chapter2 - A A E 5 90E 2 DEFINITION OF ROCKET PERFORMANCE C...

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Ch2 – 1 AAE 590E 2. DEFINITION OF ROCKET PERFORMANCE 2. DEFINITION OF ROCKET PERFORMANCE
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Ch2 – 2 AAE 590E 2.1 LAWS OF MECHANICS 2.1 LAWS OF MECHANICS
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Ch2 – 3 AAE 590E Propulsion Propulsion PROPULSION Changing the Motion of a Body JET PROPULSION Reaction Force due to momentum of ejected matter BODY m B dm ! v ejected mass ! F ! v Body ! ! v Body ! D ! F Body ! v Body BODY m B
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Ch2 – 4 AAE 590E NEWTON’S LAWS OF MOTION NEWTON’S LAWS OF MOTION Newton’s Laws of Motion describe the relationships between forces acting on a body and the motion of the body. Newton’s First Law: Law of Inertia Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare. Every body perseveres in its state of being at rest or of moving uniformly straight forward, except it is compelled to change its state by force impressed. Newton’s Second Law: Law of Resultant Force Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur. The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction. Newton’s Third Law: Law of Reciprocal Actions Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi. All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction. Source: Wikipedia
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Ch2 – 5 AAE 590E BODY IN MOTION BODY IN MOTION The motion and changing the motion of a body can be described with: BODY PROPULSION Changing the Motion of a Body ! I = ! ! p = ! p f " ! p i = ! F dt t i t f # Impulse Linear Momentum ! p = m ! v Kinetic Energy E = 1 2 mv 2 ! v Body Newton’s Laws ! F = m ! a ! F ! a Body ! F environment ! ! v Body dm ! v ejected mass JET
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Ch2 – 6 AAE 590E EQUATIONS OF MOTION EQUATIONS OF MOTION Equations of Motion describe the motion of a particle or body, onto which a force is exerted, as a function of time. Newton’s Second Law: Acceleration: Velocity: Position: F ! = m " a a = F m a = dv dt v ( t ) = adt ! = at + C v = dx dt x ( t ) = vdt ! = v 0 t + 1 2 at 2 + D
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Ch2 – 7 AAE 590E SYSTEM SYSTEM System: Moving Fluid Definitions: “System” is defined as an arbitrary quantity of mass of fixed identity. “Surrounding is everything external to this system. “Boundary” separates surroundings from system. Case: Control Volume is at rest. Control Volume is moving with a velocity. All Laws of Mechanics are written for a system stating what happens when there is an interaction between the system and its surroundings. Conservation of Mass Linear (Angular) Momentum Energy Equation !
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