HC mentioned the term "catenary" in his post and I thought I would add?ÿsomething I was a party to some time back.
A few years ago a?ÿyoung and very smart facility engineer with a power company took some of my field observations and?ÿcompared them to a calculated sag with some of their high-brow software.?ÿ Predictably the calc'd sag and the field data were very much congruent?ÿto one another.?ÿ The differences were usually in the hundredths of a foot; acceptable in the real world; and?ÿfew exceeded a tenth or so.?ÿ
At first?ÿwe chalked these up to the error found in observation and left it at that.?ÿ But the engineer checked a number of instances and found some differences that appeared to him to be in predictable spots.?ÿ Over a period of time he continued to scrutinize the differences.?ÿ?ÿ Of course he was far more interested in this than I was.?ÿ From time to time he would call me and pick my brain about field procedures and the equipment until he discovered his "aha" theory.
As in all mathematical formulae we depend on "constants".?ÿ Some of the initial "fixed" values utilized by his software was (of course) the beginning and end of the sag.?ÿ He found the field data and calc'd sag could better corroborate each other by?ÿ"fixing" the mid span values and allowing the formula to solve for the end points.?ÿ The differences were not outside of?ÿacceptable error, but did show me some haunting predictability.?ÿ The sags were always a little longer than I reported and the "attachment" elevations wound up a little higher.
He brought some typical attachment hardware out to a site and we compared what I was looking at through the TS and what was really going on.?ÿ It was a good learning moment and eye opening for both of us.
Long story short, the beginning and end of a catenary sag are critical point and possibly more critical to the observations than the sag shots taken along the conductors.?ÿ The hardware varies greatly with the type and size of the conductor.?ÿ The "beginning" and "end" of a sagging span needs to be located just as precisely as mid-span points, if not more so.
Lived and learned.
Do you mean that the cables did not form a perfect parabola (catenary)? Maybe this is due to some stiffness of the cable at the insulator ends. so that there is a bit of "hogging" ie it doesn't change direction instantaneously like a parabola.?ÿ
This was a trick question, and all of you missed it.?ÿ The real answer:?ÿ you don't locate the sag in an electric line between 2 telephone poles.?ÿ They're telephone poles, so there are no electric lines between them.
Now, if you want to talk about joint utility poles or power poles, well, that's a different matter.
Ah but if there is an electric line between two telephone poles then super important to survey it!
Posted by: squowse
Do you mean that the cables did not form a perfect parabola (catenary)? Maybe this is due to some stiffness of the cable at the insulator ends. so that there is a bit of "hogging" ie it doesn't change direction instantaneously like a parabola.?ÿ
A cable that is very flexible forms a catenary curve.?ÿ A parabola is a quite different mathematical equation.?ÿ Ignoring scale factors and letting x be distance +/- from center,
Parabola y= x^2?ÿ?ÿ?ÿ?ÿ?ÿ?ÿ Catenary y = e^x + e^-x
Departures from the catenary could indeed be caused by stiffness, particularly at the end connections, causing the curve to be more of an inverted bell shape than the mathematical catenary.
Posted by: squowse
Do you mean that the cables did not form a perfect parabola (catenary)? Maybe this is due to some stiffness of the cable at the insulator ends. so that there is a bit of "hogging" ie it doesn't change direction instantaneously like a parabola.?ÿ
A cable that is very flexible forms a catenary curve.?ÿ A parabola is a quite different mathematical equation.?ÿ Ignoring scale factors and letting x be distance +/- from center,
Parabola y= x^2?ÿ?ÿ?ÿ?ÿ?ÿ?ÿ Catenary y = e^x + e^-x
Departures from the catenary could indeed be caused by stiffness, particularly at the end connections, causing the curve to be more of an inverted bell shape than the mathematical catenary.
fair enough.
every day's a school day
Posted by: squowse
Do you mean that the cables did not form a perfect parabola (catenary)? Maybe this is due to some stiffness of the cable at the insulator ends. so that there is a bit of "hogging" ie it doesn't change direction instantaneously like a parabola.?ÿ
A cable that is very flexible forms a catenary curve.?ÿ A parabola is a quite different mathematical equation.?ÿ Ignoring scale factors and letting x be distance +/- from center,
Parabola y= x^2?ÿ?ÿ?ÿ?ÿ?ÿ?ÿ Catenary y = e^x + e^-x
Departures from the catenary could indeed be caused by stiffness, particularly at the end connections, causing the curve to be more of an inverted bell shape than the mathematical catenary.
A catenary weighted at equal intervals with equal size weights will form a parabola.
In addition to vertical offset method, It also can be solved by recording the vertical and horizontal angles from three known points. There is a formula to this method.
2 angles only observations from 2 known points will do it but the difference between this and a roof?ÿ crown (for example) is - how do you find the same points on the cable again?
Vertical offset method also leaves a lot to be desired as it's time-consuming and inaccurate to attempt to position a prism exactly underneath the cable. Might not even be safe or possible.
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I agree with Mr. Marks. Remember the coefficient of expansion for a steel tape? While doing 500KV line rebuilds the inspector told us the line can sag as much as 9' between?ÿtowers (800' between towers). We did all the lines running to/from a coal fired plant, set up about 90 degrees and shot the distance/elevation to the lines with the reflectorless EDM. It's important to note the temperature AND time of day so the electrical engineer can see what the load was on the line because it will cause sag also. We mapped the line at the hanger wire on the insulator and the sag. The elevations at the insulator points it will be a straight line between them so the sag point can be determined as the low point. The sag will not be midpoint if the towers/poles are at different elevations because of the load, temperature, and gravitational pull. It was one of the fun, interesting jobs I've done.
If you can get it with reflectorless than that is the best way. If not, then assuming there isn't much wind (note: not only can a wind blow the conductors sideways, but it will also cool them - so wind speed and direction also need to be recorded as well as air temperature, steel temperature - taken off the tower legs with a magnetic thermometer on the shaded side, and exact time of observation, ideally recorded automatically with the survey observations.) you can get a good approximation by intersection.
The way to do this is to use two stations to first intersect suspension points and the clamps at each end of the insulator strings on adjacent towers. This gives you two pairs of points which should be the same distance apart and orientated in the same direction. If the directions are significantly different then the wind is blowing the conductors sideways.
On a twin or quad conductor you can't rely on intersecting the spacers, as any movement of the conductor between instrument set ups will nullify the results. On a single conductor there is nothing to identify (birds don't sit still for long enough!)
Therefore the best intersection is to take a number of shots HA/VA along the conductor from ONE station, preferably nearly square on the the line (for twin and quad lines visually take the centroid), working from one end of the span to the other. Repeat in the reverse direction.
You then have two lots of intersections onto a plane between the two end clamp points. Calculate each set separately - they should give good agreement. Combine the pair, graph out and curve fit: you will have the best answer you can get without reflectorless. The operation is very fast (assuming your fingers are!) so the conductor load is unlikely to change much during the observations. If in doubt, pick the observation time to be between adverts on the most popular TV programme showing in the region as this is probably the most stable load moment. At advert breaks everybody switches on the electric kettle and the load peaks.
I've done this in conjunction with a "live line" team (out on the arm taking direct temperature readings from the conductor - better them than me) as part of some experimental work on a 440kV line and our results came in within a couple of cm. of the predicted load calculations.
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We do a lot of transportation work, and locating low wires are normal for us. We typically use the vertical angle offset routine. We have a crew member look for the lowest point in the line, and puts the rodman on line, and the rodman will "eyeball" themselves under the line. We'll take a ground shot, and then turn the vertical angle up to the line. We note date, time, and approximate temperature, and it seems to work fine. There are safe clearances worked into the design, so this is typically what most people do around here.
We do a lot of transportation work, and locating low wires are normal for us. We typically use the vertical angle offset routine. We have a crew member look for the lowest point in the line, and puts the rodman on line, and the rodman will "eyeball" themselves under the line. We'll take a ground shot, and then turn the vertical angle up to the line. We note date, time, and approximate temperature, and it seems to work fine. There are safe clearances worked into the design, so this is typically what most people do around here.
Must be a southern thing Jimmy. I remember when I first started doing electrical utility surveys, all the techs were using hand held lazer?ÿ distance meters. I blew them out the water.?ÿ
I know in trimble access I think it is points on a plane you shoot the two ends reflectorless and then just turn angles to the other points on the cantenary. But by the time you do that you might as well shoot them all reflectorlessly. We have to shoot all the attachment points as well. Make sure to record time and tempature.
The way I used to do this was to locate each point of attachment with a unique identifier code, then shoot the sag reflectorless with the same code.?ÿ Drew automatically.?ÿ Alternately, if it was too far for reflectorless, I would shoot a point with an obviously incorrect distance using "angles offset" then turn and store the correct HA and VA.?ÿ The line would draw automatically, but to the wrong location.?ÿ Then I'd draw a line through the two connections - draw a 3D line from the point the TS was on (must add HI) and through the incorrect shot, then exten to the line between the attachments - move the point to the end of the new 3D line.?ÿ A perfect location...
Yes a catenary curve is what you have and it has a formula
Yes a catenary curve is what you have and it has a formula
As a rhetorical comment on field procedure I would like to relate the following observations:
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Years ago at the highway department we always calc'd "low wire" clearances (with a TS) by taking a shot "under the conductor" and then turning a vertical angle up to the conductor.?ÿ While this method seemed to work there were a few times things didn't turn out so well.?ÿ
It is not so easy at times for a rodman to guess at a spot "exactly" underneath a cable crossing.?ÿ And if the instrument is fairly close, the vertical angle can be sharp enough to produce a good few tenths of a foot (I've personally seen a half a foot)?ÿor so of vertical error in a simple triangle solution.?ÿ If nothing else?ÿanother crew member?ÿshould view the span from one pole to the other and give the rodman a good "on line" location under the span.
'glass height poles or a reflectorless instrument are so much better for that application.
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The formulas I employed many years ago to do sag checks on EHV transmission lines allowed me to actually use the hyperbolic functions on my trusty 41CV.?ÿ
I don't remember where it came from but my calculations were based on an obscure paper written by some rocket scientist type guy named Donald Dean.?ÿ
Some of the inputs required were span length, weight/ft., temperature, elevation difference for attachment points. I wrote a series of programs that allowed me to sit at a convenient point offline and sight a point on the belly of the wire or to sit under one of the towers and observe the sag along the line.?ÿ
Some of the contractors used a return wave method which although a sort of flat earth approach seemed to work pretty darn good.?ÿ
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