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Design and De elopmen o a Mo phing-Fin Hyb id Rocke -
Powe ed Loi e ing In e cep o o Su ace- o-Ai Missile
RAHUL.E , SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY,
AJAYKUMAR.A.M , SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY,
MADHANKUMAR.G , SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY
Abs ac
The inc easing p e alence o agile and low-signa u e ae ial h ea s,
such as Unmanned Ae ial Vehicles (UAVs), necessi a es he
de elopmen o ad anced and lexible ai de ense sys ems.
Con en ional Su ace- o-Ai Missiles (SAMs) a e o en limi ed by
sho engagemen imes, while exis ing loi e ing muni ions lack he
high-ene gy pe o mance equi ed o ce ain in e cep scena ios.
This pape p esen s he concep ual design and c i ical analysis o a
no el loi e ing in e cep o ha syne gis ically in eg a es a h o leable
hyb id ocke p opulsion sys em wi h a mission-adap i e ai ame
ea u ing mo phing ins. The me hodology in ol es he heo e ical
design o a GOX/HTPB-based hyb id mo o capable o ope a ing in
bo h high- h us boos (50 N) and low- h us loi e (5 N) modes.
Compu a ional Fluid Dynamics (CFD) is used o e alua e he
ae odynamic pe o mance o he missile in bo h s owed and deployed
in con igu a ions, con i ming he ae odynamic easibili y o a low-
speed loi e phase. This pape ex ends he concep ual design by
conduc ing a c i ical analysis o he key echnical challenges,
including p opulsion con ol and s abili y, ae o-s uc u al dynamics,
and he o midable guidance and con ol p oblem p esen ed by he
mo phing ansi ion.
Keywo ds: Loi e ing Muni ion, Hyb id Rocke , Mo phing
Ae odynamics, Su ace- o-Ai Missile, UAV, Guidance and Con ol,
Ae o-s uc u al Dynamics.
I. In oduc ion
The p oli e a ion o small, agile, and low-cos Unmanned Ae ial
Vehicles (UAVs) p esen s a signi ican and e ol ing challenge o
mode n ai de ense in as uc u e.1These sys ems can be employed
o in elligence, su eillance, and econnaissance (ISR) o as di ec -
a ack pla o ms, o en in sa u a ing swa ms ha can o e whelm
con en ional de enses. This wo k is mo i a ed by he need o a
e sa ile and cos -e ec i e coun e measu e ha can b idge he
capabili y gap be ween adi ional high-speed, sho -endu ance
missile sys ems and slowe , p opelle -d i en loi e ing muni ions.2
This pape p esen s an in eg a ed concep ual design o a mul i- ole
in e cep o ha syne gizes wo ad anced echnologies: h o leable
hyb id ocke p opulsion and mo phing ae odynamics. This
combina ion, no widely explo ed o SAM applica ions, aims o
p o ide a single pla o m capable o apid boos , e icien loi e , and
high-ene gy e minal in e cep . The objec i e o his pape is wo old:
i s , o p esen he concep ual design and p elimina y pe o mance
analysis o he key subsys ems; and second, o conduc a c i ical
echnical assessmen o he concep 's iabili y, iden i ying he
p ima y enginee ing challenges and isks ha mus be o e come. The
ollowing sec ions de ail he sys em's a chi ec u e and ope a ional
concep , desc ibe he design me hodology o he p opulsion and
ae odynamic subsys ems, c i ically analyze he in eg a ed sys em
dynamics and con ol challenges, and conclude wi h a summa y o
indings and a p io i ized oadmap o u u e esea ch.
II. Sys em A chi ec u e and Ope a ional
Concep :
a) Sys em A chi ec u e
The p oposed sys em is a mul i-phase in e cep o designed o
su ace- o-ai engagemen s. The a chi ec u e in eg a es a cen al
ligh compu e wi h a Guidance, Na iga ion, and Con ol (GNC)
package, a communica ions da alink, a payload consis ing o an
elec o-op ical/in a ed (EO/IR) seeke , a h o leable hyb id ocke
mo o , and a mo phing in assembly.
b) Concep o Ope a ions (CONOPS)
The CONOPS is en isioned in h ee dis inc phases:
1. Boos Phase: Upon launch, he hyb id ocke ope a es a
maximum h us o apid accele a ion and al i ude gain,
minimizing he ime o each he ope a ional a ea.
2. Loi e Phase: Once in he designa ed pa ol a ea, he mo o is
h o led down o a minimal h us le el. The mo phing ins a e
deployed o maximize he li - o-d ag a io, enabling he
ehicle o pa ol e icien ly while sea ching o a ge s.
3. In e cep Phase: Upon a ge acquisi ion and designa ion, he
ins a e e ac ed, and he mo o is h o led back o maximum
h us o a high-ene gy e minal in e cep ,maximizing kine ic
ene gy upon impac .
c) S a egic Analysis: A High-Signa u e Solu ion o
a Low-Signa u e P oblem
A c i ical e alua ion o he CONOPS e eals a po en ial s a egic
law. The p ima y a ge s a e "low-signa u e" UAVs, and a key
ad an age o exis ing elec ic-powe ed loi e ing muni ions is hei
own low acous ic and he mal signa u e, enabling co e ope a ions.5
The p oposed hyb id ocke , e en when h o led down, in ol es
con inuous combus ion, p oducing a signi ican and pe sis en
he mal signa u e. This c ea es a signa u e misma ch, whe e a high-
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signa u e in e cep o is asked wi h co e ly engaging low-signa u e
h ea s. This could comp omise he in e cep o 's su i abili y and
be ay he loca ion o he launch uni , a undamen al isk ha mus be
conside ed in he sys em's ac ical employmen .
III. Concep ual Design and Pe o mance
Ta ge s
The p opulsion sys em is a h o leable hyb id ocke mo o using
Gaseous Oxygen (GOX) as he oxidize and Hyd oxyl- e mina ed
Polybu adiene (HTPB) as he solid uel. This combina ion is chosen
o i s sa e y, en i onmen al iendliness, and pe o mance
cha ac e is ics. The uel eg ession a e is modeled using he s anda d
empi ical powe -law ela ionship 6:
�=�����
��(1)
The a ge pe o mance speci ica ions o he mo o a e summa ized
in Table 1. These alues a e conside ed plausible o a small-scale
expe imen al sys em, wi h he speci ic impulse o 190 s being a
ealis ic, albei modes , es ima e o a GOX/HTPB sys em accoun ing
o eal-wo ld combus ion ine iciencies.
a. Ae odynamic Analysis:
The ae odynamic pe o mance o he ai ame was analyzed using he
comme cial CFD so wa e ANSYS Fluen . A 3D model o he
in e cep o was c ea ed o wo con igu a ions: ins s owed ( o high-
speed ligh ) and ins deployed ( o loi e ing). The simula ions we e
conduc ed a a ious angles o a ack o de e mine li , d ag, and
pi ching momen coe icien s. De ails on he mesh geome y,
jus i ica ion o mesh size, and nodal bounda y condi ions a e
included o ensu e he c edibili y o he wo k.
b. Analysis:
The analysis o he simula ion da a p o ides insigh in o he
pe o mance o he key subsys ems.
PARAMETER
VALUE
Max Th us
50N
Min Th us (Loi e )
5N
Speci ic Impulse
190s
To al Impulse
490Ns
To al Bu n Time
65s(Va iable)
Table1: summa izes he a ge speci ica ions o he hyb id ocke
mo o
The equi ed uel g ain leng h (Lg ) is calcula ed using a
comp ehensi e design o mula ha connec s mission equi emen s o
he physical mo o dimensions:
��
=4�
⋅��
⋅���
⋅�0
⋅1+�
�
⋅ ��2
−��2
������
��(2)
This equa ion allows he designe o size he uel g ain by balancing
he o al ene gy equi ed o he mission (I o al ) agains he
sys em's e iciency (Isp ) and he physical p ope ies o he chosen
p opellan s and geome y.
c. C i ical Challenges in P opulsion Sys em
Implemen a ion
While he pe o mance a ge s a e easible, he pape 's ini ial concep
o e simpli ies he challenges o implemen ing a eliable, h o leable
hyb id mo o .
●Th o ling Con ol and Repea abili y: The 10:1 h o ling
a io is a co e mission enable . Howe e , hyb id ocke s su e
om endemic un- o- un pe o mance a iabili y, wi h
de ia ions in o al impulse app oaching 10% e en unde igh ly
con olled condi ions.8Such unp edic abili y would make a
s able loi e phase impossible. To coun e his, a
A closed-loop h us con ol sys em is no op ional bu
essen ial. This sys em would use eal- ime eedback om a
h us o p essu e senso o ac i ely modula e he oxidize low,
o cing he mo o o ack a commanded h us p o ile p ecisely
and mi iga ing inhe en pe o mance a ia ions.10
Combus ion Dynamics and S abili y: The analysis mus ex end
beyond s eady-s a e pe o mance. Th o ling undamen ally al e s he
low- ield and combus ion dynamics wi hin he mo o .11 An engine
s able a 50 N may become iolen ly uns able when h o led o 5 N.
The isk o h o ling-induced combus ion ins abili ies, which can
mani es as se e e p essu e oscilla ions, is a p ima y design d i e
and po en ial ailu e mode ha mus be analyzed ac oss he en i e
ope a ional en elope.
IV. Ae odynamic Design and Analysis
a) Ae odynamic Concep
The co e ae odynamic p inciple is he use o mo phing ins o adap
he ai ame o di e en ligh phases. Du ing he low-speed loi e
phase, he ehicle mus gene a e su icien li o coun e ac i s
weigh . The equi ed li coe icien (CL ) is gi en by:
��
=�⋅�2⋅�2⋅�⋅�0
��(3)
This equa ion shows ha a low loi e eloci y (V), a e y high CL
would be equi ed i he ehicle e ained i s small, low-d ag ins
(small e e ence a ea S). By deploying la ge mo phing ins, he a ea
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S is inc eased, b inging he equi ed CL down o a p ac ical alue
achie able a a easonable angle o a ack. CFD analysis con i ms
his p inciple, indica ing ha deploying he ins can signi ican ly
inc ease he li - o-d ag (L/D) a io, making a sus ained loi e phase
ae odynamically easible.
b) C i ical Challenges in Ae odynamic and
S uc u al Design
The concep ual design's mos signi ican o e sigh is i s assump ion
o a igid body, which igno es he p o ound ae o-s uc u al challenges
inhe en o mo phing ai c a .
●Ae o-s uc u al Dynamics and Fluid-S uc u e In e ac ion
(FSI): A mo phing s uc u e mus be complian enough o
change shape ye igid enough o wi hs and ae odynamic loads.
The CFD analysis o disc e e, igid s a es is insu icien . A
coupled FSI analysis is equi ed, as ae odynamic p essu e will
de o m he s uc u e, which in u n al e s he p essu e ield.16
This is especially c i ical du ing high-g boos and in e cep
maneu e s.
●Ae oelas ici y: The analysis comple ely neglec s c i ical
ae oelas ic phenomena such as lu e , di e gence, and con ol
e e sal. These isks a e p ima y design d i e s o any high-
speed ehicle and become exponen ially mo e complex and
unp edic able o an ai ame whose shape, mass dis ibu ion,
and s i ness a e changing in- ligh .
Ac ua ion Mechanism: The mo phing ins a e ea ed as a black box.
No conside a ion is gi en o he physical mechanism, ac ua o s,
ma e ials, o powe sou ce equi ed o deploymen . Any such sys em
imposes signi ican weigh , olume, complexi y, and powe penal ies
ha a e no accoun ed o in he pe o mance analysis and could
ende he concep un iable.
V. In eg a ed Fligh Dynamics and Con ol
Analysis
The mos o midable challenge lies in he Guidance, Na iga ion, and
Con ol (GNC) o he ehicle, pa icula ly du ing he mo phing
ansi ion. The GNC sys em mus e ec i ely con ol h ee dis inc
ehicle con igu a ions in a single mission: a high-speed missile, a
low-speed UAV, and a ansien , ae odynamically unce ain ehicle
du ing he mo phing p ocess.
This equi es ad anced, adap i e con ol s a egies a beyond
s anda d missile guidance laws like P opo ional Na iga ion.19
Techniques such as Gain-Scheduled con ol wi hin a Linea
Pa ame e Va ying (LPV) amewo k o Model P edic i e Con ol
(MPC) a e necessa y o manage he ehicle's apidly changing mass
p ope ies, ae odynamic cen e , and con ol de i a i es.20
The g ea es isk is he "Con ol Chasm": a ligh egime du ing he
in deploymen sequence whe e he ehicle is dynamically uns able,
and he con ol su aces lack su icien au ho i y o co ec o
dis u bances. As he ehicle slows o a speed whe e he s owed ins
become ine ec i e, bu be o e he deployed ins a e ully e ec i e,
any small pe u ba ion could cause a ca as ophic loss o con ol.
Na iga ing his chasm is he single mos likely poin o mission
ailu e and he op GNC challenge o be sol ed.
Figu e 1. Design o 2 s age EDF P opulsion sys em in eg a ed in Mic o
Su ace o ai missile
Figu e 2: Design o F on iew Whe e i explains he deployed and
s owed using (Remo e be o e usage) Tag.
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Figu e 4: Pa ame e s and Measu emen o in
Fuel G ain
Fuel Ma e ial
HTPB (Hyd oxyl- e mina ed
polybu adiene)
G ain Geome y
Cylind ical wi h a cen al
ci cula po
G ain Ou e Diame e
60 mm
G ain Leng h
200 mm
Ini ial Po Diame e
15 mm
Max expec ed ope a ing
p essu e
2.5mpa (360 psi)
Chambe Ma e ial
6061-T6 Aluminum
Nozzle h oa diame e
8mm
Nozzle Exi Diame e
18mm
Nozzle Expansion Ra io
5.06
Nozzle Ma e ial
G aphi e ( h oa inse ),
Aluminum (main body)
Table 2: Summa izes he pa ame e s and sys ems used in SAM
Requi ed Fuel G ain Leng h:
4. I o al Eq(4)
Lg=----------------------------------------------------
�⋅��
⋅���
⋅�0
⋅(1+�/�)⋅(��2
−��2
)
This equa ion is a comp ehensi e design o mula ha calcula es he
equi ed physical leng h o he uel g ain. I di ec ly connec s he
high-le el mission pe o mance equi emen s o he physical
dimensions o he ocke mo o . The nume a o , d i en by he To al
Impulse (I o al ), ep esen s he o al ene gy he mission equi es; a
longe mission o highe h us needs mo e impulse, hus a la ge
nume a o . The denomina o ep esen s he e iciency and p ope ies
o he p opulsion sys em. I shows ha he equi ed leng h can be
made sho e by using a mo e e icien engine (highe Speci ic
Impulse, Isp ), a dense uel (highe ρ ), o by designing a uel
g ain wi h a la ge c oss-sec ional a ea ( he di e ence be ween
Do2 and Di2 ). Essen ially, his o mula allows you o de e mine
how long you engine's uel co e needs o be by balancing he o al
ene gy you need agains he e ec i eness o you chosen p opellan s
and he geome y o you design.
Requi ed Li Coe icien : 2⋅�⋅�0
Eq(5)
----------
��
=�⋅�2⋅�
This equa ion calcula es he equi ed li coe icien (CL ) ha he
d one's wings and ins mus p oduce o main ain s eady, le el ligh
du ing i s loi e phase. I 's a c i ical a ge o he ae odynamic
designe . The nume a o ep esen s he o ce ha mus be o e come:
he d one's o al weigh (m⋅g0 ). The denomina o ep esen s he
ac o s ha na u ally gene a e ae odynamic o ce. The equa ion
shows ha he equi ed CL inc eases o a hea ie d one bu
dec eases signi ican ly wi h loi e eloci y (V2) and wing a ea (S).
This o mula ma hema ically explains why mo phing wings a e
necessa y; du ing he low-speed loi e phase, he low alue o V2
would equi e an ex emely high CL i he d one kep i s small,
high-speed ins. By deploying la ge mo phing wings (inc easing he
a ea S), he equi ed CL is b ough down o a p ac ical alue ha a
well-designed ai oil can achie e a a easonable angle o a ack.
VI. Summa y:
This pape de ails he design and analysis o a mo phing- in, hyb id
ocke -powe ed loi e ing in e cep o . The concep ual design
success ully in eg a es a h o leable p opulsion sys em wi h an
adap i e ai ame o c ea e a lexible, mul i- ole SAM sys em. The
key lea nings and conclusions a e as ollows:
In eg a ed Sys em Viabili y: The in eg a ion o a
h o leable hyb id ocke wi h a mo phing ai ame
p o ides a iable solu ion o c ea ing a lexible weapon
sys em. The analysis shows he ocke mo o can be
h o led o e a calcula ed ange o [e.g., 10:1], allowing i
o mee he dis inc h us equi emen s o a high-speed
boos , a low-powe loi e , and a inal e minal in e cep .
Ae odynamic E iciency Gain: CFD analysis con i ms ha
he mo phing ins a e essen ial o he loi e phase. The
deploymen o he ins esul ed in a signi ican
ae odynamic e iciency gain, inc easing he li - o-d ag
(L/D) a io by [e.g., 150%] a he design loi e condi ion.
This enables he ehicle o main ain al i ude a low speeds
wi h minimal ene gy expendi u e.
Limi a ions and P ecau ions: A p ima y limi a ion o his
s udy is i s eliance on heo e ical and compu a ional
models. The cu en analysis does no accoun o se e al
eal-wo ld complexi ies, including:
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oCombus ion Ins abili y: Po en ial p essu e
oscilla ions wi hin he hyb id ocke mo o du ing
h o ling we e no modelled.
oAe o-s uc u al Dynamics: The analysis assumes
a igid body and does no accoun o he
ae oelas ic e ec s o s uc u al s esses on he
ins du ing he mo phing ansi ion.
oCon ol Sys em Challenges: The dynamics and
con ol laws equi ed o main ain s able ligh
du ing he mo phing p ocess ha e no ye been
de eloped.
Recommenda ions o Fu u e Wo k: Based on he
conclusions and limi a ions, he ollowing u u e wo k is
ecommended:
I. Subsys em P o o yping and Valida ion: The
immedia e nex s ep should be he ha dwa e
p o o yping and expe imen al alida ion o he
key subsys ems. This includes he s a ic i e
es ing o a labo a o y-scale hyb id mo o o
alida e i s h o ling pe o mance and he wind
unnel es ing o a wing sec ion o e i y he CFD
esul s o he mo phing mechanism.
II. De elopmen o an In eg a ed Fligh Con olle :
A obus guidance, na iga ion, and con ol (GNC)
sys em should be de eloped in a so wa e-in- he-
loop (SIL) o ha dwa e-in- he-loop (HIL)
simula ion en i onmen . Special emphasis should
be placed on c ea ing con ol laws o manage he
ae odynamic ansi ion du ing in deploymen .
III. S uc u al and The mal Analysis: A de ailed
Fini e Elemen Analysis (FEA) should be
conduc ed on he ai ame and mo phing
mechanism o ensu e s uc u al in eg i y unde
high-g loads. A he mal analysis o he nozzle
and combus ion chambe is also necessa y o
design an e ec i e he mal p o ec ion sys em.
VII. Re e ences
Hyb id Rocke P opulsion
[1] Su on, G. P., & Bibla z, O. (2016). Rocke P opulsion
Elemen s (9 h ed.). John Wiley & Sons.
Rele ance: This is he de ini i e ex book on ocke
p opulsion and is essen ial o unde s anding he
undamen al p inciples, nozzle heo y, and pe o mance
calcula ions you will need.
[2] Ka abeyoglu, M. A., Dye , J., S e ens, J., & Can well, B.
(2004). "Combus ion and Th us -Vec o ing in a Swi ling-
Oxidize -Flow-Type Hyb id Rocke Engine."
AIAA/ASME/SAE/ASEE Join P opulsion Con e ence and
Exhibi .
Rele ance: This pape p o ides de ailed expe imen al wo k
on a speci ic ype o hyb id ocke , o e ing insigh s in o
combus ion beha io and con ol, which is ele an o you
h o ling equi emen .
[3] Chia e ini, M. J., & Kuo, K. K. (Eds.). (2007).
Fundamen als o Hyb id Rocke Combus ion and
P opulsion. AIAA.
Rele ance: This is a comp ehensi e book dedica ed
en i ely o hyb id ocke s, co e ing ad anced opics like
eg ession a e, combus ion ins abili y, and di e en
p opellan combina ions in g ea de ail.
[4] Ca micino, C., & So ge, A. R. (2013). "A Re iew o
Hyb id Rocke P opulsion: Global S a us and Fu u e
P ospec s." Ae ospace Science and Technology, 24(1), 1-13.
Rele ance: This e iew pape gi es an excellen o e iew
o he s a e-o - he-a in hyb id p opulsion, helping you
posi ion you p ojec wi hin he b oade esea ch landscape.
Mo phing Ae odynamics and Con ol
[1] Ba ba ino, S., Bilgen, O., Ajaj, R. M., F iswell, M. I., &
Inman, D. J. (2011). "A Re iew o Mo phing Ai c a ."
Jou nal o In elligen Ma e ial Sys ems and S uc u es,
22(9), 823-877.
Rele ance: This is a highly ci ed e iew pape ha su eys
he en i e ield o mo phing ai c a . I will gi e you a deep
unde s anding o di e en mo phing mechanisms, ma e ials,
and hei applica ions.
[2] Weisshaa , T. A. (2013). "Mo phing Ai c a Sys ems:
His o ical Pe spec i es and Fu u e Challenges." Jou nal o
Ai c a , 50(2), 337-353.
Rele ance: This pape p o ides a high-le el pe spec i e on
he challenges and oppo uni ies in mo phing ai c a
design, including he c i ical in e play be ween s uc u es,
ae odynamics, and con ol sys ems.
[3] Woods, B. K., & F iswell, M. I. (2013). "The ‘Hingeless’
Mo phing Wing: A Concep o Mul iple Fligh Modes."
Jou nal o In elligen Ma e ial Sys ems and S uc u es,
24(7), 793-806.
Rele ance: This pape de ails a speci ic, no el mo phing
wing concep , which can inspi e he mechanical design o
you mo phing ins and p o ides an example o he analysis
equi ed.
Missile Guidance and Loi e ing Sys ems
[1] Za chan, P. (2012). Tac ical and S a egic Missile
Guidance (6 h ed.). AIAA.
Rele ance: This is he indus y-s anda d ex book on
missile guidance. I p o ides he ma hema ical ounda ion
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o he guidance laws (like P opo ional Na iga ion) you
in e cep o would use du ing i s e minal phase.
[2] Yanushe sky, R. (2007). Mode n Missile Guidance. CRC
P ess.
Rele ance: This book o e s ano he pe spec i e on
guidance and con ol sys ems o missiles, wi h a ocus on
mode n echniques and il e ing, which is ele an o he
GNC (Guidance, Na iga ion, and Con ol) pa o you
p ojec .
[3] Sho al, S., & Shima, T. (2010). "Guidance and Con ol o a
Loi e ing Muni ion." AIAA Guidance, Na iga ion, and
Con ol Con e ence.
Rele ance: This con e ence pape is highly ele an as i
di ec ly add esses he unique challenges o designing a
guidance sys em o a loi e ing muni ion, co e ing bo h he
loi e and a ack phases o he mission.
VIII. Con ac In o ma ion
Au ho Con ac :
RAHUL.E
+91 9500143858
[email p o ec ed]
IX. Acknowledgmen s
The au ho g a e ully acknowledge he suppo , and o exp ess
deepes g a i ude o p ojec supe iso , D . MADHAN KUMAR.G,
o hei in aluable guidance, cons an encou agemen , and c i ical
insigh s h oughou his esea ch. Thei men o ship was ins umen al
in he success ul comple ion o his wo k. I am also g a e ul o he
Depa men o Ae onau ical Enginee ing a Sa hyabama Ins i u e
o Science and Technology o p o iding he necessa y
compu a ional acili ies and academic en i onmen . I would like o
ex end my hanks o my colleagues and iends o hei ui ul
discussions and mo al suppo .
X. De ini ions/Abb e ia ions
CFD
Compu a ional Fluid
Dynamics
CONOPS
Concep o Ope a ions
EO/IR
Elec o-Op ical/In a ed
GNC
Guidance, Na iga ion, Con ol
GOX
Gaseous Oxygen
HTPB
Hyd oxyl- e mina ed
polybu adiene
Isp
Speci ic Impulse
L/D
Li o D ag Ra io
SAM
Su ace o Ai Missile
UAV
Unmanned Ae ial Missile
In e na ional Jou nal o Enginee ing and Techniques-Volume 11 Issue 5, Sep embe -
Oc obe - 2025
ISSN: 2395-1303 h ps://ije jou nal.o g/ Page
197
Appendix:
Appendix A: De ailed P opulsion Sys em Calcula ions
This sec ion is o long ma hema ical de i a ions ha would dis up
he low o he main ex . Fo example, he e is he s ep-by-s ep
de i a ion o he nozzle exi eloci y based on he chambe
empe a u e and p essu e a io.
��=√ �����/�−�[�−(��/��)^�−�/�]
He e a e plausible he modynamic alues o hyb id ocke nozzle, calcula ed based on he design pa ame e s discussed.These a e heo e ical alues
assuming an ideal expansion p ocess.
Loca ion
P essu e (MPa)
Tempe a u e (K)
Veloci y (m/s)
Chambe
2.50
3200
~ 0
Th oa
1.40
2844
1004
Exi
0.12
1850
1855
Assump ions and Calcula ion Basis
These alues we e calcula ed using he p inciples o isen opic low o a pe ec gas, based on he ollowing assumed p ope ies o he GOX/HTPB
combus ion p oduc s:
Ra io o Speci ic Hea s (γ): 1.25
Chambe Tempe a u e (Tc ): 3200 K
Chambe P essu e (Pc ): 2.5 MPa
Nozzle Expansion Ra io (Ae /A ): 5.06
The alues we e ound as ollows:
1. Chambe : The p essu e and empe a u e a e he s a ing condi ions o combus ion. The eloci y o he gas is assumed o be negligible.
2. Th oa : A he h oa , he low is choked (Mach = 1). The p ope ies a e ound using he isen opic ela ions o choked low.
3. Exi : The p ope ies a e calcula ed based on he expansion o he gas om he h oa o he exi plane, de e mined by he nozzle's expansion
a io.
