Over plot platform xz cable angles for 3 computation methods (.ps) (.pdf)

Over plot backstay xz cable angles for 3 computation methods (.ps) (.pdf)

** Other pages:
Cable tensions from the p50 sag
survey
Tower4 auxNorth
failure
**

Let x,y be in the horizontal plane,and z
is positive up. The sag survey computation rotates the cable
datapoints into the xz plane and the fits a catenary.

To compute the cable tension from the sag survey, you need to know
the vertical (xz) angle of the cable.

Assume the catenary fit is:

- z=A + B*(cosh(x-C)/B - 1)

- Then the cable tension is:
- Tension=B*cableLinearWeight*cos*(xzVerticalAngle)

Prior to fitting for the catenary i did a 2nd order
fit to remove outliers:

- z=c0 +c1*x +c2*x^2

Up until 19oct20 i was using the c1 coef from
the fit to compute the xz angle.

When i distributed the results of the cable tensions ,
pierre ghisbain pointed out that the vertical angles i reported
were not consistent

- Different measurements of the same cables (say the mains) were getting vertical angles that were differing by up to a degree or more
- 1 degree difference at 575 feet gives a vertical distance difference of 10feet..

When fitting a catenary to each cable data
set:

- we get the coef of the catenary fit to the data
- we also have the min,max x value used in the fitting
- Plugging the xmin,xmax values into the catenary fit will give you the vertical angle (atan(deltaz/deltax))
- In almost all measurements, xmax-xmin is less that the expected length (using drawings cable length and attachment points).
- This is mainly caused by the measured points close to the platform connection point being obscured by parts of the platform.
- using Xmax from the data set and xmin=(xmax-ExpectedXvalueFromDrawings) as the minimum value you can also compute the slope
- You could argue that the expected xmin is coming from the drawings angle.. except that i'm still using the y values from the fit...

Plots were made showing the (measured xzangle - drawingsXzangle)
for the platform and backstay cables.

- The differences were computed for:
**using the 2nd order fit**linear term to get the xzangle**using the catenary fit with the xmax,xmin**data values.**using the catenary fit with the xmax from the values and a computed xmin from the drawings**cable length and angle.- colors were used to separate out the results.

- There are 3 frames for each page:

- Tower 12, tower4 and tower 8.
- Measurements sets are separated by dashed vertical lines.
- T12: 3 platform sets, 3 backstay sets
- T4 : 4 platform sets, 2 backstay sets
- T8 : 2 platform sets, 2 backstay sets.

Over plot platform xz cable angles
for 3 computation methods (.ps) (.pdf)

- the xz angles from the drawings are: 12.77 deg mains, and
10.09 aux, so a .1 deg difference is about 1%.

- T12: main cables: the catenary computations are .2 degrees larger than the drawings value
- T4: main cables: the catenary with xmin from drawings is within .1 degrees of the drawings values
- T8: main cables: the catenary values are within .1 degrees
- The aux cables for the catenary values with xmin from drawings have differences of .1 deg or less

Over plot backstay xz cable
angles for 3 computation methods (.ps) (.pdf)

- the xz angles from the drawings are:
- main: 35.64,35.66,26.15 for T12,T4,T8
- aux: 35:45, 35.49,26.57 for T12,T4,T8
- a .1 degree difference is about .3%

- the xzangles are within .1 degrees for the catenary computation with xmin from the drawings.

- Using the linear term from the parabolic fit to the cables gave xz angles that differed from the drawings angles by up to 3 degrees.
- Using the xmax,xmin from the data set and the catenary fit gave values that agreed with the drawings angle to better than .2 degrees
- Using the catenary fit, xmax from the dataset , and computing
xmin from the drawings cable length and angle

- matched the drawings angle to better than .1 degree .. except for tower 12 main cables that were consistently .2 degrees larger than the drawings angle.
- You might argue that using the drawings cable length and angle
to compute xmin might be forcing the angle to match the
drawing angle..
**BUT:**

- Tower 12 had a .2 degree offset. At a 575 foot radius this is a vertical offset of 575*sin(.2) = 2 feet.
- The laser ranging data shows that platform corner 12 is 2
feet low (
**matching what the cable tensions show**).

* processing: x101/p50/cables/xzangle/chkxzangle.pro,
chkxzangleplot_plat/bstay.pro*

home_~phil