(Hallas 2013) gives a method for designing wire spans for application in design of antenna systems.
He offers a nomogram for the selection of an appropriate sag give other parameters. This article analyses his design method.
Hallas's example span is described as
Weight=11 pounds / 1000 feet,
Span=210 feet, Tension = 50 pounds, Answer sag = 4.7 feet.
In fairness, (Hallas 2013) is inspired by (Straw 2007), more than inspired, it is almost a literal copy, same example same failures.
Since he does not mention wind or ice loading in this context, let us assume that the tension stated is for the simple span loaded only by its own mass, unloaded by wind or ice.
|W||Weight force per unit length|
|S||Length of the span|
|T||Tension in the wire|
|Sag||The vertical deflection at span centre below the straight line between the supports.|
A catenary with very low sag can be well approximated as a parabola, Table 1 gives the formula. The parabola is easy to solve with a hand calculator, one wonders at the need for recourse to a nomogram.
Converting Hallas's example to metric units, W=0.161N/m, S=64m, T=223N, and Sag=1.43m. Using the parabolic approximation of a catenary, Sag=0.369m, quite different to Hallas's 1.43m.
A more accurate result using Antenna wire catenary calculator to solve the same catenary is 0.388m, again quite different to Hallass's 1.43m.
Rearranging the parabolic approximation to make T the subject, we find that the tension that results in Hallas's sag of 1.43m is 57.6N, just 26% of Hallass's 223N.
Why the gap between Hallas's results and theory? The nomogram does not simply related the factors he states and uses.
Hallas has followed the traditional ARRL line of using a Working Load Limit
(WLL) for the wire of one tenth of its Guaranteed Breaking Strain (GBS), and he
asserts that delivers a
reasonable safety margin.
So, it seems that including the unexplained factor of four in the nomogram, and the stated factor of 10 in wire rating, there is overall an implicit Safety Factor of 40.
Safety Factor (Factor of Safety) is the capacity of the system to withstand forces beyond the design load. Standards in various jurisdictions may specify Safety Factors for different applications, and for this application Safety Factors for static rigging are typically in the range 3.5 to 5.
In the ARRL's apparent methodology, the design load is the weight of the wire alone with no other loading (eg wind or ice). There is a very large Safety Factor of 40 apparently included in their design to cover things like dynamic forces, allowance for components having spot weakness at termination etc and wind and ice loading.
So, it is a one size fits all for wind and ice loading, and the allowance for wind and ice is hidden. Just what wind speed alone (ie no ice) will the design withstand?
We can again use Antenna wire catenary calculator to answer that question. The datasheet gives data for a range of 40% Copperweld products, the GBS for the #14 wire mostly likely to be used in this application, hard drawn HS wire is 1823N (somewhat lower than the 2230 implied by Hallas).
A 64m span of #14 HS Copperweld rigged with 1.4m of sag without wind loading has a wire tension of 58N (lower than Hallas's 223N) without wind load and with Safety Factor of 5 (US Federal Specification A475-CLA), a wind withstand of 27m/s (97km/h) (which is less than the minimum design wind speed of US TIA-222 Revision G of 40m/s). A minimum sag of 2.9m would be required for a wind withstand of 40m/s.
Alternatively, a 64m span of #14 HS Copperweld rigged with Hallas's recommended 223N of tension with no other loading would withstand a wind of 9m/s (32km/h). Hallas's rigging tension of 50 pounds or 223N demonstrates the folly of rigging with too much tension, it reduces the capacity to survive wind loading.
For a design wind speed of 70m/s applicable to some localities subject to risk of very high winds, the required sag would be 10.3m suggesting a stronger wire might be more appropriate.
Readers can explore the effect of ice using Antenna wire catenary calculator. Ice imposes a great load on long spans, both the mass of the ice and increased windage!
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