Thursday, July 27, 2023

The Geometry of a Corn Crib

Our corn crib:  built c. 1810, photographed c. 2000. 

Well used, in need of attention, like every building on the farm.



In time we replaced the roof. Then we removed rotten siding.






We were surprised!The crib's post and beam frame was scribed! It has neat, precise marriage marks which, in this part of Vermont, are found on frames which were built 1800 -1820.

On the left are 'll" on both post and brace. On the right the marks on both post and brace are "llll".


 When our house was built  in 1810, the corn crib may have been here.

It has been moved at least 3 times.  It has been repaired, reinforced; its interior reconfigured. It has held corn, feed, tools, chickens, furniture, and been home to many birds.

Its plan:

A rectangle divided into 3 equal bays. The lengthwise framing in the larger space labeled 'corn' may have been flexible partitions. The tool and grain storage space has a low ceiling to allow more head room in the loft above it.




A cross section of the crib at the partition 

It is about 15 ft. wide at the base. Today its sill is about 24" above grade on the south end, 12" on the north.





Of course I was curious about the geometry. 

A corn crib was useful, and utilitarian. It served a purpose without frills. 

What was the simple, direct way to lay out its frame?


The floor plan: a rectangle with 4 corner posts and 4 evenly spaced intermediate posts. 

The dashed line shows the slope of the walls. The slope keeps rain off the corn. It's possible that the angle also keeps the cobs from locking in place. 

The slope was determined by a simple choice - see below*.


Today a carpenter would lay out the plan with a tape measure and a steel square. In 1810, these tools did not exist. Instead the carpenter used geometry.  

Here is the basic layout for a square as drawn by Audel in 1923.  This could have been used for the corn crib.

The layout using the geometry of a circle:

A-A is the width. Its arcs become the radius of the circle. They cross at the center of the circle. Then the circle is drawn with marks where 6 arcs cross the circle. 2 of the arcs cross at B and B: 2 at C and C.

 Draw 2 lines:  A-B and A-B. They are the sides of the  plan. 

2 intermediate posts are located at C and C, where the circle's arcs cross the lines A-B.

 Swing 2 more arcs from the corners of the plan: center of the arc on A, Then swing from the other A to C.  They cross the earlier arcs at D and D. The Line D, extended divides A-C in half and is the location of the next set of posts.

The arcs with their centers on both  D's, swung from the other D, locates E which marks the length of the  corn crib floor. (I drew only one.)

I can draw this layout much faster than I can write about it. Even so, it takes too long. I think a master carpenter would already know the geometry which I've laid out here and would have used short cuts.


He would have had a framing floor, probably in a barn.  

He would know the general plan. He and his client would have reviewed size and any needed variations. The work just  needed to be laid out. He would have used twine and awls, a chalk line to mark the lines on his framing floor. 

I  have drawn the chalk line set to both points, and a squiggle where the line is not held tight

A= the width of the corn crib, the ends of the rectangle.

Both sides need to be perpendicular to A: the 3/4/5 triangle  - B - sets the corner. The carpenter could then snap his Line - D - on both sides. Folding his Line -A- in half he could lay out 3 lengths along his Line, and then connect the 2 sides. The plan for the crib was done.


The plan could be easily 'trued' by checking that the diagonals of the whole rectangle, solid lines - E, as well as those for the 3 smaller rectangles, dashed lines - F, matched.




The elevation, here laid out with a compass.  




 Again, I think it would be easier to lay out the frame with a chalk line, using the width of the crib as the unit of the square.


The square and its diagonals.

Note that the diagonals cross at the location of the  beam that carries the loft. This is the first point.



2 points are necessary to draw a Line - or to snap a chalk line. The carpenter divided his Line in half, locating the vertical center line of the square.

The diagonals on the right half cross to give the carpenter his 2 points. He could locate the beam carrying the loft over the feed bins.






Next the carpenter needed to set the wall height. He added one diagonal on the left side; then the diagonals for the upper half of the square.

He had 2 more points whose Line (dashed here) located the plates for the side walls and the roof.



Finally he used half his unit (the width of the crib between walls) as the height to the ridge of his roof.  Here I have drawn it as an arc.






 * Now he was ready to layout the slope  for the walls.

A straight line (with arrows) from the outside of the sill at the bottom is on the inside of the plate at the top of the wall. This determines the slant of the walls.

I didn't discover this myself. Someone showed me. Unfortunately I don't remember who and can't give him credit. 




The 'front' of the corn crib today. We added a window, matching  one already in the crib.


The 'back' of the crib.

We moved the door to the 'back'  as we no longer unload from a wagon.

The hollyhocks self-seeded here. They approve of our work.



Post Script:  Images of the frame



Post, plates, and rafters in a corner of the crib





 3"x4" braces cut by a sash saw, pegged.





The original rafters are 3" x 4", cut by a sash saw.

Later logs were added between the rafters and butted together. Many of the logs are birch.



The rafters were mortised and tenoned at the ridge.The large peg is visible here.

Knob and tube wiring and electrical cable are still in place though today the crib has no electricity. 

At one point there was also telephone line.

Sunday, July 2, 2023

Stratford Hall, Part II: The Geometry of the Elevations

Stratford Hall, begun in 1736 - As visitors would have seen it when they came to the house from the plantation's docks on the Potomac River.


My first post on Stratford Hall* looked at the how the foundation plan was composed of 5 equal squares. The location of the central hall which runs between the chimneys was also shown to be sited by the circle that laid out the squares.

The Master Builder, William Walker,** seems to have used  the square as his geometry to layout the house.  Did he use the square for the rest of the plans and elevations?  I obviously think he did, but we have few notes, only his actual construction as proof.


Was the width of the chimney bases determined by those squares?

Probably. The exterior dimensions of the house foundation and the chimney bases would have been set at the same time. Here are the Lines which divide the width of the square into 4 parts: one part on each side for doorways, 2 parts in the middle for chimney masonry.  The Lines are not quite accurate: note the red lines with arrows. Perhaps this is because the masons who built fireplaces had different skills than those who laid brick walls and the dimensions were not as critical. 



 Note that these Lines, when I added them to the square based on the inside of the brick walls, give no useful information.



A brick wall can be measured from the outside or the inside.

 A garden wall needs 2 parallel Lines (twine) to be staked - one on each side of the wall - to guide the construction.

 A brick wall for a building would also have 2 Lines. The bricklayer, checking his Lines for a building layout must decide which side of the wall to use.




At Stratford Hall a square and its lines define the exterior dimensions; they sets the size of the wing from ground to ridge pole at the top of the square (A).  The third points (B) mark the height of the brick walls which is the location for the  plate for the roof trusses. 

The lines which divide the square into 4 equal section locate the width of the chimney stack - note where they cross (C) in the middle of the square.





The lines of the square, based on the width from the interior side of the brick walls, cross at the floor-to-floor height of the lower level (D). This dimension tells the mason where the joist pockets for the floor joists to carry the main floor should be located. 

The central space of the house is the Hall, the place to gather and entertain. See my previous post for floor plans.*

Here the square is based on the inside dimension: brick wall to brick wall, just as it was for the wings. 

The geometry of the wings (the drawing above) applies here too: the location of the main floor and the height of the walls is the same.

The ceiling of the Hall is vaulted: a tray ceiling, sloped on all 4 sides. The height of the ceiling is not arbitrary but is determined by the height of the walls. 

 A red line encloses the hall and its ceiling;

The scale on the right side shows the wall height divided into 4 parts. The height of the sloped part of the tray ceiling is 1 part.   

4 parts = wall height, 5 parts = floor to ceiling.  

The Master Builder could have used the floor of the hall as a framing floor for this ceiling, making the height simple to calculate. 

At this small size the diagram of the square and its lines gets messy. So I chose a different way to show the relationships. 


* My first post on Stratford Hall:

** For a biography of William Walker see He was a Scotsman, probably trained as a joiner and wright in Scotland, who immigrated to Virginia before 1730. He would have known of the work of James Gibbs and Colen Campbell. He might have known them.