m0 ?
initial mass = bare vehicle mass + payload mass
m0 = mv + mpl
initial mass = propellant mass + final mass
m0 = mp + mf
mf ?
final mass = initial mass - propellant mass
mf = m0 - mp
final mass = bare vehicle + payload - propellant
mf = mv + mpl - mp
Mas ratio?
MR = mf / m0
Propellant mass ratio
zeta = mp / m0 = (m0 - mf) / m0 = 1 - MR
The rocket equation
Draw a simple engine
Simple engine areas
1 - chamber
t - nozzle throat
2 - nozzle exit
3 - atmosphere
What happens at different pressure ratios?
e.g. p2 > p3
Underexpansion (p2 > p3)
pressure thrust is positive
Opimal expansion (p2 = p3)
no pressure thrust
Overexpansion (p2 < p3) !BAD!
pressure thrust is negative
Vacuum (p3 = 0)
What happens with the atmosperic pressure at increasing altitude?
decreases
What happens with the thrust at increasing altitude?
increases
What happens with the specific impulse at increasing altitude?
Why is an ideal rocket useful?
3D rocket behaviour.
Simplification that leads to approximate solutions for many rocket propulsion systems (for chemical between 1% and 6% below measured).
How to achieve high nozzle exit velocity?
high chamber pressure
low molar mass of exhaust gas
high expansion -> low nozzle exit temperature
What are the main performance parameters for a rocket?
Effective exhaust velocity
Specific impulse
Thrust to weight ratio
Rocket power
Name propulsion systems
cold gas
liquid-monopropellant
liquid-bipropellant
solid-propellant
nuclea thermal rockets
electric propulsion systems
Cold-gas?
Gas is stored at high pressure and is released through a feed system and accelerates to a high velocity through a conventional nozzle
simple, cheap, safe to operate and do not release contaminants
liquid-monopropellant?
A single liquid is stored at high pressure reacts alone by chemical decomposition when flowing over a catalyst bed
easy and reliable
liquid-bipropellant?
fuel and oxidizer are fed to a combustion chamber -> chem. reaction -> heat is released.
Typical fuel/oxidizer H2LOX
highest performance of any conventional chemical propulsion system and highly controllable
complex and expensive
solid-propellant?
relatively simple to operate, relatively small
can not be switched off, difficult to modulate thrust
not used for orbit maintenance, orbit maneuvers and attitude control
high thrust-to-weight ratio, low Isp
used for smaller launch vehicles, boosters for larger launch vehicles and orbit insertion
Solid propellant vs. liquid propellant
Solid
Liquid
Simple design (no moving parts)
sophisticated design
rapidly ready for operation (no fuelling before launch, easy storage)
longer launch preperation (storage is more difficult, long time or fueling)
no propellant sloshing
sloshing possible (instabilities)
high thrust-to-weight ratio
lower thrust to weight ratio
low isp (< 280 s)
high Isp (up to 465 s)
Thrust and burning duration can not be controlled
cannot be switched off
cannot be tested before launch
Thrust and burning duration can be controlled
can be switched off
can be tested before launch
not restartable
restartable
high structural mass (high pressures because whole rocket is thrust chamber)
lower structural mass
propellant is expensive
less expensive
toxic
non-toxic
Nuclear thermal?
environmental and political considerations do not allow launch applications
NERVA: promising Nuclear engine
Isp: 835 s
1200 MW
890 kN
Electric propulsion?
higher exhaust velocity, higher Isp, larger delta V’s
long thrust durations -> impracticle for launch
advantegous for interplanetary missions, GEO station keeping
Resistojet?
Electrical propulsion system
operate by passing a gasous propellant through an electric heater and then expanding it through a conventional nozzle
Ion thruster?
Ions are produced and contained in the ionization chamber. Exit is covered by a double-grid structure -> high electric potential -> Ions move to the inner grid and are accelerated. Behind the grid, electrons get extracted to cobine with the ion stream to neutralize it. Necessary because ejecting particles cause the vehicle to charge up
Isp approx. 3000 s
Thrust 90 mN
Stationkeeping
Staging configrurations?
serial staging: stacked on top of each other, increase Delta V
parallel stating: increase thrust to weight ratio
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