Sunday, October 3, 2021

Geometry of the Old First Church Fanlight



This is the fanlight over the main door to the Old First Church, built in 1803-5 in Bennington, Vermont. Lavius Fillmore was the Master Builder; Oliver Abel, his Master Carpenter, and Asa Hyde, the Joiner and carver.  

 The fanlight design consists of 2 parts: the 'scallops' around the curve and the 'leaves' coming up from the base. It is simple, graceful.

How was it laid out? In 2012 - when I first wrote about this fanlight - I knew the geometry for the scallops around the curve - expanded daisy wheels on the horizontal and the vertical axis. 

The 3 leaves below the scallops?  I was lost.

Laurie Smith - English timber framer, historian, geometer, the most knowledgeable person I know about the use of circle geometry in medieval design and construction - provided the answer.
Here is our geometry for the fan light. It may not be how Lavius Fillmore laid out the pattern. 



 The  circle, its 6 points around the circumference laid out by the radius of the circle, is set on a line which defines the shape of the fan light.



The circle is surrounded by 6 circles which have their centers on the 6  points. The center pattern is a daisy wheel with 'petals'.

 The circles expanded.



This set of circles around the original circle adds petals 
to the exterior of the first circle. Add the fanlight shape and the petals  become scallops around the arc of the fanlight.





 Rotate the circles 15*  - or 1/2 a petal - and the fanlight's scallops' locations change. 





Overlapped, the daisy petals create the double scallops of the fanlight.

The overlapped petals are also the pattern of the 'leaves' in the  fanlight: too big, not in the right location, but crossed as are the leaves. 


Add regulating lines from the center of the circles to the second ring of circles and center lines in the petals.


Connect the center points of the scallops to each other. Where they cross the petals is the center of the small circles which form the leaves. 







The radius of the circles is the distance from the center of the petal to the scallop.









I've drawn it in red to make it more visible. It is a complex layout for a seemly quiet, unassuming design.

This pattern was drawn at about 3/8" = 1'-0".  A scale of 1"=1'0" might have been easier. However it would still be tiny here on the page. For clarity I left out the overlapping scallops.

The real fanlight was laid out full scale - 5+ feet across -  on a framing table or floor. The proposed design sketch would have been studied, the arcs drawn with a compass using chalk or charcoal, the lines checked, redrawn, the points pinned.  Finally, when the regulating lines were erased, the simple, clean design was visible.

I would like to have been there, listening, watching. I think they were pleased.

Thank you, Laurie, for your help. 

my drawing in 2012

Monday, August 23, 2021

Rockingham Meeting House, Rockingham, VT

The Rockingham Meetinghouse  was begun in 1787, dedicated in 1798.

 After some preliminary analysis of the design and frame I realized in 2014 I needed to see it. I wondered if it would be as spare as the Rocky Hill and Sandown meetinghouses which preceded it.

It is.



 The site, on top of a hill with a view all around, emphasizes the simplicity of the structure. One can only come to it from below, and like many 18th c. New England buildings it sits upright and confident. It is very impressive.

I returned in 2018 and early 2020,  I updated the geometry as I learned more. I revised the drawings again when I gave a Zoom presentation in spring, 2021. What I first saw as a complicated geometry became simple and direct. 

This is not a dramatic design created by a London architect like Robert Adam to wow his rich patrons. It is a meeting house for a rural community. It is a straightforward layout planned by master builder, John Fuller, for a simple timber frame to be erected by a crew of local citizens.

The Town Fathers specified a building 44 ft. by 56 ft. The HABS drawings read 44'-4" x 56'-6". The difference could easily be the addition of the sheathing and siding to the frame. The porches (the end staircases) are square: 12'-2" x 12'-2". 
The difference could also be that the rule used then and the one we use today differ slightly. I am not sure they had a 'rule'. Poles of various lengths, 4ft., 5 ft., 10 ft., are in some illustrations.


'General' John Fuller, the master builder, was also the architect, engineer, framer. He knew the meeting house required an open space in the middle so everyone on the floor and in the balcony could see the preacher in the pulpit - and be seen by him. The pulpit was centered high on one wall, a window behind,the balcony on 3 sides.


He laid out a 3/4/5 rectangle. noted here in red. Then he laid out a square in the middle which defined the open space and divided that into thirds to set the columns for the balcony and the posts for the frame. See the black square and columns.

He extended the column spacing - the dashed black lines - to place the posts on the front and rear walls.This made the balcony the same depth all the around.
The porches are squares set in the middle of the west and east walls. The exterior posts were set at the porch corners, not at the 1/3 points of the wall. This also allowed for 2 windows on each side of the porches. 




Those 4 closely spaced posts in the center support the 4 attic trusses which are braced together to span the width of the church and allow the center of the meetinghouse to be an unobstructed space.

Walter Wallace, standing in the joined trusses under the ridge, gives a sense of how big the framing is.



The HABS prints of the End Elevation and the Interior Section for the Rockingham Meeting House are hard to read but their basic dimensions are clear.

The End Elevation is composed of 2 squares. The roof is framed using the 3/4/5 triangle. 

The notation to the right of the rafters says the pitch is a 9/12, modern language for the same thing.



The porches, the name for the stair towers, are set in the center of the end walls. The diagram shows that if the overall width of the wall is 8 modules (each square divided into 4 equal parts) the porch  is 2 modules wide.  

The proportions are 3-2-3, a graceful rhythm. If instead the massing had been 3-3-3 - all the widths equal - it would have felt dull. 

John Fuller, Master Builder, understood how to create with those simple shapes.  



The Interior Section shows the roof trusses, all using the 3/4/5 geometry. I've highlighted them in black for visibility

The meeting house height is divided in half horizontally. The columns which support the balcony divide the width of the meeting house in thirds.

If those columns has been the posts in the exterior walls only 1 window would have been possible on each side of the door. As I described above, the posts in the exterior walls were set differently (the black dot/dash line). 





With his frame laid out, John Fuller now needed to place the windows. The 6 posts on the front elevation were fixed. To allow any visual space* between the 2 windows on either side of the main door had to framed against the posts.  Here you can see how they were placed; there is no room for casings. 

* 'Visual space': the windows needed to be viewed as separate shapes, not as pairs.    




The red lines on the front elevation show the locations of the 6 bents for the meeting house.


One more window was needed on either side of the main entrance.

Where would they fit so that they were part of the whole, not call attention to themselves, and enhanced the main entrance ? 

Fuller used geometry to place the outer windows in relationship with the others. 

On the right side of the entrance is the front elevation as it was built.

On the left the outer windows are shown set in relationship not to the posts, but to their next closest windows and the left side of the elevation. The entrance is flanked, but not crowded by the windows.



The 'empty' wall to the left becomes part of the geometry. It shares the  proportions, being 1/4 of the wall. It is not 'left over'.


You can see the design succeeded. The uneven spacing between the windows is interesting and enlivens the facade, but it does not detract from the main door with its pediment. On either end the stretches of wall without a window anchor the meeting house to its site. 



Here is the main door. Its height is the determining dimension. Half the height is the radius for a circle and its square, drawn in red. The rotated square is drawn in black. The intersections determine the width of the architrave, the columns. The location of the plinth blocks and the depth of the moldings in the architrave, over the door are governed by the sides of the smaller square to the original circle.

The pediment follows Serlio's instructions:
 half of the width dropped below the base of the pediment - black lines - becomes the point for an arc whose radius -dashed red line - is the distance to the edge of the pediment. The dropped line is extended up to the arc; that marks the height of the pediment.







This way of laying out a pediment is shown in Asher Benjamin's 1797 pattern book:



The door itself came after the frame was in place. It was built to fit the opening. 

First the door's rails and stiles were laid out. 

Then the Rule of Thirds divided the remaining space in half and sized the panels and the stiles between the panels.





Last picture: The windows on the sides of the meeting house were framed against the posts as they also were on the front and rear elevations.

Just as at the Rocky Hill Meeting House in Amesbury, MA, the eaves on the porches bump into those windows. Neither master builder had solved that problem.


For excellent information about trusses in meeting houses and churches see Historic American Roof Trusses, Jan Lewandoski, et al., published by the Timber Framers Guild, 2006.

The Rockingham Meeting House is not included but the theory, practice, and evolution of the trusses used for similar meeting houses is laid out with clear photographs and Jack Sobon's drawings.

If you do not know how to use of the 'Rule of Thirds' square as a design tool, see: 

Monday, July 12, 2021

The Geometry of Gunston Hall's North Porch

This post is about exploring Practical Geometry, getting lost, and finding the simple answer. I have used my working  drawings to show the process. Faint lines show where I erased possibility that didn't work.


Gunston Hall was the home of George Mason, a Virginia planter, with a big family, lots of land, and many enslaved people. He was one of the delegates to the Constitutional Convention in Philadelphia is 1787.

He was also a mason: he advised George Washington about mortar mixes. 

When he had his house built, in 1754, he made the formal dining room and parlor (on the right side of the house in this picture) larger than the family parlor and chamber (on the left side of the picture).  


That meant that the house was not symmetrical around the door.  (To see this look at the spacing between the windows on the left and right sides.) The lack of balance might have distracted those arriving to either the north or the south entrance. However the small door and windows at the entrance were probably more jarring.

William Buckland, a young architect just come from England, solved the problem. The porches he designed are so inviting they make the asymmetry is almost invisible. More importantly they enveloped the existing entries.

In  2014, I wrote about the house here:

The geometry I suggested for the north porch never quite fit. I tried other solutions.  Nothing was much better. I could see the geometry of Buckland's design but I couldn't draw it. 

Here is the HABS drawing of the north porch.




 Here is my attempt to understand what geometry had guided the proportions of the design.

It's neat. It seems to work until you consider that the intersections of the lines do not tell the carpenters how to layout the porch, where the parts should go. The diagram is interesting, but gives no useful information.

Here is a later exploration when I still wanted the diagram to describe the porch design.

Perhaps my initial square was too large, not based on the right width or height?

Would a  circle within its square work?

How about a daisy wheel ?  or an octagon?

The pencil lines, the red and blue inked lines are finally just confusing.

6+ years later I changed the question. Not, "What geometry did Buckland use?" Rather, "What was he given?" 

I knew this. I'm an architect who works with existing houses. My first questions about a house are, "What's here? What are the existing conditions?" 

The HABS drawing of the Hall show the north wall, a door with a fanlight and small side windows, a baseboard, a chair rail and an expanse of upper wall with some crown molding.  This is what existed, and seen from the outside,  just too little.

I realized that the main problem was not the lack of symmetry, it was the dinky entrance. The door and lovely fanlight are dwarfed by the expanse of brick, the windows are minuscule. 

Refer to my first picture of the house (above) to see how little the windows are compared to the windows on either side.  

Buckland couldn't change this; he had to work with what was there. 


What were the existing dimensions?
One was the height from the sill of the door to the eaves of the roof. Buckland could add inches by adding a step down, but he couldn't easily go higher.

The second dimension was the width. His width couldn't be so large that it drew attention to the uneven spacing of the left and right windows. And: the porch needed to be centered on the door,to  enhance it and its fanlight. The side windows had to be integral to the design.

He used the given height for his width. He drew a square and added the diagonals and the mid-lines. horizontal and vertical.

He added his Lines - upper center of the square to left and right corners.

The square was divided into thirds where the Lines crossed the diagonals. Placing the columns within the 1/3 of the width gave more importance to the door while keeping the rhythm, as well as keeping the steps wide and gracious, the porch airy and open. If the columns had been set on - not beside -  the 1/3 lines the design would have been static, staid.

The points where the Lines crossed the diagonals also marked the edge of the frieze (also called the architrave).

The mid-lines divided the square into 4 smaller squares. When  diagonals were added to the upper squares, where the Lines crossed the diagonals located the height of the frieze, the beginning of the gable, the roof. In the lower squares the Line crossed the diagonals at the top of the hand rail.

I have drawn these  Lines only the right side. The layout is hard to read  when all the Lines are added. On a framing floor. all the Lines would be marked and used to layout the frame.

The arch draws our attention. The half-round shape makes the porch open and welcoming. It frames the main door and its fanlight - inviting you to the house.

Its diameter is 1/3 the width of the porch. It is part of the whole.

 I've drawn it with its cascading circles because it's fun. I also wanted to note how the circle can be a tool for laying out a plan.

Palladio used a circle as his unit of measure: he called it a 'diameter'. His diameter was usually the column in his drawing. Although it's possible that the circle here was also the unit of measure, I think it more likely that it was one element Buckland knew how to use, one that would enhance and unify the porch with the house, especially as its diameter came from the basic geometry of the porch.    

For an introduction to the Rule of Thirds see: 


An after thought: George Mason used the geometry of the 3/4/5 triangle to layout Gunston Hall, including the dimensions of  his windows. If William Buckland had used the geometry of the square and its circle, its proportions would not have complimented the Hall.


Saturday, May 1, 2021

Saltbox Geometry


I have been thinking about simple house forms and their straightforward geometry. 

I was asked about window placement for a modern saltbox. I had no simple answer.  A traditional saltbox has a door in the middle and a room on each side. The windows are evenly spaced because vernacular construction in the western world was evolving from medieval to renaissance design.  A modern saltbox?  Is it an oxymoron and if not, what would be right? That's the background. Below is the geometry for a vernacular saltbox.

Settlers in the Colonies included a good number of carpenters; men who had finished at least their 7 year apprenticeships. Still every family needed a house, so a straightforward plan was required; one that was easily laid out with available tools, like twine and chalk or charcoal - a Line. A carpenter square was useful, but not always truly square; it needed to be checked by geometry.  

The form that developed was a simple vernacular American house - 2 rooms over 2 rooms with a center entrance. Common all over the Eastern Seaboard, it went west with the settlers. The lean-to - its sloping roof the signature of a saltbox - was regularly added to the back, first for storage, later to expand the house.  

 My diagrams here are for a simple generic New England saltbox.

The carpenter needed to decide how wide, how big the rooms would be. He choose the same length for the depth and width of the parlor and the hall. That first length governed all the choices, the placement, the patterns, the dimensions that followed.

He knew the fireplaces and chimney stack would be placed in the middle so he made space for them. Then he laid out a square on one side, and another on the opposite side. This became the guide for his timber frame.


 Here is the sequence that begins with a length and ends with a square. A carpenter knew practical geometry. He knew how to use a straightedge and a Line. He had no ruler or tape measure. He probably began with the 5th diagram. He didn't need a physical compass. His Line could be pinned at one end and then swung in an arc to mark the corners. The resulting square could be checked (trued) by matching its diagonals.


My mythic carpenter choose a room depth of 16 feet. 20 feet was a common length in later houses. The diagram is to scale; it is 16 ft. deep and 40ft. wide.  I have allowed 8 ft. for the fireplaces and chimney. 





The same square - 16 ft. x16 ft. - was used for the height. Here it is divided in half for the first and second floors.

The ridge of the roof frame is half the height of the box - 8 feet.

Sometimes the dimensions for the framing began at the foundation. Sometimes the dimensions began after the sill was laid, made level and true. 

Here are the posts, the beams (called girts), and the rafters laid out. Next will come the summer beam, and then the joists.

For reference I am using Abbott Lowell Cummings' framing from his booklet, Architecture in Early New England. His first diagram is entitled "Typical framing details.." . The second, "seventeenth century house plan"  shows the early fireplace and chimney configurations. (see below)





The windows were centered in the shape, right in the middle. Glass was a luxury in early houses; windows were small.

There might not have been one in the attic.


 Here is the diagram for easily finding the center line of the square. Swing the arc of the length as shown in the first square -dashed red lines, solid black lines. The crossing points are centered on the square as shown with the solid and dashed lines  in the second square,


The front elevation of the house was as simple as the floor plan and the side elevation: 2 squares with the chimney stack in the middle which also gave room for a stair and a entry door.

I've added shading to the roof.


The layout shows the post and beam frame, ready for the summer beam and the floor joists.  All of this could be laid out with Lines, made true and square by the diagonals, which are also Lines. A Line might be chalked to leave a mark ( a Line) on a framing floor, or it was a length of twine pinned in place by an awl, or tied to a stake.




 Here's the front elevation with  one window centered in each room.


 As glass became more available more windows were added.

There were 2 ways to place the windows using the geometry of the Rule of Thirds. Here on the left the square is divided into thirds, the windows centered on that Line. 

On the right the inside edges of the windows are on the Line. 


 Here is a diagram for the Rule of Thirds. The diagonals for the square are crossed by the center line. Then new diagonals - red - are added to the rectangles on either side of the center line. The diagonals of the square cross the diagonals of the rectangles at points which divide the square into thirds.

I have only shown the square's diagonals and the red diagonals in the drawing which shows window placement.  The square with all its Lines can be visually overwhelming.


This diagram shows the squares divided into thirds - the dashed lines. On the left the windows are placed on the center line - dot-dash lines. On the right the inside edge of the window is on the Line -  solid lines

In a new community settlers from different areas  brought different framing traditions. 2 houses side by side might use different patterns, reflecting the carpenter's background.

The lean-to was an obvious expansion: just an extended roof covering the new space. The space did not always include a fireplace. When a fireplace was added it was laid up against the existing masonry.

 Here is the diagram  showing the carpenter's Lines.

Note that while in a diagram the roof would meet an 8 ft deep and 8 ft high room at the upper far corner, in reality the width of the posts and beams and rafters often made for a lesser height.



The back wing was useful. It often was 10 feet deep.  The diagram shows how the roof pitch changed. If the lean-to were added after the main house was built, the rafters might join the frame under the roof. That would also lower the roof pitch. 


Here is the window placement;  all are centered on their interior spaces.

The photograph at the beginning of this post shows how owners adapted and updated the basic house. More windows were added on the sides. The front windows were sometimes enlarged. Columns and an architrave with molding were added to the front door. After 1780 front entries were added to many houses.


The rhythm. pattern, proportions - the geometry, including the window sizes, of a Georgian saltbox came from its construction, the available materials, and its function. It used timbers and hand tools to create shelter. It did not need to accommodate bathrooms or closets, nor provide much privacy. I think a modern saltbox, built with modern materials and tools for 21st Century life, will need its own rhythms, patterns, and proportions.




This is Abbott Lowell Cummings' first illustration in his pamphlet, showing the frame I have laid out  - a center chimney with a room on each side on each floor.


The main floor plan shows how the lean-to was added and used.  This plan, common on the New England seacoast, came with settlers to western Massachusetts,Vermont, and upstate New York. It is often inside what appear on the outside to be Federal and Greek Revival houses.  The chimneys move, the ceiling are taller, the stairs more gracious, but the floor plan remains.





Abbott Lowell Cummings' plan is not as 'square' as my diagrams. Here is the geometry. The Hall on the right is a square room. The dashed red arc is the width of the room transferred to the length.  

The width of the Parlor matches the Hall, but its length is shorter. It is determined by where the arcs of the width, the red dashed lines, begun at each corner of the fireplace, cross.   

The layout for the house, its rooms, begins at the chimney stack. It seems to have been placed first, the house framing against and around it.

The back wing is set true with the house using the 3/4/5 triangle which will always have a square corner,  red dotted lines. Here the wing is square, 'true', with the existing house.

* Abbott Lowell Cummings, Architecture in Early New England, Old Sturbridge Village Booklet Series, Sturbridge, MA, printed by the Meriden Gravure Company,  Meriden, CT. 1974.

 In this post I have capitalized Line because those who wrote pattern books capitalized it, and because the Line creates the design.
The name 'saltbox' was given to these houses in the late 1800's, by New Englanders who had salt boxes of  a similar shape in their kitchens. In the southern US, these roofs were/are referred to as 'cat slides'. The saltbox houses whose geometry I have studied have wonderful variations and quirks. Often these are due to the changes in  fireplace, bake oven, smoke chamber, flue, and chimney construction technology. 

The photograph of the Kimball House comes from the archives of the Andover Center for History and Culture.