Computing the cable xz vertical angle
19oct20
plots:
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
Intro (top)
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:
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..
Computing the vertical angles from the fits.
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.
Summary:
- 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