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NASA Technical Memorandum 102627

DETERMINATION OF

CENTER OF GRAVITYMEASUREMENTS

SHUTTLE ORBITERFROM FLIGHT

E. W. Hinson

J. Y. Nicholson

R. C. Blanchard

(NASA-TM-lOZ627) DCTERM[NATIQN OF SHUTTLE

ORBITER CENTER OF GRAVITY FRgM FLIGHT

MEASUREMENTS (NASA) 55 p CSCL 22B

January 1991

G3/18

NFI-I&O58

unclas

032q323

N/LSANational Aeronautics andSpace Administration

Langley Research Centert4ampton, Virginia 23665

https://ntrs.nasa.gov/search.jsp?R=19910006745 2020-04-27T14:59:28+00:00Z

DETERMINATION OF SHUTTLE ORBITER CENTER OF GRAVITYFROM FLIGHT MEASUREMENTS

Edwin W. Hinson

ST Systems Corporation

Hampton, VA 23665

John Y. Nicholson

Vigyan Research Associates, Inc.

Hampton, VA 23665

and

Robert C. Blanchard

NASA Langley Research Center

Hampton, VA 23665-5225

Abstract

Flight measurements of pitch, yaw, and roll rates and the resultant/

rotationally induce/c_inear accelerations during three orbital maneuvers on/

Shuttle mission STS 61-C have been used to calculate the actual orbiter

center-of-gravity location. The calculation technique reduces error

due to lack of absolute calibration of the accelerometer measurements and

compensates for accelerometer temperature bias and for the effects of

gravity gradient. Accuracy of the technique was found to be limited by the

nonrandom and asymmetrical distribution of orbiter structural vibration at

the accelerometer mounting location. Fourier analysis of the vibration was

performed to obtain the power spectral density profiles which show

magnitudes in excess of 104 ug2/Hz for the actual vibration and over

500 ug2/Hz for the filtered accelerometer measurements. The data from this

analysis provide a characterization of the Shuttle acceleration environment

which may be useful in future studies related to accelerometer system

application and "zero-g" investigations or processes.

Nomenclature

Ai, Bi, Ci

ag i

al i

aMi

ar i

aTi

CG

GMT

g

Ixx, Iyy, Izz

Mg

PSD

p, q, r

0

coefficients for HiRAP temperature bias correction

(i = x,z)

acceleration induced by gravity gradient (i = x,z)

total induced acceleration (i = x,z)

measured acceleration (i = x,z)

acceleration induced by rotation (i = x,y,z)

correction for zero offset and temperature bias (i = x,z)

center of gravity

Greenwich Mean Time

acceleration of gravity at sea level (9.806 m/sec 2)

orbiter moments of inertia about Xb, Yb, Zb

orbiter pitching moment induced by gravity gradient

power spectral density

angular velocities about orbiter Xb, Yb, Zb axes

angular acceleration about orbiter Xb, Yb, Zb axes

o

qg

R

t

tref

tl,t2

t3,t4

X,Y,Z

pitch angular acceleration induced by gravity gradient

distance from Earth to orbiter

time

reference time for temperature bias correction

start and end times for pre-manuever data segment

start and end times for manuever data segment

HiRAP axes (parallel to orbiter body axes)

Xb,Yb,Z b orbiter body axes

Xi ,Yi,T{i

I I I

Xi,Yi,Zi

8

Pe

0

offsets of the HiRAP X,Y,Z accelerometer from the

orbiter center of gravity along the ith body axis

(i = x,y,z)

preflight values of Xi, ?i, and Zi

angle between Xb and local vertical

Earth gravitational constant (3.989x1014 m3/sec 2)

standard deviation

orbital angular velocity

3

Introduction

Measurement of very low level linear acceleration of the Shuttle Orbiter

is one of the principal experiments being conducted as part of the Orbiter

Experiments (OEX) Project. The High Resolution Accelerometer Package (HiRAP) 1

has been providing flight measurements since the sixth Shuttle flight on all of

the 0V-102 Columbia and 0V-99 Challenger flights. HiRAP is capable of

measurement in the low 10-6 g range, which has facilitated the determination of

orbiter aerodynamic coefficients and atmospheric density in the hypersonic,

rarefied-flow transition region. An even more sensitive accelerometer system,

the Orbital Acceleration Research Experiment (OARE) 2, is ready for installation

and will return acceleration measurements in the low 10-9 g range. Accurate

interpretation of the OARE flight data will require very accurate knowledge of

the actual orbiter center-of-gravity location at the time of measurement. This

requirement is the stimulus for this analysis of the possibility of orbiter

center-of-gravity determination from flight data. Additionally, the technique

herein or the results from this study may be of interest relative to attitude

guidance and control of large-scale space structures or toexperiments

sensitive to the orbiter "gravity" environment.

4

This analysis is formulated on the concept of induced acceleration sensed

by a linear accelerometer when the body to which the accelerometer is mounted

rotates about its center of gravity. The induced acceleration is proportional

to the angular velocity of the body and the offset of the accelerometer axis

from the center of gravity. The flight measurementsof acceleration for the

analysis were obtained from the HiRAP, and the angular velocity data were

obtained from the rate gyros on the Aerodynamic Coefficient Identification

Package (ACIP), a companionOEXexperiment. This report discusses the

dedicated orbiter attitude maneuvers for the experiment, the resultant flight

data, development of the analysis technique, and results of the analysis.

STS 61-C OEX Attitude Maneuvers

Three attitude maneuvers were performed during the orbital phase of the

STS 61-C mission flown by the 0V-I02 Orbiter (Columbia) in January 1986. These

maneuvers were designed to support several OEX experiments, including this

analysis of in-flight center-of-gravity determination. The maneuver

specifications 3 were intended to produce a simple pitch rotation with minimum

forces and moments during execution of the maneuver. Figure I shows the

maneuver geometry with the orbiter initially belly forward and nose down at an

angle of 20° with the local vertical. This pre-maneuver attitude was

maintained for several minutes by holding a positive pitch rate equal to the

orbital angular velocity of 0.0658 deg/sec. The maneuver was initiated with

the firing of coarse attitude thrusters to achieve a negative pitch rate of

about 0.5 deg/sec, after which the orbiter was allowed to coast in the drift

mode (no thruster firings) to the final position with belly aft and nose up at

180 ° from local vertical. Yaw and roll rates were held to very small values

with ±5° tolerances on the target values of 0° for yaw and ro11 angles. Crew

motion, dumps, and vents were inhibited during the maneuvers. ACIP and HiRAP

data were recorded for several minutes during the pre-maneuver attitude hold,

during the pitch rotation, and for several minutes during the post-maneuver

attitude hold.

ACIP Rate Gyro Flight Data

The flight data from the ACIP rate gyros were recorded during the attitude

maneuvers and processed postflight at the OEX Data Lab (ODL) at NASA Johnson

Space Center (JSC). The processing included calibration corrections for zero

bias, temperature, cross-coupling, and other error sources. 4 The final

calibrated data were provided to NASA Langley Research Center (LaRC) in the

standard OEX computer-compatible tape (CCT) format at a data sample rate of

112.7 per second. The pitch rate measured by the q-channel rate gyro is shown

on figures 2-4 for the three maneuvers and generally conforms to the target

specifications with only three noticeable exceptions. The initial overshoot on

the pitch rate at the start of maneuver I was followed by a very slow

adjustment to acquire the final -0.67 deg/sec rate. This adjustment appears to

have been obtained by pulsing the vernier thrusters over a 30-second interval.

A second deviation occurred during maneuver 3 which shows an initial rate

during the pre-maneuver attitude hold which was below the orbital rate,

resulting in a slow drift toward local vertical. A correction was made with

the vernier thrusters at about t = 55640 seconds, which increased the rate

substantially above orbital rate and caused a slow drift in the opposite

direction. Also in maneuver 3, an unexplained pitch-up, pitch-down

perturbation occurred just before the maneuver was started.

HiRAP Accelerometer Flight Data

The HiRAP flight data were also recorded during the maneuvers and

processed on the same postflight OEX-CCT as the rate gyro data. However, no

postflight calibration of the HiRAP data was performed at the ODL, and the data

received at LaRC were in the form of raw counts from the HiRAP data

electronics. The counts from the X- and Z-axis accelerometers were converted

to units of 10-6 g and plotted (relative to the initial value) in figures

5-10. A steep negative slope caused by a large temperature-dependent bias is

clearly evident in the figures. The actual accelerations, both X- and Z-

channels, are known to be small, on the order of 10-6 g, during the

pre-maneuver hold period. During the maneuver, the theoretical induced

acceleration in the X-channel based on the measured pitch rate is about 43xi0 -6

g for maneuver I and about 21xi0 -6 g for maneuvers 2 and 3. The corresponding

values for the Z-channel are -28x10 -6 g and -13xi0 -6 g. These induced

accelerations can be seen in the plots even in the presence of the temperature

slope and large noise levels.

Rotationally Induced Acceleration

A linear accelerometer mounted on a translating, rotating body at some

distance from the body CG will have an output proportional to the algebraic

sum of the projections onto the accelerometer axis of the linear acceleration

of the body, the rotationally induced acceleration of the proof mass, and the

gravity-gradient-induced acceleration of the proof mass. Previous analysis of

the HiRAP data 5 involved the extraction of the linear contributions which

required an analytical correction for rotation based on the ACIP rate gyro

V

measurementsof rotation rates.

acceleration 6 for the three HiRAPaxes are

a rX

arY

a rZ

The equations for rotationally induced

: _(q2 + r2) Rx + (pq _ _) Yx + (pr + q) Zx

: (pq + _) Xy + (p2 + r2) _y + (qr - p) Zy

: (pr - q) Xz + (qr + I_) Yz + (p2 + q2) _z

7

ar = _ (q2 + r2) RxX

ar : q2 2zZ

where ari, i = x, y, z, are the total rotationally induced accelerations;

p, q, and r are angular velocities about Xb, Yb, and Zb; and Ri, ?i,

2i are offsets of the X, Y, and Z accelerometers from the CG along the ith

body axis. The offsets for the X- and Z-channel accelerometers are shown two

dimensionally (i = x, z) in figure 11.

An in-depth analysis of the relative contribution of the various terms,

based upon STS 61-C attitude maneuver data, was performed to aid simplification

of these equations. The Y-axis was omitted from consideration because the

orbiter CG and the Y-channel accelerometer are both very close to the lateral

plane of symmetry so that the anticipated uncertainty in determination of the

offset is of the same order of magnitude as the offset. The ACIP on STS 61-C

had an inoperative p-channel rate gyro; however, average values of p were

determined from the postflight attitude and trajectory history 7 for STS 61-C.

These values are shown for comparison with the average ACIP q and r values in

tables I and 2 for the pre-maneuver and maneuver segments, respectively.

Retaining only the terms which produce accelerations greater than 0.1xi0 -6 g

and assumming that _ = _ = _ = 0 reduces the equations to

Gravity Gradient Effects

The substantial distance (3.7 m) between the CG and the HiRAP mounting

location contributes to non-negligible gravity-gradient-induced acceleration in

both X- and Z-channels. This acceleration is given for a circular orbit (valid

assumption for STS 61-C) by

agx : 2 w2 (Xx2 + )z2)1/2 Icos B cos (e + tan I

I

Xx

ag z =-, 2)1/2 -1(Xx + _z I sin 8 cos (0 + tan ) I

X'X

where _ is the orbital angular velocity (- 0.0658 deg/sec for STS 61-C), B is

! l

the angle between the Xb axis and local vertical, and Rx and Zz refer

to pre-flight values, The maximum value of agx is 0.91x10 -6 g, which occurs

at 8 = -16.7 ° and 163.3 °, and the maximum magnitude of agz occurs at

0 = -61.7 ° and 118.3 ° with agz = -.7x10 -6 g. Since each ag i is a small

contribution (5 percent or less) to the total measured acceleration, the use of

I I

Xx and Zz introduces negligible error.

The gravity gradient torque exerted on the orbiter during the OEX

maneuvers was primarily about the Yb axis and is given by

3 PeM = (Ig R3 xx

Izz ) sin 8 cos B

The induced angular acceleration is then

o = _ _ 3 Pe

qg lyy R3 IYY

(Ixx - Izz ) sin 8 cos 8

which reduces to approximately

qg = -3.6xi0 -6 sin B cos B (sec -2)

for the STS 61-C orbiter mass properties and orbital altitude. This angular

acceleration tends to stabilize the orbiter Xb axis along the local vertical,O

either nose up or nose down. The maximum absolute value of qg,

1.8xi0 -6 sec -2, occurs at B = ±45 ° and ±135 ° and induces an X-channel linear

acceleration of about ±0.36xi0 -6 g and a Z-channel value of about

±0.56xi0 -6 g. The presence of this effect is clearly evident in figure 12,

which shows the maneuver 3 ACIP pitch rate history from B = 0° to 180 ° compared°

with the theoretical pitch rate obtained by integrating the equation for qg.

Aerodynamic Forces and Moments

The STS 61-C mission was flown during minimum solar activity when the

atmospheric density was minimum at the 61-C orbital altitude. The expected

aerodynamic acceleration for this condition, based on the latest orbiter

flight-derived free-molecule-flow aerodynamic coefficients 8, is less than

0.1xi0 -6 g and is considered to be negligible. The maximum aerodynamic

pitching moment (from C. Cooke and others at Charles Stark Draper Laboratory,

study of Shuttle experiment acquisition, tracking and pointing for Jet

Propulsion Laboratory) produces a q of 2.3x10 -7 sec-2, which would induce

negligible linear accelerations of O.05xIO -6 g in the X-channel and 0.07xi0 -6 g

in the Z-channel.

HiRAP Zero Offset and Temperature Bias

The outputs of the HiRAP accelerometer are temperature dependent and must

be calibrated accordingly for each data set to provide the desired absolute

measurement accuracy. This calibration is normally accomplished through

analysis of flight data from an on-orbit calibration sequence. 5 The zero bias

is established for a reference point, tre f, and the temperature bias slope in

10

integrated over the subsequent measurement interval based on measurements from

accelerometer-mounted thermocouples. For a linear variation in temperature

with time, this correction is equal to

aTx = Ax + Bx (t - tref) + Cx(t - tref) 2

)2= Az + Bz (t - tre f) + Cz(t - tre f

aT z

which is the form used in this analysis. However, no separate calibration

analysis was performed to solve for the coefficients Ai, Bi, and Ci;

rather, their solution was obtained simultaneously with the solution for the CG

offsets.

Solution for CG Offsets

From the foregoing considerations, the total induced accelerations from

the significant sources are

alx = _ (q2 + r2) Xx + agx + qg° _

alz = q2 _z + agz+ qg° X'z

The ith accelerometer flight measurement is then equal to these induced

accelerations plus the reference zero offset and temperature bias at time t.

o _, + Ax + Bx(t i - tre f) + Cx(t i - tref) 2aM = - (q_ + r#) Xx + ag x + qgi x

xi i

= q_ Zz + ag -, + Az + Bz(t _ + Cz(t _ 2aMz i xi - qgi Xz i tref) i tref)

These equations were used with a least squares routine with matrix inversion to

solve for the four unknowns in each equation; Xx, Ax, Bx, and Cx for

the the X-channel and Zz, Az, Bz, and Cz for the Z-channel; while

11

minimizing the difference between the measuredacceleration on the left and the

calculated acceleration on the right. The data sample used in this solution

includes a period during the pre-maneuver attitude hold and an interval during

the maneuver. The solution is equivalent to solving for the CGoffsets based

on the change in induced acceleration for a given change in the pitch angular

velocity between the two periods, an approach which is forced by the lack of

absolute calibration of the measuredaccelerations.

Selection of Data Seqments for Analysis

Figure 13 shows graphically the definition of the two data segments used

for each maneuver in the CG offset calculations. The pre-maneuver hold segment

from tI to t2 was selected to be free from major unmodeled perturbations

and to end prior to the thruster firing which initiated the maneuvers. The

maneuver segment from t3 to t4 was started after the thruster firing

accelerations had damped to a negligible level and contained no major unmodeled

perturbations. The selected segments for the three maneuvers are listed in

table 3 with the values for tre f which were taken to be the approximate time

of maneuver initiation. Each of these segments is approximately 100 seconds

long and contains about 11,200 measurements for a total of about 22,400 for

each maneuver.

CG Offset Solutions

Solutions were obtained for Xx and Zz for the three maneuvers using

the data segments defined in table 3 and also for a group of restricted data

sets. The restricted data sets were defined by applying the criterion that any

measurement whose residual (measured acceleration minus calculated

acceleration) in the unrestricted solution exceeds no is deleted from the data

set. A value of n greater than 7 produces essentially an unrestricted data

12

set, while decreasing values of n produce data sets which are increasingly more

restricted to the central measurements. The CGoffsets obtained for the

unrestricted data and for the sets with n = 6, 5, 4, 3, and 2 are listed in

table 4 and also shownin figure 14 comparedwith the pre-flight values.

Significant variations in Rx and Zz are present in the solutions from

maneuver to maneuverand also across the restricted solutions for a given

maneuver. These results show a strong sensitivity to the distribution of

"noise" in the data, which indicates violation of the assumption of random

normal distribution of noise. The distributions of residuals over the

pre-maneuver and maneuversegmentsare shownfor the unrestricted solutions in

figures 15-20 with the theoretical normal distribution curve shownfor

comparison. Somesignificant departures from randomnormal are seen in these

distributions, both in the central values which would account for the variation

in the CGoffset solution from maneuver to maneuverand in the outlying values

which would account for the variations in the restricted solutions. Without

exception, the quality of fit of the flight data obtained in each solution

varies between the two segmentswith the most pronounced difference occurring

in the maneuver3 X-axis solution, figure 17, for which the far better fit of

the maneuversegment is evident in the high concentration of central values.

In general, these distributions showmuch larger than expected (based on the

randomnormal assumption) concentrations of outlying values above 3o which are

typically non-symmetrical about the mean. Further, the outlying values are not

randomly distributed over the data segmentbut occur as one or more large

peaks. For example, the maneuver3 Z-axis pre-maneuver segment contains 43

measurementswhose residuals exceed 4o, only 3 of which are negative, with 9

positive values in one single peak and 30 positive values in a second peak. A

13

similar situation exists with the maneuversegment for this case which has 55

measurementsabove 4o, of which 46 are positive and contained within four

peaks. The probability of occurrence of values above 40 for a randomnormal

distribution is only 6xi0 -5, or one value in the 22,400 measurementscompared

with a total of 98 for this case.

Analysis of Noise/Vibration Effects

The noise level on the rate gyro data is about 4 to 6 percent of the

measured signal and appears to be random. However, the noise level in the

accelerometer data is of the same order as the rotationally induced

acceleration and frequently exceeds ±50xi0 -6 g. Figure 21 shows the X-channel

accelerometer output for an expanded time scale which depicts the variations

more clearly than does figure 5. The signal does not exhibit the

characteristics of random noise but rather reflects the expected orbiter

structural vibration characteristics; e.g., a composite waveform produced by

several vibration sources such as motors, pumps, and directional antenna

systems.

A fast Fourier transform routine was used to determine the power spectral

density in the accelerometer output for each of the data segments as shown in

figures 22-27. The sample size for this routine was 8192 (213), reduced from

the segment size of 11,200, and therefore covers only 73 seconds of the 100-

second segments. Noticeable differences between the spectra are seen when

comparing the pre-maneuver and maneuver segments for maneuvers I and 3 in both

X- and Z-channels. For example, the pre-maneuver sequence during maneuver 3

for the X-channel (figure 24(a)) shows much lower amplitudes below 2 Hz than

the maneuver segment in figure 24(b), while the opposite is true of maneuver 1

in figures 22(a) and (b). More dramatic differences are seen in the Z-channel

spectra for maneuvers I and 3 where large amplitude spikes are seen in one

14

segment (figures 25(a) and 27(b)) but not in the other segment. Also, the

orbiter structural resonance near 5 Hz (first longitudinal bending mode) is

stronger in the Z-channel. Given the changes that frequently occur between the

pre-maneuver and maneuver segments, significant changes could be expected even

during the span of a single segment. Such changes could certainly alter the

degree to which the vibration signal is randomized and thereby affect the CG

offset solution. A model of the vibration environment for the maneuver 3,

Z-axis case was developed from its component spectrum and was used to generate

a simulated vibration signal which was superimposed on the theoretical output

of HiRAP for the target orbiter rotation rates. Sine waves spaced at

0.0138 Hz from 0.I to 3.0 Hz with amplitudes consistent with the component

spectra were started at zero phase angle 50,000 sec prior to tre f in order to

randomize the composite signal. The simulated HiRAP data were input to the CG

offset solution routine which produced the residual distribution shown in

figure 28. This distribution shows more symmetry and a higher concentration

near the mean when compared with the distributions from the flight data

solutions.

Unfiltered Orbiter Vibration

The power spectral density profiles obtained from the HiRAP data contain

few clues, if any, to the nature and source of the vibrations which would lead

to improvement of the CG solutions. The possibility that the low-frequency

0 to 3 Hz spectrum could be in part due to beating of closely spaced

frequencies above 5 Hz led to the generation of power spectral density profiles

which were corrected for the 43 db per decade rolloff of HiRAP between 2 and 20

Hz. These spectra are shown in figures 29-34. The first longitudinal bending

15

mode resonance near 5 Hz is more pronounced and the large directional antenna

"dither" motion is seen at 17 Hz. Higher frequency components in the range of

5 to 15 Hz are much stronger in the Z-channel as compared with the X-channel.

No obvious correlation between the higher frequencies and the lower frequencies

is present. These data indicate, within the limits of the fast Fourier

transform technique g, the expected level of vibrationally induced acceleration

at the HiRAP mounting location, even during a so-called "quiet" period, which

would bear on any "zero-g" investigation or process.

Conclusions

The technique for determination of the orbiter center of gravity from

flight measurements as described herein produces results which are reasonably

accurate considering the complex acceleration environment in which the

measurements were obtained. The orbiter structural vibration produces a

complex acceleration waveform which is composed of a number of different

frequencies generated by various mechanical subsystems. The operating schedule

for the subsystems varies as does the degree to which the resultant waveform is

randomized. The occasional in-phase amplitude peaks are not random over the

relatively short time segments used in this analysis. Consequently, the

center-of-gravity solution is sensitive to the choice of data segment length

and position and also to any statistical culling procedure. The observed

variation in the solutions is due primarily to variations in the sample

distribution and not to measurement errors or first-order errors in the

temperature bias model; therefore, any improvement in measurement accuracy or

temperature model would not improve the solution. Such improvement would

require more sophisticated analytical and/or statistical methods beyond the

scope of this study. The improved low-pass filter on the OARE will further

16

attenuate the vibration signals and the digital filtering techniques to be

applied during the processing may further reduce the vibration-induced errors

in the center-of-gravity solution.

References

1Blanchard, R. C. and Rutherford, J. F., "Shuttle Orbiter High Resolution

Accelerometer Package Experiment: Preliminary Flight Results," Journal of

Spacecraft and Rockets, Vol. 22, No. 4, July-August 1985, pp. 474-480.

2Blanchard, R. C., et al., "Orbital Acceleration Research Experiment,"

Journal of Spacecraft and Rockets, Vol. 24, No. 6, November-December 1987,

pp. 504-511.

3Detailed Test Objective 0902, JSC-16725, Rev. G., November 1985.

4Kintzer, M. J., "Aerodynamic Coefficient Identification Package (ACIP)

Calibration Report - Calibration 2, January 1983," NASA Report No. JSC-19362

prepared by Lockheed Engineering and Management Services Co., Nov. 1983.

5Thompson, J. M., Russell, J. W., and Blanchard, R. C., "Methods for

Extracting Aerodynamic Acceleration from Orbiter High Resolution Accelerometer

Package Flight Data," AIAA Paper 87-2365, August 1987.

6Wagner, W. E. and Serold, A. C., "Formulation on Statistical Trajectory

Estimation Programs," NASA CR-1482, January 1970.

7Cooper, D. H. and Parker, K. C., "STS-61C Final Report: On-Orbit

Post-Flight Reconstruction," prepared for NASA/JSC by TRW Defense Systems Group

(TRW 47467-HOO4-UX-O0), March 1986.

8Blanchard, R. C., Hinson, E. W., and Nicholson, J. Y., "Shuttle High

Resolution Accelerometer Package Experiment Results: Atmospheric Density

Measurements Between 60 and 160 km," Journal of Spacecraft and Rockets,

Vol. 26, No. 3, May-June 1989, pp. 173-180.

17

9Southworth, R., "Autocorrelation and Spectral Analysis," in Mathematical

Methods For Diqital Computers, New York, J. Wiley and Sons, 1962, pp. 213-220.

]8

Table 1 Average rotational rates during pre-maneuver hold (deg/sec)

Maneuver 1 Maneuver 2 Maneuver 3

p .001 -.0013 .002

q .06 .06 .1

r -.014 -.013 -.011

Table 2 Average rotational rates durlng maneuvers (deg/sec)


p -.01 .018 .008

q -.67 -.47 -.47

r -.029 .0036 -.0014

Table 3 Data Segments (GNT seconds)


tI 31560 60068 55675

t2 31660 60168 55775

tRE F 31700 60177 55805

t3 31730 60210 55840

t4 31830 60310 55940

19

Table 4 CG offsets obtained for various data restrictions.

Restrictions

Xx (pre-flight value = -3.07 m)

Maneuver I, Maneuver 2, Maneuver 3,

m m m

Mean

± deviation,

none -2.932 -3.112 -3.077

6o -2.956 -3.132 -3.205

50 -2.968 -3.132 -3.285

40 -2.982 -3.123 -3.277

3o -3.019 -3.118 -3.103

2o -3.142 -2.987 -3.063

Zz (pre-flight value = 2.021 m)

Maneuver i, Maneuver 2, Maneuver 3,

Restrictions m m m

none 1.986 1.894 2.145

6o 2.058 1.971 2.145

5o 2.030 1.956 2.107

4o 2.004 1.942 2.070

30 1.953 1.933 2.125

20 1.974 1.931 2.118

-3.040 ± .078

-3.098 ± .105

-3.128 ± .129

-3.127 ± .120

-3.080 ± .044

-3.064 ± .063

Mean± deviation_ m

2.008 ± .104

2.058 ± .071

2.031 ± .062

2.005 ± .052

2.004 ± .086

2.008 ± .080

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normal

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Figure 15. Distribution of residuals, maneuver 1,X-axis unrestricted solution.

34

I

6

Fraction

of total

measurements

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• 88

• 06

.84

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(b) Maneuver segment

I

6

Figure 15. Concluded•

35

.18-

Fraction

of' total

measurements

0 - 7.4x18 -6 g•08

.86 o/_r-fltght data

-G -4 -2 0 2 4 G

Multiple of sigma


Figure IS. Distribution of residuals, maneuver 2,X-axts unrestricted solution.

Fractiono£ total

measurements

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•88

•06

•04

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0-6

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fllght data

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of total

measurements

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0-6

fllght data

.... -- .. __ , o_._._]_ _. : f -'_----_,e_..__--._: _-_ :a

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Figure 17. Distribution of residuals, maneuver 3,X-axis unrestricted solution.

36

Fr act i onof total

measurements

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• OB

. BG

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|,

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I

t %

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normal

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!

G

Figure 17. Concluded.

.10

Fractionof total

measurements

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•06

•04

•02

O- II 3x18 -s. g

, _,sflight datag

-6 -4

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Figure 18. Distribution of residuals, maneuver I,

Z-axis unrestricted solutlon.

37

Fraction

of total

measurements

.10-

•08

•06

.04

.02

0-6

O- 11.3x1_Sg

._='sffIIght data

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I

6


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of total

me asurements

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•06

•04

.02

0 = 5.4xI_ -s g

0-6

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-4 -2 0 2 4 13

Multiple of sigma


Figure 19. Distribution of residuals, maneuver 2,Z-axts unrestricted solution.

38

Fraction

of total

me asurements

.10-

•08

•06

•04

.02

0-6

O- 5 4xl_ -s• g

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°

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I

6


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Fract Ion

of total

measurements

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0 = B Ix 10 s• g

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Figure 20. Distribution of residuals, maneuver 3,Z-axis unrestricted solution.

39

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measurements

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.00

• 00

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3x 10-1e I

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42

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Frequency, Hz



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43

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4x10 -:e

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ge / Hz

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2x10 -re

IxlO -le

0 3

Frequency, Hz

I4


Figure 24. Power spectral density, maneuver 3, X-axis.

I5

IG

5x18 -18 _

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2/ Hz9

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2x18 -re

ixlO -le

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6

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3x18 -le

2x10 -le

IxlO -:e

00

L

J I....... J ......

I 2 3 4 5

Frequency, Hz


Figure 25. Power spectral density, maneuver 1, Z-axls.

I

G

PSD,

g2/ Hz

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5x10 -!e

4x10 -re

3x10 -:e

2x10 -re

lxi8 -le

80 1 2 3 4 5

Frequency, Hz



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45

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4x10 -:e

3x18 -|e

2xlg -le

ixlO -Is

0 1 2 3 4

Frequency, Hz

5


Figure 26. Power spectral density, maneuver E, Z-axis.

I6

PSD,

g2/ Hz

5xlg -le

4x10 -le

3x18 -lg

2xlO -le

ixlg -le

00 I 2 3 4 5

Frequency, Hz



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46

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3x10 -le

2x18 -m

Ix 10-Im I

0 1 2 3 4 -- 5

Frequency. Hz


Figure 27l Pouer spectral density, maneuver 3, Z-aXfs.

I

6

5x18 -le

PSI],

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3x18 -re

_ j A_

4 5

Frequency, Hz



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6

47

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Fract|on

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measurements

.25

.20

.15

.10

0 = 14.TxlB-Sg

• _ssimulated data

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Multiple of sigma


Figure 2B. Distribution of residua]s for simulated vibration.

Fract iono_ total

measurements

.30

.25

.2(]

.15

.10-

•05 -

-6

O= 14.TxlO-S g

• _7-s imu Iated data

ormal

_ I - _,,,, --- • _ ..... i, _ |, , . i

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Multiple of sigma


Figure 2B. Concluded.

48

PSD,

gZ / Hz

-?

1°t18-e

I 0 -s

-1818

-1110

-12 j10 8 5 10 15 20

Frequency, Hz


Figure 29. UnTtltered power spectra] density, maneuver 1, X-axis.

-?18

PSD,z

g / Hz

-e10

-918

-1o18

-1110

-lZ i

10 0 5 10 15 20

Frequency, Hz


F|gure 29. Concluded,

49

-718

-B10

PSD,

z /Hzg

-910

-IB10

18-::

-1210 s

0 5 10 15 EO

Frequency, Hz


Figure 30. Unfiltered power spectra! density, maneuver E, X-axis.

-710

-g10

-910

PSD,

g2 / Hz 10 -ss

10 -Is

-1210 J

0 5 10 15 EO

Frequency, Hz



5O

-718

PSD,

2/Hzg

-818

-918

-1o10

-1110

-1218 0 5 18 15

Frequency, Hz


Figure 31. UnTi|tered power spectral density, maneuver 3, X-axis.

-718

-B18

PSD,

2/Hzg

-910

-le10

10 -It

-12 ,j10 0 5 10 15 20

Frequency, Hz



51

PSI],

/Hzg

18 -7 -

10 -e

10 -s

10 -m

10 -zl

-1210 l

0 5 113 15 28

Frequency, Hz


Figure 32. Unfiltered power spectral density, maneuver 1, Z-axis.

PSD,

92 / Hz

10-;'

I 0 -s

I0 -s

_ 10 -ze

10-It

-1210 |

0 5 18 15 20

Frequency, Hz



$2

PSI:},2 /Hzg

-7

10 -e

I 0 -9

ig -lg

10 -11

-12 I

lg g 5 lg 15 2g

Frequency, Hz


Ftgure 33. Unfiltered power spectral denstty, maneuver 2, Z-axts.

-710

PSD,

2 / Hzg

1 B -e

10 -s

-lg10

-1!10

-12 b18 8 5 18 15

Frequency, Hz


Ftgure 33. Concluded.

53

-?18

PSD,

2 /Hzg

-e18 -

-918

10 -I°

0-I:z l

-1210 f

0 5 18 15 20

Frequency, Hz


Figure 34. Unfiltered power spectral density, maneuver 3, Z-axt=.

PSD,

gZ / Hz

18 .7

I0-°

I0-s

10-I°

10 -Iz

-1210 --_

0 5 18 15 20

Frequency, Hz



1. Report No. /

1NASA TM-102627

4. Title and Subtitle

Report Documentation Page

2. Government Accession No. 3. Recipient's Catalog No.

5. Report Date

Determination of Shuttle Orbiter Center of Gravity

from Flight Measurements

7. Author(s}

E. W. Hinson, J. Y. Nicholson, and R. C. Blanchard

January 1991

6. Performing Organization Code

8. Performing Organization Report No.

9, Performing Organization Name and Address

NASA Langley Research Center

Hampton, VA 23665-5225

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, DC 20546-0001

10. Work Unit No.

506-40-91-01

11. Contract or Grant No.

13. Ty_ of Re_rt and Period Cover_

Technical Memorandum

14. Sponsoring ,_gency Code

15. Supptementaw Notes

E. W. Hinson: ST Systems Corporation, Hampton, Virginia.

J. Y. Nicholson: Vigyan Research Associates, Inc., Hampton, Virginia.

R. C. Blanchard: Langley Research Center, Hampton, Virginia.

16 Abstract

Flight measurements of pitch, yaw, and roll rates and the resultant rotationallyinduced linear accelerations during three orbital maneuvers on Shuttle mission STS61-C have been used to calculate the actual orbiter center-of-gravity location. Thecalculation technique reduces error due to lack of absolute calibration of theaccelerometer measurements and compensates for accelerometer temperature biasand for the effects of gravity gradient. Accuracy of the technique was found to belimited by the nonrandom and asymmetrical distribution of orbiter structural vibrationat the accelerometer mounting location. Fourier analysis of the vibration wasperformed to obtain the power spectral density profiles which show magnitudes inexcess of 104 ug2/Hz for the actual vibration and over 500 ug2/H_z.-for fl_e filteredaccelerometer measurements. The data from this analysis provide acharacterization of the Shuttle acceleration environment which may be useful infuture studies related to accelerometer system application and "zero-g"investigations or proce.sses. .

17. Key Words(SuggestedbyAuthor(s))

Accelerometer

Center-of-gravity

Rotational dynamics

19. Security C|assif. (of this report)

18. Distribution Statement

Unclassified-Unlimited

20. Security Classif. (of this page)

Subject Category 34

21 No. of pages54Unclassified

_IASA FORM '1626 OCT 86

Unclassified

22. Price

A04

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