Catenary Arch

Part of Kiln Design

Building self-supporting catenary arch kilns — the strongest, most efficient arch form available without engineering calculations.

Why This Matters

A catenary curve is the shape a chain or rope makes when hung freely between two points. Invert that curve and you get the ideal arch — one where every point carries only compressive forces, with zero bending stress. This means a catenary arch is the strongest possible arch for its thickness, requires no buttressing, and exerts no outward thrust on its supporting walls.

For kiln builders, the catenary arch is the optimal design. It distributes heat evenly, resists thermal expansion better than any other shape, and can be built thinner than semicircular or pointed arches while carrying the same loads. Traditional kiln builders worldwide — from Japanese anagama to American salt kilns — have converged on this form through centuries of empirical optimization.

The profound advantage for rebuilding scenarios: you do not need to calculate stresses, angles, or thrust lines. Nature provides the template. Hang a chain, trace its shape, flip it upside down, and build. The physics of gravity ensures structural perfection.

Understanding the Catenary Curve

What Makes It Special

A semicircular arch concentrates bending stress at the haunches (lower sides) and crown (top), requiring thick construction and buttresses to prevent collapse. A catenary arch eliminates these stress concentrations entirely because the curve follows the natural path of gravitational force through the structure.

Property	Semicircular	Pointed (Gothic)	Catenary
Outward thrust at base	High	Moderate	Near zero
Bending stress	Present at haunches	Reduced	Zero (pure compression)
Wall thickness needed	Thick	Medium	Minimum
Buttressing required	Yes	Moderate	No
Heat distribution	Uneven (hot crown)	Better	Most even
Ease of construction	Moderate	Moderate	Simple (with chain template)

The Chain Method

The catenary curve is defined mathematically (y = a * cosh(x/a)), but you do not need mathematics. You need a chain.

1. Take a length of chain (or heavy rope, or beaded cord — anything that hangs freely under its own weight)
2. Hold both ends at the desired width apart and at the desired base height
3. The hanging shape IS the catenary curve for those proportions
4. Trace this curve onto a board or wall
5. Flip the tracing upside down — this is your arch profile

Different width-to-height ratios produce different curves:

• Narrow and tall (width = height): Chain held close together, deep sag. Produces a tall, narrow kiln — good for updraft designs.
• Wide and low (width = 2x height): Chain held far apart, shallow sag. Produces a wide, low kiln — good for large capacity.
• Equal proportions (width = 1.3x height): The most common kiln proportion, providing good capacity with reasonable height.

Choosing Proportions

For a general-purpose pottery kiln, start with an interior width of 30-36 inches (75-90 cm) and a height of 24-30 inches (60-75 cm). This accommodates standard pottery sizes while remaining manageable for a single builder. Adjust the chain hang until the shape looks right for your needs.

Building the Template

Chain-and-Board Template

This is the most reliable method for transferring the catenary curve to physical construction:

1. Obtain a flat board at least as wide as your kiln span and as tall as the rise. Plywood, a door, or planks laid side by side all work.
2. Drive two nails into the board at the points where the arch meets the supporting walls (the springing points). Space them at the desired interior kiln width.
3. Hang the chain from these nails. Adjust chain length until the lowest point of the sag gives your desired interior height. Add or remove chain links as needed.
4. Trace the chain onto the board with charcoal, chalk, or a pencil. Be precise — small errors compound over the full arch.
5. Flip the board upside down — the traced curve is now your arch template.
6. Cut along the curve with a saw if possible, or simply use the board as a visual reference during construction.

Making Multiple Templates

You need at least two identical templates — one for each end of the kiln. Cut them simultaneously:

1. Clamp two boards together
2. Trace and cut both at once, or
3. Use the first as a pattern to mark the second

If the kiln is long (barrel vault style), add intermediate templates every 18-24 inches (45-60 cm) along the length to prevent the arch from sagging between endpoints.

Wire Template

For a reusable guide during actual bricklaying:

1. Bend a heavy wire (8-10 gauge) to match the catenary curve
2. Mount it vertically at the center of the kiln on a post
3. Extend a string from each point on the wire to the corresponding course of bricks
4. The wire serves as a constant reference — rotate it as you work around the arch

Foundation and Walls

Floor Preparation

The kiln floor must be level and solid. An uneven floor means uneven wall heights, which means an asymmetric arch — and asymmetry destroys the catenary’s perfect stress distribution.

1. Excavate to stable soil or bedrock
2. Lay a foundation of flat stones or fired bricks, leveled with sand
3. Check level in all directions with a water level (a clear tube filled with water)

Supporting Walls

Catenary arches exert almost no outward thrust, so supporting walls can be thinner than for other arch types. However, they must be:

• Plumb — truly vertical. Lean creates asymmetric loading.
• Level — both walls exactly the same height at the spring line
• Strong enough for their own weight plus the arch weight above

A wall thickness of 9 inches (one brick length) is adequate for kilns up to 36 inches span. For larger kilns, use 13.5 inches (1.5 brick lengths).

Build walls to the spring line height — the point where the arch begins. For most catenary kilns, this is 12-18 inches (30-45 cm) above the kiln floor, though some designs start the arch directly from ground level (eliminating vertical walls entirely).

Constructing the Arch

Formwork Setup

1. Position the end templates at each end of the kiln, perfectly vertical and aligned
2. Brace them with temporary supports — they must not move during construction
3. Connect the templates across the top with flexible strips (lath, bamboo, bark) to create a continuous curved surface — this is the form the bricks rest on
4. Verify symmetry — measure from the centerline to the formwork at several points on each side. Both sides must be identical.

Brick Laying

For a catenary arch, standard rectangular bricks work well — because the curve is gentle and continuous, the taper needed at each joint is small and can be accommodated by varying mortar thickness. This is a significant advantage over semicircular arches where wedge bricks are often essential.

1. Start from both springers simultaneously — the first bricks on each side, resting on the supporting walls
2. Work upward from both sides equally — maintain symmetry at all times
3. Mortar joints: Slightly thicker on the outer face, thinner on the inner face. This provides the gradual taper that follows the curve.
4. Check each course against the template curve. Place a straightedge from the brick face to the nearest template — the gap should be consistent.
5. The keystone area: The top several bricks. In a catenary arch, the crown is narrower than in a semicircular arch, so the last bricks may need more pronounced wedging.

Brick Orientation

Lay bricks with their long axis running along the barrel length (perpendicular to the arch curve). This provides maximum structural depth with standard bricks. For the inner ring of a double-ring arch, bricks can be laid header-out (short face exposed) to follow tighter curves.

Course Bonding

Adjacent courses should be staggered (offset by half a brick length) to prevent continuous vertical joints. A continuous joint is a structural weakness — cracks propagate along it.

For barrel vaults, the bricks in each ring of the arch should also be offset from the ring below to create interlocking rings when building multiple layers.

Kiln Configuration Options

Updraft Catenary

The simplest configuration:

• Firebox at the front, below the ware chamber
• Single arch spans from wall to wall
• Chimney at the top rear
• Heat rises through the ware, exits through the top

Advantages: simple to build, easy to stoke. Disadvantages: uneven heating (bottom hotter than top).

Crossdraft Catenary

• Firebox on one side
• Flame path crosses horizontally through the ware chamber
• Exit flue on the opposite side
• Catenary arch spans perpendicular to the flame path

Advantages: more even heating than updraft. Disadvantages: slightly more complex construction.

Downdraft Catenary (Advanced)

• Firebox at the front
• Flame rises to the arch crown, then is deflected downward by a bagwall
• Exit flues in the floor lead to an external chimney
• The most even heating possible

Advantages: excellent heat distribution, fuel efficiency. Disadvantages: requires floor channels and external chimney.

Thermal Behavior

The catenary shape provides superior thermal performance for several reasons:

Even Heat Distribution

The curved interior has no sharp corners or flat surfaces where heat stagnates or where cold spots develop. Hot gases follow the curve smoothly, bathing all surfaces in relatively even temperature.

Thermal Expansion

All materials expand when heated. A semicircular arch develops stress concentrations at the haunches as the crown tries to expand outward. The catenary’s pure-compression geometry means expansion forces follow the same path as gravitational forces — they push bricks together rather than apart.

Reflective Heating

The curved ceiling reflects radiant heat from the fire back down onto the ware. The catenary’s narrowing crown concentrates this reflected heat more effectively than a broad semicircular dome.

First Firing: Curing the Kiln

A new kiln must be cured before full-temperature firing:

1. Day 1: Build a very small fire — enough to warm the interior to 200°F (95°C). Maintain for 4-6 hours. This drives moisture from mortar joints.
2. Day 2: Slightly larger fire, reaching 400-500°F (200-260°C). Hold for 4-6 hours.
3. Day 3: Moderate fire, reaching 800-1000°F (425-540°C). Hold for 3-4 hours.
4. Cool slowly after each session — 12+ hours before inspection.
5. Inspect after Day 3 cooling. Small cracks in mortar are normal and can be patched with fresh mortar before the next firing. Large cracks or displaced bricks indicate structural problems.

New Mortar Moisture

Freshly applied mortar contains significant water. If you patch cracks and immediately fire at full temperature, the patching mortar produces steam that blows the patch out. Allow patches to dry for at least 48 hours before the next firing.

After three curing fires, the kiln is ready for its first bisque firing at full temperature. The catenary arch, properly built, should survive hundreds of firing cycles before requiring significant repairs.

Scaling Up

The catenary arch scales well. For larger kilns:

• Increase wall thickness proportionally — 13.5 inches for spans over 36 inches, 18 inches for spans over 48 inches
• Use double-ring construction for spans over 30 inches
• Extend the barrel length rather than increasing span for more capacity — the arch strength does not decrease with length
• Add intermediate supports (cross-walls or pillars) for barrel lengths over 6 feet (1.8 m) to prevent the long barrel from sagging under its own weight between endpoints