A Circle to a Square, 1830's cottage north of Boston, Part 3

 When I was preparing for my presentation at the Timber Framers Guild annual conference in August I assumed people knew the basic geometry - how to begin with a dot and a line and construct a shape - for example, a square - that was useful in construction. I found that I was wrong.




Here are diagrams showing how to lay out a square, beginning with a line, a dot and then: another dot.






The two dots define a distance, a radius.  So a circle is drawn. Now there are 3 dots on the line, all related to each other.






 Draw 2 more circles using the dots on the circumference of the circle as the centers. All the circles are the same size.

Then take distance, whatever length you like - but it should fit on your page! Swing 2 arcs using that length and the centers of your two outer circles, one above and one below the first circle. The arcs cross.
Draw a line between the points where they cross. This line is perpendicular to your first line. and it crosses the first circle at 2 points.


Add 2 more circles, above and below the first row of 3, using the   points you just found as the centers. Now you have 5 circles all the same size, placed in relationship to each other. And you have 4 petals made by the arcs of the circles. Join the outside points of the petals, also where the circles cross. This is a square - drawn here in red.

Of course, your length (radius) needs to be constant...You need to be draft carefully. This is precision work.




This diagram applies to the 1830 house in Reading MA, which I have written about earlier.
While preparing for the Guild presentation, I realized how more complex and also how much simpler the diagram could be.

Here is the 'square construction' laid over the elevation, the base of the square on the first floor. The center line defines the ceiling of the fisrt floor, the placement of the second floor joist. The top of the square defines the ceiling of the 2nd floor, the placement of the ceiling joists which are also collar ties.
I superimposed a square diamond on the diagram - in green - because the intersections of the diamond and the square's petals marked the windows' width.





Then, I tried turning the square 45*. The upper sides of the new square is the pitch and location of the roof rafters.   The intersection of the 2 squares is the top plate of the wall, the placement for the roof rafters. The petals are the width of the windows.



All this became visible, obvious, while  I was working intently on preparing a coherent talk. I learned a lot. Now I am beginning to re-post and update my earlier diagrams.

Here is the farm house that inspired my original research. The first floor parlors had  such presence and grace I can feel them today.
The left hand wing is a later addition.









for Part 1 see: http://www.jgrarchitect.com/2010/08/regulating-lines-1830s-cottage.html
for Part 2 see: http://www.jgrarchitect.com/2013/05/regulating-lines-1830s-house-north-of.html

1830's cottage north of Boston, Part 1

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A family with a small c. 1830 story-and-a-half house asked me for advice - how to expand their home in keeping with its character.

We talked about their needs, the house constraints, the land. I suggested that a variation of "big house, little house, back house, barn" might be work. (The old jump rope rhyme refers to the massing of early New England farms. There is a book of that name describing the phenomenon.)
Back on my drafting board - after I had drawn up a sketch for the family and their contractor which reflected our discussion - I played a bit with the form. Here's what came out of it:


The floor plan provided to me was at 1/8" = 1'-0", very
small. However I later measured the house. The plan is accurate. See my post in May, 2013, for the elevations. I am happy to discuss the date of the house, if asked.

The first floor plan and a sketch of the house is here. The red line shows the outline of the original c. 1830 house plan.

The second drawing shows the original floor plan with - in red - the length of the side used as a radius for a circle.


The third drawing shows that a circle whose radius is the length of the
wall touches the 4 corners of the main house.The rectangle of the house
is determined by the circle. An arc using the same radius defines the
length of the wing, but not quite the width. The interior arcs of the
daisy wheel also define the small front entry. The 6 points of the 'daisy wheel' are shown, only 2 of the 6 'daisy petals' are drawn.

The house is simply built, perhaps by a farmer, not a joiner. Whoever he was, whatever education he had in construction, he knew circle geometry and used it to layout this house.