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# Power line sag/tension calcs2

## Power line sag/tension calcs

(OP)
Hello All

From time to time I have done calcs to determine the changes in conductor tension under differing wind loads and temperatures. But for a new job I'm starting, I need to consider the effects on sag and tension when lines are subjected to radial ice, of which I have no experience (I live in a warm area). I've performed manually calcs using an old (1940s) British text as basis ... answers seem to be reasonable, but ideally I'd like them checked.

Might be a bit cheeky here, but would it be possible for someone to run the required calcs (including ice) through a line design program to check my results if I provide all the details for a base set of conditions?

Thanks for any response.
Graeme

### RE: Power line sag/tension calcs

You can do the sag calc yourself by going to the web site Design of Overhead Distribution Lines        http://www.usda.gov/rus/regs/bulls/160-2.pdf

It has a full explaination of the Overhead sag calcs and the calcs themselfs. Overhead sag calcs are on page IV-7.

If someone does the calc for you on this tread you will still need this information to know how, why and check if it correct.

good luck

### RE: Power line sag/tension calcs

(OP)

I actually have this doc and Bull 1724E-152 which I believe supersedes it in part. As far as I can tell at a glance the basic S/T maths are pretty much the same as that which I've used.

My concern is really to see if I've correctly applied the formulae when using ICE (having had no prior experience with ice), so I'm hoping someone will be able to check my results.

Thanks
Graeme

### RE: Power line sag/tension calcs

I've got an older version of Alcoa's SAG10. If you want to post the information you have here, I'll give it a try. At a minimum, need conductor type, stringing tension and at what temperature, ruling span and length of span for which you are concerned about the sag. Also provide ice thickness, temperature and wind for maximum loading condition.

### RE: Power line sag/tension calcs

Suggestion: Reference:
1. C.L. Wadhwa "Electrical Power Systems," John Wiley & Sons, 1991,
Chapter 7 Mechanical Design of Transmission Lines includes ice coating with thickness t beside wind pressures, etc.

### RE: Power line sag/tension calcs

(OP)
Hi alehman.

Looks like just what I need! I'm in New Zealand and haven't managed to find any commonality between any US and NZ conductors [you're in the US?] so I've included parameters. Hope metric OK, but I can convert for you if need be  ...

WOLF ACSR:
A = 195.0319 mm2
Effective Overall Dia = 18.13 mm
Weight = 7.11963 N/m
Coeff of Expansion (final) = 1.782 * 10E-5 /deg C
E (final) = 79.979 MPa
UTS = 67.44 kN
Stranding = 30/2.59 Al + 7/2.59 GS
Ruling span = 130 m
Ice = 12.7 mm radial thickness @ 8.959 kN/m3.

RESULTS:
Using a starting point of 14.3 kN at 10 deg C (no ice; no wind) ...
* 8.38 kN at 50 deg C (no ice; no wind)
* 16.42 kN at 0 deg (no ice; no wind)
* 22.04 kN @ 15 deg C (no ice; 1 kPa transverse wind [includes conductor Cd = 1.2])
* 21.90 kN @ 0 deg C (WITH ICE; no wind)

I think that's it! I really appreciate your help and time. If there's anything else you need, please advise.

Thanks again
Graeme

### RE: Power line sag/tension calcs

I don't think there is a satisfactory hand-calculation method for ACSR other than a very laborious graphical method using stress-strain curves for the steel and the aluminum strands.  The calculations are very complex because of the different behavior of the steel and aluminum strands in response to tension and temperature.  You might be able to get sag-tension charts from the conductor manufacturer for your loading conditions.

The SAG10 computations would have to be made with an approximation of the Wolf ACSR conductor; there is really no single coefficient of expansion or elasticity for ACSR.  Maybe 336.4 kcmil 30/7 Oriole which has strand diameters of 2.69 mm for both steel and aluminum.

### RE: Power line sag/tension calcs

(OP)
Thanks jghrist

You're probably correct, but for our purposes the figures stated will be OK. We have used manufacturers' composite E and coeff data (also scheduled in engineering handbooks) for many years and as far as I know, have never caused a problem. In any case, the Wolf ACSR used is just an example ... I can redo for AAC or other materials if alehman prefers.

Regards
Graeme

### RE: Power line sag/tension calcs

I say there isn't a satisfactory hand method because I have used the composite E and coeff data in the (distant) past in hand calculations (actually spreadsheet) based on the Martin method developed by J.S. Martin in 1922.  I compared the hand calc results with the results from an Alcoa sag-tension program and didn't get very close answers.  I'll try running 336.4 ACSR 30/7 with your loading on SAG10 and see what the results are.

Using AAC would not be a good test of the method if it is also going to be used on composite conductors.

### RE: Power line sag/tension calcs

To my surprise, my ancient copy of SAG10 has Wolf ACSR.  Results for your initial conditions are:

50°C no ice or wind - 7.08 kN initial, 5.8 kN final vs your 8.38 kN

0°C no ice or wind - 16.2 kN initial and final vs your 16.42 kN

15°C no ice, 1 kPa wind - 15.02 kN initial and final vs your 22.40 kN

0°C, 12.7 mm ice, no wind - 17.27 kN initial and final vs your 21.9 kN

The differences are quite significant for loading conditions much different from the initial.

The program uses the same area, diameter, and weight for the conductor.  Coefficients of expansion and elasticity are not given because stress-strain curve data is used instead.

### RE: Power line sag/tension calcs

Assuming your "starting point" is a final tension, I get the following final tensions:

50C no ice, no wind - 8.44 kN
0C no ice, no wind - 16.4 kN
15C no ice, 1kPA wind - 20.2 kN
0C, 12.7mm ice, no wind - 21.8 kN

Re-running assuming your "starting point" values are initial tension, I get the following final tensions:

10C no ice, no wind - 13.3 kN
50C no ice, no wind - 7.97 kN
0C no ice, no wind - 15.3 kN
15C no ice, 1kPA wind - 19.5 kN
0C, 12.7mm ice, no wind - 20.6 kN

I'm not sure why there is such a difference with jghrist's results.

My SAG10 WOLF spec:
dia: 18.14 mm
area: 195.0 sq mm
wt: 7.14 N/M
RTS: 71.6 kN

### RE: Power line sag/tension calcs

alehman,

My input was as follows (all English units):

Conductor Type 2 - ACSR BRITISH
Codeword WOLF
Area, Dia, Wgt, RTS - .30230  .7140  .4890  16100
Chart #1-773

TEMP       ICE       WIND      TENS      CODE

32.0       0.50                            2
59.0                 20.9                  2
32.0                                       2
50.0                            3215       1
60.0                                       2
122.0                                      2

I assumed ICE to be in radial inches, WIND to be in lb/ft², and TENS to be in lb.

### RE: Power line sag/tension calcs

I used 130 ft not 130 m as a ruling span.

With the correct ruling span I get:

50°C no ice or wind - 9.84 kN initial, 8.63 kN final vs your 8.38 kN and alehman's 7.97 kN

0°C no ice or wind - 15.72 kN initial, 14.83 kN final vs your 16.42 kN and alehman's 15.3 kN

15°C no ice, 1 kPa wind - 21.01 kN initial and final vs your 22.40 kN and alehman's 19.5 kN

0°C, 12.7 mm ice, no wind - 21.78 kN initial and final vs your 21.9 kN and alehman's 20.6 kN

I converted to English units and back again instead of using the SAG10 SI unit option because I couldn't figure out what units they wanted.

### RE: Power line sag/tension calcs

My run using units=N and 14.3kN, 10C as a final tension:
Input data:

Deg C    Mm     Nsm    % or N
TEMP     ICE    WIND   TENSION CODE
═══════════════════════════════════════
0.0   12.70                      2
15.0         1000.00              2
0.0                              2
10.0                     14300    2
50.0                              2

And I get the following output:

Conductor WOLF           ACSR/British

AREA=  195.0319 Sq.Mm.
Data from Chart No. 1-773
Metric N Units

Creep is NOT a Factor
Design Points                      Final                Initial
TEMP    ICE   WIND    K     WEIGHT    SAG   TENSION        SAG   TENSION
C      Mm    Nsm    N/M     N/M     Mtrs      N          Mtrs      N
0.  12.70    .00   .00   18.156     1.76    21787.       1.76    21787.
15.    .00 ******   .00   19.489     2.04    20230.       2.04    20230.
0.    .00    .00   .00    7.136      .92    16377.        .89    16939.
10.    .00    .00   .00    7.136     1.05    14300.*       .98    15318.
50.    .00    .00   .00    7.136     1.79     8444.       1.53     9875.

### RE: Power line sag/tension calcs

(OP)
Thank you both! Excellent.

alehman, your figures especially are very close to mine ... I'd double-counted my drag coeff hence my error during wind. Now reset Cd to 1.0 at 1 kPa and get 20300 N at 15 deg. And it seems I've done the ice part OK too. So I'm rapt with correlation.

jghrist, I'll go over your answers more closely and see if I can figure why we have significant differences.

Thanks again for your time, both of you. Much appreciated!

Regards
Graeme

### RE: Power line sag/tension calcs

Impressively thorough eng-tips. Have long icicles been considered? How long? How many?

### RE: Power line sag/tension calcs

(OP)
Well, jbartos, not by me. Actually, I'm working in a minimal snow region, where the standard simply states that a 30 mm radial covering of snow at 0.4 SG be provided for. In the example I allowed 12.7 mm radial ice to keep things simple. AS/NZS 4676 standard does not consider other than radial snow or ice.

### RE: Power line sag/tension calcs

I'm not aware of any icicle calculations or standards. It is an interesting question though. If I remember right, ANSI C2 "heavy" loading is used in severe weather areas and is defined as 0.5 inch (12.7mm) of ice and 4lb/sf of wind.

Another case to consider is birds. What is the loading for a line densely populated with large birds? Also what is the wind loading on the birds? When something scares them all away, sometimes there is a very noticable uplift of the span which tells me the birds are a fairly significant load.

### RE: Power line sag/tension calcs

(OP)
In case it's unclear, my example values (including my "starting point") are Finals. After fixing my wind load error, my results are each within 1 % of alehman's. And I'm pretty happy with that!

### RE: Power line sag/tension calcs

Comment: Often, power lines are down due to the larger accumulation of ice in form of icicles.
Visit
http://www.timesfreepress.com/2000/JAN/24JAN00/NEWS0424JAN.html
for:
In Georgia, more than 10,000 residents in Catoosa County and more than 1,000 in Walker County awoke to cold and dark homes due to power outages, as iced-over trees fell onto already-sagging power lines drooping with icicles.
http://www.americanlifelinesalliance.org/pdf/IceStormSummaries.pdf
for: Storm on 1/1/1952 when:
Ice on wires 2" in diameter with 6" long icicles in MO

### RE: Power line sag/tension calcs

You are most correct jbartos. ANSI C2 (NESC) most certainly does not account for the worst cases.

Another consideration: I live in the midwestern U.S. where I have personally experienced several extended outages due to ice storms. The last one was in December of 2001, when electicity at my home was off for six days. The vast majority of the damage is normally caused by trees and limbs burdened with ice which break and fall on lines (and houses and cars). The fireworks from arcing lines and damage in general was quite amazing and took several months to clean up. Thousands of trees were destroyed. One utiltiy pole in my back yard was broken in two when a large tree limb fell on a line it supported.

As a side note, my company recently completed a study for several communities in my area on the costs and possible benefits of relocating overhead lines underground. Needless to say the costs would be rather substantial.

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