📐 Cylinder-Plane Intersection Calculator
PLANE ② (pink)
PIVOT ZX (common)
🔥 WELD SEAM
376.99 mm
10.47 mm
| N° | θ | X (mm) | Y₁ (mm) | Y₂ (mm) | Y (mm) | Plan |
|---|
🎮 3D View (drag to rotate)
📐 Flat Pattern Development
📖 Formulas (Triouleyre)
1. Parametric cylinder
x = R · cos(θ)y = R · sin(θ)
Ex DN100: R = 57.15 mm
θ = 90° → x = 0, y = 57.15
θ = 90° → x = 0, y = 57.15
2. Plane equation
z = y · tan(A) + x · tan(C)
A = inclination (rotation X)
C = ZX pivot (rotation Y)
Ex: A=30°, C=10°
z = y × 0.577 + x × 0.176
C = ZX pivot (rotation Y)
Ex: A=30°, C=10°
z = y × 0.577 + x × 0.176
3. 3D intersection curve
z = R · sin(θ) · tan(A) + R · cos(θ) · tan(C)
Ex: R=57.15, A=30°, C=0°
θ=0° → z = 0 + 57.15×0 = 0
θ=90° → z = 57.15×0.577 = 32.99
θ=180° → z = 0 + 0 = 0
θ=270° → z = -57.15×0.577 = -32.99
θ=0° → z = 0 + 57.15×0 = 0
θ=90° → z = 57.15×0.577 = 32.99
θ=180° → z = 0 + 0 = 0
θ=270° → z = -57.15×0.577 = -32.99
4. Development (flat pattern)
X = R · θ (arc length)Y = z + H (cut height)
Circumference: 2πR
DN100: C = 2π × 57.15 = 359.02 mm
H = height below Z=0
DN100: C = 2π × 57.15 = 359.02 mm
H = height below Z=0
5. Plane ② with Z offset
z₂ = y · tan(B) + x · tan(C) + Zoffset
B = plane 2 inclination
Zoffset = vertical offset
Zoffset = vertical offset
6. Resultant cutting curve
Yres = max(Y₁, Y₂)
Keep the highest point
between both planes for each θ
● = plane 1 active
● = plane 2 active
between both planes for each θ
● = plane 1 active
● = plane 2 active
7. Characteristic points
θ = 0° (weld) → generator 0θ = 90° → high point (A>0)
θ = 180° → opposite weld
θ = 270° → low point (A>0)
Reference
J. Triouleyre"Sheet Metal Layout
for Boilermaking & Piping"
Delagrave Publisher