Thursday, December 4, 2014

Geometry of a Hartford, NY barn, c.1790

A Hartford, New York, barn was carefully dismantled for reuse this fall by Green Mountain Timber Framers.
I was there and later analysed the timber frame. Dan McKeen, owner of Green Mountain TF asked me to write a guest blog on the geometry of  the barn for his website.
I wrote about the basic layout, how it was developed from just one dimension, the width of the barn.

To read that post use this link: 

Here are two more diagrams that continue the exploration of the geometry.

The section is the measured drawing of the end of the barn seen above.

I found that the mortises in all the posts (the mortises hold the tendons of the rails) were all cut in the same pattern. 

The arc the framer used to locate the intermediate lefthand post also located the upper horizontal rail.

The diagonal intersecting the arc of the length of the square can be easily rotated so that it marks a horizontal line instead of a vertical one.
The framer then turned his compass and swung an arc from lower right to upper left. The intersection of the diagonal and arc became the location for the lower rail. (See the green circles!)

All the rails for the barn are located at the same heights on the posts. This means the framer could set up one jig to cut all the mortises - simplifying his job, getting the work done faster. And  a bit of mass production, ie: a precursor to square rule framing. 

There is also the roof layout.  I have not yet drawn the diagrams. 

Be awestruck with me! Full of wonder!  

Monday, November 3, 2014

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.

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.

Sunday, October 26, 2014

Timber frame from a carriage house

Green Mountain Timber Frames of Middletown Springs, Vermont,
erected this 17 ft. by 26 ft. frame in their workshop.
Originally a carriage house, it had last been used as a garage and was for sale.

I asked Dan McKeen if I could visit and watch his crew work. I learn a lot from watching.
Dan welcome me, give me a tour, let me watch, and was happy to have me  measure this frame.
I measured both sides but only made notes on the rest.The ridge is 5 sided, the rafters are 36"o.c. The pitch? I don't know.The front and rear sides were not assembled. There was no sill.

I noted that the length and height of each side was almost equal, about 2" off; that the braces were set at 45* and that the cross beams though different sizes were set at the same height. I wondered if it had been laid out from the foundation or from the sill, as I have seen both.

The date of construction was c.1840. Based on the date I tried a 3/4/5 triangle layout. Even when I allowed for the sill it was not successful. Nothing lined up nor gave the framer any information.

The frame itself said, 'Square'. It also said 'Simple', not a tour d'force. I tried squares.

The square which begins on the outside of the bent and ends on the center post works. It and its star divide the square into thirds - red dashed lines -, locate the braces  and the top of the cross beam - red circles.

After the square was laid out snapped lines on a framing floor would have laid out the star.  6 of the lines of the star - noted here in solid red lines - mark the important intersections. They divide the upper half of the square into thirds and cross at the top of the cross beam.

The frame sold before I could return to check the pitch, the front and the back.  I had measured the mortises in the end posts which were for the front and rear walls. They are drawn on the right post.

The same square determines their locations. Here I have extended a green dashed line from the intersections of the star (green circles) to the placement of the mortises.

The 5 sided ridge and the use of the square lead me to think the carriage shed was built before 1820 or that the framer was using old-fashioned methods and did not own a 'new fangled' carpenter square.

 My earlier posts show how to layout a square - -
and how to divide the square into thirds and the ensuing star -

Tuesday, October 7, 2014

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.

Monday, September 8, 2014

A Circle to a Square, 1830's cottage north of Boston, Part 3

 When I was preparing for my presentation at the Timber Framers Guild annual conference in August I assumed people knew the basic geometry - how to begin with a dot and a line and construct a shape - for example, a square - that was useful in construction. I found that I was wrong.

Here are diagrams showing how to lay out a square, beginning with a line, a dot and then: another dot.

The two dots define a distance, a radius.  So a circle is drawn. Now there are 3 dots on the line, all related to each other.

 Draw 2 more circles using the dots on the circumference of the circle as the centers. All the circles are the same size.

Then take distance, whatever length you like - but it should fit on your page! Swing 2 arcs using that length and the centers of your two outer circles, one above and one below the first circle. The arcs cross.
Draw a line between the points where they cross. This line is perpendicular to your first line. and it crosses the first circle at 2 points.

Add 2 more circles, above and below the first row of 3, using the   points you just found as the centers. Now you have 5 circles all the same size, placed in relationship to each other. And you have 4 petals made by the arcs of the circles. Join the outside points of the petals, also where the circles cross. This is a square - drawn here in red.

Of course, your length (radius) needs to be constant...You need to be draft carefully. This is precision work.

This diagram applies to the 1830 house in Reading MA, which I have written about earlier.
While preparing for the Guild presentation, I realized how more complex and also how much simpler the diagram could be.
Here is the 'square construction' laid over the elevation, the base of the square on the first floor. The center line defines the ceiling of the fisrt floor, the placement of the second floor joist. The top of the square defines the ceiling of the 2nd floor, the placement of the ceiling joists which are also collar ties.
I superimposed a square diamond on the diagram - in green - because the intersections of the diamond and the square's petals marked the windows' width.

Then, I tried turning the square 45*. The upper sides of the new square is the pitch and location of the roof rafters.   The intersection of the 2 squares is the top plate of the wall, the placement for the roof rafters. The petals are the width of the windows.

All this became visible, obvious, while  I was working intently on preparing a coherent talk. I learned a lot. Now I am beginning to re-post and update my earlier diagrams.

Here is the farm house that inspired my original research. The first floor parlors had  such presence and grace I can feel them today.
The left hand wing is a later addition.

for Part 1 see:
for Part 2 see:

Thursday, July 31, 2014

For your viewing pleasure: Donald Duck Discovers Geometry!

I am busy preparing for the Timber Framers Guild Annual Conference next week: posters for the bus tour people  to consider at the Sandown Meeting House, a power point presentation for the session on the following day.

I have learned so much since I began blogging about geometry and construction that many of my diagrams have needed to be completely rethought and redrawn. I expect to learn more from the other speakers. I will take notes.

Meanwhile my cousin who is a Coastal Engineer sent me Donald in Mathmagic Land:

The cartoon is long, but fun and full of geometry. The Greeks play jazz and explore the Golden Section. Donald tries to play chess with Lewis Carroll's Red Queen. But it also features lots of those pentagons that Jay Cougar White Cloud has been telling me I need to learn about! I think he's right, I just haven't uncovered any yet.

Tuesday, July 8, 2014

Timber Framers Guild Conference, Manchester, NH, Aug 7-10, 2014

I will be speaking at the TFG  Conference, Friday afternoon, Aug. 8, on geometry in the  States, 1683  through 1850. I will begin with the First Period houses in Topsfield, MA, and end with the 1850's dismantled railroad shed. I will  use the diagrams and photographs from this bog.

The day before, Aug. 7th, the TFG bus tour will stop at the Sandown Meeting House. I will be there to explain the geometry.  I will have the diagrams. I will also encourage people to stand in the pulpit and sense the space. The attic will be open. Will Truax will be up there in the trusses with windows and a roof hatch open. A permanent steep stair leads up to the trusses and a board walk is in place across to a now missing chimney, so it is reasonably safe. No one should go through the 250 yr. old plaster ceiling!
The Sandown historians will be there as will First Period Colonial, Bob Pothier, the carpenter for the last set of repairs.

The recent workshop at Trillium Dell with Laurie Smith brought up lots of ideas and questions which I do not expect to answer before the talk.
Some of the issues are simple:What do we call certain recurring forms and geometries?  We need a common language.

Some more complex:
Is there any indication that the houses I am looking at  begin with circles which laid out that first square?
Were the master carpenters and owners whose houses I have laid out trained in the guilds in England? Is there a record that they studied geometry?
Am I seeing different geometries because of different framing systems? For example: the geometry noting cut lines, not center lines, for interlocked log walls in Virginia - or because the people came from different parts of England with different training? What about the Dutch? the Germans? the French and Swedes?

Am I seeing the length of a rod: 16 feet 6 inches, and not noticing? Laurie Smith finds it to be a common, basic dimension in England and Wales.
Have I missed it because I haven't been thinking about it? If the framers here were not apprenticed to someone trained in the ways of the old country would they have adopted another length?

The Timber Framers have suggested that people who might like to come only to my talk need not pay the fee for the whole day - which includes food as well as all the other sessions - but could simply make a donation.

Wednesday, July 2, 2014

Geometric Design Intensive, June 2014

I helped built this.

Laurie Smith came to Trillium Dell Timberworks in Knoxville, Illinois, in the end of June  for a 9 day  Geometric Design Intensive.
Here is how it was described in the Timber Framers' Weekly Guild Notes for May 30th:

"Taught by Laurie Smith and Rick Collins. Follow a geometrically designed octagonal hardwood frame from start (a pair of dividers) to finish (a gift to the Appleton Volunteer Fire Department and the community of Knoxville). Expand your knowledge of medieval frame design, compound roofs, and hand tools. Learn about an ancient, viable building language. It's two events in one--the entire nine-day intensive, and the weekend rendezvous-style raising. Hosted by Trillium Dell Timberworks."

I was there.
Was it intense? Did I expand my knowledge? a lot?  Do I speak a new language better than I did before?
Yes, of course. (Minor understatement!) Much more than I had imagined when I decided to attend. I had a wonderful time!

We used geometry. We used numbers only incidentally as a comparison. We put in 12 hrs. most days, about 16 the final day, the Summer Solstice. We added the evergreen swag to the pinnacle of the  frame as the sun went down.
Laurie Smith  lectured  and taught geometry 5 mornings and was present in the 'Beamery' in the afternoons, discussing, advising, teaching. All of us had come specifically to work with him.

top picture: the drawings we started with
middle picture: Laurie Smith working out a problem with Patrick while John carves the king post
bottom picture: The Beamery where we worked, left; Trillium Dell's office, right. Our finished timbers ready for assembly in the foreground.

These pictures:

the pavilion from above
the guys in the rafters
us all on the frame for the 'portrait'

these photographs, and the first one, taken by Kendell Anquist.
The others by me.

When the town determines the location  the pavilion will be located where it can be used, in town, not here in the field where we assembled it. There will be a roof, a floor, and entry porch and some porous side walls.


Monday, June 2, 2014

Cabin, Tuckahoe Plantation Goochland County, Virginia

I came to Tuckahoe Plantation to look at the cabins. Drawings for them are in the HABS archives. They are the size and layout of the houses whose floor plans Henry Glassie recorded and whose geometry I have written about.
 Dr. Glassie's book,  Folk Housing in Middle Virginia, includes photographs of poorly maintained houses, most beyond repair.

I wanted to see what they might have looked like when they were built and how tall they were. Yes, the HABS elevations show how tall they are. However, for me reading a drawing is a beginning, one  part of
understanding. I need to see the building.

It is very simple. in appearance and geometry, and not only because of its shape and lack of anything beyond the essentials.

It is just squares: 2 across the front, 2/3 of a square for the sides, 2 for the floor plan.

The chimneys are centered on the square.

The doors and windows are centered on the plan and on the center of the square for the front elevation.

The  front and side elevations are two thirds of the square.

 The roof pitch is 12/12 - the diagonal of the square - and begins at the 2/3 line of the lower square.

This way of dividing a square and using the diagonals to determine dimensions is called the Rule of Thirds.
To learn how it is drawn please see my blog post:

The book, The Chesapeake House, reports that the plastered interior walls of the house are original as is the door between the two rooms. This 'cabin' then perhaps was built for the use of an overseer, or craftsman.

As you can see from my photograph, the little house sits on a green lawn with a dirt path, surrounded by towering leafy green trees. Clean white paint, variegated wood shakes on the roof, a neat brick chimney - all in excellent condition - may give too cheerful an interpretation of conditions in 1750, but I am glad it is being preserved.
Studying the adjoining kitchen, office and storehouses, walking down the path, then around behind the cabin across the lawn to the main house, gave me enough understanding so that as I traveled back roads to Madison's Montpelier I easily spotted similar cabins, now out-buildings on farms or wings to later homes. At Montpelier, where timber framed and log cabins are being rebuilt, I was also able to better read what was there. My visit to Tuckahoe was excellent.

The Chesapeake House, architectural investigation by Colonial Williamsburg, edited by Cary Carson and Carl Lounsbury, The colonial Williamsburg Foundation and the UNC Press, Chapel Hill, 2013.

My previous post about the main house at Tuckahoe Plantation is here: