Rocket Motor Design and Missile Flight Performance Analysis

7/24/2002 ELF 1

R

Rocket Motor Design andFlight Performance Analysis for

Tactical Missiles

Rocket Motor Design andFlight Performance Analysis for

Tactical Missiles

Eugene L. FleemanSenior Technical AdvisorGeorgia Institute of Technology

7/24/2002 ELF 2

OutlineOutline

Differences of Missiles from AircraftExamples of Parameters That Drive Missile FlightPerformanceConceptual Design ProcessRocket Motor DesignMissile Flight Performance AnalysisSummary

7/24/2002 ELF 3

Superior Better Comparable Inferior

Acceleration AGM-88Maneuverability AA-11Speed PAC-3Dynamic pressure PAC-3Size JavelinWeight FIM-92Production cost GBU-31Observables AGM-129Range AGM-86Kills per use ApacheTarget acquisition LOCAAS

Tactical MissileCharacteristics

Comparison WithFighter Aircraft

––

–

–

Tactical Missiles Are Different From Fighter AircraftTactical Missiles Are Different From Fighter Aircraft

Example ofState-of-the-Art

7/24/2002 ELF 4

OutlineOutline


7/24/2002 ELF 5

Parameters That Drive Flight PerformanceParameters That Drive Flight Performance

Nose FinenessDiameter

Propellant / Fuel

Wing Geometry / Size

StabilizerGeometry / Size

Flight ControlGeometry / Size

Length

ThrustProfile

Flight Conditions ( α, M, h )

7/24/2002 ELF 6

Cruise Range Is Driven By L/D, Isp, Velocity, andPropellant or Fuel Weight Fraction

Cruise Range Is Driven By L/D, Isp, Velocity, andPropellant or Fuel Weight Fraction

Typical Value for 2,000 lb Precision Strike Missile

Note: Ramjet and Scramjet missiles booster propellant for Mach 2.5 to 4 take-over speed not included in WPfor cruise. Rockets require thrust magnitude control ( e.g., pintle, pulse, or gel motor ) for effective cruise.Max range for a rocket is usually a semi-ballistic flight profile, instead of cruise flight.

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

Parameter

L / D, Lift / DragIsp, Specific ImpulseVAVG , Average VelocityWP / WL, Cruise Propellant orFuel Weight / Launch WeightR, Cruise Range

103,000 sec1,000 ft / sec0.3

1,800 nm

51,300 sec3,500 ft / sec0.2

830 nm

31,000 sec6,000 ft / sec0.1

310 nm

5250 sec3,000 ft / sec0.4

250 nm

Solid RocketHydrocarbon FuelScramjet Missile

Liquid FuelRamjet Missile

Subsonic TurbojetMissile

7/24/2002 ELF 7

Scramjet

Specific Impulse of Tactical Missile PropulsionAlternatives

Specific Impulse of Tactical Missile PropulsionAlternatives

Turbojet

Ramjet

Solid Rocket

4,000

3,000

2,000

1,000

0

Thru

st / (

Fue

l Flo

w Ra

te ),

Spe

cific

Impu

lse, I S

P, Se

cond

s

0 2 4 6 8 10 12Mach Number

Ducted Rocket

7/24/2002 ELF 8

0

High Propellant Fraction Increases Burnout VelocityHigh Propellant Fraction Increases Burnout Velocity5000

4000

3000

2000

1000

0 0.1 0.2 0.3 0.4 0.5

Example: Rocket BaselineWi,boost = WL = 500 lb, Wp, boost = 84.8 lbISP, boost = 250 secWP, boost / Wi = 84.8 / 500 = 0.1696∆V = -32.2 ( 250 ) ln ( 1 - 0.1696 )= 1496 ft / sec

∆V, MissileIncremental

Burnout Velocity,ft / sec

WP / Wi, Propellant Weight / Initial Missile Weight

Isp = 250 sec

Isp = 200 sec

Note: T >> D, T >> W sin γ, γ = const

∆V = -gc Isp ln (1 - Wp / Wi)

7/24/2002 ELF 9

Flight Trajectory Shaping Provides Extended RangeFlight Trajectory Shaping Provides Extended Range

Altitude

RangeRMAX

Apogee or Cruise

GlideClimb

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 range– Glide from high altitude at ( L / D )Max and q ≈ 700 psf provides extended range

7/24/2002 ELF 10

Dynamic Pressure Varies With Altitude andMach Number

Dynamic Pressure Varies With Altitude andMach Number

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7M, Mach number

h, A

ltitu

de, K

ilo fe

et q = 200 psfq = 500 psfq = 1,000 psfq = 2,000 psfq = 5,000 psfq = 10,000 psfq = 20,000 psf

Note:• U.S. 1976 Standard Atmosphere• For Efficient Cruise, (L / D)Max for Cruising Lifting Body Typically Occurs for 500 lb / ft2 < q < 1,000 lb / ft2

• (L / D)Max for Cruise Missile with Low Aspect Ratio Wing Typically Occurs for 200 lb / ft2 < q < 500 lb / ft2

q = 1 / 2 ( ρ V2 )

Ramjet

Scramjet

Wingless Turbojet

Low Aspect Ratio Wing Turbojet

7/24/2002 ELF 11

0

0.5

1

1.5

Temp Density Speed ofSound

Varia

tion

from

Sta

ndar

d At

mos

pher

e Ratio: Cold-to-StandardAtmosphereRatio: Hot-to-StandardAtmosphereRatio: Polar-to-StandardAtmosphereRatio: Tropic-to-StandardAtmosphere

Note:

• Based on properties at sea level

•U. S. 1976 Standard Atmosphere: Temperature = 519 Deg. Rankine, Density = 0.002377 slugs / ft3, Speed of sound = 1116 ft / sec

( + 30 % )

( - 23% )

Design Robustness Requires Consideration ofType of Atmosphere

Design Robustness Requires Consideration ofType of Atmosphere

7/24/2002 ELF 12

Engine ShutdownTransient

Missile Guidance and Control Must Be Robustfor Changing Events and Flight Environment

Missile Guidance and Control Must Be Robustfor Changing Events and Flight Environment

Air Launch atLow Mach giveshigh α

Booster Ignition

Pitch-Up at High AlphaClimb

Booster ShutdownTransient at High Mach

Engine Start TransientPitch-Over atHigh Alpha

Terminal at HighDynamic Pressure

Example High Performance Missile Has• Low-to-High Dynamic Pressure• Negative-to-Positive Static Margin• Thrust / Weight / cg Transients• High Temperature• High Thermal Load• High Vibration• High Acoustics

Dive

Precision Impactat α ≈ 0 Deg

Level Out

Cruise

Vertical Launch in Cross Windgives high α

Pitch-Over at High Alpha

7/24/2002 ELF 13

A Collision Intercept Has Constant BearingA Collision Intercept Has Constant Bearing

Example of Miss( Line-of-Sight Angle Diverging )

Example of Collision Intercept( Line-of-Sight Angle Constant )

Overshoot Miss

Missile Target

Seeker Line-of-Sight

( LOS )1 > ( LOS )0 ( LOS )1 = ( LOS )0

Missile Target

t0

t1

t2

t0

t1

Seeker Line-of-Sight

Note: L = Missile Lead A = Target Aspect

AL L A

7/24/2002 ELF 14

Solid Rockets Have High Acceleration CapabilitySolid Rockets Have High Acceleration Capability

1,000

100

10

10 1 2 3 4 5

RamjetTMax = (π / 4 ) d2 ρ∞ V∞

2 [( Ve / V∞ )- 1 ]

TurbojetTMax = (π / 4 ) d2 ρ∞ V∞

2 [( Ve / V∞ )- 1 ]

Solid RocketTMax = 2 PC AT = m. Ve

M, Mach Number

( T / W

) Max

, ( T

hrus

t / W

eight

) Max

,

Note:PC = Chamber pressure, AT = Nozzle throat area, m. = Mass flow rated = Diameter, ρ∞ = Free stream density, V∞ = Free stream velocity,Ve = Nozzle exit velocity ( Turbojet: Ve ~ 2,000 ft / sec, Ramjet: Ve ~ 4,500 ft / sec, Rocket: Ve ~ 6,000 ft / sec )

7/24/2002 ELF 15

Subsystem Weight Is Sensitive to FlightPerformance ( Range, Speed, Maneuverability )

Subsystem Weight Is Sensitive to FlightPerformance ( Range, Speed, Maneuverability )

Very Strong –Strong Moderate Relatively Low

Dome Seeker Guidance andControl

Propulsion Wings Stabilizers

Warheadand Fuzing

AerothermalInsulation

FlightControl

PowerSupply

Structure DataLink

7/24/2002 ELF 16

Standard Missile 3 ( NTW ) PAC-3 THAAD

LOSAT LOSAT Video

Examples of Kinetic Kill MissilesExamples of Kinetic Kill Missiles

7/24/2002 ELF 17

OutlineOutline


7/24/2002 ELF 18

Conceptual Design Process Requires IterationConceptual Design Process Requires Iteration

• Mission / ScenarioDefinition

• WeaponRequirements,Trade Studiesand SensitivityAnalysis

• PhysicalIntegrationPlatform andWeapon

• Weapon ConceptDesign Synthesis

• TechnologyAssessment andDev Roadmap

InitialTech

InitialReqs

BaselineSelected

AltConcepts

Initial Carriage /Launch

Iteration

RefineWeapons

Req

Prelim Final

Trades / Eval Effectiveness / Eval

TechTrades

InitialRoadmap

RevisedRoadmap

Eval / RefineDesign StudiesFirst-Cut Designs

Update

Note: Typical conceptual design cycle is 3 to 9 months

7/24/2002 ELF 19

OutlineOutline


7/24/2002 ELF 20

Missile Concept Synthesis Requires Iteration ofPropulsion

Missile Concept Synthesis Requires Iteration ofPropulsion

Yes

Establish Baseline

Weight

Trajectory

MeetPerformance?

Measures of Merit and ConstraintsNo

No

Yes

Resize / Alt Config / Subsystems / Tech

Alt Mission

Alt Baseline

Define Mission Requirements

Aerodynamics

Propulsion

7/24/2002 ELF 21

Large Propellant Burn Area Is Required for HighChamber Pressure

Large Propellant Burn Area Is Required for HighChamber Pressure

0

200

400

600

0 500 1000 1500 2000Pc, Rocket Baseline Motor Chamber Pressure, psi

Ab, R

ocke

t Bas

eline

Pro

pella

nt B

urn

Area

, in2

Ab = gc pcAt / ( ρc*r )r = rpc=1000 psi ( pc / 1000 )n

Example for Rocket Baseline:At= 1.81 in2

ρ = 0.065 lb / in3

n = 0.3rpc = 1000 psi = 0.5 in / secc* = 5,200 ft / secTatmosphere = 70 deg FahrenheitFor sustain ( pc = 301 psi ):•r = 0.5 ( 301 / 1000 )0.3 = 0.35in / sec•Ab = 149 in2

For boost ( pc = 1,769 psi )•r = 0.59 in / sec•Ab = 514 in2

Note: Ab = propellant burn area, gc = gravitation constant, At = Nozzle throat area, ρ = density of propellant, c* = characteristic velocity,r = propellant burn rate, rpc=1000 psi = propellant burn rate at pc = 1,000 psi, pc = chamber pressure, n = burn rate exponent

7/24/2002 ELF 22

High Propellant Weight Flow Rate Requires ALarge Nozzle Throat Area

High Propellant Weight Flow Rate Requires ALarge Nozzle Throat Area

100

1000

10000

100000

1 10 100Propellant Weight Flow Rate, lb/sec

(pc)

At, C

ham

ber P

ress

ure x

Noz

zle

Thro

at A

rea,

lb

c* = 4800 ft/secc* = 5200 ft/secc* = 5600 ft/sec

At = c* w.p

/ ( gc pc )

Rocket Baseline During Boost:c* = 5200 ft / sec( pc )boost = 1,769 psiw.

p = Wp / tb = 84.8 / 3.26 = 26.0 lb /secpc At = c* w.

p / gc = 5200 ( 26.0 ) /32.2 = 4,200 lbAt = 4200 / 1769 = 2.37 in2

Note: At = nozzle throat area, c* = characteristic velocity, w.p = propellant weight flow rate, gc = gravitational constant,

pc = chamber pressure

7/24/2002 ELF 23

Maximum Specific Impulse And Thrust of RocketOccur at High Chamber Pressure and Altitude

Maximum Specific Impulse And Thrust of RocketOccur at High Chamber Pressure and Altitude

220

240

260

280

0 5 10 15 20Nozzle Expansion Ratio

Isp, S

pecif

ic Im

pulse

of R

ocke

t Bas

eline

h = SL, pc = 300 psi h = SL, pc = 1000 psih = SL, pc = 3000 psi h = 100K ft, pc > 300 psi

ISP = cd {{[ 2 γ2 / ( 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 pressurepc = chamber pressurep0 = atmospheric pressureAt = nozzle throat areaγ = specific heat ratio = 1.18 in figurecd = discharge coefficient = 0.96 in figurec* = characteristic velocity = 5,200 ft / sec in figure

Example for Rocket Baseline:ε = Ae / At = 6.2, At = 1.81 in2

h = 20 Kft, p0 = 6.48 psi( pc )boost = 1769 psi, ( ISP )boost = 257 sec( T )boost = ( 32.2 / 5200 ) ( 1769 ) (1.81 )( 257 ) = 5096 lb( pc )sustain = 301 psi, ( ISP )sustain = 239 sec( T )boost = ( 32.2 / 5200 ) ( 301 ) (1.81 )( 239 ) = 807 lb

7/24/2002 ELF 24

Single Burn Solid Rocket Thrust-Time DesignAlternatives With Propellant Cross-Section

Single Burn Solid Rocket Thrust-Time DesignAlternatives With Propellant Cross-Section

Thru

st ( lb

)Burning Time ( sec )

ConstantThrust

PropellantCross-Section

Typical VolumetricLoading (%)

RegressiveThrust

ProgressiveThrust

Boost-Sustain Thrust

Boost-Sustain-Boost Thrust

82%

79%

87%

85%

85%

Burning Time ( sec )




Thru

st ( lb

)Th

rust

( lb )

Thru

st ( lb

)Th

rust

( lb )

Medium Burn Rate Propellant

High Burn Rate PropellantNote: Thrust and chamber pressure proportional to surface burn area.

Example Mission•≈ Cruise

•Dive at ≈constantdynamicpressure

•Climb at ≈constantdynamicpressure

•Fast launch –≈ cruise

•Fast launch –≈ cruise – highspeed terminal

Thrust Profile

7/24/2002 ELF 25

Solid Rocket Propulsion Alternatives of SingleBurn and Thrust Magnitude Control

Solid Rocket Propulsion Alternatives of SingleBurn and Thrust Magnitude Control

End Burning

Single Burn ( Boost-Coast )

Single Burn ( Boost-Sustain-Coast )

Radial BoostEnd Burning Sustain

Simultaneous Burning

Radial BoostEnd Burning Sustain

Separate Burning ( Pulsed Motor )

Radial BoostRadial Sustain

Separate Burning ( Pulsed Motor )

Concentric Radial BurningHigh Burn Rate Boost

Low Burn Rate Sustain

Radial Burning

Boost PropellantSustain Propellant

Thrust Magnitude Control ( Boost-Coast-Sustain-Coast, with Delay Between Pulses )

Note: Each pulse increases motor cost approximately 40%.

7/24/2002 ELF 26

Solid Rocket Motor Thrust Magnitude ControlSolid Rocket Motor Thrust Magnitude Control

Solid Pulse Motor

Solid Pintle Motor

Bi-propellant Gel Motor

Thermal or Mechanical Barriers

Pintle

Pressurization Gelled Oxidizer Gelled Fuel

7/24/2002 ELF 27

250 - 260 0.062 0.1 - 1.5

Solid Rocket Propellant AlternativesSolid Rocket Propellant Alternatives

Superior Above Average Average Below Average

• Min Smoke. No Al fuel or APoxidizer. Either Composite withNitramine Oxidizer ( CL-20, ADN,HMX, RDX ) or Double Base. Very lowcontrail (H2O).

• Reduced Smoke. No Al ( binderfuel ). AP oxidizer. Low contrail ( HCl ).

• High Smoke. Al fuel. AP oxidizer.High smoke ( Al2O3 ).

–

ISP,SpecificImpulse,

sec

ρ,Density,lb / in3

BurnRate @

1,000 psi,in / sec Hazard Observables

– – –

–

Type

220 - 255 0.055 - 0.062 0.25 - 1.0

260 - 265 0.065 0.1 - 3.0

7/24/2002 ELF 28

Motor Case Material AlternativesMotor Case Material Alternatives

Superior Above Average Average Below Average

Steel

Aluminum

Strip Metal /Epoxy Laminate

Titanium

Composite

–

VolumetricEfficiency Weight

Airframe andLauncher

Attachment Cost

–

Type

–

–

–

– –

– –

Temper-ature

–

7/24/2002 ELF 29

Heating Drives Rocket Nozzle Materials, Weight,and Cost

Heating Drives Rocket Nozzle Materials, Weight,and Cost

HousingThroat

Exit ConeDome Closeout

Rocket Nozzle Element High Heating ( High Chamber Pressure or Long Burn ) ⇒ High Cost / Heavy Nozzle

Low Heating ( Low Chamber Pressure or Short Burn ) ⇒ Low Cost / Low Weight Nozzle

♦ Housing Material Alternatives

♦ Steel ♦ Cellulose / Phenolic ♦ Aluminum

♦ Throat Material Alternatives

♦ Tungsten Insert ♦ Molybdenum Insert

♦ Cellulose / Phenolic Insert ♦ Silica / Phenolic Insert ♦ Graphite Insert ♦ Carbon – Carbon Insert

♦ Exit Cone, Dome Closeout, and Blast Tube Material Alternatives

♦ Silica / Phenolic Insert ♦ Graphite / Phenolic Insert ♦ Silicone Elastomer Insert

♦ No Insert ♦ Glass / Phenolic Insert

7/24/2002 ELF 30

Subsystems Densities - Rocket Powered MissilesSubsystems Densities - Rocket Powered Missiles

Guidance: 0.04 lb / in3

Flight Control:0.04 lb / in3

Warhead:0.07 lb / in3

Propellant:0.06 lb / in3

Structure and Motor Case:0.10 ( Al ) to 0.27 ( steel ) lb / in3

Aero Surfaces:0.05 ( built-up Al ) to 0.27 ( solidsteel ) lb / in3

Data Link: 0.04 lb / in3

Dome: 0.1 lb / in3

7/24/2002 ELF 31

Strength – Elasticity of Airframe Material AlternativesStrength – Elasticity of Airframe Material Alternatives

Aluminum Alloy ( 2219-T81 )

400

300

200

100

0

Ft,Tensile Stress,103 psi

0 1 2 3 4 5ε, Strain, 10-2 in / in

Titanium Alloy ( Ti-6Al-4V )

High Strength Steel ( PH 15-7Mo )

Glass Fiberw / o Matrix

Kevlar Fiberw / o Matrix

Graphite Fiberw / o Matrix( 400 – 800 Kpsi )

E, Young’s Modulus, psiP, Load, lbε, Strain, in / inA, Area, in2

Room temperature

Note:• High strength fibers are:

– Very small diameter– Unidirectional– Very elastic– No yield before failure– Non forgiving failure

• Metals:– Yield before failure– Allow adjacent structure

to absorb load– More forgiving failure

Ft = P / A = E ε

7/24/2002 ELF 32

Structural Efficiency at High Temperature ofShort Duration Airframe Material AlternativesStructural Efficiency at High Temperature ofShort Duration Airframe Material Alternatives

200 400 600 800 1,0000Short Duration Temperature, Degrees F

8.0

10.0

12.0

6.0

4.0

2.0

0

F TU / ρ

, Ulti

mat

e Ten

sile S

treng

th /

Dens

ity, 1

05 In.

Graphite / Epoxy( ρ = 0.065 lb / in3 )0-±45-90 Laminate

Graphite / Polyimide ( ρ = 0.057 lb / in3 ), 0-±45-90 Laminate

Ti-6Al-4V Annealed Titanium ( ρ = 0.160 lb / in3 )

PH15-7 Mo Stainless Steel ( ρ = 0.282 lb / in3 )

Graphite

Glass

2219-T81Aluminum( ρ = 0.101 lb / in3 )

Chopped EpoxyComposites,Random Orientation( ρ = 0.094 lb / in3 )

Ti3Al ( ρ = 0.15 lb / in3 )

7/24/2002 ELF 33

Bulk Ceramics• Melt• ρ ~ 0.20 lb / in3

• Zirconium Ceramic,Hafnium Ceramic

Graphites• Pyrolytic• ρ ~ 0.08 lb / in3

• Carbon / Carbon

Max AllowableTemperature,

°R

4,000

3,000

2,000

00 1 2 3 4

Insulation Efficiency, Minutes To Reach 300°F at Back Wall

1,000

6,000

5,000

Note: Assumed Weight Per Unit Area of Insulator / Ablator = 1 lb / ft2

Porous Ceramics• Melt• Resin Impregnated• ρ ~ 0.12 lb / in3

• Carbon-SiliconCarbide

Medium Density PlasticComposites

• Charring• ρ ~ 0.03 lb / in3

• Nylon Phenolic, SilicaPhenolic, glassphenolic, carbonphenolic, graphitephenolic

Low DensityComposites• Subliming• ρ ~ 0.01 lb / in3

• Micro-QuartzPaint, GlassCork Epoxy,Silicone Rubber

Low Density Plastics• Subliming• Depolymerizing• ρ ~ 0.006 lb / in3

• Teflon

Composites Are Good Insulators / Ablators atHigh Temperature

Composites Are Good Insulators / Ablators atHigh Temperature

7/24/2002 ELF 34

Motor Case Stresses May Be Determined fromthe Pressure Vessel

Motor Case Stresses May Be Determined fromthe Pressure Vessel

For an axisymmetric motor case with a hemispherical dome, motorcase cylinder hoop stress is twice the motor dome longitudinalstress

With metals – the material also reacts body bendingIn composite motor designs, extra ( longitudinal ) fibers mustusually be added to accommodate body bending

Motor CaseCylinderHoopStress

Motor DomeLongitudinalStress

p p

TotalLoadp π r2

Ft = p π r2 / ( 2 π r t )( Ft )Longitudinal Stress = p r / ( 2 t )

Ft t = - 0∫π/2p r sinθ dθ

( Ft )Hoop Stress = p r / t

MotorDome Nozzle

Motor Case

7/24/2002 ELF 35

Motor Case Design May Be Determined byOperating Pressure

Motor Case Design May Be Determined byOperating Pressure

Calculate Maximum Effective Operating Pressure ( M.E.O.P. )M.E.O.P. = ( O.P. ) R.T. x eπk ∆ T x ( Margin for ignition spike and other design uncertainty )Rocket Baseline: Motor diameter = 8 in., length = 55 in.( O.P. )RT = Operating pressure at room temperature = 1,769 psi at R.T., πk = ( ∆ p / ∆ T ) / pc = .14% / °FHot day T = 140°F, eπk ∆ T = e0.0014 ( 140 - 70 ) = 1.10For 3σ margin, M.E.O.P. ≈ 1769 x 1.10 x 1.10 x 1.10 = 2,355 psi

Use FOS = factor of safety = 1.5Try Steel at Ft = 200,000 psi ult

tHoop = ( M.E.O.P. ) x r x ( FOS ) / Ft = 2355 x 4.0 x 1.5 / 200,000 = 0.071 intDome = 0.035 inWeight = Wcyl + WDome = ρ π d tHoop l + ρ ( π / 2 ) d2 tDome = 29.9 lbs for steel case

Try glass at Ft = 450,000 psi ult, assume 60% glass / 40% epoxy compositetHoop = 2355 x 4.0 x 1.5 / [( 450,000 ) ( 0.60 )] = .052 in radial fibers for internal pressure loadtDome = .026 inMust also add .015 in of longitudinal fibers to counteract body bending loadWeight = 10.1 lbs for composite case

7/24/2002 ELF 36

Minimum Smoke Propellant Has Low ObservablesMinimum Smoke Propellant Has Low Observables

High Smoke Example: AIM-7Particles ( e.g., metal fuel ) at allatmosphere temperature.

Reduced Smoke Example: AIM-120Contrail ( HCl from AP oxidizer ) at < -10°Fahrenheit atmospheric temperature.

Minimum Smoke Example: JavelinContrail (H2O ) at < -35º Fahrenheitatmospheric temperature.

High Smoke Motor

Reduced Smoke Motor

Minimum Smoke Motor

7/24/2002 ELF 37

Insensitive Munitions Improve Launch PlatformSurvivability

Insensitive Munitions Improve Launch PlatformSurvivability

Critical SubsystemsRocket motor propellant or engine fuelWarhead

Severity Concerns Ranking of Power Output - TypeDetonation ( ~ 0.000002 sec rise time )Partial detonation ( ~ 0.0001 sec rise time )Explosion ( ~ 0.001 sec rise time )Deflagration or propulsion ( ~ 0.1 sec rise time )Burning ( > 1 second )

Design considerations ( MIL STD 2105B )Fragment impact or blastFast / slow cook-offDropTemperatureVibrationCarrier landing ( 18 ft / sec sink rate )

7/24/2002 ELF 38

High System Reliability Is Provided by HighSubsystem Reliability and Low Parts CountHigh System Reliability Is Provided by HighSubsystem Reliability and Low Parts Count

Event / Subsystem

Rsystem = 0.920 = RArm X RLaunch X RStruct X RAuto X RAct XRSeeker X RIn Guid X RPS X RProp X RFuze X RWH

Arm ( 0.995 )

Launch ( 0.990 )

Structure ( 0.997 )Autopilot ( 0.993 )

Actuators ( 0.990 )

Seeker ( 0.985 )

Inertial Guidance ( 0.995 )

Power Supply ( 0.995 )

Propulsion ( 0.995 )

Fuze ( 0.987 )

Warhead ( 0.995 )

0.90 0.92 0.94 0.96 0.98 1.00Typical Reliability

Reliability

Robustness

Lethality

Miss Distance

ObservablesSurvivability

Reliability

Cost

Launch Platform Integration / Firepower

7/24/2002 ELF 39

Sensors, Electronics and Propulsion DriveMissile Production Cost

Sensors, Electronics and Propulsion DriveMissile Production Cost

Very High(>25% ProductionCost)

–High(>10%)

Moderate(>5%)

Relatively Low(<5%)

Dome Seeker Guidance andControl

Propulsion•Rocket•Airbreather

Wings

Stabilizers

Warheadand Fuzing

AerothermalInsulation

FlightControl

PowerSupply

Structure•Rocket•Airbreather

–

–

––––

Note:System assembly and test ~ 10% production costPropulsion and structure parts count / cost of airbreathing missiles are higher than that of rockets

CostRobustness

Lethality

Miss Distance

ObservablesSurvivability

Reliability

Cost

Launch Platform Integration / Firepower

DataLink

7/24/2002 ELF 40

Rail Launched and Ejection Launched MissilesRail Launched and Ejection Launched Missiles

Example Rail Launcher: Hellfire / Brimstone Example Ejection Launcher: AGM-86 ALCM

Video of Hellfire / Brimstone Carriage / Launch Video of AGM-86 Carriage / Launch

7/24/2002 ELF 41

Examples of Safe Store SeparationExamples of Safe Store Separation

AMRAAM Rail Launch from F-16 Video of Rapid Drop ( 16 Bombs ) from B-2

Laser Guided Bombs Drop from F-117

7/24/2002 ELF 42

Examples of Store Compatibility ProblemsExamples of Store Compatibility Problems

Unsafe Separation Hangfire Store Aeroelastic Instability

7/24/2002 ELF 43

Robustness Is Required to Satisfy Carriage andStorage Environmental Requirements

Robustness Is Required to Satisfy Carriage andStorage Environmental Requirements

Environmental Parameter Typical Requirement Video Example Environment: MLRSSurface Temperature -60°F* to 160°FSurface Humidity 5% to 100%Rain Rate 120 mm / hr**Surface Wind 100 km / hr steady***

150 km / hr gusts****Salt fog 3 grams / mm2 per yearVibration 10 g rms: MIL STD 810, 648, 1670AShock Drop height 0.5 m, half sine wave 100 g / 10 ms: MIL STD 810, 1670AAcoustic 160 dB

Note: MIL-HDBK-310 and the earlier MIL-STD-210B suggest using 1% climatic extreme as a typical design requirement.

* Lowest recorded temperature = -90°F. 20% probability temperature lower than -60°F during worst month of worst location.

** Highest recorded rain rate = 1,900 mm / hr. 0.5% probability greater than 120 mm / hr during worst month of worst location.

*** Highest recorded steady wind = 342 km / hr. 1% probability greater than 100 km / hr during worst month of worst location.

**** Highest recorded gust = 378 km / hr. 1% probability greater than 150 km / hr during worst month of worst location.

7/24/2002 ELF 44

Missile Design Validation / TechnologyDevelopment Is An Integrated ProcessMissile Design Validation / TechnologyDevelopment Is An Integrated Process

Rocket StaticTurbojet StaticRamjet Tests•Direct Connect•Freejet

StructureTest

HardwareIn-Loop

Simulation

Ballistic Tests

Lab Tests

Seeker

Actuators

Sensors

Propulsion Model

Aero Model

Model Simulation

Wind TunnelTests

Propulsion

Airframe

Guidanceand Control

Power Supply

Warhead

EnvironmentTests•Vibration•Temperature

Sled Tests

IM Tests

IM Tests

Flight Test Progression( Captive Carry, launch,Separation, UnpoweredGuided Flights, PoweredGuided Flights, LiveWarhead Flights )Lab Tests

Tower Tests

Autopilot / Electronics

Witness / Arena Tests

7/24/2002 ELF 45

Propulsion Static Firing with TVC ……………………………

Airframe Wind Tunnel Test

G&C HWL …………………………………………………………

Warhead Arena Test

Examples of Missile Development Tests andFacilities

Examples of Missile Development Tests andFacilities

7/24/2002 ELF 46

Examples of Missile Development Tests andFacilities ( cont )


Warhead Sled Test

Structure Test ………………………………………………

Insensitive Munition Test

Submunition Dispensor Sled Test ………………………

7/24/2002 ELF 47

RCS Test ………………………………………………………………

Environmental Test

Flight Test ………………………………………………………………………

Video of Facilities and Tests



7/24/2002 ELF 48

OutlineOutline


7/24/2002 ELF 49

Missile Concept Synthesis Requires Iteration ofFlight Trajectory

Missile Concept Synthesis Requires Iteration ofFlight Trajectory

Yes

Establish Baseline

MeetPerformance?


No

Yes


Alt Mission

Alt Baseline


Aerodynamics

Propulsion

Weight

Trajectory

7/24/2002 ELF 50

Missile Concept Synthesis Requires Iteration toMeet Flight Performance Requirements

Missile Concept Synthesis Requires Iteration toMeet Flight Performance Requirements

Yes

Establish Baseline

MeetPerformance?


No

Yes


Alt Mission

Alt Baseline


Aerodynamics

Propulsion

Weight

Trajectory

7/24/2002 ELF 51

Missile Flight Performance Envelope

Rear Flyout Range•Max•Min

Forward Flyout Range•Max•Min

Beam Flyout Range•Min•Max

7/24/2002 ELF 52

Example of Evolution of Short Range Air-to-AirMissile Range and Off Boresight RequirementsExample of Evolution of Short Range Air-to-AirMissile Range and Off Boresight Requirements

Archer AA-11 / R-73 ( IOC 1987 )Performance

•> +/- 60 degrees off boresight•20 nm range

New Technologies•TVC•Split canard•Neutral static margin•+/- 90 deg gimbal seeker•Imaging infrared seeker•Digital autopilot•Helmet mounted sight

Sidewinder AIM-9L ( IOC 1977 )Performance

•+/- 25 degrees off boresight•6.5 nm range

7/24/2002 ELF 53

Conceptual Design Modeling Versus PreliminaryDesign Modeling

Conceptual Design Modeling Versus PreliminaryDesign Modeling

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 ), 2 moments ( pitch, roll ),thrust, weight ]

Preliminary Design Modeling

6 DOF [ 3 forces ( normal, axial, side ), 3 moments ( pitch,roll, yaw ), thrust, weight ]

CDO

CN

CN

CN Cm

CA

CA

CA

CA

CA

Cl

ClCN Cm

CN Cm

CnCY

CY

7/24/2002 ELF 54

1 DOF Coast Equation Has Good Accuracy NearZero Angle of Attack

1 DOF Coast Equation Has Good Accuracy NearZero Angle of Attack

( V )2 DOF / ( V )1 DOF,Predicted DecelerationComparison for RocketBaseline

•

2.0

1.5

1.0

0.5

00 2 4 6 8 10

αTrim, Trim Angle of Attack, DegNote:

– ( V )2 DOF = Two degrees of freedom deceleration– ( V )1 DOF = One degree of freedom deceleration– Rocket baseline during coast– Mach 2, h = 20,000 ft– αTrim ≈ 0.3 deg for 1 g flyout

..

•

7/24/2002 ELF 55

3 DOF Simplified Equations of Motion ShowDrivers for Configuration Sizing

3 DOF Simplified Equations of Motion ShowDrivers for Configuration Sizing

Configuration Sizing Implication Ιy 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 ⇒ CNlarge, W small, q large

( W / gc ) V. ≈ T - CA SRef q - CNα

α2 SRef q - W sin γ High Speed / Long Range ⇒ TotalImpulse large, CA small, q small

+ Normal Forceα << 1 rad

γθ

δ W

+ Moment V

+ Thrust

+ Axial Force

Note: Based on aerodynamic control

7/24/2002 ELF 56

1.00E+05

1.00E+06

1.00E+07

1.00E+08

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8WP / WBC, Propellant or Fuel Weight / Weight at Begin of Cruise

R, C

ruise

Ran

ge, f

t

(VISP)(L/D) = 2,000,000 ft (VISP)(L/D) = 10,000,000 ft(VISP)(L/D) = 25,000,000 ft

For Long Range Cruise, Maximize V Isp, L / D,And Fuel or Propellant Weight Fraction

For Long Range Cruise, Maximize V Isp, L / D,And Fuel or Propellant Weight Fraction

Example: Ramjet Baseline at Mach 3 / 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 Equation

Note: R = cruise range, V = cruise velocity, ISP = specific impulse, L = lift, D = drag,WBC = weight at begin of cruise, WP, weight of propellant or fuel

Typical RocketTypical Ramjet with Axisymmetric AirframeRamjet with High L / D Airframe

7/24/2002 ELF 57

For High Rate of Climb, Maximize Thrust andVelocity While Minimizing Drag and Weight

For High Rate of Climb, Maximize Thrust andVelocity While Minimizing Drag and Weight

Steady Level Flight Steady Climb Steady Descent

T = DL = W

L

D T

W

γC

SIN γD = ( D – T ) / W = VD / V∞VD = ( D – T ) V∞/ WRD = ∆h / tan γD = ∆h ( L / D )

T – DL

DT

W

V∞γC VC

D – TL

DT

WγDVD

γD

• Small Angle of Attack• Equilibrium Flight• VC = Velocity of Climb• VD = Velocity of Descent• γC = Flight Path Angle During Climb• γD = Flight Path Angle During Descent• V∞ = Total Velocity• ∆h = Incremental Altitude• RC = Horizontal Range in steady climb• RD = Horizontal Range in steady dive ( glide )

Note:

Reference: Chin, S.S., “Missile Configuration Design,”McGraw Hill Book Company, New York, 1961

V∞T = W / ( L / D ) SIN γc = ( T – D ) / W = Vc / V∞

Vc = ( T – D ) V∞ / WRC = ∆h / tan γC = ∆h ( L / D )

7/24/2002 ELF 58

Small Turn Radius Requires High Angle of Attackand Low Altitude Flight

Small Turn Radius Requires High Angle of Attackand Low Altitude Flight

R T, E

xam

ple I

nsta

ntan

eous

Tur

n Ra

dius

, Fee

t

∆ 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 wingsCN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 α l / d = Length / Diameter = 10SRef = 2 ft2

CDO = 0.2( L / D )Max = 2.7, q( L / D )Max

= 1,000 psfα ( L / D )Max

= 15 degreesT( L / D )Max

= 740 lb

Example:∆ α = 10 degCN = 0.99h = 40K ft ( ρ = 0.00039 slugs / ft3 )RT = 2 ( 2,000 ) / [( 32.2 ) ( 0.99 ) ( 2 ) ( 0.00039 )] = 161,000 ft

RT = V / γ. ≈ 2 W / ( gc CN SRef ρ )

7/24/2002 ELF 59

Turn Rate Performance Requires High ControlEffectiveness

Turn Rate Performance Requires High ControlEffectiveness

γ. = gc n / V = [ q SRef CNα α + q SRef CNδ δ - W cos ( γ ) ] / [( W / gc ) V ]Assume Rocket Baseline @ Mach 0.8 Launch, 20K ft Altitude

• (Cmα)xcg=84.6 = (Cmα)xcg=75.7 + CNα ( 84.6 – 75.7 ) / d = - 0.40 + 0.68 ( 8.9 ) / 8 = 0.36 per deg• (Cmδ)xcg=84.6 = (Cmδ)xcg=75.7 + CNδ ( 84.6 – 75.7 ) / d = 0.60 + 0.27( 8.9 ) / 8 = 0.90 per deg• α / δ = - Cmδ / Cmα= - 0.90 / 0.36 = - 2.5• α’ = α + δ < 22 degrees, αmax = 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 / secAssume 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

7/24/2002 ELF 60

For Long Range Coast, Maximize Initial VelocityFor Long Range Coast, Maximize Initial Velocity

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2

Example for Rocket Baseline:•WBO = 367 lb, SRef = 0.349 ft2, VBO = 2,151 ft / sec, γ = 0 deg, CD0

= 0.9, h = 20,000 ft ( ρ = 0.00127 slugs / ft3 ), t = 10 sec

•t / [ 2 WBO / ( gc ρ SRef CD0 VBO )] = 10 / { 2 ( 367 ) / [ 32.2 ( 0.00127 ) ( 0.349 ) ( 0.9 ) ( 2151 ) ]} = 10 / 26.6 = 0.376

•V / VBO = 0.727, V = 0.727 x 2151 = 1564 ft / sec, R / [ 2 WBO / ( gc ρ SRef CD 0 )] = 0.319, R = 18,300 ft or 3.0 nm

t / [ 2 W / ( g ρS CD0 VBC )], Non-dimensional Coast Time

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

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

{ 2 WBO / [ gc ρAVG SRef ( CD0 )AVG VBO ]}}

Note: Based on 1DoF

dV / dt = - gc CD0 SRef q / W

Assumptions:

• γ = constant

• α ≈ 0 deg

• D > W sin γ

V = velocity during coast

VBO = velocity @ burnout ( begin coast )

R = coast range

Vx = V cos γ, Vy = V sin γ

Rx = R cos γ, Ry = R sin γ

7/24/2002 ELF 61

For Long Range Ballistic Flight, Maximize InitialVelocity

For Long Range Ballistic Flight, Maximize InitialVelocity

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2t / [ 2 W / ( g ρS CD0

Vi )], Non-dimensional Time

Vx / ( Vi cos γi ) = 1 / { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD0 )AVG Vi ]}}

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

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

Nomenclature: V = velocity during ballistic flight, Vi = initialvelocity, Rx = horizontal range, h = altitude, hi = initialaltitude, Vx = horizontal velocity, Vy = vertical velocity

Example for Rocket Baseline:

•WBO = 367 lb, SRef = 0.349 ft2, Vi = VBO = 2,151 fps, γi = 0 deg, ( CD0 )AVG = 0.9, hi = 20,000 ft, ρAVG = 0.001755 slugs / ft3, t = 35 sec

•t / [ 2 WBO / ( gc ρ SRef CD0 Vi )] = 35 / { 2 ( 367 ) / [ 32.2 ( 0.001755 ) ( 0.349 ) ( 0.9 ) ( 2151 ) ]} = 35 / 19.22 = 1.821

•Vx / ( Vi cos γi ) = 0.354 ⇒ Vx = 762 ft / sec, ( Vy + 32.2 t ) / ( Vi sin γi ) = 0.354 ⇒ Vy = - 1127 ft / sec, Rx / [ 2 Wi cos γi / ( gc ρ SRefCD 0

)] = 1.037 ⇒ Rx = 42,900 ft or 7.06 nm, ( h – hi + 16.1 t2 ) / [ 2 WBO cos γi / ( gc ρ SRef CD 0 )] = 1.037 ⇒ h = 0 ft

Rx / { 2 WBO cos γi / [ 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 γi / [ gc ρAVG SRef (CD0 )AVG ]}

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

7/24/2002 ELF 62

High Propellant Weight and High Thrust ProvideHigh Burnout Velocity

High Propellant Weight and High Thrust ProvideHigh Burnout Velocity

00.10.20.30.40.50.60.7

0 0.1 0.2 0.3 0.4 0.5Wp / Wi, Propellant Fraction

Delta

V /

( g IS

P ),

Nond

imen

sion

al

Incr

emen

tal V

eloc

ity

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 lbFor boost, WP = 84.8 lbWP / WL = 0.1696ISP = 250 secTB = 5750 lbMi = ML = 0.8, hi = hL = 20,000 ftDAVG = 635 lbDAVG / T = 0.110∆V / [( 32.2 ) ( 250 )] = - ( 1 - 0.110 ) ln ( 1 - 0.1696 ) = 0.1654 ∆V = ( 0.1654 ) ( 32.2 ) ( 250 ) = 1331 ft / sec

Note: 1 DOF Equation of Motion with α ≈ 0 deg, γ = constant, and T > W sin γ, Wi = initial weight, WP = propellantweight, 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 = V sin γ, Rx = R cos γ, Ry = R sin γNote: R = ( Vi + ∆V / 2 ) tB, where R = boost range, Vi = initial velocity, tB = boost time

7/24/2002 ELF 63

High Missile Velocity and Lead Are Required toIntercept High Speed Crossing Targets

High Missile Velocity and Lead Are Required toIntercept High Speed Crossing Targets

VM / VT

4

3

2

00 10 20 30 40 50

L, Lead Angle, Degrees

1

A = 90°

A = 45°

Note: Proportional GuidanceVM = Missile VelocityVT = Target VelocityA = Target AspectL = Missile Lead Angle

≈ Seeker Gimbal

VM VTL A

VM sin L = VT sin A, Proportional Guidance Trajectory

Example:L = 30 degreesA = 45 degreesVM / VT = sin ( 45° ) / sin ( 30° ) =1.42

7/24/2002 ELF 64

High Missile Velocity Improves Standoff RangeHigh Missile Velocity Improves Standoff Range

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Target Velocity / Missile Velocity

F-Po

le R

ange

/ La

unch

Ran

ge

VL / VM = 0VL / VM = 0.2VL / VM = 0.5VL / VM = 1.0

Example:• VL = VT• VM = 2 VT• Then VT / VM = VL / VM = 0.5• RF-Pole / RL = 0.33• RF-Pole = RD = 3.3 nm• RL = 3.3 / 0.33 = 10.0 nm

RF-Pole / RL = 1 – ( VT + VL ) / ( VM + VT ) Note: Head-on interceptRF-Pole = Standoff range at interceptRL= Launch rangeVM = Missile average velocityVT = Target velocityVL = Launch velocity

7/24/2002 ELF 65

Missile Flight Range Requirement Is Greatest fora Tail Chase Intercept

Missile Flight Range Requirement Is Greatest fora Tail Chase Intercept

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5VM / VT, Missile Velocity / Target Velocity

RF /

RL, M

issi

le F

light

Ran

ge /

Laun

ch R

ange

( RF / RL ) Head-on( RF / RL ) Tail Chase

Examples:•Head-on Intercept

•VM = 1,640 ft / sec, VT = 820 ft / sec•VM / VT = 1640 / 820 = 2•RF / RL = 2 / ( 2 + 1 ) = 0.667•RL = 10.0 nm•RF = 0.667 ( 10.0 ) = 6.67 nm

•Tail Intercept at same conditions•RF / RL = 2 / ( 2 – 1 ) = 2.0•RF = 2.0 ( 10.0 ) = 20.0 nm

( RF / RL )Head-on = ( VM / VT ) / [(VM / VT ) + 1 ]( RF / RL )TailChase = ( VM / VT ) / [(VM / VT ) - 1 ]

7/24/2002 ELF 66

Example of Spreadsheet Based ConceptualSizing Computer Code - TMD Spreadsheet


Conceptual Sizing Computer CodeTactical Missile Design ( TMD ) SpreadsheetPC compatibleWindows Excel spreadsheet

Based on Tactical Missile Design Short Course and TextbookAerodynamicsPropulsionWeightFlight trajectoryMeasures of merit

7/24/2002 ELF 67



Define 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, σmax )Weight Output [ Q, dTskin / dt, Tskin, ρskin , tskin, σbuckling, 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, τTotal,σHE, σMAN, Rdetect,CWeight, Cunit x ]

No [ RMax, RMin, VAVG ]

Yes

Yes

Alt Mission

Alt Baseline

Resize / Alt Config /Subsystems / Tech

7/24/2002 ELF 68

OutlineOutline


7/24/2002 ELF 69

Summary of Rocket Motor DesignSummary of Rocket Motor DesignDesign Methods

ThrustSpecific impulse

Design TradesPropellant burn area requirementNozzle throat areaNozzle expansion ratioRocket motor grainThrust magnitude controlSolid propellant alternativesMotor case materialNozzle materials

New Rocket Propulsion TechnologiesHigher density propellantSolid rocket thrust magnitude controlLow observable fuel / propellant

7/24/2002 ELF 70

Summary of Flight Performance AnalysisSummary of Flight Performance AnalysisFlight Performance Analysis Activity in Missile Design

Compute range, velocity, time-to-target, off boresightCompare with requirements

Discussed in This LectureEquations of motionFlight performance driversPropulsion flight performance comparisonSteady state flight relationshipsSteady climb and steady dive range predictionCruise predictionBoost predictionCoast predictionBallistic flight predictionTurn predictionTarget lead for proportional homing guidance

Flight Performance Strongly Impacted by Aerodynamics, Propulsion,and Weight

Documents

Rocket Motor Design and Missile Flight Performance Analysis