Enter the Octagon (II)

In my previous post in this series, I took a look at octagonal bay window bump outs and how they might be configured. I also mentioned the matter of octagonal construction in general and the popularization of the octagonal house in the US in the mid 1800's, following the publication of Orson Fowler's The Octagon House: A Home For All, or A New, Cheap, Convenient, and Superior Mode of Building - shortly thereafter reissued as A Home for All, or the Gravel Wall and Octagon Mode of Building. This work was re-issued by Dover in 1973 as The Octagon House, A Home for All, a copy of which I have just finished reading. The cover:

It seems that Fowler's considerable enthusiasm for octagonal building was quite infectious in its day, and more than 1000 octagonal homes were built in the US and Canada, along with octagonal barns, carriage houses, even churches and schoolhouses. Of the survivors, most of them exist in right here in the state of Massachusetts, and I plan to start checking them out when I can. In fact, there's one right here in the town where I live, though I hadn't noticed it so far on my travels.

Octagonal buildings were hardly new on the scene - for example, many octagonal one-room schoolhouses were constructed in Pennsylvania in the first half of the 19th century, like this one:

Thomas Jefferson's summer residence, Poplar Forest, near Lynchburg, Virginia is another example of an octagonal house that predates Fowler's work:

What Jefferson envisioned and created (he was in his 60's at the time) was a classical villa in the ideal of Palladio; the final result is a combination of Renaissance, Palladian, and eighteenth century French with a smattering of British and American elements. Such mish-mashes are not uncommon at all in US architectural history. I had noticed references to Fowler's book in various other places over the years, including most recently in the book Architecture, Men Women and Money in America 1600-1850, written by Roger Kennedy, the director of the Smithsonian's museum of American history. Unlike many other accounts, Kennedy did not poke fun at Fowler and suggested his work had something to offer. So I took a look, and I'm glad I did.

What surprised me the most, coming in with slightly low expectations, was how persuasive I found Fowler's argument for octagonal construction. I'm now a believer!


Besides the octagon form itself, Fowler argues for what were at the time unusual amenities, such as dumbwaiters, speaking tubes, central heating and water closets -- also known as indoor toilets. Fowler believed that houses should be well ventilated and let in lots of natural light, for the physical and emotional health of their inhabitants. I doubt most of those features, or Fowler's philosophy of building in that regard would incur argument from anyone today. And I for one wish that dumbwaiters would make a comeback - that, and laundry chutes!


I'd like to summarize though the essence of Fowler's advocation for the octagonal form, an argument which emphasizes its economy. When you get down to it, the primary considerations in residential construction, after site, style, and materials, are the costs of construction on a square foot basis. Ideally, one would think, one would like to obtain a given squre footage with a minimum expenditure of materials, or, for a given amount of material obtain the most square footage - two sides of the same coin.

The intent of Fowler's book is to demonstrate a way of building for all, that is, a form of construction which was more affordable. The reasons why an octagonal form of structure might be more affordable may not be apparent at first, so I'd like to take a closer look.


We can build houses in a wide variety of plans, however, in North America at least, the most prevalent form is the rectangle. A typical suburban house, might be, say, 24' on one side, by 44' on another:

Two obvious facts: the square footage you get for that is 24 x 44, or 1056 square feet. The wall length required is (2 x 24) + (2 x 44) = 48 + 88 = 136 linear feet. 136 linear feet of wall, sill, plate, sheathing, plaster, baseboard, etc., looked at simplistically (ignoring the thickness of the wall, interior partitioning, etc.).

The interesting point is that the more pronouncedly the house becomes rectangular, the longer the wall required to enclose the same amount of interior square footage. Let's say, for example, the house was only 12' wide on the short end of the building, which would make for a long side measuring 88'. Same square footage (12 x 88 = 1056), but the length of wall required is now (12 + 12) + (88 + 88) = (24 +176) = 200' 


If dollars and cents, yen, or pesos, etc., mean something to you, it would appear that designing long rectangular houses, or houses which stretch out by means of wings and staggered jogs, is not a good direction to go.

Let's consider that same amount of square footage, 1056,  going the other direction of plan, namely in the case of a house which is perfectly square. To obtain the measure of the side of the house, we take the square root of 1056, which I will approximate to 32.5:

Same 1056 square feet obtained, however the total length of wall, foundation, exterior sheathing etc., requires (4 x 32'-6"), 130 linear feet. So, just in shifting around the plan configuration, I have saved some 6' total in wall.

That may not seem particularly dramatic, so let's look at it another way. Given the 136 linear feet of wall we obtained with the 24' x 48' rectangular plan, we could configure a square plan with the same total length of wall, namely 136 / 4 = 34' per wall section: 

If we look to see what sort of square footage we obtain, we find 34 x 34 = 1156 sq.ft., a gain of 100 square feet, just by changing the plan configuration. A 100 sq.ft. of floor area is quite a gain, more or less equal to adding an extra room in the house if one so desired.

Now let's take a look at an octagon plan and compare. Given a perimeter of 136 linear feet, and dividing by 8 sides, we obtain a figure with sides measuring 17':

How many square feet do we get for the same 136 linear feet of wall? The formula, which I won't spend time looking at in detail in this post is:

The side, s,  measures 17, and 17 x17  = 289. Therefore:


Area = 2(289)(2.414213) = 1395.4

So, an octagonal configuration of the same wall length increases interior square footage from 1056 to 1395 or so, some 1.3 times greater! Compared to a square plan, which yielded 1156 square feet, the octagon gives about 20% more square footage. That's significant!

Now I'm not arguing for building larger homes (as Fowler in fact does), but if one can obtain a given desired square footage and economize with the same exact materials one would be using otherwise, then I can't see any disadvantage to that.


One might wonder what the consequences of other shapes of floor plans might be. It turned out that the most efficient shape for maximizing area with a minimum measure of perimeter is the circle. It's no surprise that nature chooses this form, and the spheroid forms which develop from it for so many storage devices, like seed pods, eggs and so forth. Another aspect of the circular form is that the minimum of material can cover the greatest amount of square footage - hence the reason why the circular pizza makes the most use of a given amount of dough, and allows the fewest toppings to go the furthest as well.


To obtain a square footage of 1056 sq.ft. in a circular plan, we would need a radius of 18.3 feet:
 

The total length of wall required is only 115.19, quite a savings over the 136 feet required in the original 24' x 48' rectangular example we started with.

Considered another way, if we wanted to work with the same 136 lineal feet of wall in a circular plan, we would obtain a circle with a diameter of (136 / π) = 43.29' or so. Taking half this measure (21.645') as the radius, and using the good ole' "pi x r-squared" formula from grade school, we obtain an area of π (468.509) = 1471.86 square feet. That's some 40% greater interior space for the same wall length as compared to the rectangle we looked at first. So, clearly, the circular form is the most bang for the buck in terms of wringing square footage out of a plan.

That said, the circular form is not terribly practical for building unless you are talking about tipis, yurts, or igloos, etc. Working with timbers generally tends toward working with the grain in the material, which generally runs straight in the timbers we obtain building materials from (the softwood species). Cutting circular sections from straight timbers is obviously wasteful and trying to obtain trees bowed in the right radii and then working with them involves other challenges in the way. Or one could laminate up circular wall sills and plates, cut from plywood and glue up, etc. Those challenges generally add up to dollars and cents in the end, especially if you are trying to work with commercially available materials. Then, add to that the issue of windows and doors, which are not easy to make to fit curved walls, along with plastering, finishing, and furnishing the interior of a circular dwelling with modern appurtenances (none of which are round), and you can see further hassles ahead. It's not a practical form for wooden construction, generally speaking.

With polygons, the more sides you have the closer one gets to a circular outcome, however when you look at the choices, the octagon really is the most convenient. All carpenters are familiar with working with 45˚ and 22.5˚ angles, for one thing, so the lay out and cutting is not a significant challenge, excepting the roof work. A hexagon is not as efficient at converting wall measure to square footage as compared to an octagons, but the 30˚-60˚-90˚ triangle associated to a hexagon is straightforward to employ. A heptagon, one of my favorite polygonal forms, has an odd angular value integral to it (360 / 7 = 51.428571..., with the .428571... repeating infinitely), and the nonagon with 40˚ and 140˚ angles, offers no significant advantages. Same for the decagon. Polygons with more facets than an octagon, while becoming more efficient in producing interior space, trade back the advantage in the greater number of angled and mitered cuts of all the wall and roof materials to obtain the result. A zero-sum game it would seem.

In the next post in this series I'll take a look at octagonal buildings in more detail, east and west, and consider some of the aesthetic and practical issues which associate to these forms.

Thanks for coming by the Carpentry Way. Comments always welcome.