Bulges in Classical Pillars: How Big? Formulae?

Factual Questions
1

Classical pillars did not have straight and vertical sides - they bulged in the middle so that when viewed they would appear to be straight and vertical to an observer. This is much like the old “which line is longer?” optical illusion with <-> or >-< as choices.

Is there a formula, which would presumably take both height and diameter into account, for how big the bulge should be half-way up the pillar? Is the bulge, in fact, at its maximum size half-way up or is it, perhaps, somewhat higher? Also, the sides are not two straight lines forming a shallow “V” - is there a formula for the curve they follow?

Failing formulae (and it’s a bit of a stretch to assume one in classical times) is there a rule of thumb?

2

I don’t know about a formula. But I read in car magazine a few years ago that Roll-Royce grilles are not straight for the very same reason. According to this site it is done by hand, with no measuring instruments. Other than that I have no idea, but here’s my guess:
Possibly the mere fact that the pillars a bulged, thereby breaking up the outline, defeats the optical illusion?

3

Sorry, I meant to type a car magazine, not the British mag. I think what I read was in Automobile Magazine.

4

G’day

I’m sorry, but different architects used different proportions for the entasis. It is a matter of taste rather than of formula. And the entasis tends to be more marked in Doric Order buildings than in Ionian Order or Corinthian Order.

The only real constant is that the curve is elliptical, and that is a result of the method used to draw the ‘plans’.

My grandfather was an architect, one of the associates of Sir Edwin Lutjens who did the detailed designs for public buildings in New Delhi. He used to use bulges that had their widest point at eye level (which was sometimes below the base, if you get what I mean).

Regards,
Agback

5

Hey, I just learnt a new word! Thank you, Agback! :slight_smile:

Using my wonderful new word, I was able to find some commentary at this site, but still no formulae!

I recognize that there’s a lot of subjectivity and variation, but surely some analysis has been done somewhere … ‘an ellipse with foci in these general areas with that range of eccentricity’, or whatever.

6

Yeah, entasis varies-- You’ll note that it is much more pronounced (almost comical-- it’s really visible at the Temple of Hera (the “basilica”) at Paestum, which kind of argues against a "fixing an optical illusion’ theory in favor of a ‘aesthetic taste’ theory) in early Doric but gets more subtle during the high Classic (Hera at Paestum has 5x the distortion of the Parthenon, say), but then gets exaggerated again after the 5th c (BC, duh). I really don’t think there is much of a formula-- it just tapers more gradually at the bottom than at the top-- your results will vary.
Actually, the Egyptians did something like this, too, but when they use it the column tapers at both the top AND bottom (so the greatest diameter is somewhere in the middle), while the Greeks just taper their columns more strongly as they rise (but the ‘bulge’ is never actually a greater diameter than the base of the column-- I think this answers part of your question, actually).
The Greeks did other tinkering with architectural proportions-- “stretching the metope” where the last column on each end was shifted inwards a tad, and the “curved stylobate” where the base of the building sort of sloped, higher in the middle like a road is built.

7
      • There is at least one book on collected works of an ancient Greek or Roman architect, I have seen it on the shelves in bookstores but I cannot remember its name. From the looks of it, it’s a pretty good bet. I may visit tonight, I’ll look for it if I do…
        ~
8

Doug C.-- it’s probably Vitruvius, a Roman guy who wrote about Greek stuff too (he mostly guessed, I think) and who was published in the Renaissance.

9

Okay, bail me out here. How would a bulge in the middle make it look straight. I would expect a flair at the top to make it look straight. Or perhaps a concave shape in the middle. If I’m staring at the middle (eye level) of a column it would naturally look bulged out, than five feet below and five feet above.

10

Oversimplified answer-- a tall straight sided column looks to the eye slightly concave-- thin in the middle-- so the suggestion has been made that this was done as an optical corrective. For a similar reason they tilted their columns inwards slightly so they wouldn’t appear to be bowing out and dangerously looming.

To problematize this idea-- sometimes they exaggerated this corrective to the point that it overcompensates and gets really obvious, and thus seems to be purely aesthetic.

11

Some books you should read about this subject:
“The Four Books of Architecture” by Andrea Palladio
“The Gentleman and Cabinetmaker’s Director” by Thomas Chippendale (Bow down and worship! Mortal. :D)
“The Ten Books of Architecture” by Vitruvius
“The Lost Meaning of classical Architecture” by George Hersey

I just looked up those books in my collection, and here’s what I found. I don’t have much time, so I’ll keep this short. E-mail me if you want more. I will post again with more detail if you request.

Palladio is very cavalier. I’m shocked, actually.
I’m quoting Chapter XIII of the first book: (And I can’t resist doing that 18th century f thing.)

*The method I ufe in making the profile of the fwellings is this; I divide the fuft *(tuft?) *of the column into three equal parts, and leave the lower part perpendicular; to the fide of the extremity of which I apply the edge of a thin rule, of the fame length, or a little longer than the column, and bend that part which reaches from the third part upwards, until the end touches the point of the dimunition of the upper part of the column under the collarino *(the necking BTW).I then mark as that curve directs, which gives the column a kind of fwelling in the middle, and makes it project very gracefully.

Chippendale (Again, you must bow!) has rules.
He explicitly details formulae.
Most are “picture worth a thousand words” variety, hence the lack of a Forbinpost on the topic. Essentially the column is divided into parts, those parts divided, and a “module” thus arrived at. Said module is then used , to fet off all the moldings for this order."

Hersey is an interesting fellow. It’s difficult to summarize his theories in one post, but he takes a rather scholarly approach to classical architecture. On page 58 of his book he says that the swelling of the column is meant to represent the human form. Quoting from Vitruvius, Book 3, Chapter 3, Verse 13, he expounds on the use of the word entasis. According to Hersey, entasis “means tension, straining, exertion and can refer to the human body”
As I have said, the book is too complex for me to detail in one post, but the reader is encouraged to look for similarities between columns and caryatids.

Oh curses!
I can’t find Vitruvious.

I’ve built them (columns) before. Most I build without entasis, but I did do one paneled room with pilasters that had entasis. That was twenty years ago, but I think I used Palladio’s (non) technique.

Will post more if you want more.
Ciao,
Forbin

12

Great posts, capybara and Forbin!

I have just ordered the Chippendale and Hersey books … in the face of such enthusiasm, how could I resist? I already have the Vitruvius book, bought as a result of Tales of the Ancient Engineers: How did they do it?.

13

(of OP…)

Minor point, but Vitruvius is not generally accepted as being any sort of authority on Roman (or Greek) Architecture. He just happens to be only of the very few authors to have his work survive to modern times. (Whish is, BTW, available as text here.)
In fact, there is little to show he knew anything about what he wrote, and was any more that an educated layman with an interest.

His value was on describing / laying out the 5 orders of columns in detail, as shown here.. (picture here)

14

The Formula for Entasis according to Thomas Chippendale…

I looked at “The Director” after I replied to this thread, and I’ll report what I found with regard to entasis. I will have to define some terms along the way, and paint a word picture, so bear with me. I am also going to simplify things a bit. There is more to learn from the book, but this is entasis in a nutshell.

The example I will use is the Tuscan Order.

The height of the column for any given application is seven diameters. This proportion is probably more commonly worked in reverse, i.e. a height of seven feet requiring a column would indicate a column of one-foot diameter.

Chippendale, like Palladio divides the column into three equal parts, leaving the shaft full dimension for the bottom third. He then goes on to state that the column “is diminifhed one-fifth of its semi-diameter on each side”

Now I will describe the illustration that details how the job is done:

A line segment is resting horizontally on the page. This segment represents the column diameter, and a semicircle is drawn above it, using the center of the segment for the centerpoint of the compass.
A segment representing the top two-thirds of the column perpendicularly bisects the horizontal segment.
One half of the horizontal segment, or one radius, is divided equally into five parts.
A vertical line is drawn from the fourth interval along the horizontal segment up to the top of the column indicating the minimum dimension of the column. This vertical line crosses the semicircle at (about) forty-five degrees.
The (approximately) forty-five degrees of the semicircle between the aforementioned intersection and the endpoint of the horizontal segment is divided equally into four parts. The column height is also equally divided into four parts. (Remember that the column height illustrated is only the top two-thirds. I think the number of divisions is arbitrary, and Mr. Chippendale has chosen to divide each column third into two parts.)
Vertical lines are drawn from each of these divisions to the corresponding division on the column thereby giving the artisan a point at the intersection of the lines.
The entasis is plotted to these points.
Mr.Chippendale does not illustrate the entasis method for the other orders, but does describe the parameters in the text.

For the Doric Order he says, “The column diminifhes one-sixth of it’s semi-diameter on each side, from one third part of its height, to the top of the capital”

For the Ionick Order he says, " The column diminifhes one-sixth of it’s semi-diameter on each side, from one third part of its height"

For the Corinthian Order he says, “The other dimenfions are as in the Ionick order.”

For the Composite Order he says, " The column diminifhes one-sixth of its semi-diameter on each side, from one third part of it’s height"

I have included the quaint eighteenth century spelling which excludes the possessive apostrophe.

15

Thank you Forbin for your help - it is really most appreciated!

A friend - who has very limited internet access, and whose conversation with me triggered my interest - writes:

*At the Library today I looked up the Temple of Hera in Italy, and indeed it has very cigar-shaped pillars. Barely reliable measurements off a photo indicate full diameter of 37 units to half height, then entasizing to 28 at the top: total length of 169 units,making them surprisingly squat and an obvious template for my Cuban cigars.

76 per cent of top to middle diameter is very low! and probably triggered one of your correspondent’s diatribe against the Roman treatment of Greek art. “Units” just refer to divisions on my scale. In fact,they could represent inches (possibly).*