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6. Introduction to Launchers

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6. Introduction to Launchers Introduction to launchers 205203 – Introduction to rockets Launch system A launch system is comprised of: • Launch vehicle (one or more stages) • Ground infrastructure Mission: to put a certain payload (PL) into orbit. Guiana Space Center Orbital launcher Function: • Acceleration, overcoming drag and gravity. • Insertion & maneuvers. Mission: • Launch vehicles. • Upper stage and orbital transfer vehicles. Main launch sites Kiruna Plesesk Kapustin Yar Kagoshima Vendenberg Wallops Juiquan Baikonur Kennedy Space Center Tanegashima Sriharikota Xichang Guayana Space Center Trivandrum Alcantara Plataforma San Marco Short introduction to orbital dynamics Newton’s gravitational law The plane of the orbit must always contain the Earth’s center Orbital parameters a Size of the orbit e Shape of the orbit ⌫ Position in the orbit i Orientation of ⌦ the orbit ! Orbits around the Earth Orbital launchers & mission planning Performance parameters Velocity is the fundamental measure of performance! F Specific impulse Isp = m/s mg˙ 0 mend mstart Mass flow m˙ = − kg/s ∆t Launcher manual Launcher description Introduction Vega User’s Manual, Issue 3 PAYLOAD FAIRING AVUM UPPER STAGE Fairing Size: 2.18-m diameter × 2.04-m height Diameter: 2.600 m Dry mass: 418 kg (TBC) Length: 7.880 m Propellant: 367-kg/183-kg of N2O4/UDMH Mass: 490 kg SuBsystems: Structure: Two halves - Sandwich panels CFRP Structure: Carbon-epoxy cylindrical case with 4 sheets and aluminum honeycomb core aluminum alloy propellant tanks and Acoustic protection: Thick foam sheets covered by fabric supporting frame Separation Vertical separations by means of leak-proof Propulsion RD-869 - 1 chamber pyrotechnical expanding tubes and horizontal - Thrust 2.45 kN - Vac separation by a clamp band - Isp 315,5 s - Vac - Feed system regulated pressure-fed, 87l (3,72 kg) GHe PAYLOAD ADAPTERS tank MEOP 310 bar - Burn time/ restart Up to 667 s / up to 5 controlled or depletion Off-the-shelf devices: Clampband, Ø937 (60 kg); burn Attitude Control DUAL CARRYING STRUCTURE - pitch, yaw Main engine 9 deg gimbaled nozzle or four 50- N GN2 thrusters - roll Two 50-N GN2 thrusters Off-the-shelf devices: Under development - propellant GN2; 87l (26 kg) GN2 tank MEOP 6 / 36 bar Avionics Inertial 3-axis platform, on-board computer, MINI SATELLITE CARRYING STRUCTURE TM & RF systems, Power ASAP Plate type (TBD kg); Off-the-shelf devices: . 1st STAGE 2nd STAGE (CORE) 3rd STAGE . Size: 3.00-m diameter × 11.20-m length 1.90-m diameter × 8.39-m length 1.90-m diameter × 4.12-m length Gross mass: 95 796 kg 25 751 kg 10 948 kg Propellant: 88 365-kg of HTPB 1912 solid 23 906-kg of HTPB 1912 solid 10 115-kg of HTPB 1912 solid SuBsystems: Structure Carbon-epoxy filament wound Carbon-epoxy filament wound Carbon-epoxy filament wound monolithic motor case protected by monolithic motor case protected by monolithic motor case protected by EPDM EPDM EPDM Propulsion P80FW Solid Rocket Motor (SRM) ZEFIRO 23 Solid Rocket Motor ZEFIRO 9 Solid Rocket Motor - Thrust 2261 kN – SL 1196 kN – SL 225 kN - Vac (TBC) - Isp 280 s – Vac 289 s – Vac 295 s – Vac (TBC) - Burn time 106,8 s 71,7 s 109.6 s Attitude Control Gimbaled 6.5 deg nozzle with electro Gimbaled 7 deg nozzle with electro Gimbaled 6 deg nozzle with electro actuator actuator actuator Avionics Actuators I/O electronics, power Actuators I/O electronics, power Interstage/Equipment 0/1 interstage: bay: Structure: cylinder aluminum shell/inner stiffeners Housing: Actuators I/O electronics, 29.9 m power 1/2 interstage: 2/3 interstage: 3/AVUM interstage: Structure: conical aluminum shell/inner Structure: cylinder aluminum Structure: cylinder aluminum stiffeners shell/inner stiffeners shell/inner stiffeners 3.025 3.025 m Housing: TVC local control equipment; Housing: TVC local control Housing: TVC control equipment; Safety/Destruction subsystem equipment; Safety/Destruction Safety/Destruction subsystem, subsystem power distribution, RF and telemetry subsystems Lift-off mass 137 t Stage separation: Linear Cutting Charge/Retro rocket Linear Cutting Charge/Retro rocket Clamp-band/ springs thrusters thrusters Figure 1.1 – LV property data 1-6 Arianespace©, March 2006 Ascent profile VEGA ascent profile Ascent profile VEGA altitude profile VEGA velocity profile Trajectory VEGA trajectory Payload performance One dimensional model for orbital launchers Simplified one-dimensional model T Consider no lift or very small lift F = T Mg D net − − Compute acceleration and velocity F dv a = net = a M dt Compute position W dx = v dt D Two dimensional model for orbital launchers Reference Frames: Earth Centered Inertial (ECI) • Fixed with respect to the stars. • X axis pointing to the vernal equinox. • A point is defined by right ascension and declination. Reference Frames: Earth Centered, Earth Fixed (ECEF) • Similar to the ECI frame. • Rotates with the Earth. • A point is represented by longitude and latitude. Reference Frames: East-North-Up (ENU) • Local horizontal frame that rotates with the Earth. • Commonly used in aerospace. Reference Frames: Body • Frame tied to the movement of the body. • xb pointing towards the front, zb defined 90 deg up of xb. Reference Frames: Coordinate Transformations • ECEF to ENU cos φ 0 sin φ cos λ sin λ 0 RECEF ENU = 010 sin λ cos λ 0 ! 0 sin φ 0 cos φ1 0− 0011 − @ A @ A • body to ENU 10 0 cos ✓ sin ✓ 0 Rb ENU = 0 cos χ sin χ sin ✓ cos ✓ 0 ! 00 sin χ −cos χ 1 0− 0011 @ A @ A Basics • Newton’s Second Law m!a = !F T + !F A + m!g • Acceleration on a non-inertial frame d v a = ! +2! v + ! ( ! r ) ! dt ! ⇥ ! ! ⇥ ! ⇥ ! • General equations of motion (ECEF frame) d v m ! = !F + !F + m g 2m ! v m ! ( ! r ) dt T A ! − ! ⇥ ! − ! ⇥ ! ⇥ ! Position and planet rotation vectors • Both are defined in ECEF coordinates. • Position vector: cos φ cos λ 1 !r ECEF = r cos φ sin λ !r ENU = RECEF ENU!r ECEF = r 0 0 sin φ 1 ! 001 @ A @ A • Rotation speed vector: 0 sin φ !! ECEF = ! 0 !! ENU = RECEF ENU!! ECEF = ! 0 011 ! 0cos φ1 @ A @ A Gravitational forces • Defined in ENU frame. • Contains components in x direction. g − !g ENU = 0 0 0 1 @ A Velocity and aerodynamic forces • Defined in body frame. • Also assuming that ↵ 0 so ✓ = γ . ⇡ • Velocity 0 sin γ !v b = v 1 !v ENU = Rb ENU!v b = v cos χ cos γ 001 ! 0sin χ cos γ1 @ A @ A • Aerodynamic forces cos γ !L ENU = Rb ENU!L b = L cos χ sin γ ! 0− sin χ sin γ1 L − @ A sin γ !F A = D 0− 1 !D ENU = Rb ENU!D b = D cos χ cos γ Y ! − 0sin χ cos γ1 @ A @ A Propulsive forces • Defined in body frame. Tx !F = T T 0 y1 Tz @ A Tx cos γ + Ty sin γ !FTENU = Rb ENU!FTb = Tx cos χ sin γ + Ty cos χ cos γ Tz sin χ ! 0−T sin χ sin γ + T sin χ cos γ −T cos χ1 − x y − z @ A Acceleration m!a ENU = !F TENU + !F AENU + m!g ENU • Expressed in ENU coordinates. d v a 0 = ! ENU + !⌦ v +2! v + ! ( ! r ) ! ENU dt ENU ⇥ ! ENU ! ENU ⇥ ! ENU ! ENU ⇥ ! ENU ⇥ ! ENU Derivative of Rotation of ENU wrt Rotation of ECEF wrt ECI the velocity ECEF 0 0 λ˙ sin φ φ ˙ ˙ !⌦ ENU = RECEF− ENU 0 + φ = φ ! 0 1 0− 1 0 − 1 λ˙ 0 λ˙ cos φ @ A @ A @ A 2D Simplification Let us suppose the orbit is contained in a plane… dχ dA χ,A=ct =0 =0 dt dt Kinematic relations • Let us differentiate the position of the body in ENU frame. d!r ECEF d!r ENU RECEF ENU = + !⌦ ENU !r ENU = !v ENU ! dt dt ⇥ r˙ 0 ˙ !v ENU = 0 + λr cos φ 0 1 0 ˙ 1 0 ENU φr @ A @ A dr dλ v cos χ cos γ dφ v sin χ cos γ = v sin γ = = dt dt r cos φ dt r Dynamic relations m!a ENU = !F TENU + !F AENU + m!g ENU dv T D = y g sin γ + !2r cos2 φ (sin γ cos γ tan φ sin χ) dt m − m − x − dγ T L v2 v = x + g cos γ + cos γ +2!v cos φ cos χ+ dt m m − x r !2r cos2 φ (cos γ +sinγ tan φ sin χ) dχ v =0 dt Simplifications yb xb • Small angle of attack, v therefore, lift and drag are Trajectory contained in xb and yb. L • No thrust deflection angle, ⨂ Local therefore, thrust is contained CG Horizontal in yb. ⨂ CP • Small lift force (L ≈ 0). D W • No side force (Y = 0). T Azimuth angle and altitude • It is convenient to change the flight path azimuthal angle for the azimuth angle (defined towards the “North” axis). ⇡ A = χ 2 − • It is also convenient to express the position in terms of altitude above seal level. r = RP lanet + h Contribution of planet rotation • It is generally preferable to launch towards the east due to dv T D = y g sin γ + !2r cos2 φ (sin γ cos γ tan φ sin χ) dt m − m − x − • Selecting the launch azimuth is not simple… cos i =sinA cos φ Selecting the launchsite The launch azimuth A determines the plane of our orbit. Cannot be chosen arbitrarily. cos i =sinA cos φ Plus it is desired to launch eastwards. Selecting the launchsite Kiruna Plesesk Kapustin Yar Kagoshima Vendenberg Wallops Juiquan Baikonur Kennedy Space Center Tanegashima Sriharikota Xichang Guayana Space Center Trivandrum Alcantara Plataforma San Marco EAST Selecting the launchsite Kiruna Plesesk Kapustin Yar Kagoshima Vendenberg Wallops Juiquan Baikonur Kennedy Space Center Tanegashima Sriharikota Xichang Guayana Space Center Trivandrum Alcantara Plataforma San Marco EAST Variation of launcher mass • Mass flow is a known parameter in this analysis.
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