T09‐1 T09-Ot2013 LAUNCH SYSTEMS [email protected] T09‐2 Outline •Rocket propulsion fundamentals • Launch vehicle dynamics –Gravity and drag losses – Contribution of Earth’s rotation • Launcher design –Staging – Mass fraction • Launch vehicles by agency: –Performance table • Launch sites T09‐3 Rocket propulsion fundamentals t t+dt Conservation of momentum: mv (m dm)(v dv) dmv' But v,v' abs. velocities (inertial frame) ue ejection speed (relative) v'(v dv) Hence: mv (m dm)(v dv) dm(v dv ue ) 0 mdv dmue dm m dt dv m F m u dt e T09‐4 The rocket equation The total impulse I = variation of the momentum of the ejected gas (and hence of the rocket in the opposite direction) is dv I m dt Fdt m u dt dt e If ue = constant (which is not always true), then I u mdt u dm u m e e e p with m = ejected mass. p I F I u Specific impulse Isp =impulse per unit mass: sp e m p m F ‐2 In many applications: I sp (in seconds) with g0 = 9.81 ms m g 0 T09‐5 The rocket equation The effect of the rocket engine on the vehicle can be determined from Newton’s second law dv m F I m g t dt sp 0 with mt the total mass of the vehicle. Since dm t m dt with the – sign meaning that the vehicle mass decreases, then dm I m g I g t sp 0 sp 0 dt m v I g dm m dv tf exp sp 0 t t mti I sp g 0 T09‐6 Propulsion system’s classifications 1) Function‐based classification – Primary propulsion • Acceleration, overcoming drag and gravity (launch) • Orbit insertion, orbit change maneuvers – Secondary propulsion •For pitch, yaw, and roll control, spin control, momentum wheel and gyro unloading (= attitude control), stage separation 2) Mission‐based classification – Launch vehicles and ballistic missiles – Upper stages and orbital transfer vehicles – Secondary and auxiliary propulsion – Interplanetary and space propulsion T09‐7 Launch system: definition Launch system = launch vehicle incorporating one or more stages + infrastructure for ground support. It provides velocity to place the spacecraft in the desired orbit, creates a severe ascent environment and protects the spacecraft from its surroundings. Kennedy Space Flight Center T09‐8 Launch vehicle dynamics •Space launch systems are unique forms of transportation since they are the only systems that accelerate continuously throughout their performance envelope. •Velocity is the fundamental measure of performance for launch systems. •A launch system’s ability to achieve orbital velocity comes primarily from its propulsion efficiency, with vehicle weight and drag acting against it. T09‐9 Launch vehicle dynamics Consider the motion of a launcher in a vertical plane. The following forces are acting on it: •The weight W, acting at the center of gravity cg •The thrust T, ideally acting through the centerline x (x = centerline) . •The aerodynamics forces – lift L and drag D – cg acting at the centre‐of‐pressure, cp. Trajectory γ cg Local horizontal Note that cp in general does not coincide with the aerodynamic center (ca). It does, e.g., in the case of axisymmetric bodies (not STS) T09‐10 Launch vehicle dynamics • Ideally, thrust, T, acts through the centerline of the vehicle but we can develop a control torque by gimballing the engine nozzle. •So in general T acts along a direction which forms an angle δ with the centerline •In a configuration with cg ahead of cp, L and D produce restoring torques. Trajectory γ cg Local horizontal δ T09‐11 Launch vehicle dynamics •Let’s decompose the forces into two directions: α = angle of attack • Parallel to the flight velocity (V): γ = flight‐path angle δ = gimbal angle dV [1] M T cos Mg sin D θ = pitch angle dt • Normal to the flight direction (perp. to V): d MV 2 [2] MV T sin Mg cos L cos dt r See next page T09‐12 t t // V n // L V u // Mg ur u r u // local horizon n r tu cos θ sin unur ; sinθ cos ur uuuuθ rr; θ V cos V Vt V (cosu sin u ) ru ru r r r V Vt Vt Vt V (sin u cosur ) V (cosu sinu r ) Vt Vn V (cosur sinu ) Vt Vn Vn V 2 cos V Vt Vn n r T09‐13 Pitching moment and aerodynamic stability • Separation of centre of pressure away from the centre of mass gives a restoring turning moment in pitch axis (stability) IF cp is lower than cg (this obtained by adding lift in the lower side ‐‐‐ fins = aletas) Modern full scale rockets do not usually rely on aerodynamics for stability. Full scale rockets pivot their exhaust nozzles to provide stability and control. That's why you don't see fins on a Delta, Titan, or Atlas booster. [http://www.grc.nasa.gov/WWW/k‐12/rocket/rktstab.html] T09‐14 Pitching moment •If cp is ahead of cg, L and D produce destabilizing torques in pitch. • Stabilization is obtained by adding fins or spinning the rocket (military missiles) or controlling the direction of thrust (majority of launchers use this). •IfIP = moment of inertia in pitch axis, then dh d d2 p I I dt p dt P dt 2 p d2 I L cos Dsin l T sin l P dt 2 0 T [see http://microgravity.grc.nasa.gov/education/rocket/gimbaled.html] T09‐15 Losses in the rocket equation dV T D •For small , [1] becomes g sin [3] dt M M • Thrust is given by the rate of mass flow: dM T I sp g0 dt • Substitute into [3] and obtain: dV d D I g ln M g sin dt sp 0 dt M •Then integrate to get velocity at the end of the thrust (0,t): M t t D V V I g ln 0 g sin dt dt 0 sp 0 M 0 0 M ‘Ideal velocity ‘Aerodynamic loss’ change’ ‘Gravity loss’ T09‐16 Gravity loss & gravity turn t V g sin dt A way to reduce it is minimizing the burn time g 0 •It reflects the work made by the vehicle against the Earth’s gravity •This integral cannot be computed a priori as we do not know the profile of γ and g as functions of time ( numerical integration). •In general, in order to reduce this term, we need to minimize the burn time • Satellite launch vehicles take off vertically and, at injection into orbit, they must be flying parallel to the Earth’s surface •During the initial phase, the rocket builds up speed in an almost vertical trajectory taking it above the densest layers of the atmosphere •When it transitions to the thinner upper atmosphere, the trajectory bends over, trading vertical speed for horizontal speed so that the rocket can achieve orbital perigee velocity at burnout. •This gradual transition is caused by the force of gravity and is called gravity turn T09‐17 ...Gravity turn •At lift off, the rocket is vertical and γ = 90 deg. •After clearing the tower and gaining speed, gimbaling the main engines produces a small pitchover, establishing an initial flight path angle γ0 •Thereafter γ will continue to decrease at a rate dictated by [2] d MV 2 MV T sin Mg cos L cos dt r •For simplicity, assume no lift (L=0) and no gimbaling (α+δ=0): d V 2 V g cos dt r • E.g., at h = 2 km, if γ = 85 deg and V = 110 m/s, dγ /dt = ‐0.44 deg/s •Over the ascent, the coefficient of cos γ is negative •As the speed increases, the coefficient of cos γ decreases in modulus, so the the rate of change of γ decreases (in abs. value). •Gravity turn reduces gravity loss because this term depends on sin γ T09‐18 Drag loss or aerodynamic loss t D 1 2 V dt D V ACD D 2 0 M •It reflects the work made against the aerodynamic resistance •Since M is proportional to initial mass M0, then A A 1 VD M 0 Alrocket lrocket It means that drag loss is inversely proportional to rocket length and rocket density. Shorter rockets will suffer from worse drag losses. Increasing density and decreasing drag coefficient might help T09‐19 Ideal ΔV M t t D V V I g ln 0 g sin dt dt 0 sp 0 M 0 0 M Overall V V V0 VIdeal Vg VD •We can easily estimate the velocity that a launch vehicle should provide by VIdeal V Vg VD where V is the velocity required for the desired orbit. V •We add the velocity losses, Vg and VD , to the velocity to obtain the required design velocity. T09‐20 Gravity and drag loss •Gravity loss ≈ 18% of VIdeal •Drag loss ≈ 2% of VIdeal Launcher Gravity loss (m/s) Drag loss (m/s) Ariane 4 1576 135 Atlas I 1395 110 Delta 7925 1150 136 Saturn V is the tallest Shuttle 1222 107 and suffers the smallest Saturn V 1534 40 drag loss Titan IV /Centaur 1422 156 T09‐21 Velocity increase due to Earth’s rotation N Considering the rotation of the Earth: E VIdeal V Vg VD VROT VROT E RE cos()cosa 2 φ = launch latitude a = launch azimuth ωE ∙RE = VE = velocity of a point on the Earth equator = 0.465 km/s ωE ∙RE∙cos (φ) = velocity of launch site N a On the local horizon of E launch site (a = azimuth of launch) T09‐22 Effect on allowed azimuth range At each stage burnout, the corresponding structure is jettisoned.