JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year AEROSPACE PROPULSION- II Previous Question Paper (November/December - 2020 - R15)

Specific impulse (I_sp) is a measure of the efficiency of a rocket engine, defined as the total impulse or change in momentum delivered per unit weight of propellant consumed, typically expressed in seconds. It is given by I_sp = F / (ṁ g₀), where F is thrust, ṁ is mass flow rate, and g₀ is standard gravity.

To derive the Breguet range equation for a cruise vehicle, we start with the instantaneous range increment dR = V dt. From the thrust-drag equilibrium, F = D, and the definition of specific fuel consumption (SFC or c), we have -dm = (c D / V) dt. Substituting dt = -V dm / (c D) into the range equation:

Integrating from initial mass m₀ to final mass m_f:

Where V is velocity, c is specific fuel consumption, L/D is the lift-to-drag ratio, and the natural log term represents the mass fraction.

Stage separation is critical in multi-stage rockets to discard dead weight and improve performance. Various systems are employed to ensure clean separation:

• Pyrotechnic Bolts and Explosive Charges: These are used to sever the structural connection between stages. Explosive bolts or linear shaped charges cut the interstage adapter, allowing the stages to separate.
• Retro-Rockets: Small solid-propellant motors mounted on the spent stage, firing in the opposite direction of flight to decelerate it rapidly, ensuring it does not collide with the upper stage.
• Ullage Motors: Small thrusters used to provide positive acceleration to the upper stage before its main engine ignition, ensuring propellants settle in the tanks and preventing cavitation or gas ingestion.
• Pneumatic or Spring Pushers: Mechanical systems that use compressed gas or high-tension springs to physically push the stages apart once the structural locks are released, providing a clean initial separation velocity.
• Hot Staging: A technique where the upper stage engine is ignited while the lower stage is still attached. The exhaust gases from the upper stage push against the lower stage, forcing separation. This requires a robust interstage structure with vents to exhaust the plume safely.