Saturday, March 21, 2020

A Barn and its Daisy Wheel


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. 




Friday, March 6, 2020

Railroad Warehouse Frame c. 1850, Richmond, VT

I first wrote this post in March, 2014. I have now updated it.

This is the model of the post and beam warehouse frame that Mark Goyette wanted to use as the frame for his new house.

Mark's model is not as tall as the original warehouse. He decided to lower the structure so that the ceilings for his house would be 9 ft. high instead of the original 13.

The warehouse was built along side the railroad in Richmond, VT, in the 1850's. It is square rule framed.
By 1850 the need for consistent dimensions in industrial applications had become obvious. Many different individuals owned the various railroads. However, engines, carriages and box cars needed to transfer smoothly from one set of tracks to another - all the rails needed to be exactly the same width and profile to accommodate the wheels which also needed to be the same dimensions.

I was very interested to find out if this warehouse, built to service a railroad, was framed by geometry or the new idea of standard dimensions. Mark Goyette, who restored old cars professionally, was curious too; he had, after all, built the model in order to understand better what he planned to erect. So, I drew up the section of the warehouse to find out what was there.

Such a simple, elegant design!

The necessary width determines the square which determines the height.
The 3-4-5 triangles determine the roof pitch. 2  3-4-5 rectangles are the box. The location of the cross tie  is set by the intersection of the square's diagonal and the triangle's hypotenuse.
The roof pitch is - in modern terms - a 9/12 pitch.

March 6, 2020 update:
The frame is 5 H bents. The bent shape looks like an H because of the  'dropped' plate - see the arrow This is how many barns and houses in southwestern Vermont in the Hudson River watershed were framed, and is a hallmark of Anglo-Dutch framing, 2 framing systems joined.
A Dutch frame would have bents about every 4 feet. An Anglo frame spaced the bents between 15 and 20 ft.  These bays appear to be 12 ft. apart.
A Dutch frame has the bent's plate framed into the post on the side, below the plate that carries the rafters. An English bent has both plates joined to the post at the the top, at the same height. This requires a more complex mortise and tenon joint.

Finding this hybrid frame in an ordinary service building, built by a corporation - not an individual framer who has moved upstate and taken his framing traditions with him  - in northern Vermont in 1850, is surprising and interesting .

Thanks to David B. AdolphusTravers for the photograph.

Wednesday, January 8, 2020

Practical Geometry - Drawing a Square with a Compass, Part 2

Here are 4 more ways to draw a square with a compass.

How to draw a square with a compass  #3
Peter Nicholson wrote about Practical Geometry in 1793.  His first plates are introductions to the first rules of geometry: using a compass to bisect a line,

My blog post about him is :
It includes images of Plate 2 and Plate 3.

Here I have copied just the image of a square. Nicholson includes instructions for finding the square 'abcd' by dividing the arc a-e (the black spot) in half then adding that half to a-e and b-e find d and c.

Asher Benjamin and Owen Biddle in their pattern books copy Nicholson.
They do change the order of the letters which makes the steps easier to follow: a and b are 2 corners of the square. The arcs of a and b create c. Half of arc a-c is d. Add the length b-c to the arcs of a-c and b-c to find e and f: the square has its 4 corners.

How to draw a square with a compass, #4

A 3/4/5 triangle always has a right angle (90*) where the lengths 3 and 4 meet.
2 3/4/5 triangles are a rectangle which is 3/4 of a square.
I have drawn this on graph paper for clarity.

When carpenter squares became widely available and accurate, the square corners were easy to establish. The compass was only needed to lay out the length.

Before that - before about 1830 - the carpenter could have laid out his square like this:

His length is laid out in 4 units.
He knows approximately where the 2 sides will be. He does not know if his angle is 90*.

Here I have drawn the arc of the length of 4 units - on the right side. Then the arc of 5 units with its center at 3 units  on the left side. where they meet will be the 3/4/5 triangle.

The carpenter did not need to layout the full arcs as I have drawn them.
If he held his Line at the right lengths he could have marked a bit of both arcs where he thought they cross, and then placed a peg where they did cross. He would have checked his square by matching diagonals.

The relationship between the 3/4/5 triangle and the square is good to recognize. However, the 3/4/5 triangle is usually the only geometry. Layout by a carpenter square, widely available in the 1840's, was simpler and took less training than using a compass.

This small, simple house, built c. 1840 for a cobbler, was probably laid out using a carpenter square. I've tried other geometries which almost fit. The 3/4/5 triangle does.

I wrote the original post in 2014. It's time to revisit and review.
Here's the link to the post:

How to draw a square with a compass, #5

 Lay out a perpendicular through a line. Draw a circle with its center where the lines cross.
Draw lines - here dash/dot lines - between the points where the circle crosses the lines.

This square, as a diamond, was often used by finish carpenters because it easily evolves into more complex layouts. 

Below is the entrance porch for Gunston Hall, designed by William Buckland, c. 1761. The rotated squares determine the size of the porch. They also locate the floor, the pediment, the roof pitch, the size of the arch, the height of the rail.
 My post on Gunston Hall is:

Here the glass facade of
 the Mass. Ave. entrance to MIT. For more, see:

 How to draw a square with a compass, #6

 On a line select a length - see the dots .
Using the length as the radius draw a circle using one dot as the center.
Now there are 3 dots. Draw 3 circles using all 3 dots as centers.
Drop a perpendicular line at the first circle's center.
Now there are 2 new dots for centers of more circles.
Connect the petals where the 4 circles cross.
A square.

This modest farm house, c. 1840, used the square crossed as the squares above are for the Gunston Hall porch.

One last note: the circle to square diagram #6 can also become the diagram for #5. 

Each master builder probably had his preferred way of using his compass, even when he practiced within a tradition.
Still, just as a 3/4/5 triangle is part of a square, these diagrams are also simply different choices, different perceptions of the same geometry.


Sunday, December 29, 2019

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

Draw a square with a compass? !
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:

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:

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.

Friday, December 27, 2019

English Construction Tools, 1669

John Leeke translated Giacomo Barozzi da Vignola's Regola delli cinque ordini from Italian into English in 1669.

While Leeke himself is worth attention; he was a mathematician, a professor, and land surveyor and well as fluent in Italian. He also helped rebuild London after its disastrous fire in 1666.  Here I want to focus on the frontispiece for his translation.

Leeke calls the translation
He adds Vignola's title.

Then he writes
For the USE and BENEFIT of
Free Masons, Carpenters, Joyners, Carvers, Painters,    Bricklayers Plaisterers:
In General
For all Ingenious Persons that are concerned in the Famous Art of BUILDING 

This cartouche fills half the frontispiece. It celebrates the tools used by all those craftsmen.
Sitting on a column base are:
A compass
A carpenter square
A horizontal level
A vertical level
A measure with a curved side and regular marks
Draped around the cartouche is a Line, its spool on one end, its chalk cube on the other.

These are the tools for people who built.

130 years earlier most of the same tools are on Serlio's frontispiece which he engraved about 1540, for his book, On Architecture.
The original is black and white. This cartouche is on the cover of the 1998 translation by Hart and Hicks.
I use the color image because it makes the tools easier to see:

A compass in front of a ring
The compass pierces the scroll of the cartouche and is held in place by the ring.
A large carpenter square spearing a tetrahedron
A straight edge spearing a cube incised with diagonals, graduated circles and squares. The size of each is determined by those on either side.
A round rule pierces both the tetrahedron and the cube.
A Line with a handle is in the lower left corner, entangled in the scrolling, ending with a tassel beside the handle.
Serlio does not include any levels.

 Walther Hermann Ryff, of Nuremberg, c. 1500- 1548, considered Serlio his mentor. He did not train under him.
Ryff was probably a pharmacist and published many works on medicine.

He also published Vitruvius first in Latin and then in German 1548.
This book, with a title of over 30 words, is referred to as Architecture. Part of the title says it is "The hardest, most necessary, belonging to the whole architecture of mathematical and mechanical art, regular report, and vastly clear, understandable information..."
This engraving is the frontispiece for his book. Many tools!
4 compasses are easily seen. 
Here's a close up of one, with an impressive arm that would have guaranteed accuracy - along with a knife, a plane, and calipers. 

Edward Shaw published his pattern book, The Modern Architect, in 1854, in Boston. It also had a frontispiece displaying tools,.
His engraving is in black and white: The color rendering is for clarity.

He includes:
A small compass in hand
A rule in hand
A large compass in the foreground
A hammer.
A large carpenter square
A cylinder which might be a chalk line
A saw in hand
A drawing and a portfolio of drawings
against the tool box:
A straight edge or rule
A vertical level
A brace is in the tool box.

A part of the original engraving showing most of the tools.

 The 12 presentations and workshops I gave this past year began with the portraits of master builders holding their compasses, and these engravings of their tools.
When my audience understood what tools were available before the Industrial Revolution they enjoyed seeing how a compass and a straight edge could layout a  rectangle, and then a building. Next they drew them themselves. They saw for themselves how the compass creates the first dimension and determines the next dimensions.

You who are reading this probably have not sat in on a presentation, or twirled a compass. This is my attempt to bring you up to speed  - so that the concluding sentence below makes sense!
Practical Geometry was the tool  which translated a design from an idea to construction.  It was the Practical, not Theoretical, use of Geometry.


Note: our contemporary John Leeke is the 10 generation grandson of the man mentioned above. Yes, I asked and he told me so.

Saturday, December 21, 2019

The Beatty-Cramer House and Its Daisy Wheel, Part 2 of 2


Please see Part 1 for the history of the Beatty-Cramer House in Maryland now owned by the Frederick County Landmark Association.
The Beatty house was built in the 1730's. The Cramers encased that house with a new one about 1850. These posts focus on the first house, the Beatty House, which is inside the house in the photograph.
The first post:

This daisy wheel and the 3 petals - the 'eye' - were found on an original stud on the 2nd floor frame of the Beatty House.

I was asked to explore how the diagrams could have been used to lay out the frame. This is part 2 of my report.

The Beatty Cramer daisy wheel with its 3 petals, its 'eye' in red,
showing how they are part of each other.

An aside:
This daisy wheel was found on an upstate NY barn built about 60 years later. Note that it is not perfect, as the one I drew is not perfect. 
The diagram in the Beatty Cramer House is just that - information for the builder. 
The diagram on the barn sheathing was also information.*
Neither daisy wheel needs to be perfect to be useful. It's a 'setting out' tool, a record, notes to the builders and those who will work on the house later.

My first blog post laid out how the master builder would have used the 3 petal diagram to lay out the width and length of the house, the size of the 2 rooms up and down, and the location of the bents. 
A bent is a part of a timber frame , the posts and beam, that runs front to back.
This photograph shows 4 bents about 4 feet apart in the east room, first floor. The beams hold up the second floor . The posts extend above the floor of the upper room to the plate . The second floor on the east side of the house has half walls.

The second photograph shows how the west side of the house was originally stepped down. See the tie beam which is being photographed in the center of the existing wall on the left. That beam was part of the floor frame for the west side upper room.

The drawing shows the east and the west end elevations.  The floor and wall frames that were part of the Beatty House can be determined by the mortises left behind when the frame was changed. The pitch and frame of the roof, especially the east end, is not as easy to ascertain.

The master carpenter has his first dimension: the width of the house, and he has left us his note about how to apply that dimension: the  red line at the right is the width of the house. The arcs of the eye is the way he sets out a square, finds his next dimension. 


A note about laying out the daisy wheel to find the next dimension: the carpenter could have used a Line to draw the arcs. He could also - when he wants square -  have used a long compass like then one shown to step off the dimensions. Every rectangle could be trued by checking the  diagonals, as framers do today.   

The framing elevations
First the west end - the frame on the right in the drawing above.

The width of the house becomes the radius for the arcs that determines  the height of the bents. The tie beams and the plates are set where the arcs cross This is the same geometry that determined the floor plan of the house: the 3 petals of the daisy wheel, the eye - see the previous post.

The height is divided in half to determine where the 2nd floor will be located.

The plates extend from this west side of the house to the east end. The builder has to work with that height. See the red arrow from the west to the east elevation. 
The east rooms are a few feet higher than those on the west.  How did the builder set that floor height?
He may have used the height where the diagonals cross the arcs to place the 2nd floor of the east side. See the black dashed line. The daisy wheel could then have set the sill location.

The edge of hearth in the 1st floor west room also uses those points.

Or perhaps the difference in height was set by daisy wheel from the beginning.

The house was built into the slope of the land. The simple way to excavate the storage cellar under the east rooms could be by digging into the hill from the west end. The kitchen on the west  needed to be only a few feet above grade - for easy access to the spring house. The formal chamber on the west also needed to be a few feet above the grade to keep the wood sills dry. 

I have indicated the slope of the land with a black dashed line below the framing drawing of the north elevation.  The grade on the west (left) side is as seen today.  The grade on the east  (right) side would have been at least 12" below the top of the stone foundation.

The dirt removed to create the cellar hole could have been been used to level the area on either end.

The diameter for the daisy wheel for the west rooms is the height from the sill to the plate. 
The daisy wheel is drawn with its axis horizontal to show the location of the second floor joists.
The diameter for the daisy wheel for the east rooms begins at the sill and ends above the plate. The petals of the daisy wheel are located at the underside of the plate. Here I have drawn the daisy wheel with its vertical axis. The builder would have begun his layout from the under side of the plate, which was a given.

The daisy wheel on a horizontal axis could locate the plate for the east 2nd floor ceiling. The braces could have extended to that height.  The petals already locate the studs on each side of the fireplace.

The roof ?
It's not there. Nor is the ceiling height for the east 2nd floor chamber. Only an original window location, the stud locations, and a brace with an angled cut from a reused collar beam remain. I have extended it here.

2 roof pitches have been proposed.

One, shown here, matches the Jan Breese roof built c. 1723, in New York State.
That roof would be based on the daisy wheel and a second interlocking circle. It is not a diagram used for other parts of this  frame.

The roof pitch could also be based on the eye - or as described: rafter length 3/4 the length of the roof span. The arc of the width of the  house fits the lower pitch. 
The arcs have arrows.  I have added the roof line.The plates are red.

I prefer this pitch because it comes from the geometric notes the builder has left for us. It is consistent with his overall layout.

It is time to look again, on site, with twine to mark the dimensions, swing the arcs,  and especially, consult  directly with the members of the Frederick County Landmark Association. 

*How that daisy wheel was used is in my post: