Catenary cable tension calculator. Calculates angles and forces at the supports.
Catenary cable tension calculator. Subject A Catenary is the natural curve generated by a cable or chain (with zero bending stiffness and infinite axial stiffness) when strung between two fixed points. The sag is inversely proportional to the catenary constant ie a large catenary constant represents a taut cable. The calculator simplifies Catenary curves find applications in many fields, so it's worth learning about them. That will give us the exact value for the tension. The curve effect resembles a flexible chain suspended by its ends with gravity acted upon it. The document is organized by first describing the underlying theory of the catenary curve and then explaining how practically this is handled within the O-Calc Mar 5, 2012 · Actually, that is not the equation of a catenary. Calculator for a catenary with a point load applied between its ends. Example, a Apr 9, 2025 · Calculate the length of a hanging cable (catenary) with precise formulas and derivations for practical physics and engineering applications. The document describes how to solve problems involving catenary cables using a set of formulas. is the sag of the cable. Jan 1, 2020 · Catenary calculations only apply to chains and cables that have infinite axial stiffness and negligible bending stiffness. Start with the desired sag, d and calculate T (cable) for the non-iced condition. However, there is a MUCH easier way to calculate this value! If you notice, the Θ value is extremely small due to the large difference between the length and sag. This information is fundamental for various engineering applications. STEVCAT ® software is a catenary calculator, for calculation and plotting of relevant properties of the catenary for use in pre-lay operations, rig mooring, towing and marine operations. This document provides instructions for calculating the sag and tension of an overhead conductor using the catenary equation. Calculates displacement cable sag based on the equation of a catenary curve. We also discuss Jan 27, 2020 · I've done numerous catenary cable spans, usually with points loads (traffic signals) along the span, but I never was too concerned about the vertical loads - just the horizontal force and cable tension, which are much larger due to the small sag, and the primary source of stress in the poles supporting the cable span. This is helpful in situations of shallow water depth when the catenary runs the risk of fouling by dragging on sea-bed due to high sag. The example will show specifically how to use Goal Seek for finding roots of equations in Excel. Jul 21, 2020 · Plotting the Catenary Curve Once we have all the inputs with us, we can use the catenary equations provided above to plot the catenary of the towline at any given tension T 0. Learn how catenary curve and parabola are different. Compute the length of a suspension bridge cable with given anchor points and vertical displacement The sag of a cable is influenced by factors such as the tension applied, the weight of the cable, and external loads. The catenary curve has a U-like shape, superficially similar in appearance to a parabola , which it is not. 2. Click the buttons to increase or decrease the Catenary Coefficient, C. I am suspending a 1/8 steel cable horizontally The shape of a curve that a cable assumes when kept hanging at two ends, supported by its own weight is known as catenary arch. Working Tension - (Measured in Kilogram) - Working Tension is the gravitational force, weight, acting on a hanging cable causes tension to exist. It includes the specifications of a 795 kcmil "Condor" conductor and inputs for initial and final loading conditions. This information is essential for designing stable and safe structures like suspension bridges and power lines. Perfect for structural engineers, architects, and professionals working with suspension bridges, cables, hanging chains, and tension analysis. s = cable length = 2 * x * May 16, 2017 · Catenary equations describe the relationships between the span length (distance between the structures), the cable length (the length of the cable along the curve), the cable tension, cable weight, and cable sag (how far the cable droops down in the middle between the two attachment points. The SkyCiv Cable Sag Calculator (or Cable Deflection Calculator) helps you to determine the prestress forces required to reach a certain cable sag given a particular cable setup. Learn how to calculate cable sag error in electrical or telecommunication cables with our cable sag error calculator. Cables are tension-only and they often exhibit large displacements and non-linear behavior. The article presents a detailed look at how to use the catenary equations to calculate the configuration and sag of a towline. 74 kN. Aug 19, 2017 · Thanks for reading, hopefully I am posting my first question in the correct area of the forum! I will list as many details as I have in hopes that someone will know how to calculate the amount of sag I will have and tension/force there will be. It also lists the equations used to calculate the catenary curve shape, sag, clearance, length, and tensions. Download from: Catenary. Catenary Cable Tension Calculator in Excel In this post, you’ll learn how to create a catenary cable tension calculator in Excel by solving an implicit equation. Jun 10, 2024 · Conclusion The Catenary Calculator is a valuable tool for engineers and designers working with hanging cables or chains. The sag of the conductor, D, is Cable Span - (Measured in Meter) - Cable Span is total length of cable in horizontal direction. This online graphing calculator helps you to graph a catenary curve with the given sag value, length and increment value. Sag in general words can be said that distance between the highest point of electric poles or towers and the lowest point of a conductor connected between two poles or towers. Feb 14, 2025 · A catenary calculator facilitates this process by providing accurate tension estimations based on cable properties, span, and sag. Tension is calculated using the Aug 21, 2023 · Learn how to calculate cable force with our online calculator. O-Calc Pro Sag Tension Calculations Explained O-Calc® Pro Sag Tension Calculations Explained This document is a primer that explains how O-Calc® Pro software system handles the tension and sags on cables that are attached to a pole. The sag increases with horizontal tension and decreases with cable weight per unit length, elevation difference and span. Keep reading to learn: What a catenary curve is; The catenary curve equation; Applications of the catenary curve in architecture; Where to find the catenary curve in nature; and How to use our catenary curve calculator. Get accurate results for cable systems, bridges, and more, using reliable catenary equations between two points for engineering projects. Nov 4, 2008 · This file will help solve catenary cable problems. I give a list of equations to solve for the unknowns including the Catenary Cable Tension in Excel - Solve an Implicit Equation with Goal Seek EngineerExcel 7K subscribers Subscribed Oct 28, 2022 · The tension at any point given catenary length of simple cable with udl is defined as total force acting on the supports in both horizontal and vertical direction is calculated using tension at. Jun 25, 2009 · Following on from the previous post, here is an Excel User Defined Function (UDF) to calculate the coordinates of any specified catenary, with the option of also finding the tension force at any point. Aug 7, 2024 · A catenary curve describes the shape of a flexible chain or cable that hangs between two points under its own weight and is acted upon by gravity. Whether evaluating line clearances, structure design loads, or providing section stringing information to construction, sag-tension calculations must be performed. By providing quick and accurate computations, it enhances the efficiency of structural designs in various industries. You will know how to calculate sag and sag formula. Abstract The catenary is the curve in which a uniform chain or cable hangs freely under the force of gravity from two supports. Estimate d for the added weight of ice. It then works through two example problems. Oct 14, 2024 · Decoration: Layout catenary curves in artistic endeavors. T = S + c = 150 + 12 = 162 kg 1. Jun 29, 2025 · The Catenary Curve Calculator helps determine vertical coordinates in catenary curves using the mathematical formula y=a×cosh (x/a). The calculator below can be used for cables with inclined chords and uniformly loads. We generally see a lot of overhead lines on our way. Includes catenary curve, conductor length, effects of temperature, ice, and wind. Given the length of suspended cable, L, and the horizontal distance between the supports, H, it is possible to calculate the amount of cable sag, h, and the Forces: Total rope weight: [ kg ] or Rope weight per meter: [ kg / m ] or Load per meter: [ N / m ] Jul 28, 2003 · I need to know the worst-case sag for a wire when it is strung at a known design tension/% breaking strength. Cables are used in suspension bridges, tension leg offshore platforms, transmission lines, and several other engineering applications. The cable will form in the shape of a catenary. Provides tensions and dimensions and a graphical image of the results (technical-help) Dec 17, 2021 · Sag-tension calculations are a significant aspect of transmission line design. The below calculator is an easy-to-use tool that will calculate the following values based on user input: In this post, you’ll learn how to create a catenary cable tension calculator in Excel by solving an implicit equation. Tension at Supports - (Measured in Newton) - Tension at Supports is the tension due to loading on supports. g. Whilst the theory used for the analysis of a Catenary is strictly valid for cables with zero bending stiffness and infinite axial stiffness, you can also use it to obtain approximate configurations in cables that exhibit a Wire Sag and Tension Calculator Click on the Calculate button in the table below, and a graph will appear for 3 cable examples. Determine the cable length for a 100-meter span with a uniform load and given horizontal tension. Apr 16, 2024 · CATENARY FUNCTION "TRANSMISSION LINE" The shape of a catenary is a function of the conductor weight per unit length, w, and the horizontal component of tension, H. For a cable with no wind and no ice, the catenary constant is the ratio of horizontal tension to unit mass of the cable. 3. It finds the sag is 31. Calculate T (ice), deflection of each post and cable stretch due to ice. Its shape is a catenary curve. The curve has a specific mathematical form and is relevant in various engineering and architectural applications, such as the design of suspension bridges and overhead power lines. The calculation of conductor at an equal level shown below. 2) the vertical force (fy). The tutorial covers how sag and tension are affected by various factors and outlines important references for sag-tension calculations. researchgate. The example will show specifically May 21, 2019 · I know the distance between points, and the length of the cable between them, how can I calculate the sag? How to solve this eqn for x = f(s,d)? since I know both s and d. For spans of the order of 300 meters and less, the sag and tension calculation can be carried out by parabolic formula with sufficient degree of accuracy. Even though the shape looks similar to a parabola, the shape is actually defined by a hyperbolic cosine function. If one end of the chain is fixed, and the other is looped over a smooth peg, equation 18. . The chain (cable) curve is catenary that minimizes the potential energy Subject A catenary is the natural shape of a cable or cord with zero bending stiffness and infinite axial stiffness, the properties of which are fully described in CalQlata's technical help page for the Catenary calculator. Sag and tension calculations for cable and wire spans using catenary formulas. This calculator uses SkyCiv's powerful FEA technology to iteratively work through different prestress forces to determine the required force for a particular sag or cable deflection. Apr 9, 2025 · Calculate cable tension with proven formulas, step-by-step guides, and practical tips to ensure safe, efficient, and reliable structural performance. Should be simple but my cable is inclined and I need to find the tension in each leg of the cable as a function of the load's position. Refer to the technical help page for the downloadable version of this calculator for additional assistance. So, what do you know about sag? What is Sag? Sep 15, 2024 · Catenary Curve Calculator The Catenary Curve Calculator helps determine the shape and properties of a catenary curve, which is the curve formed by a hanging chain or cable when supported at its ends and acted upon by gravity. It is common to perform sag-tension calculations using the horizontal tension component, but the average of the horizontal and support point tension is usually listed in the output. For best performance, choose points on the catenary as far apart as possible. However, cables can resist only axial Jan 1, 2015 · Sag and Tension: Sag is an interesting topic to discuss. This calculator is a practical tool for determining the vertical position of a point on a catenary curve, making it useful for engineers and designers dealing with structures involving cables or flexible Nov 5, 2024 · The Catenary Equation Calculator is a specialized tool used to determine the shape of a hanging cable or chain under its own weight. The calculator is based on an iterative algorithm where the parable shaped cable is adapted to span L, height h1 and h2 according the figure above. A parabolic cable carries a horizontally distributed load. Cables are an important and efficient structural element that need special consideration during design. The tension has a vertical and horizontal component, and is tangent to the catenary. net Nov 4, 2008 · Description Dl is the distance from the low pole to the low point of the catenary curve. 9 shows that the loosely hanging vertical portion of the chain just reaches the directrix of the catenary, and the tension at the peg is equal to the weight of the vertical portion. Thus, cables are considered highly efficient structural components, and one of the most economical ways to span a large distance is employing a cable system. Source: www. Oct 3, 2024 · a a depends on the physical characteristics of the cable or chain, including its mass per unit length and the force of gravity acting on it. For relatively short spans with small sags, the difference in weight distribution is generally negligible. Tension is calculated as 931,450. I believe the formula is a catenary but am unsure how to apply it to my The analysis of catenary cables is presented through a detailed example that explores the calculations necessary for determining maximum tension, sag, and the geometric relationships between cable lengths and supports. 2 Conductor Length Application of calculus to the catenary equation allows the calculation of the conductor length, L (x), measured along the conductor from Tension at any Point given Catenary Length of Simple Cable with UDL calculator uses Tension at Supports = sqrt((Midspan Tension^2)+(Uniformly Distributed Load*Cable Span)^2) to calculate the Tension at Supports, The Tension at any Point given Catenary Length of Simple Cable with UDL formula is defined as the total force acting on the supports in both horizontal and vertical directions. Use any consistent units for length and weight, e. 14. It discusses key concepts like the catenary curve, ruling span, conductor weight changes from ice and temperature, and tension limits. feet and pounds to enter cable parameters, Calculator for the forces and dimensions at any point along the length of a tight or loose catenary configuration (technical-help) The Catenary Equation Calculator offers a practical solution for engineers and designers grappling with the complexities of catenary curves. Catenary Catenary is idealized shape of chain or cable hanging under its weight with the fixed end points. Catenary equations of several terms are used in computer programs where greater accuracy is desired. The calculator might then reveal the height of the lowest cable point and the tension at the supports. Find the catenary length for a power line with specific weight per unit length and known sag. The second example determines the length of a cable supported at two Oct 14, 2022 · A catenary curve is the shape that a cable, wire, or chain makes when it is suspended by its ends under the force of gravity. Sep 25, 2024 · Dive deep into the sag-tension calculation process, explaining how factors such as conductor stress-strain behavior, weather conditions and the catenary equation interact to determine the optimal tension and sag for transmission lines. Oct 11, 2000 · Don't get caught with a half-installed cable because you forgot to calculate the pulling tension. Nov 6, 2012 · I've been searching for a way to calculate the tension in a cable assuming catenary configuration due to two vertical point loads, each at the third point of the span. This document provides an overview of sag-tension calculations for overhead power lines. Follow the step-by-step tutorial with examples Use the Line Sag Calculator to determine the sag, tension, and deflection of a suspended line or cable. The Catenary is idealized shape of chain or cable hanging under its weight with the fixed end points. By inputting the horizontal span and sag, the calculator provides the catenary constant and the vertical positions along the curve. Calculates angles and forces at the supports. 48 lbs. f is the vertical distance from chord joining the support points to the point where the load P is applied. The document describes using the Excel GOALSEEK command to solve the cubic equation and calculate the final horizontal tension. The parabolic equation is used for the great majority of the manual sag and tension calculations for distribution lines. The catenary constant determines the shape of the catenary. The general equation of the catenary curve in Cartesian coordinates is as follows 1: Thus, equation 5 can be evaluated at the cable start (x=0) and the cable end (x=Δx) to calculate the tension at each support. Enter span length, material properties, and temperature change to get results. The example problem calculates these values for a Feb 12, 2024 · How to model catenary cables in SkyCiv Structural 3D Cables are a special type of member that can only be analyzed via a Non-Linear Analysis. To use this online calculator for Tension at any Point given Catenary Length of Simple Cable with UDL, enter Midspan Tension (Tm), Uniformly Distributed Load (q) & Cable Span (Lspan) and hit the calculate button. A point load, applied in any direction anywhere along the length of a single catenary will automatically generate two completely separate catenaries between the original Jan 26, 2025 · Key formulas for sag and tension calculations in overhead power lines. Calculation Reference Catenary Cables Nov 25, 2006 · Calculates displacement cable sag based on the equation of a catenary curve. Jan 24, 2012 · Hi all! I have an odd question that i thought somebody with a degree could help with. A guess of the tension may help close on a solution. It provides definitions for key concepts like the catenary curve, sag point, and tensions. The cable length from sag and span is the total length of the cable between its endpoints, considering the sag and the horizontal span between the supports. Mar 9, 2008 · I am looking for a formula to calculate the deflection(sag) in steel wire that is supported between two points with a known tension. Jan 29, 2008 · Description PURPOSE: Analysis of cable sag with supports at the same vertical level. I am looking to find the formula to describe wire sag over a given length and given horizontal tension and given wire diameter. Example Scenarios Utilizing the Catenary Curve Calculator For instance, suppose you input a span (x) of 50 meters between two poles and a cable weight (y) per unit length of 2 kg/m. The first example calculates the sag and maximum tension in an electric power line suspended between two towers. Nov 21, 2024 · Easily calculate catenary curves, sag, and tension with our Catenary Equation Calculator. The chain (cable) curve is catenary that minimizes the potential energy Jul 21, 2020 · In this week’s Tuesday article update, we’re publishing an article on Calculating the Catenary and Sag of a Towline. The silk on this spider web forms multiple elastic catenaries. 2 Find cable length and cable tensionCatenary Curve Effect Calculator & Calculation Find Cable Sag & length Catenary Curve Effect Calculator Use this catenary curve calculator to graph a catenary curve using the provided length and increment values. 3. It is a U-shaped curve symmetric about a vertical axis through its low-point and was first described mathematically by Leibniz, Huygens and Johann Bernoulli in 1691 responding to a challenge put out by Jacob Bernoulli (Johann’s elder brother) to find the equation of Conductor tension is a fundamental parameter for overhead line design calculations. It assumes a parabolic drape, but it is probably close enough for your purposes. Its shape is parabolic. 1. In physics and geometry, a catenary (US: / ˈkætəˌnɛri / KAT-ə-nerr-ee, UK: / kəˈtiːnəri / kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. Anyone know where I could find the article from Harvey and Larson published in 1977? This chain, whose ends hang from two points, forms a catenary. Using the expression for the length of a catenary (or parabola) check Variables Used Cable Span - (Measured in Meter) - Cable Span is total length of cable in horizontal direction. 1. Tension is calculated using the load, span, and sag. While erecting an overhead line, it is very important that Feb 24, 2012 · A SIMPLE explanation of Sag in a Transmission Line. For this reason, we can see that the value of B is extremely close to the value of L/2. The application of various equations, specifically those relating to catenary shapes, is demonstrated to provide insight into practical problems regarding cable installations 4 Catenary Cables and Arches Catenary Cables Geometry and basic principles Cables are structural elements that can hold a great amount of tensile force with a relatively small cross-sectional area. Calculates catenary geometry, sag, length. A catenary cable carries only its own weight. For this reason it is common for distribution line designers to base their calculations on assumed tensions, which can be significantly different from actual installed tension. Dec 16, 2008 · I'm looking for a formula, calculator or spreadsheet that can calculate the tension in a cable suspended between two points with a concentrated load. Jan 24, 2007 · Ropes and CablesFiles in Ropes and CablesOrder by Jul 25, 2009 · In this case I think the best way to determine the tension (short of actually using a commercial tension meter) would be to determine the angle \theta by measuring the deflection from horizontal caused by the load (e. rig a string tightly between the anchor points and then measure the vertical deviation from this of the loaded rope). In this video I go through an example problem with a cable under a catenary load which is a cable hanging under its own weight. A negative value means that the low point is outside the span. Learn what Sag is, how to calculate Sag and Tension in a Transmission line, and the Formula for Cable Sag Calculations. Apr 16, 2021 · Cables are flexible structures that support the applied transverse loads by the tensile resistance developed in its members. Midspan Tension - (Measured in Newton) - Midspan Tension is the total tension acting in cable at midpoint. A displacement cable is best described by a catenary curve when the curve is subjected to a uniform force. May 16, 2017 · Catenary equations describe the relationships between the span length (distance between the structures), the cable length (the length of the cable along the curve), the cable tension, cable weight, and cable sag (how far the cable droops down in the middle between the two attachment points. If you belong to the electrical engineering world you must have questions regarding overhead line sag and tension. However, often, documents covering the process only present a high level concept of the variables involved without presenting a concrete or exact Dec 20, 2012 · The minimum tension is the horizontal tension in the cable (H) which can be found by drawing a free body diagram through the low point of the span and around one end. It aims to explain the fundamentals Catenary Curve Calculator and Expanded Excel Design Equation and Calculator A catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. a is the catenary constant (horizontal tension / weight of the cable) W is the weight of the cable in pounds per foot Tension is the horizontal tension in pounds Calculation Reference Catenary SpanMaster software takes users through a logical step-by-step process of information entry and produces sag and tension results for any cable span. Span having equal level supports is called level span, whereas when the level of the supports is not at an equal level is known as unequal level span. I want to be able to calculate the deflection(sag) at any point along the wire. Wire Temperature Designed horizontal tension at the current wire temperature Measured zenith angle (if checking existing wire sag) Input the necessary information into either form and select "Calculate" to view the result "Sag Wire" is used during construction to precisely place each conductor at the designed mid-span sag & horizontal tension The document describes an inclined span module that calculates variables for a catenary cable curve between two towers with different elevations. Tension at any Point given Catenary Length of Simple Cable with UDL calculator uses Tension at Supports = sqrt((Midspan Tension^2)+(Uniformly Distributed Load*Cable Span)^2) to calculate the Tension at Supports, The Tension at any Point given Catenary Length of Simple Cable with UDL formula is defined as the total force acting on the supports in both horizontal and vertical directions. I determined that the tension would be different on each end, that the shape of the suspended cable would be a catenary curve truncated at one end, and that the following would be the variables necessary in the equation: cable weight cable length vertical distance between ends horizontal distance between ends Some links that could be helpful: This article will try and cover the topic about overhead line sag tension with calculation and example. Jun 11, 2025 · Calculate the length of a cable hanging between two poles 50 meters apart with a sag of 5 meters. An example cable has 800 lb/ft load over a 600 ft span with 40 ft sag. For the case of very long spans, catenary formula gives more accurate results than parabolic. By Steve Eckardt, Product Engineer SUPERIOR ESSEX Member of NEMA, ICEA Table of contents Preface Maximum pulling tension on a cable Maximum permissible pulling length Cable grip tension Calculated pulling tension – straight section of conduit Calculated pulling tension – curved (bent) section Calculation of sag and tension in transmission line depend on the span of the conductor. zip The download file includes full open source code. 7 m and the maximum tension is 2. Find the cable force calculation formula and examples for accurate results. This requires calculating x (s) and z (s) at different values of s. However in practice installed line tension is difficult and expensive to measure. The inclined span catenary sag describes the tensions and sagging curve, or catenary, of a cable connecting two points at different elevations. pvrynxsmsljcdmubksynddgzuulvpbdeohkkippuzuzdnjnr