Thursday, March 16, 2006

Jefferson's Wall, Take Two

Thomas Jefferson famously incorporated serpentine walls into the architecture of the University of Virginia. Although on some accounts he invented that design—Wikipedia, for instance, calls them "uniquely Jeffersonian"—it in fact appears that he at best improved on the "crinkle-crankle" walls that he had admired in England. We can at least give Jefferson credit for boldness in borrowing good ideas. The serpentine wall economizes on bricks despite its meandering path because, in contrast to a straight wall, it can be made merely one brick thick. A straight wall so thin would topple easily, whereas the curves of a serpentine wall help it to resist lateral forces. You can see Jefferson's design in his own hand, here.

I've come up with a variation on the serpentine wall used by Jefferson, one that improves that original in several ways. Jefferson's serpentine wall has vertical faces throughout its length. I propose, in contrast, a wall that leans in from a wide base towards a narrow top. In other words, the base of my wall would follow a larger amplitude sine curve than would its top. (The base and top curves would run in phase.) Here's a sketch.

Why do I propose that design? Three reasons: Compared to Jefferson's wall, my design would 1) further economize on materials; 2) look more interesting and attractive; and 3) make the wall still more resistant to lateral forces.

The first point needs little elaboration. If the top of the wall follows a less wending line than the base, it will use less material. I cannot really prove the second point; it speaks to matters of taste. I will observe, though, that my wall at least offers the aesthetic virtues of originality.

The third point perhaps needs explaining. Jefferson's design has this virtue: The wall as a whole offers greater resistance to lateral forces than a conventional, straight wall does. Note, though, that individual portions of Jefferson's design may under-perform a conventional wall. Consider his wall not as a whole, but segments of arc length pi/2. (Why consider wall segments? Because masonry walls prove stronger in compression than tension, meaning they may pull apart under lateral forces.)

A short segment of Jefferson's wall offers improved strength only to lateral forces applied toward the convex sides of the wall's curves. To lateral forces applied to the concave sides of its curves, it offers even less resistance than a conventional, straight wall. My wall, in contrast, would offer increased resistance to lateral forces applied at both convex and concave points. I'll skip an engineering analysis, since the reasons should be apparent on reflection. Don't get it? Try thinking about how a force pressing against a inward-leaning section of my wall would have to lift the bricks to displace them.

That said, I recognize that my design presents some challenges. For one thing, it would probably require a specially-designed foundation, one canted at various angles at various points. For another thing, my wall would call for some complicated masonry—not the usual regular, vertical sort. Portions would lean, making brick-laying a challenge. It would help to lay the vertical portions first and then build the portions in between, as you would an arch.

A last challenge: Because the arc length of the wall would be shorter at its top than at its bottom, alternate courses of uniform brick would not line up neatly, with one row's divisions centered on the adjoining rows' bricks. That admits various cures. You could leave wider spaces between the lowest bricks, for instance, leaving the masonry complicated but not impossible. Or your could use something other than masonry, such as flexible chain link, overlapping boards, or poured concrete.

Would those problems, taken together, render my version of a serpentine wall wholly infeasible? I don't think so, but I cannot say that I know. I'd love to have a demo of my design built, to see how it works in practice. Toward that end, I'm running the idea past the architect working on our current remodeling project. He'll probably talk me out if it, the sensible fellow. Maybe I should, like Jefferson, start my own university. Institutions of higher learning seem to like nutty architecture.

dgm said...

...and there goes the neighborhood.

at the very least, this design should earn us a series of anonymous postcards from that villain known only as "landscaping man."

i kid! i kid because i love.

Tom W. Bell said...

Yeah, yeah. I bet the Canadians said the same thing about Jefferson's Declaration of Independence. "Can you believe what they're building next door? An independent nation! There go our property values, down the loo. Isn't there a zoning regulation forbidding that sort of thing?"

Glen Whitman said...

Cool. You should totally patent that. I mean, uh, buy up all those "someone improves serpentine masonry" futures before the word gets out.

But seriously, I think it's a neat idea. I'm pretty sure I have a good picture of it in my head from the verbal description, but I'm not a draftsman, so your diagrams didn't help much. Maybe a better key for the meanings of the colors would have clarified things.

Tom W. Bell said...

I suppose I *could* patent it, Glen, supposing their no prior art that gets in the way. I've poked around and found nothing. Well, anyhow, now that I've published that blog post, I have one year to file a patent.

I'm glad you can picture it, and can only apologize that I didn't do a better job of sketching it out. I drew those plans for our architect, who undoubtedly knows how to decipher plans drafted in the standard the FRONT/TOP/SIDE format. I really should just make a wee model and photograph it.

The colors, by the way, are simply sections--vertical slices through the wall, designed to help reveal its structure. They bring out, in particular, the fact that the structure of the wall creates a series of arches. That'll get you bonus points for strength.

Gavin said...

You may be way ahead of me but I was thinking about a way to build your wall. If you imagine a flat circular disk. Now cut out a concentric disk within the first one. You have a flat donut shape. Now make a radial cut across the donut. Start bending the outer edge into a sepentine curve. Eventually you will have a nearly plane surface which can rest on the ground. The inner edge will tend towards a straight line. I tried this with a piece of paper which was unsatisfactory but seemed to confirm my concept.

Tom W. Bell said...

My thinking, exactly, Gavin! But you remain ahead of me in execution; I've not gotten around to trying. I intuit two problems (hardly insurmountable, but still notable): 1) Figuring out the arc lengths of the sine curves; and 2) Fixing in place the bottom of the wall.

Regarding 1), it turns out that the calculus for deriving the arc length of a sine curve has been done already--see the Mathematica site, for instance. It's not a pretty integral, but it'll do. Also, Jefferson used a clever hack--see the notes I linked to.

Regarding 2), I suppose it ought to suffice to run a string from end to end, connecting at each vertical portion of the wall. That should save the trouble of, say, carving a sine curve into a foam base.

Jim Donovan said...

This may be only a Hawaii answer as to how this thing might be built. Lay out foundation framing using a rectangle that is 3 feet wide and the length of the wall.

Use landscaping benderboard to build meandering 2.5 foot wide base in which the S-shape repeats itself every 14 feet.

When pouring the concrete base, insert 6-foor high pieces of rebar along center of base spaces according to for added strength, tie 6-foor high metal mesh to vertical rebar pieces.

Using a'a - the rugged-looking lava rock (or other natural material - outside of Hawaii), the base of the wall would be made by placing football-sized pieces along both sides of the 2.5 foot wide, S-shaped foundation. Fill interior cavity with concrete.

Using a template (perhaps made of 2x4 lumber) shaped like the legs of a sawhorse, a second layer of lava rocks would be placed on top of the first layer, slightly narrower in depth, where additional concrete would then be poured.

The process would continue until the top of the wall (only about 0.75 feet across) would be made of smaller lava rocks, the entire wall perhaps capped off with pahoehoe (the smooth-finish lava).

The process of building the wall might be made easier if the A-frame template is made of two pieces, connected by a curved piece that conforms with the curvature of the wall.

Another thought is to bolster the frame with common chicken wire. This would faclitate adding smaller lava rocks without the concern of them falling into the cavity of the wall prior to the pouring of the concrete.

Anonymous said...

You are one arrogant SOB. Why not rewrite the Declaration of Independence, re-design the Taj Mahal, and send out blank Christmas cards?

Anonymous

roger said...

I would run it past an engineer and then see if you can sell the idea. Maybe you can make a few bucks for it.

stuart
my political forum