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IEVref:466-03-13ID:
Language:enStatus: 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=ρ( cosh X ρ 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmGadiWaaiWabaabaiaafaaake aacaWGzbGaeyypa0JaeqyWdi3aaeWaaeaaciGGJbGaai4Baiaacoha caGGObWaaSaaaeaacaWGybaabaGaeqyWdihaaiabgkHiTiaaigdaai aawIcacaGLPaaaaaa@46CE@

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

Y= 1 2ρ X 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmGadiWaaiWabaabaiaafaaake aacaWGzbGaeyypa0ZaaSaaaeaacaaIXaaabaGaaGOmaiabeg8aYbaa caWGybWaaWbaaSqabeaacaaIYaaaaaaa@407E@

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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