Thursday, February 15, 2018

The geometry of a 1870's barn

 This Vermont barn was built in the 1870's . It has been used for storage for the last 20 years.

I prepared a report on its history and structure for its owners so they could consider repair and reconstruction with some real knowledge - not just good memories and/or worry about costs.

The barn was well built by a farmer who knew his land and a framer skilled at his trade.
The frame is regular, much of it still sturdy. Its mortises,  tenons, and pegs are still secure.

Its bents use dropped girts and posts to purlins which support  common rafters, a framing system regularly used in the Hudson Valley watershed, not often seen in this area of Vermont.

While I was not asked about the barn's geometry, as I laid out the plan and the frame I could see the geometry clearly - not complex, quite simple, repetitive, and straightforward.

Here is the 3rd bent and the lower level floor plan.
The bent is one of the 4 timber frames across the barn that are then fastened together with plates and girts. Walls and flooring have been left out.
The plan is mainly the post locations. I have not included the exterior wall girts.  The braces which are visible in the photograph to the right are barely noted.

The floor plan could easily have been laid out using circle geometry.

I have added Laurie Smith's diagram for drawing a square beginning with a circle. It is a very clear description.

For his websites see:


Here is my drawing of the floor plan with its posts laid out using circles. The first  (top) 2 bays are of equal depth and width.  The dashed green line shows the layout determined by the circles.

The lower bay (between bent 3 and 4) is not as deep. Perhaps the land dropped off too steeply, or the lumber available was not as long. The dotted red line in the lower right rectangle shows how the crossing of the arcs of the square determined the depth of the bay. 

The base of bent 3 is vague on purpose. I don't really know the depth of many of the lower level posts. The land slopes west to east. The floor on the east end has been built up over the years with layers of discarded boards.  The right end has been reconfigured for cows; the left end has a false ceiling.
The main  barn level of the bents is divided into thirds. The  posts are the height of a third of the bay's width - the space they outline is a square. I've drawn it in red. The dropped girts are set at the point where the arcs of the square cross. Also drawn in red.
This is similar to how the lower level east bay's depth was determined.
The posts that support the purlins ( the roof beams ) are centered on the squares below. The height of the ridge is also determined by where the arcs of the loft square cross.

Lastly the location of the lower girt which becomes the plate for the wing is determined by the Rule of Thirds.

Such basic practical geometry tools! They are  those described by Serlio, Palladio, and Asher Benjamin - circles, arcs, lines - applied in very simple ways with impressive results.

Well thought out, straightforward without fancy flourish, the space and the frame speak to me. But I am simply the one who documented this, sharing the power, the grace, that I found.

The barn, after 150 years, is no longer essential. It is very possible that it may not survive until a new purpose discovers it.


Wednesday, February 7, 2018

How Practical Geometry is practical

This is a sequel to my previous post:

Do I think the carpenter who laid out the small simple cabin at Tuckahoe actually drew the arcs on the  ground? or on the floor  - once he had squared the foundation and set the sills?

No, I think he knew the geometry. Someone had already taught him what I drew.
I think he swung the arcs but marked only the foot or so where he  knew the crossings would be. He knew that he wanted to locate the center of each wall, and  - by basic geometric rules - he needed 2 points to draw a line perpendicular or parallel to the wall in question.

Here is a lithograph of Pere Soubise, patron saint of the Campagnons, French carpenters who have finished their apprenticeships and begin traveling from town to town, from job to job to learn new skills. (In English an Apprentice becomes a Journeyman at this stage of his training because he 'journeys'. When he has gained enough experience he is then eligible to become a Master.)

Pere Soubin is probably mythical. But the date of his portrait is known: 1863. Click on the print to read the attribution. 
In 1863 a portrait of an important man included the tool of his trade: Pere Soubise holds a compass.

I have enlarged that part of the image. He holds his hand in  a way that he would if he were using the compass to measure a distance based on the drawing held in his other arm. Or as he would to  mark joist pocket locations on a beam, stepping off from one to the next.

Today a carpenter marks stud spacing with a tape measure that has multiples of 16" highlighted in red. The carpenter doesn't count 16" each time, he uses the tape's marking as a shorthand.
Similarly the framer in 1860 did not need to swing the arc from one point to the next, he used the compass to keep his spacing consistent.

As I was writing this a timber framer who did a lot of repair of old barns mentioned that he often found common rafters laid out at 39.5". 
I laughed and told him he had given me a challenge: Why 39.5"?

Here's the arithmetic: Many of the barns were about 40 ft long. 40 ft = 480" . 12 x 39.5 " =  474", 6" shorter than the barn's length. 3" each end for the end rafters.
However, that begins with the solution. It doesn't address how the framer found his answer.

Here's the  geometry.
The framer knows he will use  3" wide rafters on each end of his 40 ft long  barn, so he will have 474" in between for his rafters.
He wants to figure out what distance will work so he can tell the men working with him where to set the rafters and cut the pockets in the plate. The plate is sitting right there in his framing yard -  which might be the floor of the barn he is building.

He could make a scale drawing on a board and scale up to the plate using his compass, like this:

Or he could stretch his line the length of the plate between his end rafters. Then fold the line in half and and then half again. Now he had the length of the plate divided into 4 equal Parts. ( #1 , # 2)
 He thinks 12 rafters should do it. That means 3 rafters for each Part. But what's the spacing? On the framing floor he draws out a square using the Part as the side.  The handy Rule of Thirds quickly divides the square into 3 equal rectangles and the Part into 3 equal lengths. (#3)
4 parts x 3 divisions = 12 rafters. Good to go.
He doesn't care that the length of each is 39.5". He cares that he has divided his plate evenly. (#4)

Note that the framer does not add, subtract, multiply or divide. He could show this system to someone who spoke a different language. Neither would need know how to read words or compute. They would need to be able to think logically and reason visually.  Geometry is a language in itself.

By the 1860's  - the time of the Pere Soubise portrait - both France and England had standardized dimensions (meters in France, feet and yards in England). Tape measures existed  but were not widely used. Wooden folding rules were popular after the Civil War,  but carpenters still understood and used compasses for layout and design. 

I have met young timber framers who journey as Compagnons.
 For more information about the French Compagonnage historically and today:
And note the compass leaning against a beam in the first engraving.

Tuesday, November 21, 2017

The Tuckahoe Cabin Geometry

 This is the double slave cabin at Tuckahoe Plantation, Thomas Jefferson's childhood home in Virginia.
I have written about it before:

The simplicity of the cabin and its HABS drawing make it an easy building to use when I teach hands-on Practical Geometry.

The beautiful hand drawn lines and details of HABS drawings fascinate students. And they get a little history.
Here the elaborate paneled front door for the plantation house, its ceiling pattern, and columns are shown with the little, uncomplicated cabin.
Craft, wealth, slavery c, 1750,  are visible side by side.

Remember that you can click the drawings to enlarge them.

The cabin illustrates the Rule of Thirds.
Students unused to geometry can grasp the basics quickly as they discover the design simplicity of the floor plan.They explore the geometry of the elevations with curiosity, not in trepidation.

For a tutorial on the Rule of Thirds:

BUT -  This is academic.
How did a carpenter actually use this knowledge?

I wasn't there. So, I am guessing? No.

I've read the written documents, 'read' the drawings that have no words - from that period and the more recent era of HABS. I've measured and documented these buildings, participated in repairing and framing them as well as their deconstruction.
I make connections to the old ways of laying out a frame from the way we lay out today using the same tools our ancestors had - a line, a square, a plumb bob, a pencil - and  a compass.

Here is a construction scenario for this cabin.

The carpenter plans to build a 2 room cabin with a loft, 2 doors, 2 windows, back to back fireplaces on this site.
The size is standard, each room about 16' x 16'. He either builds right here, or he uses a framing floor. In either case it is a flat, level surface. His geometry will establish his points and keep his frame square.
 He measures off 16' with twine, using his own handmade rule. He then stretches out his twine another 16-20 ft, pulls it taut.
He now has a straight Line.
Maybe he has chalk and snaps it, making a line.  Maybe he pegs it.
Modern carpenters snap and set lines regularly. We still call them 'lines'.

1 - On his Line he marks his first point (A).

2 - He chooses a radius and draws 2 arcs, one with its center at (B), one with its center at (C).  He now has 2 points where his arcs cross and can draw a line perpendicular to his Line.

3 - He chooses his dimension -  here, 16 ft -  puts his compass - perhaps a string with a knot at 16' -  at (A) and draws a semi-circle (D-E).
Now he has a new point (F). His cabin is now 32' long; its width is 16' (A-F)

4 - Using (F) as his center he draws another semi-circle.

5 - Then he draws 2 quarter circles using (D) and (E) as his centers. Where the arcs cross (G) and (H) are the upper corners of his cabin.

6 - He swings the other arcs, and now has 4 internal points in each room of the cabin. He marks those points.

7 - Just to be sure, he trues up the space by checking that his diagonals are equal (G-A, D-F etc.).

8 - The interior points give him the centers for the doors, windows, and fireplaces. The plan of the cabin is done.

The end elevation, or  the 3 bents of the frame:
 9 - He sets up the 16' square with its arcs.

10 - The interior points give him the location for the 2nd floor joists.

11 - The points also give him the center of his elevation. He can draw his Lines and use the Rule of Thirds to find the upper third of his square (J-K). 

12 - (J) and (K) mark the eaves for the roof. He extends the sides of the square, draws his arcs to find the upper corners ( L) and (M), adds his diagonals  (J-M) and (L-K). Ahh - there's the roof!

 The window in the eaves is placed and sized:

A carpenter before the Industrial Revolution would not need my description. He would have learned the geometry as an apprentice. If he needed a reminder he would practice a bit with his compass. He probably didn't have a drawing for such a simple cabin.

However, books with instructions to builders (not architects) did exist. Here are 2 examples.

Batty Langley in The Builder's Director, London, 1751, draws moldings "Proportioned by Minutes and by Equal Parts".  He writes that his little book is to be available to "Workmen" and "any common Laborer."

These window and door 'Weatherings' are all composed of squares and arcs of circles. Langely lays out the parts; the Workman can read the rest.

 Asher Benjamin in The Country Builder's Assistant, Greenfield, MA, 1797, says his book "will be particularly useful to Country Workmen in general".
 He assumes the Workman knows geometry.
Plate XXIX  says only
 "C, is a roof; divide the width of the building into 4 parts, one of which will be the perpendicular height. Divide Fig. D, into 7 parts,give 2 to the perpendicular height.
Fig. E, is intended for a roof to a Meetinghouse; divide the width of the building into 9 parts; give 2 to the perpendicular height; the ends of the Beams, a, a, are to be supported by columns."

My first post on Tuckahoe Plantation is here:

Wednesday, August 16, 2017

Laurie Smith, researcher of early building design in England, par excellence

Laurie Smith knows the geometric design systems used in medieval England.
He writes and teaches about geometry.

Here - as a quick introduction to his websites - is the last page of 4 of his diagram showing how to draw a square using a straight edge and a compass.
It is a beautiful drawing, easy to read on his website, hard to reproduce here.
His explanation at the bottom is also beautifully clear.

The websites are here:

The masonic guilds of medieval Europe passed down the methods of construction and the geometry used with diagrams and hands-on explanation. They did not use paper - it was barely available - and thus left notations on the buildings as decorative carvings and casual sketches, information we often don't recognize as the language of construction.
Laurie can read and translate the notes. He is one of the people in Europe researching, documenting, and teaching about medieval framing.
I suggest all those who dismiss the idea of Practical Geometry read his websites.
Those who wish to learn how to use Practical Geometry can be inspired by the diagrams as they follow his instructions.

I have attended his lectures. and was fortunate to be able to take a workshop with him at Trillium Dell Timber Frames in Knoxville, Illinois.

We built a timber frame pavilion  from scratch using geometry.

Here is Laurie consulting - in the blue shirt in the middle - as we work around him. Laurie drew, taught and advised.

I wrote about this here:

The photograph shows Laurie's diagrams for the frame posted on the wall as one of us begins the fashioning of joints.

The frame, composed of overlapping squares  was also laid out on the floor with chalk and a compass.

The whole process is described with diagrams and pictures on Laurie's website.*

A view of the mortise I helped cut as part of a 2 woman team. It fit into the frame on the first try.

We finished erecting the frame one evening at dusk.
Of course we all climbed into it to sit for a formal portrait.

* To see the whole project and the finished pavilion look for  "Appleton Octagon Pavilion, Illinois, USA" in Laurie Smith's  Historic Building Geometry website listed above.

PTN Workshops in Detroit, Sept 8-10

IPTW 2017 - The Preservation Trades Network - will be in Detroit at the Detroit Yacht Club Sept, 8-10.
I will be teaching 2 sessions on how to draw squares with a compass, how to layout frames using geometry as we did 200 yrs ago.
And some history (Vitruvius, Palladio, Serlio, Gibbs, even Isaiah in the Bible! ) on the side. 

 Of course the use of Practical Geometry didn't stop 200 years ago. The knowledge came with the settlers to the Mid-west. Houses and barns, public structures were laid out and framed using the honored patterns.

I will include examples of mid - 19th century framing and design as well as earlier 18th c. antecedents.

You can come.

Thursday, July 27, 2017

East Hoosuck Quaker Meeting House, 1786

Update: 10/25/2017
To check the reliability of the HABS drawings  I measured the Meeting House this month. Yes, the drawings used here are accurate.

This Meeting House for the East Hoosuck Society of Friends (Quakers), built in 1786, is now a museum in Adams, Massachusetts. It sits high on  a hill in its cemetery, looking east over the Hoosic River to the Berkshire mountains. This is its west side.

As I was creating a handout for the guides about the scribe rule markings visible on the frame, I wondered what the geometry might be. Quaker communities existed nearby in New York, Pennsylvania, and New Jersey. We knew Quakers migrated up the Hudson River watershed from Rhode Island and Nantucket after the  Revolution. Would I see similarities to other frames I had measured?
I did see similar ways of laying out a frame. However, without more research I cannot say these layouts were particular to Quakers.

The Friends Meeting would have told the master carpenter how large the building should be,  that windows were needed for light and ventilation, fireplaces for warmth. These Friends knew that the door should face south,  that the wind here came around the mountain from the northwest, that a chimney is best supported by bringing it through the roof at its peak.

The framer would have began with the floor plan; so I did too.  He made the meeting house 28' wide on the west end; the posts set in the corners.

 He laid out a square from the inside of the posts and marked locations for  posts on the corners.*

Why would he have begun his layout on the inside edge of the posts?

Perhaps because the trench in which to place the footings for the posts would be outside the line. The ground under the frame would not need to be excavated.

The plan could also be trued from the interior edge of the posts much more easily than from the exterior when the posts were in place: the diagonals would be made equal across the rectangle. Contractors today still 'true' foundations by pulling lines.

His center line located the middle posts on the north and south walls as well as the 8 sided posts that are located between the pews.

Using the Rule of Thirds, he laid out the eastern end. The location of the eastern wall posts is 1/3 the width of the main square beyond the square.
  I have marked the 1/3 of the square and the extension with arrows in red.

The center line running east west determined the post on the east wall.

His post locations set, the framer laid out the 4 bents. This is the eastern exterior bent.

It uses crossed squares with the side of the square the height of the wall from floor to plate.
Even the braces follow the geometry.

The height of ridge of the roof, and thus the pitch  of the roof, was set by the intersection of the arcs of the height of the wall.

This way of finding a ridge was also used in the Hartford, NY, barn I measured in  2014.

The window placement was determined by the same crossed squares geometry.
The 4 sides of the windows are determined by the geometry.
I have drawn the lower window only. The upper window requires more lines which are hard to read at this scale.

The south facade of the meeting house is 2 squares wide.

Quakers worshiped together, men and women, and children.

Their  Meetings for Business were held separately: women on the left, men on the right, with a wall between them which could be raised or lowered as needed. Thus the two doors which sit neatly within one quarter of the square.

The window sizes on the south side do not fit the geometry. They were probably enlarged  when the men's stair was added.
Both scribe and square rule framing details as well as joist pockets without joists indicate renovations.

For me it's fun to see how the first floor windows are located at the bottom of the stairs, where light would be needed for safety.

*The hybrid barns  in New Jersey which I looked at earlier were also laid out based on dimensions measured between the posts:

For more information about the Meeting House and the Quaker community in Adams please see:

Tuesday, June 27, 2017

Practical Geometry for Dutch Hybrid Barns, Part 2

This is the second part of my look at the geometry of the layouts of New York and New Jersey barns built at a time of intermingling of old world building traditions - post 1800.

Huber included 4 hybrid barn floor plans in his introduction to the second edition of John Fitchen's
The New World Dutch Barn.
This is Illus. 7, p. xxxi

As before I redrew the plan based on the given dimensions.

I found again that the framer began his layout after he had decided the size: here about 25 ft x 50 ft. Beginning from the left side, with the corner posts already in mind, he laid out 2 squares.
If I layout the squares from the right side the
geometry does not quite work.
The center of each square is just about the same distance to the right of a beam.

 If the framer laid out the squares using the rule explained by Asher Benjamin, Owen Biddle, and Peter Nicholson * he would have swung an arc the width of his proposed barn from the corner of his plan. When he swung an arc from the other corner the 2 arcs crossed. And there - where I have added a circle - he located his beam.
He would have used a cord to mark the distance on each long wall for the location of the posts.

That beam is the center for a circle that determines the locations of the other 2 beams - marked by 2 more circles.
That  first circle is also the center of a square. The framer could have laid out a square, or simply taken half the length of his end wall (already measured by the layout of the squares) and laid that out on either side of his middle posts and beam.

The 4th layout is quite different from the others;
Here are Huber's drawing and notes for Illus. 4, p. xxviii.

and my redrawing, using his dimensions.

I turned it so that the side where the framer began his layout is to the left. Knowing what he wanted to build  he could use the barn location as his framing floor.

I think he laid out a square, 38 ft on each side and placed his corner posts outside the lines.

He had several choices for placing his intermediate posts and beams using geometry.

 Here is one:  He located the center of the wall. Using half the length of the square's side he drew an arc on each end. Using the center of his square he drew a circle.
Where the arcs intersected he drew a line and located his posts on the exterior walls.

Using the distance from the exterior square of the barn to the intermediate posts as his radius he drew 2 more half circles. where the radii cross he laid put his bays and set the interior posts at the intersections.

Here are other options:

The framer could have laid out the barn with 4 squares. As each was laid out the arcs would have crossed, just as they did in the barn shown in Illus. 7.
He could also have used the circle to find the length and width of his barn. Both of these systems seem to be more complicated than the order I described.

These diagrams may become teaching tools when I give a workshop at the International Preservation Trades Network Workshops in Detroit this September.

 These ways of designing were carried with those who settled the Midwest. 2 squares side by side (as used in Illus. 7 above) is the beginning plan for the I House, so named because the shape is so common in Indiana, Illinois and Iowa.

How did these hybrid barns looked? How were they used? Unable to connect the geometry of the plan to that of the intent, the structure, the bents, and dimensions,  I might have missed critical information.

These two barns' geometries especially interest me because they use squares in a way quite similar to the barn in Hartford in upstate NY which I documented. The link to it is: 

The posts about Practical Geometry and Asher Benjamin, Owen Biddle, etc. can be read at: