5th AIAA International Communications Satellite Systems Conference (organized by APSCC) AIAA 007-3149 Thermal Proellant Gauging System for BSS 601 T. Narita. 1 JSAT Cor, 9-1 Miho-Cho, Midori-ku, Yokohama 6-0015, Jaan B. Yendler.. LMMS/COMSAT, Sunnyvale, CA, 94089, USA. Of the more oular methods of roellant estimation, namely, book-keeing, PVT (Pressure, Volume, Temerature) and the Thermal Proellant Gauging System (PGS) methods, the latter is most accurate at End-of-Life (EOL). The thermal method uses tank temerature resonses to tank heating in order to infer the roellant load in the tank. Tyically, the PGS method uses heat load from heaters which are attached to the roellant tanks. The current aer discusses a method of Thermal PGS when tanks do not have installed heaters. Secifically, this aer describes how the Thermal PGS method could be alied to an on-orbit Boeing 601 geosynchronous communications satellite. It is shown that roellant gauging is ossible even when the roellant tanks do not have heaters. This aer examines an imlementation of the Thermal PGS method on a Boeing 601 geosynchronous communications satellite which has been oerated by JSAT Cororation of Jaan. Prior to the develoment of a thermal model, a feasibility test was conducted in order to determine the tank temerature resonse to tank heating. Due to the lack of heaters on the roellant tanks, gyro (Inertial Reference Unit, or IRU) heaters were used for tank heating. During the 48-hour feasibility test, the tank temerature rose several degrees C which is sufficient for roellant estimation by the Thermal PGS method. No stationkeeing maneuvers were conducted during the eriod of data collection, in fact, the first maneuver was erformed after a cool-down eriod for the tanks. High-fidelity tank and satellite thermal models were develoed based on the results of the feasibility test, and those thermal models were used for roellant estimation. This aer discusses the results of the roellant estimation oerations and the accuracies achieved. Nomenclature C = secific heat m i = mass of i comonent T = tank temerature T env = environment temerature Q load = heater ower U = uncertainty of calculated or measured value f = generic function\ ε* = effective emissivity through Multi Layer Insulation (MLI) i = comonent index = roellant index g = gas index t = tank index 1 Deuty GM, JSAT Cor, 9-1 Miho-Cho, Midori-ku, Yokohama 6-0015, Jaan. Sr. Thermal Systems Analyst, Comsat Technical Services, 1309 Moffett ark Dr., Sunnyvale, CA 94089. Coyright 007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 1
I. Introduction The Proellant Gauging System (PGS) method of roellant estimation is based on a concet of measuring the thermal caacitance of a tank containing liquid fuel and ressurant gas by measuring the thermal resonse of the roellant tank to heating and comaring the observed temerature rise to simulation results obtained from a tank thermal model 1,. Described in Ref. 1, the PGS method emloys a very sohisticated thermal model of the roellant tank which takes into account temerature gradients in the tank. Non-uniform heater ower distribution and uneven roellant distribution inside of the tank cause a non-uniform temerature distribution on the tank surface. Non-uniformity of heater ower distribution stems from the fact that heater stris tyically cover only a fraction of the tank surface. If roellant osition in the tank is controlled by a vane-tye Proellant Management Device (PMD) in microgravity, then at EOL the roellant is located in the sum and in the corners formed by PMD vanes and the tank wall. A significant ortion of the internal tank wall is not in contact with roellant and therefore dry. All these factors lead to the formation of significant temerature gradients on the tank wall. Therefore, the temerature, which is measured by the temerature sensors on the external side of the tank wall, deends on the sensor locations. The temerature distribution on the tank surface must be determined to successfully comare the test flight data with calculated temeratures. If satellite thermal control system does not have heaters installed on the roellant tanks, the tank temerature is controlled by internal satellite thermal control system. The BSS (former Hughes) 601 geosynchronous communication satellite is an examle of such thermal control scheme 3. Such a thermal control system resents a challenge for a tyical PGS method because energy inut into a roellant tank is done not by heaters installed on the roellant tanks by rather by external heat sources like ayload or bus units which heat generation is known. An examle of such unit could be TWT or one of the bus units which generate enough heat to increase tank temerature. The key is knowledge of heater ower or/and surface temerature of the unit which is used to generate energy and to increase tank temerature. If the unit in question has a temerature sensor, heat generation by the unit can be calculated. Viceversa, knowledge of heat generation allows calculation of unit temerature which can be comared with temerature sensor reading if the unit has temerature sensor installed. In both cases, develoment of a high fidelity model of the satellite including ayload and bus units is required. Such a requirement constitutes the major difference for PGS method between satellites with and without heaters installed on the roellant tanks. If roellant tanks have heaters installed and the tanks are covered with thick Multi Layer Insulation (MLI) blanket, the tanks do not have much thermal interaction with the satellite environment. Knowledge of the satellite thermal environment is not so imortant for correct roellant estimation by the PGS method. On other hand, if ayload or/and bus unit is a heat source which used for roellant estimation, the heat source is art of the satellite environment. In this case, the tank temerature rise is determined by thermal interaction between the tank and the satellite environment. Therefore, knowledge of the satellite environment becomes very imortant for correct roellant estimation. II. Thermal models Regardless of the sacecraft tye, the PGS method emloys the same stes: Develo a thermal models of the roellant tanks and the satellite Develo a thermal models of the satellite Merge the thermal models of the satellite and roellant tanks Preare and conduct the PGS oeration Simulate the PGS oeration for different roellant loads Comare flight and simulation data Determine tank roellant load The first hase of the PGS method, namely, develoment of the tank thermal model, the develoment is mostly driven by the tank design and by the fact that heaters (if installed) create a large temerature gradient on tank walls in heaters vicinity. It means that a high fidelity tank model is required to cature
temerature gradients and to determine tank wall temerature at the temerature sensor location. In absence of the heaters on the tank surface, one can exect less temerature gradient and, therefore, less stringent requirements for caturing temerature gradients. A. High Fidelity Tank Model If temerature gradients can not be neglected, which is a common case, temerature distribution in the tank should be determined numerically with corresonding boundary and initial conditions. Previously develoed a Finite Element (FE) model of the roellant tank1, was based on grid rovided by Surface Evolver4. The develoed FEM model of the tank had several roblems including difficulty of keeing the ratio of the maximum to minimum conductances of the links between nodes in the thermal model sufficiently small to avoid ill-conditioned matrices in the thermal modeling. Also, based on Surface Evolver grid had extremely small or large conductances, which are not generally necessary. Similarly, the minimum thermal caacitance of elements affects ste size in time and thus overall comute time of the modeling. In order to avoid such roblems, a new FEM was develoed. Grid generation for such comlex geometry like tank with gas and liquid volumes, tank wall, heaters, etc is not simle task. The grid should Figure 1 Cross section and shell of final tank grid satisfy the following requirements: have high enough density to simulate thermal gradients, articular at the temerature sensor location, confirm to the rimary geometry of model comonents like, tank wall, roellant, ressurant, should confirm each other at the interfaces, confirm heater shae, etc. GridPro5 was selected as the rimary tool for creating the grid. It is a owerful tool designed to create comutational fluid dynamics (CFD) grids. Grid generation of the tank was not simle. When the geometry is comlex, it can be difficult to get a CFD style grid to converge and to model accurately the geometry. In articular, GridPro runs into roblems when the geometry becomes overly comlex, like, shar edges, or a zero-degree angle between two surfaces. The gas/fluid interface model alone is of sufficient comlexity to cause the GridPro to have difficulty of converging. Add to this, requirements for the grid to confirm to tank heaters shae, variations in the tank wall rofile, mounting lugs, etc. and it quickly becomes extremely time consuming to develo a grid that will converge. A suite of software tools was develoed in order to overcome these limitations. Figure 1 shows several cross-sections of the final grid. As one can see, the grid has higher density next to tank wall where temerature gradients are exected. B. High Fidelity Satellite Model Current aer discusses develoment the PGS method for BSS (former Hughes) 601 geosynchronous communication satellite. Figure shows a general view of the satellite which design is described in details in Ref.3. The satellite roulsion system has four sherical tanks (two fuel tanks and two oxidizer tanks). Tanks are covered with single layer MLI3. Two temerature sensors are installed on the to and on the bottom of a roellant tank (Fig.7 Ref.3). The to temerature sensor aroximates ressurant temerature. The bottom Figure BSS 601 satellite 3
temerature sensor senses the temerature of the roellant which is contained inside of the tra (Fig.7 Ref.3). Such design of the roellant tanks and the satellite requires develoment of satellite thermal model which should describe: a). radiation heat transfer between tanks and satellite comonents like anels and ayload/bus electrical and electronic units; b). heat transfer by conduction between the units and satellite structure, between satellite structure and roellant tanks. Due to a articular osition of the temerature sensors on the roellant tank wall, heat transfer between bottom of the roellant tank and the satellite resents the greatest interest. Figure 3 demonstrates a develoed satellite thermal model. The model simulates all major elements of the BSS 601 West satellite which are imortant for simulation of the PGS oeration and roellant estimation, like internal anels, MLI blankets, etc. All surfaces of the satellite internal anels are assumed ainted black, which is common ractice for communication satellites in order to increase heat rejection from the internal anels. The satellite thermal model includes solar fluxes incident on the outer surfaces of the satellite. The radiation interaction inside of the satellite and solar fluxes were simulated by Thermal Synthesizer System (TSS) software tool. Tyically, North and South anels of communication satellites house heat roducing units, like Travel Guided Tube (TWT) which usually instrumented with temerature sensors. Use of temerature sensor readings as boundary conditions simlifies the satellite thermal model because it circumvents the need to determine temerature of the North/South anels. Usually, East and West anels don t have any ayload or bus units; the temerature of such anels was calculated. III. Proellant Estimation This section discusses the PGS oeration that was erformed in 006 on one of the BSS 601 satellites of JSAT Cororation fleet. JSAT began to oerate BSS 601 satellites in 1995. Five BSS601 satellites have been oerated so far. All revious exerience related to roellant estimation for the satellites with tanks which have heaters. Prior to develoment a high fidelity models of the roellant tank and the satellite, a feasibility study was conducted. The study included simulation and flight test. The goal of the feasibility study was to determine whether the PGS method is suitable for roellant estimation due to the fact that roellant tanks do not have heaters. Due to lack of the heaters on the roellant tanks, we used IRU heaters as an external heat source. Flight exerience ointed out that roellant tank temerature went u when IRU heaters were turned ON. It shows that IRU heaters can be used for the PGS oeration, but an accuracy of such estimation was not known. As Figure 3 indicates, IRU units are located on the bus anel in vicinity of the roellant tanks. Therefore, the IRU heaters should have the greatest influence on the tank temerature. A. Feasibility study North Radiator East Figure 3 Satellite Thermal Model Cross shows IRU location South Radiator 1. Simulation In order to study an effect of heat generation by IRU heater on tank temerature, we assumed IRU temerature of 60 C when the heater is turned ON. Figure 4 shows the tank temerature trend when the heaters are turned ON and OFF. Tank temerature rises when IRU heater is ON and falling after the IRU heater is switched OFF. It suosed to take about 48 hr. to reach equilibrium with satellite environment during. The cooling eriod also should last about 48 hr. 4
Temerature[C] 36 34 3 30 8 6 4 0 Heater ON Heater OFF NE tank SE tank 18 0 4 48 7 96 10 144 168 19 Time[hr] Figure 4 Tank Temerature at the bottom; Temearture rise [C] 7 6 5 4 3 1 0 0.kg 5kg 10kg -1 0 1 4 36 48 60 7 84 96 When IRU heater is turned ON temerature of both tanks, NE and SE, increase. Heat transfer to the SE tank is conducted mostly via radiation. Heat transfers from the unit to the NE tank via conduction by base anel and via radiation across the middle wall. As exected, temerature rise of NE tank is less than temerature rise of SE tank. Tank temerature rise due to heat inut from the IRU resents the most interest, as far as the PGS method concern. Such a temerature rise has the same magnitude as tank temerature change due to daily temerature variation. This obscures temerature rise due to tank heating by the IRU heater. A normalization rocedure was develoed in order to extract such tank temerature change. Figure 5 shows behavior of the normalized temerature. Daily temerature fluctuations are removed and only temerature rise due to heat injection by the IRU heaters remains. The lot also shows an effect of tank roellant load on the temerature rise, which is the most interest to the PGS method. The data clear demonstrates that temerature rise deends on the roellant load and can be used for roellant estimation by the PGS method. Time[hr]. Flight Figure 5 Normalized Tank Temerature For the feasibility test, IRU heater was turned ON for 4 hr. During this time tank temerature has risen for several degrees (see Figure 6 and Table 1), which seemed to be sufficient for roellant estimation by the PGS method. 39.5 39.0 38.5 38.0 Tem 37.5 37.0 36.5. 36.0 35.5 35.0 34.5 34.0 IRU On 0 1 4 36 48 60 7 Time (hrs) Figure 6 Fuel Tank Temerature Sensor T3 trend IRU on for 4 hr Table 1 Flight Test Results 5
Tank Tye Temerature Rise ( C) Fuel.7 Oxidizer 5.0 B. Oerational Constraints Several considerations should be taken into account in determination of the eriod of the PGS oeration in order to minimize an influence of the sacecraft conditions on tank temerature: Avoid eclise season (change of thermal condition) No change in ayload/bus unit configuration (change of thermal condition) No stationkeeing maneuvers erformed (change of roellant load, sloshing) Enough time to cool-down for the tanks after turning heaters OFF From station-keeing viewoint, a eriod of cooling down of the roellant tanks after the heaters turned OFF should be long enough in order to reduce roellant tank ressure. Increased tank ressure might cause some variance in maneuver erformance. No stationkeeing manoeuvres were conducted during the PGS oeration because temerature and ressure of the tanks were a little bit higher than usual due to tank heating. First manoeuvre was erformed after a cool-down eriod which lasted for 48 hours. Temerature rise due to heating varied for different tanks. It could be exlained by difference of roellant loads or/and difference in environment conditions for each tank. The observed temerature rise was sufficient to estimate the remaining roellant in the tanks. C. Flight Test results The PGS oeration was erformed after successful comletion of the feasibility study. The PGS oeration consisted of two stes: PGS oeration rocedure rearation and a flight oeration. The develoed tank and sacecraft models were used in the develoment of the flight oerations rocedure. The goals of the simulation for the rocedure develoment were to determine: 1) the length of time which it takes for the tanks to reach thermal equilibrium, and ) the length of time which it takes for the tanks to cool down to the initial conditions. It was determined that it should take 3-4 day for tank temerature to reach saturation and 1- days to cool tanks down to the initial temerature. The IRU heaters had been turned ON for 3 days during the PGS oeration. The observed tank temerature rises were: Fuel Tank 1 3.5 o C, Fuel Tank 4 o C,; Oxidizer Tank 1-5.5 o C, Oxidizer Tank - 5 o C. The temerature trends for bottom temerature sensors (T3) of the roellant tanks are shown in Fig.7a. The temerature of the roellant tanks and several bus and ayload units were collected during the PGS oeration. The satellite thermal model uses temerature of bus and ayload units to characterize tank a) b) Figure 7 Flight Oeration Results a)tank (Sensor 3); b) Pressure Controllers temerature sensors 6
IV. environment. In addition to tanks, IRU heaters affect temerature of bus and ayload units. An examle of such influence is shown in Figure 7b. The resented data demonstrates temerature rise of ressure controllers when IRU heaters were turned ON. D. Proellant Estimation Proellant remaining in all four tanks was estimated using the develoed thermal models of the tanks and of BSS 601 satellite and flight data. Several simulations were run with varying roellant loads for each roellant tank. Proellant remaining was estimated using normalized flight data and normalized Temerature Rise (deg_c) 4 3.5 3.5 1.5 1 0.5 FTank 8kg 10kg 1kg 0 0 4 6 8 10 1 14 16 18 0 4 Time (hrs) Figure 8 Results of PGS estimation for Oxidizer Tank 1. Lines simulation results; Markers Temerature Sensor T3 reading IRU heater was turned ON at t=0 simulations results. Figure 8 shows an examle of the comarison of the normalized flight data with normalized simulations results for the Oxidizer tank 1. The diurnal temerature variations have been removed via data normalization rocedure which was described earlier. The normalized flight and simulation data illustrate temerature rise due to tank heating without obscuring it by daily temerature fluctuations. As one can see from Fig. 8, the comarison of flight and simulation data indicates that the roellant load of Ox1 tank is close to 10 kg with robable variation of kg. We need to stress that simulated temerature variation with roellant load of a tank does not reresent an accuracy of the PGS method. It rather illustrates the sensitivity of temerature rise to tank load. The accuracy of the PGS estimation is addressed in the next Section. However, we would like to mention that a sensitivity lot, like Fig 8, can only give eye ball estimation of the PGS accuracy. Accuracy of Proellant Estimation Tyically, a satellite oerator is interested not only in estimation of roellant remaining but also in the accuracy of the roellant estimation. The review of existing methods can be found elsewhere 6. We will use an uncertainty analysis 7 to determine an error of roellant estimation. In general, a roellant tank mass consist of three comonents, namely, roellant mass, ressurizing gas, m g, and mass of the tank itself m t. m, mass of Calculated roellant mass is function of many arameters like alied heat load Q load, environment temerature env, etc. Then, the uncertainty of roellant mass estimation is defined as: T m U = f ( T, Q ( m load m ) = T *, ε, m U( T ) g, m t, T m + Q env load, C P U( Q,...) load ) m * + U( ε ) * ε +... (1) 7
Uncertainty of absolute temerature measurement T does not have an effect on PGS accuracy of roellant estimation because the PGS method uses temerature difference for roellant estimation instead of the absolute temerature. It is convenient to exress all uncertainties in terms of temerature uncertainty. For examle, the second term in (Eq.1), which shows the mass uncertainty related to the heater ower uncertainty, can be exressed as mt mt T U( Q) = U( TQ ) ; where U( TQ ) ) = U ( Q) Q T Q () Using maniulation (Eq.) for other terms in (Eq.1), easy to resent (Eq.1) in the form m T ( m ) = δ ( T Where δ (T) is the total temerature uncertainty, defined as U [ U ( T ) + U ( T ) + U ( T ) +...] δ ( T ) * = Qload ε ) (3) When a high fidelity model of the roellant tank is used for roellant estimation, the temerature distribution in the tank is determined by numerical solution of (Eq.4) by SINDA/Fluint with corresonding boundary and initial conditions. T mc = k T + Q t (4) Therefore, the closed form of solution of (Eq.4) is imossible to obtain. In order to calculate the derivatives in (Eq.1), the terms in mass uncertainty (Eq.) are exressed in (Eq.3) form. Essentially, the derivative of tank temerature over arameter is calculated instead of finding derivative of mass over arameter. The derivative of the temerature over model arameters, like, IRU ower ( emissivity ( * ε T Q ), effective T ), etc is obtained by solving FE tank thermal model with varied arameters. The resulting uncertainty is summarized in Table for the fuel and oxidizer tanks. Table Parameter uncertainty for oxidizer and fuel tanks Effect [kg] Model Parameter Oxidizer Fuel Tank-base connection 1.47 1.7 Tank MLI e* 1.77 0.6 Black aint emissivity 0.3 0.15 External lume shield e* 1.68 0.43 Transition function 1.80 1.0 Temerature sensor (T3) resolution.77.3 Total Uncertainty [kg] 4.37 3.16 8
The uncertainty of each arameter is indeendent from each other. Therefore, the RSS method is used to determine the total uncertainty of the roellant estimation. As Table indicates, the error of roellant estimation by the PGS method is relatively small. An error of estimation of the consumed roellant obtained by the bookkeeing method tyically is in the range of ±.5 % - 3.5 %, according to Ref. 6, 8, 9. Assuming the error of 3%, the bookkeeing method has uncertainty around ± 14 kg er tank at EOL based on data on BSS 601 roellant tanks volume 3. An accuracy of the PVT method was subject of several studies. The reorted error of roellant estimation by the PVT method various significantly. For examle, the error of roellant estimation is reorted as high as 35% 10 and as low as 0.% 11 at EOL. Such difference greatly influenced by uncertainty in reading of the ressure transducer. A high resolution ressure transducer is used in Ref.11. It is not clear, however, how reliable this ressure transducer is after 10 years in flight. V. Discussion Precise estimation of remaining roellant is needed to extend the satellite mission life as long as ossible. In addition, it guarantees confident de-orbiting of the satellite at the end of its mission life. Initially, JSAT Cororation (Jaan) has used both the book-keeing and the PVT methods for estimation of remaining roellant. JSAT decided to use the PGS method for roellant estimation of one of BSS601 satellite fleet as an alternative method to the bookkeeing and the PVT methods. It allows comaring the results of all three methods in order to make more rational decision for rediction of End-of- Life of the satellite. Each method can rovide different estimation of remaining roellant and with different uncertainty. Use of different methods hels to avoid a systematic error introduced by an individual method in order to minimize a ossibility of unexected deletion. For examle, the result of the comarison between the PGS and other two methods can be used for selection of air of the roellant tank used during stationkeeing maneuvers. It also hels to have a balanced consumtion of remaining roellant to the rest of the satellite mission. JSAT lans to evaluate the results of the PGS estimation and determine if it would be ossible to track roellant deletion in deorbit oerations in the future using the PGS method. Such an evaluation will be helful for imrovement of an accuracy of the PGS method. VI. Conclusion Proosed aer shows that the thermal PGS method for roellant estimation can be alied successfully to a satellite which does not have heaters installed on the roellant tanks, like BSS (former Hughes) 601 geosynchronous communication satellite. It is shown that the PGS roellant estimation can be conducted if a ayload or a bus unit is used as heat source external to the roellant tank. However, use of the PGS method for roellant estimation requires develoment of a satellite thermal model of higher fidelity comared to the case when the roellant tanks have heaters installed and tanks are insulated from the satellite environment. It is shown that the error of roellant estimation by the PGS method is less than error of roellant estimation by the book keeing method at EOL for BSS 601 satellite. Use of the PGS method allows JSAT Cororation execute an indeendent verification of the roellant estimation obtained by the bookkeeing and PVT methods, to mitigate risk of unexected deletion and increase confidence in fleet reliability. 9
VII. Reference 1 J. Ambrose, B. Yendler, and S. H. Collicott, Modeling to Evaluate a Sacecraft Proellant Gauging System, Journal of Sacecraft and Rockets, vol. 37, Nov-Dec 000,. 833--835 A. Yi, B. Yendler, T. A. Martin, S. H. Collicott, Anik E Sacecraft Life Extension, roceeding of Eighth International Conference on Sace Oerations, Montreal, Quebec, Canada. May 17-1, 004 3 Purohit, G.P., et al. Transient Lumed Caacity Thermodynamics Model of Satellite Proellant Tanks in Microgravity, Proceedings of the 37 th AIAA conference, 11-14 January 1999, Reno, NV, USA 4 K.A. Brakke, The Surface Evolver, Exerimental Mathematics, 1():141-165, 199 5 K. Rajagoalan, P. R. Eiseman: Automatic nested refinement: a technique for the generation of high quality multi-block structured grids for multi-scale roblems using GridPro, Engineering with Comuters, Vol. 1(1): 005,. 9-35 6 Hufenbach, B., et al. Comarative Assessment of Gauging Systems and Descrition of a Liquid Level Gauging Concet for a Sin Stabilized Sacecraft, Proceedings of the Second Euroean Sacecraft Proulsion Conference,, 7-9 May 1997, Noordwijk, the Netherlands. Edited by Michael Perry. ESA SP-398. Paris: Euroean Sace Agency, 1997.,.561-570 7 B. Yendler, Review of Proellant Gauging Methods, roceeding of 44th AIAA Aerosace Sciences Meeting and Exhibit Conference, Reno, Nevada, US, January 9-1, 005 8 Hasan, D. et al, Alication of Satellite Hydrazine Proulsion System In-Orbit Monitoring Model Proceedings of the 4th International Sacecraft Proulsion Conference (ESA SP-555). - 9 June, 004, Chia Laguna (Cagliari), Sardinia, Italy. Editor: A.Wilson. Published on CDROM.,.110.1 9 Dandaleix, L, et al, Flight Validation of the Thermal Proellant Gauging Method Used at EADS Astrium. Proceedings of the 4th International Sacecraft Proulsion Conference (ESA SP-555). -9 June, 004, Chia Laguna (Cagliari), Sardinia, Italy. Editor: A.Wilson. Published on CDROM.,.9.1 10 Lal A, Raghunandan, BN, Uncertainty Analysis of Proellant Gauging System for Sacecraft, AIAA-9511-87, JOURNAL OF SPACECRAFT AND ROCKETS, Vol. 4, No. 5, Setember October 005, 943-946 11 Chovotov, M.V, Purohit, G.P., Low Gravity Proellant Gauging System for Accurate Predictions of Sacecraft End-of-Life, JOURNAL OF SPACECRAFT AND ROCKETS, Vol. 30, No. 1, January-February 1993, 9-101 10