Monday, October 18, 2021

Geometry of the Old First Church Fanlight - an Addendum


 

Considering the 'leaves' of the fanlight,  those 3 curved petals that fan out from the base of the light: how did Lavius Fillmore, the master builder, and his crew, especially Asa Hyde, the joiner, derive the pattern?

The layout that I drew of the leaves in the last post is too complex.

 

 The church is graceful and direct. 

 

The derivation in the previous post of the leaf pattern is not direct.
The geometry of the church is straight forward. The use of the circle to layout the framing, the design, would have been clear to other people in construction and to the church's congregation, as well as to anyone in that time who was educated beyond grammar school.

      

 

 

And then there's this diagram in my last post: 

I drew the way the scallops on the curve of the light can overlap simply by rotating the circles one half a petal's width around the circumference, or 15*.

It is also the pattern of the leaves, just at a scale too big for the fanlight.


 

 

 

Drawn smaller, the pattern has 3 overlapping circles at its center, across what would be the sill of the fanlight.  Here the circles come first; the leaves come from the pattern; the fanlight, its size and placement, come from the width of those combined circles.   

However, the pattern in the The Old First Church fanlight was laid out knowing the dimensions for the fanlight. The door and its surround, the placement and size of the door in the main elevation, the width and height of the fanlight were determined by the geometry of the building. They were fixed.

So: given the width and height (about 60"w x 30"h)  how were the leaves' sizes determined? 

The 3 circles across the sill were overlapped. If they were 3 in a row the proportions would be 1/1/1. Then the width could be divided into 3 equal parts. Instead the proportions of the circles are 8/6/8, or 22 equal parts.  Dividing a line into 22 segments with a compass and straight edge is complex.


 

The center lines  (faint pencil lines here) of one set of the fanlight's scallops meet at the center of the fanlight  These are the scallops that the leaves point to.



The distance between the scallops and the center of the fanlight is the diameter of the circles that will make the leaves.

The red spots are the centers of the circles.

 

  

The first 3 circles: where they cross each other and the sill they mark the centers of the next circles.

 

The 4 outer circles. The ones that continue below the sill are not completely drawn.  Note that even though the center circle begins the design it was not needed here. It was understood implicitly by the joiner laying out the pattern.

Below is the layout of the leaves with all the circles included. 


 

 

 

Sunday, October 3, 2021

Geometry of the Old First Church Fanlight

 

 

This is the fanlight over the main door to the Old First Church, built in 1803-5 in Bennington, Vermont. Lavius Fillmore was the Master Builder; Oliver Abel, his Master Carpenter, and Asa Hyde, the Joiner and carver.  

 The fanlight design consists of 2 parts: the 'scallops' around the curve and the 'leaves' coming up from the base. It is simple, graceful.

How was it laid out? In 2012 - when I first wrote about this fanlight - I knew the geometry for the scallops around the curve - expanded daisy wheels on the horizontal and the vertical axis. 

The 3 leaves below the scallops?  I was lost.

Laurie Smith - English timber framer, historian, geometer, the most knowledgeable person I know about the use of circle geometry in medieval design and construction - provided the answer.
Here is our geometry for the fan light. It may not be how Lavius Fillmore laid out the pattern. 

 

 

 The  circle, its 6 points around the circumference laid out by the radius of the circle, is set on a line which defines the shape of the fan light.


 



 

The circle is surrounded by 6 circles which have their centers on the 6  points. The center pattern is a daisy wheel with 'petals'.



 The circles expanded.

 


 

This set of circles around the original circle adds petals 
to the exterior of the first circle. Add the fanlight shape and the petals  become scallops around the arc of the fanlight.

 

 


 

 

 Rotate the circles 15*  - or 1/2 a petal - and the fanlight's scallops' locations change. 

 

 

 

 

Overlapped, the daisy petals create the double scallops of the fanlight.

The overlapped petals are also the pattern of the 'leaves' in the  fanlight: too big, not in the right location, but crossed as are the leaves. 


 

Add regulating lines from the center of the circles to the second ring of circles and center lines in the petals.






 

Connect the center points of the scallops to each other. Where they cross the petals is the center of the small circles which form the leaves. 

 

 

 

 

 

 

The radius of the circles is the distance from the center of the petal to the scallop.

 

 

 


 

 

 


 

 

I've drawn it in red to make it more visible. It is a complex layout for a seemly quiet, unassuming design.

This pattern was drawn at about 3/8" = 1'-0".  A scale of 1"=1'0" might have been easier. However it would still be tiny here on the page. For clarity I left out the overlapping scallops.

The real fanlight was laid out full scale - 5+ feet across -  on a framing table or floor. The proposed design sketch would have been studied, the arcs drawn with a compass using chalk or charcoal, the lines checked, redrawn, the points pinned.  Finally, when the regulating lines were erased, the simple, clean design was visible.

I would like to have been there, listening, watching. I think they were pleased.

Thank you, Laurie, for your help. 



my drawing in 2012