Sagging by Stopwatch (Return-Wave Method)

Scopea hill, a curve, trees, a long span. The stopwatch method needs neither line of sight nor an instrument: strike the conductor near one support and a transverse wave runs to the far structure, reflects, and comes back. Its travel speed is set by the tension and the mass per unit length, which is exactly the same pair of quantities that set the sag, so the round-trip time and the sag are two readings of one physical state -- AND THE SPAN LENGTH CANCELS OUT OF THE RELATION ENTIRELY. That is what makes the method work with no line of sight: the crew never needs to know how far away the other pole is. The relation is D = g t^2 / 32 per return, about 1.0054 t^2 with D in feet (RUS Bulletin 1726C-115 prints the same law in inches, D = 48.3 (T / 2N)^2, which is 12.075 per return). Timing several return waves rather than one is the whole accuracy trick, and it is not fussiness. Because the relation is SQUARED, a tenth of a second of stopwatch error on a single wave is a large sag error while the same tenth spread over five waves is a small one: for a 12 ft sag, three waves want 10.36 seconds (RUS 1726C-115 tabulates 10.4) and two tenths of error costs 0.47 ft, while one wave wants 3.45 seconds and the same two tenths costs 1.43 ft -- more than three times worse for the identical stopwatch and the identical hand. Three to five waves is normal practice, and the sensitivity is reported here so a crew can see what its own timing is worth rather than taking that on faith. This is the ideal taut-string relation. It assumes a free span with the wave reflecting cleanly at both ends, so it degrades where the conductor is not free to move -- through running blocks, against a hold-down, on a span with an armour rod or damper near the end, or in a section not yet clipped in. It does not account for damping, for wind moving the conductor while the wave travels, or for the sag being unequal in adjacent spans. It says nothing about tension, clearance, or whether the resulting sag is the right one: the target sag must come from the stringing chart at the ruling span and the temperature at the moment of sagging. The utility's stringing charts and construction standards and the crew's own sagging procedure govern.

Formula or tablesag S = 1.0054 (t / N)^2 with S in feet (g t^2 / 32; 12.07 in inches), t the elapsed seconds and N the number of return waves counted; inverted, t = N sqrt(S / 1.0054). The wave speed sqrt(H / m) and the sag are set by the same tension and mass per unit length, which is why the span length cancels out.

Source and editionThe return-wave (stopwatch) sagging method as standard overhead line practice, by name. Ideal taut string, free span. The utility's stringing charts and construction standards and the crew's own sagging procedure govern.

Free accessOne square root on a stopwatch reading; no stringing chart is reproduced.

What governsEstimate. AHJ and licensed professional govern.

API field nameselapsed_seconds, return_waves, target_sag_ft, stopwatch_error_seconds, target_time_seconds, period_per_wave_seconds, sag_error_ft, single_wave_sag_error_ft, error_advantage

• Ideal taut string, free span it degrades through running blocks, against a hold-down, or before clipping inoverhead line practice
• The span length cancels which is the whole point: no line of sight is neededoverhead line practice
• The target sag comes from elsewhere the stringing chart at the ruling span and the temperature at that momentthe utility's stringing charts