- Email: [email protected]
Entry Trajectory Reconstruction Using Flight Data
E!\'TRY TRA.JECTORY RECONSTRUCTION USING FLIGHT DATA
formerly now with
Raymond Morth MIT Instrumentation Laboratory Cambridge, Massachusetts Intermetrics, Inc. 380 Green Street Cambridge, Massachusetts
Abstract The excellence of the A.pollo flight data has made possible a rather complete analysis of these data. A method has evolved by which not only can the true trajectory be determined, but fairly accurate estimates can be made of the significant errors involved. This method and several examples of Apollo entry trajectories are the subjects of this paper. ...\ccelerometer data and onboard navigation data (position and velocity) from the Apollo entry are the basic material for the two-step reconstruction process. First. the acceleration data are fed into a reproduction of the onboard navigation process and the navigation is repeated. This is done so that a complete set of acceleration data can be obtained; some points are always missing from the telemetry record. In this repitition of the navigation these missing acceleration points are filled in. This complete set of data is again processed utilizing 3. model of the onboard navigation. This time the significant instrument errors such as inertialplatform misalignment and accelerometer bias are estimated in the model so that external events along the trajectory are matched. As will be described, a significant improvement in the Apollo navigation was made by correcting an instrument error detected by this method. Introduction The seven guided flights of Apollo have provided excellent flight data. Not only has there been good coverage but the quality of each individual record has been high. There have been four manned and three unmanned flights. As will be seen. the men considerably improved the quality of the flight.
manual cut-off signal to the SPS engine. The third flight (AS-502) entry \"elocity was almost 4000feet-per-second slower than planned because the SIVB engine failed to reignite during the simulated translunar injection maneuver. The manned flight experience includes two orbital entries and two escape speed entries. The orbital entries were performed by Schirra, Eisele, and Cunningham, in Apollo 7; and McDivitt, Scott, and Schweickart in Apollo 9. The two escape speed entries were Apollo 8 (Borman, Anders, and Lovell) and Apollo 10 (Stafford, Cernan, and Young). All four of these manned missions were automatically ,controlled. The decrease in steering and navigation errors in later flights shows that the earlier flights provided useful data to improve oLlr equipment and techniques. Some improvements we have derived from the flight data have not yet been flown. During the Apollo entry the telemetry data channel is blocked by the ion sheath which surrounds the vehicle. Because of this, the data are stored on a tape recorder and the tape recorder is recovered after the flight. The tape recorder record shows fewer gaps or bad words than a similar record transmitted over radio channels. The completeness of this data is important to the analysis. If it were not for the integrity of the data, this method might not have been developed. The guided entry has been described at the second IF AC conference in Ref. 1. Basically, it is a guidance based on simple analytic formulas. This has been tailored to the digital computer used in the implementation. Entry from orbit is guided by referring to a prestored reference trajectory. Entry at escape speeds uses both a constant-drag portion to dissipate some of the energy if required, and an analytically defined exit reference trajectory. Gains that control this reference trajectory have been optimized to increase the error tolerance of the system. More detailed material concerning the entry guidance can be found in Reference s 2, 3, and
4. The entries cover a wide range of velocity and flight path angle as shown in Table 1. The earliest flight. AS- 202. was a heat- shield test at the highest velocity attainable with the Satu rn 2 booste r. The second flight . .\S-501, was another heat- s hield test. This flight attained e sc ape s peed as well a s a steep entry angle. [n fact. an overspeed resulted from a late
The guidance computer segm e nt i s but a s mall part of the total telemetry record. [t con s ists of 200 s ingle-precision words tr a n s mitted every two s econds. Each word ha s fifteen binary digits. Only the data needed for the n a vigation calculations are important to this discussion. These are acceleration
712
The initial-condition error estimates are usually set to zero, because these errors are small when compared to the other error contributors. However, it was deduced that Mission AS- 502 had a rather large velocity error. This error was supposedly caused by noise in the tracking system. The manned flights showed no such error.
data and position and velocity data as calculated by the Apollo Guidance Computer (AGC). The Pulsed Integrating Pendulous Accelerometers (PIP As) which are mounted in a fixed attitude orientation in the Inertial Measurement Unit (IMU) measure acceleration in the form of velocity increments or pulses. Each pulse from the accelerometer denotes a velocity change of 5.85 cm/ s. These data are compensated for scale-factor and bias errors before being used in the navigation routine. Also included in the flight data but not vital to the calculations are the gimbal angles relating the stable member of the IMU to the spacecraft.
Shown in Fig 3 is the trajectory for the last few minutes of the flight of Apollo 8. This trajectory shows a two-mile overshoot of the target at the point where the chutes are deployed. Note also that the spacecraft drifts about two miles after the chutes are deployed. This overshoot is caused by a different flight performance of the vehicle as compared with the simulation. At a velocity of 1000 feet per second no new guidance commands are issued so that fuel may be conserved in the reactionj et control system. The guidance system is openloop from this point on. But the flight showed a straighter and slightly longer arc than that shown in the simulations, causing the bias. As navigation performance has improved, this bias has become the significant error. In subsequent flights this has been corrected in the hope that the navigation performance will continue to be as good.
The navigation algorithm is shown in Fig. 1. It is the so-called Average-G routine. Because the imperfections of the guidance equipment are severely stressed during entry, it is the best mission phase in which to determine these imperfections. This is the longest period of inertial navigation, sometimes over one hour, although the actual entry only takes about ten minutes. On the unmanned flights it was not possible to realign the IMU between launch and splash. This extended period did require a ground update of position and velocity. Significant navigation errors accrued even with this ground updating. During entry the spacecraft is also subject to severe acceleration - up to 10 g - while the vehicle attitude rates are at their highest during this period.
Shown in Fig 4 is the altitude time history for Apollo 10. The marked improvement in performance is due mainly to the shorter drift time of the inertial measurement unit. The platform was aligned about one hour before entry by the crew. So far, Dave Scott in Apollo 9 holds the record for the most accurate alignment.
The navigation can fail to indicate the true position and velocity for a variety of reasons: the IMU is subject to misalignment and drifts, The PIP As have scale factor and bias errors, and the initial conditions may also be in error.
A navigation algorithm error was detected by the trajectory reconstruction method. Some significance was lost in the magnitude of g by unnecessarily losing some precision in calculating the value of the square of R. Though this meant that g was increased incorrectly by at most 0.030/0, the method detected this error.
Extended error analyses are made to determine the effects of these errors (for example, Ref 5). A by-product of the method of this paper is the close agreement obtained with the standard error analysis. This strengthened our confidence in both methods.
Similarly , an incorrect scale factor on R was detected. In convertinl{ the data to a format compatible to the MIT computer, the position vector had been increased by about 0.002 per cent. Reproducing the on - board calculations detected this error.
One of the main goals of the flight data analysis is to determine these errors so that future improvements might be made. Results
The aerodynamic data has been described elsewhere (Ref 6), but some discussion is in order here. The lift-to-drag ratio (L/D) is available through resolution of the acceleration into components along and normal to the velocity vector. As a matter of fact, the aerodynamicist thinks of the guidance equipment as instrumentation for an extended hypersonic wind-tunnel test. If that were the goal, the equipment is overdesigned. But it does provide a superb record for an extended period of hypersonic flight. Knowledge of L/ D is critical to proper entry steering performance. For the first flight L/ D was below specification and, because of this, the vehicle fell about 200 miles short of the intended landing site. Since then, L/ D has been maintained at very close to the design value. Figure 5 shows a time history of L/ D for Apollo 8. The design value of 0.3 was almost exactly attained. The abrupt rise
Shown in Fig 2 is the altitude time history of AS- 501. The final altitude error of nearly 200,000 feet is characteristic of the early missions in which a long period of drift time elapsed before the platform was used. The platform alignment error in the critical pitch direction was determined to be 0.5 0 by this method. This was higher than the instrument preflight history had led us to expect. With this motivation, the calculation of the compensation parameters was reexamined. The gyro- bias drift term was altered so as not to correct for the G - sensitive drift as measured in the laboratory. This uncorrected compensation was used in the next flight resulting in a marked improvement in performance.
713
AVERAGE-G NAVIGATION ALGORITHM -
-
- OT
F
VI ' V + G T +"2
I '
I
AS 501
R • if + VI OT
v • VI
+l + GQ! 2
§
2
~-
where
R, V • position and velocity vectors VI
• temporary velocity vecto r
DT
• time increment
• gravitational constant • 2nd spherical harmonic coef
OR UZ
• R/R • unit north vector
SL
• sine 01 geocentriC latitude
reconst ructed J
• OR· UZ • velocity increment from acceleromete r
G
i-
- I - - + ---- - -
30.0
• gravity acceleration
F ijtu rl' 2
-r '-
APOLLO 8 GROUNOTRACK AT SPLASH
- - j - - -..
8.16 RE CONS TRUCTED PITCH MI SAliGN ME NT ' 0.02 0 • 10 SECONDS 8ETWEEN POINTS
v- lOoolps
+..· - - -·- - - - --+ - · - .........· · -30.5 TIME 11000 s J
1·· .. ----+----- -1- _
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7.0
6.0
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TA RGET
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8.13
~ ~
§
'"
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~ 8.12
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~ KNOT EASTERL Y WIND
STIERING ERROR I. 45nm
NAVIGATION ERROR 0. 33nm
- 165.06
- 165.04
~
- 165. Cl? LONGITUDE
5.0 4.0 3.0
«
2.0 1.0
OROGUE MAIN
indicated
( reconst ructed
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and fall near the end of the record is an expected characteristic of the Apollo spacecraft at transonic speeds. However, the slow steady climb in the hypersonic region is as yet not explained.
the east-west movement by adjusting accelerometer biases. Shown in Fig 8 are the pitch misalignments as deduced for each of the missions. (Typical misalignments are in the order of 0.1 deg.)
In the later flights, the calculation of LID is also accomplished on-board by the AGC and is available on the telemetry record. This has proved valuable as a "first guess" of this critical parameter. There was some thought of using this measurement in the steering equations, but this proved to be unnecessary when the actual LI D consistently came very close to the design value. Another indication of the quality of navigation in the later flights is the accuracy of this on-board LID calculation. Three significant digit agreement is common with the on- board and reconstructed trajectory calulation of LID.
Second-order clues are also helpful. Each time the vehicle shows a roll reversal there is a shift in the measured L/ D. This shift is due mostly to navigation errors, and corrections in the platform alignment can be made based on this evidence.
Analysis The first step in the two-step trajectory reconstruction is to ensure that all the data points of the acceleration time history are included. Somewhere between 3 and 20 points are missing (usually at some abrupt change in the acceleration of the vehicle such as at splash or when the chutes deploy) from each flight record, with fewer points missing on the later flights. It is relatively easy to replace these missing points since the first and second integrals, position and velocity, are available. On Mission AS-501 a particularly poor dropout of about six points came near the first acceleration peak. But these points were found, or at least the total change in velocity was determined, and then divided through the six points. The acceleration time history is shown in Fig 6. The replaced points are discernable at the pointer. The main chute, drogue chute, and splash events are clearly marked. These acceleration data are then modified with an estimate of instrument imperfections as shown in Fig 7. Both the IMU misalignments and PIP A errors are modified. These modifications are made to match external events along the trajectory. The significant external events are listed in Table 2 along with the nominal value of each point. As in all inertial navigation situations, the altitude channel is the most critical. (The altitude channel is naturally divergent, while the range and track channels are periodic.) To avoid problems of gimbal lock, the platform is aligned so that the middle gimbal angle is near zero at the start of entry. This means that the y-axis of the IMU is normal to the trajectory plane. Because the y-axis gyro defines the pitch axis, altitude variations are most sensitive to misalignments in this direction. (Typical values for the biases are 0.2 cm! s2 while typical sensitivities can be found in Ref 6.) The usual reconstruction procedure is to first control the altitude and altitude rate by adjusting the pitch alignment alone. Then to control the north - south velocity by the roll and yaw. Finally, to control
For safety reasons some loss in capability has occured with the manned flights. That is, the splash event is no longer measured, because power is turned off to avoid the possibility of short circuits. Conclusions How do we know that we have a unique solution? We don 't know. However, many different external events must be matched (most of these are strongly influenced by a unique error source) that our confidence is reasonably high. More work can certainly be done, particularly in weighting errors in each of the external events. (This appears to be a natural problem for Kalman filter techniques.) Other areas under consideration include timevarying errors such as gyro drift, and a more systematic estimate of initial-condition errors. Motivation for these improvements in the Apollo project is not strong. The raw flight data show such small errors that the instrument imperfections we are now detecting are startlingly small, as are the errors in alignment made by the astronauts. The method described is deceptively simple. No complicated mathematics are utilized. The sensitivity of the trajectory to small variations makes a powerful tool of a simple concept. We firmly believe that a strong effort should be made to get as much as possible out of the flight data. The aerodynamics, particularly the L/ D rise, is still under study after seven flights. Because of analyses like these, we expect Apollo 12 to come closer to the target than any of the previous flights. References
1. Morth, R., " Reentry Guidance for Apollo ",2nd IFAC Conference, Vienna, September, 1967. 2. Morth, R., "Entry Flight Data for Mission AS 202", MIT/IL Report E-2031, October, 1966. 3. Morth, R., "Entry Flight Data from Apollo 7", MIT/IL Report E-2404, April, 1969. 4. Morth, R., "Entry Flight Data from Apollo 8", MIT/IL Report E-2405, April, 1969. 5. Grant,F .D., Kriegsman,B., Muller,E.S., Werner,J., White,R.,"Mission G G&N Error Analysis",MIT/IL Report E-2427, July! 1969. 6. Hillje, E., "Entry Flight Aerodynamics From Apollo Mission AS-202", NASA TN D-4185, October, 1967.
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ACCElEROMtTER CORRECTIONS PITCH MISALIGNMENTS F'
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.
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MISSION
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DISCUSSION
Q. What kind of model did you use for the reconstruction of the fl ight comp lex ',as it?
dat~l,
and hol\'
A. Perhaps T s hould refer to my paper and the references T used where i1 complete set of data for Apollo 7, 8 and 9 is repeated as well as the computer progr:UlI~ hy \\'hich this was deduced. But to ans\\er your question, no there 1\'as no nw,de l \\'h:1tsoevcr for the vehicle . The reconstruction was to merely use the complete set of acce ~ erilt:ioll data , i nt egrating this again with plat fonn, hi ases, dri fts, angles , III i q 1 i gnelllents :1<; well as accelerometers until the extemrtl events were miltchecl as shOlm 011 onc 01" my slides . This turns out to be extremely sensitive; iI tiny ch:mge in onc of these error sources would more than exceed the bounds of expected error .
Q.
How long before the re-r:ntry is the p l rttfonn aligncd?
A.
It is a li gned roughly tl\'O hours before the rc-entry .
Q.
Did you use data from pre launch tcsting on the instnullent?
A. No, bu t we did use tbs data to improve the prelaunch testings. \\'e detellllined that the gyro drifts had been uncorrect l v calculated. T think it is too long to enter into it here but it is briefly described in my paper .
718
formerly now with
Raymond Morth MIT Instrumentation Laboratory Cambridge, Massachusetts Intermetrics, Inc. 380 Green Street Cambridge, Massachusetts
Abstract The excellence of the A.pollo flight data has made possible a rather complete analysis of these data. A method has evolved by which not only can the true trajectory be determined, but fairly accurate estimates can be made of the significant errors involved. This method and several examples of Apollo entry trajectories are the subjects of this paper. ...\ccelerometer data and onboard navigation data (position and velocity) from the Apollo entry are the basic material for the two-step reconstruction process. First. the acceleration data are fed into a reproduction of the onboard navigation process and the navigation is repeated. This is done so that a complete set of acceleration data can be obtained; some points are always missing from the telemetry record. In this repitition of the navigation these missing acceleration points are filled in. This complete set of data is again processed utilizing 3. model of the onboard navigation. This time the significant instrument errors such as inertialplatform misalignment and accelerometer bias are estimated in the model so that external events along the trajectory are matched. As will be described, a significant improvement in the Apollo navigation was made by correcting an instrument error detected by this method. Introduction The seven guided flights of Apollo have provided excellent flight data. Not only has there been good coverage but the quality of each individual record has been high. There have been four manned and three unmanned flights. As will be seen. the men considerably improved the quality of the flight.
manual cut-off signal to the SPS engine. The third flight (AS-502) entry \"elocity was almost 4000feet-per-second slower than planned because the SIVB engine failed to reignite during the simulated translunar injection maneuver. The manned flight experience includes two orbital entries and two escape speed entries. The orbital entries were performed by Schirra, Eisele, and Cunningham, in Apollo 7; and McDivitt, Scott, and Schweickart in Apollo 9. The two escape speed entries were Apollo 8 (Borman, Anders, and Lovell) and Apollo 10 (Stafford, Cernan, and Young). All four of these manned missions were automatically ,controlled. The decrease in steering and navigation errors in later flights shows that the earlier flights provided useful data to improve oLlr equipment and techniques. Some improvements we have derived from the flight data have not yet been flown. During the Apollo entry the telemetry data channel is blocked by the ion sheath which surrounds the vehicle. Because of this, the data are stored on a tape recorder and the tape recorder is recovered after the flight. The tape recorder record shows fewer gaps or bad words than a similar record transmitted over radio channels. The completeness of this data is important to the analysis. If it were not for the integrity of the data, this method might not have been developed. The guided entry has been described at the second IF AC conference in Ref. 1. Basically, it is a guidance based on simple analytic formulas. This has been tailored to the digital computer used in the implementation. Entry from orbit is guided by referring to a prestored reference trajectory. Entry at escape speeds uses both a constant-drag portion to dissipate some of the energy if required, and an analytically defined exit reference trajectory. Gains that control this reference trajectory have been optimized to increase the error tolerance of the system. More detailed material concerning the entry guidance can be found in Reference s 2, 3, and
4. The entries cover a wide range of velocity and flight path angle as shown in Table 1. The earliest flight. AS- 202. was a heat- shield test at the highest velocity attainable with the Satu rn 2 booste r. The second flight . .\S-501, was another heat- s hield test. This flight attained e sc ape s peed as well a s a steep entry angle. [n fact. an overspeed resulted from a late
The guidance computer segm e nt i s but a s mall part of the total telemetry record. [t con s ists of 200 s ingle-precision words tr a n s mitted every two s econds. Each word ha s fifteen binary digits. Only the data needed for the n a vigation calculations are important to this discussion. These are acceleration
712
The initial-condition error estimates are usually set to zero, because these errors are small when compared to the other error contributors. However, it was deduced that Mission AS- 502 had a rather large velocity error. This error was supposedly caused by noise in the tracking system. The manned flights showed no such error.
data and position and velocity data as calculated by the Apollo Guidance Computer (AGC). The Pulsed Integrating Pendulous Accelerometers (PIP As) which are mounted in a fixed attitude orientation in the Inertial Measurement Unit (IMU) measure acceleration in the form of velocity increments or pulses. Each pulse from the accelerometer denotes a velocity change of 5.85 cm/ s. These data are compensated for scale-factor and bias errors before being used in the navigation routine. Also included in the flight data but not vital to the calculations are the gimbal angles relating the stable member of the IMU to the spacecraft.
Shown in Fig 3 is the trajectory for the last few minutes of the flight of Apollo 8. This trajectory shows a two-mile overshoot of the target at the point where the chutes are deployed. Note also that the spacecraft drifts about two miles after the chutes are deployed. This overshoot is caused by a different flight performance of the vehicle as compared with the simulation. At a velocity of 1000 feet per second no new guidance commands are issued so that fuel may be conserved in the reactionj et control system. The guidance system is openloop from this point on. But the flight showed a straighter and slightly longer arc than that shown in the simulations, causing the bias. As navigation performance has improved, this bias has become the significant error. In subsequent flights this has been corrected in the hope that the navigation performance will continue to be as good.
The navigation algorithm is shown in Fig. 1. It is the so-called Average-G routine. Because the imperfections of the guidance equipment are severely stressed during entry, it is the best mission phase in which to determine these imperfections. This is the longest period of inertial navigation, sometimes over one hour, although the actual entry only takes about ten minutes. On the unmanned flights it was not possible to realign the IMU between launch and splash. This extended period did require a ground update of position and velocity. Significant navigation errors accrued even with this ground updating. During entry the spacecraft is also subject to severe acceleration - up to 10 g - while the vehicle attitude rates are at their highest during this period.
Shown in Fig 4 is the altitude time history for Apollo 10. The marked improvement in performance is due mainly to the shorter drift time of the inertial measurement unit. The platform was aligned about one hour before entry by the crew. So far, Dave Scott in Apollo 9 holds the record for the most accurate alignment.
The navigation can fail to indicate the true position and velocity for a variety of reasons: the IMU is subject to misalignment and drifts, The PIP As have scale factor and bias errors, and the initial conditions may also be in error.
A navigation algorithm error was detected by the trajectory reconstruction method. Some significance was lost in the magnitude of g by unnecessarily losing some precision in calculating the value of the square of R. Though this meant that g was increased incorrectly by at most 0.030/0, the method detected this error.
Extended error analyses are made to determine the effects of these errors (for example, Ref 5). A by-product of the method of this paper is the close agreement obtained with the standard error analysis. This strengthened our confidence in both methods.
Similarly , an incorrect scale factor on R was detected. In convertinl{ the data to a format compatible to the MIT computer, the position vector had been increased by about 0.002 per cent. Reproducing the on - board calculations detected this error.
One of the main goals of the flight data analysis is to determine these errors so that future improvements might be made. Results
The aerodynamic data has been described elsewhere (Ref 6), but some discussion is in order here. The lift-to-drag ratio (L/D) is available through resolution of the acceleration into components along and normal to the velocity vector. As a matter of fact, the aerodynamicist thinks of the guidance equipment as instrumentation for an extended hypersonic wind-tunnel test. If that were the goal, the equipment is overdesigned. But it does provide a superb record for an extended period of hypersonic flight. Knowledge of L/ D is critical to proper entry steering performance. For the first flight L/ D was below specification and, because of this, the vehicle fell about 200 miles short of the intended landing site. Since then, L/ D has been maintained at very close to the design value. Figure 5 shows a time history of L/ D for Apollo 8. The design value of 0.3 was almost exactly attained. The abrupt rise
Shown in Fig 2 is the altitude time history of AS- 501. The final altitude error of nearly 200,000 feet is characteristic of the early missions in which a long period of drift time elapsed before the platform was used. The platform alignment error in the critical pitch direction was determined to be 0.5 0 by this method. This was higher than the instrument preflight history had led us to expect. With this motivation, the calculation of the compensation parameters was reexamined. The gyro- bias drift term was altered so as not to correct for the G - sensitive drift as measured in the laboratory. This uncorrected compensation was used in the next flight resulting in a marked improvement in performance.
713
AVERAGE-G NAVIGATION ALGORITHM -
-
- OT
F
VI ' V + G T +"2
I '
I
AS 501
R • if + VI OT
v • VI
+l + GQ! 2
§
2
~-
where
R, V • position and velocity vectors VI
• temporary velocity vecto r
DT
• time increment
• gravitational constant • 2nd spherical harmonic coef
OR UZ
• R/R • unit north vector
SL
• sine 01 geocentriC latitude
reconst ructed J
• OR· UZ • velocity increment from acceleromete r
G
i-
- I - - + ---- - -
30.0
• gravity acceleration
F ijtu rl' 2
-r '-
APOLLO 8 GROUNOTRACK AT SPLASH
- - j - - -..
8.16 RE CONS TRUCTED PITCH MI SAliGN ME NT ' 0.02 0 • 10 SECONDS 8ETWEEN POINTS
v- lOoolps
+..· - - -·- - - - --+ - · - .........· · -30.5 TIME 11000 s J
1·· .. ----+----- -1- _
-+--..-L-'--' --'- --+---' --~'~~l~o~~>---
8. 0
8.15
7.0
6.0
8. 14
...
TA RGET
8
~
i
LAT. 8.1lJ3'\ LONG. - 165. OJ 3
8.13
~ ~
§
'"
~
;;
~ 8.12
8.1I
~ KNOT EASTERL Y WIND
STIERING ERROR I. 45nm
NAVIGATION ERROR 0. 33nm
- 165.06
- 165.04
~
- 165. Cl? LONGITUDE
5.0 4.0 3.0
«
2.0 1.0
OROGUE MAIN
indicated
( reconst ructed
-1 65
10 1 690.2
MI.l INSTRUMENTATION LABORATORY
-Comb.jOg_, Mouodlll."I'
690.4
690.6
8 /69
Ire 3
Fi l"ll r e 4
714
1_
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and fall near the end of the record is an expected characteristic of the Apollo spacecraft at transonic speeds. However, the slow steady climb in the hypersonic region is as yet not explained.
the east-west movement by adjusting accelerometer biases. Shown in Fig 8 are the pitch misalignments as deduced for each of the missions. (Typical misalignments are in the order of 0.1 deg.)
In the later flights, the calculation of LID is also accomplished on-board by the AGC and is available on the telemetry record. This has proved valuable as a "first guess" of this critical parameter. There was some thought of using this measurement in the steering equations, but this proved to be unnecessary when the actual LI D consistently came very close to the design value. Another indication of the quality of navigation in the later flights is the accuracy of this on-board LID calculation. Three significant digit agreement is common with the on- board and reconstructed trajectory calulation of LID.
Second-order clues are also helpful. Each time the vehicle shows a roll reversal there is a shift in the measured L/ D. This shift is due mostly to navigation errors, and corrections in the platform alignment can be made based on this evidence.
Analysis The first step in the two-step trajectory reconstruction is to ensure that all the data points of the acceleration time history are included. Somewhere between 3 and 20 points are missing (usually at some abrupt change in the acceleration of the vehicle such as at splash or when the chutes deploy) from each flight record, with fewer points missing on the later flights. It is relatively easy to replace these missing points since the first and second integrals, position and velocity, are available. On Mission AS-501 a particularly poor dropout of about six points came near the first acceleration peak. But these points were found, or at least the total change in velocity was determined, and then divided through the six points. The acceleration time history is shown in Fig 6. The replaced points are discernable at the pointer. The main chute, drogue chute, and splash events are clearly marked. These acceleration data are then modified with an estimate of instrument imperfections as shown in Fig 7. Both the IMU misalignments and PIP A errors are modified. These modifications are made to match external events along the trajectory. The significant external events are listed in Table 2 along with the nominal value of each point. As in all inertial navigation situations, the altitude channel is the most critical. (The altitude channel is naturally divergent, while the range and track channels are periodic.) To avoid problems of gimbal lock, the platform is aligned so that the middle gimbal angle is near zero at the start of entry. This means that the y-axis of the IMU is normal to the trajectory plane. Because the y-axis gyro defines the pitch axis, altitude variations are most sensitive to misalignments in this direction. (Typical values for the biases are 0.2 cm! s2 while typical sensitivities can be found in Ref 6.) The usual reconstruction procedure is to first control the altitude and altitude rate by adjusting the pitch alignment alone. Then to control the north - south velocity by the roll and yaw. Finally, to control
For safety reasons some loss in capability has occured with the manned flights. That is, the splash event is no longer measured, because power is turned off to avoid the possibility of short circuits. Conclusions How do we know that we have a unique solution? We don 't know. However, many different external events must be matched (most of these are strongly influenced by a unique error source) that our confidence is reasonably high. More work can certainly be done, particularly in weighting errors in each of the external events. (This appears to be a natural problem for Kalman filter techniques.) Other areas under consideration include timevarying errors such as gyro drift, and a more systematic estimate of initial-condition errors. Motivation for these improvements in the Apollo project is not strong. The raw flight data show such small errors that the instrument imperfections we are now detecting are startlingly small, as are the errors in alignment made by the astronauts. The method described is deceptively simple. No complicated mathematics are utilized. The sensitivity of the trajectory to small variations makes a powerful tool of a simple concept. We firmly believe that a strong effort should be made to get as much as possible out of the flight data. The aerodynamics, particularly the L/ D rise, is still under study after seven flights. Because of analyses like these, we expect Apollo 12 to come closer to the target than any of the previous flights. References
1. Morth, R., " Reentry Guidance for Apollo ",2nd IFAC Conference, Vienna, September, 1967. 2. Morth, R., "Entry Flight Data for Mission AS 202", MIT/IL Report E-2031, October, 1966. 3. Morth, R., "Entry Flight Data from Apollo 7", MIT/IL Report E-2404, April, 1969. 4. Morth, R., "Entry Flight Data from Apollo 8", MIT/IL Report E-2405, April, 1969. 5. Grant,F .D., Kriegsman,B., Muller,E.S., Werner,J., White,R.,"Mission G G&N Error Analysis",MIT/IL Report E-2427, July! 1969. 6. Hillje, E., "Entry Flight Aerodynamics From Apollo Mission AS-202", NASA TN D-4185, October, 1967.
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DISCUSSION
Q. What kind of model did you use for the reconstruction of the fl ight comp lex ',as it?
dat~l,
and hol\'
A. Perhaps T s hould refer to my paper and the references T used where i1 complete set of data for Apollo 7, 8 and 9 is repeated as well as the computer progr:UlI~ hy \\'hich this was deduced. But to ans\\er your question, no there 1\'as no nw,de l \\'h:1tsoevcr for the vehicle . The reconstruction was to merely use the complete set of acce ~ erilt:ioll data , i nt egrating this again with plat fonn, hi ases, dri fts, angles , III i q 1 i gnelllents :1<; well as accelerometers until the extemrtl events were miltchecl as shOlm 011 onc 01" my slides . This turns out to be extremely sensitive; iI tiny ch:mge in onc of these error sources would more than exceed the bounds of expected error .
Q.
How long before the re-r:ntry is the p l rttfonn aligncd?
A.
It is a li gned roughly tl\'O hours before the rc-entry .
Q.
Did you use data from pre launch tcsting on the instnullent?
A. No, bu t we did use tbs data to improve the prelaunch testings. \\'e detellllined that the gyro drifts had been uncorrect l v calculated. T think it is too long to enter into it here but it is briefly described in my paper .
718