Home: Catenary Applet

instructions

 A catenary is the curve assumed by a hanging chain or cable under its own weight when supported only at its ends. "The equation was obtained by Leibniz, Huygens, and Johann Bernoulli in 1691 in response to a challenge by Jakob Bernoulli." (Wolfram MathWorld) From length L of the chain and width W (distance of suspensions) the parameter a can be calculated by an iteration. The catenary sag h is the vertical difference of the lowest point of the chain Check a radio button to set the points A, B, or C (intermediate). µ is the mass per length of the chain (kg / m). Input for the ratio of length L and width AB (L>W). Having changed µ or L/W press button "Apply input". Step to change the ratio L/W.   Use the buttons (+) or (-) to apply the selected step ∆(L/W) to increase or decrease the ratio L/W, or use the keys. The radius r of curvature at the lowest point of the chain is r = a. ---

The curve below
h/(L-W) vs. L/W
does not depend on W:

Exemples:

for W=400 and L/W=1,2 (L=480, L-W=80, a=187.817):
h=116.9 and h/(L-W)=1.46

for W=600 and L/W=1,2 (L=720, L-W=120, a=281.725):
h=175.4 and h/(L-W)=1.46

for W=800 and L/W=1,2 (L=960, L-W=160, a=375.633):
h=233.9 and h/(L-W)=1.46 ---

A simple iteration:  double solveA(double L, double W) {                double x, y;         double A=0;         for (int a=0; a<=50000; a++) {             x = a;             y = 2.0*x*Math.sinh(0.5*W/x);             if (y

 Web Links Catenary (Wikipedia) Catenary (Wolfram MathWorld) The Catenary (J. B. Calvert) Cable’s Sag & Tension Calculation Tension on the ends of a cable suspended at different heights Microsoft Word - educated-monkey.doc

2017  J. Giesen

updated: 2017, Sep 29

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