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

1. 

This post follows my post on Lines: how we designed and framed using compasses and twine.   https://www.jgrarchitect.com/2018/11/lines-in-historic-and-modern.html

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.

,

Lines, in historic and modern construction

 How we build today that can be traced back to the ancient world, 
We may have forgotten how to use geometry, but we still use the concepts and tools.

Lines 
Now called Chalk Lines



Every carpenter knows :1) how to use a Line,  2) why to lay it out,  3) how to pluck the twine at the right angle.


 We learned to snap the Line from someone else, not a book.  This is hands-on teaching - master to apprentice.

We've been educating the next generation this way long before it was written down.
Theo Audel tried in 1923.
Audel's Carpenters and Builders Guide has 2 illustrations showing how to 'pluck' the Line. Other illustrations show how to set the Line with an awl.


Here is his illustration of the Line with its reel and awl.

 He explains that "The line consists of a light string or cord"  made of cotton or linen; that it can come in 20 ft., 50 ft., and 84 ft. hanks, on up to 450 - 600 ft. long lengths. That's a awfully long cord!











In 1923, tape measures were still about 5 years in the future.
We did have 6 ft long folding rules.

This one is mine: it helps me catch nuances in an existing building because I am close to what I need to document.
The tape measure is better for overall dimensions.

That word, 'Line' - the L capitalized - is often used in Practical Geometry. Serlio"s diagram and explanation is the earliest example I have found. The word was understood, not requiring any special explanation. James Gibbs says about his drawings  that they are  "Draughts of useful and convenient Buildings ...which may be executed by any Workman who knows Lines,..."

Today we use Lines for setting a wall in a straight line. The Line is along, or off-set, from where the wall needs to go. We build to it.
Rectangular foundations are 'trued' by checking with a Line that the diagonals match.


How would builder without 20th Century tools use a a Line to lay out a building?

The slave cabin of Tuckahoe is an example.

The carpenter knows how big he will make the cabin and what it will look like: 2 square boxes with roof, lofts, chimney, 2 doors and 2 windows. 

He starts with a Line (C-D) and its Perpendicular (A-B) - basic geometry that he can easily lay out with his cord.  The Lines do not yet have length, just direction.
 He chooses his length  for the width of the cabin: A-B. Probably he has a rod marked off with 5 or 10 units. See the illustration at the end of the post.
He  swings his cord  in an arc using A-B as his radius from C through B to D. Now he has the width and the length of the cabin, and 2 corners.
To find the other 2 corners, he moves to B and swings his arc from E through A to F.
He doesn't yet know where E or F are...
For that  he will stand  at D and swing the cord from A to E. Where the cord intersects with the earlier arc will be the right rear corner, E. F will be determined the same way.
Then he will check that his rectangle is true by running his diagonals F-D and C-E  If they match, he is set. If not he will adjust his Lines.
At no point does he need to use numbers. 
 
The walls of the cabin would be laid out on a framing floor with cord set from point to point, just as timber framers who work by hand do today.


Here's a 14th c. wood cut showing a rod marked in 5 units. It may be longer; it may extend behind his body to end at the rectangle with the triangle at its end - which might be for plumbing a surface.
 C. 1800 pattern books refer to 10' rods. 16.5 ' rods were used to lay out acres.





See my Bibliography for the books of Serlio and Gibbs referred to here.
See also my posts on both men, and my posts on Tuckahoe Plantation.

Audels Carpentry and Builders Guide, a practical illustrated trade assistant, Theo. Audel & Co., NYC, 1923







The subject of the next post:

 How a daisy wheel fits into the use of Lines

This daisy wheel, drawn by a compass, was on the wall of a barn in Vermont. Close examination shows that the center and the tips of the daisy's petals were regularly pricked. The radius and the diameter were regularly used as  dimensions.

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:  http://www.jgrarchitect.com/2014/06/cabin-tuckahoe-plantation-goochland.html


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:
http://www.jgrarchitect.com/2016/10/practical-geometry-drawing-diagrams.html




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:    http://www.jgrarchitect.com/2014/05/tuchahoe-planatation-richmond-virginia.htm

Tuckahoe Plantation, Richmond, Virginia, 1733-50

Update: August, 2023. This post needs revisions. 

In the last 9 years I have learned a great deal about practical geometry.  I have also read Material Witnesses, Camille Wells' book, published in 2018 by the University of Virginia Press, about domestic architecture in Early Virginia. She writes about Tuckahoe in great detail. 

I will leave this as I wrote it in 2014 until my new drawings are ready for publication. 

 

I visited Tuckahoe Plantation recently.  I wanted to see more brick work, after studying the walls of Gunston Hall.

The Tuckahoe Plantation Main House has brick end walls on the south wing, c.1733.  HABS has drawings that I could use, even though they are very small: 1/8"= 1'-0"

The  Plantation is on a bluff above the James River.Originally visitors came by boat. I came by car, turning off a narrow road onto a dirt lane lined with trees and pastures for horses and cows. Finally the buildings appeared, and parking for my car.  I liked entering on foot at a slow pace. There are few signs, and no visitors center. I was almost the only person on the grounds and enjoyed it all, even as I was studying the buildings, thinking about them carefully  I hope to go again for a thorough tour of the house (open only by appointment).

The upper photograph is of the south wing facing the James River. The second is the west wall of the south wing.



As the floor plan shows the House has two wings joined by a Great Hall. It is also surrounded by stately trees and shrubbery, therefore hard to photograph as a whole. The end walls of the south wing feel much more hand wrought than do the walls of Gunston Hall. There is also a subtle brick pattern, dark and light. The North Wing end walls are not brick.
The foundation (above grade) for the house is brick, but the north wing, added in 1750's does not seem to have a basement - no windows or doors, only vertical slits in the walls. I wondered if this difference, as well as the change in chimney construction, would also be visible in the geometry, whether it represented a change in how the north wing and possibly the Great Hall were considered, laid out, and built.

Here are the diagrams. The geometry does change.

I have drawn 3 green diamonds on the South Wing (They could be 3 squares, same proportions.) To the center one I have overlaid the red square and added the diagonals of the half squares which cross at the walls of the South Hall. The points of the diagonals also determine the window openings. The rooms are not quite square.

Both of the North Wing rooms are square - noted by green squares with their diagonals. The squares divide in thirds - red lines in upper square. Then  a new square - drawn in red - is extended to determine the width of the North Hall.

The Great Hall is 2 squares crossed. I've drawn one in green, the other in red. The space where they cross is the entry, the crossing determined by the squares divided into thirds.

I wondered if the brick end walls would be 3-4-5 triangles, which would be structurally sound. They appear to be - see the green diagonal on the south end wall. The window and door sizes and placements do not neatly fit the pattern.

The Great Hall elevation is crossed squares - in green, just as its plan is. The edges of  the squares mark the edges of the windows. The diagonals' crossings mark the height of the door, the centers of the door panels.

The North Wing end wall is 2 squares - in green, divided in halves and thirds - in red. This also continues the floor plan geometry. The roof pitch comes from  the frame - not quite a 12/12, determined by the geometry, not by numbers.

The North Elevation can be looked at two ways.
On the right I have drawn the square (the diamond which marks the centers of  the square's sides) beginning at grade, including the foundation. The left edge is at the door frame.
On the left side I have drawn a square with its diagonals. The length of the square is the height of the wood frame of the wall of the wing; it does not include the foundation. That square ends at the edge of the paneling for the entrance, which are noted on the floor plan.

I do not know enough about the framing for this house. In the Northeast I have seen and worked on many buildings from this period and have knowledge of standard framing and regional variations. I can show how the geometry determined the framing and therefore the design. I wonder if Tuckahoe's framing changed between 1733 and 1750.


Part of my reason to visit to Tuckahoe was to see its intact measured one and  two room houses that looked in the HABS drawings very much like the houses Henry Glassie wrote about. I will write about that next.