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- Part II Rocket Mechanics

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

CM

- The CM point is where the three axes of pitch,

roll and yaw all intersect

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

Your Water Rocket

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

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

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

- 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.

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

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.

- 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.)

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