Spirals in architecture

published 4th March 2024 I STARTING OUT,

PORTFOLIO

One of the more challenging tasks that you will come across as a draughtsperson in the art department is the geometric construction of a spiral.

Your research on this topic might lead you down a rabbit hole including mathematical spiral functions, the Fibonacci sequence and ancient Greece.

This post sets out to give you the fundamentals you’ll need to know to handle spirals in your design work.

We’ll cover:

Spirals as architectural ornaments
Different types of spirals and their construction methods
The archetype of the spiral in architecture
Construction methods in Ancient Greece
The spiral during the Renaissance
A step-by-step guide to laying out a spiral with the Salviati method
Spirals generated by CAD drawing software
The Fibonacci spiral and the Golden ratio

1. Spirals as architectural ornament

Spirals form the basis for many decorative elements in architecture.

You can find them in column capitals, corbels and consoles, ironwork and as the underlying framework for the acanthus leaf.

So if you are in the business of drawing architecture – whatever the purpose may be – you will come across the challenge of laying out a spiral on your drawing board.

I certainly did and found that there is very little hands-on advise on how to do it accurately.

When I reached out to my teachers and colleagues I got all kinds of advise:

From copying the spiral from an existing reference to drawing it freehand and “just winging it”.

It took a little digging and googling to get to a geometric construction method that worked and created the shape I needed.

My findings are summarised in the following paragraphs.

2. Different types of spirals and their construction methods

When you start researching spirals you will come across a multitude of spiral types and about a dozen construction methods (yes, I’ve tried them all).

What’s important to understand is that as draughtsmen we are usually only interested in one specific type of spiral (more on that later).

The majority of spirals that have their application in math and engineering (i.e. logarithmic, hyperbolic, parabolic, etc.) are not relevant for architectural drawing because they simply have the ‘wrong’ shape.

The same applies to construction methods.

Most of them, especially the simplified 2-point, 4- point and 6-point methods, won’t generate a real spiral.

They instead create a little swirl in the eye of the spiral and then produce connected, concentric circles with a stable increase in the radius from turn to turn.

That makes these spirals unsuitable for the purposes of the draughtsman because they don’t reflect the form of the spirals we see in all architectural ornaments.

3. The archetype of the spiral in architecture

But what is the optimal spiral, you might ask?

To answer this question, it’s worth going all the way back to where it all started:

With the Greeks and the Romans and the volute in the column capital of the Ionic order. It’s sort of the archetype of the spiral in architecture.

You might find other spiral in architecture, but if the style or period you are working on is based on the ancient Greek, Classicism or Renaissance, the spirals you see will be very close or identical with the one in the Ionic volute.

4. Construction methods in ancient Greece

If the spiral in the Ionic column capital is the archetype, it seems natural to ask how the Greeks and Romans laid it out.

Unfortunately, no complete instructions survived that would describe the geometric construction of the Ionic volute.

We do, however, have some information about the proportions and positioning of the volute.

Vitruvius, a Roman architect and engineer, wrote about it in his extensive work titled ‘De archictura’ in the 1st century BC.

Vitruvius describes the spiral of the Ionic volute as*

Starting at a point immediately under the abacus
Winding in a series of turns until it joins the eye
The centre of the eye is located on a vertical line parallel to the cathetus

Vitruvius also gives us some proportions for the Ionic spiral

The total height of the volute is 8 units
Diameter of the eye is 1 unit
Above the centre of the eye is 4 1/2 units
Below the centre of the eye is 3 1/2 units

That’s a good start, but far from being a step-by-step tutorial on how to get a spiral on you drawing board.

Luckily, some of our colleagues in the renaissance had the same problem.

5. The spiral during the Renaissance

In the 1500s, when the classic architecture of the ancient Greek was rediscovered and became the new benchmark, several methods were developed and documented for the geometric construction of the spiral of the Ionic volute.

Three of the most popular and publized methods were:

6 centre points and semi-circular arcs by Sebastiano Serlio (1537)
12 centre points and quarter-circle arcs of Guiseppe Salviati (1552)
12 centre points and qurter-circle arcs with a different method for determining the center points

If you are interested in how the three methods compare and how they differ, I highly recommend the paper by Denise Andrey and Mirko Galli about the ‘Geometric Methods of the 1500s for laying out the ionic volute’.

I read it, compared the methods and their results and decided to stick to the Salviati method, because it is the closest to Vitruvius’ description of how the spiral of the volute was constructed in antiquity using quarter-circle arcs and it’s the most practical for the construction on a drawing board.

By the way: If someone mentions Andrea di Pietro della Gondola or Andrea Palladio in this context. The method he describes in his ‘The 4 Books of Architecture’ (1570) is identical with the Salviati method.

6. A step-by-step guide to laying out a spiral with the Salviati method

There are several key parameters you need to keep in mind when working with the Salviati method:

The resulting spiral will have three full turns before reaching the eye
The full length is 8 units
The OD of the eye is 1 unit
The centre point of the eye sits 4,5 units from the top end of the spiral and 3,5 units from the bottom end of the spiral

Step 1:

So once you defined size of your spiral and the position of the eye you will need to draw a vertical line and divide the overall length by 8, and mark the centre point for your eye at 4,5 from the top end.

Step 2:

Draw a circle around the centre with the radius of 1/2 unit – this will be the eye of your spiral.

Step 3:

Draw a vertical and horizontal line through the centre point and connect the intersections with the circle of the eye thereby creating a square (rotated by 90 degrees, also referred to as diamond).

Step 4:

Draw two lines bisecting the sides of the diamond by using your setting square (45 degrees) and running the line through the centre point of the circle

Step 5:

Divide each line into 6 equal parts creating 12 points overall.

Step 6:

Number the points with 1 to 12 by

Starting at the top left corner and going clockwise if you want your spiral to go clockwise

Starting at the top right corner and going counter clockwise if you want your spiral to go counter clockwise

Step 7:

Draw a horizontal line from point 2 to the right hand side with the approximate length of 5 units (this is just a construction line that is needed in step 8).

Step 8:

Use point 1 as a centre point for your compass and the top point of your initial 8 unit long line as the radius to draw a quarter-circle arc until you reach the horizontal construction line constructed in step 7.

Step 9:

Repeat steps 7 and 8 moving from point 1 to 12 and using the horizontal and vertical construction lines from the respective next point to define the end point of the quarter-circle arc.

7. Spirals generated by CAD drawing software

That’s many steps and a seemingly complicated process.

Surely, CAD programs should be able to help us with that?

Unfortunately, I haven’t found a command in AutoCAD or Rhino that creates a spiral that resembles the one in the Ionic volute.

The mathematical formula used to generate the spirals in CAD software creates spirals that have the ‘wrong’ shape.

There might be an option to change the underlying math somewhere, but I wasn’t able to uncover it in my research.

So for now, it’s best to construct the spirals using the method above and copy them into your drawings if you draw using a CAD software.

8. The Fibonacci spiral and the Golden ratio

You now know the most important things about spirals for architectural drawing.

Still one other spiral deserves at least a quick mention when it comes to architecture and proportions.

The Fibonacci spiral that defines the proportions for the golden ratio.

You will probably hear both terms numerous times during your career.

The most important thing to know is that the spiral divides lengths in a proportion of 1 to 1,618.

This proportion seems to be very pleasing to the human eye and is therefore used throughout architecture, art and design.

The Fibonacci spiral is, however, not suitable as the basis for the Ionic volute.

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