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Rocket Trajectories

Rocket Trajectories. By Jan-Erik Rønningen Norwegian Rocket Technology [ contact@rocketconsult.no ] [ www.rocketconsult.no ]. Version: 1.50 2008. Contents. Different types of Rocket Trajectories Typical Suborbital Trajectory Guided Flight Trajectory Homing Flight Trajectory

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Rocket Trajectories

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  1. Rocket Trajectories By Jan-Erik Rønningen Norwegian Rocket Technology [ contact@rocketconsult.no ] [ www.rocketconsult.no ] Version: 1.50 2008

  2. Contents • Different types of Rocket Trajectories • Typical Suborbital Trajectory • Guided Flight Trajectory • Homing Flight Trajectory • Circular Orbits • Gravity • Rocket Mass Ratio • Ideal Rocket Equation • Rocket Equation with Drag, Thrust and Gravity (2) • Terminal Velocity • Trajectory Equations for a Single-Stage Rocket with Thrust, Drag and Gravity Forces (5) • Trajectory Simulation (2)

  3. Different types of Rocket Trajectories • Free Ballistic Flight Trajectory – Gravity and Drag • “Parabolic” type of trajectories, controlled by drag, gravity and thrust • Arrows, dart, stone, bullet, sounding rocket • Guided Flight Trajectory – Preprogrammed Trajectory • Trajectory shaped by i.e. lift, thrust vectoring and modulation • Launch vehicles that places payloads into circular orbits • Homing Flight Trajectory – Programmed Trajectory during Flight • Trajectory is uncertain and situation dependent. Shaped by thrust vectoring, ailerons, side-thrusters, thrust modulation etc. • Missiles with sensors that can detect target and have the ability to calculate a meeting point in time and space in order to hit the target • Circular Orbits – Gravity and Speed • Circular orbits are trajectories with almost infinity “free-fall”, shaped by speed change and gravity • Satellites, space crafts, meteorites, planets etc.

  4. Typical Suborbital Trajectory - Single-Stage Sounding Rocket • Flight Profile: Parabola (actually part of an ellipse) • Powered Phase: Rocket thrust with time • Coasting Phase: Free flight up to apogee controlled by gravity and drag mainly • Free Fall: From apogee to ground impact (or splash down)

  5. Different types of Rocket Trajectories • Free Ballistic Flight Trajectory – Gravity and Drag • “Parabolic” type of trajectories, controlled by drag, gravity and thrust • Arrows, dart, stone, bullet, sounding rocket • Guided Flight Trajectory – Preprogrammed Trajectory • Trajectory shaped by i.e. lift, thrust vectoring and modulation • Launch vehicles that places payloads into circular orbits • Homing Flight Trajectory – Programmed Trajectory during Flight • Trajectory is uncertain and situation dependent. Shaped by thrust vectoring, ailerons, side-thrusters, thrust modulation etc. • Missiles with sensors that can detect target and have the ability to calculate a meeting point in time and space in order to hit the target • Circular Orbits – Gravity and Speed • Circular orbits are trajectories with almost infinity “free-fall”, shaped by speed change and gravity • Satellites, space crafts, meteorites, planets etc.

  6. Guided Trajectory h  R0

  7. Different types of Rocket Trajectories • Free Ballistic Flight Trajectory – Gravity and Drag • “Parabolic” type of trajectories, controlled by drag, gravity and thrust • Arrows, dart, stone, bullet, sounding rocket • Guided Flight Trajectory – Preprogrammed Trajectory • Trajectory shaped by i.e. lift, thrust vectoring and modulation • Launch vehicles that places payloads into circular orbits • Homing Flight Trajectory – Programmed Trajectory during Flight • Trajectory is uncertain and situation dependent. Shaped by thrust vectoring, ailerons, side-thrusters, thrust modulation etc. • Missiles with sensors that can detect target and have the ability to calculate a meeting point in time and space in order to hit the target • Circular Orbits – Gravity and Speed • Circular orbits are trajectories with almost infinity “free-fall”, shaped by speed change and gravity • Satellites, space crafts, meteorites, planets etc.

  8. Homing Flight Trajectory X

  9. Different types of Rocket Trajectories • Free Ballistic Flight Trajectory – Gravity and Drag • “Parabolic” type of trajectories, controlled by drag, gravity and thrust • Arrows, dart, stone, bullet, sounding rocket • Guided Flight Trajectory – Preprogrammed Trajectory • Trajectory shaped by i.e. lift, thrust vectoring and modulation • Launch vehicles that places payloads into circular orbits • Homing Flight Trajectory – Programmed Trajectory during Flight • Trajectory is uncertain and situation dependent. Shaped by thrust vectoring, ailerons, side-thrusters, thrust modulation etc. • Missiles with sensors that can detect target and have the ability to calculate a meeting point in time and space in order to hit the target • Circular Orbits – Gravity and Speed • Circular orbits are trajectories with almost infinity “free-fall”, shaped by speed change and gravity • Satellites, space crafts, meteorites, planets etc.

  10. Circular Orbits v a = g G R0

  11. Gravity Earth is not a perfect sphere  g will therefore be a function of latitude  : R0=6371315m g also decreases with the square of the distance, so for high altitudes a corrected g has to be calculated : For h<120km R0 is so large in comparison to h that : [m] < 1% error

  12. Rocket Mass Ratio Burnout Mass Payload mass (mp) Rocket inert mass (mr) Start Mass Propellant mass (md) Rocket motor mass (mm)

  13. Ideal Rocket Equation -ve v dm M-dm +

  14. Rocket Equation with Drag, Thrust and Gravity (1)

  15. Negative because mass is expelled in opposite direction of movement. Rocket Equation with Drag, Thrust and Gravity (2)

  16. Terminal Velocity When drag equals gravity the net forces on the rocket is zero: Terminal Velocity is then: Higher velocity for objects that are heavier, more streamline, flying in lower atmosphere density and that has smaller frontal area.

  17. Trajectory Equations for a Single-Stage Rocket with Thrust, Drag and Gravity Forces (1) • mr= rocket mass • mm= motor mass • mp = propellant mass • g = const. = 9.81m/s2 • = const. = 1.22 kg/m3 CD = const.

  18. Trajectory Equations for a Single-Stage Rocket with Thrust, Drag and Gravity Forces (2) Constant: Drag: tb= ? & vmax = ? Integration: Burnout time: NOTE: tb = It / Tavg Normally tb is known. Simplify:

  19. Trajectory Equations for a Single-Stage Rocket with Thrust, Drag and Gravity Forces (3) Finding vmax:

  20. Trajectory Equations for a Single-Stage Rocket with Thrust, Drag and Gravity Forces (4) We now want to find the burnout altitude, hb:

  21. Trajectory Equations for a Single-Stage Rocket with Thrust, Drag and Gravity Forces (5) We now want to find the ascent altitude, ha and H: H = hCoast + hb

  22. Input values Results Trajectory Simulation (1) ”Launch” Software Download: http://users.cybercity.dk/~dko7904/software.htm

  23. Trajectory Simulation (2) Burnout Apogee

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