multi-disciplinary conceptual design knowledge of multi

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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2

(multi-discip

includes a

evaluation o

and optimize

HRE using

design know

out by me

techniques f

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

a nozzle and

3 shows th

previous stu

Generally

Multi-d

plinary optim

technique fo

of the perform

ed several kin

a GA (gen

wledge discov

eans of sev

for a single-st

the develope

e design kno

(Fig. 2a), ca

ites, which u

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

performance

Section 3 de

owledge disc

nd SOM; Se

ction 5 show

f three-stage

nclusions.

mance Eval

y deals with t

mber, an oxidi

d a payload (F

he evaluation

udy [2].

y, the regressi

isciplinary Co

mization) m

or an empir

mance of a L

nds of launch

netic algorith

veries have b

veral knowl

tage sounding

d evaluation

owledge of a

an deliver 10

used for scien

sun-synchron

SO is a geoce

nclination in

ascends or de

h’s surface a

2b shows th

study. Paraffi

uel, LOX (li

, and the com

engine. T

n, an ANOV

visualize the

map) is emplo

nized as foll

e evaluation p

escribes meth

covery techn

ection 4 def

ws the results o

hybrid rocke

luation for

the LV of a t

izer tank, a p

Fig. 2b) that h

n procedure

ion rate in th

onceptual DeUsing Data

methodology

ical-model-b

LV with an H

h vehicles wit

hm). In addit

been also car

ledge discov

g rocket [3-5

method use

a three-stage

0.0-50.0 kg c

ntific observa

nous orbit) w

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

niques such

fines the de

of the knowle

et; and Sectio

LV with H

hree-stage ro

pressurizing t

has an HRE.

proposed in

e radial direc

esign Knowlea Mining Tec

that

ased

HRE,

th an

tion,

rried

very

]. In

ed to

LV

class

ation

which

which

that

any

local

f the

070)

n) is

e is a

the

s of

lem,

on 2

r LV

r the

h as

esign

edge

on 6

HRE

ocket

tank,

Fig.

the

ction

of t

E

Fig.widengi

Fig.studHRE

and

exp

HR

into

dete

oxid

writ

In

edge of Multi-hnique

the fuel is exp

Eq. (1) is emp

(a)

. 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

dizer with th

tten as:

por&

n this study,

-stage Hybrid

pressed as fol

atrport

pirically defi

tic illustrationthe space tranuid rocket eng

(a)

(b)

al illustration RE and (b) t

are genera

r fuels with a

d here suppl

(FT-0070) fue

m the experi

he WAX fuel

0.1561ort t

a swirling-o

d Rocket

llows:

tGa noxi

ined and the

(b)

ns of rocket nsportation: (agine.

of the LV conhe three-stage

ally decided

a single port

lies the swirl

el. a and n in

iment for a

[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

q. (1) can be

t (2)

HRE, which

)

a

h t

s n

e

e

r

e

g

e

)

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


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

ratio on i

evaluated.

3. MethoDiscovery

The optim

following st

by LHS (Lat

a space fill

construction

Second, AN

design varia

SOM is app

procedure is

3.1 ANOVA

ANOVA,

carried out t

design vari

from the gl

Multi-d

CD,S-520 with

ata presented

lly estimated

he rocket is a

10logDfC

Re

nolds numbe

gth. CDp is es

SD CC 520,

S-520 is obtain

20, and CDf,S-5

term of Eq

ained by addi

g.

designwet CSq ,

e pressure dr

eparately, the

its aerodyna

odologies f

mization proc

teps. First, N

tin hypercube

ling method,

n of an initi

NOVA is ap

ables to the

plied to visua

s illustrated in

, a method

to differentiat

ables to the

obal model.

isciplinary Co

h the Mach

d in Fig. 4 ha

d by assumin

flat plate [12

2.58

0.455

1 0.144M

er is calculat

timated as:

we

weSDf S

SC 520,

ned from the

520 is calculate

. (28) is CDf

ing the press

descroDf SC ,

rag and the

e effect of th

amic perfor

for Design

cedure design

N design sam

e sampling) [

, and then a

ial Kriging s

pplied to eva

objective fu

alize the desi

n Fig. 5.

for multivar

te the contrib

e variance o

Specifically,


number. In

as been used.

ng that the o

2].

0.652M

ed based on

designet

set

,

520,

e measured fl

ed using Eq.

f, design. The t

sure drag and

DpsignC

friction drag

e rocket’s as

rmance can

n Knowle

n consists of

mples are sele

[13, 14], whic

assessed for

surrogate mo

aluate effect

unctions. Fin

gn problem.

iate analyses

ution of diffe

of the respon

, to evaluate


this

. CDf

outer

(27)

n the

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flight

(27).

total

d the

(29)

g are

spect

be

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f the

ected

ch is

the

odel.

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The

s, is

erent

nses

e the

Fig.with

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Fig.

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. 3 Flowcharth an HRE [2].

. 4 Mach numhe solid rocket

. 5 Procedure

ntribution of e

the model

ibuted to eac

ween each

omplished b

del ŷ. The v

fined as:

( )i ix y

-stage Hybrid

t of the perfor

mber vs. CD, S-5

t S-520 [2, 11].

e of design kno

each design v

is decompo

ch design var

other. T

by integratin

variance of d

1 1ˆ( ,....., )d ,ny x x x

d Rocket

rmance evaluat

520 measured in

owledge discov

variable, the t

osed into t

riable and the

The decom

ng variables

design variab

1 1...,d ,d ,..,di ix x

5

tion of the LV

n the flight test

very.

total variance

the variance

e interactions

mposition is

out of the

ble xi to μ is

d nx (30)

5

V

t

e

e

s

s

e

s

)

6

where, the to

The prop

design varia

can be expre

The valu

sensitivity o

design varia

3.2 SOM

SOM [13-

projection a

space. This

a low-dimen

gird can be e

SOM. In th

more pleasin

Each neu

n-dimension

mkn), where

that is num

functions. T

represents a

nearest neur

found from

prototype ve

grid mk are m

where, α(t)

monotonical

6 is iterated

During th

also conver

original spa

neighboring

Thus, SOM

preserving

systematical

Multi-d

otal mean μ is

ˆ(y x portion of th

able xi to the

essed as:

ˆ (y xp

ue obtained

of an objective

able.

-16] is an uns

algorithm fro

projection is

nsional array

either hexago

is paper, the

ng to the eye.

uron k on th

nal prototype

n is the dim

mber of des

To train the

a sampling

ron mc (the b

the prototyp

ectors of the

moved toward

mk = mk

) is learnin

lly with time.

until α(t) is c

he iterative tr

rged. The clo

ace, the clo

neurons in

reduces the d

their featur

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s calculated a

1 1,..., )d ,..nx x x

he variance a

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by Eq. (32

e function to

supervised le

om high to l

based on sel

of neurons. T

onal or rectan

former is u

.

he map is re

e vector mk

mension of th

sign variable

map, input

design is s

best matchin

pe vectors o

mc and its n

ds X as follow

k + α(t)(X-mk)

ng rate an

. This process

converged we

raining, proto

oser two pat

ser is the r

n the low-di

dimension of

res. The tr

d into visual


as:

..,d nx

attributed to

nce of the m

nx

2) indicates

the variance

arning, nonli

low dimensi

lf-organizatio

The lattice of

ngular to gene

sed because

epresented by

= (mk1, mk2,

he design sp

es and objec

vector X w

selected and

ng unit, BMU

on the map.

neighbors on

ws:

)

nd it decre

s as shown in

ell.

otype vectors

tterns are in

response of

imensional m

f input data w

rained SOM

information,


(31)

the

model

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the

of a

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The

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Formulatio

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nagement can

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a three-stage

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ket is launch

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3rd stage co

stion of the 2n

e of SOM train

d Rocket

e obtained.

software mo

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analysis [16].

are revealed

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this map can

alues (that is,

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be compared

and it is not

s should be

n this study,

used together

Correlations

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mponent plane

matching is

good at. The

ven easier if

zed so that

ar each other.

HRE, which

apogee = 800

sumed flight

e south at an

immediately

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he oval orbit

ompleted.

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After this

shown in Fig

The desig

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problems, th

minimized.

payload we

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


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


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


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


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


ar to

ngly

the

pares

Mpay.

esign

obje

Mpa

resu

obje

Mpay/Mtot and (b)

(a)

(b)

(c) among design

d design variab


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


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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