# Sovereignty Module: Raise the Arch

## Complete Arch and Vault Construction: From Brick to Span

The arch is one of humanity's greatest structural inventions, spanning openings that flat beams cannot. This campaign covers arch types, centering, construction, and vault building.

### Chapter 1: Arch Types

| Type | Shape | Span Ratio | Strength | Difficulty | Historical Period |
|---|---|---|---|---|---|
| Round (Roman) | Semicircle | Height = 1/2 span | Very high | Moderate | Roman, 500 BCE+ |
| Segmental | Arc less than semicircle | Height < 1/2 span | High | Moderate | Medieval+ |
| Pointed (Gothic) | Two arcs meeting at point | Variable | Very high | Moderate-high | Gothic, 1100+ |
| Flat (jack arch) | Nearly flat with slight rise | Height = 1/20 span | Moderate | High | All periods |
| Parabolic | Parabola | Variable | Very high | High | Modern |
| Corbelled | Stepped overhang | Variable | Moderate | Low | Ancient, 3000 BCE+ |

### Chapter 2: Centering (Formwork)

Centering construction: 1) Centering is the temporary wooden form that supports the arch during construction. 2) Build two identical curved ribs from lumber (cut to arch profile). 3) Connect ribs with cross pieces (spacers at arch width). 4) Cover top surface with thin boards or plywood (lagging). 5) Support centering on posts or wedges at correct height. 6) Centering must be strong enough to support all bricks until keystone is placed. 7) After keystone is placed and mortar cures, remove centering. 8) Remove by knocking out wedges (centering drops slightly, separates from arch).

| Component | Material | Purpose | Specification |
|---|---|---|---|
| Ribs | 2x lumber, cut to curve | Define arch shape | Two per arch, match arch profile |
| Lagging | Thin boards or plywood | Support bricks during laying | Cover top of ribs |
| Cross pieces | 2x lumber | Space ribs at arch width | Same width as wall |
| Support posts | 4x4 or timber | Hold centering at correct height | Plumb, on solid base |
| Wedges | Wood wedges | Allow centering removal | Under support posts |

### Chapter 3: Brick Arch Construction

Round arch construction: 1) Build wall to spring line (where arch begins). 2) Set centering in place at correct height. 3) Verify centering is level and at correct span. 4) Begin laying bricks from both sides simultaneously. 5) Bricks radiate from center point (all joints point to center of circle). 6) Use tapered mortar joints (wider on outside, thinner on inside). 7) Or use tapered bricks (voussoirs) for uniform joints. 8) Work from both sides toward the top. 9) Place keystone (center brick at top) last. 10) Keystone locks the arch and transfers load to both sides. 11) Allow mortar to cure 7 days minimum. 12) Remove centering by knocking out wedges.

| Principle | Rule | Why |
|---|---|---|
| Radial joints | All joints point to arch center | Even load distribution |
| Symmetrical loading | Build both sides equally | Prevents centering from tipping |
| Keystone last | Center stone placed last | Locks arch, transfers all loads |
| Mortar cure before striking | Wait 7+ days | Mortar must reach strength before centering removal |
| Adequate abutment | Walls beside arch must be thick enough | Arch pushes outward (thrust); walls must resist |

### Chapter 4: Vault Construction

| Vault Type | Shape | Complexity | Span | Best For |
|---|---|---|---|---|
| Barrel vault | Extended arch (tunnel) | Moderate | Up to 20 feet | Cellars, tunnels, long rooms |
| Groin vault | Two barrel vaults crossing | High | Up to 20 feet | Square rooms, intersections |
| Ribbed vault | Ribs at edges, thin fill | Very high | Up to 40 feet | Large spaces, Gothic |
| Dome | Rotated arch | High | Up to 30 feet | Round rooms, cisterns |
| Catalan vault (tile vault) | Thin tile layers | Moderate | Up to 15 feet | Floors, roofs, stairs |

Barrel vault: 1) Build two parallel walls to desired height. 2) Set centering (full-length arch form) between walls. 3) Lay bricks in arched courses from one end to the other. 4) Each course is a complete arch. 5) Courses stack from one end of vault to the other. 6) Backfill above vault with rubble and earth. 7) Remove centering after mortar cures.

### Chapter 5: Structural Principles

| Force | Direction | Resistance | Design Response |
|---|---|---|---|
| Compression | Along arch curve | Stone/brick are strong in compression | Arch works entirely in compression |
| Thrust | Outward at base (horizontal) | Thick walls, buttresses, tie rods | Abutments must resist outward push |
| Dead load | Downward (gravity) | Arch transfers to abutments | Arch converts vertical load to diagonal |
| Live load | Variable (people, wind, snow) | Distributed through arch | Symmetrical loading is ideal |

### Reference Card

1. The keystone locks the arch (the center stone at the top of the arch is placed last; it wedges between the two halves and transfers all loads to the abutments). 2. All joints point to the center (every mortar joint in a round arch radiates from the center point of the circle; this ensures even compression throughout the arch). 3. Build both sides equally (laying bricks from both sides simultaneously keeps the centering balanced; loading one side causes the centering to tip). 4. The arch works in compression (stone and brick are strong in compression but weak in tension; the arch shape converts all loads into compression, which is why arches can span great distances). 5. Thrust pushes outward (an arch pushes outward at its base; the walls or buttresses beside the arch must be thick and heavy enough to resist this outward thrust). 6. Wait before removing centering (mortar must cure for at least 7 days before the centering is removed; premature removal causes the arch to collapse). 7. A corbelled arch is the simplest (each course of brick or stone overhangs the one below until the two sides meet; it requires no centering but spans less distance than a true arch). 8. The arch enabled civilization (without the arch, buildings were limited to the span of a single beam; the arch allowed Romans to build aqueducts, bridges, and buildings that still stand 2,000 years later).