Space Flight Technology, German Space Operations Center (GSOC) Deutsches Zentrum für Luft- und Raumfahrt (DLR) e.v. O. Montenbruck, M. Markgraf, A. Stamminger Doc. No. : SFX-RB-RP-010 Version : 1.0 Date : Nov 9, 2005
Document Title: ii Document Change Record Issue Date Pages Description of Change 1.0 Nov 9, 2005 All First release
Document Title: iii Table of Contents Document Change Record...ii Table of Contents...iii Acronyms and Abbreviations...iv Scope...1 1. Introduction...3 1.1 Mission Overview...3 1.2 Sequence of Events...4 1.3 GPS System Description...5 2. Flight Data Analysis...7 2.1 Trajectory...7 2.2 Tracking Status and Signal Quality...7 2.3 Boot Phase...9 2.4 Impact Point Prediction...10 2.5 Trajectory Aiding and Signal Acquisition...11 Summary and Conclusions...12 References...13 Annex A...15 A.1 Trajectory Polynomials...15
Document Title: iv Acronyms and Abbreviations C/A Coarse/Acqusition Code C/N 0 Carrier-to-Noise ratio [db-hz] DLR Deutsches Zentrum für Luft- und Raumfahrt GPS Global Positioning System GSOC German Space Operations Center IIP Instantaneous Impact Point L 1 GPS frequency (1575.42 MHz) NCO Numerically Controlled Oscillator (NCO) PRN Pseudo-Random Noise R/F Radio Frequency SHEFEX Sharp Edge Flight Experiment WGS84 World Geodetic System 1984
Scope This document provides an analysis of GPS data collected during the flight of the SHEFEX sounding rocket on 27 Oct 2006.
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Document Title: 3 1. Introduction 1.1 Mission Overview The Sharp Edge Flight Experiment (SHEFEX) aims at the investigation of new thermal protection concepts for re-entry vehicles making use of multi-facetted surfaces with sharp edges. To assess the aerodynamic and thermal properties of this novel type of heat shields under realistic conditions, a test payload for a sounding rocket was developed, which had to achieve a velocity of Mach 6.5 for 30s during re-entry. A dual-stage rocket was designed for the SHEFEX mission which combines a Brazilian VS30 motor as its first stage and an Improved Orion (=Hawk) upper stage (cf. Fig.1.1). SHEFEX was launched from Andøya Rocket Range near Andenes, Norway, on Oct. 27, 2005 at 13:45:30 UTC. The motors burned for roughly one minute and accelerated the payload to a total velocity of 1785 m/s. A peak thrust acceleration of approximately 14 g was measured five seconds after ignition of the second stage. Four minutes after leaving the launch pad, SHEFEX reached the apogee at an altitude of 210 km. The second stage motor and fins remained attached to the payload for enhanced aerodynamic stability during the re-entry. Here a velocity of Mach 7 was achieved and temperatures raised to 1600 C. Fig 1.1 The SHEFEX rocket on the launch pad at Andøya Rocket Range Following a premature release of the parachute system initiated by a barometric switch the payload entered the North Atlantic with a final sink rate of about 100 m/s. When telemetry was lost prior to touch down, at t=543 s, the vehicle was located at λ WGS84 = +12.158 φ WGS84 =+70.341 h WGS84 =2.1 km in a distance of 189 km and azimuth 310 from the launch site.
Document Title: 4 1.2 Sequence of Events Key events of the SHEFEX mission are summarized in Table 1.1. All times refer to Thursday, 27 Oct. 2005 (day of year 300, GPS week 1346). Table 1.1 SHEFEX main events given in time since launch, UTC time, and GPS time Event h [km] t [s] UTC GPS sec Switch from blade to tip antennas 0.1 ca. -148.4 13:43:02.0 394995.0 Lift-off 0.1 0.0 13:45:30.4 395143.4 Peak thrust (6 g) 8.5 19.6 13:45:50.0 395163.0 Separation of 1 st stage 15.5 28.6 13:45:59.0 395172.0 Ignition 2 nd stage 17.7 31.6 13:46:02.0 395175.0 Peak thrust (15 g) 21.2 35.6 13:46:06.0 395179.0 Peak velocity (1785 m/s) 52.1 56.6 13:46:27:0 395200.0 Tip ejection and loss of GPS tracking 90.1 80.1 13:46:50.5 395223.5 Apogee ca. 210.6 240.6 13:49:31.0 395384.0 Start re-entry (h=100 km) 99.6 396.6 13:52:07.0 395540.0 Motor separation and parachute release ca. 12 km 450.0 13:53:00.4 395593.4 Reacquisition of GPS signals ca. 7 km 486.6 13:53:37.0 395630.0 GPS navigation solution re-established 2.8 522.0 13:54:12.5 395665.5 Loss of telemetry 2.1 534.1 13:54:24.5 395677.5
Document Title: 5 1.3 GPS System Description The SHEFEX GPS system (Table 1.2) comprised a Phoenix GPS receiver [1] with external low noise amplifier and a switchable set of GPS antennas. Table 1.2 Hardware components of the SHEFEX GPS system Item Description GPS receiver Phoenix #19 Software D08D (Shefex; build 05/10/06) Preamplifier Vectronic PA-5V28, S/N PA1005 R/F switch NAIS ARD10024, S/N 30911448 Power divider MCLI PS2-2, S/N 1353 (or 1354??) Tip antenna DLR/Moraba Blade antennas (2x) DLR/Moraba The receiver unit combines a Phoenix-HD GPS receiver board with backup battery and a mission specific interface board with serial line drivers in a cigarette-box sized housing (Figs. 1.2 and 1.3). The Phoenix receiver itself offers 12 correlator channels for L1 C/A code tracking and a software specifically adapted to the needs of high-dynamics and sounding rocket applications. Key features include provisions for acquisition aiding trough ballistic trajectory polynomials, optimized tracking loops and the generation of instantaneous impact point predictions. The Phoenix receiver supersedes the earlier Orion-HD design and has been flightvalidated as part of the VSB-30 and Texus-41 missions. Fig. 1.2 Phoenix-HD GPS unit for the SHEFEX mission. Fig. 1.3 GPS with preamplifier and r/f switch integrated into the SHEFEX service module. For use on SHEFEX the Phoenix receiver was configured to provide navigation solutions (F40) and IIP messages (F47) and raw measurements (F62) at a 2 Hz update rate. In addition, channel status data (F43) and general status data (F48) were issued once per second. A wide bandwidth for the FLL assisted PLL was selected in accord with the expected signal dynamics. In view of signal losses expected during re-entry of the vehicle in an uncontrolled attitude, measurement screening was disabled in the Phoenix receiver software for SHEFEX. Pseudorange measurements could therefore immediately be used in the navigation solution after short outages even if a full bit or frame lock was not yet achieved. For best tracking conditions throughout all flight phases, the SHEFEX mission employed a switchable GPS antenna system. A nose cone antenna (Fig. 1.4) ensured optimum visibility during the boost phase while a set of two blade antennas combined via power divider was provided for the flight phase following the tip separation. Due to the deferred execution of a manual switch command, the blade antenna system was not, however, activated until after
Document Title: 6 the re-entry. Thus GPS measurements could only be gathered during the first 80 s of the flight and close to the final touch down. Fig. 1.4 Helical tip antenna with radome for GPS tracking of SHEFEX during the early flight phase. The blade antenna pair was also activated during launch preparation up to 2.5 min prior to lift-off. Due to a linear polarization, the blade antennas are highly receptive to reflected GPS signals. In addition interferences occur due to a partly overlapping field-of-view of the two individual antennas. Both effects contribute to notable degradation of the position accuracy at the launch site.
Document Title: 7 2. Flight Data Analysis 2.1 Trajectory Due to the loss of GPS tracking after tip ejection, only part of the ascent phase is covered by position and velocity measurements. Based on the measured state vector prior at t=80s, the motion of SHEFEX has been numerically integrated using a 10 x 10 gravity model but neglecting aerodynamic forces. This provides an adequate approximation of the flight phase up to the reentry and even gives a good approximation of the final touch down point. The peak altitude was determined as 210.6 km (Fig. 2.1) and the total flight range amounts to roughly 190 km. 250 200 GPS Predicted Altitude [km] 150 100 50 0 0 50 100 150 200 250 Range [km] Fig 2.1 SHEFEX trajectory 2.2 Tracking Status and Signal Quality Within a few seconds after lift-off, the number of tracked satellites increased from 7 to 10. Thus, all visible satellites above the 5 elevation mask were properly tracked by the Phoenix receiver (Fig.2.2). After activation of the blade antenna system in the final descent, a first satellite is tracked at t=487s. A 3D navigation fix with 5 tracked satellites is only achieved 35s thereafter. Number of Tracked Satellites 12 10 8 6 4 2 0-100 0 100 200 300 400 500 600 Time since launch [s] Fig 2.2 Number of tracked GPS satellites
Document Title: 8 The carrier-to-noise density immediately prior to launch ranges from 40 db-hz to 46 db-hz for the seven observed GPS satellites, but drops by typically 1-2 db after lift-off. As shown in Fig. 2.4 some jitter in the C/N 0 readings is encountered near the peak jerks at ignition of the first and second stage as well as the end of the primary boost phase of the second stage Orion motor. Overall, the satellites tracked with the tip antenna during the ascent of the SHEFEX vehicle exhibit C/N 0 values of 36-45 db-hz. 48 46 Carrier-to-Noise Density [db-hz] 44 42 40 38 36 34 32 PRN01 PRN02 PRN04 PRN05 PRN06 PRN14 PRN20 PRN23 PRN25 PRN30 30-10 0 10 20 30 40 50 60 70 80 90 Time since launch [s] Fig 2.3 Carrier-to-noise density ratios (C/N 0 ) obtained with the GPS nose cone antenna during the initial flight phase of the SHEFEX vehicle For completeness, carrier-to-noise densities collected at the launch site during the final minutes of the countdown are provided in Fig. 2.4. It may be recognized that strong interferences occur when using the blade antenna system until to 2.5 min before lift-off. These can be attributed to multi-path reflections as well as interference of signals that are simultaneously received by both blade antennas. These result in GPS navigation errors with a standard deviation of almost 50m prior. The tip antenna, in contrast is only sensitive to right-hand polarized signals and provides an adequate suppression of reflected signals. 50 PRN01 45 PRN02 Carrier-to-Noise Density [db-hz] 40 35 30 25 Blade Antennas Switch Tip Antenna Lift-Off PRN04 PRN05 PRN06 PRN14 PRN20 PRN23 PRN24 PRN25 PRN30 20-500 -400-300 -200-100 0 100 GPS secs of week Fig 2.4 Carrier-to-noise density ratios (C/N 0 ) prior to lift-off
Document Title: 9 2.3 Boost Phase The dual-stage configuration of the SHEFEX rocket and the dual boost phase of the Orion second stage result in a complex pattern of the total acceleration during the propelled flight. This is illustrated in Fig. 2.5, which shows the vertical velocity and acceleration profile during the first 80s of the SHEFEX flight up to the loss of GPS signals. 2000 200 1800 160 1600 120 Up-Velocity [m/s] 1400 1200 1000 800 600 400 v_up a_up 80 40 0-40 -80-120 Up-Acceleration [m/s^2] 200-160 0-10 0 10 20 30 40 50 60 70 80 90 Time since launch [s] -200 Fig 2.5 Vertical component of the velocity and acceleration vector in the launcher reference frame The VS-30 first stage generated an acceleration of roughly 4 G (in the Earth-fixed launcheframe) during the first 20s. After burn end, which took place in the dense part of the atmosphere, SHEFEX experienced a strong acceleration in anti-flight direction (approx. 1.7 G) due to the combined action of Earth gravity and air drag. The Improved Orion second stage (which employs the motor of a former Hawk anti-aircraft missile) generates its peak thrust during less than 5s after ignition. This resulted in a peak vertical acceleration of 12.6 G at about 35 s from lift-off. Thereafter the acceleration dropped down to 1.4 G (corresponding to 2.4 G in the body frame) before it raised again to a secondary maximum (4 G) as the second-stage fuel was depleted and the overall mass of SHEFEX decreased. Near burnout, a vertical peak velocity of 1720 m/s was achieved and the speed over ground amounted to 472 m/s. The accelerations given above refer to an Earth-fixed frame and are typically 1 G lower than the corresponding values in the body-frame as a result of the gravitational acceleration of the Earth. All values have been derived from GPS velocity measurements expressed in a launcher-centered East-North-Up system using a symmetric difference quotient over time intervals of ±0.5 s. This results in a moderate smoothing and an attenuation of the resultant values in case of extreme jerks. As a result, the measured peak acceleration of 13 G (3D) in the launcher frame is slightly lower than expected from accelerometer measurements (15.2 G in body frame). Also the jerk of approximately 7 G/s at boost start of the Improved Orion motor as inferred from GPS navigation measurements is much smaller than the value indicated by the accelerometers.
Document Title: 10 2.4 Impact Point Prediction The Phoenix-HD receiver software supports a real-time prediction of the instantaneous impact point (IIP) based on the GPS navigation solution. A modified parabolic flight model with corrections for gravity variations and Coriolis forces (but neglecting atmospheric forces) is employed that has earlier been established in [2]. Fig 2.6 Impact point prediction (open circles) and actual flight path (solid red line) as determined by the Phoenix GPS receiver and displayed with the OrionMonitor s/w during the SHEFEX flight. The display of the impact points computed by the Phoenix receiver (Fig. 2.6) clearly reflects the boost profile of the SHEFEX vehicle. A rapid motion of the IIP occurs after ignition of the Improved Orion motor, at which time the velocity of the vehicle increases by roughly 65 m/s between consecutive 2 Hz navigation solutions. After termination of the second stage at an altitude above 50 km, the predicted impact point recedes slightly as SHEFEX is gradually decelerated by residual drag forces. A single outlier in the predicted impact point can finally be recognized at the instance of tip separation when the GPS signal is suddenly lost. Inspection of the predicted impact points after burn end shows a good agreement with the final touch down point. However, a small difference (approx. 15s) in the predicted time-toimpact was noted in comparison with offline computations as part of the post-mission analysis. These could be attributed to the neglect of a corrective term ( h + u τ )( h τ ) 1 δτ = h ( τ ) / uimp = 0 0,up 5 0 + u 3R u imp 0, up (1) for the remaining flight time up the impact (cf. eqn. 23 of [2]). The error is of little relevance from an operational point of view but will be fixed in an upcoming release of the receiver software.
Document Title: 11 2.5 Signal Acquisition and Aiding The Phoenix receiver for the SHEFEX mission was configured for aiding with a priori trajectory information, to enable a rapid reacquisition after signal losses. To this end, a set of 13 second-order polynomials describing the nominal trajectory in a WGS84 coordinate system was loaded into the receiver prior to the launch. A listing of the respective receiver commands, which have been generated based on a ROSI trajectory file, is provided in Annex A. It should be noted that the reference trajectory information loaded into the receiver did not fully match the true flight profile due to late changes in the azimuth and elevation settings of the launcher, but was nevertheless adequate for aiding purposes. No outages occurred during the boost phase but the GPS signal was entirely lost when the nose cone was separated without switching to the blade antenna system. The receiver then entered a sequential search during which it scanned the received signal in frequency bins of 500 Hz width while performing a code search for the allocated PRN in half chip steps. At a 1 ms correlation time the search of 1023 C/A-code bits takes roughly 2 s, which must be repeated for each 500 Hz bin. With a specified Doppler window of ±11.5 khz, the receiver thus required roughly 90 s to complete a full search. 15000 10000 5000 Doppler Shift [Hz] -5000 0-100 0 100 200 300 400 500 600-10000 Predicted Offset -15000 Time since launch Fig 2.6 Predicted Doppler shift of PRN30 and offset between predicted value and setting of the numerically controlled oscillator (NCO) The search process and aiding is illustrated for a sample satellite in Fig. 2.6. During the boost phase, maximum differences between the predicted and measured Doppler shifts of about 500 Hz are obtained, which would have allowed a reacquisition of within a few seconds after a signal loss during this mission phase.
Document Title: 12 Summary and Conclusions The Phoenix GPS receiver worked to expectations and provided continuous navigation data during the early phase of the SHEFEX mission. After tip separation, GPS tracking was interrupted until the very end of the flight when the blade antenna system was ultimately activated through manual commanding. The following key findings regarding the overall system performance were made: 1. The receiver showed no signs of outages or problems during the entire boost phase with accelerations of up to 13 G (in Earth-fixed coordinates) and jerks up to (at least) 7 G/s. Apparent errors in the navigation solution are only encountered for one second at the loss of signal after ejection of the nose cone antenna. 2. For an improved analysis of boost profiles in future missions carrying no inertial measurements unit, the use of 5 Hz navigation solution appears advisable. 3. If proper aiding information is available, the Doppler window might be reduced to 5 khz (presently 11.5 khz) to speed up the signal search in case of loss of track. 4. Use of the blade antennas at the launch site results in large navigation errors and signal strength variations due to interference and multipath effects. Their use should be restricted to missions phases where the tip antenna is no longer available. 5. The time-to-impact provided in the F47 (IIP) message was found to be too low due to a neglect of the gravity correction to the total flight time. This does not affect the computation of the IIP coordinates and is of little relevance during mission operations but should be fixed in the next software release.
Document Title: 13 References [1] Montenbruck O., Markgraf M.; User s Manual for the Phoenix GPS Receiver; GTN-MAN-0120; Issue 1.6, Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen (2005). [2] Montenbruck O., Markgraf M., Jung W., Bull B., Engler W.; GPS Based Prediction of the Instantaneous Impact Point for Sounding Rockets; Aerospace Science and Technology 6, 283-294 (2002).
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Document Title: 15 Annex A A.1 Trajectory Polynomials A listing of Phoenix F51 receiver commands with polynomial coefficients describing the nominal SHEFEX trajectory for a launcher azimuth of 320 and elevation 83 is given below. Each command provides a set of second order polynomial coefficients for the WGS84 position component in a time interval starting at a specified epoch after lift-off. See [1] for a further explanations. F51 0 +0.000 +2174053.5 +4.5768 +5.041609 +624170.8 +7.5275-1.536897 +5943796.7-2.8732 +21.37482579 F51 1 +18.000 +2175753.0 +185.0591 +3.409091 +623800.9-55.3667-2.090909 +5950634.7 +780.9364 +17.30303079 F51 2 +22.500 +2176649.9 +213.3903-2.285001 +623511.4-73.7082-0.230735 +5954477.2 +926.9650-7.36741162 F51 3 +32.500 +2178555.0 +163.5096 +12.214452 +622751.2-75.5706-7.398601 +5963009.9 +756.5594 +61.34265760 F51 4 +37.500 +2179681.1 +284.5819 +1.726184 +622185.0-148.4283-2.518731 +5968344.8 +1362.2800 +12.32206476 F51 5 +52.000 +2184170.5 +346.5585 +0.471235 +619501.8-230.5079-1.982547 +5990693.0 +1784.3617 +6.6228186B F51 6 +59.000 +2186824.9 +334.8875-1.559218 +618273.4-270.0300-0.363104 +6003649.6 +1820.2291-4.33401366 F51 7 +465.000 +2065921.5-922.8274 +7.589286 +449469.2-540.2202 +5.053571 +6027937.8-1703.3988 +12.5416676B F51 8 +472.000 +2059842.4-819.7545 +42.272727 +445940.2-469.8364 +24.181818 +6016644.7-1532.9000 +77.00000062 F51 9 +474.000 +2058369.0-616.5119 +40.642857 +445095.8-352.3333 +23.714286 +6013881.7-1158.3452 +74.9761906C F5110 +477.500 +2056697.9-329.5270 +15.289710 +444147.0-185.5330 +9.019980 +6010726.1-628.4530 +28.18281776 F5111 +483.000 +2055334.7-164.0295 +4.452012 +443392.1-88.3379 +2.750995 +6008097.4-324.6209 +7.89237866 F5112 +492.000 +2054206.1-85.8411 +1.083319 +442811.8-39.9987 +0.730076 +6005791.3-187.1930 +1.69609374 F5113 +508.000 +2053105.0 +0.0000 +0.000000 +442355.0 +0.0000 +0.000000 +6003221.0 +0.0000 +0.00000078