C. 1825 workman's cottage, north of Boston

This small house, built about 1825, was one of several built on a country road across from a factory.
Today a park has replaced the factory. The house is in-town. Over the years wings have been added on 3 sides. I have cropped the photograph in order to focus on the original  house.

The post and beam frame includes recycled beams. 2 have beaded edges - probably recycled from the best room of a pre-1760 house.









Here is its section - a slice through the house showing its basic layout.









Here is the 3-4-5 triangle used to determine the size and location of the walls, the pitch (angle) of the roof                       










Here is the 3-4-5 triangle used to locate the 2nd floor joists and the ceiling joists.
The dot and dash triangle determines the height of the collar ties (ceiling joists). Its
vertical leg crosses the first triangle at the location of the second floor. The second floor window locations are also set by this line.
All this also makes me think that the house frame was laid out in the traditional way, on a flat space called a framing yard and then dismantled and re-erected on site. Contractors lay out rafters in this same way today as they frame a roof.  They use the floor of the house just below the roof as their framing yard.








Here is the floor plan. I've noted the chimneys. The lathe and plaster box around the lower one includes modern plumbing, heating and electrical systems.









And here is how the 3-4-5 triangle was used to layout the floor plan. Just as the exterior sills and walls were placed inside the box determined  by the triangle, so the beams on either side of the stair were placed inside the box. The walls, set above the beams, are on the inside edge.

The chimney locations are set by the triangle, but the windows on the opposite wall are not. They are centered on the rooms.




The windows on the side walls are located by a square -  in green - based on the shortest leg of the triangle.

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

Arnold House, Westfield, Massachusetts - Part 2

Here is the Arnold House around 1933.

And below is the measured drawing of the front done at the same time for the Historic American Building survey, a project of the WPA. The drawings and picture are available at the HABS website.


In the upper left corner of the drawing I have added the 3-4-5 triangle with its 90*, right angle. To see why I think this house was designed using that ratio see the previous post, Arnold House, Part 1. Click on the illustrations to enlarge.

On the left side I have drawn in red dashed lines the 3-4-5 triangle using the first floor as the base and the ceiling of the second floor as the top. A house-wright would have used that line to determine his top plate. See (A).

The center of the  resultant rectangle is marked by the red 'x'. The 'x' is the location of the second floor beam.
The right hand edge of the rectangle is the edge for the door, telling the framer where to locate the rough opening. The windows and doors do not appear to be determined by the elevation, but by the plan. See my earlier post on the Arnold House - Part 1.

As drawn on the right side - see (B) a red dash and dot line - the space on either side of the door is a square. But the windows are not symmetrical within the box. I tried using the Golden Section. It doesn't fit. Circle geometry - here a circle based on the square - almost fits: several inches too large.

Here I used the 'face' of the house clapboard from foundation to eaves, as I think the concern of the master carpenter would have shifted from framing to presentation - how the house appears to the community.

Two squares with the arcs from their circles would have fit across the front of the house, meeting at the middle of the front door IF the house had been 9" longer - 40 ft, not 39'-3", a true 3-4-5 rectangle. Was the foundation not true? The house-wright inexperienced or lax? If the wood was green would it have shrunk 9"? Or?

For reference I have added a diagram of a square with the circle whose radius is half the square's diagonal.


This house is no longer there. I would very much like to be able to see it,walk through the rooms, sense the proportions. I want to know if it feels differently because the ratio is mathematic, not geometric.


The 3-4-5 triangle is not the Root-Two Rectangle. The diagram here shows the difference geometrically : the triangle is marked off in red, the ratio (a square and the length of it's diagonal) in black.

 In algebraic language : (a x a) + (b x b) = (c x c)
                            (3 x 3) + (4 x 4) = (5 x 5)  or   9 + 16 = 25

For the Root-Two Rectangle to equal the triangle, if the side were 3 then  the diagonal of the square would have to equal 4. It doesn't.
                    (3 x 3) + (3 x 3) = 18   the square root of 18 is about 4.25


I think the evidence is too strong that the house-wright was using the  3-4-5 triangle to put together a traditional looking house. The fact that circle geometry almost works is just that - it is almost the same. But it isn't.

updated 12/31/15

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.

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?

1830's cottage north of Boston, Part 2

This is an update to the post about the floor plan of this house written in August, 2010.

 Last week I realized that the builder of this cottage would probably have used the same kind of geometry for the elevations that he used for  the floor plan.

This is an obvious observation. Really! Makes me roll my eyes to know that it only took me 3 years to figure this out!
It is clear from the photograph that the house has been expanded over the years. The siding was 'updated' about 40 years ago. My diagrams refer only to the part of the house under the gable, to the right.




So here are the diagrams and drawings - click to enlarge:

The floor plan is shown with the complete daisy wheel for reference. The main rectangle of the house plan is determined by where 4 petals of the daisy touch the circle; the wing's size determined by the arcs of 2 of the outer circles. This is a straight forward use of circle geometry. The elevations use a slightly different pattern.





The side elevation measure by me and drawn to scale:

.
The circle geometry I think the builder used for the elevations:
The upper diagram shows 2 circles intersecting - the outside of each touches the center of the other. The place where the circles overlap is called a vesica piscis ('fish bladder' in Latin). The red line bisects the vesica piscis.
The lower diagram shows one circle with 4 circles intersecting it, creating 4 intersecting vesicae piscis. The red lines are only partially shown for clarity.
The diagrams show how the shape and dimensions of the elevation were determined.

On the elevation the circle is the same size as that used for the floor plan. Its radius is the length of the wall. It surrounds the house. Its center is the fat red line between the second floor windows. The upper circle is drawn in full, but only part of the lower circle is shown. The lines through the vesicae piscis determine the peak of the roof, the center of the first floor windows.
I have drawn only part of one of the circles on the sides, the left one. The vesica piscis there follows  the wall of the house.
 Note that the center of the main circle not only positions the 2nd floor windows but also marks the square of the wall, the top of which is where the builder will set his rafters.The square is outlined in green. The circle which determined the floor plan, its dimensions, is also used to determine dimensions of the elevations.


for part 1 see: http://www.jgrarchitect.com/2010/08/regulating-lines-1830s-cottage.html
for Part 3 see: http://www.jgrarchitect.com/2014/09/how-to-construct-square.html