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Catenary curve length calculator Changing the parameter makes both of the curves longer or shorter while maintaining the equal length. While the paper is still on the wall you might lay out another line of a shorter length but same percentage of drop per length to see how much different the curves are. For each desired loading condition, calculate the sag-tension information. Mathematically, the catenary curve is the graph of the hyperbolic cosine function. Click the buttons to increase or decrease the Catenary Coefficient, C. Get more Excel Training for Engineers at: https://www. The catenary is a curve which has an equation defined by a hyperbolic cosine function and a scaling factor. Remember, cable length calculations consider the sag and span of the cable to determine the total length. By inputting the horizontal span and sag, the calculator provides the catenary constant and the vertical positions along the curve. Accordingly, when first loading Catenary+ you will need to generate an unloaded catenary. How does a catenary arch work? Catenary arches are very 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. This calculator is useful in fields like physics, engineering, and architecture to analyze and design structures involving curves. that I have 2 fix end points with different x & y co-ordinates. What factors does the Catenary Equation Calculator consider? It considers Horizontal Force (H), Distance (d), and Weight per Unit Length (w) to compute the sag (S) of the catenary curve. It is well established that a catenary is the best way to model the curve of a power line cable. Perfect for engineering, architecture, and physics applications involving hanging chains or cables. 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. Despite the complication of the formula, it is always advisable to use catenary calculations. 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. The point (0, a) is the lowest point, or vertex, of the curve. (s^2 + a^2)k = -a s (t) = a Understanding the formula and utilizing the Cable Length Calculator from Sag, Span Calculator enables engineers to accurately estimate cable lengths, plan installations, and ensure the proper functionality and safety of cable systems. Mar 9, 2024 · Given the length of a catenary and the distance between between its supports, estimate how much lower the catenary is in the middle. In Catenary calculator Catenary mooring system A catenary mooring system is the most common mooring system in shallow waters. Imagine we want to find the length of a curve Apr 4, 2012 · How to calculate cable length for a bridge by first defining parabolic curve. Fortunately, there is one equation that can directly calculate the width of the catenary span between two poles knowing the length of the wire and the height of the poles. Catenary / Parabola Curve Calculator So I have used various curve generators in the past successfully after getting use to how they function. Example - Known Tension at the Supports - Calculate Sagging and Length of Cable For a 30 m long cable with uniform load 4 kN/m the resulting tension in the cable at the end supports are 100 kN. engineerexcel. For instance, such a tool might determine the required cable length for a suspension bridge given the span and desired sag. This curve, known as a catenary, appears in various applications, such as suspension bridges, power lines, and decorative arches. Free online calculator with step-by-step solutions for calculus and geometry. With this calculator/generator you only need to input the length of the curve and the desired depth of the curve. Based on the ship's Allowable displacement and it's weight; the forces one the mooring line varies. The constructon follows the wikipedia article on catenary curves, i. Oct 14, 2024 · A: The calculator uses the parameters of the catenary equation, which involves the chain length, the height of the endpoints, and the horizontal distance between the endpoints to compute the shape of the curve. It will output the x and y cords for the curve. You can also use the catenary equation calculator on the left. Calculates angles and forces at the supports. 4. 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 analytic catenary equations used in OrcaFlex account for simple properties of a line such as its weight, buoyancy and axial stiffness. CHAPTER 18 THE CATENARY 18. Cable unit length weight is also known. e. Catenary is idealized shape of chain or cable hanging under its weight with the fixed end points. Catenary Curve If the lowest point of the curve above is the origin, the following Dec 6, 2014 · Hi, my problem with this is. This, in turn determines the length of the mooring line required and also the shape of the Calculator for catenary anchor chains on ships at anchor. Jun 10, 2024 · Conclusion The Catenary Calculator is a valuable tool for engineers and designers working with hanging cables or chains. 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. This will generate your basic catenary/parabola curves needed for cat-cut-tarps and bridge hammocks. Run plot_catenary. Dec 17, 2021 · Use the creep curve for creep loading conditions and the initial curve for high loading conditions. The catenary curve has a U-like shape, superficially similar in appearance to a parabola. Dec 5, 2024 · Final Words: The Catenary Equation Calculator is a valuable tool for calculating the shape, sag, and length of a catenary curve, typically used in mechanics and engineering applications. This information is essential for designing stable and safe structures like suspension bridges and power lines. Wire Sag and Tension Calculator Click on the Calculate button in the table below, and a graph will appear for 3 cable examples. In practice, if a cable stretches less than 1% over its entire length, whilst inaccurate, the catenary calculation remains valid. This is the most you can pull before the end of the rope lifts off the bottom and begins to apply a vertical, pull out, force on the anchor. 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 Calculate arc length for curves, parametric equations, and polar coordinates instantly. 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 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. Length of a Hanging Cable Abstract The shape of a cable hanging under its own weight and uniform horizontal tension between two power poles is a catenary. The key to creating a dipole sag model is to use the software optimization function. It is common on distribution lines. ) Find the actual length of each of the cables in Figure P4. In this equation, 'a' is a parameter that determines the curve's shape and scale; it is related to the ratio of the horizontal tension component to the weight per unit length of the cable. Now with 1:1 scale SVG export. Essential tool for civil engineering projects, architectural design, and structural calculations involving suspended Explore math with our beautiful, free online graphing calculator. Feb 14, 2025 · A software tool designed to model and analyze the curve known as a catenary the shape formed by a chain or cable suspended between two points under its own weight typically provides parameters like cable length, sag, tension, and horizontal distance. The curve that a haning flexible wire or chain forms when it is supported at its ends. If they are close, you could cut out the larger curve and mark it's center, then use the center portion of the curve for the shorter sides. Step-by-step guide for precise hanging cable math. The calculator provides users with the ability to model and analyze the catenary shape based on specific parameters, making it Calculate catenary curve properties instantly with our free online calculator. in JavaScript games A catenary is a funicular shape for an unloaded cable and is determined solely by the self-weight of the cable, which is uniformly distributed along its length. Cable sag error calculator to calculate the catenary curve effect in cables. Find cable length and cable tensionCatenary Curve Effect Calculator & Calculation Find Cable Sag & length Catenary Curve Effect Calculator Calculator for the forces and dimensions at any point along the length of a tight or loose catenary configuration (technical-help) This is the construction of the catenary curve y=a*cosh ( (x-c)/a)+b of length s (like a chain of length s), hanging on points A and B. Works with snubber, bridle, and just only rope. . How do you calculate catenary length? Calculate the length of the catenary y=acosh (xa) on the interval [−50,50]. Download from: Catenary. Jan 18, 2025 · A catenary curve calculator’s core functionality relies on a robust mathematical model accurately representing the physical phenomenon of a hanging chain or cable. “Although commercially available wires and cables are not truly flexible, they will, in very short spans, conform closer to a catenary than to any other curve. The word catenary (Latin for chain) was coined as a description for this curve by none other than Thomas Jefferson! Despite the image the word brings to mind of a chain of links, the word catenary is actually defined as the curve the chain approaches in the limit of taking smaller and smaller links, keeping the length of the chain constant. The calculator simplifies 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. View CAS to see details. A catenary mooring line will have a part which is laying on the seafloor and a part of the mooring line suspended in the seawater. 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. One physical application of hyperbolic functions involves hanging cables. Abstract The catenary is the curve in which a uniform chain or cable hangs freely under the force of gravity from two supports. The catenaries are hanging horizontally at the seabed. Understanding the Fundamentals The calculation of a chain or curved line’s length is a vital Sep 27, 2020 · Anchor scope calculator: Calculates required minimal anchor chain and/or anchor rope length based on vessel characteristics and weather/sea conditions. Nov 10, 2021 · Catenary Calculator CalQlata’s technical support for our theoretical & practical catenary configuration calculator including full and tight curves. And to the math experts, yes Calculation Setup This catenary calculator has been designed to apply a point-load to a predefined (unloaded) catenary. Can the calculator handle different units of measurement? 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. feet and pounds to enter cable parameters, Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Galileo had originally claimed that the curve of the chin would be a parabola. Also find arc length of a helix, higher dimension curve, polar coordinates. Compute the chain length with endpoints at (0, 0) and (5, 8) for a hanging chain. It can be shown 2 that with the apex at (0, a), the equation of the catenary is y = a cosh x a. Enables comparison of two drafts, with upper and lower bound anchor holding powers. Nov 14, 2025 · The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. The remaining input data A catenary curve calculator employs mathematical formulas to determine the properties of the catenary, such as its shape, length, and tension in the chain or cable. This curve is the shape of a perfectly flexible chain suspended by its ends and acted on by gravity. The curve effect resembles a flexible chain suspended by its ends with gravity acted upon it. In addition to the response results, the calculator will also plot the selected function. Oct 10, 2012 · Given two points in the vertical plane and a given length of rope, the supplied function computes the trajectory of the catenary between those points. App available for iOS and Android. (Your answer will be in terms of a. Visualizing the curve’s shape, tension distribution, and support reactions enhances comprehension of the system’s mechanics and facilitates informed design decisions. Apr 9, 2025 · Example Prompts Calculate the arc length between two points for y = 3x². Follow the step-by-step tutorial with examples A displacement cable is best described by a catenary curve when the curve is subjected to a uniform force. Jan 13, 2019 · Explanation of the steps on calculating the length of the catenary Ask Question Asked 6 years, 10 months ago Modified 6 years, 10 months ago The standard equation for a catenary curve centred on the y-axis is given by y = a cosh (x/a). Figure P4 shows three such curves with \ (a=50\) (red), \ (100\) (green), and \ (200\) (blue) on the interval \ ( [-50,50]\). Calculates anchor load and pulling angle at anchor shank. (Your answer will be in terms of \ (a\). Use the calculator to dynamically change values. Galileo posed the problem and observed that the curve followed by the wire was approximately an arc of parabola, the approximation improves when you extend the wire. This online graphing calculator helps you to graph a catenary curve with the given sag value, length and increment value. Even though the shape looks similar to a parabola, the shape is actually defined by a hyperbolic cosine function. Situations of towline dragging on the sea bed will lead to fouling of the towline and can be avoided by knowing the maximum sag. g. Jun 29, 2025 · The Catenary Curve Calculator helps determine vertical coordinates in catenary curves using the mathematical formula y=a×cosh (x/a). The maximum sag is the most critical parameter to know for safe towing operation. 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. Calculates displacement cable sag based on the equation of a catenary curve. ) Find the Calculates catenary geometry, sag, length. 3. 18. Some design engineers assume that the curve is parabolic for ease of analysis. To determine the parameters the implementation follows Explore math with our beautiful, free online graphing calculator. Utilizing a specific formula, it calculates the shape of a hanging chain or cable under the influence of gravity. Oct 3, 2024 · 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 chains. Perfect for students, teachers, and professionals. In what follows, we sketch a brief outline of the analytic catenary equations solved by OrcaFlex. Using Calculus to find the length of a curve. Any freely hanging cable or string assumes this shape, also called a chainette, if the body is of uniform mass per unit of length and is acted upon If a flexible chain or rope is loosely hung between two fixed points, it hangs in a curve that looks a little like a parabola, but in fact is not quite a parabola; it is a curve called a catenary, … Catenary analysis software for hanging cable systems - moorings, umbilicals, flexible risers. Feb 14, 2025 · Utilize the calculator’s visualization capabilities to gain a deeper understanding of the catenary curve and its behavior under varying conditions. " In 1669, Jungius disproved Galileo's claim that the curve of a chain hanging under gravity would be a parabola (MacTutor Archive). I need to draw catenary curve, and calculate length of cable required. High-voltage power lines, chains hanging between two posts, and strands of a spider’s web all form catenaries. The Y cords is the length of the curve in increments of 1 and the x cords adjacent to it are the measurements for the depth of the curve. A Catenary Curve Calculator website is an online tool that allows users to input parameters related to a catenary curve, such as the length of the chain and the height of the supports, to calculate and visualize the properties of the curve. The parabolic approximation is true only when the sag is minimal in comparison to the span length. Get precise results with step-by-step solutions and explanations. ) for that decimal point and commas (,) for that 1000 separator. In case your computer reverses this arrangement, you will have to swap them using Microsoft’s ‘Word’ (or similar word The catenary is the shape taken by an inextensible, homogeneous, infinitely thin, flexible, massive wire hanging from two points, placed in a uniform gravitational field. first solve for a by solving sqrt (s^2-v^2)=2a*sinh (h/ (2a)), then solve for b and c. Q: How does the radius of curvature of a catenary curve vary along its length? The cable will form in the shape of a catenary. A catenary curve describes the shape the displacement cable takes when subjected to a uniform force such as gravity. So far I have the equations to model a catenary cable hanging between 2 points of unequal height provided that the cable sags below the lowest support at some point along the span (That is, dy/dx = 0 at some point Exercise 18 3 1 By expanding Equation 18. Bending stiffness 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. Feb 28, 2019 · Effectively, the catenary curve stays the same, and all that happens is that in this graph the seabed and the water surface are moving (in synch) higher such that the chain is sliding along the catenary, occupying a different segment along the catenary curve that starts already with an angle at the anchor. To run the model you merely set a sag ratio. First, denote the height of the taller pole by H, the height of the shorter pole by K, the distance between the poles by D, and the length of the chain by L. If a cable of uniform density is suspended between two supports without any load other than its own weight, the cable forms a curve called a catenary. The unloaded catenary requires the following input data: x₂, y₂, L and w; inputs d and p are required only for the properties at any point along its length. zip The download file includes full open source code. The equation was Aug 29, 2023 · Example 8 3 1: Catenary A catenary —a hanging uniform cable whose ends are fastened at the same height h a distance L apart—has its lowest point—the apex —a distance a> 0 above the ground. The word catenary is derived from the Latin word for "chain. Catenary Catenary is idealized shape of chain or cable hanging under its weight with the fixed end points. 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 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. Catenary curves find applications in many fields, so it's worth learning about them. Find the curved line length for y = sin (x) from 0 to π. s = cable length = 2 * x * CATENARY chain curve calculator With the CATENARY Trigonometric Function Calculator, you can calculate catenary chain curve values. Calculate the plastic strains for the layers using the catenary constant acquired above and the internal average tension equations. Catenary, in mathematics, a curve that describes the shape of a flexible hanging chain or cable—the name derives from the Latin catenaria (“chain”). It assumes the towing gear is the same weight, bouyancy, and surface area, per foot along its entire length. Calculate the length of the catenary \ (y=a\,\cosh\left (\frac {x} {a}\right)\) on the interval \ ( [-50,50]\). The catenary curve graph is a fundamental concept in mathematics and physics, describing the shape of a hanging chain under its own weight. One aspect of power lines that is not intuitive is the effect that adding a small length of conductor into a span can make on the sag. In this post, you’ll learn how to create a catenary cable tension calculator in Excel by solving an implicit equation. m for an interactive demo. May 29, 2025 · Calculate the horizontal span between suspension poles using catenary curves and hyperbolic functions. This curve has numerous applications in engineering, architecture, and design. Quick to set up and manage catenary data. com Apr 9, 2025 · Calculation of the length of a hanging cable (catenary) Designing structures with hanging cables requires precise calculation of the catenary curve length. The example will show specifically […] Dec 13, 2023 · The Catenary Calculator is a mathematical tool designed to determine the vertical position of a chain given a horizontal distance from its lowest point. Perfect for structural engineers, architects, and professionals working with suspension bridges, cables, hanging chains, and tension analysis. The equation to calculate this is: Where s is the length of the rope and d is the distance between the cliffs we want to find. Accuracy ensures stability, safety, and efficient material use, preventing excessive tension or sag. Use any consistent units for length and weight, e. To simplify calculations and analysis, an expanded Excel calculator can be utilized, providing a user-friendly interface for inputting variables and obtaining accurate results Forces: Total rope weight: [ kg ] or Rope weight per meter: [ kg / m ] or Load per meter: [ N / m ] Calculator for the forces and dimensions at any point along the length of a tight or loose catenary configuration Nov 25, 2006 · Calculates displacement cable sag based on the equation of a catenary curve. Using the equations for the shape of a catenary (see box), the maximum rope tension, 84 pounds, can be calculated. Jan 1, 2020 · This is because the weight per unit length of a cable that stretches under tension will vary along its length in a catenary, invalidating the calculation formula. 4 as far as x 2, show that, near the bottom of the catenary, or for a tightly stretched catenary with a small sag, the curve is approximately a parabola. Estimate sag and support reactions for a uniformly loaded overhead cable using a parabolic approximation to the catenary equation. With this calculator, engineers can easily find solutions to catenary equations between two points, ensuring safe and efficient designs for power lines, suspension bridges, and other structures that rely on Calculate catenary curve properties instantly with our free online calculator. This demonstrates that with a weight per unit length of 10, a horizontal distance between supports of 20, and a horizontal force of 5, the sag of the catenary curve would be 100 units of length. Cracking the Code with Python and Javascript Armed with our equations, let's solve them using Python and Javascript. The following figure shows chains hanging from a row of posts. See full list on themathematicsmaster. The program will experimentally try a length of wire, find the catenary span for that sag A catenary curve describes the shape the displacement cable takes when subjected to a uniform force such as gravity. Catenary calculator Catenary mooring system A catenary mooring system is the most common mooring system in shallow waters. Sep 6, 2023 · However I draw the catenary cuve between these 2 points is ok as long as the final length of the curve (arclength) is equal to what I mentioned in the program because I used this value for parameterization of curvature (steepness of the curve). Oct 26, 2024 · In the context of a catenary curve, the radius of curvature is important for understanding the forces acting on the cable or chain and for designing structures that can support the weight of the cable. These are Leibniz, Jean Bernoulli and Huygens who found Calculate approximated catenary curves for hanging ropes, strings, bridges etc. The curve is also called the alysoid and chainette. The part that is suspended in the seawater will take on a catenary shape. Find the arc length of the catenary. Suppose the three curves in Figure P4 represent cables strung (at different heights) between poles that are 100 meters apart. Please Be Aware: All of our calculators use full-stops (. The chain (cable) curve is catenary that minimizes the potential energy Catenary Curve (Cat Cut) Calculator for Tarps and Tents A free tool to calculate the catenary curve needed to cut into a tarp or tent seam for a perfectly taut pitch. 3. The curve appears in the design of certain types of arches and as a cross section of the catenoid —the shape assumed by a soap film bounded by two parallel circular rings. 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. (Please read about Derivatives and Integrals first). With a coordinate system defined as shown in Figure 19 3 1, the equation of the catenary is found to be Figure 19 3 1: A chain hanging under its own weight, forming a catenary curve. Jul 21, 2020 · Maximum Sag The most interesting data from the catenary curve above is the maximum sag in the catenary, which is at the mid-catenary. Over the past projects I have repeatedly tweaked them until I have finally ended up with a condensed ultra simple version. Solution Explore math with our beautiful, free online graphing calculator. These equations vary depending upon whether the line is suspended above the seabed or laid down Jul 29, 2009 · Hi, I have been working on developing a catenary cable toolbox for matlab. For math, science, nutrition, history Jul 31, 2020 · I see a problem with your calculation method and catenary curve. The chain (cable) curve is catenary that minimizes the potential energy The inclined span catenary sag describes the tensions and sagging curve, or catenary, of a cable connecting two points at different elevations. Jun 11, 2025 · Learn how to calculate the length of a hanging cable (catenary) using mathematical formulas for accurate engineering and physics applications. com/free-tr In this video, we solve an implicit equation in Excel to calculate the tension in a 免费使用Desmos精美的在线图形计算器来探索数学奥妙。功能包含绘制函数图形和散点图，视化代数方程式、新增滑块，动画图表等。快来使用我们既精美又免费的在线图形计算器，一同探索数学！其丰富功能包括绘制函数图形、散点图、代数方程式可视化、添加滑块和图表动画等等。 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. Through gravity the catenaries, between the floating unit and the seabed, will show the typical shape of a free hanging line. Figure 1 shows the curved shape of a typical 200 foot, 5/8" diameter, nylon anchor rope in 30 feet of water. 1 Introduction If a flexible chain or rope is loosely hung between two fixed points, it hangs in a curve that looks a little like a parabola, but in fact is not quite a parabola; it is a curve called a catenary, which is a word derived from the Latin catena, a chain. Determine the chain length for a catenary with a = 4 meters and x-range of 6 meters. 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. Formula for a catenary: x (t) = t y (t) = 1/2 a [e^ (t/a) + e^ (-t/a)] = a cosh (t/a) t = 0 corresponds to the vertex Cesaro equation expresses a curve in terms of arc length "s", and curvature "k". More complicated effects, such as bend stiffness, are ignored. Any help? Calculate pipe catenary profile maximum lay bending moment from water depth and lay tension for a multi layer pipe. Feb 9, 2018 · The radius of curvature of the catenary (2) is [Math Processing Error] a cosh 2 x a, which is the same as length of the normal line of the catenary between the curve and the [Math Processing Error] x -axis. The sag increases with horizontal tension and decreases with cable weight per unit length, elevation difference and span. A catenary cable sags under such a uniformly distributed load along its length, and transfers the load to its two supports in equal shares. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. With appropriate placement of axes, a catenary is the graph of \ (y=a\,\cosh\left (\frac {x} {a}\right)\). Jul 12, 2023 · We also know the total length of the rope is along the curve of the catenary. Sailors are always interested Calculate catenary effortlessly with our free online calculator. In this calculator we calculate the cable sag and cable length for given cable tension, straight line distance, force perpendicular to cable length and mass of the cable per unit length. The catenary profile is useful as a first pass estimate of the pipe lay profile. Jan 26, 2025 · How do engineers calculate sag and tension in overhead power lines? This article breaks down the key formulas, including the catenary curve and conductor length, and explains how factors like weather and temperature affect these calculations. The equation of a catenary in Cartesian coordinates has the form: When only the length of the catenary and the two anchor points ( ) and ( ) are given, the values for , and have to be found numerically. Learn how to calculate cable sag error in electrical or telecommunication cables with our cable sag error calculator. Chain not long enough? The Anchor Chain Calculator app will tell you what effect this has. grjtx alscb vpqdg swtsz vvit