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02/10/10 ELF 1

Eugene L. FleemanSenior Technical AdvisorGeorgia Institute of Techno

Maximizing Missile Flight Performance



02/10/10 ELF 2

OutlineOutline

Parameters and Technologies That Drive MissileFlight Performance

Missile Flight Performance Prediction

Examples of Maximizing Missile Flight Performance

( Workshop ) Summary



02/10/10 ELF 3

Parameters That Drive MissileFlight Performance

Parameters That Drive MissileFlight Performance

Nose FinenessDiameter

Propellant / Fuel

Wing Geometry/ Size

StabilizerGeometry /Size

Flight

ControlGeometry /Size

Lengt

h

Thrust

Profil

e

Flight Conditions( α , M, h )



02/10/10 ELF 4

Low Drag

Low Drag

10

100

1000

10000

100000

4 8 12 16 20

d, Diameter, inches

D / C D ,

D r a g

/ D r a g C o e f f i c i e n t , l

Dynamic Pressure =1,000 psf



Example for Rocket Baseline:

d = 8 inches = 0.667 ft

Mach 2, h = 20K ft, ( CD0)Powered = 0.95

q = 1/2 ρ V2 = 1/2 ρ ( M a )2

= 1/2 ( 0.001267 ) [( 2 ) ( 1037 )]2 = 2,

D0 / CD0= 0.785 ( 2725 ) ( 0.667 )2 = 95

D0 = 0.95 ( 952 ) = 900 lb

D = CD q SRef = 0.785 CD q d2

Note: D = drag in lb, CD = drag coefficient, q =

dynamic pressure in psf, d = diameter( reference length ) in ft

i hil S b i



02/10/10 ELF 5

Nose Fineness While SubsonicDrag is Driven by Skin FrictionNose F neness W e u son cDrag is Driven by Skin Friction

0.01

0.1

1

10

0 1 2 3 4 5

M, Mach Number

(CD0)Body,Wave;lN / d =0.5

(CD0)Body,Wave;lN / d =1



(CD)Base,Coast


( CD0)Body, Wave ( CD0

)Body, Friction

( CD )Base

lN / d = 2.4, Ae = 11.22 in2, SRef = 50.26 in2, M = 2, h = 20K ft,q = 2725 psf, l / d = 18, l = 12ft

( CD0)Body, Wave = 0.14

( CD )Base Coast = 0.25 / 2 = 0.13

( CD )BasePowered = ( 1 - 0.223 )( 0.25 / 2 ) = 0.10

( CD0)Body, Friction = 0.053 ( 18 )

{ ( 2 ) / [( 2725 ) ( 12 ) ]}0.2 =0.14

( CD0)Body, Coast = 0.14 + 0.13 +

0.14 = 0.41

( CD0)Body, Wave = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69 , for M > 1.

Based on Bonney reference, tan-1 in rad.

( CD0)Base,Coast = 0.25 / M, if M > 1 and (C

D0)

Base,Coast= ( 0.12 + 0.13 M2 ), if M < 1

( CD0 )Base,Powered = ( 1 – Ae / SRef ) ( 0.25 / M ), if M > 1 and ( CD0 )Base,Powered = ( 1 –Ae / SRef ) ( 0.12 + 0.13 M2 ), if M < 1

(CD0

)Body,Friction = 0.053 ( l / d ) [ M / ( q l )]0.2 . Based on Jerger reference,

turbulent boundary layer, q in psf, l in ft.

( CD0)Body = ( CD0

)Body, Wave + ( CD0)Base + (C

D0 )Body,Friction

Note: ( CD0 )Body,Wave = body zero-lift wave drag coefficient, ( CD0 )Base = body base dragcoefficient, ( CD0

)Body, Friction = body skin friction drag coefficient, ( CD0)Body = body zero-lift

drag coefficient, lN = nose length, d = missile diameter, l = missile body length, Ae =nozzle exit area, SRef = reference area, q = dynamic pressure, tan-1 [ 0.5 / ( lN / d )] in rad



N l F dN l F d


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Normal Force and Maneuverability

Normal Force and Maneuverability

3

3.5

M <1.35, based on slen

M =2, based on linear

M =5, based on linearN

Wing

REF

W,

Wing

NormalF

orc

e

Coeffi c

ientf

or

Rocke

tBase l

ine

α ’ = α W = α + δ , Wing Effective Angle of Attack, Deg

( CN )Wing = [ 4sin α ’ cos α ’ / ( M2 – 1 )1/2 + 2 sin2α ’ ] ( SW / SRef ), if M >

{ 1 + [ 8 / ( π A )]2 }1/2

( CN )Wing = [ ( π A / 2) sin α ’ cos α ’+ 2 sin2α ’ ] ( SW / SRef ), if M < { 1

+ [ 8 / ( π A )]2 }1/2

Note: Linear wing theory applicable if M > { 1 + [ 8 / ( π A )]2 }1/2 , slender wingtheory applicable if M < { 1 + [ 8 / ( π A )]2 }1/2 , A = Aspect Ratio, SW = Wing

Planform Area, SRef = Reference Area

Example for RocketBaseline

AW = 2.82

SW = 2.55 ft2

SRef = 0.349 ft2

δ = 13 deg, α = 9deg

M = 2

{ 1 +[ 8 / ( π A )]2 }1/2 = 1.35

Since M > 1.35, uselinear wing theory +

Newtonian theoryα ’ = α W = α + δ =

22°( CN )Wing SRef / SW = [ 4

sin 22° cos 22° / ( 22 –1 )1/2 + 2 sin2 22°] =1.083

( CN )Wing = 1.08( 2.55 ) / 0.349 = 7.91

Th Sh k W D f ThiTh Sh k W D f Thi



Than Shock Wave Drag for a ThinWing

Than Shock Wave Drag for a ThinWing

0

0.005

0.01

0.015

0.02

100 1000 10000

q, Dynamic Pressure, psf

M/ cmac =0.01 / ft M/ cmac =0.1 / ft

M/ cmac =1 / ft M/ cmac =10 / ft

( CD0)Wing,Friction = nW { 0.0133 [ M / ( q cmac )]0.2 } ( 2 SW / SRef ), based on

Jerger, turbulent, q in psf, cmac in ft

( CDO)Wing,Wave = nW [ 2 / ( γ MΛ LE

2 )]{{[( γ + 1 ) MΛ LE

2 ] / 2 }γ / ( γ - 1) {( γ + 1

) / [ 2 γ MΛ LE2 – ( γ - 1 )]}1/ ( γ - 1) – 1 } sin2 δ LE cos Λ LE tmac b / SRef , based

on Newtonian impact theory( CDO

)Wing = ( CDO)Wing,Wave + ( CDO

)Wing,Friction

nW = number of wings ( cruciform

= 2 )

q = dynamic pressure in psf

cmac = length of mean aero chord

in ft

γ = Specific heat ratio = 1.4

MΛ LE= M cos Λ LE = Mach number ⊥

leading edge

δ LE = leading edge section total

angle

Λ LE = leading edge sweep angle

tmac = max thickness of mac

b = span

Example for Rocket Baseline Wing:

nW = 2, h = 20K ft ( q = 2,725 psf ),cmac = 1.108 ft, SRef = 50.26 in2, SW =367 in2, δ LE = 10.01 deg, Λ LE = 45deg, tmac = 0.585 in, b = 32.2 in, M =2 ( MΛ LE

= 1.41 )

( CDO)Wing,Friction SRef / [ nW SW ] = 2

{( 0.0133 ) { 2 / [( 2725 )

( 1.108 )]}0.2

} = 0.00615( CD0

)Wing,Friction = 0.00615 ( 2 ) ( 367 )

(C

D0

) Wing,Friction

S

Ref

/

(n

W

SW

)

Hi h T i A l f A k dHi h T i A l f Att k d



Higher Trim Angle of Attack and Higher Normal Force

Higher Trim Angle of Attack and Higher Normal Force

CN, Trim , TrimmedNormal ForceCoefficient of RocketBaseline

0 4 8 12 16 20 24

16

12

8

4

0

α Trim , Trim Angle of Attack,

Deg

Note: Rocket Baseline

XCG = 75.7 in.Mach 2

( α + δ )Max = 21.8 Deg, ( CNTrim)Max

α / δ = 0.75, ( Static Margin = 0.88 Diam )

α / δ = 1.5, ( SM = 0.43 Diam )

α / δ = ∞ , ( SM = 0 )

Hi h Th t d R d F lHi h Th t d R d F l



Scramjet

Higher Thrust and Reduces Fuel Consumption

Higher Thrust and Reduces Fuel Consumption

Turbojet

Ramjet

SolidRocket

4,000

3,000

2,000

1,000

0Thrus

t/(FuelFlow

Rate),Spec if

ic

Impuls

e,I SP,

Secon

ds

0 2 4 6 8 10 12

Mach Number

DuctedRocket



Acceleration Capability

Acceleration Capability

1,000

100

10

10 1 2 3 4 5

RamjetTMax = (π / 4 ) d2 ρ ∞ V∞

2

[( Ve / V∞ ) - 1 ]

Solid RocketTMax = 2 PC At = m

.Ve

M, Mach Number

(T

/W

) Max

,(Thrust/W

eight ) M

ax,

Note:

PC = Chamber pressure, At = Nozzle throat area, m.= Mass flow rate

d = Diameter, ρ ∞ = Free stream density, V∞ = Free stream velocity,Ve = Nozzle exit velocity ( Turbojet: Ve ~ 2,000 ft / sec, Ramjet: Ve ~ 4,500

TurbojetTMax = (π / 4 ) d2 ρ ∞ V∞

2

[( Ve / V∞ ) - 1 ]

f M h 3 t 5 ith Hi hM t 5 t H



from Mach 3 to 5 with HighCombustion Temperaturerom Mac to 5 w t H gCombustion Temperature

0

5

10

15

20

25

0 1 2 3 4 5

M, Mach Number

T / [ P H I ( p 0 ) ( A 3 ) ] , N o n d i m

i m e n s i o n a l T h r u s t i f S p e c i f i

H e a t R a t i o = 1 . 2 9

T4 / T0 =3 T4 / T0 =5 T4 / T0 =10 T4/ T0 =15

T / ( φ p0 A3 ) = γ M02 {{[ T4 / T0 ] / { 1 + [( γ - 1 ) / 2 ]

M02 }}1/2 - 1 }

Note: Ideal ramjet, isentropic flow, exit pressure = free streampressure, φ ≤ 1, T in °R

Example for Ramjet Baseline:

M = 3.5, h = 60 Kft, T4 = 4,000deg R, ( f / a ) = 0.06, φ =0.900, T0 = 392 Rankine, p0 =1.047 psi, A3 = 287.1 in2, γ =1.29

T / ( φ p0 A3 ) = 1.29 ( 3.5 )2 {{[4000 / 392 ] / { 1 + [( 1.29 –1 ) / 2 ] ( 3.5 )2 }}1/2 – 1 } =14.49

T = 14.49 ( 0.900 ) ( 1.047 )( 287.1 ) = 3920 lb

Note:

T = Thrust

p0 = Free stream static

pressure

A3 = Combustor flameholderentrance area

γ = Specific heat ratio

M0 = Free stream Mach number

T4 = Combustor exit

temperature

T0 = Free stream temperature

Th t f R k t O t Hi hTh t f R k t O t Hi h



Thrust of Rocket Occur at HighChamber Pressure and AltitudeThrust of Rocket Occur at HighChamber Pressure and Altitude

220

240

260

280

0 5 10 15 20

Nozzle Expansion Ratio

I s p , S p e c i f i c I m p u l s e o

f R o c k e t B a s e l i n e

h =SL, pc =300 psi h =SL, pc =1000 psi

h =SL, pc =3000 psi h =100K ft, pc >300 psi

ISP = cd {{[ 2 γ 2 / ( γ - 1)] [ 2 / ( γ + 1)] ( γ - 1) / ( γ +1) [ 1 – ( pe / pc ) ( γ - 1) /

γ ]}1/2 + ( pe / pc ) ε - ( p0 / pc ) ε } c* / gc

T = ( gc / c* ) pc At ISP

ε = {[ 2 / ( γ + 1)1/ ( γ - 1) ][( γ -1) / ( γ + 1 )]1/2 ]} / {( pe / pc )1/ γ [ 1 -( pe / pc ) ( γ - 1) / γ ]1/2 }

Note:ε = nozzle expansion ratiope = exit pressure

pc = chamber pressure

p0 = atmospheric pressure

At = nozzle throat area

γ = specific heat ratio = 1.18 infigurecd = discharge coefficient = 0.96 in

figurec* = characteristic velocity =5,200 ft / sec in figure


ε = Ae / At = 6.2, At = 1.81 in2

h = 20 Kft, p0 = 6.48 psi

( pc )boost = 1769 psi, ( ISP )boost = 257sec

( T )boost = ( 32.2 / 5200 ) ( 1769 )(1.81 )( 257 ) = 5096 lb

( pc )sustain = 301 psi, ( ISP )sustain = 239sec

( T )boost

= ( 32.2 / 5200 ) ( 301 )(1.81 )( 239 ) = 807 lb

V l it d P ll t F lV l it d P ll t F l



Velocity, and Propellant or Fuel Weight Fraction

Velocity, and Propellant or Fuel Weight Fraction

Typical Value for 2,000 lb Precision Strike Missil

Note: Ramjet and Scramjet missiles booster propellant for Mach 2.5 to 4 take-over speed not included in WP

for cruise. Rockets require thrust magnitude control ( e.g., pintle, pulse,

or gel motor ) for effective cruise. Max range for a rocket is usually asemi-ballistic flight profile, instead of cruise flight.

R = ( L / D ) Isp V In [ WL / ( WL – WP )] , Breguet Range Equation

Parame

ter

L / D, Lift / Drag

Isp , Specific Impulse

VAVG , Average Velocity

WP / WL, Cruise

Propellant or FuelWeight / LaunchWeightR, Cruise Range

10

3,000sec

1,000ft / sec

0.3

1,800

nm

5

1,300sec

3,500ft / sec

0.2

830 nm

3

1,000sec

6,000ft / sec

0.1

310 nm

5

250 sec

3,000

ft / sec0.4

250 nm

Solid RocketHydrocarbon FuelScramjet Missile

Liquid FuelRamjet Missile

Subsonic TurbojetMissile

P k i P id E t d dP P E t



Packaging Provide Extended Range Ramjet

Pac ag ng Prov e Exten eRange Ramjet

Propulsion / Configuration Fuel Type / VolumetricPerformance (BTU / in3) /

Density (lb / in3)

Fuel Volume (in3) /Fuel Weight (lb)

ISP (sec) / CruiseRange at Mach 3.5,

60K ft (nm)Liquid Fuel Ramjet

RJ-5 / 581 / 0.040 11900 / 476 1120 / 390

Ducted Rocket ( Low Smoke )

Solid Hydrocarbon / 1132 /0.075

7922 / 594 677 / 294

Ducted Rocket ( HighPerformance )

Boron / 2040 / 0.082 7922 / 649 769 / 366

Solid Fuel Ramjet

Boron / 2040 / 0.082 7056 / 579 1170 / 496

Slurry Fuel Ramjet 40% JP-10, 60% boroncarbide / 1191 / 0.050

11900 / 595 1835 / 770

Note: Flow Path Available Fuel Rcruise = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )]



Extended Range

Extended Range

Altitude

Range RMAX

Apogee or Cruise

Glid

e

Climb

Rapid Pitch Up

Line-Of-Sight Trajectory

RMAX

Design Guidelines for Horizontal Launch:– High thrust-to-weight ≈ 10 for safe separation– Rapid pitch up minimizes time / propellant to reach efficient

altitude– Climb at a ≈ 0 deg with thrust-to-weight ≈ 2 and q ≈ 700 psf

minimizes drag / propellant to reach efficient cruise altitude for

( L / D )MAX

– High altitude cruise at ( L / D )MAX and q ≈ 700 psf maximizes

r en rope an e gr en rope an e g



r ven y SP , rope an e g ,Drag, and Static Margin

r ven y SP , rope an e g ,Drag, and Static Margin

-1

-0.5

0

0.5

1

1.5

Isp Prop.

Weight

CD0 Drag-

Due-to-

Lift

Static

Margin

Thrust Inert

Weight

Parameter

Nondimensional

RangeSensitivity to

Parameter

Note: Rocket baseline:

hL = 20k ft, ML = 0.7, MEC = 1.5

R@ML=0.7, hL=20Kft = 9.5 nm

Example: 10% increase inpropellant weight ⇒ 8.8%increase in flight range

y ue e g rus any u u



y SP , ue e g , rus , an Zero-Lift Drag Coefficient

y SP , u , u , Zero-Lift Drag Coefficient

-1

-0.5

0

0.5

1

1.5

Inert

Weight

Fuel

Weight

CD0, Zero-

Lift Drag

Coefficient

CLA, Lift-

Curve-

Slope

Coefficient

Thrust ISP

Parameter

N o n d i m e n s i o n a l R a n g e S e n s i t i v i t y

t o P

a r a m e t e r

Sea Level Flyout at Mach 2.3 20 Kft Flyout at Mach 2.5

40 Kft Flyout at Mach 2.8 60 Kft Flyout at Mach 3.0

Example: At Mach 3.0 /60K ft altitude cruise,10% increase in fuelweight ⇒ 9.6% increase inflight range



Uncertainty Is +/- 7%, 1 σ Uncertainty Is +/- 7%, 1 σ

Parameter Baseline Value at Mach3.0 / 60k ft

Uncertainty in Parameter ∆R / R due to Uncertainty

1. Inert Weight 1205 lb +/- 2%, 1σ +/- 0.8%, 1σ

2. Ramjet Fuel Weight 476 lb +/- 1%, 1σ +/- 0.9%, 1σ

3. Zero-Lift Drag Coefficient 0.17 +/- 5%, 1σ +/- 4%, 1σ

4. Lift Curve Slope Coefficient 0.13 / deg +/- 3%, 1σ +/- 1%, 1σ

5. Cruise Thrust (φ=0.39 ) 458 lb +/- 5%, 1σ +/- 2%, 1σ

6. Specific Impulse 1040 sec +/- 5%, 1σ +/- 5%, 1σ

aturity of Ramjet Baseline Based on Flight Demo of Prototype and Subsystem

unnel tests

connect, freejet, and booster firing propulsion tests

ure test

are-in-loop simulation

ht Range Uncertainty at Mach 3.0 / 60K ft Flyout

= [ (∆ R / R )1

2

+ (∆ R / R )2

2

+ (∆ R / R )3

2

+ (∆ R / R )4

2

+ (∆ R / R )5

2

+ (∆ R / R )6

2

]1/2

= +/- 6.5 nm +/- 31 nm, 1σ

Programs Provide EnhancedPrograms Provide Enhanced



Programs Provide Enhanced Performance

Programs Provide Enhanced Performance

Year Entering EMD

AIM-9X ( maneuverability ),

1996 - HughesAIM-120 ( speed, range ), 1981- Hughes

Long Range ATS, AGM-86,1973 - Boeing

AGM-129 ( RCS ), 1983 -General Dynamics

PAC-3 (accuracy), 1992 -Lockheed MartinLong Range STA, MIM-104,1966 - Raytheon

1950 1965 1970 1975 1980 1985 1990 1995 >2000

AGM-88 ( speed, range ),1983 - TI

Man-portable STS, M-47, 1970 -McDonnell Douglas

Anti-radar ATS, AGM-45, 1961 - TI

Short Range ATA, AIM-9,

1949 - Raytheon

Javelin ( gunnersurvivability,lethality, weight ),1989 - TI

Medium Range ATA, AIM-7,1951 - Raytheon

Medium Range ATS, AGM-130,1983 - Rockwell

JASSM ( range,observables ), 1999 -Lockheed Martin

HypersonicMissile, ~2005

HypersonicMissile ~2005

Long Range STS, BGM-109, 1972 -General Dynamics

HypersonicMissile ~2005

f th A t Ad t Mi ilf th A t Ad t Mi il



of-the-Art Advancement: MissileManeuverability

of-the-Art Advancement: MissileManeuverability

0

10

20

30

40

50

60

1950 1960 1970 1980 1990 2000 2010

Year IOC

O p e r a t i o n a l A n g l e o f A t t a c k , D e g r e e

AIM-7A

AM-9BR530

AA-8

AIM-54

R550

Skyflash

Python 3

AA-10

Aspide

Super 530D

AA-11

AIM-120

Python 4

AA-12

MICA

AIM-132AIM-9X

ControlsAugmentedwithPropulsionDevices ( TVC,Reaction Jet )

f th A t Ad t S iof the Art Ad ancement S personic



02/10/10 ELF 22

of-the-Art Advancement: Supersonic Air Breathing Missiles

of-the-Art Advancement: Supersonic Air Breathing Missiles

0

1

2

3

4

5

6

7

1950 1960 1970 1980 1990 2000 2010

Year Flight Demonstration

M c r u i s e , C r u i s e M a c h N u m b e

Cobra

Vandal / TalosRARE

Bloodhound

BOMARC

Typhon

CROW

SA-6

Sea DartLASRM

ALVRJ

3M80

ASALM

Kh-31

ASMP

ANS

Kh-41

SLAT

HyFly

Scram jet

Ramjet

New Tec no og es T at En anceew ec no og es at n ance



02/10/10 ELF 23

New Tec no og es T at En anceTactical Missile Performanceew ec no og es at n anceTactical Missile Performance

me

aceted / Windowulti-lens

Seeker

StrapdownHigh Gimbal

G & C

GPS / INSIn-flightOptimizeα , β Feedback

PropulsionLiquid / Solid FuelRamjetVariable FlowDucted Rocket

ScramjetHigh TemperatureCombustorHigh Density Fuel /PropellantHigh Throttle FuelControl

Endothermic FuelComposite Case

InsulationHypersonicHigh Density

Flight Control

TVC /Reaction Jet

PowerMEMS

AirframeLifting BodyNeutral StaticMarginLattice Fins

Low Drag InletMixed Comp.InletCompositeTitanium AlloyMEMS DataCollection

Split CanardFree-to-roll



02/10/10 ELF 24

OutlineOutline

Parameters and Technologies That Drive MissileFlight Performance


Examples of Maximizing Missile Flight Performance

( Workshop ) Summary

Max Range ma M n Range



02/10/10 ELF 25

Max Range, ma M n Range,and Large Off Boresight

Rear FlyoutRange•Max•Min

Forward FlyoutRange•Max•Min

Beam Off BoresightFlyout Range•Min•Max

Examples of Air Launched MissileExamples of Air Launched Missile



02/10/10 ELF 26

Examples of Air Launched MissileFlight Performance

Examples of Air Launched MissileFlight Performance

Examples of Surface LaunchedExamples of Surface Launched



02/10/10 ELF 27

Examples of Surface Launched Missile Flight Performance

Examples of Surface Launched Missile Flight Performance

Versus Preliminary DesignVersus Preliminary Design



02/10/10 ELF 28

Versus Preliminary DesignModeling

Versus Preliminary DesignModeling

Conceptual Design Modeling

1 DOF [ Axial force ( CDO), thrust,

weight ]

2 DOF [ Normal force ( CN ), axial force,

thrust, weight ]

3 DOF point mass [ 3 forces ( normal,axial, side ), thrust, weight ]

3 DOF pitch [ 2 forces ( normal, axial ),

1 moment ( pitch ), thrust, weight ]

4 DOF [ 2 forces ( normal, axial ), 2moments ( pitch, roll ), thrust, weight ]

Preliminary Design Modeling

CDO

CN

CN

CN Cm

CA

CA

CA

CA

CA

Cl

Cl

CN Cm

CNCm

CnC Y

C Y

Motion Show Drivers forMotion Show Drivers for



02/10/10 ELF 29

Motion Show Drivers for Configuration Sizing

Motion Show Drivers for Configuration Sizing

Configuration SizingImplication

Ι y θ .. ≈ q SRef d Cmα α + q SRef d Cmδ

δ High Control

Effectiveness ⇒ Cmδ> Cmα

,

Iy small ( W small ), q large

( W / gc ) V γ . ≈ q SRef CNα

α + q SRef CNδ δ - W cos γ Large

/ Fast Heading Change ⇒ CN

+ Normal Force

α << 1 rad

γ

δ W

+ MomentV

+ Thrust

+ Axial Force

Note: Based onaerodynamic control

n ue or rope ann ue or rope an



02/10/10 ELF 30

1.00E+07

1.00E+08

R

a n g e , f

sp , , n ue or rope anWeight Fraction

sp , , n ue or rope anWeight Fraction

Example: Ramjet Baseline at Mach3 / 60 Kft altR = 2901 ( 1040 ) ( 3.15 ) ln[ 1739 / ( 1739 - 476 )]= ( 9,503,676 ) ln [ 1 / ( 1 -0.2737 )] = 3,039,469 ft = 500 nm

R = ( V Isp ) ( L / D ) ln [ WBC / ( WBC - WP )] , Breguet Range Equ

Note: R = cruise range, V = cruise velocity, ISP = specificimpulse, L = lift, D = drag, WBC = weight at begin of

cruise, WP = weight of propellant or fuel

T y p ica l Roc k

e t T y p i c a l R a m

j e t w i t h A x i

s y m m e t r i c A

i r f r a m e Ram je t

w i t h H ig h L /

D A ir frame

Enhanced by High L / D and LightEnhanced by High L / D and Light



02/10/10 ELF 31

Enhanced by High L / D and Light Weight

Enhanced by High L / D and Light Weight

teady Level Flight Steady Climb Steady Descent

T = DL = W

L

D T

W

γ C

SIN γ D = ( D – T ) /

W = VD / V∞

VD = ( D – T ) V∞/ W

RD = ∆ h / tan γ D =

∆ h ( L / D )

T – DL

DT

W

V∞γ C VC

D – T L

D

TW

γ DVD

γ D

all Angle of Attack uilibrium Flight

= Velocity of Climb= Velocity of Descent

C = Flight Path Angle During Climb

D = Flight Path Angle During Descent

= Total Velocity

h = Incremental Altitude

= Horizontal Range in Steady Climb= Horizontal Range in Steady Dive ( Glide )

Note:

Reference: Chin, S.S., “MissileConfiguration Design,” McGraw Hill

Book Company, New York, 1961

V∞T = W / ( L / D )

SIN γ c = ( T – D ) / W =

Vc / V∞

Vc = ( T – D ) V∞ / W

RC = ∆ h / tan γ C = ∆ h

( L / D )

Angle of Attack and Low AltitudeAngle of Attack and Low Altitude



02/10/10 ELF 32

Angle of Attack and Low AltitudeFlight

Angle of Attack and Low AltitudeFlight

RT

,Exam

pleIns

tantan

eousTurn

Radius

,Feet

∆ α = Increment in Angle of Attack Required to Turn, Degrees

h = 100 K ft ( M(L/D) Max = 7.9 )

h = 80 K ft ( M(L/D) Max= 5.0 )

h = 60 K ft ( M(L/D) Max= 3.1 )

h = 40 K ft ( M(L/D) Max= 1.9 )

10,000,000

1,000,000

100,000

10,000

1,0000 5 10 15 20

• • • •

•

•

•

•

•

•

•

•

Note for Example:W = Weight = 2,000 lba / b = 1 ( circular cross section ), No wingsC

N

= sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2

l / d = Length / Diameter = 10SRef = 2 ft2

CDO= 0.2

( L / D )Max = 2.7, q( L/ D) Max= 1,000 psf

α ( L/ D) Max= 15 degrees

T( L/ D) Max= 740 lb

Example:

∆ α = 10 degCN = 0.99

h = 40K ft ( ρ = 0.00039 slugs / ft3 )

RT = 2 ( 2,000 ) / [( 32.2 ) ( 0.99 ) ( 2 ) ( 0.00039 )] = 161,0

RT = V / γ . ≈ 2 W / ( gc CN SRef ρ )

Turn Rate Performance RequiresTurn Rate Performance Requires



02/10/10 ELF 33

Turn Rate Performance RequiresHigh Control Effectiveness

Turn Rate Performance RequiresHigh Control Effectiveness

γ .= gc n / V = [ q SRef C

Nα α + q SRef C

Nδ δ - W cos ( γ ) ] / [( W / gc ) V ]

Assume Rocket Baseline @ Mach 0.8 Launch, 20K ft Altitude

(C

mα)

xcg=84.6= (C

mα)

xcg=75.7+ C

Nα ( 84.6 – 75.7 ) / d = - 0.40 + 0.68 ( 8.9 ) / 8 = 0.36 per deg

(C

mδ)

xcg=84.6= (C

mδ)

xcg=75.7+ C

Nδ ( 84.6 – 75.7 ) / d = 0.60 + 0.27( 8.9 ) / 8 = 0.90 per deg

α / δ = - C

mδ / C

mα= - 0.90 / 0.36 = - 2.5

α ’ = α + δ < 22 degrees, α max = 30 deg ⇒ α = 30 deg, δ = - 12 deg

γ .= [ 436 ( 0.349 )( 0.68 )( 30 ) + 436 ( 0.349 )( 0.27 )( - 12 ) – 500 ( 1 )] / [( 500 / 32.2 )( 830 )] = 0.164 rad / sec or 9.4 deg / sec

Assume Rocket Baseline @ Mach 2 Coast, 20K ft Altitude

α / δ = 0.75

α ’ = α + δ = 22 degrees ⇒ δ = 12.6 deg, α = 9.4 deg γ .

= [ 2725 ( 0.349 )( 0.60 )( 9.4 ) +2725 ( 0.349 )( 0.19 )( 12.6 ) – 367 ( 1 )] / ( 367 / 32.2 )( 2074 ) = 0.31 rad / sec or 18 deg / sec

Note: High q, statically stable, forward wing control, lighter weight ⇒ higher climb capability

Note: Forward wing deflection to trim increases normal force



For Long Range Ballistic FlightFor Long Range Ballistic Flight



02/10/10 ELF 35

For Long Range Ballistic Flight,Maximize Initial Velocity

For Long Range Ballistic Flight,Maximize Initial Velocity

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2

t / [ 2 W / ( g ρS CD0Vi )], Non-

dimensional Time

Vx / ( Vi cos γ i ) = 1 / { 1 + t / { 2 WBO / [ gc ρAVG SRef

( CD0)AVG Vi ]}}

( Vy + gc t ) / ( Vi sin γ i ) = 1 / { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD0)AVG Vi ]}

Assumptions: T = 0, α = 0 deg, D > W sin γ ,

flat earthNomenclature: V = velocity during ballistic

flight, Vi = initial velocity, Rx =

horizontal range, h = altitude, hi =

initial altitude, Vx = horizontal velocity,

Vy = vertical velocityExample for Rocket Baseline:

•WBO = 367 lb, SRef = 0.349 ft2, Vi = VBO = 2,151 fps, γ i = 0 deg, ( CD0)AVG = 0.9, hi =

20,000 ft, ρAVG = 0.001755 slugs / ft3, t = 35 sec

•t / [ 2 WBO / ( gc ρ SRef CD0Vi )] = 35 / { 2 ( 367 ) / [ 32.2 ( 0.001755 ) ( 0.349 ) ( 0.9 )

( 2151 ) ]} = 35 / 19.22 = 1.821

•

Vx / ( Vi cos γ i ) = 0.354 ⇒ Vx = 762 ft / sec, ( Vy + 32.2 t ) / ( Vi sin γ i ) = 0.354 ⇒ Vy =- 1127 ft / sec, Rx / [ 2 Wi cos γ i / ( gc ρ SRef CD 0

)] = 1.037 ⇒ Rx = 42,900 ft or 7.06 nm,

Rx / { 2 WBO cos γ i / [ gc ρAVG SRef (CD0 )AVG ]} = ln { 1 + t / { 2 WBO / [ gc ( ρ )AVG

SRef ( CD0)AVG Vi ]}}

( h – hi + gc t2 / 2 ) / { 2 WBO sin γ i / [ gc

ρAVG SRef (CD0)AVG ]} = ln { 1 + t / { 2 WBO

/ [ gc ρAVG SRef ( CD0 )AVG Vi ]}

Thrust Provide High BurnoutT rust Prov e H g Burnout



02/10/10 ELF 36

Thrust Provide High Burnout Velocity

T rust Prov e H g Burnout Velocity

0

0.1

0.2

0.3

0.4

0.5

0.60.7

0 0.1 0.2 0.3 0.4 0.5

Wp / Wi, Propellant Fraction

D e l t a V / ( g I S P ) , N o n d i m e n s i o n a l

I n c r e m e n t a l V e l o c i t y

DAVG / T =0 DAVG / T =0.5 DAVG / T =1.0

∆ V / ( gc ISP ) = - ( 1 - DAVG / T ) ln( 1 - Wp / Wi )

Example for Rocket Baseline

Wi = WL = 500 lb

For boost, WP = 84.8 lb

WP / WL = 0.1696

ISP = 250 sec

TB = 5750 lb

Mi

= ML

= 0.8, hi

= hL

= 20,0

DAVG = 635 lb

DAVG / T = 0.110

∆ V / [( 32.2 ) ( 250 )] = - ( 1

0.110 ) ln ( 1 - 0.1696 ) = 0.

∆ V = ( 0.1654 ) ( 32.2 ) ( 2

= 1331 ft / sec

Note: 1 DOF Equation of Motion with α ≈ 0 deg, γ = constant, and T > W sinγ , Wi = initial weight, WP = propellant weight, ISP = specific impulse, T =thrust, Mi = initial Mach number, hi = initial altitude, DAVG = average drag,∆ V = incremental velocity, gc = gravitation constant, Vx = V cos γ , Vy = Vsin γ , R

x

= R cos γ , Ry

= R sin γ

Note: R = ( Vi + ∆ V / 2 ) tB, where R = boost range, Vi = initial velocity, tB =



Conceptual Sizing Computeronceptua z ng omputer



02/10/10 ELF 38

Conceptual Sizing Computer Code - TMD Spreadsheet onceptua z ng omputer Code - TMD Spreadsheet

efine Mission Requirements [ Flight Performance ( RMax , RMin , VAVG ) , MOM, Constraints ]

Establish Baseline ( Rocket ,Ramjet )

Aerodynamics Input ( d, l, lN, A, c,

t, xcg ) Aerodynamics Output [ CD0,

CN, XAC , Cmδ, L / D, ST ]

Propulsion Input ( pc, ε , c*, Ab, At, A3, Hf , ϕ ,

T4, Inlet Type ) Propulsion Output [ Isp , Tcruise ,

pt2/ pt0

, w., Tboost , Tsustain , ∆ VBoost

]

Weight Input ( WL, WP, σ max )

Weight Output [ Q, dTskin / dt, Tskin , ρ skin , tskin , σ buckling , MB, ( Ft )Motor , W, xcg , Iy ]

Trajectory Input ( hi, Vi, Type ( cruise, boost, coast,

ballistic, turn, glide )

Trajectory Output ( R, V, and γ versus time )

MeetPerformance?

Measures of Merit and Constraints

No [ pBlast , PK ,

nHits , Vfragments ,

PKE , KEWarhead ,

τ Total , σ HE ,

σ MAN , Rdetect ,CWeight , Cunit x ]

No [ RMax , RMin , VAVG ]

Yes

Yes

Alt Missio

Alt Baselin

Resize / AltConfig /

Subsystems /Tech



02/10/10 ELF 39

OutlineOutline

Examples of Parameters and TechnologiesThat Drive Missile Flight Performance


Examples of Maximizing Missile Flight

Performance ( Workshop ) Summary

C fi tiC fi ti



02/10/10 ELF 40

Configuration Configuration

STA 60.8

19.4

3.418.5

STA 125.4

LEMAC at STA 67.0BL 10.2

Λ = 45°

40.2

STA 0 19.2 46.1 62.6 84.5 138.6

Note: Dimensions in inches

Source: Bithell, R.A. and Stoner, R.C., “Rapid Approach for MissileSynthesis, Vol. 1, Rocket Synthesis Handbook,” AFWAL-TR-81-3022, Vol. 1,March 1982.

Nose Forebody PayloadBay

Midbody Aftbody Tailcone

Rocket Motor

Λ = 57°

12.0

LEMAC at

STA131.6BL 8.0

16.18.0 d

cgBO cgLaunch

143.9

Propellant Weight Is 27% of thePropellant Weight Is 27% of the



02/10/10 ELF 41

Propellant Weight Is 27% of theLaunch Weight

Propellant Weight Is 27% of theLaunch Weight

1 Nose ( Radome ) 4.1 12.03 Forebody structure 12.4 30.5Guidance 46.6 32.6

2 Payload Bay Structure 7.6 54.3Warhead 77.7 54.3

4 Midbody Structure 10.2 73.5

Control Actuation System61.0 75.55 Aftbody Structure 0.0 –

Rocket Motor Case 47.3 107.5Insulation 23.0 117.2

6 Tailcone Structure 6.5 141.2Nozzle 5.8 141.2

Fixed Surfaces 26.2 137.8Movable Surfaces 38.6 75.5

Burnout Total 367.0 76.2Propellant 133.0 107.8

Launch Total 500.0 84.6

Component Weight, lbs. C.G. STA, In.

Boost-Sustain Thrust - Timeoost- usta n rust - me



02/10/10 ELF 42

Boost Sustain Thrust TimeHistory

oost usta n rust meHistory

Time – Seconds

0 4 8 12 160

2

4

6

8

hrust – 1,000 lbs

Note: Sea Level, 60°F

H g er Maneuvera ty at H gg er aneuvera y a g



02/10/10 ELF 43

H g er Maneuvera ty at H g Angle of Attack

g er aneuvera y a g Angle of Attack

4

0

0 4 8 12 16

α , Angle of Attack – Degrees

12

8

20

CN

,N

orm

alForce

Co

efficient

20

16

24

1.2

0.6

M = 1.2

1.5

2.02.352.873.95

4.60

SRef = 0.349 ft2, lRef = d = 0.667 ft, C.G. at STA 75.7, δ = 0 deg

Effectiveness and Drag Areect veness an rag re



02/10/10 ELF 44

Effectiveness and Drag AreDriven by Mach Number ect veness an rag re

Driven by Mach Number

0.4

00 1 2 3 4

M, Mach Number

1.2

0.8

5

CAa

t

=0°

0.1

0

Power Off

Power On

0.2

0.3

C

N

~Per

Degre

e

A l tiA l ti



02/10/10 ELF 45

10

15

o n , g

Acceleration Acceleration

Note:tf = 24.4 sec

ML = 0.8

hL = 20,000 ft

TB = 5750 lb

tB = 3.26 sec

TS

= 1018 lb

tS = 10.86 sec

D = 99 lb at Mach 0.8D = 1020 lb at Mach 2.1

WL = 500 lb

WP = 133 LB

nX = ( T - D ) / W

Boost

Sustain

Coast

Nearly Constant Velocity DuringNear y onstant Ve oc ty Dur ng



02/10/10 ELF 46

2000

3000

e c

Nearly Constant Velocity DuringSustain

Near y onstant Ve oc ty Dur ngSustain

Boost

Sustain

Coast

∆ V / ( gc ISP ) = - ( 1 - DAVG / T ) ln ( 1 - Wp / Wi ),During Boost

V / VBO = 1 / { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD0 )AVG VBO ]}}, During Coast

Note:

ML = 0.8

hL = 20K feet

Range Is About Eight NauticalRange Is About Eight Nautical



02/10/10 ELF 47

Range Is About Eight Nautical Miles

Range Is About Eight Nautical Miles

0

2

4

6

8

10

0 5 10 15 20 25

t, Time, sec

R , F l i g h t

R a n g e , n

Boost

Sustain

Coast

R = ∆ Rboost + ∆ Rsustain + ∆ Rcoast

Note:

ML = 0.8hL = 20K feet

Rocket Baseline Missile HasRocket Baseline Missile Has



02/10/10 ELF 48

Rocket Baseline Missile Has About 30 G Maneuverability Rocket Baseline Missile Has

About 30 G Maneuverability ( nZ ) = ( nZ )Body + ( nZ )Wing + ( nZ )Taill

Rocket Baseline @ •Mach 2•20,000 ft altitude•367 lb weight ( burnout )

Compute

α Wing = α ’Max = ( α + δ )Max = 22 deg for rocket baseline

α = 0.75δ , α Body = α Tail = 9.4 deg

( nZ )Body = q SRef ( CN )Body / W = 2725 ( 0.35 ) ( 1.1 ) / 367 = 2.9 g

( from body )

( nZ )Wing = q SWing [( CN )Wing (SRef / SWing )] / W = 2725 ( 2.55 ) ( 1.08 ) /367 = 20.4 g ( from wing )

( nZ )Tail = q STail [( CN )Tail ( SRef / STail )] / W = 2725 ( 1.54 ) ( 0.50 ) / 367= 5.7 g ( from tail )

nZ = 2.9 + 20.4 + 5.7 = 29 g



Example of Boost Climb -Examp e o Boost m -



02/10/10 ELF 50

Example of Boost Climb Ballistic Trajectory ( cont )Examp e o Boost m

Ballistic Trajectory ( cont )

Velocity, Horizontal Range, and Altitude During Ballistic Flighthf = hi = 0 ft ⇒ tballistic = 59 sec )

Vx = Vi cos γ i / { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD0 )AVG VBO ]}} = 1972 ( 0.707 ) / { 1 + 59 / { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 )( 0.95 ) ( 1972 )]}} = 395 ft / sec

Vy = Vi sin γ i / { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD0)AVG VBO ]} – 32.2 t = 1972 ( 0.707 ) / { 1 + 59 / { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) (

0.95 ) ( 1972 )]}} – 32.2 ( 59 ) = - 1,505 ft / sec

Rx = { 2 WBO cos γ i / [ gc ρAVG SRef (CD0)AVG ]} ln { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD0

)AVG VBO ]}} = { 2 ( 367 ) ( 0.707 ) / [ 32.2 ( 0.001496 )

( 0.349 ) ( 0.95 )]} ln { 1 + 59 / { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} = 40,991 ft

h = hi + { 2 WBO sin γ i / [ gc ρAVG SRef ( CD0)AVG ]} ln { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD0

)AVG VBO ]} - 16.1 t2 = 14493 + { 2 ( 367 ) ( 0.707 ) / [

32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 )]} ln { 1 + 59 / { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} – 16.1 ( 59 ) 2 = 0 ft

Total Time of Flight and Horizontal Range

t = Σ ∆ t = ∆ tboost + ∆ tsustain + ∆ tballistic = 3.26 + 10.86 + 59 = 73 sec

Rx = Σ ∆ Rx = ∆ Rx,boost + ∆ Rx,sustain + ∆ Rx,ballistic = 1598 + 12895 + 40991 = 55,894 ft = 9.2 nm

Trajectory Provides ExtendedTrajectory Provides Extended



02/10/10 ELF 51

Trajectory Provides Extended Range

Trajectory Provides Extended Range

Rocket Baseline @ γ i = 45 deg, hi = hf = 0 ft

From Previous Example, the Boost Climb – Ballistic Conditions at Apogee are:

t = 36 sec

γ = 0 deg

V = 702 ft / sec

h = 28,994 ft

∆ Rx = 36,786 ft

q = 227 psf

M = 0.7

( L / D )max = 5.22

α (L/D) max

= 5.5 deg

Incremental Horizontal Range During the ( L / D )max Glide from Apogee to the Ground is given by

∆ Rx = ( L / D ) ∆ h = 5.22 ( 28994 ) = 151,349 ft

Total Horizontal Range for a Boost Climb – Ballistic – Glide Trajectory is

Rx = Σ ∆ Rx = ∆ Rx,BoostClimb-Ballistic + ∆ Rx,Glide = 36786 + 151349 = 188,135 ft = 31.0 nm

max

E t d d Rmax

E tended Range



02/10/10 ELF 52

Extended Range Extended Range

0

10

20

30

0 10 20 30 40

R, Range, nm

h , A l t i t u d e , K i l o F e e t

S u

s t

a i n

B a l l i s

t i c

Note: Rocket Baseline

End of boost, t = 3.26 sec, γ = 45deg, V = 1387 ft / sec

End of sustain, t = 14.12 sec, γ = 45deg, V = 1972 ft / sec

Apogee, t = 36 sec, γ = 0 deg, V = 702ft / sec

Ballistic impact, t = 73 sec, γ = - 65deg, V = 1556 ft / sec

Glide impact, t = 286 sec, γ = - 10.8deg, V = 500 ft / sec

B a l

l i s t i c

G l i d e a t ( L /

D ) m a x



Soda Straw Rocket ( cont )Soda Straw Rocket ( cont )



02/10/10 ELF 54


Design – Soda Straw Rocket

Compatible with Furnished Property Launch System

Launch tube outside diameter: ¼ in

Launch tube length: 6 in

Launch static gauge pressure: up to 30 psi

Design Body and Tails for

Maximum flight range

Accurate and stable flight

Calculate Aerodynamic Drag Coefficient

Skin friction drag

Base drag

Calculate Thrust and Thrust Duration

Measure Weight

± 0.1 gram accuracy

Predict Flight Range and Altitude for Proscribed

Launch pressure

Elevation angle




02/10/10 ELF 55


Build - Soda Straw Rocket Using Either

Furnished Material Or Can Use Own Material

Fly - Soda Straw Rocket Proscribed Target Location, Launch Location, Launch Pressure, and Launch

Angle

Compare Flight Test Results for Alternative ConceptsHighest vertical location of impact

Smallest horizontal dispersal from impact aim pointDiscuss Reasons for Performance of Alternative Concepts

Example Baseline ConfigurationExamp e Base ne on gurat on



02/10/10 ELF 56

a p e ase e Co gu a oGeometry, Weight, and Balance

a p e ase e o gu a oGeometry, Weight, and Balance

Example Baseline Configuration

Diameter = d = ¼ in = 0.0208 ft

Outside Length = l = 5 in = 0.417 ft

Inside Cavity Length Available for Launch Tube = lc = 4 in = 0.333 ft

Hemispherical Nose

Reference Area = SRef = ( π / 4 ) d2 = 0.0491 in2 = 0.000341 ft2

4 Tail Panels ( Cruciform Tails, nT = 2 )

Each tail panel ½ in by 1 in

Mean aerodynamic chord = cmac = 1 in = 0.0833 ft

Exposed area of 2 tail panels = ST = 1 in2 = 0.00694 ft2

Exposed aspect ratio of 2 tail panels = A = b2 / ST = ( 1 )2 / ( 1 ) = 1.0

Example Baseline Weight and Balance

W = 1.9 gram = 0.0042 lb

Xcg / l = 0.55

llccll

Performance Performance



02/10/10 ELF 57

PerformancePerformance

During Boost, Thrust ( T ) Provided by Pressurized Launch Tube

T = ( p – p0 ) A = pgauge ( 1 – e –t / τ ) A

A = SRef = 0.0491 in2

, τ = Rise Time to Open Valve

Assume pgauge = 20 psi, τ = 0.2 sec

T = 20 ( 1 - e –t / 0.2 ) ( 0.0491 ) = 0.982 ( 1 - e –5.00t )

Actual Thrust Lower ( Pressure Loss, Boundary Layer, Launch Tube Friction )

Acceleration ( a ), Velocity ( V ), and Distance ( s ) During Boost

a ≈ 32.2 T / W = 32.2 ( 0.982 ) ( 1 - e –5.00t ) / 0.0042 = 7528.667 ( 1 - e –5.00t )

V = 7528.667 t + 1505.733 e –5.00t – 1505.733

s = 3764.333 t2 – 301.147 e –5.00t – 1505.733 t + 301.147

End of Boost Conditions

s = lc = 0.333 ft ⇒ t = 0.0382 sec

V = 25.8 ft / sec

q = ½ ρ V2 = ½ ( 0.002378 ) ( 25.8 )2 = 0.791 psf

M = V / c = 25.8 / 1116 = 0.0231

Coefficient Coefficient



02/10/10 ELF 58

Coefficient Coefficient

Total Drag Coefficient CD0= (CD0

)Body + (CD0)Tail

During Coast, CD0 = ( CD0 )Body,Friction + (CD0 )Base,Coast + ( CD0 )Tail,Friction = 0.053 ( l / d ) [ M / ( q l )]0.2 +0.12 + nT { 0.0133 [ M / ( q cmac )]0.2 } ( 2 ST / SRef )

CD0= 0.053 ( 20 ){ 0.0231 / [( 0.791 ) ( 0. 417 )]}0.2 + 0.12 + 2 { 0.0133 { 0.0231 / [( 0.791 )

( 0.0833 )]}0.2 }[ 2 ( 0.00694 ) / 0.000341 )] = 0.62 + 0.12 + 0.88 = 1.62

Above Drag Coefficient Not Exact

Based on Assumption of Turbulent Boundary Layer

Soda Straw Rocket Is Small Size and Low Velocity ⇒ Laminar Boundary Layer

Performance Performance



02/10/10 ELF 59

PerformancePerformance

Horizontal Range Equation

Rx = { 2 W cos γ i / [ gc ρ SRef CD0 ]} ln { 1 + t / { 2 W / [ gc ρ SRef CD0 Vi ]} = { 2 ( 0.0042 ) cos γ i / [ 32.2( 0.002378 ) ( 0.000341 ) ( 1.62 )]} ln { 1 + t / { 2 ( 0.0042 ) / [ 32.2 ( 0.002378 ) ( 0.000341 )( 1.62 ) ( 25.8 )]} = 199 cos γ i ln ( 1 + 0.130 t )

Height Equation

h = { 2 W sin γ i / [ gc ρ SRef CD0]} ln { 1 + t / { 2 W / [ gc ρ SRef CD0

Vi ]} + hi - gc t2 / 2 = { 2 ( 0.0042 )

sin γ i / [ 32.2 ( 0.002378 ) ( 0.000341 ) ( 1.62 )} ln { 1 + t / { 2 ( 0.0042 ) / [ 32.2 ( 0.002378 )( 0.000341 ) ( 1.62 ) ( 25.8 )]} + h i – 32.2 t2 / 2 = 199 sin γ i ln ( 1 + 0.130 t ) + hi – 32.2 t2 / 2

Assume γ i = 45 deg, t = timpact = 0.9 sec

Rx = 199 ( 0.707 ) ln [ 1 + 0.130 ( 0.9 )] = 15.5 ft h = 199 ( 0.707 ) ln [ 1 + 0.130 ( 0.9 )] + h i – 32.2 ( 0.9 )2 / 2 = hi +2.5



OutlineOutline



02/10/10 ELF 61

OutlineOutline

Examples of Parameters and TechnologiesThat Drive Missile Flight Performance


Examples of Maximizing Missile Flight

Performance ( Workshop ) Summary

SummarySummary



02/10/10 ELF 62

Summary Summary

Flight Performance Analysis Activity in Missile Design and Analysis

Compute Range, Velocity, Time-to-Target, Off Boresight

Compare with Requirements and Data

Maximizing Flight Performance Strongly Impacted by Aerodynamics

Propulsion

Weight

Flight Trajectory

Lecture Topics

Aerodynamics Parameters, Prediction and Technologies

Drag Coefficient

Normal Force Coefficient

Propulsion Parameters, Prediction, and Technologies

Thrust

Specific Impulse

Summary ( cont )Summary ( cont )



02/10/10 ELF 63


Lecture Topics ( continued )

Flight Performance Parameters and Technologies

Cruise Range

High Density Fuel and Packaging

Flight Trajectory Shaping

Range Sensitivity to Driving Parameters

Missile Follow-on Programs

Examples of State-of-the-Art Advancements

Summary of New Technologies

Flight Performance Envelope

Videos of Flight Performance

Modeling of Degrees of Freedom

Equations of Motion and Flight Performance Drivers

Steady State Flight Relationships

Flight Performance Prediction

Steady Climb and Steady Dive Range Prediction

Cruise Prediction




02/10/10 ELF 64


Lecture Topics ( continued )

Flight Performance Prediction ( continued )

Boost Prediction

Coast Prediction

Ballistic Flight Prediction

Turn Prediction

Target Lead for Proportional Homing Guidance

Tactical Missile Design Spreadsheet

Workshop Examples

Rocket Boost-Coast Range

Rocket Maneuverability

Rocket Ballistic Range

Rocket Trajectory Optimization

Soda Straw Rocket Design, Build, and Fly



Sites

Sites



02/10/10 ELF 66

SitesSites “Missile.index,” http://www.index.ne.jp/missile_e/

AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993.

Bonney, E.A., et al, Aerodynamics, Propulsion, Structures, and Design Practice, “ Principles of Guided Missile

Design”, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1956

Chin, S.S., Missile Configuration Design, McGraw-Hill Book Company, New York, 1961

Mason, L.A., Devan, L., and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWCTR 81-156, 1981

Pitts, W.C., Nielsen, J.N., and Kaattari, G.E., “Lift and Center of Pressure of Wing-Body-Tail Combinations atSubsonic, Transonic, and Supersonic Speeds,” NACA Report 1307, 1957.

Jorgensen, L.H., “Prediction of Static Aerodynamic Characteristics for Space-Shuttle-Like, and Other Bodies atAngles of Attack From 0° to 180°,” NASA TND 6996, January 1973

Hoak, D.E., et al., “USAF Stability and Control Datcom,” AFWAL TR-83-3048, Global Engineering Documents, Irvine,CA, 1978

“Nielsen Engineering & Research (NEAR) Aerodynamic Software Products,”http://www.nearinc.com/near/software.htm

Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, “ Principles of Guided Missile Design”, D.Van Nostrand Company, Inc., Princeton, New Jersey, 1960

Schneider, S.H., Encyclopedia of Climate and Weather, Oxford University Press, 1996

Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997

US Army Ordnance Pamphlet ORDP-20-290-Warheads, 1980

Nicholas, T. and Rossi, R., “US Missile Data Book, 1996,” Data Search Associates, 1996

Bithell, R.A., and Stoner, R.C., “Rapid Approach for Missile Synthesis,” AFWAL TR 81-3022, Vol. I, March 1982

Fleeman, E.L. and Donatelli, G.A., “Conceptual Design Procedure Applied to a Typical Air-Launched Missile,” AIAA 81-1688, August 1981

Hindes, J.W., “Advanced Design of Aerodynamic Missiles ( ADAM ),” October 1993

Sites ( cont )

Sites ( cont )

http://www.index.ne.jp/missile_e/


http://www.nearinc.com/near/software.htm

http://www.nearinc.com/near/software.htm




02/10/10 ELF 67

Sites ( cont )Sites ( cont )

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Moore, F.G., et al, “Application of the 1998 Version of the Aeroprediction Code,” Journal of Spacecraft and Rockets, Vol. 36, No. 5, September-October 1999 Fleeman, E.L., “Tactical Missile Design,” American Institute of Aeronautics and Astronautics,

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0091, January 1979 Nicolai, L.M., Fundamentals of Aircraft Design, METS, Inc., San Jose, CA, 1984 Lindsey, G.H. and Redman, D.R., “Tactical Missile Design,” Naval Postgraduate School, 1986 Lee, R. G., et al, Guided Weapons, Third Edition, Brassey’s, London, 1998 Giragosian, P.A., “Rapid Synthesis for Evaluating Missile Maneuverability Parameters,” 10th

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Lesieutre, D., et al, “Recent Applications and Improvements to the Engineering-Level Aerodynamic Prediction Software MISL3,’’ AIAA-2002-0274Sutton, G.P., Rocket Propulsion Elements, John Wiley & Sons, New York, 1986“Tri-Service Rocket Motor Trade-off Study, Missile Designer’s Rocket Motorhandbook,” CPIA 322, May 1980Chemical Information Propulsion Agency, http://www.jhu.edu/~cpia/index.html

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Follow-up CommunicationFollow-up Communication

I would appreciate receiving your comments and

corrections on this text, as well as any data,examples, or references that you may offer.

Thank you,

Gene Fleeman

4472 Anne Arundel CourtLilburn, GA 30047

Telephone: +1 770-925-4635 ( home )+1 404-894-7777 ( work )

Fax: +1 404-894-6596E-mail: [email protected] ( home )

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