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Part II: Rocket Mechanics

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Title: Part II: Rocket Mechanics


1
  • Part II Rocket Mechanics

2
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

3
CM
  • The CM point is where the three axes of pitch,
    roll and yaw all intersect

4
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

5
Your Water Rocket
  • In the diagram of a
  • water rocket, can
  • you determine
  • where
  • the CM and CP
  • should be
  • located at?

6
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

7
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

8
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9
de Laval Rocket Nozzle
10
  • 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.

11
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.

12
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15
Other Concepts
16
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.

17
  • 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.)

18
  • Now you are
  • becoming real
  • rocket scientists!!!!!
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