Saturday, March 9, 2019

The Geometry of Fences, c. 1830

Asher Benjamin's The Architect or Practical House Carpenter, published in 1830, includes a plate with 3 designs for fashionable fencing,  2 for gates. The lower drawing also includes a post.

While Benjamin includes a scale between the middle and the lower illustrations, he gives no other dimensions or information. He assumes the reader will know how to lay out the design.

The 2 right hand designs are repeated diagonals. quite simple to draw: cross your rectangle, lay in the horizontal and vertical center lines, embellish as you wish.
The bottom drawing is the fence for the gate above and shows the post and its ball.

What about the fence with curved balusters and the gate below it with rectangles and crosses?

First: the fence with curved balusters: 
The center of the rail is the center of the arc. The extended arc becomes a semi-circle  whose radius appears to be the distance to the edge of the bottom rail from the center and the height to the post below the ball and its base.

The arc determines the curve of the baluster. The circle using the same radius, centered on the baluster, follows the reverse curve. Both balusters are shown in red. 
Using Benjamin's scale the balusters could be cut from boards about 3 feet long and 8 inches wide. They are all the same shape.

The circles intersect  - see the vertical dashed lines in black. That intersection gives the spacing for the balusters.
Drawing the next circle using the point where the first circle's circumference crosses the center line, adding the vertical at the intersection, the placement for the balusters, noted in red. continues.

The gate seems at first glance to be more complex.

In my exploration I decided the size and the structure of the gate was known - its width, the framing members, the depth of the bottom rail. The black rectangle outline is what's left - the space for the fret work.
The diagonals are easy to draw - corner to corner. The space can be easily divided in half horizontally and vertically. I have not noted those lines.
But what about the inner rectangle?  The little corner squares?

Two radii are drawn; both A and B are arcs the height of the space, their centers are in the bottom corners, they arc from the top to the bottom - follow A and B's arrows.  They cross at C which is both the vertical center of the rectangle and the depth of the cross brace.

Reverse the arcs.  Now A and B land on the bottom rail  and mark the placement of the vertical braces. C marks the horizontal brace .

The horizontal and vertical braces are noted in red.

The rectangle of the space could be larger or smaller without changing the way the design developed or the general appearance. The proportions would still relate to each other.

The reader in 1830 - probably a house carpenter - would not have required my explanation to copy or adapt the  designs for his own use. He would have learned Practical Geometry as an apprentice. He would have read the design development automatically; he needed no words of explanation.
He might have drawn  his own small diagram on a board. Then he would have drawn the arcs full size on his framing floor - or table, as this is not very big - and found his lengths. The diagram would have remained until all the parts were made.

Plate XXXIII, Asher Benjamin's The Architect or Practical House Carpenter, 1830, L. Coffin, Boston. From the Dover Reprint first published in 1988.

This Asher Benjamin pattern book especially interests me because a diary was written by a local farmer in this period. Its author notes that his friend, a carpenter, traveled twice to Albany to buy his copy of the pattern book when it was first published. The details in several local houses seem to indicate that the joiner worked directly from Benjamin's plates.

Tuesday, January 22, 2019

the Geometry of the Kirkland Temple

.A reader of this blog asked me to look at the geometry of the Kirkland Mormon Temple in Kirkland, Ohio.  He saw similarities between the geometry of the Cabin at Tuckahoe Plantation and the Temple.

I have not seen the Temple, but HABS drawings are available on the Library of Congress website; and the Kirkland Temple has good exterior and interior pictures on their website.

The Kirkland Temple, built 1833-6, has a design specific to its use, not a traditional church form adapted to a new way of worship. I am not referring to belief, but about how the religious group planned to meet together.The Temple has 3 floors, each for a specific use: the Church floor, the Apostolic floor, the School and Quorum floor,  and the accompanying a Vestibule and Stair Well. This is different from the churches the people who built this would have known.
However, the red organizing diagram for the frame was not new; it was the ancient pattern that the craftsmen had learned as apprentices. They used the Square and  its Lines to plan the facade. The diagonals mark the placement of the Palladian window, the Lines encompass the ellipse in the pediment.

The builders did not use the division of  Lines into thirds. They seem to have preferred dividing in half and then in half again.

I have marked the 'third points' with red circles; the design does not depend on them. I could have left them out of the diagram.
Half the square also determines very little - maybe the sash location of the Gothic windows.  However, the body of the facade is 3/4 of the square, the pediment 1/4. The pitch of the roof is the diagonal from the center to the upper corner.

The  body divided in half - or the square divided into 3/8 and 5/8 - determines the 2nd floor location - the horizontal red dashed line.

For clarity I  have only laid out one quarter of the possible facade Lines - the red square on the lower left.  Half the quarter seems to set the height for the Gothic windows on the first floor. 3/4 of the small square seems to locate the door with its fanlight. The location of the Gothic windows does not quite work - the vertical red dashed lines.
The west elevation is  much the same, not quite symmetrical. The plans show that the windows were set to accommodate the stairs in the Vestibule and the seating the Church and Apostolic spaces.   


The plan is a square, solid red lines, and an overlapping 2nd rectangle whose length is determined by the overlapping arcs of its width, dashed red lines.

Again I would like to compliment my analysis by the experience of being there, walking through it as well as around the outside. For example here the 2 overlapping squares seem to include the platforms and stairs in front of the Temple. If I were there I might understand if the stairs had been part of the intention of the original design.

The division of the square into quarters locates the  columns and the beams along the length of  the whole structure. The spacing of the columns across the width probably is 1/4, 2/4, 1/4. The columns in the  interior elevations look wider than they are drawn in plan here.

The 5 columns at the east end (bottom of the  drawing)  support the tower.

The Gothic windows and the Federal doors also use  squares, and their division into halves as the initial layout.  The interior dimensions  - the panes, the panels -  do not seem to follows the same pattern.


The Church sanctuary and the Apostolic floor both have a central square flanked with smaller ones on each side. The regular spacing of the columns, the square side aisle bays between them, and the central naves with arched ceilings facing Palladian windows create 2 dramatic spaces. 
I do wish there was more information about the framing. Look at that blank space above the side aisles!

I was curious about the Temple partly because Joseph Smith, Jr. was born in Vermont where I live. I wondered if the framing traditions I see here were used in Kirkland, Ohio. I was curious about what forms the early Mormons used.  I wanted to compare it to the Streetsboro Baptist Church - built about 15 years earlier - near by.
I found a use of Practical Geometry that was very basic. Perhaps it allowed untrained members of the community to help with the construction.
From the photographs on the Kirkland Temple website the community seems to have created a striking building with effective spaces. 

The structure was measured in the 1930's for the US Dept of the Interior; the drawings are now part of the HABS collection in the Library of Congress. 

Sunday, January 6, 2019

Finding a Simpler Way to Layout a Building

The builders knew how they were using Practical Geometry - where they would begin, how they would use the diagrams. 
I don't.  I look at their frames, their finished buildings. I see a rhythm, a pattern. I try to discover the steps. When I can record a plausible geometry I draw it and write about it.

This year, fine tuning the power point presentations I would give 4 times, I thought that my diagrams were too complicated. Maybe not for a joiner building the main door of a church; but for the timber framers in a framing yard, I thought, "Too complex, too many lines!"

 Asher Benjamin's design for a "House Intended for the Country" belonged in my presentation. My audience usually knew about Benjamin. If they didn't, I needed to introduce them to him and his designs.
As I added it, I saw how the center square was the main idea - everything else came from it. The width of the wings comes from the Arc of the Diagonal of the Central Square.  So simple!

Then I drew the Central Square on the plan  - inside the walls as this was to give information to the men framing the interior.  The square, its Diagonal, and its Lines locate the entry hall width, the back edge of the curving stair and the wall for the upper left room, as well as the fireplace locations. The left and right sides of the house beyond the square are 1/3 the width of the square.

These are simple, small illustrations in a pattern book,  about 3" square, necessarily generalized. Even so, they convey the information needed by a builder to layout a similar house.

I then revisited the framing layout for the Rockingham Meeting House in Rockingham, Vermont, begun in 1780, finished by 1800.

Here is the geometry for the  plan. A center Red Square with its Black Posts  on the half and  thirds. The width is determined by extending each side 1/2 the square. The length is also extended 1/2 the square.  The Dashed  Red Lines show how the line extended located the posts on the exterior. 
Note on the left how the stair wing is laid out on the opposite side of the Line.

This is a much simpler layout than what I drew in  2014. 

The geometry for the front elevation of the Rockingham Meeting House seems to be most easily laid out as I drew it originally. 

That post is at:   
Details about the stair wings are included. 

The  size of the meeting house could be seen as a 3/4/5 rectangle: 3 deep, 4 long. The post placement does not follow that pattern. Perhaps that is why the window placement on the front and rear elevations is not regular.

The post and beam placement required that the 2 windows on either side of the door be framed against the posts - a little tight.  

The photograph shows hows the windows come against the posts. The exposed beams here holds up the gallery. That curved ceiling results from the slope of the floor above.

The Vail House geometry follows this pattern. I wrote about it here:

I have no name for this pattern. The previous name I used to describe this way of designing, "crossed squares",  is retired as interesting but too complex: not Practical.

Asher Benjamin, The American Builder's Companion, 1804,  Plate 55, 'Designs for a House intended for the Country'.