photograph it so the light would shine at one of the seams. The use of a bucket to pour the molten glass into a mold instead of blowing up the glass glob on the end of a tube was a major change. Flat glass techniques changed too so window panes could be bigger.



The later goblet - 1880's or so - has a 3 piece base holding a seamless bowl. Wow! Compare the technology involved to mass produce this - buckets that were filled, moved and tipped, molds that closed and opened, machinery that brought the two parts together while they were still mailable - to the simple tool used to blow the bull's eye, the way of making glass for that had been used for centuries.

I also had a piece of window glass, c. 1900, with some waves in it. Extruding glass with a smooth surface was not easily done until around 1940.


Finally, I brought a modern art glass tankard because it showed the molten qualities of glass so well.
And here I was surprised at my response. This is the mug I use at home. Now I saw the air bumbles that mean the glass wasn't as carefully blown as early window glass was. It had the pontil mark - the place where the molten glass was attached to the blowing tube, and I liked seeing how the mug was made. But the piece was heavy, not light and airy. The glass was thick, not clear and delicate. The light shone through the others 'better'. The handle was just a snake, a blob of glass, crude.

I know the glass blower probably chose to make it like this - the nature of molten glass right there to see. But right now, partly because I understand the skills required to create them, I much prefer the other pieces.




Thursday, February 11, 2010

regulating lines - in this case, circles

Interesting - the place to buy a compass these days is in a quilting shop.
I wanted a good one, not the flimsy kind I had in elementary school. I wanted to see and touch it, so buying it on-line was not an option. I am still looking for a bigger one.

So, now I am playing! This morning I added circles to the sketch of Lorenzo.


The results are interesting. The radius for the arc of the fan light over the door has its center in the center of the door. The circle encloses the entry as it did for the 1795 entrance I just rebuilt.
The same circle fits the curve over the windows that unites the pilasters. The ellipse is the same curve as the fanlight coming back upon itself.

I know I like this. It is so simple, so straightforward: no wonder the house feels so right! The elements reinforce the important places. The parts speaks to each other, they're related.

It's also how architects and contractors on the job actually work. Imagine the mason thinking about the arch he needs to build over the door. He makes a wood frame to set in the opening so he can lay up the bricks from one side to the other. (Once the bricks are mortared in place the frame is removed.) Then he needs to span the spaces above, which happen to be the same width. So, use the same frame - obvious!

In 1800, masons did not have stone lintels to use over door and window openings. The brick arch spanned the distance. Here the arch transferred the roof load to the brick pilasters, leaving much less weight to be carried over the windows - structurally a smart idea. The arch, which had to be there, was not hidden. It generated the graceful design that still resonated today - art and science intertwined.

I also know I am working with a drawing based on a photograph and the scale is about 1 inch= 10 feet. Lots of margin for error. Still, it does please me.





Wednesday, February 10, 2010

regulating lines for Lorenzo



The back cover of the brochure for Lorenzo, shows this picture accompanied by a good discussion of Vitruvius and his principles.

Unfortunately no one signed the article. I would like to discuss the ideas, especially 'regulating lines', with the author, but I haven't yet found a way. So I am posting this here.

I don't think the star shows the regulating lines used to design the house. The star is not regular in shape. Shutters like the ones on the house in the photograph were not in use until about 20 years after the house was built, so those points are not important elements of the design. The pediment was also added later.

My sketch shows the basic elements of the original house: the shape of the facade, the pilasters which sit on brick pedestals that are part of the foundation, the arches which join the pilasters, the door with its sidelights and fan. The windows sit quietly between the columns.


Here are the regulating lines - superimposed in red - that I think were probably used to determine the proportion, rhythm, and details of the house. These lines were easily drawn with a compass ( or dividers), one of the tools we know house wrights owned in the early 1800's. The center block of the house is a square. The width of the wings on each side is determined by the diagonal of the square used as a radius. The three bays in the center box are also the same width as the wings, and are delineated by the pilasters. The importance of the pilasters is emphasized by the pedestals in the foundation wall, the arches which join them, and the placement of the posts topped by urns in the roof balustrade. Curves, circles, ellipses draw the eye: here to the 5 bays, the door.

The height of the entrance is determined by the center of the square. When the pediment was added, its height was determined by extending the arc of the diagonal. Its ellipse is the same curve as the fan light. Pretty simple: each piece is determined by the whole. The curves reinforce the concept.

I played with the arch over the windows. Hmmm. It was a structurally sound way to finish the brick pilasters and create a frieze. It emphasizes the bays and formal composition. But the curve? The photograph is too small to figure out where the radius of that arc originates.





Wednesday, January 20, 2010

first picture of new entrance

The contractor called: the old door and its pediment were down, the new entrance was going up.
Of course, I showed up!

The original sheathing was exposed. But, almost no ghosting - the tell-tale signs of where the first entrance had been. Two boards showed evidence of a hand rail. A beam had been cut away a bit. Neither was enough to determine the original dimensions or profiles (the shape of the mouldings used). The contractor, joiner, and I all really wished there was more to look at, learn from.

The new door, sidelights and columns were in place. The men lifted the fanlight and its surround and set it above the door for me to see. The winter sunlight bouncing off the snow was brilliant.

Not bad.
But hard to see: so white in the winter sunshine, jarring between the pink house and the blue door. As I expected, it looked too new: not enough layers of paint. The mouldings seemed fine: the shadows in the right places. The columns attenuated as they should, the fan shape right, but was it too flat? The 2009 door and sidelight seemed out of place: clearly modern. I was so involved I couldn't see it!

For me, this is a common reaction. I won't go back now for a while. I'll turn down the road as if by accident, and come across the house unexpectedly - and see then how it feels.











Monday, January 18, 2010

the fan light for the new 1795 entrance


We had originally assumed the fanlight would be a Fypon composite. Fypon reproductions are based on real pieces, so we knew it would look OK. The only disconnect would be that the piece they copied would be generic, not specific to our entrance.

However, the Fypon fan was really bigger than what had been there originally. It made the entrance too tall. Listening to my frustration, Jack suggested he build a smaller fan from scratch - same cost to the owners. Excellent!

When the photograph of the entrance was blown up the shape of the fanlight could be seen as an arc with flat ends. Jack said this detail made it easier to assemble neatly to the sill above the door. Good.

So, back I went to the dimensions Jack needed to actually build this. He needed an arc with a radius for the fan... As I drew it, choosing a random semi-circle from my circle template, I stopped in surprise:
The circle which fit the arc of the fanlight, using the center of the door as its center, encompassed the whole entrance.
The squares, the overlapping Golden Section rectangles were clean. The circle centered on the entrance is not quite as clear. I love the way it covers the entrance to the house, protecting it. But it's not crisp. Do I have it right?

new 1795 entrance

More on the 1795 house entrance

  
One of the ways I come to understand a building is to measure it and then draw it on paper. Using a tape measure, a clipboard and a pen to record the space inside and out is, for me, a way to spend time sensing the character of a place. Putting those dimensions on paper lets me revisit and more clearly know what I saw and felt.

So, I measured the front of the 1795 house, and put it on paper. Then I looked at what was there using the proportions of the Golden Section - mostly the square and the rectangle derived from its diagonal.
And there was the pattern - each side of the house was a square. The windows on each side were also symmetrically placed on each side of the center of the square. That square is the determining shape and dimension for this house. You can see the squares marked on the first drawing.

In the second drawing you can see the arcs derived from the diagonal of the square. They determine the size of the center bay. (Yes, they don't meet exactly. However, considering that they are only 6" or so off over a building 38 feet long, that's pretty close.)

I was delighted. I knew then how wide the entrance had been, and not just because I'm an experienced architect with an 'educated eye'.






Tuesday, January 12, 2010

Dividers aka a Compass

This post is undergoing revision to make it clearer - my editor stopped by and gave advice, but I have not yet acted on her suggestions.

I ignored them, much as I ignored those pages of geometry in the pattern books.

But if you use proportions to determine how big something should be, dividers - or a compass - are how you transfer a dimension from one place to another. Dividing your window into 6 parts to find the width of your casing? Use the divider to transfer that dimension from the window to your piece of wood.

Today we would discuss it this way: "6 inches +?" "6 1/4 inches?" "How about only 6 3/8 inches?" Tricky to figure out, right? The divider is easier.

A compass serve a similar function as a ruler or a measuring tape, but it always refer back to a real thing. Intellectually, inches and feet are abstract numbers, with no relationship to any other thing at all. If you ask, "Why use a 5-1/2 inch casing for that window rather than one that's 6-1/2 inches?", an answer might have to do with cost or personal preference. The answer, "Is the 5-1/2 inch casing a better proportion for the window?" doesn't come automatically. When you get to that question using dividers you have already included the window, that's where you began.

I find I am in uncharted territory. At first I thought I was talking about 'calipers'. Then I found the tool I was thinking about is called 'dividers' or 'a compass' .

So far I haven't found very much written that confirms what I am seeing. I do know that proportions and relationships in medieval construction were often based on the circle and how it can be divided and combined. 17th and 18th century woodworking tool box lists include dividers and compasses. However, the drawing comes from Eric Sloan's Museum of Early American Tools , and he places it among the wheelwright's tools, not with the joiners'.











Saturday, January 2, 2010

New 1795 entrance

Next chapter in working on the 1795 house entrance:

The client wants to use a modern door and sidelights: energy efficient, less expensive, tax credits.
That means that part of the entrance size is known: 60 inches wide, 80 inches high. The proportions and moulding of the door and the sidelights are also fixed.

The existing door is post-WWII, Mid-Century - and I read it immediately as such. I am not sure, even if I copy on old door exactly, that I can design a door that doesn't read 'Early-21st Century'.
The subtlety of a period has to do with tools, materials, joinery, as well as proportion, parts, and details. Weathering, layers of paint, dings (ie: being used for 200 years), matter too.

Still, I want to try, you know: such a fine challenge!