A Barn and its Daisy Wheel

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Not a very neat daisy wheel is it?



About 8" across, it was found during the dismantling of an upstate NY barn, c. 1790, scribed onto a board used to sheath the roof. The lines were drawn with a divider, not a marker. They can be seen in a raking light.The board is still in its proper place. This is a tracing made of the pattern carved by the pin of the divider.




The barn is probably the first of 4 connecting barns, c.1790. Green Mountain Timber Frames recently dismantled, repaired, and sold this barn for reuse.

It has modified gunstock posts, a 5 sided ridge pole, rafters spaced 38" on center.












The daisy wheel determined the framing layout.

The petals are the arcs of the radii. The points of the petals divide the circumference and locate the diameter. The sheathing board with the daisy wheel was a template, the reference for lengths and relationships. When it was no longer needed it became sheathing.

The master carpenter could rotate the daisy wheel first with one diameter  vertical and then with one diameter horizontal. He could use all 12 points and spokes. The radius and the distance between each point are the same length.

So how did the carpenter begin? He and the farmer knew the approximate size and location of the proposed barn. He decided on a width (the radius of his circle) and drew his daisy wheel.

Using the points on the circumference and a line, he marked the width and the rectangle of the circle  ( the 'x') - The green dashed lines show how he determined the length of the barn. The dashed red lines show the floor plan . 





The farmer wanted an English barn with a center door. The door needed to be a certain width for easy movement. 
Was 32' long enough? Would a 12' wide door give him enough working space on either side of the door? Would a 12' high wall work?  If that 12' were also the height of the barn wall there would be enough space for a lintel at the top of the door frame for strength. And what size are his timbers? 




He decided 11'-2" was wide enough, 12'-4" tall enough. The
carpenter laid out the door within the circle.
The width of the door is the radius of the circle, and the height of the barn wall.
The square laid out by the arcs of the radius.






The placement of the door lintel is set at the crossing of the arcs of the radius.

Since the door is in the center of the wall, the right side mirrors the left.  The arcs  - dashed red line -  locate the center of the circle to the right. 
The right side could also have been stepped off with a large compass.


 


The interior bents of the barn fit neatly into the daisy wheel geometry. The rectangle is laid out by the division of the circumference into 6 equal parts. The dashed red line shows the rectangle of the daisy wheel. While the layout of the barn is a traditional English pattern, dropped beams are the regional Anglo-Dutch vernacular tradition. They are placed using the same geometry as the lintel.

The end elevations fit into the daisy wheel too. Of course! interior and end bents need to be the same size. The plates are not dropped.

This is the first pattern I saw when I began to study how this daisy wheel was used in this barn. I thought the layout began here.
I now think he began, not with this simple end bent, but with the door.



The gable's ridge is 22' high.  22' is also the width of the bent, the side of the square which enclosed the gable end.

The roof pitch was determined by a square using the width of the barn as the dimension.
A carpenter used a framing floor to lay out his bents, mark his mortises and tenons.  This bent could have been laid out on the dirt floor of this barn using twine the width of the barn.   



The daisy wheel was the design for the barn. The carpenter knew how to use it.
The specific 8" daisy wheel probably was the dimension - measured across the diameter - used to locate the holes for the peg: they are all at 32" 4 lengths of the daisy wheel diameter.  The distance between holes for pegs on the braces appears to be 48", 6 lengths. 
Today I have no way to check this. I hope I do in the future.


3/21/2020: This post is a complete revision of a post I first wrote in 2014. 










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Practical Geometry - Drawing a Square with a Compass, Part 1

Draw a square with a compass? !
Yes.
Here are 2 ways. There are several more.

Compasses make circles. Straight edges make straight lines. Together they can lay out whatever you can imagine.
 
How to Draw a Square with a Compass #1

1)   Choose a length: A-B.  It is also the radius: dashed black line A-B,  for drawing a circle with a compass.
2)   Draw the circle.

I have drawn these diagrams on graph paper, a reference to help show how the square grows.

3)  Switch ends. Hold the compass on B. Swing the arc from one side of the circle to the other: G-A-C.
Hold the compass on C. Swing the arc to find D.
Use D to find E; E to find F. along the circumference of the circle.


The circumference of every circle will always be divided into 6 equal parts by the radius of that circle. The length between each 2 points around the circumference will always equal the radius.

It's easy to draw a daisy wheel. 

However, to construct a square the petals are not needed, only the 6 points on the circumference.

4 )  F-G is the line. It is the same length as the one chosen at the beginning, just in a different location.

G and C are 2 points. that can be connected by a line.
So are F and D. 
They are the same distance apart so they are parallel.

A square has 4 equal sides.  (Just a reminder)
5)  An arc the length of  F-G swung from either F or G will mark  G-H and F-I the same length as F-G.  This is the same length as the chosen line A


 







A square drawn using Practical Geometry, using a compass.  
To check: lay out the diagonals. If their lengths are equal the square is true.   

This upstate NY barn was dismantled for reuse by Green Mountain Timber. It had a daisy wheel scribed on one wall.  The  barn laid out using the 6 points of the circle. The frame of the east elevation is drawn below.

The square frame for the door is in the center. Either side completes the rectangle of the circle.

My post describing this barn:

https://www.jgrarchitect.com/2020/03/a-barn-and-its-daisy-wheel.html




How to Draw a Square  with a Compass, #2

Draw a line.  Mark 2 points on the line.
Open the compass wider than the distance between the  points. Swing an arc across the line, below and above it from each point.
The arcs will cross at 2 points. Draw a line between those points. The new line will be perpendicular to the first line.

Then choose the length of the side of the square A-B. Mark it off on both lines.See the arc B-B.
Swing new arcs the same length (A-B)  from both B's.  See the dashed and dash/dotted lines. They cross at both A's.
All the sides are equal: a square.

St. Jerome's Catholic Church, East Dorset, VT, 1873, was laid out using that simple square  - including how the arcs cross each other. 

My post about it is here:
https://www.jgrarchitect.com/2016/12/st-jerome-catholic-church-east-dorset.html

Part 2 is here:  https://www.jgrarchitect.com/2020/01/practical-geometry-drawing-square-with.html

I explain these ways of using a compass,a straight edge, and a marker to lay out squares and rectangles when I give presentations. I add them here because such information should be readily available on line.

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.

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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 https://www.greenmountaintimberframes.com/

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. 

A barn built in the 1830's

Green Mountain Timber Frames http://www.greenmountaintimberframes.com/ measured this barn before they dismantled it to use its frame anew.

Due to the wood used - poplar, beech, hemlock - the layout and the construction we think this barn was built by a farmer without an extensive background in framing. We think it dates to the  1830's.

 The floor was dirt, the head room under the hay loft not quite 6 ft.
What was it used for? Sheep perhaps? Sheds, windows and a silo were added over the last 180 years, making the original purpose hard to read.


I start with the farmer.
He had some wood of a certain size and length he could use for posts and beams for a barn. He knew how the barn would be used and where it would go.

Probably he had a carpenter square - they were readily available. But maybe not, as his dimensions don't quite fit. And he was much more comfortable with the old-fashioned geometry of the 'whirling square'.

He started with the width - 18 feet. He made a square: 18 ft wide, 18 ft. high - first diagram.\
Or so it seems. Today that height is 17'-10", 2". I think originally the width was also 17'-10". His inch seems to have been just a bit smaller than today's inch

He could have started with a string about 18 ft. long. He could have used a compass with a 27" radius, stepped it out twice for 4'-6", twice more for 9' and doubled that for 18'; or a pole 4'-6" long.

In his square he laid out his center lines and then the star that joins the points - the second and third diagrams. This is a medieval framing system which came to New England with the English colonists.

I have added circles to mark how the lines of the star cross at the locations of the girts, I've added a green dashed line to show how the height of the wall is 2/3 the height of the end wall. Almost. It's off by 2"

Using a carpenter square to layout a 3/4/5 triangle does not work as well. The wall height isn't high enough. The lower girt can be determined - see the green circles - but not the upper one.

While the frame appears governed by the traditional English framing geometry, the frame itself has dropped girts - a Dutch traditional way of framing. The girts are mortised into the posts below the upper beam. This combination of framing methods is sometimes referred to as 'American'.


The floor plan is simple: three 3/4/5 triangles. If the width is 18'  the length should be 40'-6" . It was 40'-2" measured on site. The men repairing the frame tell me it is 40'-1"; that the 2 interior bents are at 13'-4 1/2" from each end.

If one arm of the 3/4/5 triangle is 17'-10", the other is 13'-4 1/2".
3/4 of one side of a 17'-10" square = 13'-4 1/2". So either framing system fits the floor plan.

Dan McKeen, GM Timber Frames, also tell me 3 girts are beech, one poplar.The top plates are poplar and in good shape. The posts are sawn hemlock and hewn beech. The ties are sawn hemlock.

I looked at how did this farmer/framer laid out his girts in the side walls.
Here I tried - on the right in red - 3/4/5 triangles. The intersections - red circles - using a triangle that includes the rafter tails, are close, but convoluted. Not simple.
However, a square laid out inside the frame - on the left in green - neatly divides the space in thirds - green circles.

The star of the square used for the gable end laid out along the side also notes the placement of all the  girts.








The numbers on the early carpenter squares were engraved by hand. It is possible that this farmer/framer owned a square that was very slightly off. Or he used his own measure.

The man who built this frame comes alive as I study it; I've met him. Now I want to ask how he learned to frame - who taught him? what tools did he like? where did he start? were we right about his choice of materials?

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:

 http://blog.greenmountaintimberframes.com/2014/12/04/geometry-in-historical-frames-a-guest-blog/ 

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!