Roll Amplification Of Solid Rocket... (O. Sudiana dan P. Teofilatto)

ROLL AMPLIFICATION OF SOLID ROCKET MOTOR IN LAPAN
SOUNDING ROCKET
(AMPLIFIKASI PUTAR GULING MOTOR ROKET PADAT DI ROKET
SONDA LAPAN)
O. Sudiana1, P. Teofilatto2
1Rocket Technology Center, LAPAN
2School of Aerospace Engineering, Sapienza University of Rome
1e-mail: sudiana.oka@gmail.com

Diterima : 6 Juni 2020; Direvisi : 16 Juni 2020; Disetujui : 20 Juli 2020

ABSTRAK
Roket sonda telah digunakan untuk penelitian ilmiah, dan di implementasikan dalam
meteorologi dan studi atmosfer lapisan atas sejak akhir 1950-an. Roket sonda membawa muatan suborbital yang mengikuti lintasan terbang parabola dari peluncuran hingga pendaratan. Mendukung peta
jalan pengembangan roket Peluncur Satelit, LAPAN telah meluncurkan Program roket sonda.
Amplifikasi putar guling dari hasil produksi kecepatan putar yang tidak terduga terdeteksi selama
dorongan dari roket sonda, meskipun sirip roket sayap dalam konfigurasi salib. Salah satu fenomena
ini dapat dipengaruhi oleh aliran gas pada ruang pembakaran selama waktu pembakaran. Ide dasar
dari penelitian ini adalah untuk memodelkan amplifikasi putar guling sebagai efek gerakan berputarputar

dari

bagian

gas

buang

yang

berpartisipasi

dalam

dinamika

rotasi

dari roket dibandingkan dengan mengalir keluar langsung dari ruang bakar. Data penerbangan tersedia
diperoleh dari hasil tes terbang terakhir tersaji. Data tersebut menunjukkan adanya amplifikasi putar
guling yang signifikan ketika motor roket padat digunakan selama waktu pembakaran. Hasil pemodelan
memiliki pendekatan yang baik bahwa Kehadiran bagian gas buang mempengaruhi amplifikasi putar
guling yang tidak terduga.
Kata kunci: Roket sonda, motor roket padat, amplifikasi putar guling

ABSTRACT
Sounding rockets have been used for scientific research and implemented in meteorological and
upper atmosphere studies since the late 1950s. Sounding rockets are sub-orbital carriers that follow a
parabolic trajectory from launch to landing. Supporting the roadmap of Satellite Launch Vehicle
development, LAPAN had launched The Sounding Rocket Program. A roll amplification of the
unpredicted roll rate production was detected during the boost of the sounding rocket, despite the tail
wings in cruciform configuration. One of this phenomenon can be influenced by the flow field of the
combustion chamber during the boosting time. The basic idea of this research is to model the roll
amplification effect as a swirling motion of exhaust gas portion that participate to the rotation dynamics
of the rocket rather than immediately flow to the combustion chamber. Available flight data where is
obtained from the last flight test presented. It showed the presence of a significant roll amplification
when solid rocket motor is used during the burning time. The result has a good agreement that the
presence of the exhaust gas portion influences the unpredicted roll amplification.
Keywords: Sounding rocket, solid rocket motor, roll amplification.

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Jurnal Teknologi Dirgantara Vol. 18 No. 1 Juni 2020 : hal 63 - 72

NOMENCLATURES
𝜌"

Exhaust gas density

𝜌#

Propellant density

𝜌$%&'

Solid Rocket Motor case
density

𝐿#

Propellant length

𝛬

Propellant-exhaust gas
density ratio

𝜔+

Initial angular velocity

𝜔

Angular velocity at time 𝑡

𝜀

Propellant participatory

𝑟

Radius of propellant at time
𝑡

𝑟+

Inner radius of propellant

𝑟'/0

Outer radius of propellant

𝑟1

Radius of case

∆𝑟

Thickness of case

𝐼+

Moment of inertia of initial
propellant

𝐼$%&'

Moment of inertia of case

𝐼#
𝐼"
1

Moment of inertia of
propellant at time 𝑡
Moment of inertia of
exhaust gas at time 𝑡

INTRODUCTION
(Heru, 2013) wrote that based on the
Decree of the Head of the National
Institute of Aeronautics and Space
(LAPAN) Number: 2 of 2011 concerning
the organization and work procedures
within
the
National
Institute
of
Aeronautics and Space. The Deputy of
Aeronautics and Space Technology
responsible
for
carrying
out
the
formulation and implementation of
policies in the field of aerospace
technology. The National Institute of
Aeronautics and Space (LAPAN) priority
programs as presented by the chairman
of LAPAN are development of Satellite
Launch Vehicle (SLV) and rocket
propellant raw material. These priority

64

programs
are
under
the
rocket
technology center.
According to (Hardhienata, 2008),
Fabrication and ground test of SLV will be
planned in the near future, and hopefully
it will launch at orbital flight phase.
Failure in recent flight test allegedly was
caused by lack of design, quality of
fabrication, and the use of ballistic rocket
type to launch.
Along with the development process of
the sounding rocket program, some
failures occurred in both static test and
flight tests. In addition, the claims for
highly flight distances and apogee are too
early and have not been proven by
comparing the results of calculations
with actual flight tests.
The
attitude
and
dynamics
determination of the sounding rocket
along flight trajectory has not been
revealed before. Although it has passive
stability when it flies, it is difficult to
know the dynamics of sounding rocket
behavior either in the ideal flight or in the
anomalies (failures) flight trajectory.
However, a successful launch was
verified on the flight test in December
2017. The sensitive amplification of the
unpredicted roll rate production was
detected during the boost of the sounding
rocket.
This amplification also had been
observed by (Stella, 2012). He wrote that
during the launch of Mu-V, a Japan solidpropellant rocket system, roll torque was
observed in all launches. The strength of
the torque is typically very large
immediately soon after the launch. Since
many modern launchers, such as VEGA
and ARES, European Launch Vehicle, are
designed with solid rocket motor at first
stage.
(Stella, 2012) also described that the
phenomenon of roll amplification cannot
be ignored since it repeats in the flight
test. Moreover, the problem of the roll
torque production cannot be neglected

Roll Amplification Of Solid Rocket... (O. Sudiana dan P. Teofilatto)

because many modern launchers are
designed with a solid rocket motor as
theirfirst stage. The presence of roll
amplification is usually stronger during
the initial phase of flight.
2

ROLL
AMPLIFICATION
MECHANISM
(Waesche, & Summerfield, 1965) did
the research in the solid combustion
chamber. They found that the major
unsolved problems in the field of solid
propellant rockets is the phenomenon of
combustion instability. This instability
phenomenon
can
be
found
in
encountered
source
of
the
selfamplification of a disturbance, the
dynamic coupling of the oscillatory
pressure field, and the combustion zone
near the surface.
The result in Figure 2-1 has been
done by (Di Mascio, et.al. 2014) showed

the X-vorticity field in four different
transversal planes (YZ) along the SRM
axis,
together
with
the
relevant
streamlines in the YZ planes. The
presence of two counter-rotating shear
layer structures aligned with the SRM
axis that are responsible for the
fluctuations of the flow field.
(Flandro, 1964) report that mentioned
by (Stella, 2012) showed star-shaped
cavities are capable of producing several
levels of the roll amplification, depending
upon the number of star-points. About
concerning roll amplification generation,
(Stella, 2012) took historical data
reported from (Knauber, 1996) where star
grain or finned type grain motors are the
best candidates to produce the significant
roll amplification.

Figure 2-1: Vorticity of combustion and exhaust gas YZ Streamlines flow patterns
(Di Mascio, A., et.al. 2014)

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3

THE COMPUTATIONS OF PREDICT
ROLL AMPLIFICATION
The basic idea is to model the roll
amplification effect as a swirling motion
of gas portion that participate to the
rotation dynamics of the rocket (Figure 31.b) rather than the gas was immediately
exit the combustion chamber (Figure 31.a and Figure 3-1.c)

Figure 3-2: Propellant grain dimension
𝐼+ is the moment of inertia. While
burning, the moment of inertia 𝐼+ looses.
The hollow cylinder of propellant has
internal radius 𝑟>? and external radius
𝑟'/ .
The moment of inertia of propellant
equation can be obtain as:
Figure 3-1: Gas
portion
flows
combustion chamber

the

If the external forces are zero, so that:
d
Iω = 0
dt

(3-1)

The Eq. (3-1) above can be written as:
d Iω = dI. ω + I. dω
(3-2)

(3-3)

At time 𝑡 = 0, is before propulsion
burning 𝑟 0 = 𝑟+ . And then at time 𝑡, the
radius of the cylinder of the propellant
grain is 𝑟 𝑡 = 𝑟. The moment of inertia of
the engine (case+grain) is the one of a
hollow cylinder of radii 𝑟1 + ∆𝑟 and 𝑟+ ,
where ∆𝑟 is the thickness of the case.

66

1
C
𝑚 𝑟 C + 𝑟>?
2 # '/

(3-4)

Since the propellant mass is consist of
component mass density 𝜌 and volume 𝑉,
it can be obtain as:
𝐼# =

1
F
𝜋𝜌 𝐿 𝑟 F − 𝑟>?
2 # # '/

(3-5)

when 𝜌# is the propellant density and
𝐿# is the length of cylinder.

Then, it has to evaluate:
dI = I t + dt − I t

𝐼# =

This portion of propellant becomes
gas leaving the combustion chamber
through the nozzle. Suppose that a
portion of such gas does not leave the
grain
surface
immediately,
but
participate to the rotation of the rocket as
if it is an added “rigid body” attached to
the unburned grain. it must add the
moment of this portion of gas to the
rocket moment of motion.

Roll Amplification Of Solid Rocket... (O. Sudiana dan P. Teofilatto)

The hypothesis is that the gas portion
of the propellant participates to the
rotational motion is equal to ε.
Parameterε can be calculated from the
case boundary as the following figure:

Figure 3-3: Propellant participatory

Now:
dI = I t + dt − I t
dI =

(3-12)

∂I
dr
∂r

(3-13)

1
dI = − πρL LK 4r P Λ − 1
2
+ 4 r − ε P dr

(3-14)

dI = −2πρL LK r P Λ − 1

(3-15)

+ r−ε
Then, if 𝑟 > 𝜀. It must have to add the
hollow cylinder of gas:
𝐼" =

1
𝜋𝜌 𝐿 𝑟 F − 𝑟 − 𝜀 F
2 " #

P

dr

Then substitute the Eq. (3-11) and (315) into Eq. (3-2), it can be obtained as:

(3-6)
d Iω = −2πρL LK r P Λ − 1 +
H

where, 𝜌" is the density of exhaust
gas.
Summing up all moment of inertia in
rocket motor:
𝐼 𝑡 = 𝐼+ − 𝐼# + 𝐼"

(3-7)

H

F
𝐼 𝑡 = 𝐼+ − 𝜋𝜌# 𝐿# 𝑟 F − 𝑟>?
+
C

H
C

𝜀

(3-8)

F

𝜋𝜌" 𝐿# 𝑟 − 𝑟 −

r − ε P ωd + I+ − πρL LK r F Λ −
C

(3-16)

F
1 + ΛrTU
+ r − ε F dω

To take into account that the gas
participating to the rocket rotation after a
while leaves the combustion chamber,
the first term:
2𝜋𝜌" 𝐿# 𝛬𝑟 − 𝜀 𝑟 + 𝑑𝑟 − 𝜀 C 𝜔𝑑𝑟
Must be included in the balance up to
𝑑𝑟 , this term is equal to:
2𝜋𝜌" 𝐿# 𝛬𝑟 − 𝜀 𝑟 − 𝜀 C 𝜔𝑑𝑟

F

C

𝜌# F
1
𝐼 𝑡 = 𝐼+ − 𝜋𝜌" 𝐿#
𝑟 − 𝑟F
2
𝜌"
𝜌# F
+
𝑟
𝜌" >?

(3-9)

Adding all the term, it becomes as:
2πρL LK

Λr − ε r − ε C

− r P Λ − 1 + r − ε P ωdr

+ 𝑟−𝜀 F

+ I+
1
F
− πρL LK r F Λ − 1 + ΛrTU
2

Introducing:
Λ=

ρK kg
mP
ρL

(3-10)

+ r − ε F dω = 0

(3-17)

Considering the ∗ term in 𝜔𝑑𝑟:
Substitute the Eq. (3-10) into Eq. (39), can be written as:
1
I t = I+ − πρL LK r F Λ − 1
2
F
+ ΛrTU
r−ε F

(3-11)

Λr − ε r − ε C
− rP Λ − 1 + r − ε P
= Λ − 1 εC r − 2εr C

(3-18)

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Jurnal Teknologi Dirgantara Vol. 18 No. 1 Juni 2020 : hal 63 - 72

Then, substitute the ∗ term in 𝜔𝑑𝑟
which is described above to theEq. (3-17),
can be written as:
2πρL LK Λ − 1 εC r
− 2εr C ωdr
+ I+
1
F
− πρL LK r F Λ − 1 + ΛrTU
2

(3-19)

Then the Eq. (3-19) can be written as:
2𝜋𝜌" 𝐿# 𝛬 − 1 2𝜀𝑟 C − 𝜀 C 𝑟 𝜔𝑑𝑟 =
H

F
𝐼+ − 𝜋𝜌" 𝐿# 𝑟 F 𝛬 − 1 + 𝛬𝑟>?
+ 𝑟 − 𝜀 F 𝑑𝜔
\

1

= 2πρL LK Λ −
C]^_ `]_ ^
c
ab ` def gh ^i j`H kj^ilm k ^`] i
_

\b

1

C]^_ `]_ ^

^
^b ab `cdef gh ^i j`H kj^i k ^`] i
_

dr (3-20)

Integrating the Eq. (3-20), will be
obtained as:

dr

lm

RESULT AND ANALYSIS
The results from the data recording
on the sounding rocket flight test, in
spite of flying without any problems, an
anomaly occurred on the gyroscope
readings can be seen in Figure 4-1
It appears in Figure 4-1 that roll rate
increases significantly in negative value
until the peak when burning end and
then headed to equilibrium even though
it still rolling occurs during the flight.
A temporary hypothesis of an
amplitude waves occur in the combustion
chamber during propellant combustion.
The gas portion around the combustion
chamber may affect tothe rotational
motion of the rocket.

Figure 4-1: Gyroscope readings in flight test (Salman, 2017)

68

(3-21)

= 2πρL LK Λ −

4

+ r − ε F dω = 0

C
[\

nU \

Roll Amplification Of Solid Rocket... (O. Sudiana dan P. Teofilatto)

The geometrical dimensions and
properties of the solid rocket motor are
taken
in
this
roll
amplification
calculation, as follows:

Table 4-2: EXHAUST GAS PROPERTIES
(Cai, Thakre, & Yang, 2008)
Gas properties

Figure 4-2: Propellant grain dimension
(Badi and M.H. Aulia, 2015)
Table 4-1: PROPELLANT GEOMETRY
AND PROPERTIES (Badi and Aulia,
2015; Wibowo, 2018)
Propellant length

𝐿# = 3.7 𝑚

Propellant external

𝑟'/ = 0.216 𝑚

radius
Propellant av. Internal

𝑟>? = 0.083 𝑚

radius
Propellant grain

𝜌# = 1635 𝑘𝑔 𝑚P

density

The result of Solid Rocket Motor
combustion in the combustion chamber
produces the exhaust gas with the
following contents:

Mol/100g

𝐶𝑂C (𝐶𝑎𝑟𝑏𝑜𝑛𝐷𝑖𝑜𝑥𝑖𝑑𝑒)

0.83

𝐶𝑂 (𝐶𝑎𝑟𝑏𝑜𝑛𝑀𝑜𝑛𝑜𝑥𝑖𝑑𝑒)

0.88

𝐻C 𝑂 (𝑤𝑎𝑡𝑒𝑟)

0.37

𝐻𝐶𝑙 (𝐻𝑦𝑑𝑟𝑜𝑔𝑒𝑛𝐶ℎ𝑙𝑜𝑟𝑖𝑑𝑒)

0.58

𝐻C (𝐻𝑦𝑑𝑟𝑜𝑔𝑒𝑛)

1.17

𝑁C (𝑁𝑖𝑡𝑟𝑜𝑔𝑒𝑛)

0.29

𝐴𝑙C 𝑂P (𝐴𝑙𝑢𝑚𝑖𝑛𝑖𝑢𝑚𝑂𝑥𝑖𝑑𝑒)

0.35

At Combustion Pressure = 7MPa;
Combustion Temperature = 3533 K
From Figure 4-1, it shows that the
rocket has a prefix roll on 45 degrees
which triggers amplification. The rocket
is rolling until it reaches a roll rate peak
of 330 deg/sec, more than 7 times from
the initial roll. Afterwards, the rocket is
experiencing a slowdown until it reaches
equilibrium with an average roll rate on
240 deg/sec.
According to the model in numerical
simulation, we get a factor slightly to 7
times of initial roll rate. In fact,the
experience in previous flight test reveals
thefactor was closely to 7.5 times.
The model considers a cylindrical slot
in the grain geometry to simplify
thenumerical simulation, instead of starshaped slot geometry which was used on
the actual rocket shown in Figure 4-2.
However, according to numerical test
that had been done by (Stella, 2012), the
geometry of the grain is rather important.
For instance, the different geometry of the
grain in Stella has produced very different
result. Figure 4-4 and Figure 4-5 depict
the result that the higher ratio of the
propellant slot the higher roll torque.

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Figure 4-3: Roll amplification rasio

Figure 4-4: Ratio of propellant slot (Stella, 2012)

70

Roll Amplification Of Solid Rocket... (O. Sudiana dan P. Teofilatto)

Figure 4-5: Roll torque as a function of slot aspect ratio (Stella, 2012)
Summarizing, numerical simulation
models and experimental tests can
improve the understanding of the roll
anomaly and suggest solutions in next
future.
5

CONCLUSIONS
The computation and analysis results
of roll amplification outline are able to
describe the events in the rocket motor
combustion chamber during the flight
test.
Star-shaped cavities are capable of
producing
several
levels
of
roll
amplification, depending upon the
number of star-points. The model
considers cylindrical slot in the grain
geometry to simplify the numerical
simulation, instead of star-shaped slot
geometry. However, the geometry of the
grain is rather important. The different
geometry of the grain produces very
different result. Higher ratio of propellant
slot increased the roll torque higher.
The numerical simulation result
isclosely enough to represent roll

amplification on the experiment flight test
and may predict the roll amplification
since the production of sounding rocket
may use similar treatment.
The analysis result can help in
designing of future solid rockets and
advanced control systems to overcome
these problems. Numerical models and
experimental tests can improve the
understanding of the roll anomaly and
suggest solutions in next future.
ACKNOWLEDGEMENTS
Foremost, I would like to express my
sincere gratitude to Prof. Paolo Teofilatto
and co-supervisor Stefano Carletta, PhD
cand. for the continuous support of my
research, for their patience, motivation,
enthusiasm, and immense knowledge.
Their guidance helped me in all the time
of research and academic. Special thanks
addressed to Kemenristekdikti through
RisetPRO program for financial support
in doing this research. Also thanks to
Rocket
Technology
Center,
LAPAN
Indonesia which has provided supporting
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Jurnal Teknologi Dirgantara Vol. 18 No. 1 Juni 2020 : hal 63 - 72

data for my research, which is very useful
for completing the research.
CONTRIBUTORSHIP STATEMENTS
O. Sudiana is the main contributor
and do the numerical simulation analysis
in this research, while P. Teofilatto
contributes to a mission analysis.
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