Acta Astronautica 57 (2005) 851 – 863 www.elsevier.com/locate/actaastro
Preliminary design of a space system operating a ground-penetrating radar Marco D’Erricoa , Salvatore Pontea , Michele Grassib,∗ , Antonio Mocciab a Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Università di Napoli Via Roma 29, 81031 Aversa (CE), Italy b Dipartimento di Scienza e Ingegneria dello Spazio, Università degli Studi di Napoli “Federico II” P.le V. Tecchio 80, 80125 Napoli, Italy
Received 29 March 2004; received in revised form 30 March 2005; accepted 4 April 2005 Available online 29 June 2005
Abstract Ground-penetrating radars (GPR) are currently used only in ground campaigns or in few airborne installations. A feasibility analysis of a space mission operating a GPR for archaeological applications is presented in this work with emphasis on spacecraft critical aspects: antenna dimension and power required for achieving adequate depth and accuracy. Sensor parametric design is performed considering two operating altitudes (250 and 500 km) and user requirements, such as minimum skin depth, vertical and horizontal resolution. A 500-km altitude, 6 a.m.–6 p.m. sun-synchronous orbit is an adequate compromise between atmospheric drag and payload transmitted average power (12 kW) to achieve a 3-m penetration depth. The satellite bus preliminary design is then performed, with focus on critical subsystems and technologies. The payload average power requirement can be kept within feasible limits (1 kW) by using NiH2 batteries to supply the radar transmitter, and with a strong reduction of the mission duty cycle (40 km × 1100 km are observed per orbit). As for the electric power subsystem, a dual-voltage strategy is adopted, with the battery charge regulator supplied at 126 V and the bus loads at 50 V. The overall average power (1.9 kW), accounting for both payload and bus needs, can be supplied by a 20 m2 GaAs solar panel for a three-year lifetime. Finally, the satellite mass is kept within reasonable limits (1.6 tons) using inflatable-rigidisable structure for both the payload antenna and the solar panels. © 2005 Elsevier Ltd. All rights reserved.
1. Introduction Spaceborne remote sensing, and in particular SARs, is usually limited to the Earth surface. On the other ∗ Corresponding author. Tel.: +39 081 7682217;
fax: +39 081 7682160. E-mail addresses:
[email protected] (M. D’Errico),
[email protected] (S. Ponte),
[email protected] (M. Grassi),
[email protected] (A. Moccia). 0094-5765/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2005.04.010
hand, many scientific applications can get great advantage from collecting information at some depth. They cover all the cases where electromagnetic signal penetration is required and possible, such as forestry, ice and arid land. Some examples are [1–3]: identification of man-made and natural cavities, detection of buried mines, detection of archaeological sites, sounding of ice caps, hydrogeological surveying, soil moisture mapping, mapping geological structural changes; mapping sub-superficial geomorphologic
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Nomenclature a A AR As ACS B BCR c clife cp cpTRA cT CD d D F Gt Gr GPR LEO mTRA MM MP OBDH OCS Pat Ppt PAY PBCR PBUS PRF Q R R⊕ S
orbit semimajor axis satellite cross section radiator surface transmitted signal amplitude attitude control subsystem bandwidth battery charge regulator velocity of light environmental degradation coefficient packaging factor transmitter mean specific heat temperature degradation coefficient drag coefficient penetration depth range noise figure transmitting antenna gain receiving antenna gain ground penetrating radar low-earth orbit transmitter mass mass memory propellant mass on-board data handling orbit control subsystem average transmitted power peak transmitted power payload average BCR power average BUS power pulse repetition frequency repetition factor slant range earth radius solar constant
characteristics. Additional applications could be moisture analysis, land and ice features classification. Ground penetrating radars (GPR) data quality depends on terrain characteristics and, in particular, humidity, salt content (which influences the dielectric constant), rugosity, etc. Therefore, as a function of these parameters, different kinds of surface can be observed with different performance [4,5]. Furthermore,
SL SN SAR SNR STR tR T TC Ti T0 Tsunlight TC THC VHF vb vsc vD,c Y ran az εr cells PCU DC–DC ϑ ϑ3 dB,az k s v V
maximum accepted swath variation nominal swath synthetic aperture radar signal-to-noise ratio structure transmitter cooling time equivalent antenna noise temperature battery charge time integration time transmitter initial temperature sunlight phase duration telecommunication thermal control very high frequency beam velocity spacecraft velocity battery cell discharge voltage satellite lifetime soil attenuation range processing gains azimuth processing gains relative dielectric constant cell efficiency power control unit efficiency DC–DC converter efficiency nominal look angle 3-dB azimuth beamwidth Stefan–Boltzmann constant wavelength radar cross section pulse duration transmitted signal phase mean atmospheric density vertical resolution velocity increment
low-frequency SARs can also give the capability of three-dimensional observations [6]. Nevertheless, GPR have been only recently introduced in the field of remote sensing. In particular, a number of airborne GPR1 /SAR sensors have been designed and developed. 1 See Nomenclature.
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As an example, an airborne GPR was developed in 1991 by INTARI [7], a Russian company specialised in the study of the earth polar areas, with the cooperation of University institutes in Saint Petersburg and Mosque. It is basically an advanced side-looking SAR operating at a 1.5/2 m wavelength, which allows to penetrate dry soil up to 100 m. CARABAS (Coherent All Radio Band Sensing) is another airborne SAR, mounted on board a Rockwell Sabreliner, designed by FOA (National Institute of Research for Defence) in Sweden, for vegetation penetration and buried objects monitoring [8]. This sensor, operating in the VLF band with 5-m antennas, was developed and tested in 1992. Furthermore, between 1990 and 1995 the Stanford Research Institute (SRI) developed FOLPEN II, which is a GPR for vegetation and ground penetration. It is a SAR operating in the 100–500 MHz frequency range with two separated antennas, one for receiving and the other for transmitting, mounted under the aircraft (BAC J-31) wings. FOLPEN II [9] is able to produce real-time images with 1 m × 1 m resolution. The operating altitude is from 300 to 3000 m. In the 1990s, Lockheed Martin developed a Modular SAR (MSAR) with ground penetration capability, operating in the 500–800 MHz (UHF) frequency range with side-looking angles of 30◦ and 60◦ . The MSAR resolution is of the order of the meter. The transmitted peak power is 20 W at an operating altitude of 2000 m (the swath width is 200 m). Another example of airborne GPR is the one developed by the Lawrence Livermore National Laboratory, CA, USA [1]. It is a sidelooking SAR with ground penetration capability for mine detection. The radar is mounted on a 18-m long rigid boom. Airborne GPRs have been developed also by ERIM (Environmental Research Institute of Michigan), Ann Arbor, Michigan, USA [10]. This system is an ultrawideband (UWB) SAR for the Foliage Penetration (FOPEN). The antenna beam is steerable from 15◦ to 60◦ (angle between the local vertical and the boresight direction). FOPEN is operated on board a DHC Dash 7 vehicle with a cruise velocity of 116 m/s at an altitude of 6400 m. The antenna beamwidth in the range direction, of the order of 30◦ , allows the visualisation of a target at a maximum off-nadir angle of 75◦ (slant range of 24610 m). FOPEN is candidate to be used on anUAV (Unmanned Aerial Vehicle). Despite the potential of GPR applications, no spaceborne GPR sensors have been flown. In the fol-
853
lowing, the authors presents a feasibility study of a spaceborne GPR for archaeological applications. In particular, sensor design, orbit analysis and satellite bus design are preliminarily performed with focus on critical issues.
2. Sensor design This section outlines a conceptual sensor design in order to derive requirements for the space system design. To this end, mission objectives and expected performance must be preliminary defined. First of all, range/azimuth resolutions, swath width and observation geometry comparable to existing spaceborne SAR must be envisaged. In fact, this allows gathering data in different microwave bands, which can be used for multifrequency analysis and cross-calibration procedures. It is worth noting that spaceborne GPR data collected for the first time would obviously require development of original software both for focussing and calibrating raw data and for extracting physical parameters of interest. Regarding penetration depth and vertical resolution, assumed input performance must guarantee discrimination of main subsurface archaeological patterns. Finally, GPR SNR and dynamic range must be assigned on the basis of a trade-off basically between obvious limitations in power budget connected to spaceborne applications and capability to penetrate soils of major interest [11] for accurate detection. On the basis of the above considerations, Table 1 lists expected sensor performance necessary to satisfy user requirements. These values are used as input for sensor design. As an example, the trade-off between reasonable penetration depths and acceptable spatial resolution leads to the use of carrier frequencies in the VHF region. Then the constraint on the
Table 1 User requirements Skin depth Vertical (depth) resolution Horizontal (range/azimuth) resolution Input signal dynamic range 3-dB azimuth beamwidth Swath width SNR
3–5 m 1–2 m 10–30 m > 60 dB, up to 96 dB < 30◦ < 50 km at least 10 dB
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horizontal resolution pushes toward the use of chirplike, wideband signals with high time-bandwidth product, and possible use of synthetic-aperture techniques. Parametric studies are carried out at 500-km height, typical of the International Space Station and LEO satellites, and at 250 km, typical of Space Shuttlehosted remote-sensing missions. The focus is on the following performance areas: wave-soil interaction, penetration depth, surface clutter rejection from radar echoes, spatial performance and signal-to-clutter ratio (SCR), limitations to the use of GPR techniques and antenna design [12].
is a key issue in exploitation of remotely operated GPRs, as shown in [8,9], and it is advisable, a thorough test campaign for calibrating airborne and spaceborne GPRs by making use of reference scatterers representing expected subsurface structures, which could act as buried corner reflectors and/or active radar calibrators. A 20-MHz range chirp allows ground range resolution of the order of 10 m at the selected heights for a 35◦ nominal look angle. Main sensor parameters and overall functional architecture are derived from a ground-based stepped-frequency GPR developed and successfully tested at CORISTA [12].
2.1. Transmitted signal
2.2. Antenna subsystem
The devised hardware architecture consists of a stepped-frequency FM radar, a technique used in UWB radars [13] and also useful for penetrating radar applications, because it reduces the fractional bandwidth and increases the penetration depth [11]. The radar pulse can be synthesised in the frequency domain, with a series of five small-bandwidth (4 MHz) “sub-chirp” pulses, coherently generated and added, attaining a total bandwidth of 20 MHz and, therefore, a slant range resolution of 7.5 m. Regarding vertical resolution, i.e. the capability to discriminate between bright targets buried at different depths, slant range equation can be modified as follows:
The proposed solution is a planar array operating at a centre frequency of 100 MHz with 50-MHz bandwidth, made up of 6 (along track) ×3 (across track) 3-element Yagi subarrays, spaced by 2.1 m in both dimensions. The deployed antenna has overall dimensions of 12 × 6 × 3 m3 . The predicted beamwidths are of the order of 10◦ in azimuth and 20◦ in range, the gain is 30 dB and the sidelobe levels less than −20 dB. The corresponding Doppler bandwidth is of the order of 1–3 kHz at the operating frequencies and heights. Due to the antenna configuration complexity (see Fig. 5 for a schematic view), the antenna storage at launch and its successive in-orbit deployment are critical aspects of the mission. The use of rigidisable-inflatable structures reduces these problems and, in addition, allows an antenna structure mass saving up to 50% and a packaging factor improvement up to 25% [18]. Moreover, it reduces the coupling between platform attitude and structure vibration modes and the structure thermal expansion coefficient [19]. An overall mass of about 90 kg is estimated for the sensor antenna.
v =
1.39 c √ 2B εr
(1)
to account for velocity of electromagnetic wave propagation [14]. If the propagation medium is air εr = 1, whereas εr ∈ [2, 16] for terrain of archaeological interest [15]. As a consequence, penetration resolution can be improved with respect to slant range one up to 400%. This effect can be considered as a chirp bandwidth enlargement, which can be exploited to discriminate subsurface echoes by means of gating techniques [16]. In other words the sensor has to be pulse-limited, rather than beam-limited as in conventional Synthetic Aperture Radar processing, due to the stronger surface backscattered echo, which has to be removed from the collected electromagnetic returns. Furthermore, this effects can also be seen as a range variation of subsurface targets with respect to superficial ones, which can be investigated to put them in evidence [17]. As a matter of fact, capability to separate superficial echoes
2.3. Allowable swath width and PRF selection A simple range ambiguity analysis gives values of PRF less than 3.7 kHz at 250-km height and less than 1.7 kHz at 500-km height [12]. 10◦ beamwidth centred around the nominal look angle is assumed. The operating PRF value of 3 kHz is chosen for the 250-km orbit, and 1.5 kHz for the 500-km orbit. The corresponding slant range swath dimensions are of the order of 40 and 86 km at the two heights, respectively. With the selected values of PRF and heights, a
M. D’Errico et al. / Acta Astronautica 57 (2005) 851 – 863 20
7 6 alpha = 3 dB/m
5 4 3 2
alpha = 2 dB/m
1 105
110
(a)
115
120
125
130
135
140
145
d = 3 m, h = 500 km
18
Average transmitted power (kW)
Average transmitted power (kW)
d = 3 m, h = 250 km
0 100
855
16 alpha = 2 dB/m
14 12 10 8 6 4
alpha = 1 dB/m
2 0 100
150
105
110
115
(b)
Frequency (MHz)
120
125
130
135
140
145
150
Frequency (MHz)
Fig. 1. Average transmitted power at the two design orbits (250 km (a) and 500 km (b)), with fixed penetration depth (3 m).
and is of the order of 55 km at 250-km height, 120 km at 500-km height. The full-Doppler azimuth resolution turns out to be of the order of 6.5 m, allowing possible multilook processing to reduce speckle and obtain a square pixel in the final image.
4 height = 250 km 3.5 3 2.5 2 1.5 1
height = 500 km
0.5 0
2
4
6
8
10
12
14
16
18
20
Attenuation coefficient (dB/m)
Fig. 2. Penetration depth as a function of the soil attenuation at the two design heights.
2.4. Power budget The radar equation is evaluated using a sample radar cross section of −10 dB m2 (a sphere of absorbing material with refraction index of the order of 1.3, buried at 3 m in a soil with dielectric constant ε). The penetration depth, the transmitted peak and average power are, respectively, given by [20] Ppt Gt Gr 2 ran az 1 d= , ln 2 (4 )3 R 4 kTBF SNR SNR(4 )3 R 4 kTBF 2d e , Gt Gr 2 ran az Pat = Ppt PRF,
5 4.5
Penetration depth (m)
suitable pulse duration is found to be 30 s. The azimuth swath width SW az is given by R SW az = vb Ti = cos sin−1 sin ϑ a 2 − a 2 sin2 ϑ a cos ϑ − R⊕ × ϑ3 dB,az , (2) vsc
Ppt =
(3)
where the design value of the noise figure has been set to 5 dB, and the equivalent noise temperature is
250 K. The duty cycle (PRF) turns out to be equal to 10%, with the choices made on B and . It is worth noting that 10% is the sensor duty cycle when on, and it must not be confused with the overall mission duty cycle. Fig. 1 shows Pat in the frequency range [100–150 MHz], with d = 3 m and different values of (from 1 to 3 dB/m), at the two design heights. In order to minimise power requirements, the transmitted bandwidth (20 MHz) is centred at 110 MHz, thus allowing for average transmitted power of the order of 4 and 12 kW, respectively, at the design heights (assuming maximum equal to 3 dB/m for 250-km height and maximum equal to 2 dB/m for 500-km height) and a final frequency range of [100–120 MHz]. Fig.
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Table 2 Sensor design summary Heights Platform velocity Operating mode, operating frequencies Nominal off-nadir angle, ϑ Range chirp bandwidth Pulse duration () Range compression gain (B ) Azimuth compression gain (BD Tint ) Receiver bandwidth Average transmitted power for 3-m penetration depth
250 km/500 km 7.75 km s−1 /7.61 km s−1 Stepped-frequency SAR, 100–120 MHz 35◦ 20 MHz, synthesised in 5 steps (M = 5) 30 s 600 46,200 50 MHz 4 kW @ 250-km height ( 3 dB/m) 12 kW @ 500-km height ( 2 dB/m) 40 kW @ 250-km height 120 kW @ 500-km height 3 kHz @ 250-km height 1.5 kHz @ 500-km height 10% 10 m, 5–8 m single-look 7.2 s @ 250-km height 15.4 s @ 500-km height 2–3 m 5 MHz 10◦ (range/azimuth) 40 × 50 km2 @ 250-km height 40 × 110 km2 @ 500-km height 78–96 dB, 12–16 46.4 Mbps @ 250-km height 99.2 Mbps @500-km height
Peak transmitted power PRF Duty cycle (PRF) Ground range, azimuth resolution Integration time Penetration depth Sampling frequency 3-dB beamwidths Swath width (range×azimuth) Dynamic range, bits/sample Data rate
Table 3 Sensor mass and power budgets
Antenna structure technology Antenna total mass (kg) Sensor transmitter technology Sensor transmitter efficiency (%) Sensor transmitter configuration Sensor transmitter duty cycle (%) Transmitter PRF (kHz)
12 (along track) ×6 (across track) ×3 (vertical) Rigidisable inflatable structure 90 solid state, MOSFET 67 3.3 kW modules 10 Upto 100
Altitude (km) Sensor transmitter mass (kg) Sensor electronics size (mm) Radiated mean power (kW) Radiated peak power (kW)
250 40 550 × 270 × 600 (D) 4 40
Antenna structure size (m)
2 shows the penetration depth as a function of with peak transmitted powers of 40 and 120 kW (assuming a duty cycle of 10%), respectively, at the two heights. Typical values of at 100 MHz are in the range from
500 120 550 × 810 × 600 (D) 12 120
0.1 (water, fresh snow, permafrost) to 10 dB (wet clay, wet concrete). These high power levels can be obtained by the use of transmitters consisting of parallelconnect 3 kW modules [21]. As a consequence, the
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two operating altitudes require two different transmitter configurations, with different mass and power requirements. Table 2 shows the final sensor configuration for the two selected orbits, and Table 3 gives the estimated sensor mass and power budgets for the selected orbits.
3.1. Position and pointing requirements These requirements have been defined assuming a maximum percentage error of 1% in the observed area Table 4 500-km orbit parameters Altitude (km) Inclination (◦ ) Repetition factor Keplerian period (s) Distance between successive ground tracks at the equator (km) Distance between adjacent ground tracks at the equator (km) Potential swath across track (km) Potential swath projection on the equator (km)
497.34 97.397 15.208 5674.0 2635.3 109.79 109.09 110.00
σ β
σY
σγ σ
D
For the satellite design only the 500-km altitude is considered. In order to define candidate orbits, a GPR mission aimed at archaeological observations is envisaged. To this end, it is worth noting that the major archaeological sites are located within the range of latitudes 20◦ S–50◦ N. As a consequence, to optimise observations of such sites, an orbital inclination of about 50◦ should be realised. Nevertheless, the selection of a sun-synchronous orbit with ascending node at 6 a.m. simplifies the problems related to the solar array sizing and orientation along the orbit, as well as it minimises the eclipse period duration. In this case, a reduction in the number of passages at lower latitudes must be accepted. Table 4 shows the parameters of the selected orbit. In the following, starting from the payload requirements, the satellite layout and mass and power budgets are preliminary derived. Particular emphasis is given to the electric power subsystem design, which will result the most critical.
X
σα
H
ϑ
Earth axis
orbit satellite
3. Satellite design
857
swath R ⊕
ξ Earth equatorial plane O ⊕
Fig. 3. Observation geometry.
and a maximum swath variation of 1 km with respect to the nominal one. Assuming that pointing and attitude knowledge errors produce the same percentage variation in the swath, with reference to Fig. 3 the attitude control and position knowledge uncertainties can be found in the orbiting reference frame (origin at the satellite centre of mass, z-axis directed downward, xaxis in the velocity direction and the y-axis completing a right-handed reference frame) as follows [22]: ϑ SN roll = √ , 6 SN ϑ SN pitch = √ , 6 sin ϑ SN 1 + cos2 (ϑ + ) ϑ SN yaw = √ 1 +
, 4 sin ϑ cos(ϑ + ) 6 sin ϑ SN aϑ SN X = √ , 6(a/D − cos ϑ) SN aϑ SN Y = √ , 6(a cos ϑ/D − 1) SN Dϑ SN h = √ , (4) 6 sin ϑ SN where the roll, pitch and yaw angles describe the rotation of the satellite-fixed axes with respect to the
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orbiting reference frame and D sin ϑ = sin−1 . R⊕
20 EPS MM
OBDH
TC
5
THC
10
ACS
15 RCS
Therefore, considering the sensor off-nadir angle (Table 2), a three-axis attitude control accuracy of 10−2 deg (which means an attitude measurement accuracy of at least 10−3 deg) and a position component knowledge accuracy of 100 m are computed. It is worth noting that these requirements can be satisfied by the use of traditional sensors and actuators. As a consequence, the design of the attitude and orbit control subsystems does not require innovative solutions to be identified.
PAY
25
(5)
MARGIN
STR 30
% of total mass
858
0
Fig. 4. Mass budget.
Solar array Sun
3.2. Satellite mass budget and layout The satellite mass budget is performed using typical values and formulas (with reference to already-flown space missions and the literature [23,24]) to evaluate the mass and power requirements of standard-like subsystems. Thus, the masses of the structure (excluding the payload antenna), thermal control and orbit and attitude control subsystems are preliminary evaluated as percentages of the satellite dry mass as follows: √ Dry MOCS = (0.01 + 0.0115 Y )MSC ,
Earth
Dry
MACS = 49.6 + 0.022MSC , Dry MSTR = (0.3)MSC , Dry MTHC = (0.04)MSC
Fig. 5. Satellite overall characteristics.
+ MRAD ,
(6)
where MRAD is the mass of a radiating surface designed for the sensor transmitter cooling. The platform total mass is then evaluated according to the following formula: Dry
L MSC = MSC + MP ,
Table 5 Satellite overall characteristics Module
Mass (kg)
Dimensions (m)
Main body Solar array Payload antenna
1443.5 24.5 90
2×2×5 4×5 12 × 6 × 3
(7) Dry
where MP is the propellant mass and MSC is obtained by simply adding the masses of the various subsystems [23]. Fig. 4 shows the masses of the various subsystems as percentages of the satellite total mass. Assuming a 20% margin, to include design uncertainties [22], the total satellite mass is 1558 kg. Finally, Fig. 5 shows the satellite schematic view and Table 5 summarises the mass and size of the main satellite modules.
3.3. Electric power subsystem Due to the high power level, the design of the electric power subsystem is the most critical one. To this end, the architecture of the payload supply system is firstly defined in order to derive mass and power budgets for the overall satellite. The schematic of the payload supply system is shown in Fig. 6, as part of the electric power subsystem scheme, which also includes
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Table 6 NiH2 battery Cell Cell Cell Cell Cell
charge voltage discharge voltage at C/1.67 output resistance capacity mass
Cell number (per battery) Battery number Battery total mass Battery discharge rate Cell discharge voltage Discharge time Eclipse time (worst case) DOD Charge time Charge rate Battery charge current Battery charge voltage
Fig. 6. Electric power subsystem scheme.
the power control unit (PCU), the power distribution unit (PDU) and the solar array. In particular, in the platform design it is assumed that the payload is not directly supplied by the solar arrays but by NiH2 batteries (Table 6) [25,26]. Therefore, the concept of accumulating electric power during the sunlight phase of the orbit is used. This allows platform mass and power budgets to be kept within feasible limits. 3.3.1. Payload battery design In order to reduce payload average power demand, it is assumed that only ten images per orbit, corresponding to a strip-acquisition of 40 km × 1100 km, are acquired. This corresponds to a payload operation time of about 154 s (3% of the orbital period). In addition, for the payload supply, a battery discharge voltage of 70 V is considered, as required by the sensor transmitter amplifiers (Fig. 6). The transmitter driver stage and modulators are supplied by DC–DC converters, which have a typical efficiency of 85% [23].
1.5 V 1.25 V 3 m 30 Ah 0.89 kg 84 2 149.5 kg 4.7 C 0.88 V 154 s 1419.7 s 20% 4105 s C/5.7 10.5 A 126 V
As a consequence, the electric power to be supplied to the sensor transmitter is 18.6 kW (70 V at 265.6 A) for 154 s. This power is used as design value for the batteries. In order to limit the power dissipation, advanced battery discharge (BDR) and battery charge regulators (BCR) are considered [27], with efficiency ranging from 94% to 98%. Therefore, the power input to the BDR is 19.8 kW (70 V at 282.5 A), while the battery discharge current is 282.5 A. This high current suggests the use of NiH2 batteries. In particular, the use of two parallel-connected batteries gives a total battery capacity of 60 Ah and limits the discharge current value at 141.3 A. Considering the battery parameters in Table 6, the number of series-connected cells is given by VD + nf Vdiode Nc,S = 1 + INT nf + , (8) VD,c where nf (3) accounts for allowed cell failure and Vdiode (about 0.35 V) is the Schotchy diode voltage drop. As a consequence, the nominal battery discharge voltage is 74 V, without failure. A discharge time of 154 s implies a discharged battery capacity per orbit of 12 Ah, which corresponds to a 20% Depth of Discharge (DOD), and a discharge rate of 4.7 C (limited to 3% of the orbit). Assuming a charge time equal to 90% of the worst case-sunlight duration (at the summer solstice), corresponding to
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Table 7 Required power, current and voltage
Bus→BCR BCR→battery Battery→BDR BDR→DC–DC converter DC–DC converter→amplifier DC–DC converter→driver stage DC–DC converter→linear pulse modulator DC–DC converter→linear pulse modulator
Voltage (V)
Current (A)
Power (kW)
Time (s)
126 126 70 70 70 35 15 −15
11.2 10.5 282.5 265.6 75 20 6 1
1.407 1.323 19.78 18.59 5.250 0.700 0.090 0.015
4105 4105 154 154 154 154 154 154
about 72% of the orbital period, the charge current is 10.5 A, which gives a charge rate of C/5.7 and a battery charge voltage of 126 V. As a consequence the battery charge power is 1323 W with the BCR supplied with 1407 W (126 V at 11.2 A). Finally, Table 7 summarises the required powers, currents and voltages along the various supply lines. 3.3.2. Satellite power budget From the previous, the payload average power requirement over an orbit results 1017 W. The satellite bus power demand is then computed assuming that the payload average power requirement is 60% of the total amount [23]. Thus, the bus average power requirement is 678 W. Thanks to the fact that the battery-discharged capacity due to the payload operation is only 20%, the same battery is also used for the bus supply during eclipse (Fig. 6). To this end, the battery must supply an additional power of 849 W (considering the BDR and DC–DC converter efficiency), which leads to a discharge rate and a DOD per orbit of C/4.9 and 28%, respectively. Both these values are compatible with the selected battery. If a 28% capacity (instead of 20%) is to be recharged within the time span of 4105 s, the charge current must be incremented of 4.2 A (@126 V), corresponding to a charge power increment of about 565 W (considering also the BCR efficiency). 3.3.3. Solar array design It is assumed that the solar panel voltage is regulated at 126 V by the Power Control Unit, while the bus voltage is regulated at 50 V, by means of DC–DC converters, in order to be compatible with ESA
Table 8 Power budget BCR supply (W): Payload Bus Total Bus supply (W) Average power required (W) 10% margin (W) Total power (W)
1407 567 1972 678 3179 317.9 3497
standards. A selection unit selects the line to be used for the bus supply as a function of the orbit phase (sunlight or eclipse). The solar array design is performed considering the power requirements in Table 8 and using the following formula [23]: Pbus Tsunlight PBCR TC 1 Psa = . (9) + Tsunlight PCU PCU DC–DC Assuming for the voltage regulator and the DC–DC converters a typical efficiency of 85% and considering a 10% design margin, an average power requirement of about 3.5 kW is computed. The solar panel area is then given by the following expression [23]: Asa =
Psa , ScT cp clife cells
(10)
which gives a 20-m2 area, considering GaAs solar cells (18% efficiency) and a 3-yr lifetime and using a 0.9 packaging factor, a 0.85 temperature-dependant degradation coefficient, and a 2.5%/year environmentdependant degradation coefficient [23]. The use of inflatable-rigidisable technology allows a mass density of about 7 kg/kW, which gives a solar array mass of
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25 kg [18]. Finally, a total mass of 70 kg is estimated for the power control unit and the power distribution unit using typical values [23]. 3.4. Thermal control Thermal analysis does not pose particular issues. The only critical aspect could be the control of the large power dissipation caused by the payload operation. To this end, an ad-hoc radiating surface is designed using the following simplified thermal-balance model: AR εR kT 4 = mTRA cpTRA
dT , dt
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Table 9 Propellant budget CD (kg/m3 ) V (km/s) A (m2 ) Manoeuvre frequency (days) Altitude variation between two successive manoeuvres (m) Minimum required V (m/s) Total required V (m/s) Propellant specific impulse (s) Total required propellant mass (% of the satellite mass)
2.2 10−12 7.61 4 8.2 212 0.117 16 235 0.7
(11)
where εR is the radiating surface emissivity (0.9). Equation (11) is written under the following simplifying assumptions: (1) the transmitter–radiator system is thermally insulated by the rest of the satellite; (2) all the thermal power is radiated through the radiator and (3) the radiator mass is negligible with respect to the transmitter one. It is then possible to estimate the radiator surface as follows: mTRA cpTRA 1 1 AR = = 0.416 m2 , (12) − 3 3kεR tR T03 TTRA where the transmitter initial temperature is assumed to be equal to an estimated satellite equilibrium temperature of 293 K, the cooling time is 4955 s and the transmitter mean specific heat is estimated as 200 J/kg K. Therefore, assuming that the radiator is a 1-mm thick aluminium sheet its mass comes to be about 1 kg. 3.5. Orbit maintenance In order to evaluate the satellite total mass, the propellant mass needed for orbit maintenance must be computed. To this end, the manoeuvring frequency is first computed considering a maximum swath variation of 1 km with respect to the nominal one. The time between two successive manoeuvres can be computed as follows [28]: Dry SL MSC vsc m = . (13) √ 15Q aCD A The propellant mass can be then evaluated using the values in Table 9 for the parameters in Eq. (13) and
considering that the altitude variation between two successive manoeuvres is given by [28] √ 55 aCD Am . (14) H = Dry MSC Out-of-plane manoeuvres for orbit inclination corrections are not required [29]. 3.6. Telecommunication and on-board data handling For the evaluation of the telecommunication subsystem mass the typical values of a S-band system have been used [23], which lead to a total mass of 25 kg. The requirements for the design of the on-board data handling subsystem are proportional to the satellite complexity. Except for the electric power subsystem and the payload antenna, the proposed system has a standard architecture. Therefore, the design of the on-board data handling subsystem does not present particular issues with respect to more traditional space systems. As a consequence, it can be assumed that system functionality is guaranteed by a central command unit, with redundant processing unit. In nominal conditions, one of the two CPUs is totally dedicated to satellite guidance, navigation and control. The satellite subsystems are linked to the central unit by a RS-422 standard bus. Using typical values [23], a 40 kg-mass is then estimated for the on-board data handling subsystem (including CPU, decoder and encoder). Considering the payload high data rate (99.2 Mbps), particular attention is given to the mass memory selection. Considering that about 15 Gb are acquired per orbit and the time necessary for data downlink is
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about 2.56 min, using standard hardware [30] the mass memory required power per orbit can be evaluated as follows: PREC TREC + PREPR TREPR + PSTB TSTB TORB = 13.22 W, (15)
PMM =
where TREC , TREPR and TSTB are the recording, reproduction and stand-by times, respectively, and TORB is the orbital period. 3.7. Structure and mechanisms Except for the payload antenna structure, this subsystem does not present particular issues: its mass is evaluated as a percentage of the satellite dry mass (Eqs. (6)).
4. Conclusions The authors presented a feasibility study for flying a ground penetrating radar from space. In particular, the payload preliminary design is presented and it showed that, as expected, the stringent power requirements could reduce the effective use of GPR/SAR images acquired from unfavourable (i.e. with high attenuation) soils, especially at the 500-km height, which is preferable, though, due to the greater orbital stability. Careful use of the VHF carriers has to be planned in order to avoid interference with ground installations operating in the 100–200-MHz frequency range (FM broadcast, VHF Omnirange (VOR) for air navigation, for example). Moreover, integration of the GPR/SAR sensor with accurate positioning systems (INS, GPS) is necessary for correct trajectory reconstruction and motion compensation (integration times are larger than typical airborne or spaceborne SARs, and motion instabilities could affect the overall image quality). Finally, the advantage of global coverage has to be weighted against the disadvantage of a restricted class of “useful” soil, in particular those with little attenuation (less than 5 dB/m at 100 MHz). As for the impact of payload design on satellite bus, the design main driver obviously is the large amount of transmitted power. Therefore, apart from the possibility of flying the sensor onboard the Space Shuttle or the Space Station, if a free satellite is envisaged a
sunsynchronous, 6 a.m.–6 p.m., 500 km altitude orbit is a solution which adequately trades off the atmospheric drag and the power to be transmitted by the payload antenna. As far as satellite preliminary design is concerned, a strategy was selected to cope with a large power requirement and to reduce both the average power requirement and the solar panel dimensions. In particular, it was decided to supply the payload by a NiH2 battery and to reduce the overall mission duty cycle so that a swath of 40 km × 1100 km per orbit is acquired. In addition, a dual voltage bus regulation was adopted, the BCR being regulated at 126 V and the bus loads at 50 V. The former was selected in order to have an adequate supply voltage to the transmitter, while the latter accounts for the need to have a standard voltage (ESA specifications). An overall satellite mass of about 1.6 tons, an average load power of 1.9 kW, and a beginning-of-life solar panel power of 3.5 kW resulted from design. In conclusion, mission feasibility was demonstrated if a large satellite is envisaged. To reduce satellite mass and size, a number of technological developments are to be achieved: high efficiency solar cells; high specific energy batteries with high discharge current, more efficient DC–DC converters, new techniques for data compression are some examples.
Acknowledgements This work has been performed with the financial contribution of the Italian Ministry for Education, University and Research.
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