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Comparison of observation of actual span with calculated model

No wind loading

The following compares measurements of a span with two calculated models, a parabolic approximation and a true catenary model.

The span is part of an Inverted-L antenna, the wire is 2mm HDC.

The span was measured using a theodolite and level staff. A very slight breeze caused the wire to sway a little adding error to measurement of the vertical angle at the centre of the span. The measurements and data reduction are reported in Table 1.

Table 1: Observations of actual span
Serial Item Value Notes
1 Vertical height of collimation plane 1.40m measured using theodolite and staff
2 Horizontal distance to LH end 16.1m measured using 10:1 stadia marks on theodolite cross hair and staff
3 Horizontal angle to LH end 0°00'00" measured using theodolite
4 Vertical angle to LH end 68°57'45" measured using theodolite, zenith=0
5 Horizontal distance to RH end 16.6m measured using 10:1 stadia marks on theodolite cross hair and staff
6 Horizontal angle to RH end 71°40'40" measured using theodolite
7 Vertical angle to RH end 73°14'48" measured using theodolite, zenith=0
8 Horizontal angle to "middle" 35°50'20" measured using theodolite
9 Vertical angle to "middle" 68°00'30" measured using theodolite, zenith=0
10 Horizontal distance to "middle" 13.05m calculated from 2 & 5
11 Height of LH end 7.59m calculated using 1, 2 & 4
12 Height of RH end 6.40m calculated using 1, 5 & 7
13 Height of "middle" 6.67m calculated using 1, 9 & 10
14 Run of span 19.15m calculated using cosine rule from 2, 5, 3 & 6
15 Rise of span 1.20m calculated using 11 & 12
16 Sag 0.324m calculated using 11, 12 & 13

Table 2 shows a parabolic approximation of the span. The greatest source of error is the measured tension due to friction in the halyard pulley and accuracy of the spring scale.

Table 2: Estimate of sag using parabolic approximation
Serial Item Value Notes
1 Tension 40N measured using spring scale
2 Force per unit length (weight) 0.28N/m calculated from material properties
3 Span 19.15m measured
4 Sag 0.319m calculated from 1, 2 & 3, Sag=(WS2)/(8T)

Table 3 shows a catenary of the span. The greatest source of error is again the measured tension due to friction in the halyard pulley and accuracy of the spring scale.

Table 3: Estimate of sag using catenary
Serial Item Value Notes
1 Tension 40N measured using spring scale
2 Force per unit length (weight) 0.28N/m calculated from material properties
3 Span 19.15m measured
4 Rise 1.20m  
5 Sag 0.316m calculated from 1, 2, 3 & 4

Table 4 compares the sag derived from the three methods. The three results are within reasonable tolerance given the accuracy of the measurements and known data.

Table 4: Comparison of sag using different methods
Method Value
Measured 0.324m
Parabolic approximation 0.319m
Catenary 0.316m

Wind loading

Measurements were not made under wind loading owing in part at least to the difficulty in proving a calibrated wind for observation. Nevertheless this section shows the sag required to fully load the wire, and therefore the minimum sag to assure survival of the design wind speed.

Wind loading at 40m/s (144km/h) would increase the force per unit length to 2.32N/m.

Table 2 shows a parabolic approximation of the span loaded to 100% of GBS with safety factor 3.5.

Table 2: Estimate of sag using parabolic approximation
Serial Item Value Notes
1 Tension 386N measured using spring scale
2 Force per unit length (weight) 2.32N/m calculated from material properties
3 Span 19.15m measured
4 Sag 0.276m calculated from 1, 2 & 3, Sag=(WS2)/(8T)

Table 3 shows a catenary of the span loaded to 100% of GBS with safety factor 3.5.

Table 3: Estimate of sag using catenary
Serial Item Value Notes
1 Tension 386N measured using spring scale
2 Force per unit length (weight) 2.32N/m calculated from material properties
3 Span 19.15m measured
4 Rise 1.20m  
5 Sag 0.278m calculated from 1, 2, 3 & 4

The two methods produce almost identical sags, the error in using the parabolic approximation for shallow spans is very low.

Changes

Version Date Description
1.01 24/09/2006 Initial.
1.02    
1.03    
1.04    
     

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