**Hexagonal Groin Vault**

**Barrel** profile following a **Catenary**

*Formulas for Slope and Arc Length*

*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°

*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)

*Values produced by tracing the Integration Graph ...*

*Development of Vault Surface*

*3D Models** of ***Section**

extracted from **Hexagonal Vault**

*Plan View*

*Oblique View*

Equation of Barrel ... *y* = cosh (*x*/2) – 1

Width = 10 ... – 5 ≤ *x* ≤ 5

Rise = 5.132289

*Side View of Valley Arch*

Equation of Valley ... *y* = cosh (*x*/4) – 1

Run = 10 ... 0 ≤ *x* ≤ 10

Rise = 5.132289

*Back View of Valley Arches*