Catenary Curve Calculator
About Catenary Curves
A catenary curve is the natural shape that a hanging chain or cable takes under its own weight.
Formula:
y = a cosh(x/a) + b
where:
a = T₀/(ρg)
b = y₁ - a cosh(x₁/a)
T₀ = horizontal tension
ρ = linear density
g = gravitational acceleration
y = a cosh(x/a) + b
where:
a = T₀/(ρg)
b = y₁ - a cosh(x₁/a)
T₀ = horizontal tension
ρ = linear density
g = gravitational acceleration
Properties:
- Natural shape of hanging chains
- Minimum potential energy
- Constant tension along the curve
- Used in architecture and engineering
Applications:
- Suspension bridges
- Power lines
- Architectural design
- Chain analysis
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