Analysis of Rocket Propulsion P M V Subbarao

Analysis of Rocket Propulsion P M V Subbarao Professor Mechanical Engineering Department Maximization of Pay Loads ….

Geostationary orbit • A circular geosynchronous orbit in the plane of the Earth's equator has a radius of approximately 42, 164 km from the center of the Earth. • A satellite in such an orbit is at an altitude of approximately 35, 786 km above mean sea level. • It maintains the same position relative to the Earth's surface. • If one could see a satellite in geostationary orbit, it would appear to hover at the same point in the sky. • Orbital velocity is 11, 066 km/hr= 3. 07 km/sec. Consider a simpler example : vertical ascent by a rocket vehicle

Analysis of Vertical Ascent Rocket Vertical ascent o. d. e. : Gravity: Propellant consumption :

Frictionless Vertical Ascent of Rocket Aerodynamic drag: , neglect Updated o. d. e. : Integrate to arrive at t>0: , 0 < tb

Reaching the Destination Hgeo-sys=35, 786 km Orbital velocity = 3. 07 km/sec

Time of Travel & Economics The burn time: • Want to reduce burn time as much as possible while accelerating against a gravity field • Short burn time reduces energy consumed in lifting propellants • Very short burn time implies very high accelerations – Structural limitations , High mass flows, lots of weight for nozzles, turbo-machinery, cooling, etc, – Drag goes as V 2 • Is there an optimum acceleration for a given rocket configuration? • In limit of no drag and no gravity, burn time has no influence on velocity increment

Actual Flight trajectory of launch vehicle up to orbital altitude & speed.

Modern Launch Systems

MULTISTAGE ROCKETS • With current technology and fuels, a single stage rocket to orbit is still not possible. • It is necessary to reach orbit using a multistage system where a certain fraction of the vehicle mass is dropped off after use thus allowing the non-payload mass carried to orbit to be as small as possible. • The final velocity of an n stage launch system is the sum of the velocity gains from each stage.

Series Stage Rocket 3 rd Stage Thrusting

Clustered Rocket in First Stage

Travel Cycle of Modern Spacecrafts

Multistage Rockets : Definitions • Total mass of rocket, may be written as sum of 3 primary components: – Payload mass, m. L – Propellant mass, mp – Structural mass, ms • Includes everything but payload and propellant • Engines, tanks, controls, etc. If rocket consumes all its propellant during firing, burnout mass consists of structure and payload:

Concept of Multistage Rockets m. L : The payload mass mti : The total initial mass of the ith stage prior to firing mpi : The mass of propellant to be consumed in the ith stage. msi : Structural mass of the ith stage alone including the mass of its engine, controllers and instrumentation as well as any residual propellant which is not expended by the end of the burn.

$Dynamic Mass of the Rocket : Mass fractions Mass ratio for ith stage$