fit for td tension y08_y09.

21feb10 (updated 30mar10)

Links to sections:
Correcting for load cell drift
Histograms of the dataset
Fitting the data
Plotting the fit results
Looking at the fit coefficients
Summary

Links to Plots:
the drift in the cable tensions for the dataset (.ps) (.pdf)
histograms of the data set (.ps) (.pdf)
the results of the fit (.ps) (.pdf)

A fit was done to the tiedown tensions using data from 2008 and 2009.

The data set :

Each tiedown (index 0,1,2 as td12,td4,td8) has two cables with a load cell on each cable. The tension on a tiedown is the sum of these two load cells.
All of 2008,2009, Td data that was interpolated to 2 minute steps to align with the platform height/temperature measurements from the distomats. The data input was:

az,zagr,zach, tdPos[0:2],temp, platformHght, tkKips[0:2]

Npoints raw: 1,049,909 before throwing out bad data.

Correcting for load cell drift:

The amplifiers for the load cells drift over time. Often the drift is in 1 load cell amplifier of the pair at a tiedown. When this happened, i tried to replace the drifting load cell with the one for that same tiedown that was not drifting. To do this:

grab all the data around the most common points: temp=73.9,az=285,zaGr=9.9,zaCh=8.8,tdPos:15.1,15.4,15.1. These should have the same kip values over time.
For each tiedown plot the individual cable tensions for these common points.
Over plot the cable difference (with an offset).
Look to see which of the two cables were causing the difference in tension in the 2 cables.

The plots show the drift in the cable tensions for the dataset (.ps) (.pdf):

Black is the difference in cable tensions (cable1-cable2) with an offsets for plotting for all the data
Red is the tension is cable 1, green is the tension in cable2 for the common points chosen above.
Top td12. Green (cable2) has drifted. red (cable 1) is more stable.
Middle td4: Green cable2 is drifting while red (cable 1) is more stable.
bottom: td8: both tensions are relatively stable.

Correcting for the drifts:

Td 12: use (tensionCable1)*2 for td12 tensions
Td 4: use (tensionCable1)*2 for td4 tensions
Td 8: use tension Cable1 + tension cable2 for td8 tensions.

Throwing out bad data

To remove bad data points the following requirements were put on the data:

2kips < Tension1cable < 60Kips

2kipsmin:Once a cable loses tension, the linear fits can have trouble (since the tension can no be negative).
60kipsmax: to get rid of bad measurements.

55F < tempDegF< 100F. This was to get rid of bad temperature measurements.
platformHght > 1255.8 feet (nominal 1256.22). This is to get rid of bad distomat readings.
1049909 Raw data points
907934 points after applying filter.

Histograms of the dataset:

Histograms were made of the dataset after applying the above filters.
The plots show histograms of the data set (.ps) (.pdf) after apply the data quality filters.

Page 1:temp, az,gr,ch positions

top: temperature. 73.9 F most common.
2nd: azimuth position. The most common azimuths were: 168,180,270,285 and 360 degrees.
3rd: dome za: 9.9,11, and 15 (the az swings of aeronomy).
4th: ch za: 8.8 this is stow. 0 deg is for aeronomy.

Page 2: tiedown jack pull downs (in inches).

1 td12
2 td4
3 td8

Page 3: tiedown tensions measured from the load cells.

this is the sum of the two cable tensions
top, to bottom is td12,4,8.
td4 has a higher average tension than the other 2. Td4 pulls harder than the other two jacks to compensate for the main cable length differences.

Fitting the data.

The fit used:

For each tiedown a fit was done to:

Let i=0,1,2 be tiedown 12,4,8
TensionTd[i]= C0 + C1*(temp-73) +
C2*tdPos[0] + C3*tdPos[1] + C4*tdPos[2] +
C5*cos(az-azTd)*sin(domeZa) + C6*cos(az-azTd)*cos(domeZa) +
C7*cos(az-azTd)*sin(chZa).
The cos(az-azTd) projects the moment arm of the azimuth onto the tiedown direction.
The sin(domeza) cos(domeZa) is used to fit for ampGr*sin(zaGr-zaGr0). The dome has a non-zero za offset because of the fixed counterweight on the ch size of the azimuth arm. There is no counterweight for the ch.
Three fits were done:

All data
8am to 6pm
0 to 6am and 6pm to midnight

tdKips=c0 +c1*(temp-73) + c2*tdPos12+c3*tdpos4+c4*tdpos8+cos(az-tdaz)*(c5*sin(gr)+c6*cos(gr)+c7*sin(ch))
td	c0 constant	C1 tempCoef	C2 td12Pos	C3 td4pos	C4 td8pos	C5 cos(az-tdAz)*sinGr	C6 cos(az-tdAz)*cosGr	C7 cos(az-tdAz)*sinCh	fit Sigmas
12	5.5732276	-0.7407116	1.4399629	0.4627205	0.8141619	-182.4695759	21.1679523	30.2854401	1.7
4	5.5481072	-0.7608992	0.4903692	1.5331098	0.8986088	-179.9594440	20.8633769	31.4882659	1.6
8	-2.2657032	-0.7431898	0.4191552	0.5005065	1.8854497	-183.3214785	20.9092364	29.3240446	1.5
Fit daytime (06 to 18 hours)
12	5.6455217	-0.7150638	1.4364386	0.4544647	0.7800069	-180.9760537	20.8268316	30.5142980	1.7
4	4.9735031	-0.7403918	0.4726905	1.5324140	0.9163808	-180.9848987	21.0036030	31.1481109	1.7
8	-2.8533123	-0.7076089	0.4001283	0.4995190	1.9007027	-184.8074029	21.4216825	28.7082903	1.6
Fit night time (00-06 and 18-24 hours)
12	14.1768464	-0.7223369	0.9779562	-1.2681817	2.5060998	-183.1928313	21.2055318	30.7845388	1.4
4	15.8548171	-0.7434472	0.3061097	2.5335186	-0.5698448	-177.9378664	20.6767039	28.7994148	1.2
8	7.6089936	-0.7352189	0.1031195	1.1601542	0.9238263	-183.6302476	20.7704556	32.3331326	1.0

Plotting the fit results:

The plots show the results of the fit (.ps) (.pdf):

Page 1: 19jan10 while aeronomy did az spins with dome=15,ch=0,all day long.

top: Measured temperature.
middle: measured kips in each tiedown
Bottom: Measured kips - fitkips for each tiedown.

td12 (black) has is about 4 kips below the other. This is because cable2 of td12 is about 4 kips less than cable 1 (it has a dc offset). Putting this back into the difference, the fit of td12 is close to the others.
During the day, the fit does not perform as well as the evenings. This is probably because the air temperature that is used is not the same as the cable temperature. At night these are much closer.

Page 2: Show fit kips for az=182.7, dome going 2-20 degrees. The platform is at the focus position.

top: ch=8.8 degrees stow
bottom: ch=0 degrees

Page 3: The North,south moment arm caused by the tiedown tension for page 2 motion.

Black ch=8.8 degrees
red ch=0 degrees.
The moment arm direction opposes the moment arm caused by the dome motion. Positive is pulling down at td 12 (while the dome goes up 180 degrees from td12).

Looking at the Fit coefs

Temperature:

This shows how the tension in the tiedowns change with temperature while all else remains constant.. But.. the platform height can move with the temperature change so this is not the value that is needed to keep the platform in focus.
-.75 Kips/degF at each tiedown.
2.25Kips (3cables) /degF is the increase in the tension with lowering temperature.
A fit was done for the average tdPos vs temperature when the platform was at the focus (1256.22feet)

avgTdPos=c0 + c1*temp when platform at focus
data set	tdInch/DegF C1	offset C0
allData	-0.322326	38.425
Day (6am to 8pm)	-0.314786	37.6874
nite (0-6am,8pm-00)	-0.234406	32.3917

TdPosition

Kips change when a tiedown is moved by 1 inch.
moving a tiedown will cause the tension in the other 2 to change (in the same direction) because the average height of the platform will be changed.

The night time fits have some negative numbers (they should all be the sign). The tiedown positions my be interacting with a limited number of azimuth positions.

The total tension change for 1 tiedown inch on all 3 tiedowns it around 8kips/tdinch

The tiedown cables move 1.7 inches for every platform inch.
It should take about 8 kips to move the platform 1 inch.
1.7 tiedown inches would be 14.2 kips/platform inch.. .this is a bit high.

kips change while moving all tiedowns 1 inch


	td12	td4	td8	TotalKips all 3 cables
allData	2.7	2.9	2.8	8.4
Daytime	2.7	2.9	2.8	8.4
niteTime	2.2	2.3	2.2	6.7

Ratio Dome/ch weights.

Using the coef's c5,c6, c7 you can compute the ratio of DomeWeight/chWeight:

Ratio=sqrt(c5^2 + c6^2)/c6
Alldata : Wdome/Wch= 6.04
NiteData:Wdome/Wch=5.98
How to the standard dome, ch weights agree with this ratio:

The table below shows the dome/ch ratio for the accepted weights values as well as how much we would have to change the dome or ch to get a ratio of 6.02.

type	Wdome Kips	Wch Kips	Ratio
acceptedVals	215	35	6.14
modDome	210.7	35	6.02
modCh	215	35.7	6.02

Where the dome balances the counterWeights (chza=0)

Measuring the Dome za (zaEGr0) that balances the counterweight when zaEch=0

Terminology:

let E be encoder za
let Cm be za for dome center of Mass
let zaEGr0 be the the za where the dome balances the counterweight with the ch at za=0

When the ch is at 0 deg za, the dome balances the counter weight at zaEGr0 degrees.

The counter weight includes: 45 kips at 145 feet, the vertex shelter, stairway to bottom chord, ..etc.

We measure zaEGr0 from the fit coefficients C5 and C6:

grAmp*sin(zaEGr-zaEGr0)=grAmp*[cos(zaEGr0)sin(zaEGr) - sin(zaEGr0)cos(zaEGr)]=[c5*sin(zaEGr) + c6*cos(zaEGr)]
C5=grAmp*cos(zaEGr0)
-C6=grAmp*sin(zaEGr0)
grAmp=sqrt(c5^2 + c6^2)
zaEGr0=atan(-c6/c5)
Using the 3 separate td fits we get:

td12: zaEGr0=6.6, td4:zaEGr0=6.6,td8: zaEGr0=6.5 degrees za.
zaEGr0= 6.5 deg (encoder/optic axis za) where the optic axis za is uphill from the za for the center of mass.

Going from optic axis zaE to center of mass zaCm for the dome.

The zaE in the fit uses the za encoder (optical axis za). This is 1.1113 degrees uphill from the dome centerline.
Jose Maldonado's dome weighing of 27feb03 showed a discrepancy in the uphill, downhill weights of the dome:

uphill 48,040, downhill 167,620 lbs.
Assuming the lift points were +/= 10.75 feed from the dome centerline, and the radius for the 10.75 foot lift separation is 425 feet:

Center of mass dome=asin[(48-167)/(48+167)*10.75 /425ft]=-.802 degrees downhill from the dome centerline.

Combining the optic axis and weight unbalance gives:

zaCmGr= zaEGr-1.913 degrees. The center of mass is downhill from the encoder za

zaCmGr0=6.5 - 1.913 = 4.59 zaCmGr

Standard tiedown position for focus.

When the platform is in focus (1256.22 feet), the average tiedown position is only a function of the temperature. This equation can then be used to predict the tiedown positions for any temp when the platform is in focus.
The dataset to do this used the following specs:

tdRefPos=[14.9969,15.2455,15.0182] (td12,4,8) at 73 degF
Require the platform to be within .1 inches of 1256.22
require the tiedown offsets to be within .1 inches of the correct value.

The fit was done using data all day. It was also done using 6:20 hrs for daytime and [0:6],[20:24] for nightime
The fit results were:

AvgTiedown Position vs Temp when platform in focus
	c0	c1 tdInch/degF	sigma td inches
all data	38.5557	-.323769	.54
daytime [6:20] hours	37.9014	-.317351	.62
night: [0:6] and [20:24]	32.4796	-.235531	.21

The plot shows the fit residual vs hour of day (.ps) (.pdf):

the data was median filtered by a factor of 20 to cut down on the file size. This made some of the excursions smaller.
The rms increases around sunup 7-8 am. It then falls during the day.

when the residual increases, the tiedowns need to be pulled down more, so the main cables are colder than the temperature reading.
When the residual drops below 0, the tiedowns need to be pushed up, so the main cables are warmer than the temperature sensor reading.
The drop during the day is explained by the cables getting heated by the sun.
The jump up at sunrise (7,8 am) having the cable colder is a bit harder to explain. It could be some kind of condensation on the cables (but 8am is a bit late for that).

SUMMARY:

	Measurement	Result
	quality of fit	robust rms of fit = 1.7 kips for each td tension.
	Kips change with Temperature This does not leave the platform in focus	-.75kips/degF at each tiedown -2.25Kips/degF combine 3 tiedowns
	Kips change with tiedown position. move all 3 tiedowns together 1 td inch This does not leave the platform in focus 8.4 kips should move the platform 1".. 1.7 td"/platform" so this value is high by a factor of (1.7 day),or (1.4 nite)	[td12,td4,td8] [2.7 ,2.9,2.8]kips all data and daytime [2.2 ,2.2,2.3]kips nightime 8.4 kips total 3 tds day,all data 6.7 kips total 3 tds night.
	Ratio DomeWeight/ChWeight The ratio makes no assumptions about the dome or ch weight. It uses the tension fits for ch,dome za dependence.	6.02 (average of all data, and nightime meaurements. Using dome=215,ch=35 ==> ratio=6.14 Using dome=210.7, ch=35 ==> ratio=6.02 using dome=215, ch=35.7 ==> ratio=6.02
	Offset zaCenterMass to zaEncoder	1.913 degrees (the encoder za is the same as the optic axis za and is uphill from the center of mass za)
	Where dome za balances all counter weights (zach=0)	zaEGr=6.6 zaCmGr=4.56
	Reference positions for most common data with the platform close to focus (1256.22feet)	tdRef =[14.8594,15.1085,14.8809] tdOffset=[ -.0902 , 0.1589 -0.0687] temp: 73.5F
	Notes
	1.The fit will not work if the computed value is < 0 (the tiedown cables can not have negative kips).
	2.The fit is available in the idl routine tdkips09 (@prfinit)

processing: x101/100217/tdkipsfit.pro

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