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
