Part II: Rocket Mechanics

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• Part II Rocket Mechanics

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Rocket Stability

• Stability is maintained through two major ideas
• First is the Center of Mass (CM)
• This is the point where
• the mass of the rocket
• is perfectly balanced
• It should be about
• halfway up the rocket

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CM

• The CM point is where the three axes of pitch,
  roll and yaw all intersect

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Center of Pressure (CP)

• This is the second important concept
• It only exists when air is flowing over the
  moving rocket
• The rockets surface area helps to determine the
  total CP
• The CP ought to be between the CM and the engine
  end of the rocket
• The CP location can be controlled by using
  movable fins, a gimbaled (movable nozzle) and of
  course, the overall rocket design

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Your Water Rocket

• In the diagram of a
• water rocket, can
• you determine
• where
• the CM and CP
• should be
• located at?

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Rocket Mass

• Ideally the mass of a rocket should be about 91
  fuel 3 rocket and 6 payload
• This is determined
• through the use of the
• mass fraction (MF)
• MF m propellant
• m rocket

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Rocket Propulsion

• Rockets use
• either liquid fuel
• or solid fuel
• Liquid fuel is a
• mix of liquid oxygen
• and liquid hydrogen
• These gases must
• be at -423o F to
• become liquefied

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de Laval Rocket Nozzle
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• The linear velocity of the exiting exhaust gases
  can be calculated using the following equation
• where Ve Exhaust velocity at nozzle exit, m/sT
  absolute temperature of inlet gas, KR Universal
  gas law constant 8314.5 J/(kmolK)M the gas
  molecular mass, kg/kmol    (also known as the
  molecular weight)k cp/cv isentropic expansion
  factorcp specific heat of the gas at constant
  pressurecv specific heat of the gas at constant
  volumePe absolute pressure of exhaust gas at
  nozzle exit, PaP absolute pressure of inlet gas,
  Pa
• Some typical values of the exhaust gas velocity
  Ve for rocket engines burning various propellants
  are
• 1700 to 2900 m/s (3,800 to 6,500 mph) for liquid
  monopropellants
• 2900 to 4500 m/s (6,500 to 10,100 mph) for liquid
  bipropellants
• 2100 to 3200 m/s (4,700 to 7,200 mph) for solid
  propellants
• As a note of interest, Ve is sometimes referred
  to as the ideal exhaust gas velocity because it
  based on the assumption that the exhaust gas
  behaves as an ideal gas.

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Newtons Laws and Rockets

• Every object in a state of uniform motion tends
  to remain in that state of motion unless an
  external force is applied to it.
• The relationship between an object's mass m, its
  acceleration a, and the applied force F is F
  ma. Acceleration and force are vectors (as
  indicated by their symbols being displayed in
  slant bold font) in this law the direction of
  the force vector is the same as the direction of
  the acceleration vector.
• For every action there is an equal and opposite
  reaction.

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Other Concepts
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Escape Velocity

• Isaac Newton's analysis of escape velocity.
  Projectiles A and B fall back to earth.
  Projectile C achieves a circular orbit, D an
  elliptical one. Projectile E escapes.

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• Escape velocity is defined to be the minimum
  velocity an object must have in order to escape
  the gravitational field of the earth, that is,
  escape the earth without ever falling back. The
  object must have greater energy than its
  gravitational binding energy to escape the
  earth's gravitational field. So 1/2 mv2
  GMm/R Where m is the mass of the object, M mass
  of the earth, G is the gravitational constant, R
  is the radius of the earth, and v is the escape
  velocity. It simplifies to v sqrt(2GM/R) -
  or -v sqrt(2gR) Where g is acceleration of
  gravity on the earth's surface. The value
  evaluates to be approximately 11 100 m/s40
  200 km/h25 000 mi/hSo, an object which has
  this velocity at the surface of the earth, will
  totally escape the earth's gravitational field
  (ignoring the losses due to the atmosphere.)

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• Now you are
• becoming real
• rocket scientists!!!!!