EAS 4710 Aerospace Design 2

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EAS 4710 Aerospace Design 2
4. Launch Dynamics
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Space Shuttle Launch (STS 115 Atlantis) as seen
from ISS
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Space Shuttle Launch (from ISS)
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Space shuttle mission profile
On orbit maneuvers
Ascend to orbit
MECOmain engine cut-off OMSorbital maneuvering
system
De-orbit
Entry interface,400kft
Abort and proceed to alternate landing site
Abort and return to launch site
Launch SRB ET impact impact
ET impact To landing
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Space Shuttle Transportation System Mission
Profile

• For a fairly detailed narrative description of
  the SSTS mission shown on the previous slide go
  to
• http//spaceflight.nasa.gov/shuttle/reference/shut
  ref/sts/profile.html

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Space launch sites
www.spacetoday.org/Rockets/Spaceports/LaunchSites.
html
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Boost trajectory with zero lift
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Simplified boost analysis
Mass changes due to propellant consumption so at
any time the mass is
constant (thrust and flow rate are constant)
Note The engine can only run until fuel runs out
so the mass of the vehicle at burn-out is mb-o
m0 - mfuel m0 - Ttb-o /gEIsp,
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Features of a liquid propellant rocket
Combustion chamber is under high pressure, up to
200 atm in the SSME
Fuel and oxidizer may be pumped or pressure-fed
Regenerative cooling protects nozzle and prepares
fuel for injection
Nozzle is the major factor in performance
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The nozzle as energy transformer
Powerhead, thermal energy released
Throat area, At where flow is accelerated to M1
Nozzle transforms thermal energy (Ts) into
kinetic energy (V2/2)
Expansion ratio eAe/At
Exit area, Ae where high Ve produces thrust
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Thrust coefficient
Thrust
a
l (1cosa)/2
Thrust coefficient
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Specific impulse
Definition of specific impulse
Specific impulse depends on Ve and pe
Nozzle area ratio for gas with constant g
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Expansion ratio and Me for various g
Space engines
Typical rocket engines
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Typical expansion ratios for liquid rocket engines
LH2-LOX
CH4/LOX
RP-1/LOX
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Chamber pressures in liquid rocket motors
LH2/LOX
CH4/LOX
RP-1/LOX
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Specific impulse change with altitude
When p00
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Variation of Isp with altitude
High e
Low e
Fixed g1.2 and chamber pressure pc200 atm for
different expansion ratios, e. The specific
impulse is normalized to the product of g and
chamber sound speed ac.
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Nozzles with different e
1 e10, Me3.92, pe7.33 psia, Te1227R 2,
e25, Me5.00, pe1.89 psia, Te833R
Two position nozzle
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Two-position bell nozzle
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Flight over a non-rotating planet
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Lift and Drag during boost

• During launch and ascent BmgE/CDS is largest
  because mass is largest
• Typical (e.g., space shuttle) qmax30kPa
• Large L would give rise to large bending moments
  on slender thin-walled launch vehicles

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Simplified eqs for LD0 Tconst
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Flight path accelerations
an
g0, U1
g(t)
gp/2, U0
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Simplified descriptive trajectories
Using dhVC sing dt
VC
VCsing dh/dt
If we knew UU(h) we could integrate this. For
example, assume (U/Uf)1/2VC/VC,f (h/hf)n
where f denotes final Then
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Some simplified trajectories (cont.)
We obtain, using subscript i to denote launch
(or initial) conditions
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Some simplified trajectories (cont.)
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Some simplified trajectories (cont.)
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Back to launch equations for LD0
dh VC sing dt dx VC cosg dt
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Thrust to weight ratios for launchers
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Payload weight fraction
Wpay/Wt-o1
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Manned Launchers
Space shuttle - 5.7Mlbs
Soyuz 728klbs
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Launch vehicles
Long March 1.33 Mlbs
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Soyuz first stage propulsion system
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Approx. solution for the launch eqs
Direct numerical solution is suggested. An
approximate numerical calculation scheme is given
by
Note that the exact initial condition is
typically gp/2 and Vc0 but these give rise to
singularities so slightly different conditions
are suggested.
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Boost analysis with Lift and Drag
Reusability means airbreathing engines to reduce
the required propellant load along with lifting
wings to aid in ascent For airbreathing engines
Isp f(Vc) and the top equation must be adjusted
accordingly.
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Approximate boost analysis
assume average values
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Approx. boost analysis Drag
Since
constant for a rocket
The drag to thrust ratio is
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Estimate of Drag contribution

• (T/W)0 O(1) and CDO(1)
• Spd2/4Volume/length of booster
  W0/(rs)(length)
• D/Tq/(lrstructure), where the term rstructure
  represents the average density of the complete
  launch vehicle at launch.
• A reasonable estimate is rstructure rpropellant
  gt50lb/cu.ft
• qmax500 lbs/ft2
• D/Tlt500/50llt0.1 thus this is small as initially
  assumed

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Characteristics of common propellants for launch
vehicles
Note weight density of water is 62.4 lbs/cu.ft.
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Approx. solution when D neglected
Expanding the log term for
yields
the weight term is significant only at the
earliest times, since singavg is always less than
unity. For preliminary design purposes we may
choose a value for singavg, say 0.5.
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Fuel burn duration
The fuel burned between to and any time t is is
But the fuel weight must be less than the launch
weight
Typical initial values T/W1.3 and Isp400
Therefore maximum burn times are around 300
seconds.
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An introduction to staging of rockets
For an engine burn starting at tti where VCVC,i
The weight of fuel consumed during the burn is
The weight of a launch vehicle decreases as the
fuel burns, It would be efficient to jettison
structural weight continuously during
ascent. Instead jettison discrete portions of the
structure and tankage along the flight path when
fuel is completely consumed.
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SSTO burn-out
payload
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single-stage to orbit (SSTO) example
The weight is made up of payload and propulsive
unit
To put the payload into circular orbit with one
stage requires
Consider a single stage rocket with(T/W)01.3 and
Isp450 s,
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single-stage to orbit (SSTO) example
Burn-out
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single-stage to orbit (SSTO) example
For a burn-out time tb-o300 seconds
Wfuel/W00.8667. Then
Engine weight is found to be correlated to engine
thrust
0.095 LOX LH 0.07 LOX-RP1
K
An estimate for the structure plus engine weight
is (WstrWeng) /Wfuel0.1
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Engine weight correlations
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Structural weight correlation
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Structure engine wt. correlation
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The SSTO example continued
Inserting the structure plus engine weight
approximation yields
Assuming a payload weight of 23,275 lbs (10,544kg)
The launch weight is thus W0500,000 lbs, and the
thrust required is therefore T650,000 lbs.
Three J-2 engines (Saturn 2nd stage engines, 5
used) each of which has Isp 427 seconds and T
230,000 lbs.
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Correcting the flight path angle
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Two-Stage to Orbit (2STO) example
Now take 2 stages and again (T/W)01.3, Isp 450s
and singavg0.5 1st stage velocity history same
as the SSTO, Since we have 2 stages we truncate
the burn at some time, say tb-o,1 200 seconds
where VC 2.82 km/s (9,250
fps). The fuel fraction consumed during this 200
second burn may be determined from
Wfuel/W00.5778
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First stage burn-out
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Weight breakdown for 2STO
Weight of 1st launch stack
Weight of 2nd launch stack
In the SSTO case
Now Wfuel/W0 WfuelI /W0I 0.5778 so for TSTO we
have
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The launch stack
3rd launch stack
2nd launch stack
1st Launch stack
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2STO weight advantage
For Wpl 23,275 lbs, the weight of the second
stage is W0II 147,500 lbs. Then W0I404,800 lbs.
The thrust required for the first stage is
therefore T526,200 lbs, that is, two J-2S
engines (Isp435 and T265,000 lbs). Thus to
launch the same payload into LEO, the two-stage
system weighs almost 20 less than a single stage
system
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Three-Stage to Orbit (3STO) example
Assume tb-o,1 200 seconds again, so at first
stage burn-out VC2.883 km/s and the fuel
fraction is still Wfuel, b-o, 1 0.5778.This
equation yields W0II0.3644W0I. Taking the
burn-out time to be, say, tb-o,2 360 seconds
Which leads to VC,b-o,24.981 km/s and
The weight of the second stack is then
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Three-Stage to Orbit (3STO) example
Substituting known values yields
W0III0.4916W0II0.4916(0.3644W0I)
0.1791W0I 3rd stage fires and accelerates to
VC7.8 km/s. One may determine the burn-out time
by using the velocity relation
The resulting time is tb-o,3565 seconds and
therefore Wfuel,3/W0III.002889(565-360)0.5922
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Three-Stage to Orbit (3STO) example
The 3rd stack weight is
W0III66,770 lbs, W0I372,800 lbs, and
W0II135,700 lbs. TI 484,700, TII176,400 lbs,
and TIII86,710 lbs. The requirement for the
1st stack can be met by two J-2 engines, but that
for the 2nd and 3rd stacks are not readily met by
existing LOX-LH2 engines. The reduction in
launch weight achieved by using 3 stages instead
of 1 is 25, while the reduction in weight
compared to two stages is about 8.
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Comparison of staging trajectories
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Comparison of launch weights
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Some launch weights for human space flight systems