The Old First Church Geometry - the Floor Plan - Part 4

 I first wrote about the geometry of the Old First Church in Bennington, Vermont, in September, 2012, focusing on the 2nd floor windows with their round tops.
http://www.jgrarchitect.com/2012/09/geometry-of-old-first-church-bennington.htm

I will not repeat that post and the ones that followed -  just expand upon it here.

As I studied how the church was designed I saw that the window design was the logical extension of the basic design.

This spring the full window design and then the geometry of the floor plan - which had eluded me - became obvious.

The circle geometry which determined the curves in the half round top also determined the size of the window itself and muntin pattern  in the lower section.
The completed circle of the top half intersects with the circle which begins in the lower sash. The circles divided in 4 determine the size
of the window panes.




The panes themselves are not quite square because of the thickness of the frame.

The pattern in the rounded top is made by 7 intersecting circles. The window itself is 2 intersecting circles.

I have called these 'rolling circles' because visually they seem able to roll one way or the other. Perhaps in a church the circles roll toward each other and meet..
It would be fitting symbolism for Old First Church whose covenant says the members hope to " ... become a people whom the Lord hath bound up together... "









Here is this geometry:
looking at the windows in the balcony in the church,

Here is the floor plan, measured and drawn in the 1930's by Denison Bingham Hull, the architect who supervised the church's restoration.

I superimposed a circle with its rectangle marked in red which  matches the circles that define the east interior elevation and the exterior front elevation.










This is what I had not seen before -  how the geometry of the floor layout uses the same forms as the windows. Both are 2 intersecting circles.


The rectangles laid out by the circles determine the size of the sanctuary. The diamond shape where the 2 circles cross, the center of the church,  is the  location of the dome -an acoustic device - a technological tour-de-force in 1805. The narthex fills and over flows the lower quarter of the circle. The depth and width of the front bay is determined by the arc of the circle's perimeter.









Expanding the circles in the way that the window design    'roll'  I saw that Lavius Fillmore, the master builder, did not need divide his circles into daisy wheels to locate columns and determine proportions.


This relationship of one circle to another in a linear (up and down, side to side) pattern rather than relating one circle to the next by moving around the perimeter is seen in all the elevations and plans for the Old First Church.










In the drawing to the left I have added small circles at the intersections of the arcs which mark the lines of the columns, the corners of the front bay and intersect with the perimeters of the circles at the 4 major columns - the black squares - which run from  piers in the basement through the sanctuary into the attic to anchor the trusses which carry the roof and the trusses from which the dome is suspended.

Fillmore need not have drawn a daisy wheel with its 6 petals to refine his design.
He might just have rolled his circles.


In many ways these different approaches to 'basic geometry' - as Asher Benjamin calls it - cross-reference each other. The daisy wheel and the rolling circles are variations of the same proportions.
My 'aha' moment is when I find for one way of working that is clean, simple and 'obvious'.

Here are the earlier posts about the church geometry. Each one was posted when I learned (taught myself) more about how circle geometry can be used for design. Part 1, therefore. is a preliminary understanding.  

Part 3     http://www.jgrarchitect.com/2014/11/old-first-church-and-daisy-wheel-part-3.html
Part 2     http://www.jgrarchitect.com/2014/01/old-first-church-and-daisy-wheel-part-2.html
Part 1     http://www.jgrarchitect.com/2013/01/old-first-church-and-daisy-wheel.html

.

Owen Biddle's 'Plan and Elevation for a Small House'

Owen Biddle published his Young Carpenter's Assistant in 1805 in Philadelphia, PA. He included 2 house designs as teaching tools. Biddle wrote that his drawings were not meant to be "eligible for the builder". Instead they were "aiming at instruction for the student".

In 1797, Asher Benjamin published The Country Builder's Assistant in Boston, MA. It also included house designs. Benjamin used crossed squares and the rule of threes in his designs,*

What geometry did Biddle use?
Here is his "small house" - Plate 36.

The layout is 2 squares side by side for the plan and the elevation. The elevation measures the square from the  first floor to the top of the brick coursing. He writes that the student "suppose the building to be raised just above the principle floor, and the wall made level all around."

I enjoyed this because a contractor today still wants his foundation and first floor level before he starts his partitions, of course!

Note on the plan  that the depth of the front porch is determined by extending the diagonals.

Usually I draw both diagonals to denote a square. Here since I will be adding other lines I decided to simplify for legibility.








Biddle designs using the square divided into quarters. On the elevation the top of the first floor windows is determined by the horizontal center line. The placement of the windows is determined by the vertical center line.

The floor plan follows the same geometry. The edge of the window frame is determined by the vertical center line.

Still using the squares, Biddle divides one half in half again, vertically.  This locates the columns - and the size of the front porch - at the 3/4 mark of the squares on each side. Note that the horizontal center line dictates not the top of the fan light casing but the height of the brickwork. These are structural dimensions, information for the brick layer, the sash maker.
The curve of the entrance stair follows the diagonal.
The width of the window is determined by the intersection of the diagonals.

On the floor plan the right hand  side of the square is divided in half; it determines the location of the wall between the rooms and the hall.










The porch is 1/4 of the square.

Here I have drawn the lines that layout the portico in red and given the pattern of the division across the bottom: 2-1-1-1-1-2.
The architrave and the roof are 1/3 of the square of the porch.







When I first saw this I thought the portico and the doorway used the rule of thirds. I was wrong. The door itself may be 1/3 of the porch, but the casing around the door is placed at  1/4 the width of the porch.  The height of the fan light is 1/4 of the square; the door below 3/4.



Note the shadow  to the right of the porch. Biddle wanted his book to teach drawing and presentation. He tells the student (reader) to "enliven the drawing by giving the appearance of shadow". (Plate 36).

This house was an exercise, just as Asher Benjamin's were. The geometry he uses comes naturally and easily, Although he knows the rule of thirds he barely uses it. He does not use crossed squares. Benjamin uses both.

This is not the geometry seen in New England nor in the folk houses documented by Glassie. It might be the geometry of Philadelphia.



 *To compare see my post:
 http://www.jgrarchitect.com/2014/05/the-country-builders-assistant-by-asher.html 


Owen Biddle, Biddle's Young Carpenter's Assistant; or A System of Architecture Adapted to the Style of Buildings in the United States, Benjamin Johnson, Philadelphia, and Ronalds & London, New York; 1805
Dover Publications, Inc. edition, 2006, unabridged republication

Old First Church Geometry, the Elevations - Part 3

This is part of a series on the geometry of the Old First Church (OFC). Bennington, Vermont.



I began looking at the geometry of the church in 2012 beginning with the  'rolling circle' muntin pattern in the rounded tops of the windows.









I found that the repetition of the circle I saw in the windows was used in the window and column placement of the side elevations. The length of the sanctuary is also governed by the repeating circles.

The circle divided into its 6 parts - the daisy wheel - defines the church's width and height and its roof.



These drawings I have already discussed in the earlier posts.  

Now for the new ones,





The daisy wheel rotated 30*, or with a horizontal axis instead of a vertical one, the line between the 'petals' defines the column placement - the outer side of the columns.
The diagram below shows how the same proportions - the main nave of the church and it's side aisles can be laid out by locating the circles 90* instead of 60* to each other ( 4 petals on the daisy instead of 6).






The front elevation of the church is governed by the same circle.
Then the first circle's center is the bottom point of the diameter the second circle. The second circle's center is the bottom point of the third circle's diameter. The 3 circles together encompass the church and its tower.
They lay out
1) the height and width of the church meeting space
2) the height of the first 2 levels of the tower
3) the location of the Palladian window in the tower

If the center of the middle circle is used as the outer edge for parallel circles on either side, the 4 petals that result determine 4) the size of the protrusion of the narthex - and the location of the columns inside,
5) the location of the bottom chord of the pediment,
6) the placement of the bell platform
7) the height of the architrave above the columns and their arches that surround the bell.

I have drawn the diagonals of the bottom circle in green which mark the rectangle of the church body. Note how it determines the roof of the main door. I have added dashed red lines at the sides of the extended narthex ('porch')  and extended those lines up to meet with the line marking the top of the belfry.


Here is the diagram of circles extending both horizontally and vertically, creating squares instead of daisy wheels. It's just a reminder. 
I've laid out its construction in earlier posts.
http://www.jgrarchitect.com/2014/09/how-to-construct-square.html














Lastly, here are the circles in the same rhythm as those which determine the pattern in the windows.

(1) The first red circle at the bottom encompasses the church. Its center is at the top of the pediment over the main door.
(2) The second red circle sits on the center of the first. Its center is the Palladian window in the tower.
(3) The green circle's center is on the line laid out by where the first 2 circles cross which is also the peak of the oerdiment over the 2nd floor Palladian window. It extends from the floor of the church to the  rail of the belfry.

The circles can 'roll', just as does the muntin pattern of the windows.
 Here are some of the circles that grow of the 3 laid out above. Each circle's location is determined by those on either side.
The centers are noted with small red circles. Note that they determine important features of the facade.

The circles themselves were numbered in green - visually it was too confusing.


 There are many points I have not called out. It is just clutter at this small scale. Remember that pictures can be enlarged by clicking.

Arnold House, Westfield, Massachusetts - Part 1

The Arnold House,Westford, Mass. c. 1800, was measured by Edward E. Jordan for the Historic American Building Survey.
On the first HABS sheet is written: "Note: house partly destroyed by fire during winter of 1933-34." I know very little about the house or the family. Probably the builder was Joseph Arnold who died in 1823.


While I was thinking about how this house was laid out, a friend asked if I had ever seen the 3-4-5 triangle used for design. Like the circle and the square it is independent of fixed dimensions. It is simply a ratio that always produces a right (90*) angle.


I had not seen it, but I began to pay attention.







So - look at this house. Click on illustrations to enlarge.

Note the outside dimensions -
 30'-6"  by  39'-3".
For a wood frame, post and beam, hand hewn house that's close enough to 30ft. and 40 ft. So for the 3-4-5 triangle the diagonal across the house, (A), should be about 50 feet long. It is.

Then look at (B), the diagonals of the front rooms. The same angle gives the dimension of the parlor. The diagonal (B) in the Living Room is not as clean, but still defines the size of the fire places and chimneys and the post location at the rear of the house. (C) determines the post location in the Dining Room.

The 3-4-5 ratio also gives the locations of the windows, at least one door and the size of the Room behind the Parlor.
Here I have added what I think was the original back wall of the Parlor for clarity (X). I have also used a red line with a dot for the rectangles created and the center lines of the doors and windows
(D) shows the Parlor window placement on the side directly on the center of the room, the front windows equidistant from the center.
(E) shows the window spacing in the Living Room determined by the rectangle turned on its side
(F) places the center line for the Dining Room window and door at the edge of the rectangle.
(G) determines the size of the Room behind the Parlor and the location of the stairs.

Next I will post the front elevation and add some ideas I have about the house design.