Hexagonal Groin Vault
Barrel profile following a Catenary


Formulas for Slope and Arc Length
Catenary Formulas

Graph of Barrel and Valley Curves
Equations of Tangent Lines at y = 3
produced with the
WZ Function Grapher created by Walter Zorn

At equal heights, y ...
Valley Slope = Barrel Slope sin Plan Angle
Example ... .96825 = 1.93649 sin 30

Graphs of Barrel and Valley Curves, and Equations of Tangents at y = 3

Development of Barrel and Valley Arches

Development of Barrel and Valley Arches

Integration Graph produced with the
WZ Function Grapher created by Walter Zorn

x = station measured from zero (barrel center)
y = arc length measured from zero (barrel center)

WZ Function Grapher ... Integration Graph
Values produced by tracing the Integration Graph ...
Dimensioned Development of Vault Surface
Development of Vault Surface

Development of Vault Surface

3D Models of Section
extracted from Hexagonal Vault



Plan View

3D Model ... Plan View

Oblique View
Equation of Barrel ... y = cosh (x/2) 1
Width = 10 ... 5 ≤ x ≤ 5
Rise = 5.132289


3D Model ... Oblique View

Side View of Valley Arch
Equation of Valley ... y = cosh (x/4) 1
Run = 10 ... 0 ≤ x ≤ 10
Rise = 5.132289


3D Model ... Side View of Valley Arch

Back View of Valley Arches

3D Model ... Back View of Valley Arches

Joe Bartok