IEVref: | 466-03-13 | ID: | |

Language: | en | Status: Standard | |

Term: | catenary | ||

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Definition: | shape of the curve assumed by a perfectly flexible, inextensible cord suspended at its ends, and given by the equation: $Y=\rho \left(\mathrm{cosh}\frac{X}{\rho}-1\right)$
Note 1 to entry: In practice, the simple parabola is often used $Y=\frac{1}{2\rho}{X}^{2}$ which represents the first two terms of the series expansion of the equation of the catenary. Note 2 to entry: The catenary curve represents a cable with constant weight per unit of length of curve, while the parabola represents a wire with a constant weight per horizontal unit of length. The sag calculated by the parabolic equation is smaller than that calculated by the catenary equation. For long spans or for very sloping spans the parabolic approximation can introduce unacceptable errors. | ||

Publication date: | 1990-10 | ||

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Internal notes: | 2016-03-21: Editorial corrections: Y and X corrected to italic, 2nd sentence transferred to a note to entry, and current note renumbered. See correspondence RS and JS. JGO 2017-06-02: Cleanup - Remove Attached Image 466-03-131.gif 2017-06-02: Cleanup - Remove Attached Image 466-03-132.gif | ||

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$Y=\rho \left(\mathrm{cosh}\frac{X}{\rho}-1\right)$

Note 1 to entry: In practice, the simple parabola is often used

$Y=\frac{1}{2\rho}{X}^{2}$

which represents the first two terms of the series expansion of the equation of the catenary.

Note 2 to entry: The catenary curve represents a cable with constant weight per unit of length of curve, while the parabola represents a wire with a constant weight per horizontal unit of length. The sag calculated by the parabolic equation is smaller than that calculated by the catenary equation. For long spans or for very sloping spans the parabolic approximation can introduce unacceptable errors.