Pipe Deformation Calculator

Circumference Conservation

This calculator is based on the principle that when a circular pipe is deformed into an elliptical shape, the circumference (perimeter) must remain constant, assuming no material stretching or compression.

Original Circle: C = πd (where d is the diameter)

Ramanujan's Ellipse Perimeter Approximation

For the deformed elliptical shape, we use the highly accurate approximation developed by mathematician Srinivasa Ramanujan:

Where a and b are the semi-major and semi-minor axes of the ellipse.

This approximation is accurate to within 0.5% for all ellipse eccentricities and provides an excellent balance between computational efficiency and precision.

Calculation Process

1. Calculate original pipe circumference: C = πd
2. For given target width, use binary search to find minimum height where Ramanujan's perimeter equals original circumference
3. Compare minimum achievable height with required height
4. Calculate margin and deformation percentage
5. Issue warning if deformation exceeds 30% (potential material failure threshold)