ANALYSIS OF HALL-EFFECT THRUSTERS AND ION ENGINES FOR EARTH-TO-MOON TRANSFER

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1 IEPC ANALYSIS OF HALL-EFFECT THRUSTERS AND ION ENGINES FOR EARTH-TO-MOON TRANSFER A. Bober, M. Guelan Asher Space Research Institute, Technion-Israel Institute of Technology, 3000 Haifa, Israel ABSTRACT Analytical ethods were cobined with actual thruster data to create a odel for predicting the perforance of systes based on two types of electric propulsion thrusters, Hall-effect thrusters and ion engines, for Earth-to-Moon transfer. This paper presents the analysis of flights fro an initial Earth-centered trajectory to Moon neighborhood. Analysis perfored on the basis of the restricted three body equations showed that the required velocity increent could be closely approxiated by a sooth logarithic function of the ecific ipulse and ecific power. The possible applications of different electric thrusters were considered and possible flight characteristics were deterined for initial acecraft asses fro 100kg up to 1500kg. 1. Introduction Electric thrusters have long been known to be an efficient eans of propulsion for ace issions. Thirtyyears Stationary Plasa Thrusters (SPT) ace operation deonstrated their high reliability. The rearkable NASA Solar Electric Propulsion Technology Application Readiness (NSTAR) ion engine operation as the priary propulsion for the Deep Space 1 (DS-1) probe deonstrated high versatility for varying flight tasks and satellite perforances. Earth-to-Moon transfer with electric propulsion essentially differs fro one with cheical transfer. As a rule, a transfer with cheical thruster is a two-ipulsive Hohann aneuver. This aneuver consists of three stages: i) thrust ipulse on the initial orbit ii) coasting flight on an elliptical orbit iii) thrust ipulse in the apogee of this elliptical orbit. The flight tie fro initial circular orbit with altitude 00k to Moon orbit, is less than 5 days. The required propellant ass at ecific ipulse I =350s is approxiately 68% of initial on-orbit acecraft ass. The transfer with electric propulsion is otion along a iral trajectory as a result of continuous thruster operation. As is well known, transfer with electric propulsion is uch slower than one with cheical thruster. However, as large loads are tranorted by slow ships and not by fast planes, the sae approach ay well apply for ace flights. Furtherore, it is possible to consider a ission with a nuber of sall electrically propelled acecraft consecutively initiating flight fro low Earth orbit, "slowly" oving in ace in the course of one year, and siultaneously observing condition of ace at various points. This paper presents a general analysis of electrically propelled acecraft flights fro an initial Earthcentered orbit to Moon neighborhood.. Proble Stateent For the Earth-to-Moon transfer depicted in Fig.1, the syste equations describing the acecraft trajectories correond to those of the restricted three-body proble. The Earth and Moon will be assued to ove in circles around their coon center of ass (barycenter) and their gravitational fields will be assued herical. X e, X, the Earth and Moon centers distances to barycenter are given by, 1

2 X e = R = R, X R X e e + µ e + µ µ =, Y Spacecraft R 1 θ X R R X e Barycenter Earth X Moon Fig.1: Spacecraft in Earth-Moon Rotating Frae where R is the constant Earth-oon range, e,, e = G e µ = G µ ; are the Earth and oon asses and gravitational constants reectively and G is the universal constant of gravitation. R, R 1 and R are the acecraft's distances to barycenter and to centers of Earth and Moon, reectively. The equations of otion of the acecraft in the Earth-Moon rotating coordinate syste, centered at their barycenter, are given by (Ref.1) µ µ µ X µ X ax (1) e e e X = ωy + ω X + X R R R1 R µ µ ay () e Y = ωx + ω Y + Y R R 1 where X, Y are the acecrafts coordinates, R = X + Y ; ω is the orbital angular Moon velocity; a is the control acceleration, a = a x + a y. The control acceleration is F a =, where F is thrust and M s / c the actual acecraft ass, with initial M s / c value M 0 and final value M f. The acecraft ass by M s / c = M 0 & st with t the burning tie. M / for constant propellant ass flow rate & s is given s c In an electric engine, propellant ass flow rate, thrust and control acceleration are reectively given by, P & s = ηt (3) I

3 P F = & s Pηt = ηt (4) I a = M 0 M 0 Ps & s Ps ηt = η t (5) M M I s / c s / c with η t thrust efficiency, a function of ecific ipulse; P power consuption; P s = P / M 0 ecific power and I ecific ipulse. Let us define acecraft noralized ass M M s / c Psηt = = 1 t (6) M I 0 Control acceleration is thus given by, a P η s t = (7) MI Now that all necessary equations are defined we shall deterine the acecraft trajectories fro initial Earthcentered orbit to Moon here of influence. We shall assue that constant thrust is applied along the acecraft velocity vector, ax X Y = a ;ay = a (8) (X ) + (Y ) (X ) + (Y ) Even though optial thrust is varying both in aplitude and direction, due to the alost flat characteristics of the cost function this approxiation is good enough to study the influence of various thrusters on overall syste perforance. The calculations goal is deterination of the flight tie and noralized final ass for difference thruster perforances. 3. Input data The possibilities of use of various thrusters as given in Table 1 will be discussed in this work. Their reective data was obtained fro public available sources Specific ipulse The values of ecific ipulse considered for calculations are: I = 10, 0, 30, 40 k / s. Thrusters' perforances are all within this range. 3. Relative power 3

4 Present achieved relative power levels are 3-5W/kg (Ref.3). Predicted relative power can be ore than 6W/kg. For calculations following values were eployed: P s = 3, 5, 7 W/kg. Table 1: Electric Thrusters Characteristics Thruster Operation ode Specific ipulse, k/s Power consuption, W Efficiency Country of origin KM Russia HETI Israel KM HETI SPT Russia HETI TAL-D Russia NSTAR USA SPT Russia PPS France NSTAR NSTAR Propellant and efficiency Xenon is assued the propellant for all thrusters. Efficiency according to Ref. is assued I t = 0.75e 5/ η. (9) 3.4.Initial orbit We assue an initial low Earth circular orbit with radius R 0 = 6800 k, initial angle θ, shown in Fig.1 is deterined for each case in order to reach Moon here of influence Constants The constants eployed for all siulations are: R = k; µ = k / s ; µ = k / s ; ω = rad / s. e 5 4. Results of calculations Results of calculations at constant operation odes are presented in Table. The calculations were realized at constant operation odes (ecific ipulse and power are constant) and at variable operation odes. The way to reach the optial variable operation ode was obtained in Ref.1: optial control acceleration is a decreasing function of flight tie in order to achieve a axiu final ass. In this work, actual ipleentation of the optial control acceleration was approxiated the following way: The ass flow rate and/or the ecific ipulse were piecewise changed with ecific ipulse increased within the range 10 to 40k/s and ecific power decreased within the range 7 to 1W/kg. With this approxiation, thrust decreased 4

5 by a factor of five at end of flight. The axial thrust decrease was liited by existing thruster perforances. Results for variable operation ode are presented in Table 3. Table : Constant Operation Mode Results Specific power, W/kg Specific ipulse, k/s Flight tie, days Noralized final ass Table 3: Variable Operation Mode Results Specific power (average), Initial ecific ipulse, Specific ipulse (average), Ratio of initial to final thrust Flight tie, days Relative final ass W/kg k/s k/s Data obtained at constant operation ode are visualized in Fig.. Noralized final ass decreases by less than 5% for a ecific power increase fro 3W/kg to 7W/kg while flight tie decreases ore than twice for the sae ecific power increase. Final acecraft ass decreases with increasing ecific power. In order to avoid ass loss ecific ipulse is increased and, hence, also flight tie. Flight tie increase is approxiately 5-8 days per 1k/s of ecific ipulse increase. All obtained data are visualized in Fig.3 where noralized final ass is shown as a function of ecific ipulse. As usual in electric thrusters the final ass function is fairly flat. On the other hand, sall ass increase is accopanied by sizeable flight tie increase. This ecific characteristic of electric propulsion systes has an iportant consequence: even under a propulsion or power syste partial failure, the delivered final ass will reain alost the sae, at the expense of a later ission copletion. For constant thrust, velocity increent is given by, V = I M (9) ln 5

6 Ps=3W/kg Ps=5W/kg Ps=7W/kg Noralized final ass Tie, year Specific ipulse, k/s I = 10 k / s I = 30 k / s Final ass, noralized units I =0 k / s I =40 k / s var fro 0 k / s var fro 30 k /s Flight tie, days Fig.: Transfers in constant operation ode Fig. 3: All operation odes The value of I / η. P s t V for the various thruster cases is shown in Fig. 4 as a function of thruster paraeter const OM var OM Log (const OM) Velocity increent, /s Thruster paraeter I / P s η t Fig.4: Velocity increent as a function of thruster paraeter Required velocity increent can be closely approxiated by a sooth logarithic function, V = 1.064ln( I / P s ηt ) (10) In this approxiation the constants appearing in Equation (10) were calculated with ecific ipulse in k/s, ecific power in kw/kg, velocity increent in k/s and flight tie in days. Fro Equations (9) and (10) follows that noralized final ass is M s 1.064/ I t ) / I = ( I / P η e (11) In view of Equation (9) and equality: 1 M = & st / M 0, flight tie is 6

7 T = (1 M ) I /17. 8P s η t (1) The following diensions were eployed in Equations (10)-(1): Specific ipulse-k/s, Specific powerkw/kg, Velocity increent k/s; Flight tie -days. The thruster paraeters averages were used in calculations for variable operation odes, and the sae equations (10)-(1) can be also used for assessent of flight perforances with variable operation odes. The deviation fro the logarithic approxiation line is below 400/s. This correonds to less than a 3% acecraft ass error at average ecific ipulses between 0 to 30 k/s. 5. Thrusters Options We shall now assess possible flight characteristics for different initial acecraft asses taking into account thrusters' perforances fro Table 1. Flight tie and noralized final ass can be directly obtained fro Equations (11), (1). However, actual final ass still requires further analysis. In general, power capacity of a acecraft with an electric propulsion subsyste can be divided into three parts. The first part is necessary for acecraft basic functions (structure, attitude and theral control, counications, etc.). The second part is intended for the payload. In general, it is this part that is assued for use copletely or partially by the electric propulsion syste during transfer. The third part is soe additional power required by the electric propulsion syste. It is not required when using cheical propulsion. So, the final ass value as obtained fro Eq.11 should be decreased to take into account the additional ass requireents of the power syste. Based on previous experience we shall correct for the final ass according to the following expression, M fr = M f M 0 ( Ps 3M 0) / α (13) where α is power syste ecific power, assued to be α = 30W / kg. Results of calculations are presented in Fig for various values of initial acecraft ass. The nuber of thrusters for each case assured that noralized final ass M The following notation was used for the various thrusters: AAAA (BB_CCC*D), where AAAA is thruster nae; BB- rounded off ecific ipulse, k/s; CCC- power consuption, Watt; D nuber of thrusters operated siultaneously. fr Final ass, kg Flight tie, days KM-37 (14_00*1) HETI (13_15*1) KM-37 (16_300*1) KM-37 (14_00*) HETI (13_15*) HETI (13_50*1) KM-37 (16_300*) SPT-70 (14_750*1) HETI (16_790*1) TAL-D38 (18_800*1) NSTAR (9_1018*1) Fig. 5: Initial acecraft ass 100kg. 7

8 Final ass, kg Flight tie, days KM -37(14_00*1) HETI ( 13 _15* 1) KM -37(16_300*1) KM -37(14_00*) HETI ( 13 _15* ) HETI ( 13 _50* 1) KM -37(16_300*) SPT -70(14_750*1) HETI ( 16 _790* 1) TAL - D 38(18 _800 *1) NSTAR(9_1018*1) HETI ( 13 _50* ) SPT -100 ( 15 _ 1350 *1) PPS -1350(17_1500 * 1 ) SPT -70(14_750*) NSTAR(31_1579*1) HETI ( 16 _790* ) TAL - D 38(18 _800 *) Fig. 6: Initial acecraft ass 00kg The thruster lifetie characteristics were not taken into account in the calculation of the diagras. Evidently, the sallest thrusters cannot operate during the required tie. It is necessary to add additional thrusters, thruster selection unit, tubes, valves and cables. As a result final ass will be decreased by 8-1 kg. It would see that ore powerful thrusters, operating in an on-off ode, can replace less powerful thrusters copletely. But on-off operation will result in an increase of propellant consuption and reduction of final ass. All M fr -T diagras with points representing different types of thrusters have siilar characteristics. We see both, groupings of thrusters and epty intervals. Groupings of thrusters are a positive characteristic. In this case, ore than option is available to fulfill the ission with different types of electric thrusters. Final ass, kg Flight tie, days HETI(13_50*1) KM -37(16_300*) SPT-7014_750*1) HETI(16_790*1) TAL-D38(18_800*1) NSTAR(9_1018*1) HETI(13_50*) SPT-100(15_1350*1) - PPS-1350(17_1500*1) SPT-70(14_750*) NSTAR(31_1579*1) HETI(16_790*) TAL-D38(18_800*) NSTAR(9_1018*) NSTAR(31_35*1) NSTAR(31_1579*) Fig. 7: Initial acecraft ass 300kg 8

9 Final ass, kg Flight tie, days SPT-70(14_750*1) HETI(16_790*1) HETI(13_50*) SPT-100(15_1350*1) PPS-1350(17_1500*1) SPT-70(14_750*) NSTAR(31_1579*1) HETI(16_790*) TAL-D38(18_800*) NSTAR(9_1018*) NSTAR(31_35*1) SPT-100(15_1350*) PPS-1350 (17_ 1500 * ) NSTAR(31_1579*) NSTAR(31_35*) Fig. 8: Initial acecraft ass 500kg Final ass, kg SPT -70(14 _750 *) HETI (16 _790 *) SPT -100(15_ 1350 * ) PPS-1350(17_1500*) NSTAR(31_1579*) NSTAR(31_35*) Flight tie, days Fig. 9: Initial acecraft ass 1000kg Final ass, kg SPT-100(15_1350*) PPS-1350(17_1500*) NSTAR( *) NSTAR(31-35*) Flight tie, days Fig. 10: Initial acecraft ass 1500kg 9

10 Enlarging adissible operation odes of existent thrusters can fill the diagras epty intervals. NSTAR is presently the best exaple. This approach is sipler and less expensive than new thruster developent for every case. Range of operation odes should be considered as one of the ain characteristics of an electric thruster, the sae way as ecific ipulse and lifetie. 6. Suary and Conclusions Coputations perfored on the basis of the restricted three-body equations of otion enabled to deterine the final acecraft ass, flight tie and required velocity increent. Analysis of the results showed that required velocity increent for Earth to oon transfer could be approxiated by a sooth logarithic function of a basic electric thruster paraeter, the ratio of ecific ipulse to ecific power. The possible applications of different engines with their actual characteristics taken into account are calculated for initial on-orbit acecraft asses fro 100kg up to 1500kg. Nuber of eployed siultaneous thrusters was defined according to thruster paraeters. Exaining obtained points on final ass-flight tie plane it is possible to see a grouping of thrusters (any thrusters with siilar perforances) and any epty intervals. Enlarging adissible operation odes of existent thrusters can fill the discovered epty intervals. Range of operation odes should be considered as one of the ain characteristics of an electric thruster, the sae way as ecific ipulse and lifetie. The proposed thruster paraeter and obtained ass and tie equations can be used for definition of the required ranges of ecific ipulse and power at selected acecraft asses and estiated flight durations. 7. References 1. M. Guelan, Earth-to-Moon Transfer with a Liited Power Engine, Journal of Guidance, Control and Dynaics. Vol.18, No.5, Septeber-October A. Bober, Electric Propulsion. Basic Considerations, Asher Space Research Institute, Technion-Israel Institute of Technology, Report No M. Martinez-Sanchez, J. E. Pollard, Spacecraft Electric Propulsion An Overview, Journal of Propulsion and Power, Vol.14, No 5, Septeber-October