# Antenna wire catenary calculator

 This calculator is an adjunct to the article Sufficient sag for wire antenna spans for wind survival and should be used in conjunction with the article.

## Overview

This is a simple calculator for solving the antenna wire catenary between to end points given the design wind speed, mass per unit length of the wire, wire diameter and Gross Breaking Strength of the wire.

The solution is for a simple span with no concentrated loading, a feed line or the like suspended from a span invalidates this model. The calculator ignores the effects of wire stretching, creep, thermal contraction and expansion, and assumes rigid supports and a smooth circular cross section. Unless the scenario modelled uses data for ice, snow or other form of loading, those effects are excluded.

National or local standards or codes may set out requirements for design wind speed, material selection, safety factor and design methods for different applications. This calculator does not replace or override any regulated requirements.

The calculator uses ISO metric quantities for all input data, and the two end points are represented in an X-Y coordinate system where X is the horizontal dimension.

## Modelling unequal heights

The two endpoints do not need to be at the same height. Note that the calculator considers weight forces to act downwards (ie in the -ve Y direction) and for the worst case applies wind forces downwards. If modelling unequal heights, give full consideration to the direction that wind forces are applied in the model.

## Calculator input form

 Title: Wind speed: m/s Windage diameter: m Mass / unit length kg/m Guaranteed Breaking Strength: N Safety Factor: Radial ice thickness m End 1   X:  Y: m m End 2:    X:  Y: m m Export vars:

## What do the results mean

This catenary calculator finds the catenary that fits the endpoints and working load limits for the worst case where wind loads are in the same direction as weight loading, ie both vertical and the resultant catenary will be in the vertical plane. Wind forces will often be in a different direction to weight forces, and the resultant catenary and calculated forces will be different, particularly where unequal heights are specified.

The calculator assumes acceleration due to gravity is 9.8m/s^2.

The Working Load Limit is the tension in the wire when fully loaded (weight and wind).

The Wind Pressure is for information only.

The Horizontal force at end <x> is the horizontal force exerted by the wire on the support full loading.

The Lateral force at end <x> is the lateral force exerted by the wire on the support full loading.

The Wire Length is the length of the catenary arc. Be aware that wire stretches under tension, and this model does not include the effect of stretch (you didn't supply Young's modulus, did you), and its length varies with temperature (no temperature coefficient of expansion provided), these effects are ignored by the calculator.

Min Vertical Sag is the minimum vertical sag that must be provided to ensure that the tension is not more than the WLL when fully loaded. If you use a vertical measure to sag a span, use this quantity.

Min Normal Sag is the minimum  sag normal to the wire that must be provided to ensure that the tension is not more than the WLL when fully loaded. If you use sag boards to sag a span, use this quantity.

The Lowest Point give the location and height of the lowest point on the arc.

Slope at End 1 is the slope of the wire at End 1 as a ratio and in degrees. This can be used for setting the span tension with an inclinometer or the like.

Intercept of End 1 slope with vertical below End 2 is the intercept of a line from End 1 with slope the same as the wire at End 1, with a vertical line projected down from End 2. This value can be use for setting the span tension by sighting along the wire at End 1 to a point marked on the vertical support at End 2.

Max Tension Under Wire Weight Force Alone (no wind, no ice) gives the maximum tension for rigging a span when it is not wind loaded. The figure is force in Newtons, which can be approximately converted to kgf by dividing it by 10 if you were using a spring scale to set the unloaded span tension. For example 2, you would not rig the span with an unloaded tension of more than 45N or 4.5kgf, otherwise it would not survive the the design wind speed with the specified safety factor.

Min Wave Return Time Under Wire Weight Force Alone (no wind, no ice) is the time for a transverse wave caused by a lateral bump at one end of the span to propagate to the other end, reflect and return to the first end when the wire is loaded only by the weight force. This can be used (mainly on long spans) to set the unloaded span tension where the span is struck near one support and the wave time (or the time for two or three passes) measured with a stopwatch. A multiple greater than 3 s is also calculated for convenience with a stopwatch.

The Catenary is the expression for the catenary solution to the input data. You could cut and paste it into Excel to calculate points along the catenary, replace x with a reference to the X value.

MatWeb

Wire Tables

## Implementation

The calculator involves this page (which includes some java scripting) and a results page which is written in PHP.

## Notes / FAQ

All values calculated in the result table are from a catenary representation of the span.

The most accurate way to set span tension is to use a dynamometer to directly measure tension, and this is the only way to set very low sag spans. When sag is greater, sag board, inclinometers, sighting an intercept, and wave timing become practical substitutes.

### Can sag be estimated from wave return time?

Sag may be approximated as Sag=0.306*WaveReturnTime2. This approximation depends on a parabolic approximation and so is only valid for low sag and relatively equal end heights.

### Can the calculator model guy wires?

The calculator was designed principally for antenna wire spans, but can model guy wires (as rigged, tensioned without wind loading). Use a safety factor of 1, wind speed 0, set the GBS to the design working tension (often around 10% of GBS for the guy material), enter the mass per unit length of the guy material, and wire diameter (though it is not used), and enter the end point coordinates. The results will show the sag amounts and the wave return time which can be used for setting guy tension. See the discussion above about modelling unequal heights and wind forces.

### Can the calculator model ice loading?

The calculator allows specification of radial ice thickness for ice loading of the wire.

This is unlikely to represent a real life scenario where for example, driven snow builds up on the windward side of the line, making the line heavy on that side, which in turn twists the line and so over time the ice builds up as a spiralling thickness. The shape of such an ice build is not consistent with the model used in this calculator, the assumed diameter, coefficient of drag, and laminar flow are invalid.

### What safety factor is appropriate?

Safety factors may be specified in standards relevant to the application, for example:

• US Federal Specification A475-CLA: 5;
• AS1418.5 standing ropes, fixed guys:  3.5;
• NESC effectively allows a safety factor of 4 on spans designed on the final unloaded conditions.

V1.01. Use at your own risk, not warranted for any purpose. Do not depend on any results without independent verification.

Other VK1OD tools.