Minimum-time problem resolution under constraints for low-thrust stage trajectory computation Nathalie DELATTRE Space Transportation Page 1
Introduction Purpose : Taking into account new technology for upper stage and/or satellite like solar propulsion or electric propulsion, reassess the satellite launcher task sharing The payload is considered at the telecommunications system on board satellite (usually considered as the satellite payload) Two tools are available to answer the question Page 2
Launch analysis : Insertion by low thrust stage MIPELEC : resolution of minimum-time problem Quick optimisation tool, initially developed under a thesis at CNES, then industrialised through EADS-ST and CNES shared contract by LAAS (CNRS) finds the optimal command for minimum time transfer (continuous thrust) applications: slow insertion from Earth orbit to escape orbit by electrical, solar-thermal or nuclear propulsion very user-friendly tool very quick optimisation solving (~ 1 min) used for any advance-project, but does not consider constraints like eclipses or visibility constraint by ground station Page 3
Launch analysis: Insertion by low thrust stage (2) TOPE : resolution of minimum-time problem under constraints finds a quasi-optimal command for minimum time transfer including constraints (quasi-continuous thrust) takes eclipses into account (burn interruption during shadow period) and visibility constraint (burn possible only during given set of ground station visibility) applications: slow insertion from Earth orbit to escape orbit by electrical, solar-thermal or nuclear propulsion very user-friendly tool quick optimisation solving (a few minutes) successfully benchmarked with MIPELEC for the unconstrained case Page 4
ELECTRIC PROPULSION FOR SATELLITES (1) Work logic Phase 1 Mission and Market considerations Satellites market analysis -Payload characteristics (required power system) -Short and long terms scenarios (EP, mixed, chemical satellites repartition) Satellites associated costs -Insurance -Operator s investment -Satellite exploitation -Maximum transfer duration (operators constraint) Phase 2 Short term Satellites model LEO/MEO & GEO applications -Architecture model mass repartition = f(payload) -Costs model (fabrication) -Constraints (Van Allen, ) Propulsion data -Electric & mixed propulsion models mass, thrust, Isp = f(power) -Constraints -Costs model (EP, mixed, chemical) Launchers data -Characteristics -Launch costs models Reference satellites selection LEO/MEO & GEO applications -Propulsion characteristics -Mass repartition -Constraints -Short term Mission analysis LEO/MEO & GEO applications -Injection strategy trade-off -Impact on launcher filling ratio -Comparison with competitors Short term scenario synthesis Europe launchers positioning vs competitors (sensitivity wrt satellites market scenario) Short term economical aspects LEO/MEO & GEO applications -Global cost (operators point of view) -Gain assessment (comparison with classic chemical satellite) Page 5
ELECTRIC PROPULSION FOR SATELLITES (2) Satellite á propulsion électrique - Transfert en temps minimum de MEO (7 deg) vers GEO avec contrainte d éclairement 40000 35000 30000 25000 20000 15000 10000 5000 Deformation de l orbite avec zone d eclipse km 0-5000 -10000-15000 -20000-25000 -30000-35000 -40000-30000 -10000 10000 30000 km Page 6
ELECTRIC PROPULSION FOR SATELLITES (3) Scenarios STRATEGY INJECTION ORBIT (ORBIT 1) ELECTRICAL PROPULSION BEGINNING (ORBIT 2) designation Za / Zp / 7 designation Za / Zp / 7 100% chemical GTO 200 / 35 786 / 7 100% electrical hybrid MEO Za / Za / 7 = orbit 1 GTO+ Zp / 35 786 / 7 = orbit 1 GTO 200 / 35 786 / 7 GTO+ Zp / 35 786 / 7 subgto 200 / Za / 7 MEO Za / Za / 7 supgto 200 / Za / 7 supgto Zp / Za / 7 with (Za+Zp)/2 = 35786 km Page 7
ELECTRIC PROPULSION FOR SATELLITES (4) Satellite á propulsion électrique : masse initiale 3410 kg, poussée 1N, ISP 1700s Transfert en temps minimum de GTO+ (14000km / 35786km / 0deg) vers GEO Durée du transfert : 38.52j / Masse consommée : 199.56kg / Nombre de révolutions : 46.05 40000 Altitudes apogée et périgée (km) 3400 Masse totale (kg) 35000 3380 3360 altitude (km) 30000 25000 masse (kg) 3340 3320 3300 3280 20000 3260 3240 15000 3220 0 5 10 15 20 25 30 35 date (j) 0 5 10 15 20 25 30 35 date (j) Page 8
STOTS (1) Solar-Thermal Orbital Transfer Stage Propulsion system principles: 3 sub-systems Concentrator Array and Tracking System (CATS) which collects and focuses the sun light Receiver Absorber Converter (RAC) which converts the concentrated sunlight into usable heat used to vaporise LH2 Propellant Feed and Storage System (PFSS) which stores the propellant and feeds the engine Page 9
STOTS (2) Intermittent thrust mode Same architecture as described before, except that the RAC is now a Receiver Accumulator Converter Introduction of a thermal storage mass heated by solar energy The heat is later extracted by the propellant for propulsion purpose The transfer is made of succession of thrusting and recharging phases, driven by the RAC temperature Highest admissible temperature Recharging RAC (eclipse case) Recharging RAC (no eclipse) Lowest admissible temperature Perigee first Apogee next Goal of the study Thrusting Thrusting Thrusting Design the optimal components of the solar-thermal engine together with the payload optimisation process for the transfer from LEO to GEO Page 10
STOTS (3) To avoid large gravity losses, the boost durations have to be optimised depending on the amount of heat accumulated by the RAC The sun lighted duration increases while raising the apogee, so the boost duration may be increased One orbit model inputs: Solving process: Use of a linear model T boost (iorb) = T boost (1) + T boost. iorb Where iorb = orbit number, T boost (1) and T boost are the optimised parameters (2 for apogee, 2 for perigee) current orbit characteristics (apogee, perigee, inclination) sun relative location, solar flux state of the propulsive system thanks to a model (RAC temperature, PFSS state, ) control: mass flow, boost location (apogee or perigee) and duration, inclination correction estimation of eclipse duration on the current orbit estimation of power at the entrance of RAC (CATS model) RAC heating during balistic sun lighted phase PFSS functionning RAC characteristics (temperature, phase change, Isp(t), F(t), V delivered, Isp, F) gravity losses estimation (see later) apogee, perigee and inclination modification after the boost Page 11
STOTS (4) The one orbit model is used several times until the final conditions are reached Global performance of the system Design of the propulsion system: The 3 most influent parameters have been selected: Energy storage mass ( RAC mass) allows to increase Isp, but then mass balance penalised CATS area Mass flow Page 12
STOTS (5) Ballistic phase : Output: eclipse durations, lit ballistic phase (t sun ) CATS model Input : solar area, solar flux, optical efficiency, concentration ratio Output : power at the entrance of RAC (P CATS ), mass (M CATS ) Orbit characteristics : Input : Apogee, Perigee, Sun location t sun q prop, t boost PFSS model Input : pressure, external flux Output : TVS, heater, selfpressurization, going out propellant characteristics (H prop ), mass (M PFSS ), geometry t sun H q prop, t boost prop P CATS Orbit performance : Output : V boost, <Isp>, <F> RAC model ( ballistic and boost ) Input : material, insulation, storage mass, initial temperature Output : final temperatures (GH2, RAC), phase change, Isp(t), F(t), M RAC Boost Input : propellant flow rate (q prop ) Output : duration (t boost ) ORBIT LOOP Whole optimisation process Criterion: maximise payload Parameters (7): MRAC Qprop CATS area T boost (1) and T boost for apogee T boost (1) and T boost for perigee M CATS V boost M RAC M PFSS Global performance : Output : V, duration, mass budget, payload mass Page 13