This document summarizes research on the design optimization of a launch vehicle concept using a clustered hybrid rocket engine for future space transportation. The researchers developed a design methodology for a launch vehicle with clustered hybrid rocket engines and investigated combinations of unit engines. Their objectives were to maximize payload to gross weight ratio and minimize gross weight. They defined four design cases and used multi-objective genetic algorithms and data visualization techniques to optimize the design variables. The results showed that a design with optimized engines for each stage performed best by avoiding excess unburnt fuel from shared engines across stages. Future work could further reduce unburnt fuel and improve payload ratio.

1. Design Optimization of Launch
Vehicle Concept Using
Cluster Hybrid Rocket Engine for
Future Space Transportation
Shoma Ito (Tokyo Metropolitan University)
Fumio Kanamori (Tokyo Metropolitan University)
Masaki Nakamiya (Kyoto University)
Koki Kitagawa (ISAS/JAXA)
Masahiro Kanazaki (Tokyo Metropolitan University)
Toru Shimada (ISAS/JAXA)
1OS8:Flow Dynamics and Combustion in Hybrid Rockets
OS 8-9 2014 Eleventh International Conference on Flow Dynamics
October 8-10. Sendai, Japan

2. Contents
• Background
• Objectives
• Rocket Configuration and Structure
• Design and Evaluation Methods
• Problem Definition
• Results
• Conclusions
2

3. Background
Advantage of hybrid
rocket engine(HRE)
 Higher safety
 Lower cost
 Lower environmental
impact
Hybrid rocket has possibility
to be next generation
efficient launch vehicle.
Space ship two※1
※1,VirginGalactic http://www.virgingalactic.com/
※2, [1] Y. Kitagawa, K. Kitagawa, M. Nakamiya, M. Kanazaki, T.
Shimada, T JSASS, 55(2012), R4
3
Our previous research※2
 Development of multi-
disciplinary design methodology
 Optimization for single stage and
three stage launch vehicle

4. Background
Cluster rocket
 Installed several unit engines in a stage for
sufficient thrust.
4
Hybrid Launcher※3
Soyuz※2 (using liquid engine)
※2 Wikipedia
http://ja.wikipedia.org/wiki/%E3%82%BD%E3%83%A6%E3%83%BC%E3%82%BA#mediaviewer/File:Soyu
z_tma-3_transported_to_launch_pad.jpg
※3 ANTARES Hybridtaken e.V. http://www.hybridraketen.de/Homepage/antares.html

5. Advantage of Cluster Rocket
Cluster rocket
 Advantage
 High thrust without enhance the cost.
 Disadvantage
 Increase the weight due to remain unburnt fuel.
 Difficulty of simulations control of unit engines.
Single engine rocket
 Limitation of total thrust.
5

6. Objectives
Design Optimization of Launch
Vehicle (LV) Concept Using Three
Stage Clustered Hybrid Rocket (HRE)
6
 Development design methodology for LV with
clustered HRE
 Investigation of the combination of the unit
engine

7. Rocket Configuration and Structure
7

8. Fuel Design
Regression rate rport is calculated by
n
tport Gatr ][)( )(0
8
.
.
Radius of fuel is calculated by rport and tb
(tb is design variables) .
G0(t) Oxidizer mass flux
a Fixed number decided by kind of fuel
n
β Simulating fuel circling
.

9. Configuration of Engines on 1st Stage
In 1st stage, eight engines are installed.
9

10. Configuration of Engines on 2nd Stage
In 2nd stage, two engines are installed.
10

11. Cluster Rocket Design Method
Evaluation of rocket radius
Radius of 2nd and 3rd stage exterior wall is equal to
radius of 2nd stage.
Radius of 1st stage is calculated independently.
11
Kind of fuel and oxidizer: Fuel…FT0070 Oxidizer…O2
FT0070
spec
Chemical formula Density[kg/m3] Index n Coefficient a
C35H72 910.0 0.3905 0.1561
n
tport Gatr ][)( )(0

12. Overview of Evaluation and
Optimization Method
12

13. Optimization Method
• Multi-objective Genetic Algorithm(MOGA)
Search non-dominated solutions based on
global explorations .
GA Flow
13

14. Data Mining Method
Parallel Coordinate Plot (PCP)
• One of the statistical visualization techniques from
high-dimensional data into two dimensional graph.
• Normalized design variables and objective functions
by upper bound and lower bound of design space.
• One design is expressed as a line in this graph.
0.0
0.2
0.4
0.6
0.8
1.0
dv1 dv2 dv3 dv4 dv5 H W L/D
Design variable or objective function name
Normalizedvalues
ilowerboundiupperbound
ilowerboundi
xx
xx
Xi
,,
,



14

15. Rocket Design Method 15

16. Problem Definition
16

17. Problem Definition
Objective functions
Maximize payload to gross weight ratio(Mpay/Mtot)
Minimize gross weight(Mtot)
 Constraints
After 3rd stage combustion
• Height ≧ 250km
• Angular momentum ≧ 52413.5km2/s
• 0.5deg ≧ Flight path angle ≧-0.5deg
On 1st and 2nd stage
• (Atmospheric pressure)×4 ≦ Pressure of nozzle exit
when start burning
• Radius of nozzle exit ≦ Radius of engine
Rocket aspect ratio ≦ 20
(Area of nozzle throat)×2 ≦ Area of grain port
Radius of 3rd stage nozzle exit ≦ Radius of 2nd stage
exterior wall
17
On the assumption that launch
the super micro satellite

18. Design Cases
Definition of four design cases.
Shared engines have same chamber. Nozzle size and burning time
are defined for each stages.
 Case1: Employment of optimized engines for all stage Cluster
rocket
 Case2: Employment of shared engines for 1st and 2nd stage
Cluster rocket
 Case3: Employment of shared engines for all stage Cluster rocket
 Non-clustered rocket(Non-clustered rocket)
18
 The shared engine is designed by 1st stage design variables.

19. Result
19

20. Result of Design Optimization
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0
Mtot/Mpay[%]
Mtot[ton]
Case1 Case2 Case3 Non-clustered rocket
 Trade off can be shown between two objective functions in each case.
 Case1 show similar result as non-clustered case.
 Case3 which employs same shared engine for each stage achieves
less than half performance compared with Case1.
 Unburnt fuel is appeared when one engine design is shared in
two or three stages.
Optimum
Direction
20
Des1 Des0
Des2
Des3
Mpay=100[kg]

21. Comparison from Pareto Solutions
 Des1 has slender engines.
 Des1 and Des2 use small engine in 3rd stage.
↔ Des3 uses largest engine in 3rd stage.
21
Length Radius
18.46[m] 0.60[m]
Length Radius
21.62[m] 0.59[m]
Length Radius(1st) Radius(2nd)
16.64[m] 1.42[m] 0.79[m]
Length Radius(1st) Radius(2nd)
14.83[m] 1.22[m] 0.68[m]
Des0
Des1
Des3
Des2

22. Comparison of Payload 100kg Rocket(PCP)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
mo1
O/F1
a1
Go1
tb1
Pc1
Ppt1
ε1
Des1 Des2 Des3
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
mo2
O/F2
a2
Go2
tb2
Pc2
Ppt2
ε2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
mo3
O/F3
a3
Go3
tb3
Pc3
Ppt3
ε3
 For 1st stage, mo1 is small
in each case.
 For 2nd stage, O/F2 of Des3
is the highest. Sufficient
thrust is small, so fuel
become less.
 For 3rd stage, tb3 of Des3 is
small while mo3 is the
highest.1st Stage
2nd Stage 3rd Stage
22

23. Comparison of time history of engine thrust per an engine
23Comparison of payload 100kg Rocket(Thrust)
Unit engine thrust
= Total thrust by each stage/Number of engines in a stage
 1st stage thrust is
influenced by total mass
and drag. Des3 has big
total mass and drag, so it
has the highest thrust.
 Des0, Des1 and Des2 show
similar result in 3rd stage,
because these cases
optimized engine only for
3rd stage.

24. Comparison of payload 100kg Rocket(Isp) 24
220
230
240
250
260
270
280
290
300
310
320
0 50 100 150 200 250 300 350 400 450
Isp[s]
Time[s]
 While Des3 achieves the highest thrust in all stage, Isp of
3rd stage is the lowest.
 Engines of Des3 are not only optimized for 3rd stage.
 2nd stage of Des1 achieves the lowest Isp.
 The efficiency is limited because the radius of 1st stage is
small.

25. Comparison of Payload 100kg Rocket(Altitude)25
 Des3 achieves high
acceleration at low altitude.
 Des3 achieves high
thrust in 1st and 2nd
stage.
 Des3 has the shortest flying
time.
 Des3 become heavy by
using shared engines.
Optimized to rise quickly.
 Des0 and Des1 have long
coasting time.

26. Comparison of Payload 100kg Rocket(Numerical Value)
Mtot
[ton]
Mpay/Mtot
[%]
Des1 9.31 1.10
Des2 13.3 0.75
Des3 15.5 0.64
 Payload ratio of Des3 is 0.5% less than Des1.
 Because of unburnt fuel, total mass of Des3 become heavy.
Fuel Filling Ratio
1st stage 2nd stage 3rd stage
Des1 63[%] 80[%] 93[%]
Des2 86[%] 86[%] 88[%]
Des3 84[%] 84[%] 84[%]
 Fuel filling ratio of Des1 is the smallest in 1st stage.
 Des1 has slender engines to reduce aerodynamic drag.
 Fuel filling ratio of Des2 and Des3 are high.
 Because of the appearance of the unburnt fuel, payload
ratio of Des2 and 3 becomes lower than Des1.
 It is also required to reduce unburnt fuel.
→(Future work)Addition of objective function objective function:
Minimize unburnt fuel
26
Fuel Filling Ratio=Area of fuel/Area of chamber

27. Conclusions
Optimization of LV using clustered HRE was
carried out.
 Development of the clustered LV evaluation
using HRE.
Investigate of the LV performance using shared
endings. Three cases are compared.
In case of design of shared engine for one stage,
the non-dominated front is the best among three
cases.
Because of the unburnt fuel is not appeared.
Installation of the shared engine for two or three
stages, the unburnt fuel is appeared.
27
Future Work
 To generate high payload ratio cluster rocket,
reconsider the design method of engine.

28. Thank you for listening
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