Multi-disciplinary Conceptual Design Knowledge of Multi ...
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Journal of Mechanics Engineering and Automation 5 (2015) 1-9 doi: 10.17265/2159-5275/2015.01.001
Multi-disciplinary Conceptual Design Knowledge of
Multi-stage Hybrid Rocket Using Data Mining Technique
Masahiro Kanazaki1, Kazuhisa Chiba2, Koki Kitagawa3, Toru Shimada3 and Masashi Nakamiya4
1. Department of Aerospace Engineering, Graduate School of System Design, Tokyo Metropolitan University, Tokyo 191-0065,
Japan
2. Graduate School of Engineering, Hokkaido University of Science, Sapporo 006-8585, Japan
3. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara 252-5210, Japan
4. Research Institute for Sustainable Humanosphere, Kyoto University, Kyoto 606-8501, Japan
Received: November 18, 2014 / Accepted: December 01, 2014 / Published: January 25, 2015. Abstract: This paper deals with the application of data mining techniques to the conceptual design knowledge for a LV (launch vehicle) with a HRE (hybrid rocket engine). This LV is a concept of the space transportation, which can deliver micro-satellite to the SSO (sun-synchronous orbit). To design the higher performance LV with HRE, the optimum size of each component, such as an oxidizer tank containing liquid oxidizer, a combustion chamber containing solid fuel, a pressurizing tank and a nozzle, should be acquired. The Kriging based ANOVA (analysis of variance) and SOM (self-organizing map) are employed as data mining techniques for knowledge discovery. In this study, the paraffin (FT-0070) is used as a propellant of HRE. Then, the relationship among LV performances and design variables are investigated through the analysis and the visualization. To calculate the engine performance, the regression rate is computed based on an empirical expression. The design knowledge is extracted for the design knowledge of the multi-stage LV with HRE by analysis using ANOVA and SOM. As a result, the useful design knowledge on the present design problem is obtained to design HRE for space transportation. Key words: Hybrid rocket, data mining techniques, multidisciplinary design.
1. Introduction
The kind of rocket presently used for space
transportation is either a solid rocket or liquid rocket
(Fig. 1). The HRE (hybrid rocket engine) is a different
type of rocket that uses a liquid oxidizer and a solid
fuel. This rocket has advantages of being high safe,
low cost and environment-friendly. Therefore, there
are expectations for the HRE as a safe and green
means of propulsion for future space transport. The
HRE was successfully put to practical use for
Space-Ship One [1], which completed the first private
manned space flight.
On the other hand, the most serious problem of the
Corresponding author: Masahiro Kanazaki, research fields:
Ph.D., associate professor, research fields: aeronautics, aerodynamic design, computational fluid dynamics, design optimization. E-mail: [email protected].
HRE as a form of space transportation is the low fuel
regression rate which is the melting rate of the solid
fuel. Due to the low regression rate, if the engine
design is not appropriate, the thrust of the HRE will be
insufficient compared with that of the solid rocket and
liquid rocket engines. The thrust of the HRE is
affected by the mass flow of the vaporized fuel. The
mass flow of vaporized fuel is decided by the oxidizer
mass flow, the fuel grain length and the inner radius of
the fuel grain port. If these parameters are combined
optimally, the thrust will be sufficient. Since these
parameters also decide the engine geometry, the
weight and trajectory are also affected. As a result,
knowledge discovery techniques are desirable for a
multi-disciplinary design of an HRE for a LV (launch
vehicle).
A previous study [2] developed a MDO
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(multi-discip
includes a
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and optimize
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design know
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this study, t
discover the
with HRE (
micro-satelli
of the Earth
is 800 km a
combines al
an object on
given point
mean solar
engine desig
[6] is empl
employed as
swirling-oxi
quantitative
variance) is
a SOM (self
This pap
presents the
using HRE;
design kno
ANOVA an
problem; Se
discovery of
gives the con
2. Perform
This study
with a cham
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3 shows th
previous stu
Generally
Multi-d
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of the perform
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a GA (gen
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for a single-st
the develope
e design kno
(Fig. 2a), ca
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h, to a SSO (s
ltitude. A SS
ltitude and in
n that orbit a
of the Earth
time. Fig.
gned in this s
oyed as a fu
s an oxidizer,
idizer-type
information
applied. To
f-organizing m
per is organ
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Section 3 de
owledge disc
nd SOM; Se
ction 5 show
f three-stage
nclusions.
mance Eval
y deals with t
mber, an oxidi
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he evaluation
udy [2].
y, the regressi
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or an empir
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owledge of a
an deliver 10
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2b shows th
study. Paraffi
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n, an ANOV
visualize the
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escribes meth
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ws the results o
hybrid rocke
luation for
the LV of a t
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Fig. 2b) that h
n procedure
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ical-model-b
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0.0-50.0 kg c
ntific observa
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entric orbit w
such a way
escends over
at the same l
he image of
in fuel (FT-00
iquid oxygen
mbustion type
To obtain
VA (analysis
design prob
oyed.
lows: Sectio
procedure for
hodologies for
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LV with H
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]. In
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ocket
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. 1 Schemately used for tine and (b) liqu
. 2 Conceptudy: (a) the HRE.
d index n
periments for
RE considered
o the WAX (
ermined from
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tten as:
por&
n this study,
-stage Hybrid
pressed as fol
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pirically defi
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(a)
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al illustration RE and (b) t
are genera
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d here suppl
(FT-0070) fue
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he WAX fuel
0.1561ort t
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llows:
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(b)
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of the LV conhe three-stage
ally decided
a single port
lies the swirl
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[6]; then, Eq
-3 0.390510 oxiG
oxidizer-type
(1)
coefficient a
)
engine whicha) solid rocket
sidered in thise LV with an
d from the
t [2, 6]. The
ling oxidizer
n Eq. (1) are
non-swirling
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t (2)
HRE, which
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h
Multi-disciplinary Conceptual Design Knowledge of Multi-stage Hybrid Rocket Using Data Mining Technique
3
can achieve a higher regression rate [7], is assumed.
For this purpose, the empirical multiplication with the
coefficient of Eq. (2) is carried out.
0.3905_ _ _
-3_ 0.1561 10
port m m oxi m
m
r t a G ta
&
(3)
In this study, this coefficient, a_m, is a part of the
design variables that determine the strength of the
oxidizer swirl. The range of α used to decide the
design range of a_m is from 4 to 10. The estimation
methods for the engine size and performance are
presented in the following sections.
2.1 Grain Configuration
The combustion chamber considered in this study
contains solid fuel with a single port to supply the
oxidizer. rport_m(0) and Lfuel_m are calculated for each
stage as follows:
__
_
00
0oxi m
port moxi m
mr
G
& (4)
__
_ _
0
2 0 0fuel m
fuel mport m port m fuel
mL
r r
&
& (5)
Here, 0_ mfuelm is obtained from the definition of
O/F ( tmtmtFO fueloxi / ),
0
00
_
__
m
moximfuel FO
mm
(6)
0_ moxim , Goxi_m(0), and O/F_m(0) are part of the
design parameters listed in the developed evaluation
module.
2.2 O/F and Chamber Pressure Evaluation
O/F at time t is calculated as the absolute value of
sir n can be written as:
tm
tmtFO
mfuel
moxim
_
__
(7)
tm mfuel _ is estimated based on tr mport _ obtained
from Eq.(3) as follows:
_ _ _ _2fuel m port m fuel m fuel port mm t r t L r t & & (8)
Pch_m at time t is calculated as:
mthr
mpropmch A
CtmtP
_
__
*
(9)
Here, tm mprop _ is obtained by adding tm moxi _
and tm mfuel _ . C*(t) is obtained from O/F_m(t-Δt),
P_m(t-Δt) and ε_m using the NASA-CEA (National
Aeronautics and Space Administration-Chemical
Equilibrium with Applications) program [8].
2.3 Weight Estimation
In this study, LOX is employed as an oxidizer and
WAX (FT-0070) is used as the fuel. The required
oxidizer mass, Moxi_m, and fuel mass, Mfurl_m, are
calculated for each stage as follows:
_
_ _0d
mtc
oxi m oxi mM m t t (10)
_
_ _0d
mtc
fuel m fuel mM m t t (11)
Here, tc_m is one of the design parameters. Helium
gas is used as the pressurizing gas. The mass of the
pressurizing gas required is obtained by solving the
state equation as follows:
RTiMVolP mHemprempt ___ )0( (12)
Assuming that Ppt_m is equal to Pot_m when the
supply of helium gas is stopped, the state equation can
be expressed as follows:
RTfMVolVoltcP mHemresmpremmot _____ )( (13)
Eliminating Volot from Eqs. (12) and (13), MHe_m
can be calculated. The temperature of helium after
combustion, i.e., Tf, is calculated as:
1
_
_
)0(
)(
mpt
mot
P
tcPTiTf (14)
The initial helium temperature Ti is 273 K, and its κ
is 1.66. In this study, Ppt_m(0) is one of the design
variables.
The structure of the engine is assumed to be the
same as that of the solid rocket M-V [9]. In this study,
the combustion chamber and the pressurizing tank are
Multi-disciplinary Conceptual Design Knowledge of Multi-stage Hybrid Rocket Using Data Mining Technique
4
assumed to be made of CFRP (carbon-fiber-reinforced
plastic) to reduce the structural weight. The
thicknesses of the shells used for the chamber and the
tank are calculated by assuming that σch and sf values
for these tanks are 2.4 GPa and 1.5 GPa [2],
respectively. Mch_m and Mpt_m are calculated using:
4
___ 103.17
mchmchmch
VolPM (15)
4
___ 103.17
mptmptmpt
VolPM (16)
Here, the denominator on the right-hand side is the
measure of the structural performance. In this study,
the same values as those used in Ref. [9] have been
used in Eqs. (15) and (16). The oxidizer tank is
assumed to be made of CFRP with an aluminum liner,
which can prevent microcracks at extremely low
temperatures. This tank has a 0.05 m thick
heat-insulating material. The thickness of the shell
used for the tank is calculated by assuming that σot and
sf are set to 2.4 GPa and 1.5 GPa [2], respectively.
The LOX tank used in this study is assumed to have a
structure similar to the conventional the liquid helium
(LHe2) tank. In this study, Pot_m(0) is twice of Pch_m.
Mot_m is calculated as follows:
4
__
4
___
104.4
)0(2104.4
)0(
motmch
motmotmot
VolP
VolPM
(17)
Here, Pot_m (0) and Ppt_m(0) are design variables. In
this study, the length (Lch_m, Lpt_m and Lot_m), diameters,
and volumes (Volch_m, Volpt_m and Volot_m) of the
chamber and tanks of the designed engine are
determined using the same calculation procedure as
that used in Ref. [2].
An empirical equation [10] as expressed by Eq. (18),
is used to calculate Mnoz_m:
2 1
3 4_ _
_ 125.05,400.0 10.0
prop m mnoz m
MM
(18)
Here, Mprop_m is obtained by adding Moxi_m and
Mfuel_m. ε_m is one of the design parameters.
Using an empirical equation [10], the mass of other
equipment (an injector, an igniter, ducts and control
devices) is found to be approximately 30% of the total
structural mass of the engine Mtot_m. Therefore, the
total mass of the m-th stage is expressed by Eq. (19)
as:
mnozmptmotmch
mHempropmpaymtot
MMMM
MMMM
____
____
3.1
(19)
The rocket length Ltot_m is calculated by taking the
sum total of Lch_m, Lpt_m, Lot_m and Lnoz_m. In order to
load the payload on the 3rd stage, Ltot_3 is multiplied
by the coefficient 1.5.
2.4 Trajectory Estimation
This study assumes the rocket to be a mass point
from the time of launch to the target orbit. Its
equations of motion are expressed as:
dsin
d
rV
t
(20)
d cos cos
d cos
V
t r
(21)
d cos sin
d
V
t r
(22)
_dsin
dmTh DV
gt M
(23)
dcos
d
V g
t r V
(24)
d cos tan cos
d
V
t r
(25)
Th_m is calculated as:
meamemmpropCCFm APPuemTh ____*_ (26)
In this study, ηCF is assumed to be 0.98 and ηC* is
assumed to be 0.95 in magnitude [9, 10]. ue_m and Pe_m
can be obtained from O/F_m(t), Pch_m(t) and ε_m using
NASA-CEA program.
The drag estimation is based on the flight data of
JAXA’s solid rocket S-520 [11]. Fig. 4 shows the
variation in
study, the d
is empirical
surface of th
C
The Reyn
rocket’s leng
DpC
Here, CD,
data of S-52
The second
drag is obta
friction drag
D
Since the
estimated se
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ANOVA,
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ata presented
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he rocket is a
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Re
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20, and CDf,S-5
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tion of the LV
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projection a
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more pleasin
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Thus, SOM
preserving
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The desig
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minimized.
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operation co
Mpay and M
discovery.
The trajec
The fli
combustion
The an
kg·km2/s aft
to ensure tha
The flig
stage is betw
The const
The asp
The dia
all stages;
The are
nozzle throa
5. Results
5.1 Result of
Fig. 8 sh
According
(dv17) are
Mpay/Mtot. A
larger engin
3rd stages h
more efficie
(dv1) has th
dv9 also infl
of the fuel a
be heavier.
5.2 Result of
Fig. 9a s
Multi-d
coasting, the
g. 7, is also o
gn variables
In common
he gross we
Additionally,
ight to the d
ost of the roc
Mpay/Mtot, ar
ctory constrai
ight altitude
of the 3rd sta
ngular mome
ter the combu
at the rocket r
ght path angl
ween ±5.0°.
traints for the
pect ratio of t
ameter of the
ea of the grai
at area of all s
and Discus
f ANOVA
hows the AN
to Fig. 7a,
important
A heavier pay
ne in the 1st
have to be ca
ent launch. Ac
he dominant
fluence Mtot. T
and oxidizer
f SOM
shows the S
isciplinary Co
e 3rd stage is
one of the des
and their ran
aerospace
eight of a ve
, in this study
drag weight
cket. Thus, to
re evaluated
ints assumed
is over 25
age;
entum is mor
ustion of the 3
reaches 800 k
le after comb
e structure are
the rocket is l
nozzle exit is
in port is mo
stages.
ssion
NOVA visu _ 2 0oxim& (dv9
parameters
yload can be
stage. Howe
arefully desig
ccording to F
effect on Mt
They determi
and that the
OM visualiz
onceptual DeUsing Data
s ignited. tcoas
ign variables
nges are liste
vehicle de
ehicle should
y, the ratio of
is offset by
otal weight, M
for knowle
are as follow
50 km after
re than 52,4
3rd stage in o
km at the apo
bustion of the
e as follows:
less than 20.0
s less than tha
re than twice
alization res
9) and _oxim&
for improv
launched wi
ever, the 2nd
gned to ensu
Fig. 7b, _oxim&
tot. tc_1 (dv5)
ine the total m
1st stage sho
zation result
esign Knowlea Mining Tec
st, as
s.
ed in
esign
d be
f the
y the
Mtot,
edge
ws:
the
13.5
order
ogee;
e 3rd
0;
at of
e the
sults.
3 0
ving
ith a
and
ure a
1 0 and
mass
ould
s as
Tab
are
d
d
d
d
d
d
d
d
d
dv
dv
dv
dv
dv
dv
dv
dv
dv
dv
dv
dv
dv
dv
dv
dv
Fig.
map
and
on
edge of Multi-hnique
ble 1 Design s
for 2nd stage a
Design var
dv1 1_oxim
dv2 O/F_
dv3 a_1(
dv4 Goxi_1(0
dv5 tc
dv6 Pch_1(
dv7 Ppt_1(0
dv8 ε_
dv9 2_oxim
v10 O/F_
v11 a_2(
v12 Goxi_2(0
v13 tc
v14 Pch_2(
v15 Ppt_2(0
v16 ε_
v17 03_oxim
v18 O/F_
v19 a_3(
v20 Goxi_3(0
v21 tc
v22 Pch_2(
v23 Ppt_2(0
v24 ε_
v25 tco
. 7 Flight of t
ps colored by
d objective fu
the similarity
-stage Hybrid
space (dv1-dv8
and dv17-dv25
riable
0 (kg/s)
F_1(0) (-)
(×10-3)
0) (kg/m2s)
c_1(s)
0) (MPa)
0) (MPa)
_1 (-)
0 (kg/s)
F_2(0) (-)
(×10-3)
0) (kg/m2s)
c_2 (s)
0) (MPa)
0) (MPa)
_2 (-)
0 (kg/s.)
F_3(0) (-)
(×10-3)
0) (kg/m2s)
c_3 (s)
0) (MPa)
0) (MPa)
_3 (-)
oast(s)
the designed ro
y each attribu
unctions), and
y in color pa
d Rocket
are for 1st sta
is for 3rd stag
Lower
50.0
2.0
0.39025
200.0
40.0
0.5
15.0
2.0
01.0 1_oxim
2.0
0.6244
10.0
tc_1 + 30.0
0.5
10.0
20.0
01.0 2_oxim
2.0
0.6244
10.0
tc_2 + 20.0
0.1
15.0
40.0
140.0
ocket.
ute value (des
d they are clu
atterns. Acco
7
age, dv9-dv16
ge).
Upper
150.0
3.0
1.0927
400.0
60.0
3.0
40.0
8.0
0)6/1( 1_oxim
3.0
1.561
200.0
tc_1 + 50.0
2.0
30.0
50.0
02.0 2_oxim
3.0
1.4049
120.0
tc_2 + 20.0
1.0
40.0
70.0
180.0
sign variables
ustered based
ording to the
7
s
d
e
8
maps, dv1 i
Mpay/Mtot. Th
related eac
ANOVA v
trained map
These maps
Fig. 8 Visua
Fig. 9 Visuaeach objective
Multi-d
is similar to
hese results s
ch other. Th
visualization
ps colored b
s show a trad
alization with A
alization by me function and
isciplinary Co
Mtot, and dv
suggest that t
his result a
results. Fig
by Mpay/Mtot,
deoff between
(a)
ANOVA: (a) se
eans SOM: (ad (c) SOM colo
onceptual DeUsing Data
v17 is simila
they are stron
agrees with
g. 9b comp
Mtot, and M
n the two de
ensitivity to Mp
) relationship red by selected
esign Knowlea Mining Tec
ar to
ngly
the
pares
Mpay.
esign
obje
Mpa
resu
obje
Mpay/Mtot and (b)
(a)
(b)
(c) among design
d design variab
edge of Multi-hnique
ectives. In ad
ay but did no
ult suggests
ective functio
) sensitivity to
n variables andbles.
-stage Hybrid
ddition, the S
ot always sho
that Mpay/Mt
on with regar
(b)
Mtot.
d objective fun
d Rocket
SOM unit sho
ow a high Mp
ot is a reason
rd to the rock
nctions; (b) SO
owed a heavy
Mpay/Mtot. This
nable design
ket efficiency
OM colored by
y
s
n
y
y
Multi-disciplinary Conceptual Design Knowledge of Multi-stage Hybrid Rocket Using Data Mining Technique
9
for a rocket to deliver a heavier payload. Fig. 9c
shows maps colored with design variables. Here, dv1,
dv5, Pch_1(0) (dv6), dv9, Pch_3(0) (dv14), and dv17
were selected according to the ANOVA results (Fig.
7) and correlation among attribute values (Fig. 8a)
According to Figs. 9b and 9c, dv5, dv6 and dv14
should be smaller, and dv9 and dv17 should be larger.
Remarkably, dv1 did not need to be maximized for the
design of an efficient LV (i.e., high Mpay/Mtot). Because
an excessively large or small dv1 does not allow for a
high Mpay/Mtot, it should be carefully determined.
6. Conclusions
In this study, knowledge discovery techniques were
used to discover the design knowledge for an LV with
an HRE that delivers micro-satellites to an SSO. The
launch vehicle performances (the flight, the weight
and the propulsion) were evaluated based on empirical
model. The evaluated functions were to the total mass
of the rocket, the maximum payload mass and to
maximize the ratio of the payload mass to the total
mass in terms of the cost. The results were visualized
by ANOVA and SOM. ANOVA result showed that
the oxidizer mass flow of every stage is very
important. The oxidizer mass flow at the 1st stage has
predominant effect to the vehicle total mass. On the
other hand, the oxidizer mass flow at the 2nd and 3rd
stages effective to the payload and total mass ratio.
SOM result suggested that a tradeoff between
Mpay/Mtot, and Mtot. In addition, the relationship among
design variables and evaluated performances could be
visualized.
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