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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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. 

Practical Geometry - what our ancestors called this geometry

Practical Geometry.
It's what our ancestors called these diagrams I draw.


 Here is Peter Nicholson who wrote about Practical Geometry. His writings make clear that geometry was once an expected and necessary part of construction, used both by the designer and the artisan.

His first book, The Carpenter's New Guide, published in London in 1792.

He begins with a Preface, some of which I quoted in an earlier post: http://www.jgrarchitect.com/2016/08/practical-geometry-as-described-by_16.html


Page 2 is copied here.

The use of geometry in construction was so accepted that Peter Nicholson waits until his third paragraph before he shares that geometry is useful in mathematics and science too.



By the time of his death in 1844, Nicholson had published 27 books in London, New York City, and Philadelphia.  More than 10 years later his books were still in print.

This portrait is in his updated book The New and Improved Practical Builder, published in 1837.

This time he writes a whole paragraph explaining Practical Geometry. Has he been asked to be more thorough? Have the new uses of geometry in science changed the perception of what geometry is? Have men become carpenters by necessity - especially in the New World - rather than by apprenticeship, and thus desire to educate themselves?




Here is the Introductory Chapter. 

The second paragraph describes the 2 branches of Geometry: Theoretical and Practical.
Now  the Theory of  Geometry is carefully described, including a reference to Euclid, but it is still one of the 2 branches of Geometry.
The other branch, Practical Geometry,
 allows "the architect to regulate his designs and the artisan to construct his lines".



Later, on page vii, he writes, "There is no mechanical profession that does not derive considerable advantage from it."


first portrait: by James Green, 1816, now in the National Portrait Gallery, London
second portrait: the frontispiece of The New and Improved Practical Builder. Don't miss his compass.

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!  

"The Country Builder's Assistant", by Asher Benjamin, 1797

 Here is the first page of Asher Benjamin's pattern book, printed in Greenfield, Massachusetts in 1797. I show here that page and Plates 25 and 26 from my copy of the 1992 reprint by Applewood Books, Bedford, MA.
The original prints of The Country Builder's Assistant which I've read (available  in rare book libraries) are full of smudges and notes made by their owners. Clearly the books were well used.  200 years old: they feel ready to be used again.

They are quite small, about 5" x 8, so I think the engravings were intended as concepts.
Benjamin says, just above his name on the first page, "with a PRINTED EXPLANATION  to each". But there is none for these plans and elevations. Did he expect that those using his book would need no more explanation to adapt these drawings to their own use? That they, having served apprenticeships with master-builders and joiners, could read the geometry? It has been suggested that these and the church design were after thoughts, dropped in. Perhaps. However in the sequence of the book they come in logical order: after stairs and before roofs.


These are a way to present ideas, not fully realized designs. He draws them causally: no sash in the windows, no framing notations, just a sketch.  Did he use geometry? Yes.


Plate 25
uses the same geometry for plan and elevation - 2 squares crossed.  The width of the hall is determined, 8 1/2  units, the length set: 26 units. Starting from the left and right walls of the hall, one square goes to the right - red solid lines - the other to the left - red dashed lines.  The left front room is square, the back room the left-over space. The right front room - the kitchen with its circular baking oven - is deeper, its size and those of the rear rooms laid out by smaller and smaller squares - see the red dots where the lines cross. I have drawn the diagonals of the half squares for fun because they locate the columns dividing the front hall from the stair hall. -dashed green lines.
The elevation uses the same geometry, crossed squares. I drew them from the base. The space where they cross is the width of the dramatic entrance. If I had started them at the line of the first floor, where the granite blocks give way to clapboard, the squares would have outlined the Palladian window above.
On the right the windows are located on the half and quarter marks of the square - red verticals.  The diagonals of the half squares touch the tips of both sides of the Palladian window. I have marked them in green as well as the squares around the entrance and the  window.
 

Plate 26
A 3 story Federal house - with its characteristic smaller third floor windows, a  balustrade to hide the roof, and a entrance with columns and a fanlight.
There are 2 possible geometries here: 2 crossed squares - shown in red on the elevation - lining up neatly on each side of the entrance - or a square on end in the center - half shown in dashed green, left of center. The focus on the center would be a tentative nod to Palladio.  The windows are set by the center lines - green verticals.

In plan the same choices exist, crossed squares - in green -  or a square in the center overlapping a square of the same size on end (en pointe?)  - in red. Its sides extend beyond the drawing.
The centered square locates the center lines of the windows, the stair hall wall. The crossed squares overlaid on the centered squares locate the head of the stair and the width of the hall - red circles.

 There is more... see the green arrows which show a smaller square within the larger, determining the location of the side windows.

I think Asher Benjamin was having fun: no client to please, no budget, only himself; a quick and neat presentation of ideas on a very small scale where precision didn't matter. I also think his audience could read 'geometry'. It was not a foreign language.  

Wing for a Georgian Federal farm house

This renovated and new wing belongs to the house for which I recreated a new entrance. See my posts about the 1795 Federal entrance for pictures of the main house which so beautifully uses the Golden Section for its elevations.

Before I was hired to fix the front door, the family asked me to design garage and storage space and to facilitate repair to the shed/family room.

From the left: existing kitchen with slider, renovated shed, new storage and garage, seen from the east.

The views of the shed are from the west.

The shed, a workshop, c. 1830, had been moved against the house

in the 1950's. It had been an awkward, inadequate garage before it became the family room.

The shed was not square or level. Every piece of the new wing which connected to it needed to be scribed. There had to be 'wiggle room' in the new wing's plans, elevations and framing so it could fit against the shed, be water tight, structurally sound and meet code.

The work could not have been done successfully without an excellent restoration contractor who liked working with me. He had to interpret and refine my drawings. Obviously, he did so beautifully.

Thanks, John.