REENTRY TRAJECTORIES FOR SPACE VEHICLES

Transcription

1 REENTRY TRAJECTORIES FOR SPACE VEHICLES Tutorial Lectures at the 4th ICATT, Madrid 2010 J. F. GOESTER Centre National d Etudes Spatiales DCT/SB/MO jean-francois.goester@cnes.fr

2 SPACE VEHICLE REENTRY deorbit V atmosphere Terre atmospheric arc orbital arc E point: (Z=120 km) initial orbit Natural reentries DEORBIT MANEUVER ORBITAL ARC ATMOSPHERIC ARC Controlled reentries 2

3 SPACE VEHICLE REENTRY : DEORBITATION deorbit V atmosphere Terre atmospheric arc orbital arc E point: (Z=120 km) initial orbit Natural reentries DEORBIT MANEUVER ORBITAL ARC ATMOSPHERIC ARC Controlled reentries 3

4 DEORBITATION : POSITION-VELOCITY PARAMETERS To fully define the center of mass motion, we need 6 parameters : x,y,z,v x,v y,v z Orbital motion study leads to choose other set of parameters speaking for themselves" as : a, e, i, ω, Ω, v Classical flight dynamics will use : Z, lat, lon, V, γ, χ Z : lat : lon : V : Topocentric or geodetic altitude (or r : radius) Topocentric or geodetic latitude Longitude / Greenwich Velocity module local horizontal plane γ : Flight Path Angle χ : Velocity Azimuth Ion North r Iat V 4

5 DEORBITATION : MANEUVER PARAMETERS INTENSITY If impulsive maneuver : V : velocity increment (m/s) else: r s γ 0 Ψ ω V γ s ω V S F : thrust level (Newton) V 0 Isp : specific impulse (s) F=q.g 0.Isp with q = -dm/dt α e DIRECTION ω : angle between thrust direction and orbital plane ω : angle between projection of thrust direction on the orbital plane and velocity (or horizontal) γ e β e V e Ψ 5

6 DEORBITATION : IMPULSIVE ASSUMPTION (1/5) PARAMETERS : Before maneuver : [ r s, α s, β s, V s, γ s, ψ s ] Maneuver : [ V, ω, ω ] After maneuver : [r 0, α 0, β 0, V 0, γ 0, ψ 0 ] At Z = 120km : [r e, α e, β e, V e, γ e, ψ e ] FIRST SIMPLIFICATIONS : Reference relative to initial conditions : α s = 0, β s = 0 et ψ s = 0 Impulsive assumption : r 0 = r s, α 0 = α s et β 0 = β s Keplerian orbit : ψ 0 = ψ e = ψ By definition : r e = r T km Initial conditions Final conditions KEEPING PARAMETERS : [ r s, V s, γ s ], [ V, ω, ω ], [ V 0, γ 0, ψ ], [α e, β e, V e, γ e ] 6

7 MOTION EQUATIONS : vectorial relation : V = V 0 V S V sin( ω' ) V cos( ω' )cos( ω γ V cos( ω' ) sin( ω γ Conservation of the total energy on the orbital arc: Conservation of the kinetic moment on the orbital arc: = V DEORBITATION : IMPULSIVE ASSUMPTION (2/5) 0 cos( γ s s 0 ) ) sin( ψ) = V 0 ) = V cos( γ 0 sin( γ V 2 e 0 0 )cos( ψ) V ) + V s cos( γ s s cos( γ = V0 + 2µ ( ) re r0 r0v0 cos( γ0) = re Ve cos( γ ) s ) e ) Relation on the longitudinal range α e (implicit equation) : µ (1 cos( αe )) r0 cos( αe + γ ) + e = 2 r V cos( ) re cos( 0) 0 0 γ γ 0 Relation on the cross range β e (spherical trigonometry) : 0 sin( β e ) = sin( α e ) sin( ψ) 7

8 DEORBITATION : IMPULSIVE ASSUMPTION (3/5) V [m/s] Influence of the ω parameter (γe = -1.3 deg ; ω = 0 deg) 200 km 300 km 400 km In plane thrust direction [deg]

9 300 V [m/s] DEORBITATION : IMPULSIVE ASSUMPTION (4/5) Influence of the ω parameter (γe = -1.3 deg ; ω = 180 deg) Out of plane thrust direction [deg] Ye [km] Out of plane thrust direction [deg]

10 DEORBITATION : IMPULSIVE ASSUMPTION (5/5) Initial values (γe = -1.3 deg): hs = 300 km Vs = γs = 0. deg V = km/s m/s ω = 180. deg ω = 0. deg Dispersions on initial values : d(h s ) = 10. m d(v s ) = 0.02 m/s d(γ s ) = 0. deg d( V )= -1. m/s d(ω ) = 1. deg d(ω ) = 1. deg δz s [m] δv s [m/s] δγ s [deg] δ V [m/s] δω [deg] δω [deg] Somme quadratique δv e [m/s] δγ e [deg] δx e [km] δy e [km]

11 DEORBITATION: CONTINUOUS THRUST (1/11) When the «thrust / mass» ratio is low and involves longer maneuvers durations (order of magnitude comparable to orbital period). Hermes or ATV example : F = 800 to 1600 N (Isp ~ 310 s) mass ~ 20 tons mg Isp by integration of the equation F = qg 0 Isp, we obtain : t = (1 e F => up to t > 1000 s for orbital periods of about 5500 s Problems linked to these durations: greater needed V (thus higher ergols consumption) precision at Z=120 km (in position and velocity) Cases of impossibility to obtain aimed conditions at Z=120 km V 0 g0isp ) 11

12 DEORBITATION: CONTINUOUS THRUST (2/11) γ e EVOLUTION FOR AN AIMED PERIGEE ALTITUDE OF 0 KM -0,80 γ e [deg] -0,90-1,00-1,10-1,20-1,30-1,40-1,50-1,60-1,70-1,80-1,90 Altitude of the initial circular orbit [km]

13 DEORBITATION : CONTINUOUS THRUST (3/11) t [sec] THRUST DURATION (H per = 0 km ; F = 1600 N ; Isp = 310 s ; m = 20 t) Continuous thrust Altitude of the initial circular orbit [km]

14 DEORBITATION : CONTINUOUS THRUST (4/11) V [m/s] DIFFERENCE ON V (Hper = 0 km ; F = 1600 N ; Isp = 310 s ; m = 20 t) Continuous thrust Impulsive thrust Altitude of the initial circular orbit [km]

15 DEORBITATION : CONTINUOUS THRUST (5/11) 1200 Merg [kg] DIFFERENCE ON ERGOLS CONSUMPTION (Hper = 0 km ; F = 1600 N ; Isp = 310 s ; m = 20 t) Continuous thrust Impulsive thrust Altitude of the initial circular orbit [km]

16 DEORBITATION : CONTINUOUS THRUST (6/11) DIFFERENCE ON TIME REMAINING AFTER END OF BOOST (Hper = 0 km ; F = 1600 N ; Isp = 310 s ; m = 20 t) T120 [mn] Continuous thrust Impulsive thrust Altitude of the initial circular orbit [km]

17 DEORBITATION: CONTINUOUS THRUST (7/11) Thrust duration V imp E E initial orbit initial orbit γ e γ e Terre Terre Z = 120 km Z = 120 km Thrust direction optimization and/or several maneuvers 17

18 DEORBITATION : CONTINUOUS THRUST (8/11) TWO MANEUVERS STRATEGIES: 2 braking V V1 V2 1 accelerating V and 1 braking V intermediate orbit V2 Terre Terre intermediate orbit initial orbit initial orbit 18 V1

19 DEORBITATION : CONTINUOUS THRUST (9/11) ADVANTAGES : duration of each boost is shorter (divided by about two in case of two breaking V s) ergols consumption is lower (5 to 10 %) Time between end of last maneuver and Z=120 km is longer => opportunities recovery (for low initial altitudes) Computation of the second maneuver can be done w.r.t the first one (dispersions issued from its realization can be taken into account) DRAWBACKS : Longer duration of the deorbit phase Intermediate elliptic orbit: Lower perigee (atmospheric drag) Drift of the apsides line versus the landing site longitude Nominal landing site 19

20 DEORBITATION : CONTINUOUS THRUST (10/11) V [m/s] DIFFERENCE ON V (Hper = 0 km ; F = 1600 N ; Isp = 310 s ; m = 20 t) maneuver 2 braking maneuvers Impulsive thrust Altitude of the initial circular orbit [km]

21 DEORBITATION : CONTINUOUS THRUST (11/11) DIFFERENCE ON TIME REMAINING AFTER END OF BOOST (Hper = 0 km ; F = 1600 N ; Isp = 310 s ; m = 20 t) T120 [mn] 1 maneuver 2 braking maneuvers Impulsive thrust Altitude of the initial circular orbit [km]

22 MIR de-orbiting (1/2) No specific MIR engines were available, so it was chosen to use engines of a Progress vehicle previously docked MIR mass (about 130/140 tons) and thrust acceleration produced by this Progress vehicle engines did not allow to carry out the deorbitation only with one maneuver. Originally, it was foreseen to execute up to 4 maneuvers distributed on several days but uncertainties on AOCS at those unusual very low orbits lead to envisage the following strategy : 2 initial maneuvers of about 10 m/s each on daily orbits 15/16 to prepare for the third and final impulse (i.e. semi major axis sufficiently high to stay 24 hours in orbit and a well phased apsides line). Those maneuvers executed using the 8 Progress attitude control engines A final maneuver of about 25 m/s executed in two sub phases : First with the main engine + the attitude control engines Then, only with the attitude control engines 22

23 MIR de-orbiting (2/2) Also due to uncertainties on the AOCS, it has been chosen to keep an inertial attitude including during the boosts. In order not to be too far from the optimal attitude (opposite to velocity), a pitch angle was computed in to have the direction almost aligned on the velocity/horizontal line at the middle of the boost (+ a 4 deg bias due to position of the center of gravity). Then, for so critical maneuvers, it was absolutely required to have a maximum of visibility from the ground : Maneuvers were foreseen on daily orbit numbers 15, 16 and 02 to get also visibility on orbits 13, 14 and 01 (orbits with large visibilities with Russian ground stations) A particular constraint was applied on the end of the two first maneuvers to be in visibility of the Petropavlovsk (PPK) ground station for a complete passage (to get a full diagnostic in case of problems occur on the attitude control). 23

24 MIR de-orbiting (3/3) 24

25 Vehicle constraints : «Flight dynamics» constraints ASTRA 1K De-orbiting (1/2) Maneuver can only be executed when Sun pointed (or anti Sun pointed) because only Sun sensors were operational (but not Earth sensors). Maneuver has to be programmed between time when satellite was entering in eclipse + 10 mn and time when it was exiting + 20 mn because of thermal constraints on propulsive engines. Maneuver has to occur above 150 km of altitude (AOCS constraints) To get thrust direction as close as possible to the orbital plane (for a best thrust efficiency) To align thrust direction as close as possible to the velocity axis (for a best efficiency on the semi-major) To set the maneuver as close as possible to the apogee To control perigee positioning to be phased with the landing site 25

26 ASTRA 1K De-orbiting (2/2) Beginning of the maneuver End of the maneuver Impacts Fragmentation Command: s ( m/s) on 10th Dec 2002 / 00:42:21 26

27 ATV De-orbiting (1/3) Main ATV vehicle constraints : The duration of the maneuvers must not exceed 30 minutes. => influence on the amount of maneuvers since ATV has a low thrust/mass ratio. The perigee altitude of the intermediary orbits must not be lower than 200 km at 3 σ in order not to degrade the solar arrays. The delay between the end of the last deorbitation maneuver and 120 km altitude must be typically 20 min (10 min for the tumbling acquisition and typically 10 min more for onboard operational verifications after tumbling acquisition). Main ATV mission constraints : Before the maneuvers, minimum 3h00 (2 orbits) must be scheduled in order to perform orbit determination, maneuver computation and on-board loading. A back-up deorbitation orbit is required a day (thus 2 opportunities per day). A back-up day must be foreseen. It means that it must be possible to deorbit on the same orbit numbers one day later. 27

28 ATV De-orbiting (2/3) The deorbitation sequence consists in transferring the ATV from an orbital point to a ground point by decreasing its perigee altitude through two maneuvers. The first maneuver will have two objectives: The first one is to put the ATV from a circular orbit to an elliptical orbit with the required apside line orientation (phasing with the entry point). The second objective is to decrease the perigee altitude. The second maneuver is then located at the apogee of the intermediary orbit and decrease the perigee altitude up to 0 km. V1 final orbit V2 Earth H per = 0 km intermediate orbit initial orbit 28

29 ATV De-orbiting (3/3) Generic nominal reentry : The ATV has waited for the entry opportunity docked to the ISS. As soon as ATV is in visibility of the Russian ground stations, dedocking is performed. Several orbits later, the deorbit sequence starts Jules Verne mission : Dedocking three weeks before the reentry (5th September) Rephasing in order to get visibility from ISS during the reentry => Additional maneuvers Reentry observation with airborne means night time observation => Orbit number and reentry epoch modification 29

30 DEO2 DEO1 29/09/08 10:00:24 (UTC) V = m/s (388.3 s) ATV REENTRY (altitude profile) 29/09/08 12:58:18 (UTC) V = m/s ( s) ~ 13:31:34 (UTC) Z ~ 120 km Deorbitation phase orbital phase atmospheric phase ~ 13:36:19 (UTC) Explosion (Z ~75 km) ~ 13:43:09 (UTC) first impacts South Pacific Ocean 30

31 ATV REENTRY (ground track) nominal impact point (mean fragment) lat = lon = area 31

32 ATV REENTRY : fragmentation 32

33 SPACE VEHICLE REENTRY : ATMOSPHERIC ARC deorbit V atmosphere Terre atmospheric arc orbital arc E point: (Z=120 km) initial orbit Natural reentries DEORBIT MANEUVER ORBITAL ARC ATMOSPHERIC ARC Controlled reentries 33

34 Attitude parameters : α, β, µ, p, q, r ATMOSPHERIC ARC : ATTITUDE X AV X AER Y AER α : angle of attack β : slip side angle µ : bank angle α β V AER G β X AV p (roll) Y AV q (pitch) G YAV p : roll rate q : pitch rate l : yaw rate ZAV α µ ZAER ZH LOCAL = i Z AV r (yaw) 34

35 Main forces : ATMOSPHERIC ARC : FORCES Gravitational forces (central term + J2 term) Aerodynamic forces (drag + lift [assumption β = 0]) Weight = mg [ ( sinγ ) i' + ( cos γ ) j' ] i Drag = 1 ρ 2 SC aérov 2 i x j µ k 1 ρ 2 [ k ] 2 z Lift = SC aérov ( cos µ ) j + ( sin µ ) Lift 35

36 ATMOSPHERIC ARC : EQUATIONS Assumptions : no side slip angle (β = 0) ; central term of geopotential (J 2 = 0) Derivation of position : dr/dt dr ( ) d ( ) d( lon) ( ) ( χ) = V sin γ lat V dt = cos γ cos dt r Derivation of velocity : dv/dt dt = V r cos ( γ) ( χ) ( ) sin cos lat dv dt = gsin 1 2 SC 2 2 ( γ) ρ x V + terme en ω m E dγ dt dχ dt = g V + 2ω cos 1 SC = ρ 2 m E 1 2 SC V r ( ) z 2 γ + ρ V cos( µ ) + cos( γ) + 2ωcos( lat) sin( χ) + terme en ω z V 2 sin µ m V r ( ) + cos( γ) tg( lat) sin( χ) 2 ( sin( lat) tg( γ) cos( lat) cos( χ) ) + terme en ω E E 36

37 ATMOSPHERIC ARC : SIMPLIFYING ASSUMPTIONS FIRST REBOUND ASSUMPTION : no side slip angle (β =0) central term of geopotential (J 2 =0) Fixed Earth frame (ω E =0) small γ (sin γ = γ and cos γ = 1) (V 2 /r - g) small vs lift term V γ 2 2 = = V γ 2 e 2 e e 2C D CL cos ( ) ( γ γe ) µ SCL cos βm ( µ ) ( ρ ρ ) e EQUILIBRIUM ASSUMPTION : no side slip angle (β =0) central term of geopotential (J 2 =0) Fixed Earth frame (ω E =0) small γ (sin γ = 0 and cos γ = 1) d γ /dt small vs other terms of the equation d γ /dt = 37

38 ATMOSPHERIC ARC : EQUILIBRIUM ASSUMPTION dv dt = 2 V 1 g (L /D)cos( µ ) avec V = V gr T et L /D = C C Z X deceleration is inversely proportional to L/D γ = βr T C 2CX β(z z0 ) avec ρ = ρ 2 0e Z cos( µ )V X X r T Y Y r T Ψ = π e e = = χ = L D 1 V cos( µ )Log( 1 V L D L D e 1 V sin( µ )cos( µ ) Log( 1 V sin( µ )Log( V V 2 e ) 2 2 e 1 r L 1 V 1+ V t t = T cos( µ ) Log( e e ) 2 g D 1+ V 1 Ve ) Longitudinal range is proportional to L/D ) V e 1 V Log( 1+ V 1+ V 1 V e e ) Cross range is proportional to square of L/D 38

39 ATMOSPHERIC ARC : ANALYTIC / NUMERICAL COMPARISON ANALYTIC / NUMERICAL COMPARISON SCx / m = m 2 /kg L/D = 0.2 First rebound assumption γe = -5 deg Altitude (km) Numerical simulation Equilibrium assumption Velocity (m/s) 39

40 ANALYTICAL MODELS LIMITATIONS: Low precision of atmospheric models Fixed Earth frame hypothesis aerodynamic coefficients variations along the flight: Depends on the Mach, Reynolds or Knudsen number Depends on angle of attack (AoA) Depends on altitude variations on attitude angles (command laws) ATMOSPHERIC ARC : NUMERICAL INTEGRATION STRONGLY NON LINEAR MOTION => NUMERICAL INTEGRATION : varied atmospheric models : US76, GRAM, CIRA, MSIS + Martian models more precise aerodynamic data bases (for example, dependence on Mach, altitude, AOA, side slip angle, etc) More sophisticated guidance laws and more realistic attitude motion (6 degrees of freedom motion) 40

41 ATMOSPHERIC ARC : METHODOLOGY Objective : to find guidance laws during hypersonic phase in order to maximize cross range and minimize heat quantity while respecting varied mechanical and/or thermal constraints. Methodology : flight domain determination Optimization under constraints simplified laws Guidance Dispersions studies 41

42 ATMOSPHERIC ARC : GNC/NGC definitions measurements NAVIGATION θ, dθ/dt + other estimated parameters X, dx/dt, θ, dθ/dt other estimated parameters GUIDANCE commanded α, β, µ CONTROL Actuator commands 42

43 ATMOSPHERIC ARC : EXAMPLES «THEORETICAL» STUDY OF INHABITED CAPSULES GEMINI CAPSULES GUIDANCE SOYUZ GUIDANCE L/D HYPERSONIC GUIDANCE ARD MISSION 43

44 ATMOSPHERIC ARC : INHABITED CAPSULE (1/6) HYPOTHESES: initial circular equatorial orbit; altitude = 400 km impulsive V standard US76 atmosphere two types of vehicles: «type A» «type B» mass 5.5 t 8 t Sref 13.2 m m 2 L/D max

45 ATMOSPHERIC ARC : INHABITED CAPSULE (2/6) COMMAND LAWS : «type A» AoA Bank angle Mach > deg 90 deg 23.7 < Mach < deg 90 -> 45 deg 15 < Mach < deg 45 -> 12 deg 1 < Mach < deg 12 deg «type B» AoA Bank angle Mach > deg 90 deg 22.5 < Mach < deg 90 -> 45 deg 1 < Mach < deg 45 -> 5 deg α α V V 45

46 ATMOSPHERIC ARC : INHABITED CAPSULE (3/6) BANK ANGLE COMMAND LAWS Bank Angle [deg] "Type A" "Type B" t [sec] Initial ground track µ=90 deg Cross Range Cross Range 46

47 ATMOSPHERIC ARC : INHABITED CAPSULE (4/6) TRAJECTORIES : «type A» «type B» V AoA Cross range Longitudinal range nmax Pdyn max Φref max Heat quantity 97.8 m/s 145 deg 108 km 5850 km 2.52 g 9.39 kpa kw/m MJ/ m 2 98 m/s 130 deg 519 km 8180 km 1.58 g 7.61 kpa kw/m MJ/ m 2 47

48 CONSTRAINTS ATMOSPHERIC ARC : INHABITED CAPSULE (5/6) Load factor [g] 3,0 2,5 2,0 1,5 1,0 0,5 0,0 "Type A" "Type B" t [sec] reference heat flux [kw/m 2 ] "Type A" "Type B" t [sec]

49 ORBITAL DISPERSIONS : ATMOSPHERIC ARC : INHABITED CAPSULE (6/6) δ( V) of +/- 1 m/s ATMOSPHERIC DISPERSIONS : T of +/- 20 K on US76 atmosphere DISPERSIONS AERODYNAMIQUES: +/- 10% on Cx +/- 10% on L/D (Cz/Cx) «type A» «type B» Cross range error Longitudinal range error nmax Φref max Pdyn max -26 / +31 km -505 / +587 km 2.69 g kw/m kpa / km / +800 km 1.69 g 536 kw/m kpa 49

50 ATMOSPHERIC ARC : GEMINI CAPSULES GUIDANCE guidance initialization altitude guidance initialization Lifting trajectory altitude Half lifting trajectory Full lifting trajectory Ballistic trajectories TARGET maneuver capacities ROLL GUIDANCE (GEMINI III,IV,VIII,IX-A,X,XI,XII) Longitudinal range Ballistic trajectory TARGET maneuver capacities Longitudinal 50 range CONSTANT BANK ANGLE GUIDANCE (GEMINI V,VI-A,VII)

51 t deb t fin = t deb + t d ATMOSPHERIC ARC : SOYUZ CAPSULES GUIDANCE Start of the deorbit maneuver End of the deorbit maneuver Separation (H=140km) t sep = t deb + t sep (soft cycle) or t sep = t deb s + τ (hard cycle) H=100 km Start of guidance (Vs=25.6m/s;H~80km) avec : Vs = t tsep. V ( t) dt Vs=1024.4m/s γ com = c(1-2s)(60 o +δγ cor ) = c te for extra-atmospheric correction γ com = c(1-2s)(60 o +δγ cor ) for atmospheric correction DEORBITATION PARAMETERS : - V = m/s - Duration ~ 4 mn - LANDING AREAS: KAZAKHSTAN (ARKALYK,DZHEKAZGAN) - RAAN longitude: 20 o East to 55 o West - OPPORTUNITIES PER DAY: 3 to 4 Roll-reversal (Vs=4300.8m/s) c = -1 End of guidance (Vs=7372.8m/s;H~21km) γ com = -(1-2S)60 o Impact point Parachute phase (H~10.7km) 51

52 Flight domain : ATMOSPHERIC ARC : L/D HYPERSONIC GUIDANCE (1/9) altitude Equilibrium glide Thermal limit Load factor limit Dynamic pressure limit velocity Deceleration Load factor limit Dynamic pressure limit Thermal limit (V,Z) => Mach => α (α,mach,z) => Cx Z => ρ (ρ,cx,v) => D Equilibrium glide velocity 52

53 Optimization / reference profile ATMOSPHERIC ARC : L/D HYPERSONIC GUIDANCE (2/9) Deceleration Load factor limit margins Dynamic pressure limit Thermal limit iso-d linear D linear Vz Equilibrium glide iso-t velocity 53

54 ATMOSPHERIC ARC : L/D HYPERSONIC GUIDANCE (3/9) If neglecting terms due to Earth rotation and considering γ 0: dv 1 SC ρ dt 2 m A way to interact on drag deceleration is to modify C x V C x = f ( α, Mach = ) V son By modifying AoA, deceleration is then instantaneously modified Problems: instability controllability x 2 V influence on thermal protection surfaces 54

55 ATMOSPHERIC ARC : L/D HYPERSONIC GUIDANCE (4/9) Another way to interact on drag deceleration is to use bank angle variations V 2 = abs 1 SC Vγ g + ρ z V 2 cos µ r 2 m µ makes dγ/dt varying dγ/dt makes γ varying then Vz = dz/dt = Vsin(γ) dz/dt makes Z varying then ρ et thus D = f(ρ) Most of the time, we will keep relatively simple angle of attack profiles and will compute bank angle variations to follow a drag deceleration profile ( ) 55

56 lateral guidance : ATMOSPHERIC ARC : L/D HYPERSONIC GUIDANCE (5/9) Projection of the relative velocity On the local horizontal plane ROAD Landing runway road Current point great circle arc velocity : roll-reversals 56

57 α (deg) Reference AoA Real AoA ATMOSPHERIC ARC : L/D HYPERSONIC GUIDANCE (6/9) ANGLE OF ATTACK Total velocity (m/s) SIDE SLIP ANGLE β (deg) 0,100 0,050 0,000-0,050 commanded side slip angle real side slip angle Total velocity (m/s) ,100 µ (deg) BANK ANGLE commanded bank angle 30 real bank angle Total velocity (m/s)

58 ATMOSPHERIC ARC : L/D HYPERSONIC GUIDANCE (7/9) DRAG DECELERATION DREF DCOM Dreal 5 D (m/s^2) Total velocity (m/s) 58

59 ATMOSPHERIC ARC : L/D HYPERSONIC GUIDANCE (8/9) Landing site distance (dland) deceleration Dref comp. k(dland) comp. Dcom comp k 1 k 3 P.I.D Roll reversals tests lateral guidance ddref/dv comp. µ ref comp. Vz Vzref comp. - + k µ com comp. µ com comp. Reference AoA AoA modulation k α α ref comp. α com comp. - + k µ 59

60 ATMOSPHERIC ARC : L/D HYPERSONIC GUIDANCE (9/9) 40 GROUND TRACK 1st roll-reversal 2nd roll-reversal End of Black-Out 20 latitude (deg) 0-20 Z= 120 km 1st bank maneuver Beginning of Black-Out longitude (deg) 60

61 Characteristics Control : mass: 2716 kg reference surface: m 2 APOLLO shape Angle of Attack: about 160 deg. via 7 hydrazine thrusters On-board navigation IMU GPS Atmospheric guidance (Apollo/Shuttle derived) reference drag deceleration profile longitudinal range roll-reversals for lateral guidance ATMOSPHERIC ARC : ARD MISSION (1/4) 61

62 ATMOSPHERIC ARC : ARD MISSION (2/4) 62

63 ATMOSPHERIC ARC : ARD MISSION (3/4) 63

64 Good precision on orbit based on GPS PVT measurements Very good representation of the simulations of orbital arcs and especially atmospheric arc (with guidance) Good consideration of wind profiles obtained at H0-30 mn Final difference between real point (issued from GPS) and predicted one : 4.93 km ATMOSPHERIC ARC : ARD MISSION (4/4) 64

65 REENTRY TRAJECTORIES FOR SPACE VEHICLES Tutorial Lectures at the 4th ICATT, Madrid 2010 J. F. GOESTER Centre National d Etudes Spatiales DCT/SB/MO jean-francois.goester@cnes.fr

66 ARD : Air Range Instrumentation Aircraft 66

67 ARD : RECOVERY 67