Tuesday, January 28, 2014

Old First Church Geometry, Interior Elevations - Part 2

The first post on the Old First Church geometry using the daisy wheel, showed how the geometry of the daisy wheel was used to layout the interior view facing east (north/south cross section)  of the church.

The daisy wheel was also used to layout the longitudinal (east/west section) shown here.
(The red circle with its 6 petals is the 'daisy wheel'."
Just as in the first section the top of the circle is the roof of the church. The left and right sides of the circle mark the ends of the sanctuary. The part of the church to the left is the 'porch' or narthex and also the base for the tower.

The balcony on the second floor extends into the tower frame. It is to the left in the photograph. The left hand column is the column at the left side of the daisy wheel above.

The height of the sanctuary - not including the dome - is set by the 4 side petals of the daisy wheel.

The bottom of the circle may have originally been the floor of the basement. The foundation and piers for the columns have been repaired and rebuilt, so it is not possible to be sure where the base of the church really was when the construction began.

The square (4 sides) and its circle  - not the daisy wheel (6 sides in its circle) - determine the wall proportions. The elevation divides neatly into 2 squares.

(See the red x'ed squares that meet at windows centered under the dome.) 
The circles which surround the squares and are generated from a radius made up of half the square's diagonal cross at those centered windows, creating a  'vesica piscis'.  

(Or fish's bladder - the pointy oval, boat shape where the circles overlap.)

On outside of each circle, also the edges of the vesica piscis are the columns.
That spacing is the interval for the columns. It is like the circles that determine the glass pattern in the arched tops of the windows, a pattern that can run either way, or that comes from each side and meets here.

(See my post titled "Geometry of the Old First Church, Bennington, VT" for diagrams of the windows.)

I think a carpenter would have used his dividers to transfer the column and windows spacing instead of drawing all the intersecting circles. To make the pattern clear I show here all the vesicas and part of the circles. I find it complex to read. It wasn't easy to draw.
On the left end I have laid out in green the vesica centered on the column instead of surrounding the window, just to show that the pattern can start with either the window placement or the column placement.

Finally when the 2 squares and their circles are moved so that the edge of the right circle defines the location of the east wall of the sanctuary, the edge of the left circle defines the west wall.

Here I have outlined the sanctuary space in black - showing how the balcony extends over the narthex, but not quite to the front of the tower. The squares and their circles in my first diagram above are simply moved over.

I have written 7 posts on the Old First Church.  Except for the post on the VAS, they are all about the geometry used to design the church.

Sunday, January 19, 2014

The French Andrews House Geometry - Part 2 of 2

The geometry of the floor plan of the French Andrews house focused on the fireplace and chimney mass. Two squares determined the space and the surrounding post and beam frame.  (See Part 1)
Did the framer used the same pattern on the elevations.
He did.
The red squares in the center of the front elevation show this. Starting from the stone foundation, the width of the firebox is also the height to the 2nd floor - the location of the 2nd floor beam. The square above determines the attic floor - the placement of beam at the eaves. The top of the third box is at the height of the ridge pole.
Both sides of the front elevation are squares with one longer side determined by the radius of the circle which fits around the square.  For clarity I have only drawn the square with its diagonals on the west side and I have only drawn the arc in question, 1/4 of the circle.    

 The east and west elevations are identical except that the location of the 1st floor door shown here is the location of a window on the east side.
Again the square is the determining geometry. I could have overlaid my red squares in several different patterns which all worked. I chose this one because it shows how the arc hits the center of the window, the center of the original house, and the edge of the square is also the edge of the door frame.
The north side of the west elevation is a duplicate, reversed, of the one shown. Again I didn't draw it so that the pattern would be easier to read.

 This is a geometry for framing. The squares lay out beam and post locations, not necessarily walls and room sizes.

I wondered how the lean-to was laid out, especially since it was added later and its floor plan used the 3-4-5 triangle, not squares, so that the wing would line up squarely with the existing house.
The lean-to elevation is also laid out with squares, but these begin not from the foundation, but from the first floor - which makes sense  - it was a given.

The roof pitch surprised me because it is so obvious: the diagonal through 2 squares. Given the pattern already established it came naturally and is steep enough when shingled with wood shakes to keep out the rain.

Sometimes when I see these patterns emerge I shake my head and look at myself askance, "Of course! What else would have worked so easily?"

 On the second floor plan are dotted lines indicating the exposed beams overhead. Using my calipers I scaled them and found they made a square. They are not the dimensions of the 'chambers' - they mark the outer edges for the placement of the posts and beams.
Next, drawing the arc based on the length of the square I marked where the arc crosses the diagonal - the Golden Section. All the windows in the south elevation (except the one above the front door, see Part 1) are placed by the Golden Section. The windows are not centered by the Golden Section as they would be a few decades later. Instead the line marks the side of the window. It tells the carpenter where to start to frame the window opening.

Enjoy how the stair hall space within the beams is also a square, although the hall itself is slightly wider as the walls have been placed on the other edge of the beams.

Sunday, January 12, 2014

The French- Andrews House geometry, Topsfield, MA - Part 1 of 2

When I was thinking about the original salt box shape of the Locke Tavern, I looked at other early Georgian saltboxes I knew for a comparison.
I thought I would find a similar geometry that would reinforce what I had already seen. Instead I found another way to use squares and the circles that fit around them to organize a frame.

This house I have only seen from a distance. However, measured drawings for it are available on HABS. And
a website for the French Family includes many pictures and a time line.


The French Family site says the house dates to 1675. The HABS drawings, done for SPNEA in 1933, say 1710. Abbot Lowell Cummings says 1718. In any case it predates the Locke Tavern, and it was built in the same neighborhood.
Here is what I can see about its construction by looking at its geometry.

 Notes on the drawings for the second floor say at the wall between the lean-to and the upstairs bedrooms: "rear wall old weathered clapboards... balance of wall is shingled". This means the lean-to was added; the exterior siding left in place. I have seen this in other early houses. It is not unusual.

It does mean that the front of the house, the chimney, the hall and the chamber were built first.

The geometry for the main house is the Golden Section. The entry and chimney block consisting of 2 squares (red x's in the center) The corners would be the location of posts and bearing for the summer beams - the beams which are in the center of the rooms.
The size of the rooms is determined by the extended square and its diagonal (dotted red line showing the square and the diagonal).

The front door is not centered. For a while I thought this might mean one side of the house was built before the other. But then I realized that for the door to swing fully open it had to be off-centered, and that I had seen this layout in other early small houses.
You can see in the elevation that the hall window above the front door is also not quite centered - but carefully placed to minimize the asymmetry so that it would not apparent at first glance.
Here I have to stop and appreciate the builder who understood how far off from the center of the door and then, from the spot equidistant between the 2nd floor windows he could position the window where it would least call attention to the discrepancy. A fine mind there, one which speaks to me today. He succeeded.

The lean-to dimensions were determined by the 3-4-5 triangle (the green triangle on the plan).
This made the framing square to the house - the joists, purlins and sheathing would fit neatly, the house would be tight.
From the drawings we can tell that the width of the house was already 45'-6". The depth of the house became 34'-6".
45.5' divided by 4 is 11.375'.
34.5' divided by 3 is 11.5' .
Was the master carpenter 4+" off? Maybe. But I do not know from what place he began his dimensions - the foundation? the outside of the frame? the outside of the sheathing?
Perhaps the house shifted in 200+ years between its construction and  its measuring, or was re-sheathed. And the measurements might be 4" off.

Saturday, January 4, 2014

The Locke Tavern, once a saltbox - Part 4 of 4

During the recent updating of the plumbing  for the Locke Tavern  the floor between the first and second stories behind the center chimney was removed.
I took this photograph standing on the first floor looking up at the exposed second floor wall between the old bathroom and the northwest bedroom while the carpenters worked around me. They were very pleased to share what they had uncovered. Here is what we saw:
* Modern plumbing running next to the chimney stack to the left as we expected.
* A diagonal beam with stud framing below and above that do not match up - ie: the beam was there before the framing.
* A door opening into the nw bedroom  - the white angle on the right.

The diagonal beam is the beam for the original roof over the back wing .
On the top edge of the beam you can see where the purlins were let in. Over that would have been laid the sheathing and then wood roof shingles.

The Locke Tavern once had a lean-to back wing. The space was served by a third fireplace set against the chimney block.
This house shape is referred to as a 'salt box'.
Sometimes these wings were added later, the new roof laid over the existing one, often at a slightly different angle. I have not yet seen how these 2 roofs join.

For readers who don't know about the  form: Here is a picture of a saltbox c. 1715: the John Kimball House in Ipswich Mass. The name was applied to this way of  extending a house much later, in the 1890's. It comes from the shape of a kitchen salt box of that period. Another name for this roof configuration is a "cat slide". 
I chose this house as an example because Kimballs also lived in Andover, Mass. The picture comes from the HABS archives.

This means the northwest wing was extended and a second floor added over the lean-to when the house was enlarged and updated around 1790.

How was the size of the lean-to determined? I think the master carpenter used  the geometry of the square and the Golden Section just as he did for the main house.
 In the diagram the lean-to is outlined in black (a). The square and its diagonal extended (the Golden Section)  determine both the left and right sides (b).
The center section (c) is more problematic. I wish I had been able to photograph and  measure it on site when it was open. The drawings I am using are of the house before it was opened up. Clearly the framing extends on each side of the chimney block with the kitchen fireplace set in between. There are posts in the outside wall and posts on each side of the chimney, at the back corners of the front rooms. Maybe the shape is a rectangle that has sides determined by the 3-4-5 triangle. But I don't know precisely.

It would have been so easy if the basic floor plan were a 3-4-5 triangle! But it isn't. The house measures 36 ft x 28 ft.