mae-nas.eng.usu.edumae-nas.eng.usu.edu/mae_5540_web/propulsion_systems/section3/...mae-nas.eng.usu.edu...

MAE 5540 - Propulsion Systems

!"#$%&'()$"*+%,'--./0(+*1$,+2$"3'45#"6+2$,'27'826+2$

F�%@??:9�,9/��4-7,=E��.3,;?0=� �9

Stephen Whitmore

Taylor, Chapters 2, 3.


:1"3';2<3='!"#$%&'>$"3),+,

!"#$%&'(")*+%,-./*01'-2-3#'-(/?<@+6"3'=1,+A$,'"'!"#$!%&'#((#)"&*+,-%.*)+/&0)+%,.1&2%3,(!(&04#31*&*)&',5#'#6%&7,/4),8B1<72<*"$%1'C&+31'%2*B3)+$A'C+6&'6&1',"6133+61"$='3"#$%&'D1&+%31'%2$,6<"+$6,E'F,+$A'6&1'9:;%3+%%&)0&<+%%8)'&2+)3+,' 72<'?B6+*+G"6+2$'27'H+*#3"6+2$'I<"J1%62<+1,KL?HIMN'"'=1,+<1='2<@+6'+,',B1%+7+1='"$='"',16'27'2B6+*+G"6+2$'B"<"*161<,'"$='%2$,6<"+$6,'"<1'=1,+A$"61=E'>BB<2B<+"61'="6"'72<'*",,'B<2B1<6+1,N'"1<2=)$"*+%,N'"$='*262<'@"33+,6+%,'"<1'+$B#6EL?HI'6&1$',131%6,'D"3#1,'72<'6&1'2B6+*+G"6+2$'B"<"*161<,'6&"6'6"<A16'6&1'=1,+<1='2<@+6'C+6&',B1%+7+1='%2$,6<"+$6,'2$'O1)'B"<"*161<,',#%&'",'"$A31'27'"66"%ON'=)$"*+%'32"=+$AN'B")32"='6&1<*"3N'"$='A<2#$='6<"%OE'=0*%+&2>?@&1,(&A%%"&!(%8&*)&8%*%+'#"%&*1%&)7*#'!'&4,!".1&*+,-%.*)+/B&,&2%3,(!(:(7%.#0#.&(#5&8%3+%%&)0&<+%%8)'&(#'!4,*#)"&7+)3+,' +,'#,1='62'D1<+7)'I<"J1%62<)'"%%1B6"@+3+6)'C+6&'<1"3+,6+%'"66+6#=1'=)$"*+%,N'+$%3#=+$A',1B"<"6+2$'"$"3),+,'2$'"33',6"A1,E

F��0(?P',+*#3"6+2$,Q2,6,'=&C>@D I2'<#$>$='"<1'6)B+%"33)R26'#,1='72<'I<"J1%62<)'=1,+A$S

F�)0�,=0�2:492�?:�/0A07:;>',+*B31'EF:; %2=1I&"6'C2<O,'C133P2<'*+,,+2$'B<27+31'=1D132B*1$6 /


?<@+6"3'4$1<A)

T


��

!"#$"%&'(#)**+,-


?<@+6"3'()$"*+%,F� @>?�=0>:=?�?:�!0B?:9K>�7,B>�?:�/0>.=4-06&1,1'2<@+6,

U


Coordinate TransformationsCoordinate Transformations:

i

ji r

i!

!

!

{i, j} fixed in space


Coordinate Transformations:(cont;d)

i

ji r

i!

!

!

• A Matrix "trick" for coordinate transform in 2-D

Coordinate Transformations


L1<+72%"3'Q22<=+$"61'H),61*

V


L1<+72%"3'Q22<=+$"61'H),61*H#@02<@+6"3'-*"A1

VrV�

�

W


X132%+6)'X1%62<

Y


>%%131<"6+2$'X1%62<

Z


>%%131<"6+2$'X1%62<'�.:9?K/�

9[


!0B?:9K>�%0.:9/��,B

99


!0B?:9K>�%0.:9/��,B

9/


\<"D+6"6+2$"3'K%2$,1<D"6+D1M'P2<%1,

F��>>@80�>;30=4.,7�0,=?3��7B,D>�,.?>�49�4< =+<1%6+2$

� ��!/"]

!

9T


X1&+%31'8",,

-$+6+"3'*",,'27'D1&+%31

9^


R2$0Q2$,1<D"6+D1'P2<%1,'

� � 6"$�9 #!#�

#

%$

.

0/

$!%$�%

#

%

$$$$

.

0

////

�

'$&"'( %2,K� M� $)!*+ ,+$K� M� $(,!-.( ,+$K�M'� �%

�'$&"'( ,+$K� M� $)!*+ %2,K� M� $(,!-.( %2,K�M'� �

%

#

%

$$$$$

.

0

/////

� � � �

9U

MAE 6530, Propulsion Systems II

RS 101: SummaryExternal Forces Acting on Rocket

2

•Lift – acts perpendicular to flight path (non-conservative)•Drag – acts along flight path (non-conservative)•Thrust – acts along longitudinal axis of rocket (non-conservative)•Gravity – acts downward (conservative)

Becauseliftactsperpendiculartoflightpath,dragistheprimarydissipativeforceactingonairframe


>1<2=)$"*+%'P2<%1,

$&"'( � /01!2' 3]

� � /01!2'9

/��#�

/

$)!*+ � /41!2' 3]

� � /41!2'9

/��#�

/

��

><17G�=010=09.0�=0,�G�;7,91:=8?<'=+"*161<'@",1=

9V


>1<2=)$"*+%'P2<%1,'�.:9?K/� �4=�I>?4.6>J�?:4"<6&'@2#$="<)

3]

� �9

/��#�

/ �#� � #]

"52!("*&�#]

*(%6.7,2!2 � #]

"52!("*&��]

2*!(,� 8]

-$1<6+"3'X132%+6)''''''''''''''''

>+<,B11=

9W


>1<2=)$"*+%'P2<%1,'�.:9?K/�

F��::/��;;=:C48,?4:9� #� � #]

"52!("*&�#]

2*!(,�#]

9"5)

?%%&,77%"8#5&G&,*&%"8&)0&(4#8%(

9Y


>1<2=)$"*+%'P2<%1,'K<1D+,+61=MF��::6�,?�%&%� 0"1<2'1_"*B3100Q!N'Q( 6)B+%"33)'7#$%6+2$'27'8"%&N'

00I)B+%"33)'+*B31*1$61='",6"@31'322O#B � � � �

9Z


>1<2=)$"*+%'P2<%1,'�.:9?K/�

F��::6�,?�%&%� 0"1<2'1_"*B31

/[


>1<2=)$"*+%'P2<%1,'�.:9?K/�

F��::6�,?�%&%� 0"1<2'1_"*B31

/9

MAE 6530, Propulsion Systems II3

Types of Aerodynamic Drag

M = 1

+ Base Drag

MAE 6530, Propulsion Systems II 4

Types of Aerodynamic Drag (2)

Drag Mechanisms Acting on Launch Vehicles (LVs)• Subsonic

o Viscous drag–Wetted Area Skin Friction–Flow Separation (small for LVs)

o Pressure drag (form drag)– Forebody– Interference (fin roots)– Base

o Induced (lift drag, small for LVs)• Supersonic

o Wave drago Compressive drag due to lift

• “Dither” Drag due to unsteady a modulation• Total drag


5

Skin Friction Drag

dAτwall

Flow Momentum lost due to surface viscosity

CF =τwall ⋅dA

surf∫∫q ⋅ Awet

Awet

CDF=

Awet

Aref

⋅CF →

CF = skin friction coefficient

Awet = forebody wetted surface area

Aref = vehicle reference area, π4⋅Dmax

2


Forebody Form (Pressure) Drag

9

• Subsonic form drag directly related to boundary layer development along body. • Knowing friction drag, subsonic form drag (CD0 ) correlated with skin friction

coefficient (CF) and body fineness ratio (L/D)

CD0 =κ ⋅AwetAref⋅CF

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟

High l/t Profile

lt

Low l/t Profile

lt

k

Drew and Jenn, “Pressure Drag Calculations on Axisymmetric Bodies of Arbitrary Mold Line,” AIAA 90-0280, 28th Aerospace Sciences Meeting, 8-11 Jan., 1990, Reno NV.

MAE 6530, Propulsion Systems II 10

• Boundary Layer on Vehicle Base Area Separates

• Low Pressure Separated Region Forms• Low Pressure Causes a Large net Pressure

Difference• Especially significant on Launch Vehicle

after motor burnout

Base Drag


Base Drag (3)

12

Base Drag

Base Drag

Burning Rocket Pressurizes Base Area, Eliminating Base Drag


Base Drag (4)

13

• Effect of “Boat Tailing” – Boat tail used on the rear end of rocket to reduce the base drag force by reducing area against which aft end pressure suction acts

• Effect of “Boat Tailing” – Boat tail Also serves to reduce the severity of the flow separation by reducing the exit turning angle

CDboattail≈CDbase ⋅

dD

⎛

⎝⎜⎜⎜⎞

⎠⎟⎟⎟⎟

2


Fin “Dither” Drag

14

• Even along Ballistic Trajectory where nominal a ~ 0, fins can contribute induced drag to configuration due to unsteady “dither” or fin misalignment

• Shed Vortex from base is Unsteady and Contributes to Pitch Oscillations to Vehicle

•”Dither” Drag due to Small angle of attack oscillations results in RMS drag contribution

20 ft.

7.5 ft.

5 ft.

9.5 ft.

M2-F1

"Vortex Street"

Figure 4: Von Karman "Vortex Street" Formation Trailing M2-F1 Aircraft

“Vortex Street” trailing M2-F1

δα>0

δα= 0

δα<0


Fin “Dither” Drag (2)

15

δα>0

δα= 0

δα<0

Dither” = Unsteady Induced Drag Component

Asurf = Planform area

CLα= Lift−curve slope

AR = Aspect ratio

δαdither = RMS angle of attack dither

CD "dither"=AsurfAref

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⋅CL

2

π ⋅ AR

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟=

AsurfAref

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⋅CLα

2

π ⋅ AR

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⋅δαdither

2


Fin Leading Edge Drag

18

• Stagnation Pressure Coefficient calculated based on Mach number Normal to leading edge of fins

• Scaled by leading edge area, W•t• Assumed fin thickness, t

Cpmax =qc− p∞q

=p∞ ⋅ 1+

γ−12M⊥

2⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

γγ−1− p∞

γ2p∞M⊥

2=1+ γ−1

2⋅ M∞ ⋅cosθL.E .( )2

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

γγ−1−1

γ2⋅ M∞ ⋅cosθL.E .( )2

CDL .E .( )totalfins

=Wi ⋅tiAref

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟i=1

N fins

∑ ⋅ CPmax( )subsonic{ }

i=

Wi ⋅tiAref

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟i=1

N fins

∑ ⋅1+ γ−1

2⋅ M∞ ⋅cosθL.E .( )

i

2⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

γγ−1−1

γ2⋅ M∞ ⋅cosθL.E .( )

i

2

⎧

⎨

⎪⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪⎪

⎫

⎬

⎪⎪⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪⎪⎪i


Total Drag Correlation Model

19

CD( )total=CDF +CD0 +CDbase +CDDither +CDL .E .

Skin FrictionDrag

Nose/BodyProfile Pressure

Drag

Base AreaWake Drag

Unsteady DitherDrag, Fins Fins, Leading

Edge Pressure Drag

• Medium Fidelity Engineering Model for “First Cut” Drag Coefficient Estimator.

• Calculates Subsonic Drag Coefficient in Incompressible Flight Regime ~ Mach 0.3

• Rigorously, each term of the above equation should be scaled for compressibility at Higher Mach numbers

• Operationally, Bulk scaling of is often used CD( )total

• Does not Model Wave Drag


Correcting for Compressibility

20

wdpdfdd

wavepressurefriction

cccc

DDDD

,,, ++=

++= Only at transonic andsupersonic speedsDwave= 0 for subsonic speedsbelow Mdrag-divergence

Profile DragProfile Drag coefficient relatively constant with M∞ at subsonic speeds

Credit: D. R. KirkFIT, 2011

Supersonic CDVaries as …

Subsonic CDVaries as ~…

MCR

Viscosity Effects


X1%62<'P2<*'27'H6"61'45#"6+2$,

;F� ' ;N$(,!-.( N��

;F�

#F

!

#F

�

!F

�F

%F

#

%

$$$$$$$$$$$$

.

0

////////////

� ' ;N$(,!-.( N��

#�/

!�$&"'( %2,K� M � $)!*+ ,+$K� M � $(,!-.( ,+$K�M

%�

�!/

�#!#�

!�$&"'( ,+$K� M � $)!*+ %2,K� M � $(,!-.( %2,K�M

%#

%$

.

0/

#!#�

!

�$(,!-.(+[:.7

#

%

$$$$$$$$$$$$$

.

0

/////////////

�� 6"$�9 #!

#�

#

%$

.

0/

� � � �

/V

Independent Variables: F

thrust,

…. TWO DEGREES OF FREEDOM

COLLECTED


`"33+,6+%'D1<,#,'R2$'0`"33+,6+%'I<"J1%62<+1,

F�!:90@"33+,6+%'6<"J1%62<+1,',#,6"+$,+A$+7+%"$63)'$2$'0G1<2'"$A31,'27'"66"%O��

�� !� ��

/W


4_"*B31'27'R2$0`"33+,6+%'I<"J1%62<)

/Y


Space

shuttle

mission

profile

/Z


4_"*B31'27'`"33+,6+%'I<"J1%62<)

b'H)**16<+%6<"J1%62<)

F��,774>?4.�&=,50.?:=40>?771<'*+$+*#*'=<"A'B<27+31,K b'[00cR2'+$=#%1='=<"AM

T/


`"33+,6+%'Q2177+%+1$6F�;&1$'1771%6,'27'3+76'"<1'$1A3+A+@31'"1<2=)$"*+%'1771%6,'%"$'@1'+$%2<B2<"61='+$62'"',+$A31'B"<"*161<

G��L,44#(*#.&M)%00#.#%"*&N�O

F�� 4>�,��80,>@=0�:1�,�;=:50.?470�>�,-474?D�?:�.:,>?��G� d'"e#=$%&'G�" 4>�?30�;=:50.?470�>�8,>>�,9/�G�#=$ +,'6&1'=<"A''(%)*'+,-(%E'

F��?�,9D�24A09�A07:.4?D�,9/�,4=�/09>4?D��?30�/0.070=,?4:9�:1�,�<2%O16'7<2*'=<"A'+,'+$D1<,13)'B<2B2<6+2$"3'62'�

��<)+&L,44#(*#.&M)%00#.#%"*&M,4.!4,*#)"&H5,'74%(

TT


Q2331%61='45#"6+2$,N'`"33+,6+%'I<"J1%62<)

� � 6"$�9 #!#�

#

%$

.

0/

#F

!

#F

�

!F

�F

%F

#

%

$$$$$$$$$$$$

.

0

////////////

�

#�/

!�

�!/

�$(,!-.(%

��#�

/

/�#

%$

.

0/,+$K� M

�#!#�

!�$(,!-.(%

��#�

/

/�#

%$

.

0/%2,K� M

#!#�

!

�$(,!-.(+[:.7

#

%

$$$$$$$$$$$$$$

.

0

////////////// �[

� 'd'*

Q(1!2''

;F� ' ;N$(,!-.(� �

T^


!"#$%&'`"33+,6+%,':1D+,+61=

F�!:90@"33+,6+%'6<"J1%62<+1,',#,6"+$,+A$+7+%"$63)'$2$'0G1<2'"$A31,'27'"66"%O��

�� !� ��

TU


!"#$%&'`"33+,6+%,':1D+,+61='K/M

F��9�;=,.?4.0�-,774>?4.I<"J1%62<+1,'A+D1I7:1?0/�:=-4?>J�B4?3P%+/&1#31&,7)3%%&=4*#*!8%(G

R11='62'��"6',2*1'$2$0G1<2',"34%:)0:,**,.J 62'A16'B<2B1<>B2A11eD132%+6)'B&",+$A'

TV


`"33+,6+%'EE'`2662*'!+$1

F��9�;=,.?4.0�-,774>?4.I<"J1%62<+1,'A+D1I7:1?0/�:=-4?>J�B4?3P%+/&1#31&,7)3%%&=4*#*!8%(G

R11='62'��"6',2*1'$2$0G1<2',"34%:)0:,**,.J 62'A16'B<2B1<>B2A11eD132%+6)'B&",+$A'

F�I;4?.3�;=:1470J��0D�?:�,..@=,?0?<@+6'+$,1<6+2$

F�!02,?4A0�741?�@>0/�?:�I?@=9�?30�.:=90=J�/@=492�

F��9/@.0/��=,2�#09,7?D�>%%1B61='62'"%&+1D1'%2<<1%6'2<@+6'B"<"*161<,

��

TY


?&'I&"6S'\<"D+6)'I#<$

T9

K!7&*1#(&#(&+%,4D


:=0�I�=,A4?D�&@=9J

Space Shuttle Launch (STS 115 � Atlantis) as seen from ISS

��

T[


R#*1<+%"3'>$"3),+,'27'6&1'/0('!"#$%&'45#"6+2$,'27'826+2$

TZ


R2$0`"33+,6+%'I<"J1%62<+1,N'<1D+,+61=

#F

!

#F

�

!F

�F

%F

#

%

$$$$$$$$$$$$

.

0

////////////

�

#�/

!�$&"'( %2,K� M� $)!*+ ,+$K� M� $(,!-.( ,+$K�M

%�

�!/

�#!#�

!�$&"'( ,+$K� M� $)!*+ %2,K� M� $(,!-.( %2,K�M

%#

%$

.

0/

#!#�

!

�$(,!-.(+[:.7

#

%

$$$$$$$$$$$$$

.

0

/////////////

��

I;4?.3�;=:1470Jf1)'62'"%%#<"61?<@+6'+$,1<6+2$

TW

INDEPENDENT VARIABLES: F

Thrust,

O


X1%62<'P2<*'27'H6"61'45#"6+2$,

;F� ' ;N$(,!-.( N��

;F�

#F

!

#F

�

!F

�F

%F

#

%

$$$$$$$$$$$$

.

0

////////////

� ' ;N$(,!-.( N��

#�/

!�$&"'( %2,K� M � $)!*+ ,+$K� M � $(,!-.( ,+$K�M

%�

�!/

�#!#�

!�$&"'( ,+$K� M � $)!*+ %2,K� M � $(,!-.( %2,K�M

%#

%$

.

0/

#!#�

!

�$(,!-.(+[:.7

#

%

$$$$$$$$$$$$$

.

0

/////////////

�� 6"$�9 #!

#�

#

%$

.

0/

� � � �

/V

Independent Variables: F

thrust,

…. TWO DEGREES OF FREEDOM


-$61A<"61='45#"6+2$,'27'826+2$

;F� ' ;N$(,!-.( N�� ;K(M � ;K([ M� ' ;N$(,!-.( N�� )(

([

(

*

� "BB<2_+*"61'2D1<'7+_1='+$61<D"3'�I�

;K([ � �(M � ;K([ M � ' ;N$(,!-.( N�� ([

([ ��(

* )(

^[

t


R#*1<+%"3'>BB<2_+*"6+2$'276&1'-$61A<"3

^9


R#*1<+%"3'>BB<2_+*"6+2$'276&1'-$61A<"3'�.:9?K/�

x(t) x(t+ �t)

I&=,;0E:4/,7�=@70J

;K([ � �(M � ;K([ M� ' ;N$(,!-.( N�� ([

([ ��(

* )(

^/


"=�B0�.,9�@>0��494?0��4110=09.0>J

^T


R#*1<+%"3'>BB<2_+*"6+2$'276&1'-$61A<"3'�.:9?K/�

I&=,;0E:4/,7�=@70J '< � ' ;< N$(,!-.( < N�<#%

.0

'<�9 � ' ;<�9N$(,!-.( <�9 N�<�9#% .0

'gb

<�9 � ' ;gb

<�9N$(,!-.( <�9 N�<�9#

%$$

.

0// ^^


R#*1<+%"3'>BB<2_+*"6+2$'276&1'-$61A<"3'�.:9?K/�

��

^U


L<1=+%62<eQ2<<1%62<'>3A2<+6&*

��

�(N;g

< N$(,!-.( < N�<#%$

.0/

� ;gb

< � ;g

<� �( '' ;g

< N$(,!-.( < N�<#%$

.0/

� ;g

<�9 � ;g

<��(/' ' ;

g

< N$(,!-.( < N�<#%$

.0/� ' ;

gb

<�9N$(,!-.( <�9 N�<�9#

%$$

.

0//

&')

()

12)

3)

^V

+1


h+A&1<'?<=1<'-$61A<"62<,F%48;70�%0.:9/�"=/0=�;=0/4.?:=�.:==0.?:=�B:=6>�B077�1:=H*"3306208:/0=,?0�>?0;�>4E0>�G�-@?�,?�7,=20=�>?0;�>4E0>�.,9�@1'%2*1'#$,6"@31

F��::/�?:�3,A0�,�34230=�:=/0=�49?02=,?4:9�,%&1*1'+$'2#<'.+/*('*-((01

F� ?3�"=/0=�$@9200f#66"'*16&2='+,'2$1'*2,6'%2**2$3)'#,1=

F��:?>�:1�,=.,90�/0=4A,?4:9>�,9/�"21-&%2 C+6&'<1A"<='62&34>�80?3:/�G�70?>�.70,=�?34>�@;��

^W


^6&'?<=1<':#$A10f#66"'816&2=

x(t) x(t+ �t)

!16,'"=='6C2'*2<1'B2+$6,I2'6&1'%#<D1'@172<1',#**+$A

^Y


^6&'?<=1<':#$A10f#66"'816&2=�.:9?K/�

F�&30�-,>4.��4110=09?4,7�0<@,?4:9�4>�

F��;;=:C48,?0�?30�14=>?�/0=4A,?4A0�-D�1494?0�/4110=09.0

^Z


^6&'?<=1<':#$A10f#66"'816&2=�.:9?K/�

F�!:B�.:==0.?�?34>�/0=4A,?4A0�0>?48,?0�B4?3�B3,?�B0�3,A0�70,=90/

F�&34>�4>�,78:>?�0<@4A,709?�?:�B3,?�B0�3,A0�,7=0,/D�/:90

U[


^6&'?<=1<':#$A10f#66"'816&2=�.:9?K/�

F�$0;0,?�?34>�;=:.0>>�?B4.0�8:=0�?:�24A0�@>� �;:49?>�:9�?30�.@=A0

U9


^6&'?<=1<':#$A10f#66"'816&2=�.:9?K/�

F��49,77D�?,60�,�B0423?0/�,A0=,20�:1�?30�=0>@7?>

U/


^6&'?<=1<':#$A10f#66"'816&2=�.:9?K/�

F�)3,?�3,;;09>�41�?30��9;@?��&3=@>?��4>�9:?��:9>?,9?��G

%48;7D�I>;74?�?30�/4110=09.0J�-0?B009��6&<#,6'O "$='P6&<#,6''Oi9G�>,80�,;;740>�?:�?30?,��/=:;;0/�1:=�>48;74.4?D�

UT


^6&'?<=1<':#$A10f#66"'816&2=�.:9?K/�

F�I>;74?�?30�/4110=09.0J�-0?B009��6&<#,6'O "$='P6&<#,6''Oi9G�>,80�,;;740>�?:�?30?,��/=:;;0/�1:=�>48;74.4?D�

U^


H#**"<)'H3+=1,'2$'4E?E8E

UU


Q2331%61='\1$1<"3'/0('45#"6+2$,

� � 6"$�9 #!#�

#

%$

.

0/

#F

!

#F

�

!F

�F

%F

#

%

$$$$$$$$$$$$

.

0

////////////

�

#�/

!�$&"'( %2,K� M� $)!*+ ,+$K� M� $(,!-.( ,+$K�M

%�

�!/

�#!#�

!�$&"'( ,+$K� M� $)!*+ %2,K� M� $(,!-.( %2,K�M

%#

%$

.

0/

#!#�

!

�$(,!-.(+[:.7

#

%

$$$$$$$$$$$$$

.

0

/////////////

;F� ' ;N$(,!-.( N�� UV

��


Q2331%61='45#"6+2$,N'`"33+,6+%'I<"J1%62<)

� � 6"$�9 #!#�

#

%$

.

0/

#F

!

#F

�

!F

�F

%F

#

%

$$$$$$$$$$$$

.

0

////////////

�

#�/

!�

�!/

�$(,!-.(%

��#�

/

/�#

%$

.

0/,+$K� M

�#!#�

!�$(,!-.(%

��#�

/

/�#

%$

.

0/%2,K� M

#!#�

!

�$(,!-.(+[:.7

#

%

$$$$$$$$$$$$$$

.

0

////////////// �[

� 'd'*

Q(1!2''

;F� ' ;N$(,!-.(� �

UW


L<1=+%62<eQ2<<1%62<'>3A2<+6&*

��

�(N;g

< N$(,!-.( < N�<#%$

.0/

� ;gb

<�9 � ;g

<� �( '' ;g

< N$(,!-.( < N�<#%$

.0/

� ;g

<�9 � ;g

<��(/' ' ;

g

< N$(,!-.( < N�<#%$

.0/� ' ;

gb

<�9N$(,!-.( <�9 N�<�9#

%$$

.

0//

&')

()

12)

3)

UY


^6&'?<=1<':#$A10f#66"'816&2=H#**"<)

F�%74/0��9/4.0>�,9/�=0;0,?UZ

MAE 5540 - Propulsion Systems V^

(��$:.60?��C,8;70�G��,774>?4.�&=,50.?:=D


X0/':2%O16P+<,6'?B'1<"6+2$"3'

H),61*


I&1'X/

F Q&"331$A1'C",'62'=13+D1<'"'2$1'62$'C"<&1"=N'9Y['$*'<"$A1EF P+$"3'=1,+A$.''L2C1<1='@)'>^'<2%O16'*262<N'/T[['3@'C"<&1"=N'9Z['$*'KTU/'O*M''<"$A1E'^W'76'32$AN'UE^'76'=+"*161<N'/YN//Z'3@'6"O1277'C1+A&6E'UZNU[['3@'6&<#,6'72<'VY',1%2$=,E

F V^[['C1"B2$'3"#$%&1,F I&1'>*1<+%"$,'A26'X2$'`<"#$'"$='99W'26&1<',%+1$6+,6,N'"$='"@2#6'9[['<2%O16,E''I&1'H2D+16,'A26'6&1'7"%+3+6+1,'"$='"@2#6'6&1',"*1'$#*@1<'27'<2%O16,E

F ��;7@>�(�K>�,9/�(��8:/>�B0=0�7,@9.30/�49�?30�7,?0� K>�49�'%��77�C1<1',#@02<@+6"3N'&+A&1,6'"36+6#=1'C",'/^^'*+31,

F !?ke>3%2&23'L<2B133"$6,

Stephen Whitmore

Stephen Whitmore


>0^':2%O16'4$A+$1


X/':2%O16'L"<"*161<,Parameter ValueFvac (Nt) 311,800.0F sl (Nt) 264,745.3Isp (sec) 239

Vexit (m/sec) 2200M��(kg) 4008

Mpropellant (kg) 8797GTOW (kg-f) 12805

Payload weight(warhead) (kg-f)

1043.56


X/':2%O16'L"<"*161<,'K/M

G�>==+6+2$"3'HB1%,


>==+6+2$"3'X/'("6"K&66B.ee1$EC+O+B1=+"E2<AeC+O+eX0/M


X/'90('I&<#,6'82=13

� �

� � � �0

thrust exit exit ambient exit

vac sl exit exit exit exit exit sl exit

vac sl sl exit

vac slexit

sl

F m V P P A

F F m V P A m V P P A

F F P A

F FAP

� � � � �

� � � � � � � � � � � �# . # .% 0 % 0� � � �

�� T99Y[[E[ /V^W^UET�

9[9T/Ud'[E^V^TZ'*/

QR&STUVWXY&'&%00%.*#I%&%5#*&8#,'%*%+


X/'90('I&<#,6'82=13'K/M

� � � �0 0

vac vacsp vac

sp vac

propellantburn

F FI mg m g I

MT

m

� � � ��

� �

d'9TTE[T/'OAe,1%

T99Y[[ZEY[VW /TZ�

YWZW9TTE[T/ d'VVE9T',1%

?4#31*&#".)"(#(*%"./&#"&7+)A4%'&(7%.#0#.,*#)"&NVW&(%.&3#I%"O

R11='X"%##*'A1B @*CDEFGG*1&, 62'A+D1'HI*1&, @#<$'6+*1'72<'A+D1$'B<2B133"$6'*",,'JIGKG*L/M


X/'90('I&<#,6'82=13'KTM

� � vac exitvac exit exit exit exit

exit

F m VF m V P A PA� �

� � � � � � � ��

T99Y[[ 9TTE[T/ //[[��[E^V^TZ d'^9N9Z/EZV'L"'


X/'90('I&<#,6'82=13'K^M

� �

2

/sec

/sec

133.032220041,192.960.46439


kg

mexit

Paexit

exit m

F m V P P A

mVPA

� � � � �

# .# .$ /$ /$ /$ /� �$ /$ /$ /$ /$ /% 0 % 0


:2%O16'45#"6+2$'Q"3%#3"6+2$K,M'

�# � +[ � :.7 � 3$F"5"("*&

F '"5*&

"!

+

-, �

N+1&9*(4*A1B @*COK*1&,ZEY[VW /TZ

9/Y[U^[[Y" -

+3$�

@*CGCCFDC*)P1&,*JKI!!FGD*L)P5%M

�# � +[ � :.7 � 3$F"5"("*&

F '"5*&

"!

+

-, �

N+1&9*(4*A1B @*CDEFGG*1&,

d'CGKKFED*)P1&,*JQ!;!GIFOH*L)P5%M

ZEY[VW /^UEWW9/Y[U^[[Y" -

+3$�

Z3")+%(&8+,3&,"8&3+,I#*/&4)((%(


Q2331%61='45#"6+2$,N'`"33+,6+%'I<"J1%62<)

� � 6"$�9 #!#�

#

%$

.

0/

#F

!

#F

�

!F

�F

%F

#

%

$$$$$$$$$$$$

.

0

////////////

�

#�/

!�

�!/

�$(,!-.(%

��#�

/

/�#

%$

.

0/,+$K� M

�#!#�

!�$(,!-.(%

��#�

/

/�#

%$

.

0/%2,K� M

#!#�

!

�$(,!-.(+[:.7

#

%

$$$$$$$$$$$$$$

.

0

////////////// �[

� 'd'*

Q(1!2''

;F� ' ;N$(,!-.(� �

WV


4_"*B31'27'`"33+,6+%'I<"J1%62<)

b'H)**16<+%6<"J1%62<)

F��,774>?4.�&=,50.?:=40>?771<'*+$+*#*'=<"A'B<27+31,K b'[00cR2'+$=#%1='=<"AM

WW


X/'Q2*B#6"6+2$"3'4_"*B31>,,#*1'%2$,6"$6'K2$3)'*"<A+$"33)'%2<<1%6M'=<"A'%2177+%+1$6

#RS!FDD;*$%&'*@CFQOIC*)C

� �J-M*@*"J-MPJ#R $%&'M

H"3#"%&[&C,!".1&\,((&;,*,

� �2

2

1( )1 22 ( )


rag D ref

F m V P P A

M t VD C A V

t

��

�

� � � � �

+� �! , + " -� � � � �! ," -


X/'Q2*B#6"6+2$"3'4_"*B31'K/M

=4*#*!8%[@#'% =4*#*!8%[],"3%

=..%4%+,*#)"P%4).#*/


X/'Q2*B#6"6+2$"3'4_"*B31'KTM

2#*.1&="34% ="34%&)0&=**,.J>'I<#1'`"33+,6+%'L<27+31


X/'Q2*B#6"6+2$"3'4_"*B31'K^M

=4*#*!8%[@#'%


4_"*B31'--.'Q2*B"<+,2$'27'Q2$,6"$6'I&<#,6'8"$1#D1<

X1<,#,'-*B#3,+D1'8"$1#D1<

��*+,"(0%+&

��*+,-%.*)+/

��

Y/


Q2*B"<+,2$'27'Q2$,6"$6'I&<#,6'8"$1#D1<X1<,#,'-*B#3,+D1'8"$1#D1<'�.:9?K/�

F��:9?49@:@>I&<#,6'6<"$,71<

YT


Q2*B"<+,2$'27'Q2$,6"$6'I&<#,6'8"$1#D1<X1<,#,'-*B#3,+D1'8"$1#D1<'�.:9?K/�

F��:9?49@:@>I&<#,6'6<"$,71<

h+A&1<I&<#,6I<"$,71<

Y^


;2<O1='4L'4_"*B31

YU


?<@+6"3'-$+6+"3'Q2$=+6+2$,

YV


?<@+6"3'-$+6+"3'Q2$=+6+2$,

YW


;2<O1='4_"*B31'�.:9?K/�

YY


;2<O1='4_"*B31'�.:9?K/�

10.00000

Thrust (Newtons)

2500.0

Isp (seconds)

�� **91#&%&"#:'*;#,,

********<===>.YZ


;2<O1='4_"*B31'�.:9?K/�

"K9i1M

Z[


Worked Example (cont'd)

!?"5,'*!%"2-/#'-(/

@A0*0"B-'

7-/#8**C&(/'-/5(5,D'?"5,'E**

0"B-'

7-/#8*�F**4%G5-"%H*'(*

I-"&58#"-3%*0"B-'

��

Z9


;2<O1='4_"*B31'�.:9?K/�

Z/


;2<O1='4_"*B31'�.:9?K/�

ZT


;2<O1='4_"*B31'�.:9?K/�

Z^


;2<O1='4_"*B31'�.:9?K/�

ZU


;2<O1='4_"*B31'�.:9?K/�

ZV


;2<O1='4_"*B31'�.:9?K/�

ZW


Q2*B"<1'62'h2&*"$$'6<"$,71<'#,+$A'Q2$D1$6+2$"3'L<2B#3,+2$

ZY


Big Advantages

,mu

P F��423��>;''%2$6+$#2#,'6&#,6''"332C,',*"33'B<2B133"$6''*",,'7<"%6+2$,

F�%8,77�&3=@>?�$0<@4=0>''!2$A'?B1<"6+$A'!+71''P2<'4$A+$1

4LN'+$'6&1':+A&6'Q+<%#*,6"$%1,

ZZ


4LN'+$'6&1':+A&6'Q+<%#*,6"$%1,

9[[

MAE 5540 - Propulsion Systems 9[9


Benefits of Electric Propulsion

Chemical Electric

15%

30%

30%

25%

StructureBusPropellantPayload

15%

32%

6%

47%

StructureBusPropellantPayload

++ 9[/


J11%/H-K*<L*J-",1%%H*I#8&58#'-(/*AK#218%,

9[U


>+<,B11=N'l@"<N'4_"*B31

F��C,8;70��

>':2%O16'3"#$%&1,'"6'"$'+$1<6+"3'73+A&6'B"6&'"$A31'27YU� "6'"$'"G+*#6&'"$A31'27'VU�7<2*'6<#1'$2<6&

I&1'+$1<6+"3'D132%+6)'+,'9'O*e,1%N'6&1'"36+6#=1'+,'9['O*N'"$=

I&1'#BB1<'31D13'C+$=,'"6'9['O*''"<1'@32C+$A'7<2*'6&1'1",6'"6'WU�P<2*'6<#1'$2<6&'"6'U['*e,1%'

I&1'%#<<1$6'3"#$%&'3"6+6#=1'+,'TU� $2<6&

;&"6'+,'6&1'"+<,B11=a'()$"*+%'L<1,,#<1a';&"6'+,'*"%&'$#*@1<a

9[V


>+<,B11=N'l@"<N'4_"*B31'�.:9?K/�North

East

Local Horizontal Plane (Topodetic Coordinates)

65 �

Vertical

Horizontal

85 �

Local Vertical Plane (Topodetic Coordinates)

Local Horizontal/ Vertical Plane (Topodetic)

F��::6>6'32%"3'1"<6&I"$A1$6'B3"$1X132%+6+1,

9[W


>+<,B11=N'l@"<N'4_"*B31'�.:9?K/�F��,7.@7,?0�!:=?3��0,>?��,9/�A0=?4.,7��90=?4,7�(07:.4?D��:8;:909?>

9[[[�9Y[

YU" - +,+$

d'TVEYT'*e,1%

#]

"52!("*& "

+- 56!(,

� #]

"52!("*& %2,K� M%2,K1@M �

#]

"52!("*& "

+- G2!("=*&

� #]

"52!("*& ,+$K� M �

9[[[�9Y[

YU" - +%2,

�9Y[

VU" - +%2,�

d'ZZVE/'*e,1%

#]

"52!("*& "

+- 2*.(

� #]

"52!("*& %2,K� M,+$K1@M �

9[[[�9Y[

YU" - +%2,

�9Y[

VU" - +,+$� d'WYEZZ'*e,1%

9[Y


>+<,B11=N'l@"<N'4_"*B31'�.:9?K/�F��,7.@7,?0�(1"<6&'K-$1<6+"3'`22,6M

)cos(*VVelocity e lat�

Latitude cos(lat) velocity (km/sec)

velocity (ft/sec)

0 1 0.4638 152110 0.98481 0.45675 1497.8925920 0.93969 0.43583 1429.2724830 0.86603 0.40166 1317.2246440 0.76604 0.35529 1165.1536050 0.64279 0.29812 977.6799560 0.50000 0.23190 760.5000070 0.34202 0.15863 520.2126480 0.17365 0.08054 264.1188890 0.00000 0.00000 0.00000

d [E^VTY�9Y[

TU" - +%2, dTWZEZ'*e,1%

I0,>?J��4=0.?4:9

9[Z


>+<,B11=N'l@"<N'4_"*B31'�.:9?K/�F��,7.@7,?0�)49/�A07:.4?40>

I&1'#BB1<'31D13'C+$=,'"6'9['O*''"<1'@32C+$A''%()*-5&*&+1- "6'WU�P<2*'6<#1'$2<6&'"6'U['*e,1%' North

East

Local Horizontal Plane (Topodetic Coordinates)

255 �

#]

9"5) "

+- 56!(,

� #]

9"5) %2,K9"5) M �

U[�9Y[

/UU" - +%2, d09/EZ^9'*e,1%

d0^YE/ZV'*e,1%

#]

9"5) "

+- 2*.(

� #]

9"5) ,+$K9"5) M �

U[�9Y[

/UU" - +,+$

99[


>+<,B11=N'l@"<N'4_"*B31'�.:9?K/�F��//�@;�.:8;:909?>�,9/�?,60�,4=>;00/�8,294?@/0

#� � #]

"52!("*&�#]

2*!(,�#]

9"5)

#� �

#]

"52!("*&�#]

2*!(,�#]

9"5) "

+-

/

56!(,� #

]

"52!("*&�#]

2*!(,�#]

9"5) "

+-

/

2*.(� #

]

"52!("*&�#]

2*!(,�#]

9"5) "

+-

/

G2!("=*&�

TVEYT [� 9/EZ^9�� / WYEZZ TWZEZ� ^YE/ZV�� / ZZVE//i i� �[EU

d9[/YEZT'*e,1%'000c'>+<,B11='+,'"%6#"33)'A<1"61<6&"$'6&1'-$1<6+"3',B11='+$'6&+,'%",1

999


>+<,B11=N'l@"<N'4_"*B31'�.:9?K/�F��:8;@?0��D9,84.�#=0>>@=0

F�'%��%?,9/,=/��?8:>;30=0

3]�9/��#�

/ �9/[E^9/W 9[/YEZT/� �

9[[[ d/9YE^V'OB"''K^UV/EV'B,7'?#%&SM

F��:8;@?0� ,.3�9@8-0=

= � � 8+H� � 9E^ /YWE[UU //TE9U� �� [EU d/ZZE^V'*e,1%

8� d'X'� e%'d'9[/YEZTe/ZZE^V'd'TE^^ 99/


>+<,B11=N'l@"<N'4_"*B31'�.:9?K/�F��:B�,-:@?�,�/@0�0,>?�7,@9.3�@9/0=�>,80�.:9/4?4:9>�B4?3�490=?4,7�A07:.4?D27'/'O*e,1%'"$='73+A&6'B"6&'"$A31'27'Û�

d'[E['*e,1%

#]

"52!("*& "

+- 56!(,

� #]

"52!("*& %2,K� M%2,K1@M �

#]

"52!("*& "

+- G2!("=*&

� #]

"52!("*& ,+$K� M �

d'9^9Ê/'*e,1%

#]

"52!("*& "

+- 2*.(

� #]

"52!("*& %2,K� M,+$K1@M �

d'9^9Ê/'*e,1%

/[[[�9Y[

Û" - +,+$

/[[[�9Y[

Û" - +%2,

�9Y[

Z[" - +%2,�

/[[[�9Y[

Û" - +%2,

�9Y[

Z[" - +,+$�

99T


>+<,B11=N'l@"<N'4_"*B31'�.:9?K/�

#� � #]

"52!("*&�#]

2*!(,�#]

9"5)

#� �

#]

"52!("*&�#]

2*!(,�#]

9"5) "

+-

/

56!(,� #

]

"52!("*&�#]

2*!(,�#]

9"5) "

+-

/

2*.(� #

]

"52!("*&�#]

2*!(,�#]

9"5) "

+-

/

G2!("=*&�

d9WY9E[U'*e,1%'000��4=>;00/�49�?34>�.,>0�4>�70>>�?3,9�,4=>;00/�G�4?�,77�/0;09/>2$'6&1'=+<1%6+2$'6&"6')2#'3"#$%&S

[ [� 9/EZ^9�� / 9^9^E/ TWZEZ� ^YE/ZV�� / 9^9^E//i i� �[EU

99^


>BB1$=+_'/.'!"#$%&'-$+6+"3'Q2$=+6+2$,

99U


-$+6+"3'Q2$=+6+2$,

R11=',6"<6+$A'%2$=+6+2$,'72<',6"61'D1%62<'k

;F� ' ;N$(,!-.( N��

;F�

#F

!

#F

�

!F

�F

%F

#

%

$$$$$$$$$$$$

.

0

////////////

� ' ;N$(,!-.( N��

#�/

!�$&"'( %2,K� M � $)!*+ ,+$K� M � $(,!-.( ,+$K�M

%�

�!/

�#!#�

!�$&"'( ,+$K� M � $)!*+ %2,K� M � $(,!-.( %2,K�M

%#

%$

.

0/

#!#�

!

�$(,!-.(+[:.7

#

%

$$$$$$$$$$$$$

.

0

/////////////

�� 6"$�9 #!

#�

#

%$

.

0/

� � � �

99V


-$+6+"3'Q2$=+6+2$,.\<2#$='!"#$%&N':26"6+$A'4"<6&

:5"("*& '#2&6="(>'#2=(6! .#! � #[ ,+$K� +!6-5) M�#[ � :5"("*& '?!6-5).722)

#� � #[ %2,K*@&*-5=, M%2, � +!6-5)� �#% .0/� #[ ,+$K*@&*-5=, M%2, � +!6-5)� ��#A 23 %2, 0*(� �#

%.0/

#

%

$$$

.

0

///

85�

15 m/sec34(%-5 3&+1-

:5"("*& 'jB!C"(j

* ��

/�:1K0*( M � ,

� #!/ �#�

/#% .0#

%$$

.

0//

2 �:1K0*( M � ,

�#�

/ ��

:1K0*( M � ,

"!

+

-,

/

� #!#�� /

#

%

$$$$$$$$

.

0

////////

��

V[


-$+6+"3'Q2$=+6+2$,.\<2#$='!"#$%&N':26"6+$A'4"<6&'�.:9?K/�

85�

15 m/sec

F��94?4,7� ,>>��8[

:5"("*& 'D6."("65! � :1K0*( M � ,

� � *(*5E*!9� 2/#% .0

#!#�

N*!9� 2/#% .0 �9

&'(

123

#

%

$$$

.

0

///

��

V9


\<2#$='!"#$%&.'(2C$':"$A1'Q"3%#3"6+2$F��9?02=,?0/�?=,50.?:=D�24A0>

F��90=?4,7��:B9=,920!N�

d�rd�

r

�8 � !)5�9

�/

* �! �

9� � � ! �

/� �

/

#%$

.0/

�/ ��9� �

4%&5",-6%*7("258#

8"�9 � 8" �!"�9 � !"/

#%$

.0/

� "�9 �� "� �� V/


X132%+6)'?77'27'6&1':"+3

85�

15 m/sec3%+60

� !*"&

7-5%81-

7'%6,

79%+/ � �%

/41!2'

+ ��

82 � ,� �/

#

%

$$$$$

.

0

/////

� =*!2'-&S'9"(,'-5"(.

#F

!*"& � ��#!*"&

/

/��

�82 � ,� �/

,+$K� !*"& M � /' � %2,K� !*"& M#% .0 �$(,!-.(%

%F''' � �

$(,!-.(+[:.7

:�%+60;*3%+60<==>/%(849*%&0+-6?&

:3!@!;*)!@"-(-+0<

��

VT


-$+6+"3'Q2$=+6+2$,.\<2#$='!"#$%&N':26"6+$A'4"<6&

F��90=?4,7��7423?�#,?3��9270

F��=:@9/�$07,?4A0��7423?�#,?3��9270

� "52!("*& � 6"$�9 #!#�

#

%$

.

0/

� +!6-5) � 6"$�9 #!#� �#A 23 %2, 0*(� �

#

%$$

.

0//

99W


!"#$%&'-EQE'4_"*B31.

85�

15 m/sec

F�$:.60?��,@9.3�1=:8��=009�$4A0=�F6"&'00 TY� RE'3"6+6#=1N'TZW['76E'"36+6#=1'K9E/9'O*M

F�$:.60?��0,A0>��,@9.3�$,47�,?YU� "$A31'62'!2%"3'X1<6+%"3

F��:8;@?0��=:@9/�$07,?4A0��90=?4,7P3+A&6'B"6&'>$A31N'-$+6+"3'L2,+6+2$N'X132%+6)'X1%62<

H23"<'=").YV9V^E9',1%1"<6&.'WE/Z/99U10[EU'<"=e,1%

99Y


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

F��,=?3�=,/4@>�,>��@9.?4:9�:1��,?4?@/0

99Z


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

F��,=?3�=,/4@>�,?�7,@9.3�7,?4?@/0

:1"<6&'d

VTWYE9TV^Z

9 [E[Y9Y9ZTZ/

9 [E[Y9Y9ZTZ/�

�9Y[

TY" - +,+$/i

" -! , + [EU

dVTW[E[9'O*

9/[


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

85�

15 m/secF��,=?3�$,/4@>��

F�(1"<6& d'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''d'[ETVV99'O*e,1%

F��(< d'''''''''''''''''''''d'9ÊZ^/'*e,1%

F��(� d'''''''''''''''''''''d'9ET[WT'*e,1%'i'TVVE99'*e,1%'d'TVWE^/'*e,1%

F �+$1<6+"3 d'''''''''''''''''''''''''''''''d'/ET/Z�

F �A<2#$= d''''''''''''''''''''''''''''''''''''''''''''''''d'YÊZY�

F <'d':1i&'d'VTW[E[9i9E/9d'VTW9E//'O*

WE/Z/99U9[ U� VTW[E[9 9E/9i� � TY�9Y[" -

+%2,�

9U�9Y[

YU" - +,+$

9U�9Y[

YU" - +%2,

9Y[�

9ÊZ^/TVWE^/" -

+"6"$

9Y[�

9ÊZ^/TVWE^/ TVVE99�" -

+"6"$

F��:B�/:�B0�.:8;@?0+$+6+"3'D"3#1'72<'��G

9/9


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

85�

15 m/secF�+:@�3,A0�?:�>:7A0�1:=�?30�I49>?,9?,90:@>:=-4?J��G�1&)6*)+T(%*+U61*'6%1-

F # / �/�!

��*

� * ��

/�!

�# /#%$

.0/

� * ��

/�!

� #!/ �#�

/#% .0#%$

.0/

d' TEZYV 9[U�

/ TEZYV 9[U� �VTW[E[9 9E/9i� �

9^EZ^/9[[[" -

+/ TVWE^/

9[[[" - +

/i

" -! , +

�

d'T9YZE[UV'O*

9//


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

85�

15 m/secF�+:@�3,A0�?:�>:7A0�1:=�?30�I:=-4?J��G�&,,&4-%6,6-2*4&U-

F�/01490�I0..09?=4.4?D�A0.?:=J

F� ,294?@/0��..09?=4.4?D

2]�9�

# / ��!

#%$

.0/8]� 8

]�#]#

%$.0/#]

"!+-,

2] /

�9�

# / ��!

#%$

.0/! "]

!� !#!� � #! "]

!�#� "]

�#%$

.0/

"!

+-,

/

�

2] /

�9�#!/ �#�

/ ��!

#%$

.0/! �!#!

/

� "!

+-,

/

�!#!#�

� "!

+-,

/

�

!#!/

��!#�

/

��9�

!#!/

� "!

+-,

/

�!#!#�

� "!

+-,

/

�!#�

/

��9

"!

+-,

/

�!#!#�

� "!

+-,

/

�

2 �!�

#�/ �

�!

"!

+-,/

� #!#�� /

9/T


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

85�

15 m/secF�#=:A0

F��=:8��0;70=K>�%0.:9/�7,B

2 �!�

#�/ �

�!

"!

+-,/

� #!#�� /

#]� !�

2,+$ �� 9� 2%2, ��

"]

!� "]

�

#

%$

.

0/ � ,#@'+$62'"@2D1�

�!�

!�� / � �!

"!

+-,/

� !�� / 2,+$ �� 9� 2%2, ��

"!+

-,

"!

+

-,

/

9/^


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

85�

15 m/sec F��=:8��0;70=K>�&34=/�7,B

F�%@-�49?:�;=0A4:@>

!�� / �!/�!

"!

+-,

/

�&!

"!

+-,/

� �&/

* 9� 2/� �� !�� / �

&!

"!

+-,/

��* 9� 2/� �

!/�

�!* 9� 2/� �!

��!9� 2%2, �� #% .0

�!�

�!

��!2%2, ��

! "!

+-,/

��!9� 2%2, �� #% .0

2,+$ �� 9� 2%2, ��

"!+

-,

"!

+

-,

/

�

!�

�!2%2, ��

"!+-,/

��!2,+$ ��

"!+-,/

�!�

�!2 %2, �� / � ,+$ �� / � 2

lE4E(E9/U


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

85�

15 m/sec

2 �!�

#�/ �

�!

"!

+-,/

� #!#�� /

VTW[E[9 9E/9i� �

TEZYV 9[U�

TVWE^/9[[[" -

+/ TEZYV 9[U�

VTW[E[9 9E/9i� ��

" -! , + / TVWE^/

9[[[9^EZ^/9[[[" -

+/

i" -! , + [EU

d

d'[EZZWY^// I$0,77D�%6499D�"=-4?J

9/V


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

85�

15 m/sec

F��49,77D�G�>:7A0�1:=��

F��=:8��0;70=K>��4=>?�7,B

#!#�

� 6"$K� M �2,+$ ��

9� 2%2, ��

! �* 9� 2/#% .09� 2%2, ��

F�%:7A0�1:=�>49��M

�* 9� 2/#% .02!

6"$K� M � ,+$ �� 9/W


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

85�

15 m/sec

F�>:7A0�1:=�.:>��=:8��0;70=K>��4=>?�7,B

! �* 9� 2/#% .09� 2%2, ��

� %2, �� 92* 9� 2/#% .0

!�9

#

%$$

.

0//

6"$K�M �,+$ �� %2, ��

�

* 9� 2/#% .02!

6"$K� M

92* 9� 2/#% .0

!�9

#

%$$

.

0//

�

*!9� 2/#% .0

#!#�

*!9� 2/#% .0 �9#

%$.0/

�

� � *(*5E*!9� 2/#% .0

#!#�

N*!9� 2/#% .0 �9

&'(

123

9/Y


!"#$%&'-EQE'4_"*B31.'�.:9?K/�

85�

15 m/sec

� � *(*5E*!9� 2/#% .0

#!#�

N*!9� 2/#% .0 �9

&'(

123

9Y[9Y[�

T9YZE[UVVTW[E[9 9E/9i� �

9 [EZZWY^//[U/�� 9^EZ^/

TVWE^/T9YZE[UV

VTW[E[9 9E/9i� �9 [EZZWY^//[U/�� 9�

" -! ,! ,! ,! ,! ,! ,! , +

"6"$id

d'9WZEZZU�

9/Z


\<2#$='!"#$%&.'(2C$':"$A1'Q"3%#3"6+2$F��9?02=,?0/�?=,50.?:=D�24A0>

F��90=?4,7��:B9=,920!N�

d�rd�

r

�8 � !)5�9

�/

* �! �

9� � � ! �

/� �

/

#%$

.0/

�/ ��9� �

4%&5",-6%*7("258#

8"�9 � 8" �!"�9 � !"/

#%$

.0/

� "�9 �� "� �9T[


\<2#$='!"#$%&.'(2C$':"$A1'Q"3%#3"6+2$�.:9?K/�

F��=:@9/�$07,?4A0��:B9=,920F��..:@9?�1:=��,=?3�$:?,?4:9

:1"<6& � 8%2,K1@M� �/ � 8,+$K1@M�#2*!(, �H EBE$� �/

&480�:1�17423?�G?480�1=:8!"#$%&'62'+*B"%6'"36+6#=1

9T9


P+_1='4"<6&'>BB<2_+*"6+2$

F��29:=0�0110.?>�:1�=:?,?4:9

F�(+$1<6+"3dXA<2#$=

F��+$1<6+"3d�A<2#$=

F� +$1<6+"3d A<2#$=

F��..@=,?0�1:=�%3:=?��@=,?4:932C1<'"36+6#=1'73+A&6,

9T/

Theta


X132%+6)?77'27'6&1':"+3'K9M

85�

15 m/sec3%+60

� !*"&

'&3

7-5%81-

'&3&(#"N�+,#4O

'&3&.)(N�+,#4O

7'%6,

79%+/

% � 1!*"& � $(,!-.( � $+!*G � $'!"= � $)!*+

''''''''''''''''''''$+!*G � % � + � ,+$K� !*"& M � %�

82 � ,� �/� ,+$K� !*"& M

$)!*+ � /41!2'9/�#!*"&

/ "!

+-,� %

�#!*"&/

/�

$'!"= I/' �J56!%!*"&� /' �% � +%2,K� !*"& M � /' �%

�82 � ,� �/

� %2,K� !*"& M

#

%

$$$$$$$$

.

0

////////9TT


X132%+6)?77'27'6&1':"+3'K/M

85�

15 m/sec3%+60

� !*"&

7-5%81-

7'%6,

79%+/ % � 1!*"& � $(,!-.( � $+!*G � $'!"= � $)!*+

� �%

/41!2'

+ ��

82 � ,� �/

#

%

$$$$$

.

0

/////

� =*!2'-&S'9"(,'-5"(.

#F

!*"& � ��#!*"&

/

/��

�82 � ,� �/

,+$K� !*"& M � /' � %2,K� !*"& M#% .0 �$(,!-.(%

%F''' � �

$(,!-.(+[:.7

:�%+60;*3%+60<==>/%(849*%&0+-6?&

:3!@!;*)!@"-(-+0< 9T^


>BB1$=+_'T.'`"33+,6+%'Q2177+%+1$6'4_"*B31,

9TU


4_"*B31'`"33+,6+%'Q2177+%+1$6,

F k0TW';1+A&6'd'W[[['3@F ><17 d'99NTYV'+$/

F (<"A'Q2177+%+1$6H Q= d'[E9'KG1<2'"3B&"M

F `"33+,6+%'Q217'K�M'd';eKQ=><17MH � d'VE9^Y'3@e+$/ KG1<2'"3B&"M

�!"#$%$#&'()*'+',-&./)0',.1+23�4$'5/./+)678)0.)9,1"$,'()+$::1")*'+',-&./;�<+/')9=;)8>7??)0.>

�@+//)2./'5)#+'A),1/00$,$/".)�9B#;)7CC�4+'A)(122)0',.1+)#&/)01+).D1)�*'+',-&./),(&2./+)7?C)9E7F)�01+)2$"A(/)*'+',-&./;�B-&./)D/$A-.)GF)(:2H/'

F�*0TW'?<@+6"3'I<"$,71<'X1&+%31

9TV


4_"*B31'`"33+,6+%'Q2177+%+1$6,'�.:9?K/�

F X1&+%31';+6&'90 L"<"%&#61,F ;1+A&6'd'W9/['3@F ><17 d'99NTYV'+$/

F `"33+,6+%'Q217'K�M'd';eKQ=H<17M'3@e+$/

H ��%&#61 d' 9EUU^'3@e+$/

F k0TW';1+A&6'd'W[[['3@F k%EAE'd'9WYEWUF H<17 d'99NTYV'+$/F >,,#*1'(<"A'Q2177+%+1$6

H Q= d'[E9'KG1<2'"3B&"M

F `"33+,6+%'Q217'K�M'd';eKQ=H<17MH � d'VE9^Y'3@e+$/ KG1<2'"3B&"M

�d W[V[ 9^^ ^/EZZ [EUU�� 99TYV

[E9i" - + 99TYV" -

+9�

F��0?K>�/0;7:D��.3@?0

9TW


4_"*B31'`"33+,6+%'Q2177+%+1$6,'�.:9?K/�

F X1&+%31';+6&'/0 L"<"%&#61,F ;1+A&6'd'W9/['3@F ><17 d'99NTYV'+$/

F `"33+,6+%'Q217'K�M'd';eKQ=H<17M'3@e+$/

H ��%&#61 d' [EZTUZ'3@e+$/

F k0TW';1+A&6'd'W[[['3@F k%EAE'd'9WYEWUF H<17 d'99NTYV'+$/F >,,#*1'(<"A'Q2177+%+1$6

H Q= d'[E9'KG1<2'"3B&"M

F `"33+,6+%'Q217'K�M'd';eKQ=H<17MH � d'VE9^Y'3@e+$/ KG1<2'"3B&"M

�d

F��0?K>�/0;7:D��.3@?0>

W9/[ / 9^^ ^/EZZ [EUU�� [EZU� ��99TYV

[E9i" - + 99TYV" -

+9�

9TY


>BB1$=+_'^.'Q2*B"<+,2$'27'`"33+,6+%'"$='R2$0`"33+,6+%'6<"J1%62<+1,

9TZ


4_"*B31'-.'8+$26"#<'X'!"#$%&'62'81=+#*'4"<6&'I<"$,71<'?<@+6'K8I?M1st Stage � TU-9032nd Stage � SR-119 3rd Stage � SR-1204th Stage � Star 48B long 5th Stage � Star 27 with 25-30% propellant offload(depending on final payload mass)

��

�� 400+ kg payload delivery to 19,000 km altitude MEO orbit without 6th stage

Star 27

9^[


8+,,+2$'Q?R?LHeI+*13+$1

9^9


!"#$%&'8+,,+2$'L3"$

H6"A1'-X'`#<$2#6

!""""#""""""

$!""""#""""""

$%&"""#""""""

$%'"""#""""""

$%("""#""""""

$%!"""#""""""

$%""""#""""""

$&"""#""""""

$'"""#""""""

$("""#""""""

$!"""#""""""

"#""""""

!"""#""""""

("""#""""""

'"""#""""""

&"""#""""""

%""""#""""""

%!"""#""""""

%("""#""""""

%'"""#""""""

%&"""#""""""

%!"""#"""""""$!&"""#""""""" $%""""#""""""" "#"""""""

F��4=0.?�49>0=?4:9�49?:� &"�:=-4?

9^/


!"#$%&'8+,,+2$'L3"$

)*"""#"

$)*"""#"

$)""""#"

$!""""#"

$%""""#"

"#"

%""""#"

!""""#"

)""""#"

)*"""#"$)*"""#" $!""""#" "#" !""""#"

+,-.,/012.3456789/,678-06

)*"""#"

$)*"""#"

$)""""#"

$!""""#"

$%""""#"

"#"

%""""#"

!""""#"

)""""#"

)*"""#"$)*"""#" $!""""#" "#" !""""#"

+,-.,/012.6:456789/,678-0

)*"""#"

$)*"""#"

$)""""#"

$!""""#"

$%""""#"

"#"

%""""#"

!""""#"

)""""#"

)*"""#"$)*"""#" $!""""#" "#" !""""#"

+,-.,/012.634:6789/,678-06

3D MTOOrbit Profile(ref. First Point of Ares)8 August 2010 launch

I<"$,71<'2<@+6

P+$"3'2<@+6

9^T


`"33+,6+%'!"#$%&'L<27+31

9^^


L+6%&'L<27+31'?B6+*+G"6+2$

`"33+,6+%'6<"J1%62<)

01'-2-3%H*M-'&?*M"(:-8%

��-Degree of freedom Launch simulation used to optimize pitch profile for maximum stage IV mass to MTO

�� 9^U


?B6+*+G1='KR2$0`"33+,6+%M'!"#$%&'L<27+31

9^V

mae-nas.eng.usu.edumae-nas.eng.usu.edu/mae_5540_web/propulsion_systems/section3/...mae-nas.eng.usu.edu...

Documents