Transcript Physical Science Rocket Mechanics

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 rocket’s 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
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/(kmol·K)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.
Newton’s 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.
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/s
40 200 km/h
25 000 mi/h
So, 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!!!!!