Drafting a Persian Karbandi vault involves projecting a planar compass-divided star polygon into three-dimensional parabolic space. The perimeter base of the room is circumscribed by a circle subdivided into n equal sectors, establishing the 'Pa-kar' (springing points). Interlacing arch chords bridge across specified intervals (skipping 1, 2, or 3 points). Where these chords intersect in plan and elevation, they define 'Sar-kar' spatial nodes, producing mathematically rigid, self-supporting spatial geometries.
At a Glance: Key Takeaways
- Arch Geometry: Five-centered Persian pointed arch (Panj-o-Haft arch)
- Base Angular Division: θ = 360° / N (where N = 12, 16, 20, 24)
- Chord Chord Jump Rule: Jump factor k (typically k = 3 or 4 points)
- Drafting Medium: Traditional gypsum-plaster drafting floor (Gach-kary floor)
Full-Scale Drafting on the Gach Plaster Drawing Floor
Historically, Iranian master builders did not work from small paper blueprints. Complex three-dimensional vaults were drawn full-scale (1:1 ratio) directly onto a smooth, whitewashed gypsum plaster floor (Zamin-e Gach-kary) poured specifically for the project.
Using oversized wooden beam compasses (pargar-e choobi) with iron scribing spikes and chalked cords, the Ostad scribed the exact perimeter walls, diagonals, and concentric reference circles. This planar drawing served as the direct template for fabricating wooden arch guides and pre-assembling complex decorative tiles.
Calculating Pa-Kar Points and Chord Jump Modules
The perimeter springing points—the Pa-kar—are determined by dividing the inscribed circle of the room into an even integer of sectors (N). For a standard 16-point Karbandi, the central angle is precisely 22.5 degrees (360° / 16).
The structural character of the vault is dictated by the jump factor (k)—the number of Pa-kar points each arch rib skips before touching the opposite wall. In a 16-point system, jumping 5 points produces a broad, low-rise dome with wide central skylight opening; jumping 7 points creates steep, dramatic cathedral-like ribs meeting near the vault apex.
Sar-Kar Coordinate Calculation and 3D Node Intersection
Where two planar arch trajectories intersect in plan view, a Sar-kar node is established. However, because both arch ribs follow vertical curves—most commonly the classical Persian five-centered pointed arch (Panj-o-Haft)—the true height of the Sar-kar node must be determined by vertical projection.
By rotating the arch profiles into elevation, the builder calculates the exact Z-axis elevation of every intersection point. When the masonry ribs are erected, the physical bricks must meet at this exact coordinate, locking both arches in mutual compressive support and preventing lateral buckling.
Facet Decomposition: Shaprak, Simi, and Pabarik Geometries
The interlacing rib skeleton naturally subdivides the interior dome surface into distinct geometric facets. The lowest triangular zones abutting the wall are known as Pabarik (narrow foot facets); the intermediate kite-shaped concave panels are Simi; and the uppermost triangular infills flanking the crown are Shaprak (butterfly wings).
Because every category of facet repeats symmetrically around the vault perimeter, artisans could pre-cut brick infill courses and glazed tile mosaics in identical modular sets, speeding construction and guaranteeing visual symmetry.
Karbandi Geometric Parameter & Chord Jump Matrix
Use this reference table to calculate exact physical dimensions, ratios, and specifications before purchasing:
| Total Pa-Kar (N) | Sector Angle (θ) | Standard Jump (k) | Apex Oculus Shape | Number of Sar-Kar Nodes |
|---|---|---|---|---|
| 12 Points | 30.0° | Jump 4 points | Hexagonal oculus | 12 intersection nodes |
| 16 Points | 22.5° | Jump 5 points | Octagonal oculus | 24 intersection nodes |
| 20 Points | 18.0° | Jump 7 points | Decagonal oculus | 40 intersection nodes |
| 24 Points | 15.0° | Jump 8 points | Dodecagonal oculus | 60 intersection nodes |
Practical Constraints
Every successful decoration project must account for physical and environmental constraints:
Wall Rectangularity Tolerances in Vernacular Masonry
Real-world rooms are rarely perfect squares; builders must adjust compass radii along elliptical axes to avoid asymmetric corner gaps.
Complex 3D Curve Fabrication for Tile Mosaics
Glazed tile panels must be curved in two planes to fit concave Shaprak infill facets, requiring custom clay formers.
Execution Blueprint & Craftsmanship Sequence
Execute this professional sequence to achieve flawless results without backtracking:
Gypsum Drafting Slab Preparation
Pour a smooth 15mm level gypsum plaster layer over a designated workshop floor area; allow to cure to a clean white chalkboard finish.
Chamber Dimensioning and Axis Scribing
Scribe orthogonal centerlines (X and Y axes) through the chamber center; draw the inscribed circle tangent to all four perimeter walls.
Radial Circle Division (Pa-Kar Mapping)
Using a beam compass, bisect quadrants into 16 equal 22.5-degree sectors, scribing sharp coordinate lines to define all Pa-kar points.
Chord Layout and Intersection Mapping
Snap chalk lines connecting each Pa-kar point across the selected jump interval (k=5), marking planar intersection nodes (Sar-kar).
Elevation Profile Projection (Panj-o-Haft)
Draw the true elevation curve of the Persian pointed arch, projecting Z-height coordinates for every Sar-kar intersection point.
Facet Template Extraction
Trace individual Pabarik, Simi, and Shaprak facet shapes onto timber boards to create cutting templates for brick and tile masons.
Common Mistakes & Countermeasures
Avoid these costly errors that compromise aesthetics, ergonomics, and budget:
Drafting on Uneven or Out-of-Level Floors
Using Semicircular Instead of Pointed Arch Profiles
Project Execution Checklist
Track your physical progress. Checkboxes persist automatically on this device:
Frequently Asked Questions
What is the 'Panj-o-Haft' arch used in Persian Karbandi?
Panj-o-Haft (literally 'Five and Seven') is a classical Persian pointed arch constructed using five radius centers based on an equilateral triangle proportion, renowned for high load capacity and low lateral thrust.
Can Karbandi vaults be drafted using modern CAD software?
Yes. Modern heritage architects model Karbandi networks in 3D parametric software (such as Rhino/Grasshopper), verifying structural stress distributions with finite element analysis before cutting restoration components.
