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"_-4r
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
?
i
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)
Maneuver 1 Maneuver 2 Maneuver 3
p -.01 .018 .008
q -.67 -.47 -.47
r -.029 .0036 -.0014
Table 3 Data Segments (GNT seconds)
Maneuver 1 Maneuver 2 Maneuver 3
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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It
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it
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Ef...
O"(3
O
O
Oi.
O)
b.
Fr act ion
of total
measurements
.10
.08
•06
•04
•02
B-6
0 13 2x10 -6
,,,|
-4
.sfl__ ight data.-
normal
-2 0 2 4
Multiple of sigma
(a) Pre-maneuver segment
Figure 15. Distribution of residuals, maneuver 1,X-axis unrestricted solution.
34
I
6
Fraction
of total
measurements
.10
• 88
• 06
.84
• 02
0 - 13.2x10 -6 g
0-6
'Flight data
al
'- -'"f'_l , I , .___L "_-""*,.._.__ L.. _ _ _ ,
-4 -E 0 2 4
Multiple of sigma
(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
(a) Pre-maneuver segment
Figure IS. Distribution of residuals, maneuver 2,X-axts unrestricted solution.
Fractiono£ total
measurements
.10-
•88
•06
•04
•82
0-6
0 = 7 4xl_]-s• g
fllght data
0
_. _normal
-4 -2 0 2 4
Multiple of sigma
(b) Maneuver segment
I
6
Figure IG. Concluded.
.10
Fract |on
of total
measurements
•00
•00
•04
•02
-B0 = 10,4x10 g
0-6
fllght data
.... -- .. __ , o_._._]_ _. : f -'_----_,e_..__--._: _-_ :a
-4 -2 0 2 4 6
Multiple of sigma
(a) Pre-maneuver segment
Figure 17. Distribution of residuals, maneuver 3,X-axis unrestricted solution.
36
Fr act i onof total
measurements
.10-
• OB
. BG
• 04
• 02
O-G
O- 10.4xl_6g
|,
-4
I
t %
D
normal
• I
-2 0 2 4
Nultlple of sigma
(b) Maneuver segment
!
G
Figure 17. Concluded.
.10
Fractionof total
measurements
.08
•06
•04
•02
O- II 3x18 -s. g
, _,sflight datag
-6 -4
_no rma 1
-2 0 2 4 6
Multiple of sigma
(a) Pre-maneuver segment
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
mlg g
_w._normal
I___.__ "--'''_ ].-____.L-__ I, , ... I_'=_- _-_ '
-4 -2 0 2 4
Multiple of sigma
(b) Maneuver segment
I
6
Figure 18. Concluded.
.10-
Fract ion
of total
me asurements
•08
•06
•04
.02
0 = 5.4xI_ -s g
0-6
• _f]tght data/
-4 -2 0 2 4 13
Multiple of sigma
(a) Pre-maneuver segment
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
='o,,ffltght data
°
_= : -- t___ __ _ J
-4 -2 0 2 4
Plulttple of sigma
(b) Maneuver segment
I
6
Figure 19. Concluded.
.10
Fract Ion
of total
measurements
•OB
•04
•02
0 = B Ix 10 s• g
Multiple of sigma
(a) Pre-maneuver segment
Figure 20. Distribution of residuals, maneuver 3,Z-axis unrestricted solution.
39
Fr act t onof total
measurements
.10
.00
• 00
.04
• 02
0-6
0 = B. lxl(_ -sg
• /--flight data
•/
-2 0 2 4
Multiple o'£ sigma
(b) Maneuver segment
!
6
Figure 20. Concluded.
40
L L.- _-._
(_ _ u')._, !
03
I
u
(4
,q.
Mo(4
"oe
"o
nxo
LG>
c
E
m
:3C2.
+)
O
I)>
q..
4.)M
I)I.
eCC
t-UI
:X:
n
n,
T
- O)(_J
eL
O)q,,.
LL.
41
PSI],
g2 / Hz
5x 10 -le
4×10 -le
3x 10-1e I
2×10 -ze
I×10 -le
0 i 2 3I4
Frequency, Hz
(a) Pre-maneuver eegment
Figure 22. Power spectra| density, maneuver I, X-a×fs.
5r G
5×10 -18 _
PSD,
ga/Hz
4x10 -:°
3x 10 -IB
-102x10
Ix18 -le
e _. _ i _ I _I I0 3 4 5 6
Frequency, Hz
(b) Maneuver eegment
Figure 22. Concluded.
42
5×18 -le
PSD,
gz/ Hz
4xi0 -le
3x10 -le
2x18 -le
08 I 2! i I I3 4 5 G
Frequency, Hz
(a) Pre-maneuver segment
Figure 23. Power spectral density, maneuver 2, X-axls.
5×10 -:8
PSD,
gZ/ Hz
4x10 -la
3x10 -ze
2x18 -ta _
00 I 2 3
Frequency, Hz
(b) Maneuver segment
Figure 23. Concluded.
I _ I I
4 5 6
43
5x10 -18
4x10 -:e
PSD,
ge / Hz
3×18 -le
2x10 -re
IxlO -le
0 3
Frequency, Hz
I4
(a) Pre-maneuver segment
Figure 24. Power spectral density, maneuver 3, X-axis.
I5
IG
5x18 -18 _
PSD,
2/ Hz9
4x 18 -10
3x18 -le
2x18 -re
ixlO -le
00
|4
Frequency, Hz
(b) Maneuver segment
Figure 24. Concluded.
. !
5I
6
44
5xl0 -le
PSD,
g_/ Hz
4x10 -ze
3x18 -le
2x10 -le
IxlO -:e
00
L
J I....... J ......
I 2 3 4 5
Frequency, Hz
(a) Pre-maneuver segment
Figure 25. Power spectral density, maneuver 1, Z-axls.
I
G
PSD,
g2/ Hz
Gxl8 -le
5x10 -!e
4x10 -re
3x10 -:e
2x10 -re
lxi8 -le
80 1 2 3 4 5
Frequency, Hz
(b) Maneuver segment
Figure 25. Concluded.
I6
45
PSD,
g2/ Hz
5x18 -le
4x10 -:e
3x18 -|e
2xlg -le
ixlO -Is
0 1 2 3 4
Frequency, Hz
5
(a) Pre-maneuver segment
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
(b) Maneuver segment
Figure 26. Concluded.
I6
46
5x10 -18 _
PSD,
2/ Hzg
4x18 -le _
3x10 -le
2x18 -m
Ix 10-Im I
0 1 2 3 4 -- 5
Frequency. Hz
(a) Pre-maneuver segment
Figure 27l Pouer spectral density, maneuver 3, Z-aXfs.
I
6
5x18 -le
PSI],
g2/ Hz
4x10 -le
3x18 -re
_ j A_
4 5
Frequency, Hz
(b) Maneuver segment
Figure 27. Concluded.
I
6
47
.30
Fract|on
o_ total
measurements
.25
.20
.15
.10
0 = 14.TxlB-Sg
• _ssimulated data
0-6 -4 -2 0 2 4 B
Multiple of sigma
(a) Pre-maneuver segment
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
-4 -2 (_ 2 4 6
Multiple of sigma
(b) Maneuver segment
Figure 2B. Concluded.
48
PSD,
gZ / Hz
-?
1°t18-e
I 0 -s
-1818
-1110
-12 j10 8 5 10 15 20
Frequency, Hz
(a) Pre-maneuver segment
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
(b) Maneuver segment
F|gure 29. Concluded,
49
-718
-B10
PSD,
z /Hzg
-910
-IB10
18-::
-1210 s
0 5 10 15 EO
Frequency, Hz
(a) Pre-maneuver segment
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
(b) Maneuver segment
Figure 30. Concluded.
5O
-718
PSD,
2/Hzg
-818
-918
-1o10
-1110
-1218 0 5 18 15
Frequency, Hz
(a) Pre-maneuver segment
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
(b) Maneuver segment
Figure 31. Concluded.
51
PSI],
/Hzg
18 -7 -
10 -e
10 -s
10 -m
10 -zl
-1210 l
0 5 113 15 28
Frequency, Hz
(a) Pre-maneuver segment
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
(b) Maneuver segment
Figure 32. Concluded.
$2
PSI:},2 /Hzg
-7
10 -e
I 0 -9
ig -lg
10 -11
-12 I
lg g 5 lg 15 2g
Frequency, Hz
(a) Pre-maneuver segment
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
(b) Maneuver segment
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
(a) Pre-maneuver segment
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
(b) Maneuver segment
Figure 34. Concluded.
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