• computing the xz vertical angle for the cables
  

• Tension plots of individual measurements
• Over plotting all measurements by location
• plots:   Over plotting tower to platform cables (.ps) (.pdf)
• plots:   Over plotting tower to anchor (backstay) cables (.ps)  (.pdf)
• The average  tension
• plots:   Plotting the average cable tensions (.ps) (.pdf)
• Consistency check of the measurements: north/south, east/west tension imbalance
• Unbalanced  tensions at the top of the towers.
• catwalk cable tensions
• plots:  Plot of the catwalk cable tensions (.ps) (.pdf)

• ASCII textfile  containing the cable tensions, cable angles

Updates:

• 19oct20: updated all computations to use xz cable angle computed from catenary fit. (more info)
• 29oct20:  updated to include 2 measurements of T8 platform cables from road at base of T8 tower.
  

Other pages
Tower4 AuxNorth failure

Intro (top)

    The 305m north Auxmain cable on tower 4 failed on 10aug20 (more info). Felix and I scanned the main and backstays cables aug-sept 2020 using the leica p50 laser scanner.
We scanned one location at a time (t4 main,t8mains, t12 backstays...etc). We ended up scanning each location multiple times to check if the scanning location had an effect on the measurement results.

    After scanning, the data were input (via the leica software) and output  as .las files. A set of idl routines was written to

• input the .las files
• select the scanned points laying on the cables
• fit a catenary to the points on a cable
• compute the cable tension from the catenary parameters.
  

    Plots were then made of the cable  tensions by location. Tension imbalances in the measurements as well as a imbalances on the towers  were investigated.

Scanning the cables with the p50 laser scanner. (top)

    Measuring the cables with the p50 scanner

• This explains how the cables were scanned
• It includes a table with explanation of each measurement location as well as tension plots for each measurement set.
  

Computing the tensions from the p50 surveys.

• An explanation of how the tension was computed from the sag measurements
  

Results of the tension measurements (top)

Tension plots of individual measurements

• Plots of individual measurements can be found in the sag survey measurement table.

Over plotting all measurements by location:

    The cables at each location were measured multiple times from different p50 locations.
This allowed a check if the scanner location had any effect on the measurements.

• There are 3 frames: top: tower 12, middle  tower4, bottom  tower8.
  
• The vertical scan is kips
• the horizontal scale is cable index number
• 1 - first aux cable, 2 to  n-1 main cables, then last aux cable
• The aux cables are labeled north,south,east,west to orient the numbers
• Looking down at the x,y plane the first index is the cable farthest ClockWise. The numbers then increase moving counter clockwise (t4 cable 1 is south aux).
• the pink and blue dashed horizontal lines show the operating load for the aux and main cables (from the drawings).
• The middle  right prints the breaking load for the aux and main cables.
• The dashed vertical purple lines delimit the main cables.
• Each measurement is plotted in a different color.
  
• A colored label shows the date, location of p50, and the min/max distance of the measurement (in meters).
• The upper right shows the p50 maxRange and the sampling resolution used  (1.6mm at 10m)

 Over plotting tower to platform cables (.ps) (.pdf) (top)

•  Top frame: tower 12
• 3 measurements:
• 200831 - from visitor center balcony (under the cables)
• 200902 - from NW side of rim wall (west aux cable end blocked by platform)
• 200904 - from NE side of rim wall (east aux cable end blocked by platform)
• The 200831 auxeast and  main cables came out about 20kips more than the other two measurements.
  
• what could have caused the difference?
• the rimwall measurements used maxrange > 1km while 200831 used 270m
• the 200831 measurements used multiple sections (fences) to complete the measurements. the rimwall used 1 long set.
  
• The rimwall east and rimwall west measurements gave exactly the same values for the the mains and both aux cables
• So having the last part of the aux cable blocked by the platform made no difference
  
• This is to be expected since we fit the entire cable. Losing a small part should not make a large difference.
• Center frame: tower 4
• 4 measurements:
• 200828: from base of tower 4. This inadvertently used 120m max range so it never made it all the way to the platform
• 200901:reshot 200823 from base of t4 using 270m max range. Maybe a 10 kips difference difference in the values.
• 200902:from SE rimwall. Used > 1km range. Duplicates 200901 exactly.
• 200916: shot from the helipad. the 2nd main cable differs by 20 kips. The other cables are closer to the previous kj2 measurements.
• Tower 4 has the failed auxNorth cable.
• I included 200828 in the final average.. not sure if leaving it out would make a large difference.
• Bottom frame: tower 8
• 200901: from sw rim wall looking north. auxNorth is partially blocked by platform.
  
• 209815: from nw rim wall looking south. auxSouth is partially blocked by platform.
• 201021:  from base of tower 8 (1km max range)
• 201021: from base of tower 8 (270 meters max range)
  
• The main cables match exactly for all p50 locations
• auxCables:
• Aux south:
  
• 270 meter max range from sw p50 location is an outlier (shows a flatter cable.. more tension)
• nw location and 2 from under the cable match within a few kips
• Aux north
• 1km max range from nw location is outlier
• other 3 measurements are closer together
• Looks like shooting the aux cables from a particular side gives a higher tension for the aux cable on that side.
• It might be interesting to should a .8mm resolution from under the cable.
  

Over plotting tower to anchor (backstay) cables (.ps)  (.pdf)  (top)

• Top frame: Backstays T12
  
• 200814: from under the cables by sband power supply building. very short distances (39 to 99 meters)
• 200915: from helipad. missed bottom of cables
• 200915: from base of tower 4. missed bottom of cables.
• The last 2 measurements were pretty far: 300 to 450 m.
  
• The spread in the 3 measurements is less than 10 kips.
• Middle frame: Backstays T4
• 200828: from base of tower 4.  relatively short distances: 59 to 130 m.. but shooting straight up took a few sections(fences)
• 200915: from helipad. Missed bottom of cables.
  
• The spread is ranges from 0 to 20 kips.
  
• Bottom frame: Backstays T8
• 200903: from under the cables. Short distances: 23 to 97meters. Instead of using many sections, we just shot everything.
• 200915: from base of tower 4. Long shot: 373 to 469 meters.
• These were surprisingly close considering the differences in the distances measured.
• The main cable  tension variation is consistent.

processing: x101/p50/cables/plottension_bstay.pro

Plotting the average cable tensions (.ps) (.pdf)  (top)

• This averages all measurements at each location.
• The frames are T12,T4,T8
• The cable tensions are printed at the bottom of each frame.
  
• Page 1: platform cables
• T12: Large difference in auxEast,auxWest probably caused by platforms CCW rotation (looking down at it)
• T4: missing auxnorth. The main cables have taken up the missing cable tension.
• auxSouth should have had a lower tension (from platform rotation) but it doesn't, so maybe it took up an equal amount of tension.
• T8: 2 aux cables show large difference from platform rotation.
• Page 2: Backstay cables.
• T12: see some difference in AuxWest,AuxEast. May  be from auxWest slippage,.
• T4,T8; the aux cables  are all less than the drawing operational loads.
• I doesn't look like the rotation in the platform aux cables has been transferred to the backstay cables. 
  

Tension imbalance - platform cables (top)

N/S, E/W tension imbalance on the platform.

    The platform is suspended from the platform cables, and is pulled vertically by the tiedown cables (only t4 and t8 have tension).
Since the platform is stationary (horizontally), the N/S and E/W tensions should sum to 0.

• The average tensions were used to compute the horizontal imbalance.
• North and West are chosen to be positive (to match the setup used by Thorton Tomasetti).
• The first table shows the computed imbalance done by  AO using the average of all datasets.
• The 2nd table shows the  computed imbalance done by Thornton Tomasetti (using the first complete dataset).
• This does not include their balance correction terms.
  

• The plots use the values from the tables.
  
• The main cables show the average cable value (not the sum of the 4 cables)
  
• Page 1: Ratio Thorton/AO calculations
• Top: Axial ratio.
• The largest difference is main T8 main cables (9%)
• Middle: north, south imbalance
• bottom: east,west imbalance
• Page 2: Difference Thorton - AO calculations.
• The T8 difference is about 40 kips per cable.

    Looking at the page that over plots the platform measurements   (Over plotting tower to platform cables (.ps) (.pdf)),
you can see that the T8 mains were measured four times (from 3  different locations).
All of these measurements gave main cable values that matched to within a few kips.

Tension imbalance at the towers. (top)

    The tension imbalance on the towers was computed using the backstay and platform cable tensions.
There are two terms:

• A radial term along the line from platform to tower. Toward the platform is taken as positive.
• A term perpendicular to the radial term. Positive is taken as  CCW from the radial term (looking from above).

The catwalk cables:

    In addition to the platform, backstay cables, each tower has 1 or more cables used to suspend the catwalk.

• These cables do not touch the platform.
• They are connected by a union joint above the catwalk landing.
• Tower 12 has an extra cable that goes from tower 12 to the midpoint of the catwalk (the drawings call this a tieup cable
• the catwalk union joint has 2 more cables that support the catwalk. They connect to the catwalk anchor (next to T12)
• They don't contribute to the T12 force, but they supply a horizontal that increases the southward component of T4 and T8
• This is why the T4 and T8 tensions are higher than the T12 tension.

    Plot of the catwalk cable tensions (.ps) (.pdf)

• Top frame: axial tension for each of the 4 cables
• Cen means the center of the t12,t4,t8 .. What I've called the catwalk union joint above the catwalk landing.
• MidCw is the middle of the catwalk. this is the cable from T12 to the middle of the catwalk.
• Middle frame: horizontal radial tensions.
  
• Since the x,z angles are small: (t12=10.5, t12Mid=37.5, t4=11.77,t8=5.99 deg)  the horizontal values are close to the axial values (cos(th))
• Bottom frame: horizontal radial tensions (sum T12 cables)
• The T4, T8 values are about 60 kips higher than the sum of the T12 cables.
• This is due to the 2 catwalk suspension cables that go from the catwalk union joint to the catwalk anchor.
  
• These two cable pull the catwalk union northward.

The table shows the tension imbalance for the radial and perpendicular  forces on the towers.

• the -62.8 kip perpendicular  imbalance on T4 is from T4AuxNorth failure (+ is CCW or to the north of T4 cables).
  

Summary: (top)

•  Platform weight
• During these measurements, the tiedowns tension varied from 40 to 50 kips (so I'll use an average of 45 kips)

• Computation	Measured value kips	Td Kips	Platform Weight kips
  Ao	2005	45	1960
  thorton (no correction)	1942	45	1897
  thorton (with balance correction)	1925	45	1880

• 
  
• balancing the north/south  and east/west tensions on the platform gave a discrepancy of about 1.3%
• The measured horizontal radial imbalance on the towers is
• T12: 47kips
• T4 22Kips
• T8 43kips (positive is towards the platform)
  
• The measured perpendicular (to the tower,platform line) imbalance forces were:
• T12: 32kips
• T4 -63kips
• -63kips is caused by the missing T4auxNorth cable
  
• T8 14 kips (positive is CCW form toward platform line)
  
• 
  
• Text file containing the average cable tensions and angles used (cbltension.txt)
  

DataNotes:

• Data was take from 14 aug through 21oct10t.
• Temperature variations will cause a change in the tensions.
• We observed during the day (when it wasn't raining).
• Looking at the platform temperature sensor, the air temperature varied from 80 to 87 F during this time
• (the cable temperatures could have been different)..