The cobbler's house north of Boston, c. 1840. Part 4 of 4

Organizing my drawings and thoughts for  presentation has required me to revisit earlier ideas. So here is how I now think this simple house may have been designed.  




Here is a new post on this house, built north of Boston in the Merrimack watershed c. 1840. The previous posts include its history.





First: the geometry of the 3/4/5 triangle:

A triangle by definition has 3 legs. If the legs are in proportion to each other so that the shortest is 3 units, the middle one is 4 units and the longest is 5 units. the triangle will always be shaped like the diagram here - with the 2 shorter sides meeting at a 90*, the longer side always the hypotenuse.

A 90*, a right angle, is what carpenters and brick layers need - a   way to be sure they are erecting a stable shape that in construction will keep the loads directly over their bases and transfer those load to the ground.

The wide spread availability of carpenter squares after 1820 in the United States made the 3/4/5 triangle the easy and flexible choice for layout. 2 triangles with their hypotenuses side by side made a rectangle. The long and short sides of the triangle could be flipped.


Here in the floor plan of the  cobbler's house, The right side, the main house, is 2 rectangles made up of 3/4/5 triangles. (A) is the triangle laid out. (B) is 2 triangles turned - one starts from one corner, the other from the opposite. Where they cross is the center of the rectangle. The back wing is one 3/4/5 rectangle and a little more, The size of the 'little more' (C) is  determined by the 3/4/5 ratio.

The rectangles of the 3/4/5 triangle can be set side by side, as they are here, or they can be slide past each other as can be seen in the diagram.









Here is the side elevation of the cobbler's house - a 3/4/5 rectangle with 2 more for the roof - arranged much as was the floor plan of the house. (A) is the main box, (B) is the 2 triangles set back to back.

 Add the lines for the other triangles - the diagonals for the rectangle.Where the lines cross determines the placement of the 2nd floor beam and joist (dash and dotted lines above central 1st fl. window).
The intersections also mark the center of the house, thus where the 1st floor window goes, as well as the spacing between the 2nd floor windows.






The first drawing assumed the width of the house was the '4 units' of the triangle, that the height was '3 units'. If the height is seen as '4 units', the resulting triangles cross below the 1st fl. window, That space where they cross is the width of the window.

Here it is clear that the numerical length of the unit does not matter.
The relationship between the lengths, their ratio, is what determines the layout.





What happens on the front of the house?
The front elevation is made up of 2 squares. However, the layout of the door and windows does not come from those proportions.
It comes from the use of the 3/4/5 triangles - with the wall height '3 units'.  The 3/4/5 rectangles, begun on each end of the elevation cross in the middle. Their edges place the windows on either side of the door.

Lay out the rectangles (drawn here on the left side): the diagonals cross on the center of first windows.
Swing the triangle to its other leg (drawn here on the right side): the resulting rectangle's diagonals cross at the edge of the outer windows and mark where to place the window jambs of the inner windows.







January 2020: 5 years after I wrote this I think I should check the geometry once more. If the layout of the frame began at the sills  - as I have often found - the geometry is simpler.




Originally I thought that the geometry determined the design, I now think the geometry was used for the framing. The design came from the frame. These vernacular houses did not have an 'architect' but instead a master carpenter. While I am sure they thought about what a house looked like, they were builders, not draftsmen.
These houses resonate with us because we sense the geometry which relates all the pieces to the whole.

Cobbler's house north of Boston, c. 1840 - Part 3 of 4

I have just finished writing about the Arnold House: how it uses the 3-4-5 triangle as a regulating principal and how it is almost but is not the same as the Golden Section.

If you don't know what that is, please read the posts on the Arnold House. Thank you.

I said the same thing about this house: it 'almost used Circle Geometry', but didn't. I realized I needed to look again.

I do love the grace of the Golden Section and Circle Geometry.
But look at how the 3-4-5 triangle fits.
(A)  marks the diagonal of the rectangle created by the 3-4-5 triangle. It's half the house. The other side matches it.
(B) marks the corner of the smaller room on the right, its size determined by the triangle. The larger rectangle forms half of the house footprint. The room's proportions are determined by the proportions of the house itself.
The back wing, a rectangle that matches the 2 front sections, is a little longer. (C) shows how the extra space is determined by half a 3-4-5 rectangle.



I rather hoped the end elevation wouldn't fit the pattern!
It does.
(A) shows the rectangle created by 2  3-4-5  triangles. It fits the size of the house, easily giving the master carpenter the dimensions he needed for post and beams. It even determines the roof pitch! Not a 9/12 or a 10/12 pitch, ratios commonly used today, but the 3-4-5 triangle.

However, the floor heights, the window placement, the elevations still seem determined by both circle geometry and the Golden Section.

The house's outline - its footprint, height and roof pitch - do seem governed by the triangle.

How nice it would be if I could teleport back to 1840, watch the house-wright at work, and ask questions!

My great thanks to Jay Cougar White Cloud for his good questions that pushed me to consider the simplicity of  framing with the 3-4-5 triangle.

For the next post, and a more thorough analysis of the house click here:  http://www.jgrarchitect.com/2014/10/the-cobblers-house-c-1840.html

cobbler's house north of Boston, c. 1840 Part 2 of 4

Note: I have extensively revised the posts on this house. I thought at first circle geometry had been used even though it didn't quite fit. Then I tried using the 3/4/5 proportions of a right triangle. Those proportions do work. The new post can be found here: http://www.jgrarchitect.com/2014/10/the-cobblers-house-c-1840.html .
I have left this post because of its introduction to the house and the floor plan with circles.

Here is the farm house, a story and a half cape, the contemporary shape for 1840, but in the old fashioned pattern: center entrance, 2 windows on each side.

Its first owner is listed as a cobbler. There is a spot to the side of the house where a very small work shop probably stood. He may have made shoes for the community or done piece work for a jobber who took the work to a factory in a near by town. Often men worked in the shop  while women did similar work in the house.

In 1837, the market for wool which had made fortunes for New England farmers,- including the farms in this neighborhood - disappeared. Australia could produce wool cheaper. A 'Panic' ensued  - today we would call it a depression.

So the owner of this house was cautious and frugal. The house is small. Its windows are tiny with 27" x 22' sash - the part that goes up and down - in an era when most sash were about 30" x 30".



In my last post I wondered if my measurements were off. So I checked, redrew very carefully, and then laid out the circle geometry: 2 circles with the same radius, each circumference running though the center of the other. My last post includes a diagram of this.

It is off, just barely. If the house were 4" smaller the circles would overlap as they should on their centers.

Cobbler's house north of Boston, c. 1840 Part 1 of 4

NOTE:
This post was definitely a work in progress. For some of the answers please see the next posts, especially Part 4.
 I have kept this post because it shows how the different geometries are almost the same, and how they were used in similar ways.
The new post can be found here: http://www.jgrarchitect.com/2014/10/the-cobblers-house-c-1840.html 

Here is a simple farm house c.1840, about 40 miles north of and 10 years newer than the house in the last post.

I know the house quite well, and have measured it.
 Please click on the pictures to enlarge them.

As is clear in the photograph it is well sited, with graceful proportions, a late Georgian cottage at a time when more urban houses were Greek Revival. The shutters are updates.
It is in the Merrimack River watershed, as is the Locke Tavern  - see previous posts. I wondered if  the Golden Section used by the Tavern had perhaps migrated with a house wright up river to be used here.  Or whether the builder used a variation of circle geometry, or maybe, due to the advent of the Industrial Revolution, neither.

The floor plan shows the main  house with walls and stair. The back wing is indicated only by its exterior walls since the inside has been extensively remodeled. It was probably a summer kitchen, shed and storage space, the covered way to the barn. There is no fireplace. A chimney was most likely beside the stair. A modern stack is now outside the original footprint.

When I think about the geometry I also think about the owner and the house-wright. This small house has 7 ft. ceilings on the first floor and little windows. It lacks the frills the owner would have seen on other houses in the neighborhood and on trips to market. So I think the geometry used would have matched the house: bare and simple.

The 2 circle pattern works here. The circles are within the frame. I think of the framer, knowing how deep the house would be, laying out the circles in his framing yard to determine its length and height. The interconnection of the proportions gives the house its grace.

 The intersection of the circles - the vesica piscis - is the middle of the house, the position of the front door - see 'a'. It also determines the width of the back wing - see 'a' - and the front windows' placement - see 'b' .
I have drawn one of the squares which fits around the circles - the green x.  The front hall walls and the left front windows - see 'd' in green - seem determined by the intersection of the diagonal of the square and the the circle. The side window - see 'e' in green - is centered by the circle and the square.
The shed's width follows the  geometry of the main house, but its length doesn't quite - Two of the windows in the shed seem to determined by the circles' intersections - see 'c' in red.

 I wonder if my dimensions are off: the house is swathed in vinyl. The main wing has been expanded which makes accurate measurement of the original size somewhat problematic. The back wing has been rebuilt at least twice in the last 170 years. The length of the wing is off by about 12". If my circles are 4" too small, or I've missed the extra thickness of a plumbing wall, the geometry fits.   
Or as I found out, I was using the wrong geometry!





Unlike the 1830's house which used one geometry for the plan, another for the elevation, this house uses the same pattern for both. Here is the side elevation with dot and dash lines to indicate 1st and 2nd floors.

 The red circles are the two circle configuration that was used for the floor plan. Here the intersection of the circles marks the height of the front and back walls, the beginning of the roof. The center of the circle marks the placement of the 2nd floor; the top of the circle, the collar ties for the roof.


I am not sure how the roof pitch and the ridge were determined. I have rejected several possibilities as being too complex for this simple house. This one may the answer:
 The top of the wall , which is also the centerline of the vesica piscis, is obviously the beginning of the roof , therefore, one point - see 'a'. If the square of the house is  divided in half and a diagonal drawn -  see green square, rectangle and diagonal -  a second point is determined by the intersection of the diagonal and the circle  - 'b' in green. The line through 'a' and 'b' is the roof slope, about a '9/12 pitch' in modern terms.

Does the geometry determine the design or the structure? In this case I think both.

Why doesn't this geometry show up in the pattern books? Was it just something that was common knowledge? Or was it passed from master to apprentice as privileged knowledge?