Saturday, December 29, 2018

Framing a Barn with Practical Geometry in 1791

 I wrote this post for Green Mountain Timber Framers' website blog in Dec. 2014.
As I often refer to it and use the diagrams when I lecture and teach, I copied it here for easy accessibility - with a few edits for clarity.

I invited myself to a Green Mountain Timber Frames barn dismantling in the fall of 2014. I wanted to watch it come down. I also wanted to investigate its geometry.

Here's what I saw.

The three barns sat beside the road  on the uphill slope of a valley, connected in an L shape.
None of them faced the road on their west and windy side. Instead they faced south and east, creating a protected barnyard, a sun pocket.

In the middle, protected from storms and wind, was the corn crib. Other farm buildings repeated the pattern, facing south, no doors on the west.

The main barn also had a door to the north, directly across from the one facing south. It fronted the farm road and looked at the house across the way. Two doors across from each other allowed for easy moving of machinery, ventilation and threshing. A north facing door was for bringing in hay and grain on the shady side of the barn in the summer.

After we had climbed up to and down from the rafters, Dan McKeen (who then owned Green Mountain Timber Frames) handed me prints o f the measured frame.
To have a sense of the building I checked some of the dimensions. The framers really did make his barn 30'-1" wide. He also made it 42'-6" long.

Why those dimensions? Laurie Smith, the English Geometer, suggested that a layout using the diagonal of the square was the reason.
The diagram shows how a framer would have used that set of proportions (which is the square root of 2) to layout the floor. This is easily drawn.
The rest of the barn frame comes directly from this diagram .

Both the extra inch and the square root are indications that the master carpenter for this barn used geometry to determine its size and framing. The ruler the carpenter used was not accurate by today's standards. Because he used Practical Geometry for his layout -  proportions and relationships between parts, not fixed dimensions - it didn't matter.

The second diagram shows the floor plan of the barn.

The height of the  new rectangle on the end of the square was a good height for the barn wall. So the framer drew a square in each corner. Using the diagonals for those squares he swung an arc on both sides. Where they met marked the ridge for the roof.

I have drawn the diagram as if the framer used the barn floor for his layout. Carpenters today use the floor of a house to layout the walls  and the rafters for the roof above, so this is a reasonable assumption.

The measured drawings of the barn show how the diagrams were applied to frame the west end wall.
The red X on the right is the diagonals of the original square. The DASHED LINE is the arc of the diagonal locating the ridge.

The green DIAGONAL of the SQUARE on the left is cut by the green ARC of the length of the square. That intersection is the location of the left interior post.

The east end uses the same geometry as the west end.

Here is the diagram for he diagonal cut by the arc. It is easy to draw and based on dimensions already being used by the framer. Locating the posts is straight forward and simple, easy to do with a straight edge, some twine and a way to hold the twine taut.
The north and south walls also use matching diagrams.

 Shown here is the north wall. The RIGHT SIDE matches the layout of left end of the west wall shown above: the divided by its DIAGONAL AND ARC INTERSECTION,.
Then comes the SQUARE door opening; its lintel determined by the INTERSECTION OF THE TWO ARCS of the square.

The left side was divided in half as shown by the DIAGONALS


Note that the braces and the poles are also located using the same geometry: just turn the diagram above upside down.  The diagram here shows all 4 arcs within the square. 
Green Mountain Timber Frames website is

The  measured drawings used here were produced by James Plastteter in May 2014. Platteter is a master furniture maker. His website is down, but his fine work can be seen by searching by his name. 

Sunday, December 2, 2018

The Daisy Wheel - a Module, a Diameter, a Part

This post follows my post on Lines: how we designed and framed using compasses and twine.

I used the Tuckahoe Plantation cabin as a my example.
Its floor plan is composed of 2 squares. Its elevations come from the division of the square into thirds, easily done on a framing floor with cords anchored in place on each end.

As long as the original length, here A-B, was on site to use as a reference, the cabin frame would fit neatly together.

The windows however might be made by a joiner, off site. He could take a length of twine with him that matched A-B. But his windows would be smaller. How does he figure out the needed window size?

He would refer to a daisy wheel drawn by the master carpenter.

The diameter of the circle is a fixed length; the daisy wheel shows the craftsman where that diameter is. It is the Module, the Diameter, the Part described by Vitruvius and Palladio, referenced by the pattern book writers.
'P' on a drawing can also refer to the Latin 'pes' or the Italian 'piede', meaning 'foot'. 

Vitruvius, (Book I, Chapter II, Symmetry,) says. "Symmetry is a proper agreement between the members of the work itself, and relation between the different parts and the whole general scheme, in accordance to a certain part selected as a standard. ... In the case of temples symmetry may be calculated from the thickness of a column, from a triglyph or even from a module."

Asher Benjamin divides the lower chord in his truss diagrams into 4, 7, and 9 Parts. 
The Country Builder's Assistant, Greenfield, MA, 1797, half of Plate 29.

Owen Biddle adds a line below his fireplace mantle which divides the width into 5 Parts; and one of those  parts into 4 smaller parts.
Owen Biddle, Biddle's Young Carpenter's Assistant, Philadelphia, 1805, half of Plate 21

The master carpenter chose his circle diameter - often a hand's breath, about 8", or  from thumb to first finger, about 6".
He drew his circle on a board and stepped the radius around the circle 6 times, swinging an arc each time. The pattern is a daisy wheel.
Always, in every circle, the tips of the petals mark the diameter of that circle.  The other carpenters could measure the diameter with a compass whenever they needed.

The cabin width might be the daisy wheel stepped off 3 times, then that length stepped off 10 times. If the daisy wheel was about 8", the width would have been about 20 ft, a common size for small houses before 1850. Or perhaps and I house: 2 rooms 16 ft square and a center hall 8 ft wide, all laid out by stepping off.
The windows might be 3 daisy wheels wide. The joiner fashioning windows needed only take the daisy wheel's diameter with his compass and transfer that length to his work to make the window fit the cabin.

*   *   *           *           *           *            *           *           *            *           *           *           *           *

Here - the asterisks in red - I have counted off 3 units, then used that dimension to count off 10 lengths.

Other daisy wheels have been found on roof and wall sheathing boards. After a building was framed the daisy wheel was no longer needed but the board still was.

Daisy wheels drawn for practice or perhaps to alleviate boredom also exist.

This pattern is on a bedroom wall where it is known that someone was confined due to illness for a long time. It shows no signs of being used as a reference.

The daisy wheel at the beginning of this post is on this board leaning against my breezeway wall. The 9 ft. tall sheathing board was part of an 1780 Vermont barn. The wheel was about 4 ft off the floor - easily accessible. It was drawn by compass; the center and the tips of the daisy's petals were regularly pricked. The radius and the diameter were used as dimensions. As it was in a protected and easily seen location it was probably also used for other buildings nearby.
Its owner gave it to me.

Vitruvius', Asher Benjamin's, and Owen Biddle's books are listed in my post of my bibliography.

If you do not know how to draw a daisy wheel, the steps are shown here.

#1 Draw a circle
#2  using the same radius, place your compass on the circumference - the line of the circle - and draw an arc.
  #3 Where your arc crosses the circle's circumference, place your compass and draw an arc. Do this a total of 6 times.

 #4 When you get all the way around the circumference you have made a daisy wheel.