tmd spreadsheet release v1.0
DESCRIPTION
tactical missile design spread sheetTRANSCRIPT
Design Inputs 2001 TACTICAL MISSILE DESIGN SPREADSHEET v1.0 1Developed by: Gene Fleeman, Andrew Frits, and Jack Zentner
Primary Range / Flyout Calculations USER GUIDEThe following input sections are used to calculate a 'final range' for a boost/sustain/coast missile at a co-altitude flight
Missile Characteristics ROCKET RAMJETDescription Variable Name Value Default Value Default Value Units Additonal Information
Launch Mach Number M 0.8 0.8 0.8 DO NOT USE M=0.0
Launch Altitude h 20000 20000 40000 ft = User input
Missile Weight at Launch 500 500 2230 lbm = Automated Response
Weight of Cruise/Sustain Propellant 48.2 48.2 476 lbm
Weight of Boost Propellant 84.8 84.8 449 lbm
Weight of Booster Ejectables 0 0 42.5 lbm
Missile Center of Gravity 76.2 76.2 82.5 inches Zero defaults to length/2
Flight termination Mach Number M 1.5 1.5 1.5 DO NOT USE M=0.0
Acceleration of Gravity g 32.2 32.2 32.2
Air Specific heat ratio g 1.40 1.4 1.4
Air Density r 1.27E-03 slugs/ft^3
Speed of sound a 1036.9 ft/sec
Air Temperature 447.4 Rankine
Atmospheric Pressure 6.76 psi
Aerodynamics ROCKET RAMJETDescription Variable Name Value Default Value Default Value Units Additonal Information
Missile Body Input
Missile Length l 143.90 143.90 171.00 inches
Missile Boby Major Diameter 2a 8.00 8.00 20.38 inchesMissile Body Minor Diameter 2b 0.00 0.00 0.00 inches Zero defaults to circular cross-section
Nose Length 19.20 19.20 23.50 inches
5% 5% 5%
Missile Wing/Canard Input
Number of wings (0,1,2) N 2 2 0 2 panels per wing
Wing Area 367.2 367.2 0.0 N=1 is a straight wing
Wing LE Thickness Angle 10 10 0 deg N=2 is a cruiciform wing
Wing Airfoil Thickness to Cord, max t/c,max 4.40% 4.40% 0.00% %
Wing Incident Angle Waoa 0.0 0.0 0.0 deg
Wing Aspect Ratio War 2.82 2.82 0.00
Station of Wing leading edge Wle 60.8 60.8 0 inches
Wing taper ratio Wtr 0.175 0.175 0
Missile Tail Input
Number of Tail Wings 2 2 2
Mach Number for Tail Sizing Mtail 1.5 1.5 1.5
AOA for Tail Sizing Taoa 0.0 0 0 deg
Tail Aspect Ratio Tar 2.59 2.59 1.64
Tail Taper Ratio Ttr 0 0 0.7
Station of Tail LE Tle 125.4 125.4 150.33 inches
Tail Thickness-to-Chord, max t/c,max 2.7% 2.7% 4.0%
Tail LE Thickness Angle 6.2 6.2 9.1 deg
Propulsion ROCKET RAMJETDescription Variable Name Value Default Value Default Value Units Additonal Information
Boost Input Values
Engine Type 1 Solid Rocket Solid Rocket no units
Fuel Type 4 High Smoke Comp High Smoke Comp no units
Expansion Ratio e 6.00 6.00 6.00 psi
Chamber Pressure a 1769 1769 2000 psi
Boost Burn Time 3.26 3.26 5.05 sec
Cruise/Sustain Input Values
Engine Type 1 Solid Rocket Ramjet no units
Fuel Type 4 High Smoke Comp RJ-n no units
Combustor Temperature 0 0 4000 Rankine Only needed for Ramjet
Expansion Ratio e 6.00 6.00 0 psi Only needed for Rocket
Chamber Pressure a 301 301 0 psi Only needed for Rocket
Sustain Burn Time 10.86 10.86 0 sec Only needed for Rocket
WLaunch
WCruise
WBoost
Wejectables
XCG
ft/sec2
TAmbient
PAmbient
LN
Nose Bluntness (0 = sharp nose,1 = hemispherical nose) DHemi
SW inches2
tb
Tcombuster
tsustain
- User should input values only in blue colored regions- Units must be those specified in the Units column for consistency amongst the algorithms
- Master Input Page controls all the inputs for the entire document.- All output is included on the page "Master Output" and "Summary", though some figures may be given on disciplinary pages.- Note that there is a purposeful circular reference in the Propulsion spreadsheet. Therefore, "iterations" must be on in the Excel Options Menu. See Propulsion sheet for more info.- Note that only aerodynamics, 'flyout', and propulsion are linked together to calculate a single range value. Structures and other pages are not integrally linked with the flyout calculations- Often an Excel Warning Message "Not enough system resources to display completely" pops up for this page. Just ignore it and move on. It is probalby due to all the linking between this page and the rest of the spreadsheet.
PAGE SUMMARY
Master Input -- Controls all design inputsMaster Output -- Output from all disciplinary pages, often output from one discipline is used as an input by a second disciplineSummary -- Summary of the total flight trajectory and rangeTrajectory -- Calculation of the trajectory/range of the missileAero -- Aerodynamics pagePropulsion -- Propulsion calculations for both the boost and the sustain motorStructure -- Structural weight and temperature calculationsRadar -- Radar range calculationsWarhead -- Warhead lethality calculationsDynamics -- Vehicle dynamics and time-constant calculationsAtmosphere -- Table of atmospheric data
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0
-30.0
-20.0
-10.0
0.0
10.0
20.0
30.0Missile Outline
(figure NOT to scale)
N=1
N=2
Secondary Vehicle CalculationsThe following input sections are not integrated into the overall trajectory calculationsThey should be used for aerodynamic or measure of merit calculations at any arbitrary "Alternate flight condition"
Alternate Flight ConditionDescription Variable Name Value Default Value Units Additonal Information
Mach number M 2 2 DO NOT USE M=0.0
Altitude h 30000 30000 ft
Density r 0.0008907
Velocity V 1989.6 ft/sec
Angle of attack a 0 2 deg
Roll Angle f 0 0 degrees
StructuresDescription Variable Name Value Default Value Units Additonal Information
Missile Nose CG 0 15.696 in
Missile Nose Weight 15.9 15.9 lbm
Fuel Deinsity 0.06 0.06 lbm/in^3
Recovery Factor 0.9 0.9
Standard Day Temperature 70 70 deg. F
Hot day Temperature 140 140 deg. F
Pi sub-k (hoop stress parameter) 0.14% 0.14% 1/F
Skin Initial Temperature 460 460 R
Factor of Safety f.o.s 1.5 1.5
Material Type 1 High Strength Steel
Ejection Load (g's) 20 20 g's
Load Type 4 Ejection Load
Wall Heat Capacity 0.215 0.215 BTU/lbm/R
Nozzle Length 4.9 4.9 inches
RadarDescription Variable Name Value Default Value Units Additonal Information
Missile Characteristics
Radar Wavelength l 0.03 0.03 m
Antenna Diameter 10 10 inches
Transmitted Power 1000 1000 watts
Transmitter Frequency f 1.00E+10 1.00E+10 Hz
Receiver Temperature 290 290 K
Reciever Thermal Noise Bandwidth 1.00E+06 1.00E+06 Hz
Transmitter Loss Factor L 5 5
Boltzmann Constant K 1.38E-23 1.38E-23 Joule/K
Number of Pulses Integrated n 100 100
Receiver Noise Factor F 5 5
Signal to Noise Ratio for Detection S/N 10 10
Missile Radar Cross-Section 0.01 0.01 m^2
Target Radar Cross-Section 10 10 m^2
Visual Detection Constant 0.2 0.2
Threat Sensor Characteristics
Transmitter Power 10000 10000 watts
Threat Reciever Sensitivity 1.00E-14 1.00E-14 watts
Threat Transmitter Gain 40.0 40.0 dB
Threat Reciever Gain 40.0 40.0 dB
Threat Radar Wavelength 0.03 0.03 m
WarheadDescription Variable Name Value Default Value Units Additonal Information
Type of Warhead -1 Blast/Frag Blast-Frag Warhead Reqd Field
Hit-to-Kill Warhead? -1 Detonation Only Detonation-Only Warhead Reqd Field
Missile Mass 11.39 11.39 slugs Reqd Field
Warhead Mass 2.4 2.4 slugs Reqd Field
Atmospheric Pressure 6.76 6.76 psi Reqd Field
Target Range at Detonation (Miss Dist) 8 8 ft Reqd Field
Target Presented Area 20 20 Reqd Field
Target Vulnerable Area 2 2 Reqd Field
Charge-to-Metal Ratio 1 1 Reqd Field
slugs/ft3
Dant
PT
Trec
Bn
RCSM
RCST
Ct
Pt,T
Pr,T
Gt
Gr
lT
MM
Mwh
Po
RT,det
Ap ft2
Av ft2
MC/MM
Charge Energy [(2Ec)^(1/2)] 10230 10230 ft/sec Reqd Field
Fragment Mass 0.00022 0.00022 slugs Reqd Field
Fragment Density 15.2 15.2 slugs/ft^3 Reqd Field
Penetrator Length 14 14 inches N/A
Penetrator Diameter 2 2 inches N/A
Penetrator Material 1 Steel N/A
Target Material 5 Alum (2014-T6) N/A
Impact Velocity 2000 2000 ft/sec N/A
DynamicsDescription Variable Name Value Default Value Units Additonal Information
Missile Time Constant 2 User-Defined
User Input Time Constant t 0.5 0.5 sec Reqd Field
Mass Moment of Inertia in Y 94 94 N/A
Maximum Angle of Attack 12 12 deg N/A
Maximum Surface Deflection 15 15 deg N/A
Maximum Surface Deflection Rate 360 360 deg/sec N/A
Coefficient of Surface Deflection Moment 35.8 35.8 1/radian N/A
Radar Wavelength 0.03 0.03 meters N/A
Radar Frequency Agility fdf 0.02 0.02 N/A
Cn-alpha 38 38 1 / radian N/A
Filter Time Constant 0 0 sec N/A
Seeker Lock-on Range 125 125 ft Reqd Field
Target Position Offset 3 3 ft Reqd Field
Missile Navigation Ratio N' 4 4 Reqd Field
Cn-max 0.99 0.99 Reqd Field
Target Acceleration 3 3 g's Reqd Field
Target Direction 1 1 Reqd Field
Target Velocity 820 820 ft/sec Reqd Field
Launcher Velocity 820 820 ft/sec Reqd Field
Launch Range 60790 60790 ft Reqd Field
Ec
Mfrag
Dfrag
Lpen
Dpen
Vimpact
Iy slugs-ft2
amax
dmax
Cmde
lM
Cna
tfilter
RML
XT
CN
AT
VT
VL
RL
δ̇max
Design Outputs 2
Aerodynamics *Significantly more Aero data can be found on Aero SheetDescription Variable Name Value Units
Semi-major Axis a 4.00 inchesSemi-minor Axis b 4.00 inches
Missile Refence Area S 50.27Effective Missile Diameter D 8.00 inchesMissile Fineness Ratio l/d 17.99
Tail Area 248.26Nose Length 19.20 inchesWing Semi-span (b/2) aero_wing_span 16.09 inchesWing Root Chord aero_wing_root 19.42 inchesWing Tip Chord aero_wing_tip 3.40 inchesWing Sweep aero_wing_sweep 45.12 degTail Semi-Span (b/2) aero_tail_span 12.68 inchesTail Root Chord aero_tail_root 19.58 inchesTail Tip Chord aero_tail_tip 0.00 inchesTail Sweep aero_tail_sweep 57.08 degAlternate Flight Condition Values
Zero Lift Drag coefficent, Power off 1.022Zero Lift Drag coefficent, Power on 0.986
PropulsionDescription Variable Name Value Units
Boost MotorSpecfic Heat Ratio 1.217 no unitsThrust Coeff. Cf_b 1.643 no unitsExpansion Ratio 6 no unitsChara. Exit Velocity c_star_b 5298 ft/secBooster thrust Thrust_b 7036 lbfBooster Isp Isp_b 271 secBooster Throat Area A_throat_b 2.419 inches^2Booster Exit Area A_exit_b 14.52 inches^2Exit Pressure Pe_b 42.2958 psiSustain/Cruise MotorFuel Heating Value H_f n/a ft-lbf/lbmCruise Isp Isp_c 252 secCruise Thrust Thrust_c 1119 lbfExit Pressure Pe_c 7.20 psiCruise Throat Area A_throat_c 2.426 inches^2Cruise Exit Area A_exit_c 14.56 inches^2
Trajectory
Description Variable Name Value Units
Average Boost Cdo boost_cdo_t 1.02
inches2
ST inches2
ln
CD0
CD0
g_b
e_b
Delta V due to boost engine Boost Delta V 1465.2 ft/sec
Vel. @ end of boost V_boost_t 2294.7 ft/secMach @ end of boost M_boost_t 2.21Booster time Boost_time_t 3.26 secBooster range Boost_range_t 5092 ftAverage Cl for Cruise Cruise_Cl_t N/AVel. At beginning of cruise V_cruise_t 2294.7 ft/secMach at Start of Cruise M_cruise_t 2.213Vel. At end of cruise V_cruise_end_t 2061.3 ft/secMach at end of cruise M_cruise_end_t 1.99Cruise time Cruise_time_t 10.9 secCruise Range Cruise_range_t 23653 ftVel. @ end of coast V_coast_t 1555.35 ft/secMach @ end of coast M_coast_t 1.5Coast time Coast_time_t 7.10 secCoast range Coast_range_t 12674 ftAverage Cdo for Coast coast_cdo_t 1.145Total flight time Total_time_t 21.22 secTotal flight range Total_range_t 41419 ftEnd Mach # from No-Drag Boost Eqn No_drag_boost_mach_t 2.4End Mach from no-drag sustain eqn No_drag_cruise_mach_t 3.18
Weight at launch W_begin_boost_t 500 lbmWeight at end of boost W_end_boost_t 415.2 lbmWeight at beginning of cruise W_begin_cruise_t 415.2 lbmWeight at end of cruise W_end_cruise_t 367.0 lbm
Weight at end of coast W_end_coast_t 367.0 lbm
Aerodynamics Required for Trajectory CalculationsDescription Variable Name Value Units
Launch Cdo, Power on 1.168End of no-drag boost, Cdo, Power on 0.873Beginning of Coast, Cdo, Power off 1.027Flight Termination Cdo 1.264Alpha for Cruise Condition #VALUE! #N/A expected for Rocket-based Sustain MotorL/D for Cruise Condition #VALUE! #N/A expected for Rocket-based Sustain MotorCruise Cdo, Power On 0.915End of no-drag sustain, Power On 0.705
StructuresDescription Variable Name Value Units
Motor Case Thickness s_motor 0.071 inchesDome Thickness s_dome 0.036 inchesMotor Cylinder Weight 22.92 lbmMotor Dome Weight 1.01 lbmTotal Case Weight 23.93 lbmTheoretical Max Skin Temp 342.7 FActual Max Skin Temp 283.8 F
RadarDescription Variable Name Value Units
3-dB Beam Width beamwidth 0.120 radTarget Detection Range (nm) R0_nm 8.84 nmiTarget Detection Range (ft) R0_ft 53697 feetThreat's Detection Range (nm) Rthreat_nm 14.01 nmiThreat's Detection Range (ft) Rthreat_ft 85141 feetMissile 50% Visual Detection Range Rd 0.288 nmiMissile 50% Visual Recognition Range Rr 0.084 nmi
WarheadDescription Variable Name Value Units
Peak Overpressure at Target Ppeak 131.80 psiMass of Charge Mc 1.2 slugsMass of Metal Mm 1.2 slugsHit-to-Kill Charge Energy Multiplier EtEc 1 Not a Hit-to-Kill WarheadInitial Fragment Velocity Vf 8352.8 ft/secFragment Hits on Target Fhit 135.64Probability of Kill Pk 0.99999938Hardened Target Penetration penetrate N/A inches
DynamicsDescription Variable Name Value Units
Time ConstantsPitch Moment Control Time Constant taucontrol N/A secPiching Moment Control Rate Time Constant taurate N/A secSeeker Dome Error Slope dome_error N/A deg/degSeeker Dome Time Constant taudome N/A secTotal Missile Time Constant taumissile 0.5 secEngagement KinematicsHorizontal Turn Radius rad_turn 100895 feetMissile Closing Velocity Vclose 2810 ft/secLauncher Closing Velocity Vclose_launcher 1640 ft/secF-Pole Range Rf_pole 25306 feetF-Pole Range / Launch Range Rf_pole_Rl 0.42Missile Flight Range/Launch Range (Head-On) Rf_Rl_HO 0.71Missile Flight Range/Launch Range (Tail-Chase) Rf_Rl_TC 1.70Missile Flight Range (Head-On) HO_Frange 43048 feetMissile Flight Range (Tail-Chase) TC_Frange 103410 feetStatic Target AnalysisExpected Time of Homing tof 0.044 sInitial Heading Error G_naught 0.024 radMaximum Miss Distance Miss_Distance 0.357 feetAcceleration Reqd to Correct Heading Error Acceleration 4292 ft/sec^2Maneuvering Target AnalysisRequired Acceleration Ratio (missile/target) acc_ratio 2Maximum Miss Distance man_miss_dist 3.15 feet
AerodynamicsINPUTS
Description Variable Value UnitsMissile Body Input
Nose Length aero_len_nose 19.20 inchesMissile Length aero_length 143.90 inches
Missile Major Dia (2a) aero_2a 8.00 inchesMissile Minor Dia (2b) aero_2b 8.00 inches
Nose Bluntness aero_nose_blunt 5%Missile Center of Gravity aero_cg 76.2 inches
Nozzle Exit Area aero_exit_area 14.56
Air Density aero_density 1.27E-03Speed of Sound aero_vsound 1036.9 ft/secgamma aero_gamma 1.40Missile Wing Input 8Number of Wings (0,1,2) aero_num_wings 2 8Wing Incident Angle aero_wing_angle 0 deg 8
Wing Planform Area aero_wing_area 367.2 8Thickness-to-Chord, max aero_t_over_c 4.4%Wing LE Thickness Angle aero_le_thick_angle 10 degWing Aspect Ratio aero_aspect_ratio 2.82Station of Wing leading edge aero_wing_le 60.8 inchesWing taper ratio aero_wing_taper 0.175 8Missile Tail Input 8Number of Tail Wings (0,1,2) aero_tail_wings 2 8Tail Aspect Ratio aero_tail_aspect 2.59 8Tail Taper Ratio aero_tail_taper 0Station of Tail LE aero_tail_le 125.4 inchesTail Thickness-to-Chord, max aero_tail_t_over_c 0.027Tail LE Thickness Angle aero_tail_le_angle 6.2 deg
AOA for Tail Sizing aero_tsize_aoa 0 deg 8Description Variable Value Units
Flight Condition Input
Tail Sizing Mach Number aero_mach_1 1.5Lauch Mach Number aero_mach_2 0.8Zero-Drag Mach Number aero_mach_3 2.4Cruise/Sust. Mach Number aero_mach_4 2.2Zero-drag End Cruise Mach # aero_mach_5 3.2Begin Coast Mach # aero_mach_6 2.0Flight Term. Mach Number aero_mach_7 1.5Alt. Flight Cond. Mach Num. aero_mach_8 2.0Tail Sizing Roll Angle aero_roll_1 0 degLauch Roll Angle aero_roll_2 0 degZero-Drag Roll Angle aero_roll_3 0 degCruise/Sust. Roll Angle aero_roll_4 0 degNot Used aero_roll_5 0 degNot Used aero_roll_6 0 degFlight Term. Roll Angle aero_roll_7 0 degAlt. Flight Cond. Roll Angle aero_roll_8 0 deg
inches2
slugs/ft3
inches2
Required Cl for Cruise aero_cruise_cl N/A
*Assumed to be for small angle of attack
*Assumed to be for small angle of attack
There is no tail incident angle, it is assumed to be zero.The tail is sized for zero static margin at the tail-sizing mach number.
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0
-30.0
-20.0
-10.0
0.0
10.0
20.0
30.0 Missile Outline(figure NOT to scale)
4OUTPUTS
Description Variable Value UnitsBody Geometry Parameters
Nose Fineness Ratio aero_fn 2.4Body Fineness Ratio aero_fbody 18.0
Reference Area aero_ref_area 50.265Nose Hemispherical Dia. aero_hemi_dia 0.4 inches
Hemi Nose Ref Area aero_hemi_ref 0.126Major Axis aero_a 4 inches
Minor Axis aero_b 4 inches
Missile Diameter aero_ref_dia 8 inchesWing Geometry Paramaters
Wing Incident Angle (rad) aero_wing_inc_rad 0.00 radWing Semi-span (b/2) aero_wing_span 16.09 inchesWing Root Chord aero_wing_root 19.42 inchesWing Tip Chord aero_wing_tip 3.40 inches
Wing Sweep aero_wing_sweep 0.79 rad 45.11696 degWing Mean Aero Chord aero_mean_chord 13.29 inchesWing Outboard (Y) Cp (from root) aero_wing_y_cp 5.70 inchesStation of Wing MAC LE aero_wing_mac_le 66.94 inchesTail Geometry ParametersTail Semi-Span (b/2) aero_tail_span 12.68 inchesTail Root Chord aero_tail_root 19.58 inchesTail Tip Chord aero_tail_tip 0.00 inchesTail Sweep aero_tail_sweep 1.00 rad 57.07694 degTail Mean Aerodynamic Chord aero_tail_mac 13.05 inchesTail Aerodynamic Center
(from tail MAC leading edge) aero_tail_ac_le 6.1 inches(from nose) aero_tail_ac_nose 138.0 inches
Tail Area aero_tail_area 248.3Tail Outboard (Y) Cp (from root) aero_tail_y_cp 4.2 inches
Variations with Mach NumberTail Sizing # Launch End Boost Sustain End Sustain
Mach Number 1.5 0.8 2.4 2.2 3.2Air Speed (ft/sec) 1555.4 829.5 2448.3 2294.7 3296.4Dynamic Pressure (psf) 1533 436 3797 3336 6884Cdo, Wave, Sharp Nose 0.857 0.000 0.574 0.609 0.437Cdo, Wave, Blunt Nose 0.857 0.003 0.576 0.610 0.439Cdo, Base Drag, Coast 0.167 0.323 0.106 0.113 0.079Cdo, Base Drag, Power On 0.118 0.906 0.075 0.080 0.056Cdo, Body Friction 0.145 0.165 0.132 0.134 0.125Cdo, Wing Wave 0.021 0.000 0.025 0.025 0.027Cdo, Wing Friction 0.044 0.056 0.037 0.038 0.033Cdo, Wing 0.065 0.056 0.062 0.062 0.059Wing Aerodynamic Center (in)
(from leading edge of mean chord) 3.32 3.32 6.44 6.42 6.50(from missile nose) 70.26 70.26 73.38 73.36 73.44
inches2
inches2
inches2
Note that the Tail is iteratively sized. It is sized to provide zero static margin at the "Tail Sizing Mach number", with the given geometry and leading edge position.
Cdo, Tail Wave 0.000 0.000 0.003 0.003 0.004Cdo, Tail Friction 0.030 0.038 0.025 0.026 0.022Cdo, Tail 0.030 0.038 0.028 0.029 0.026Cdo, Body, P on 1.121 1.073 0.783 0.824 0.620Cdo, Body, P off 1.169 0.490 0.814 0.857 0.642Cdo, Body+Wing, P on 1.186 1.130 0.845 0.887 0.679Cdo, Body+Wing, P off 1.234 0.547 0.876 0.919 0.702Cdo, Body+Wing+Tail, P on 1.216 1.168 0.873 0.915 0.705Cdo, Body+Wing+Tail, P off 1.264 0.585 0.904 0.948 0.727Cn-alpha, Body 2 2 2 2 2Cn-Alpha, Wing 3.58 4.43 1.87 2.03 1.33Cn-Alpha, Tail 3.58 4.07 1.87 2.03 1.33
Cruise/Sustain L/D needed to meet Required Cl
(assumes power is on) Cl alpha(deg) L/DLow Value #N/A #N/A #N/A *Will be #N/A for non-Rocket Sustain Motors
Exact Cl N/A #VALUE! #VALUE!High Value #N/A #N/A #N/A
Guess for Tail Area aero_tail_guess 0.0ITERATIVE TAIL SIZING
Tail Sizing Mach Number: 1.5Angle of Attack: 0 deg Xcp,Body: 12.096 inchesIteration 1 2 3 4 5Tail Area 0 388.5 236.2 249.5 248.1Tail Semi-Span 0 15.9 12.4 12.7 12.7Tail Root Chord 0 24.5 19.1 19.6 19.6Tail Tip Chord 0 0 0 0 0Tail Mean Aerodynamic Chord 12.9 16.3 12.7 13.1 13.1Tail Aerodynamic Center
(from tail MAC leading edge) 3.2 7.6 5.9 6.1 6.1
inches2
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0
-30.0
-20.0
-10.0
0.0
10.0
20.0
30.0 Missile Outline(figure NOT to scale)
(from nose) 115.7 141.2 137.7 138.0 138.0Calculated Tail Area 388.5 236.2 249.5 248.1 248.3
DrawingX Y X Y
Body 0.0 0.019.2 4.0
143.9 4.0143.9 0.0143.9 -4.019.2 -4.00.0 0.0
Wing 60.8 4.0 60.8 -4.076.8 20.1 76.8 -20.180.2 20.1 80.2 -20.180.2 4.0 80.2 -4.0
Tail 125.4 4.0 125.4 -4.0145.0 16.7 145.0 -16.7145.0 16.7 145.0 -16.7145.0 4.0 145.0 -4.0143.9 4.0 143.9 -4.0
CG 76.2 0.0Cp 12.1 0.0
70.3 9.7138.0 8.270.3 -9.7
138.0 -8.2
Conversion to radians
Roll Angle 1 aero_roll_1r 0 radRoll Angle 2 aero_roll_2r 0 radRoll Angle 3 aero_roll_3r 0 radRoll Angle 4 aero_roll_4r 0 radRoll Angle 5 aero_roll_5r 0 radRoll Angle 6 aero_roll_6r 0 radRoll Angle 7 aero_roll_7r 0 radRoll Angle 8 aero_roll_8r 0 rad
AERODYNAMIC LOOK UP TABLESBody Position 1 (for Tail Sizing)
Center of Roll angle: 0 Mach #
alpha alpha Pressure
(deg) (rad) (inches)
-5 -0.087 12.6 -2.92 -1.82 -0.10
-4.5 -0.079 12.5 -2.62 -1.63 -0.07
-4 -0.070 12.4 -2.32 -1.45 -0.04
-3.5 -0.061 12.3 -2.03 -1.26 -0.01
-3 -0.052 12.3 -1.73 -1.08 -0.01
-2.5 -0.044 12.2 -1.44 -0.89 -0.02
-2 -0.035 12.2 -1.15 -0.71 -0.03
-1.5 -0.026 12.1 -0.86 -0.53 -0.03
-1 -0.017 12.1 -0.57 -0.35 -0.02
-0.75 -0.013 12.1 -0.43 -0.26 -0.02
-0.5 -0.009 12.1 -0.28 -0.18 -0.01
-0.25 -0.004 12.1 -0.14 -0.09 -0.01
0 0.000 12.1 0.00 0.00 0.00
0.25 0.004 12.1 0.14 0.09 0.01
0.5 0.009 12.1 0.28 0.18 0.02
0.75 0.013 12.1 0.43 0.26 0.03
1 0.017 12.1 0.57 0.35 0.05
1.5 0.026 12.1 0.86 0.53 0.08
2 0.035 12.2 1.15 0.71 0.11
2.5 0.044 12.2 1.44 0.89 0.16
3 0.052 12.3 1.73 1.08 0.20
3.5 0.061 12.3 2.03 1.26 0.26
4 0.070 12.4 2.32 1.45 0.31
4.5 0.079 12.5 2.62 1.63 0.38
5 0.087 12.6 2.92 1.82 0.45
5.5 0.096 12.6 3.22 2.01 0.52
6 0.105 12.7 3.52 2.20 0.60
6.5 0.113 12.9 3.83 2.39 0.69Begin Coast Terminate Alternate 7 0.122 13.0 4.13 2.58 0.78
2.0 1.5 2.0 7.5 0.131 13.1 4.44 2.77 0.872061.3 1555.4 2073.8 8 0.140 13.3 4.74 2.96 0.972692 1533 2724 8.5 0.148 13.4 5.05 3.15 1.080.670 0.857 0.667 9 0.157 13.6 5.36 3.35 1.190.671 0.857 0.667 9.5 0.166 13.7 5.67 3.54 1.300.126 0.167 0.125 10 0.175 13.9 5.97 3.73 1.430.089 0.118 0.089 10.5 0.183 14.1 6.28 3.93 1.550.137 0.145 0.137 11 0.192 14.3 6.59 4.12 1.680.024 0.021 0.024 11.5 0.201 14.5 6.90 4.32 1.820.039 0.044 0.039 12 0.209 14.7 7.21 4.51 1.960.063 0.065 0.063 12.5 0.218 14.9 7.52 4.71 2.11
13 0.227 15.1 7.83 4.90 2.266.38 3.32 6.39 13.5 0.236 15.4 8.14 5.10 2.41
73.32 70.26 73.32 14 0.244 15.6 8.45 5.29 2.57
CN, Wing CN, Tail CN, Body
Note that the Tail is iteratively sized. It is sized to provide zero static margin at the "Tail Sizing Mach number", with the given geometry and leading edge position.
0.003 0.000 0.003 14.5 0.253 15.8 8.76 5.49 2.740.027 0.030 0.027 15 0.262 16.1 9.07 5.69 2.910.030 0.030 0.030 16 0.279 16.6 9.68 6.07 3.260.898 1.121 0.893 17 0.297 17.2 10.30 6.46 3.630.934 1.169 0.929 18 0.314 17.8 10.91 6.85 4.020.961 1.186 0.956 19 0.332 18.4 11.51 7.23 4.420.997 1.234 0.992 20 0.349 19.1 12.11 7.61 4.840.990 1.216 0.986 21 0.367 19.8 12.70 7.99 5.281.027 1.264 1.022 22 0.384 20.5 13.29 8.37 5.73
2 2 2 23 0.401 21.2 13.87 8.74 6.202.33 3.58 2.31 24 0.419 22.0 14.44 9.10 6.682.33 3.58 2.31 25 0.436 22.8 15.00 9.46 7.17
26 0.454 23.6 15.56 9.82 7.68
27 0.471 24.4 16.10 10.16 8.20
28 0.489 25.3 16.63 10.51 8.73
*Will be #N/A for non-Rocket Sustain Motors 29 0.506 26.2 17.16 10.84 9.28
30 0.524 27.1 17.66 11.17 9.83
for mach : 0.800
alpha Cn Cn Cn
(deg) Body Body+Wing B+W+Tail
-5 -0.100 -3.0 -4.840
-4.5 -0.065 -2.7 -4.319
-4 -0.036 -2.4 -3.805
-3.5 -0.012 -2.0 -3.300
-3 -0.006 -1.7 -2.814
-2.5 -0.019 -1.5 -2.351
-2 -0.026 -1.2 -1.885
ITERATIVE TAIL SIZING -1.5 -0.028 -0.9 -1.417
-1 -0.024 -0.6 -0.947
-0.5 -0.015 -0.3 -0.4746 0 0.000 0.0 0.000
248.3 0.5 0.020 0.3 0.48012.7 1 0.046 0.6 0.96919.6 1.5 0.077 0.9 1.466
0 2 0.114 1.3 1.97313.1 2.5 0.156 1.6 2.488
3 0.203 1.9 3.0126.1 3.5 0.256 2.3 3.543
CN Plot
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0
-30.0
-20.0
-10.0
0.0
10.0
20.0
30.0 Missile Outline(figure NOT to scale)
0 5 10 15 20 25 300
10
20
30
40
50
CN Contributions
Body Body + Wing Body + Wing + Tail
Angle of Attack (deg)
CN
138.0 4 0.314 2.6 4.083248.3 4.5 0.378 3.0 4.631
5 0.447 3.4 5.187
5.5 0.521 3.7 5.750
6 0.601 4.1 6.321
6.5 0.686 4.5 6.899
7 0.776 4.9 7.484
7.5 0.871 5.3 8.076
8 0.972 5.7 8.675
8.5 1.078 6.1 9.280
9 1.188 6.5 9.892
9.5 1.304 7.0 10.510
10 1.425 7.4 11.134
10.5 1.552 7.8 11.764
11 1.683 8.3 12.399
11.5 1.819 8.7 13.040
12 1.960 9.2 13.686
12.5 2.105 9.6 14.336
13 2.256 10.1 14.992
13.5 2.411 10.6 15.653
14 2.571 11.0 16.317
14.5 2.736 11.5 16.986
15 2.906 12.0 17.659
16 3.258 12.9 19.017
17 3.628 13.9 20.387
18 4.016 14.9 21.770
19 4.420 15.9 23.163
20 4.841 17.0 24.564
21 5.278 18.0 25.972
22 5.730 19.0 27.385
23 6.197 20.1 28.802
24 6.678 21.1 30.220
25 7.173 22.2 31.638
26 7.681 23.2 33.054
27 8.201 24.3 34.466
28 8.733 25.4 35.874
29 9.277 26.4 37.274
30 9.830 27.5 38.665
AERODYNAMIC LOOK UP TABLESPosition 1 (for Tail Sizing) Position 4 (Cruise) -- Needed for Analytical Trajectory Calculations
0.8 0.00 Roll angle: 0 Mach # 2.213043283
L/D Power On Power Off
Power On Power Off Cl Cd Cl Cd
-4.84 -2.89 -2.80 -4.72 1.63 -4.71 1.68 -1.40 -0.94 -0.10 -2.44
-4.32 -2.71 -2.63 -4.21 1.55 -4.21 1.60 -1.25 -0.84 -0.07 -2.16
-3.81 -2.51 -2.43 -3.71 1.48 -3.71 1.53 -1.10 -0.74 -0.04 -1.88
-3.30 -2.28 -2.20 -3.22 1.41 -3.22 1.46 -0.96 -0.65 -0.01 -1.62
-2.81 -2.02 -1.95 -2.75 1.36 -2.74 1.41 -0.81 -0.55 -0.01 -1.37
-2.35 -1.74 -1.68 -2.30 1.32 -2.29 1.37 -0.67 -0.45 -0.02 -1.15
-1.89 -1.44 -1.38 -1.84 1.28 -1.84 1.33 -0.53 -0.36 -0.03 -0.92
-1.42 -1.11 -1.06 -1.38 1.25 -1.38 1.30 -0.40 -0.27 -0.03 -0.69
-0.95 -0.75 -0.72 -0.93 1.23 -0.92 1.28 -0.26 -0.18 -0.02 -0.46
-0.71 -0.57 -0.55 -0.69 1.22 -0.69 1.27 -0.20 -0.13 -0.02 -0.35
-0.47 -0.38 -0.37 -0.46 1.22 -0.46 1.27 -0.13 -0.09 -0.01 -0.23
-0.24 -0.19 -0.18 -0.23 1.22 -0.23 1.26 -0.06 -0.04 -0.01 -0.12
0.00 0.00 0.00 0.00 1.22 0.00 1.26 0.00 0.00 0.00 0.00
0.24 0.19 0.18 0.23 1.22 0.23 1.26 0.06 0.04 0.01 0.12
0.48 0.38 0.37 0.47 1.22 0.47 1.27 0.13 0.09 0.02 0.24
0.72 0.58 0.55 0.71 1.22 0.71 1.27 0.20 0.13 0.03 0.36
0.97 0.77 0.74 0.95 1.23 0.95 1.28 0.26 0.18 0.05 0.49
1.47 1.14 1.10 1.43 1.25 1.43 1.30 0.40 0.27 0.08 0.74
1.97 1.50 1.45 1.93 1.28 1.93 1.33 0.53 0.36 0.11 1.01
2.49 1.84 1.77 2.43 1.32 2.43 1.37 0.67 0.45 0.16 1.28
3.01 2.15 2.07 2.94 1.37 2.94 1.42 0.81 0.55 0.20 1.57
3.54 2.42 2.34 3.46 1.43 3.46 1.48 0.96 0.65 0.26 1.86
4.08 2.66 2.58 3.99 1.50 3.99 1.55 1.10 0.74 0.31 2.16
4.63 2.87 2.78 4.52 1.58 4.52 1.62 1.25 0.84 0.38 2.47
5.19 3.04 2.96 5.06 1.66 5.06 1.71 1.40 0.94 0.45 2.79
5.75 3.18 3.10 5.61 1.76 5.60 1.81 1.55 1.05 0.52 3.11
6.32 3.29 3.21 6.16 1.87 6.15 1.92 1.70 1.15 0.60 3.45
6.90 3.38 3.30 6.72 1.99 6.71 2.04 1.85 1.25 0.69 3.79
7.48 3.44 3.36 7.28 2.12 7.27 2.17 2.01 1.36 0.78 4.14
8.08 3.47 3.40 7.85 2.26 7.84 2.31 2.16 1.46 0.87 4.50
8.68 3.49 3.42 8.42 2.41 8.41 2.46 2.32 1.57 0.97 4.87
9.28 3.50 3.43 9.00 2.57 8.99 2.62 2.48 1.68 1.08 5.24
9.89 3.49 3.42 9.58 2.75 9.57 2.80 2.64 1.79 1.19 5.62
10.51 3.47 3.41 10.17 2.93 10.16 2.98 2.81 1.90 1.30 6.01
11.13 3.44 3.38 10.75 3.13 10.75 3.18 2.97 2.01 1.43 6.41
11.76 3.40 3.35 11.35 3.34 11.34 3.39 3.14 2.12 1.55 6.81
12.40 3.35 3.31 11.94 3.56 11.93 3.61 3.30 2.23 1.68 7.22
13.04 3.31 3.26 12.54 3.79 12.53 3.84 3.47 2.35 1.82 7.64
13.69 3.26 3.22 13.13 4.03 13.12 4.08 3.64 2.46 1.96 8.06
14.34 3.20 3.16 13.73 4.29 13.72 4.34 3.81 2.58 2.11 8.49
14.99 3.15 3.11 14.33 4.56 14.32 4.60 3.98 2.69 2.26 8.93
15.65 3.09 3.06 14.94 4.84 14.93 4.88 4.16 2.81 2.41 9.38
16.32 3.03 3.00 15.54 5.13 15.53 5.17 4.33 2.93 2.57 9.83
(M2-1)1/2:
CN, Total CN, Wing CN, Tail CN, Body CN, Total
16.99 2.97 2.95 16.14 5.43 16.13 5.48 4.50 3.05 2.74 10.29
17.66 2.91 2.89 16.74 5.74 16.73 5.79 4.68 3.16 2.91 10.75
19.02 2.80 2.78 17.94 6.41 17.93 6.46 5.03 3.40 3.26 11.69
20.39 2.69 2.67 19.14 7.12 19.13 7.17 5.39 3.64 3.63 12.66
21.77 2.58 2.56 20.33 7.88 20.31 7.93 5.75 3.88 4.02 13.65
23.16 2.47 2.46 21.51 8.69 21.49 8.74 6.10 4.13 4.42 14.65
24.56 2.38 2.36 22.67 9.54 22.65 9.59 6.47 4.37 4.84 15.68
25.97 2.28 2.27 23.81 10.44 23.79 10.49 6.83 4.62 5.28 16.72
27.39 2.19 2.18 24.94 11.39 24.92 11.43 7.19 4.86 5.73 17.78
28.80 2.10 2.10 26.04 12.37 26.02 12.42 7.55 5.11 6.20 18.86
30.22 2.02 2.01 27.11 13.40 27.09 13.45 7.92 5.35 6.68 19.95
31.64 1.95 1.94 28.16 14.47 28.14 14.52 8.28 5.60 7.17 21.05
33.05 1.87 1.87 29.18 15.58 29.15 15.63 8.64 5.84 7.68 22.16
34.47 1.80 1.80 30.16 16.73 30.14 16.77 9.00 6.08 8.20 23.28
35.87 1.74 1.73 31.10 17.91 31.08 17.96 9.36 6.33 8.73 24.41
37.27 1.67 1.67 32.01 19.13 31.99 19.18 9.71 6.56 9.28 25.55
38.67 1.61 1.61 32.88 20.39 32.85 20.43 10.06 6.80 9.83 26.69
0 5 10 15 20 25 300
10
20
30
40
50
CN Contributions
Body Body + Wing Body + Wing + Tail
Angle of Attack (deg)
CN
AERODYNAMIC LOOK UP TABLESPosition 4 (Cruise) -- Needed for Analytical Trajectory Calculations Position 7 (Alternate Flight Condition)
1.97 Roll angle: 0 Mach # 2 1.73
L/D Power On Power Off L/D
Power On Power Off Cl Cd Cl Cd Power On Power Off
-1.63 -1.58 -2.32 1.42 -2.32 1.47 -1.58 -1.07 -0.10 -2.74 -1.81 -1.75
-1.49 -1.43 -2.05 1.38 -2.05 1.43 -1.41 -0.95 -0.07 -2.43 -1.66 -1.60
-1.33 -1.28 -1.79 1.34 -1.79 1.39 -1.25 -0.84 -0.04 -2.12 -1.49 -1.44
-1.17 -1.13 -1.54 1.31 -1.54 1.36 -1.08 -0.73 -0.01 -1.83 -1.32 -1.27
-1.01 -0.98 -1.30 1.29 -1.30 1.33 -0.92 -0.62 -0.01 -1.55 -1.15 -1.10
-0.86 -0.83 -1.09 1.26 -1.09 1.31 -0.76 -0.52 -0.02 -1.30 -0.98 -0.94
-0.70 -0.68 -0.88 1.25 -0.88 1.30 -0.61 -0.41 -0.03 -1.04 -0.80 -0.77
-0.54 -0.52 -0.66 1.23 -0.66 1.28 -0.45 -0.31 -0.03 -0.78 -0.61 -0.58
-0.36 -0.35 -0.44 1.22 -0.44 1.27 -0.30 -0.20 -0.02 -0.52 -0.41 -0.39
-0.27 -0.26 -0.33 1.22 -0.33 1.27 -0.22 -0.15 -0.02 -0.39 -0.31 -0.30
-0.18 -0.18 -0.22 1.22 -0.22 1.27 -0.15 -0.10 -0.01 -0.26 -0.21 -0.20
-0.09 -0.09 -0.11 1.22 -0.11 1.26 -0.07 -0.05 -0.01 -0.13 -0.10 -0.10
0.00 0.00 0.00 1.22 0.00 1.26 0.00 0.00 0.00 0.00 0.00 0.00
0.09 0.09 0.11 1.22 0.11 1.26 0.07 0.05 0.01 0.13 0.11 0.10
0.19 0.18 0.23 1.22 0.23 1.27 0.15 0.10 0.02 0.27 0.21 0.20
0.28 0.27 0.35 1.22 0.34 1.27 0.22 0.15 0.03 0.41 0.32 0.31
0.38 0.36 0.46 1.22 0.46 1.27 0.30 0.20 0.05 0.55 0.43 0.41
0.58 0.55 0.71 1.23 0.71 1.28 0.45 0.31 0.08 0.83 0.65 0.62
0.77 0.74 0.97 1.25 0.96 1.30 0.61 0.41 0.11 1.13 0.87 0.83
0.97 0.93 1.23 1.27 1.23 1.32 0.76 0.52 0.16 1.43 1.08 1.04
1.16 1.11 1.50 1.30 1.50 1.34 0.92 0.62 0.20 1.75 1.29 1.24
1.34 1.29 1.78 1.33 1.78 1.37 1.08 0.73 0.26 2.07 1.49 1.43
1.52 1.46 2.07 1.36 2.07 1.41 1.25 0.84 0.31 2.40 1.67 1.62
1.68 1.62 2.37 1.41 2.36 1.45 1.41 0.95 0.38 2.74 1.85 1.78
1.84 1.78 2.67 1.45 2.67 1.50 1.58 1.07 0.45 3.09 2.01 1.94
1.98 1.91 2.98 1.51 2.98 1.56 1.74 1.18 0.52 3.44 2.15 2.08
2.10 2.04 3.30 1.57 3.30 1.62 1.91 1.29 0.60 3.81 2.28 2.21
2.22 2.15 3.63 1.64 3.62 1.68 2.08 1.41 0.69 4.18 2.39 2.32
2.32 2.25 3.96 1.71 3.96 1.76 2.26 1.53 0.78 4.56 2.48 2.42
2.40 2.33 4.30 1.79 4.30 1.84 2.43 1.64 0.87 4.95 2.56 2.50
2.47 2.41 4.65 1.88 4.64 1.93 2.61 1.76 0.97 5.34 2.63 2.56
2.53 2.47 5.00 1.98 4.99 2.02 2.79 1.88 1.08 5.75 2.68 2.62
2.58 2.52 5.36 2.08 5.35 2.13 2.96 2.00 1.19 6.16 2.72 2.66
2.61 2.55 5.73 2.19 5.72 2.24 3.14 2.13 1.30 6.57 2.75 2.69
2.64 2.58 6.10 2.31 6.09 2.36 3.33 2.25 1.43 7.00 2.77 2.71
2.66 2.60 6.47 2.44 6.47 2.48 3.51 2.37 1.55 7.43 2.78 2.73
2.67 2.61 6.86 2.57 6.85 2.62 3.69 2.50 1.68 7.87 2.78 2.73
2.67 2.62 7.24 2.71 7.23 2.76 3.88 2.62 1.82 8.32 2.78 2.73
2.66 2.62 7.63 2.87 7.62 2.91 4.06 2.75 1.96 8.77 2.76 2.72
2.65 2.61 8.03 3.03 8.02 3.07 4.25 2.87 2.11 9.23 2.75 2.70
2.64 2.60 8.43 3.19 8.42 3.24 4.44 3.00 2.26 9.69 2.73 2.68
2.62 2.58 8.83 3.37 8.82 3.42 4.63 3.13 2.41 10.16 2.70 2.66
2.60 2.56 9.24 3.56 9.23 3.60 4.82 3.26 2.57 10.64 2.67 2.64
(M2-1)1/2: (M2-1)1/2:
CN, Wing CN, Tail CN, Body CN, Total
2.57 2.54 9.65 3.75 9.64 3.80 5.01 3.38 2.74 11.13 2.64 2.61
2.54 2.51 10.07 3.96 10.05 4.00 5.20 3.51 2.91 11.62 2.61 2.58
2.48 2.45 10.90 4.39 10.89 4.44 5.58 3.77 3.26 12.61 2.54 2.51
2.42 2.39 11.75 4.86 11.74 4.91 5.97 4.03 3.63 13.63 2.46 2.44
2.35 2.32 12.60 5.37 12.59 5.42 6.35 4.30 4.02 14.66 2.39 2.36
2.27 2.25 13.46 5.92 13.44 5.97 6.74 4.56 4.42 15.72 2.31 2.29
2.20 2.18 14.32 6.50 14.30 6.55 7.13 4.82 4.84 16.79 2.23 2.21
2.13 2.11 15.18 7.13 15.16 7.17 7.52 5.08 5.28 17.88 2.16 2.14
2.06 2.04 16.03 7.79 16.01 7.83 7.91 5.35 5.73 18.99 2.08 2.07
1.99 1.98 16.88 8.49 16.87 8.53 8.30 5.61 6.20 20.11 2.01 2.00
1.92 1.91 17.73 9.22 17.71 9.27 8.69 5.87 6.68 21.24 1.94 1.93
1.86 1.85 18.56 10.00 18.54 10.04 9.07 6.13 7.17 22.38 1.87 1.86
1.79 1.78 19.39 10.81 19.36 10.85 9.45 6.39 7.68 23.53 1.81 1.80
1.73 1.72 20.19 11.65 20.17 11.70 9.84 6.65 8.20 24.69 1.74 1.74
1.67 1.67 20.99 12.54 20.96 12.58 10.21 6.91 8.73 25.85 1.68 1.68
1.62 1.61 21.76 13.45 21.74 13.49 10.59 7.16 9.28 27.02 1.63 1.62
1.56 1.56 22.51 14.40 22.49 14.44 10.96 7.41 9.83 28.20 1.57 1.57
AERODYNAMIC LOOK UP TABLESPosition 7 (Alternate Flight Condition)
Power On Power Off
Cl Cd Cl Cd
-2.62 1.45 -2.62 1.50
-2.32 1.40 -2.32 1.45
-2.03 1.36 -2.03 1.41
-1.75 1.32 -1.75 1.37
-1.49 1.30 -1.48 1.34
-1.24 1.27 -1.24 1.32
-1.00 1.25 -1.00 1.30
-0.75 1.24 -0.75 1.28
-0.50 1.22 -0.50 1.27
-0.38 1.22 -0.38 1.27
-0.25 1.22 -0.25 1.27
-0.13 1.22 -0.13 1.26
0.00 1.22 0.00 1.26
0.13 1.22 0.13 1.26
0.26 1.22 0.26 1.27
0.39 1.22 0.39 1.27
0.53 1.22 0.52 1.27
0.80 1.24 0.80 1.29
1.09 1.25 1.08 1.30
1.38 1.28 1.38 1.33
1.68 1.31 1.68 1.35
1.99 1.34 1.99 1.39
2.31 1.38 2.31 1.43
2.64 1.43 2.63 1.47
2.97 1.48 2.97 1.53
3.31 1.54 3.31 1.59
3.66 1.61 3.65 1.65
4.02 1.68 4.01 1.73
4.38 1.76 4.37 1.81
4.75 1.85 4.74 1.90
5.12 1.95 5.12 2.00
5.50 2.05 5.50 2.10
5.89 2.16 5.88 2.21
6.28 2.28 6.28 2.33
6.68 2.41 6.67 2.46
7.09 2.55 7.08 2.60
7.49 2.70 7.48 2.74
7.91 2.85 7.90 2.90
8.32 3.01 8.31 3.06
8.75 3.18 8.74 3.23
9.17 3.36 9.16 3.41
9.60 3.55 9.59 3.60
10.03 3.75 10.02 3.80
10.47 3.96 10.46 4.01
10.90 4.18 10.89 4.23
11.79 4.64 11.77 4.69
12.68 5.15 12.66 5.19
13.57 5.69 13.56 5.73
14.47 6.27 14.45 6.31
15.37 6.89 15.35 6.93
16.26 7.54 16.24 7.59
17.15 8.24 17.13 8.28
18.03 8.98 18.01 9.02
18.91 9.75 18.89 9.79
19.77 10.56 19.75 10.60
20.61 11.41 20.59 11.45
21.44 12.29 21.42 12.33
22.26 13.21 22.23 13.25
23.05 14.16 23.02 14.21
23.81 15.15 23.79 15.19
Summary of FlyoutFlight Characteristics Summary Altitude = 20000 ft
Weight Velocity(sec) (sec) (lbm) (nmi) (nmi) (ft/sec)
Launch Condition 0.00 0.00 500.0 0.0 0.00 829.5End of Boost 3.26 3.26 415.2 0.84 0.84 2294.7Begin Cruise --- 3.26 415.2 --- 0.84 2294.7End Cruise 10.86 14.12 367.0 3.89 4.73 2061.3End Coast 7.10 21.22 367.0 2.09 6.82 1555.4
StageTime
TotalTime
StageRange
Total Downrange
0 5 10 15 20 25
0
1
2
3
4
5
6
7
8
Missile Range vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Do
wn
ran
ge
(n
mi)
0 5 10 15 20 25
0
500
1000
1500
2000
2500
Missile Velocity vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Ve
loc
ity
(ft
/se
c)
0 5 10 15 20 25
0
100
200
300
400
500
600
Missile Mass vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Ma
ss
(lb
m)
0 5 10 15 20 25
0.0
0.5
1.0
1.5
2.0
2.5
Missile Mach vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Ma
ch
Nu
mb
er
3
Mach Cdo Isp
0.80 1.168 --2.21 1.02 270.52.21 0.915 252.11.99 1.027 252.11.50 1.145 --
0 5 10 15 20 25
0
500
1000
1500
2000
2500
Missile Velocity vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Ve
loc
ity
(ft
/se
c)
0 5 10 15 20 25
0.0
0.5
1.0
1.5
2.0
2.5
Missile Mach vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Ma
ch
Nu
mb
er
Propulsion*** The Propulsion Interim Input Values are linked directly to the Flyout Sheet, not through Master Output, as other sheets are doneBoost Input ValuesDescription Variable Value for calc. Default Value UnitsEngine Type Engine_type_b 1 1 no units
Fuel Type Fuel_type_b 4 4 no units
Chamber Pressure Pc_b 1769 1769 psi
Expansion Ratio 6.0 6 no units
Boost Burn Time t_b 3.26000 3.26 sec
Boost Interim Input ValuesDescription Variable Value for calc. Default Value UnitsAlt @ launch Alt_t 20000 20000 feetWt. booster propellant W_prop_boost_t 84.8 84.8 lbmReference Area Sref_b 50.27 50.27 inches^2
Boost Interim Calculation ValuesDescription Variable Value for calc. Default Value UnitsSpecfic Heat Ratio 1.217 1.236 no unitsAtmos. Prssure Pa_b 6.76 6.75 psiThrust Coeff. Cf_b 1.643 1.638 no unitsChara. Exit Velocity c_star_b 5298 5258 ft/secmass flow mdot_b 26.012 26 lbm/secExit Pressure Ratio Pe_Pc_b 0.0239094249 0.024 no unitsExit Pressure Pe_b 42.2958 45.79 psiBooster Throat Area A_throat_b 2.419 2.419 inches^2Booster Exit Area A_exit_b 14.52 14.52 inches^2
Boost Output ValuesDescription Variable Value for calc. Default Value UnitsBooster thrust Thrust_b 7036 7000 lbfBooster Isp Isp_b 271 268 sec
e_b
g_b
If the exit area is too large (larger than the reference area), it may be decreased in two ways. First, one may decrease the expansion ratio, this will hurt Isp. Second, one may decrease the throat size, either by increasing the chamber pressure or by decreasing the mass flow rate.
Note that this page has a couple of self-iterating cells (exit pressure ratios). In order for these cells to calculate automatically, under Excel's "Tools" menu, select the "Options" Menu. Then, under the "calculation tab", "Iteration" must be checked, with a max iteration at 50 or higher set, and a limit around: 0.0001
Sometimes the self-iterating cells will create an error. If this happens, the only way to 'reset' the cell and get a solution is to copy the cell and paste it back in. It sounds silly, but it is the only way to get Excel to 'reset' the starting value and converge to a solution (otherwise it starts from whatever current value the cell has, and if this value is bad, the result will be bad).
If the exit area is too large (larger than the reference area), it may be decreased in two ways. First, one may decrease the expansion ratio, this will hurt Isp. Second, one may decrease the throat size, either by increasing the chamber pressure or by decreasing the mass flow rate.
Note that this page has a couple of self-iterating cells (exit pressure ratios). In order for these cells to calculate automatically, under Excel's "Tools" menu, select the "Options" Menu. Then, under the "calculation tab", "Iteration" must be checked, with a max iteration at 50 or higher set, and a limit around: 0.0001
Sometimes the self-iterating cells will create an error. If this happens, the only way to 'reset' the cell and get a solution is to copy the cell and paste it back in. It sounds silly, but it is the only way to get Excel to 'reset' the starting value and converge to a solution (otherwise it starts from whatever current value the cell has, and if this value is bad, the result will be bad).
5*** The Propulsion Interim Input Values are linked directly to the Flyout Sheet, not through Master Output, as other sheets are done Fuel Type Designation
Cruise Input Values Description Variable Value for calc. Default Value UnitsEngine Type Engine_type_c 1 1 no units
Fuel Type Fuel_type_c 4 4 no units
Combustor Temperature T4_c 0 4000 Rankine
Atmospheric Temperature T0_c 447.4 447.4 Rankine
Atmos. Specfic Heat Ratio 1.40 1.4 no units
Chamber Pressure Pc_c 301 301 psiSustain Burn Time t_sustain 10.86 10.86 secExpansion Ratio 6.0 6.2 no units
Cruise Interim Input ValuesDescription Variable Value for calc. Default Value UnitsMach @ Boost End M_cruise_t 2.21 1.99 no unitsSpeed of sound @ Cruise a_t 1037 1037 ft/secWt. Cruise propellant W_prop_cruise_ 48.2 48.2 lbm
Cruise Interim Calculation ValuesDescription Variable Value for calc. Default Value UnitsFuel Heating Value H_f n/a 15,535,588 ft-lbf/lbmSpecfic Heat Ratio 1.217 n/a no unitsAtmos. Prssure Pa_c 6.76 6.75 psiThrust Coeff. Cf_c 1.531 1.530 no unitsChara. Exit Velocity c_star_c 5298 5300 ft/secmass flow mdot_c 4.438 4.4 lbm/secExit Pressure Ratio Pe_Pc_c 0.0239094249 0.024 no unitsExit Pressure Pe_c 7.20 45.79 psiCruise Throat Area A_throat_c 2.426 2.419 inches^2Cruise Exit Area A_exit_c 14.56 14.52 inches^2
Cruise Output ValuesDescription Variable Value for calc. Default Value UnitsCruise Isp Isp_c 252 250 secCruise Thrust Thrust_c 1119 1018 lbf
So
lid
Ro
ck
et
Pro
pe
lla
nts
g_c_atm
Air
Bre
ath
ing
Fu
els
F
or
Cru
ise
e_c
g_c
Fuel Type DesignationVolumetric Heating Heating Specfic Chara.
Density Performance Value Value Heat Ratio Exit Vel.Type Desig. lbm/in^3 Btu/in^3 Btu/lbm ft-lbf/lbm no units ft/sec
HMX 1 0.0686 - - - 1.236 5258
RDX 2 0.0656 - - - 1.236 5264
CL20 3 0.0712 - - - 1.238 5193
High Smoke Composite 4 0.0619 - - - 1.217 5298
Reduced Smoke Composite 5 0.0609 - - - 1.186 4939JP-n 6 0.028 559 19,964 15,535,588 - -RJ-n 7 0.04 581 14,525 11,302,905 - -Carbon Slurry 8 0.049 801 16,347 12,720,681 - -Solid Hydrocarbon 9 0.075 1132 15,093 11,745,164 - -Aluminum Slurry 10 0.072 866 12,028 9,359,644 - -Boron Carbide Slurry 11 0.05 1191 23,820 18,535,986 - -Solid Magnesium 12 0.068 1300 19,118 14,876,760 - -Solid Aluminium 13 0.1 1300 13,000 10,116,197 - -Solid Boron 14 0.082 2040 24,878 19,359,326 - -
Engine Type DesignationBaseline
Type Desig. Ispsolid rocket 1 Calculatedramjet 2 Calculatedscramjet - high performance 3 n/ascramjet - low performance 4 n/aturbofan - high performance 5 3,021turbofan - mid performance 6 2,305turbofan - low performance 7 1,669turbojet - high performace 8 3,021turbojet - mid performace 9 2,305turbojet - low performace 10 1,669
Trajectory 6 Input Data is Retrieved from:Master Input
How Does this page work? AerodynamicsPropulsion
Input ValuesDescription Variable Value for calc. Default Value UnitsMach @ launch M_launch_t 0.80 0.80Alt @ launch Alt_t 20000 20000 feetWeight @ launch W_launch_t 500 500 lbmWt. booster propellant W_prop_boost_t 84.8 84.8 lbmBooster Ejectables W_boost_eject_t 0 0 lbmBooster thrust Thrust_boost_t 7036 7036 lbfBooster Isp Isp_boost_t 271 271 secCd0 at launch Launch_cd_t 1.168219214 0.01Wt cruise propellant W_prop_cruise_t 48.2 48.2 lbmCruise Isp Isp_cruise_t 252 252 secCruise Thrust (rocket only) Thrust_cruise_t 1119 1119 lbfFlight termination Mach Final_mach_t 1.5 1.5Gravity g_t 32.2 32.2 ft/sec^2Air density rho_t 1.27E-03 1.27E-03 slugs/ft^3Speed of sound a_t 1036.9 1037 ft/secReference area Sref_t 0.3490658504 0.349 ft^2Sustain Engine Type eng_type_t 1 rocket
Interim Input Values (values calculated on other pages)Description Variable Value for calc. Default Value UnitsCd from no-drag boost eqn No_drag_boost_cd_t 0.8731918629L/D for cruise L_D_cruise_t N/ACd0 at Flight Termination Mach Number Coast_final_Cdo_t 1.2638453777Cd0 at Beginning of Coast Coast_initial_Cdo_t 1.026641262Cdo at Beginning of Sustain sustain_initial_Cdo_t 0.9154331852Cdo at End of no-boost Sustain sustain_no_drag_Cdo_t 0.704703052
Output ValuesDescription Variable Value UnitsEnd Mach from no-drag boost eqn No_drag_boost_mach_t 2.36Average Boost Cdo boost_cdo_t 1.02Delta V due to boost engine Boost_Delta V 1465.2 ft/secVel. @ end of boost V_boost_t 2294.7 ft/secMach @ end of boost M_boost_t 2.21Booster time Boost_time_t 3.26 secBooster range Boost_range_t 5092 ftEnd Mach from no-drag sustain eqn No_drag_cruise_mach_t 3Average Cl for Cruise Cruise_Cl_t N/AVel. during cruise V_cruise_t 2294.7 ft/secMach at start of cruise M_cruise_t 2.21Vel. at end of cruise V_cruise_end_t 2061.3 ft/secMach at end of cruise M_cruise_end_t 1.99
Cruise time Cruise_time_t 10.9 secCruise Range Cruise_range_t 23653 ftVel. @ end of coast V_coast_t 1555.4 ft/secMach @ end of coast M_coast_t 1.5Average Cdo for Coast coast_cdo_t 1.145Coast time Coast_time_t 7.10 secCoast range Coast_range_t 12673.9 ftTotal flight time Total_time_t 21.22 secTotal flight range Total_range_t 41419.2 ftWeight at launch W_begin_boost_t 500 lbmWeight at end of boost W_end_boost_t 415.2 lbmWeight at beginning of cruise W_begin_cruise_t 415.2 lbmWeight at end of cruise W_end_cruise_t 367.0 lbmWeight at end of coast W_end_coast_t 367.0 lbm
BOOST CALCULATIONS: WEIGHTS:V_launch_t 829.52 ft/sec Launch 500.0 lbmNo-drag Delta_V 1618.8 ft/sec End Boost 415.2 lbmNo-drag Final V 2448.3 Begin Cruise 415.2 lbmNo-drag Mach # 2.36 End Cruise 367.0 lbmDrag_avg 667.6 lbf End Coast 367.0 lbmAvg Boost Cdo 1.021Boost Delta V 1465.2 ft/secBoost End Vel. 2294.7 ft/secBoost End Mach 2.21 TOTAL FLIGHT SUMMARY:Boost Time 3.26 secAverage Velocity 1562 ft/sec Boost Time 3.26 secBoost Range 5,092 ft/sec Cruise Time 10.86 secBoost Range 0.84 nmi Coast Time 7.10 sec
Total Flight Time 21.22 secCRUISE CALCULATIONS:(for air-breather) Boost Range 5092.49 ftBeg. Cruise req Cl 0.36 Cruise Range 23652.84 ftEnd Cruise req. Cl 0.32 Coast Range 12673.92 ftAvg. Cruise Cl 0.34 Total Flight Range 41419.25 ftCruise Velocity 2294.7 ft/secBoost End Mach 2.21 Launch Velocity 0.80 machCruise Range #VALUE! ft Boost End Vel. 2.21 machCruise Range #VALUE! nmi Cruise End Vel. 1.99 machCruise Time #VALUE! sec Coast End Vel. 1.50 mach
CRUISE CALCULATIONS:(for rocket-sustain) Time WeightSustain_initial_Vel. 2294.7 ft/sec (sec) (lbm)Sustain_initial_Mach 2.21 Launch Condition 0.00 500.0No-drag Delta_V 1001.7 ft/sec End of Boost 3.26 415.2No-drag Final V 3296.4 ft/sec Begin Cruise 3.26 415.2No-drag Mach # 3.18 End Cruise 14.12 367.0Cd0 for initial cruise 0.915 End Coast 21.22 367.0Cdo for no-drag final 0.705Avg sustain drag 1379.6 lbfSustain Delta V -233.5 ft/secSustain End Velocity 2061.3 ft/secCruise End Mach 1.99Cruise Time 10.9 secCruise Average Vel. 2178.0 ft/secCruise Range 23,653 ftCruise Range 3.89 nmi
COAST CALCULATIONS:Avg. Coast Cdo 1.145End of Coast Vel 1555.4 ft/secTime to Coast 7.10 sec
0 5 10 15 20 25
0
500
1000
1500
2000
2500
Missile Velocity vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Vel
oci
ty (
ft/s
ec)
Range of Coast 12673.9 ftCoast Range 2.1 nmi
0 5 10 15 20 25
0
1
2
3
4
5
6
7
8
Missile Range vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Do
wn
ran
ge
(nm
i)
0 5 10 15 20 25
0
500
1000
1500
2000
2500
Missile Velocity vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Vel
oci
ty (
ft/s
ec)
0 5 10 15 20 25
0
100
200
300
400
500
600
Missile Mass vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Ma
ss
(lb
m)
0 5 10 15 20 25
0.0
0.5
1.0
1.5
2.0
2.5
Missile Mach vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Ma
ch
Nu
mb
er
0.054 min0.181 min0.118 min0.354 min
0.84 nm3.89 nm2.09 nm6.82 nm
829.52 ft/sec2294.70 ft/sec2061.25 ft/sec1555.35 ft/sec
Range Velocity Mach(nmi) (ft/sec)0.00 829.5 0.800.84 2294.7 2.210.84 2294.7 2.214.73 2061.3 1.996.82 1555.4 1.50
0 5 10 15 20 25
0
500
1000
1500
2000
2500
Missile Velocity vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Vel
oci
ty (
ft/s
ec)
0 5 10 15 20 25
0
1
2
3
4
5
6
7
8
Missile Range vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Do
wn
ran
ge
(nm
i)
0 5 10 15 20 25
0
500
1000
1500
2000
2500
Missile Velocity vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Vel
oci
ty (
ft/s
ec)
0 5 10 15 20 25
0.0
0.5
1.0
1.5
2.0
2.5
Missile Mach vs. Flight Time
Boost
Cruise
Coast
Flight Time (sec)
Ma
ch
Nu
mb
er
Structure 7Input ValuesDescription Variable Value for calc. Default Value Units
Missile Diameter s_dia 8.00 8 inchesMissile Length s_len 143.90 144 inchesMissile Launch Weight s_wt_launch 500 500 lbmMissile CG s_mis_cg 76.2 76.2 inches
Missile Nose Length s_nose_len 19.20 19.2 inchesMissile Nose CG s_nose_cg 12.8 15.696 inchesMissile Nose Weight s_nose_wt 15.9 15.9 lbm
Fuel Density s_fuel_den 0.06 0.06
gravitation acceleration s_g 32.2 32.2Freestream Density s_den_free 1.27E-03 0.001267 slugs/ft^3Freestream Temperature s_temp_free 447.4 450 RRecovery factor s_recovery 0.9 0.9Flight Mach Numbers:Mach 1 - Launch 0.80 0.8Mach 2 - End Boost 2.21 2.2Mach 3 - End Sustain 1.99 2.2Mach 4 - End Coast 1.50 1.5Missile End Boost Weight 415.2 415.2 lbmMissile Begin Sustain Weight 415.2 415.2 lbmMissile End Sustain Weight 367 367 lbmMissile End Coast Weight 367 367 lbm
Engine Chamber Pressure s_c_press 1769 1769 psiStandard Day Temp s_day_temp 70 70 FHot Day Temp s_hot_temp 140 140 FPi sub-k s_pi_k 0.14% 0.14% 1/FSkin Initial Temperature s_temp_init 460 460 RSustain Motor Time s_cruise_time 10.86 10.86 secFactor of Safety s_fos 1.5 1.5
Material Type s_material 1 1 High Strength SteelMaterial Ultimate Stress s_material_ult 200000 200000(steel) psiMaterial Density s_material_den 0.2820 0.282 lbm/in3Ejection Load (g's) s_eject 20 20 g'sLoad Type 4Load Distribution (c parameter) s_distribution 4 4 (ejection load)Wall (heat capacity) Insulation s_insulate 0.215 0.215 BTU/lbm/RNozzle Length s_nozzle 4.9 4 inches
Output ValuesDescription Variable Value Units
Motor Case Thickness s_motor 0.071 inchesDome Thickness s_dome 0.036 inchesMotor Cylinder Weight 22.92 lbm
lbm/in3
ft/sec2
Motor Dome Weight 1.01 lbm
Total Case Weight 23.93 lbmTheoretical Max Skin Temp 343 FActual Max Skin Temp 283.8 F
Materials DatabaseMaterial Strength Material Density Ultimate Stress
Number (slug/ft^3) (psi)High Strength Steel 1 0.282 200,000Aluminum 2219-T81 2 0.101 65,000Titanium Alloy 3 0.06 140,000Graphite Fibers (0 +/- 45-90 deg ply) 4 0.065 140,000Kevlar Fibers(0 +/- 45-90 deg ply) 5 0.057 130,000Glass Fibers (0 +/- 45-90 deg ply) 6 0.094 130,000
Loads Number c - valueUniform Load 1 8Linear Load 2 7.8Centered Linear Load 3 6Ejection Load 4 4
Estimated Weight 368.384 lbm(from weight regression)
Moment of Inertia'sEntire Vehicle, Assuming a Constant CylinderDiameter in feet 0.67 ft
s_Iy_cylinder 186.51
Nose Moment of Inertia, Assuming a cone
Diameter in feet 0.667 ft
s_ly_nose 0.056
Calculation of Hoop Stress for Motore multiplier 1.102962785Maximum effective operating pressure (M.E.O.P) -- 3 sigma marginM.E.O.P 2374 psiThickness for Motor Case 0.071 inchesThickness for Dome 0.036 inches
Calculation of Ejection Bending LoadMax Bending load 359,750 lbf-inThickness for Motor Case 0.054 inches
Motor Case WeightMotor Cylinder Wt 22.92 lbmMotor Dome Wt 1.01 lbm
Total Case Weight 23.93 lbm
High Strength Steel 487.296Wall Thickness 0.005934039 ft
Surface TemperaturesMach Number Recovery TempLaunch 0.80 499 RBoost 2.21 842 RCruise 1.99 766 RCoast 1.50 629 R
Avg Cruise Mach: 2.10 803 R
slugs-ft2
slugs-ft2
Material Density (lb/ft3) lb/ft31 2 3 4
0
100
200
300
400
500
600
700
800
900
Recovery Temperature Per Flight Phase
Flight Phase (boost, sustain, coast)
Re
co
ve
ry T
em
pe
ratu
re (
R)
High Temperature Rate
Freestream Density 3.93478E-05Mach = 1.1 Mach =
x (ft) Q Dtwall/dt Q(ft) (deg F/sec)
0.00833333333333333 5.646 9.082 30.1130.599583333333333 2.401 3.862 12.804
1.19916666666667 2.090 3.362 11.1471.79875 1.927 3.100 10.279
2.39833333333333 1.820 2.927 9.7042.99791666666667 1.740 2.799 9.280
4.496875 1.605 2.581 8.5575.99583333333333 1.515 2.437 8.079
8.99375 1.397 2.247 7.45011.9916666666667 1.319 2.121 7.033
1 2.167 3.486 11.559
Mach Dtwall/dt1.1 3.486
2 18.5933 57.8634 129.4875 241.8666 402.979
lbm/ft3
(BTU/ft2/sec) (BTU/ft2/sec)
0 2 4 6 8 10 12 14
0.000
100.000
200.000
300.000
400.000
500.000
600.000
700.000
Temperature Rate
1.1
2
3
5
Distance from Nose (ft)
DT
wa
ll/D
t (d
eg
F/s
ec
)
END-BURN CIRCUMFERENTIAL BURNMoment of Moment of **All Moment of Inertia
Flight Phase Missile Wt C.G. Inertia C.G. Inertia Caclulations assume
(lbm) (inches) (inches) a constant-densityLaunch 500 76.2 186.51 76.2 186.51 cylinderEnd Boost 415.2 66.35 98.62 68.01 154.88Begin Sustain 415.2 66.35 98.62 68.01 154.88
End Sustain 367 61.70 64.29 61.67 64.29End Coast 367 61.70 64.29 61.67 64.29
Fuel Density: 0.06 lbm/in3
End Burn: Circumferential Burn:Boost Fuel Len 29.1 inches Fuel Len 45.4 inchesBoost Fuel CG 124.4 inches Fuel CG 116.3 inchesSustain Fuel Len 16.27 inchesSustain Fuel CG 101.72 inches
x Q Dtwall/dt Skin Temp Skin Temp(ft) (deg F/sec) (deg R) (deg F)
0.008333333333 34.543 55.562 743.8 283.80.599583333333 14.688 23.625 640.6 180.61.199166666667 12.786 20.567 624.1 164.1
1.79875 11.791 18.965 614.8 154.82.398333333333 11.131 17.905 608.4 148.42.997916666667 10.645 17.123 603.5 143.5
4.496875 9.816 15.789 594.9 134.95.995833333333 9.267 14.906 589.0 129.0
8.99375 8.546 13.745 581.0 121.011.99166666667 8.068 12.977 575.5 115.5
(slugs-ft2) (slugs-ft2)
(BTU/ft2/sec)
1 2 3 4
0
100
200
300
400
500
600
700
800
900
Recovery Temperature Per Flight Phase
Flight Phase (boost, sustain, coast)
Re
co
ve
ry T
em
pe
ratu
re (
R)
Launch End Boost Begin Sustain End Sustain End Coast
0102030405060708090
CG per Phase
End Burning Circumferential Burn
Phase (boost,ejectable,sustain,coast)
C.G
. L
oc
ati
on
(in
ch
es
)
Launch End Boost Begin Sustain End Sustain End Coast
0
20
40
60
80
100
120
140
160
180
200
Moment of Inertia Variation
End Burning Circumferential Burn
Phase (boost,ejectable,sustain,coast)
Mo
me
nt
of
Ine
rtia
(s
lug
s-f
t2)
0 2 4 6 8 10 12 14
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Skin Temperature at End of Cruise
Distance from nose (ft)
Sk
in T
em
p (
de
g F
)
2 Mach = 3 Mach = 4 Mach = 5 Mach = Dtwall/dt Q Dtwall/dt Q Dtwall/dt Q Dtwall/dt Q
(deg F/sec) (deg F/sec) (deg F/sec) (deg F/sec)48.437 93.717 150.742 209.722 337.336 391.735 630.102 652.68020.596 39.848 64.096 89.174 143.436 166.566 267.920 277.52017.929 34.690 55.798 77.631 124.868 145.004 233.238 241.59516.533 31.988 51.452 71.584 115.142 133.709 215.070 222.77715.608 30.199 48.575 67.581 108.704 126.233 203.045 210.32114.927 28.881 46.455 64.632 103.959 120.724 194.183 201.14113.765 26.632 42.837 59.597 95.862 111.320 179.057 185.47312.995 25.143 40.442 56.265 90.502 105.096 169.046 175.10311.983 23.184 37.292 51.882 83.452 96.910 155.879 161.46411.313 21.888 35.206 48.982 78.786 91.491 147.163 152.436
18.593 35.973 57.863 80.502 129.487 150.368 241.866 250.532
(BTU/ft2/sec) (BTU/ft2/sec) (BTU/ft2/sec) (BTU/ft2/sec)
0 2 4 6 8 10 12 14
0.000
100.000
200.000
300.000
400.000
500.000
600.000
700.000
Temperature Rate
1.1
2
3
5
Distance from Nose (ft)
DT
wa
ll/D
t (d
eg
F/s
ec
)
MACH
0 1 2 3 4 5 6 7
0.000
50.000
100.000
150.000
200.000
250.000
300.000
350.000
400.000
450.000
Temperature Rate
Mach Number
DT
wa
ll/D
t (d
eg
F/s
ec
)
0 2 4 6 8 10 12 14
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Skin Temperature at End of Cruise
Distance from nose (ft)
Sk
in T
em
p (
de
g F
)
Launch End Boost Begin Sustain End Sustain End Coast
0102030405060708090
CG per Phase
End Burning Circumferential Burn
Phase (boost,ejectable,sustain,coast)
C.G
. L
oc
ati
on
(in
ch
es
)
Launch End Boost Begin Sustain End Sustain End Coast
0
20
40
60
80
100
120
140
160
180
200
Moment of Inertia Variation
End Burning Circumferential Burn
Phase (boost,ejectable,sustain,coast)
Mo
me
nt
of
Ine
rtia
(s
lug
s-f
t2)
0 2 4 6 8 10 12 14
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Skin Temperature at End of Cruise
Distance from nose (ft)
Sk
in T
em
p (
de
g F
)
6Dtwall/dt
(deg F/sec)1049.829446.388388.603358.334338.299323.533298.332281.652259.713245.192
402.979
0 1 2 3 4 5 6 7
0.000
50.000
100.000
150.000
200.000
250.000
300.000
350.000
400.000
450.000
Temperature Rate
Mach Number
DT
wa
ll/D
t (d
eg
F/s
ec
)
0 2 4 6 8 10 12 14
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Skin Temperature at End of Cruise
Distance from nose (ft)
Sk
in T
em
p (
de
g F
)
WarheadINPUT BLOCK
Variable Name Value Units Other UnitsType of Warhead Reqd Field w_type 1 Blast-Frag WarheadHit-to-Kill Warhead? Reqd Field htokill 0 Detonation-Only WarheadMissile Mass Reqd Field Mmiss 11.39 slugsWarhead Mass Reqd Field Mwh 2.4 slugs 77.28Atmospheric Pressure Reqd Field Po 6.76 psiTarget Range at Detonation (Miss Dist) Reqd Field Trange 8 ft
Target Presented Area Reqd Field Tarea 20
Target Vulnerable Area Reqd Field Tvuln 2Charge-to-Metal Ratio Reqd Field charratio 1Charge Energy [(2Ec)^(1/2)] Reqd Field Ec 10230 ft/secFragment Weight Reqd Field Mf 0.00022 slugs 3.210658Fragment Density Reqd Field Dfrag 15.2 slugs/ft^3Penetrator Length N/A Lpen 14 inchesPenetrator Diameter N/A Dpen 2 inchesPenetrator Material N/A 1Target Material N/A 4Impact Velocity N/A Vimpact 2000 ft/sec
Following Values Set by Pentrator / Target Material TypePenetrator Density N/A RHOpen 15.2 slugs/ft^3Target Density N/A RHOtarg 5.4 slugs/ft^3Target Ultimate Yield Stress N/A YIELDtarg 10080000 psf 70000
OUTPUT BLOCKVariable Name Value Units Other UnitsPeak Overpressure at Target Ppeak 131.8 psiMass of Charge Mc 1.2 slugs 38.64 lbsMass of Metal Mm 1.2 slugs 38.64 lbsHit-to-Kill Charge Energy Multiplier EtEc 1 Not a Hit-to-Kill WarheadInitial Fragment Velocity Vf 8352.76 ft/secFragment Hits on Target Fhit 135.6434Probability of Kill Pk 0.999999Hardened Target Penetration penetrate N/A inches N/A feet
ft2
ft2
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 55000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hard Target Penetration vs. Impact Velocity(only available for penetrator warhead)
Impact Velocity (ft/sec)
Pen
etra
tio
n (
feet
)
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 55000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hard Target Penetration vs. Impact Velocity(only available for penetrator warhead)
Impact Velocity (ft/sec)
Pen
etra
tio
n (
feet
)
8
Other Units Mass CalculationsMass of charge
Detonation-Only Warhead Mc 1.2 slugsMass of metal
lbs Mm 1.2 slugsExplosive Weightwtexpl 38.64 lbs
Initial Fragment Velocity Cylindrical Warhead AssumptionVf 8352.76002 ft/sec
grams Hit-to-Kill Warhead Fragment Vel.Fragment Energy MultilplierEtEc 1
Explosion Geometry Perfect Spherical AssumptionNumber of fragmentsNfrag 5454.54545Fragment length Square Fragments AssumptionLfrag 0.29244281 inches
psi fragment impacts per areafragarea 6.78217087 # frag / ft^2Number of fragment hitsFhit 135.643417Miss Distance 8 ftCalculations for Warhead Fragment Penetration to Follow in Spreadsheet Addition
Ratio of vulnerable to preseneted areaAvAp 0.1Probability of killPk 0.99999938
Pressure CalculationsZ=R/C^1/3Zpo^(1/3)
Z 2.366zpo 4.474
Overpressure Calculations For a bare sphere of pentolite:Peak Pressure (psi):Ppeak 131.804799
Penetration Analysis Assumes Penetrator Does not Disintegrate on Impact
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 55000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hard Target Penetration vs. Impact Velocity(only available for penetrator warhead)
Impact Velocity (ft/sec)
Pen
etra
tio
n (
feet
)
penetrate 33.4940388 inches2.7911699 feet
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 55000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hard Target Penetration vs. Impact Velocity(only available for penetrator warhead)
Impact Velocity (ft/sec)
Pen
etra
tio
n (
feet
)
MATERIAL DATABASEID Number Material: Density: Ultimate Stress:
slug/ft^3 slug/in^3 lb/in^2 (psi)1 Steel Alloy 15.2 0.008796296 2000002 Tungsten Alloy 37 0.021412037 2200003 Titanium Alloy 8.7 0.005034722 1400004 Aluminum (2014-T6) 5.4 0.003125 65000
5 Reinforced Concrete 4.02 0.002326389 5000
6 User Input 1 07 User Input 2 0
MATERIAL DATABASEUltimate Stress:
lb/ft^2 (psf) 2 117280000 No Warhead Detonation Only57600000 Blast/Frag Hit-to-Kill Warhead10080000 Penetration10080000 Combined Penetration-Blast/Frag
720000
00
Penetration FigurePenetration Penetration
Velocity(ft/sec) (in) (ft) * only given for penetration warhead1000 28.54989 01200 29.63773 01400 30.66647 01600 31.64718 01800 32.58775 02000 33.49404 02200 34.37056 02400 35.22088 02600 36.04787 02800 36.8539 03000 37.64095 03200 38.41068 03400 39.16454 03600 39.90375 03800 40.62938 04000 41.34239 04200 42.04361 04400 42.73378 04600 43.41357 04800 44.08357 05000 44.74434 0
* only given for penetration warhead
Radar 9INPUT BLOCK Missile Tracking Target Calculations:
Variable Name Value Units Radar Range Calculations:Missile Characteristics Ant. DiaRadar Wavelength lamda 0.03 mAntenna Diameter dia 10 inches 3-dB Beam WidthTransmitter Power Pt 1000 watts beamwidthTransmitter Frequency freq 1E+10 HzReceiver Temperature Rtemp 290 K Missile Tracking Target Radar Range EquationReciever Thermal Noise Bandwidth Bn 1.00E+06 Hz R0_inTransmitter Loss Factor loss 5 R0_mBoltzmann Constant boltz 1.38E-23 Joule/K R0_nmNumber of Pulses Integrated num_pulse 100 R0_ftReceiver Noise Factor rec_noise 5Signal to Noise Ratio for Detection sig_noise 10Missile Radar Cross-Section miss_rcs 0.01 m^2Target Radar Cross-Section rcs 10 m^2 Threat Tracking Missile Radar Range Calculations:Visual Detection Constant Ct 0.2 Slant Range
Rthreat_mThreat Sensor Characteristics Rthreat_inTransmitter Power t_Pt 10000 watts Rthreat_nmThreat Reciever Sensitivity t_Pr 1E-14 watts Rthreat_ftThreat Transmitter Gain GainT 40 dBThreat Reciever Gain GainR 40 dB Visual DetectionThreat Radar Wavelength t_lamda 0.03 m Rd
Rr
Output BlockVariable Name Value Units3-dB Beam Width beamwidth 0.1205 radTarget Detection Range (nm) R0_nm 8.837 nmiTarget Detection Range (ft) R0_ft 53697 feetThreat's Detection Range (nm) Rthreat_nm 14.012 nmiThreat's Detection Range (ft) Rthreat_ft 85141 feetMissile 50% Visual Detection Range Rd 0.288 nmiMissile 50% Visual Recognition Range Rr 0.084 nmi
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.00
20
40
60
80
100
Required Missile Safe Distance*Neglects Terrain Masking Effects
500 ft2000 ftColumn OColumn O
Ground Range (10^3 ft)
Th
rea
t T
ran
sm
itte
r P
ow
er
(10
^3
Wa
tts
)
Altitude
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.00
20
40
60
80
100
Required Missile Safe Distance*Neglects Terrain Masking Effects
500 ft2000 ftColumn OColumn O
Ground Range (10^3 ft)
Th
rea
t T
ran
sm
itte
r P
ow
er
(10
^3
Wa
tts
)
Altitude
Missile Tracking Target Calculations:Radar Range Calculations: Negligible clutter, interference, and attenuation
dia_m 0.254 meters Uniformly illuminated circular aperture
3-dB Beam Width0.12047244 rad
Maximum Target Detection Range by MissileMissile Tracking Target Radar Range Equation Target RCS
644359 inches (m^2)16367 meters
8.84 nmi 0.00153697 feet 0.1
110
100Threat Tracking Missile Radar Range Calculations: 1000
Assumes Signal-to-Noise Ratio of 1! *Assumes a fixed transmitter power25951 m
1021691 in Missile's Minimum Range to Avoid Detection by a Threat System14.01 nmi Power
85141 feet (Kwatts)
Visual Detection 0.10.28826225 nmi 10.08359605 nmi 5
10203050
100
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.00
20
40
60
80
100
Required Missile Safe Distance*Neglects Terrain Masking Effects
500 ft2000 ftColumn OColumn O
Ground Range (10^3 ft)
Th
rea
t T
ran
sm
itte
r P
ow
er
(10
^3
Wa
tts
)
Altitude
0 20 40 60 80 100 120 140 160 180 2000.001
0.01
0.1
1
10
100
1000
Target Detection Range
500 ftColumn OColumn OColumn O
Ground Range (10^3 ft)
Ta
rge
t R
ad
ar
Cro
ss
Se
cti
on
(m
^2
)
Altitude
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.00
20
40
60
80
100
Required Missile Safe Distance*Neglects Terrain Masking Effects
500 ft2000 ftColumn OColumn O
Ground Range (10^3 ft)
Th
rea
t T
ran
sm
itte
r P
ow
er
(10
^3
Wa
tts
)
Altitude
0 20 40 60 80 100 120 140 160 180 2000.001
0.01
0.1
1
10
100
1000
Target Detection Range
500 ftColumn OColumn OColumn O
Ground Range (10^3 ft)
Ta
rge
t R
ad
ar
Cro
ss
Se
cti
on
(m
^2
)
Altitude
Maximum Target Detection Range by MissileSlant R Grnd R Slant R Grnd R Slant R Grnd R Slant R Grnd R
(ft) (10^3 ft) (ft) (10^3 ft) (ft) (10^3 ft) (ft) (10^3 ft)500 2000 10000 30000 Altitude (feet)
6021.28 6.000484 6021.28 5.67942 6021.28 0 6021.28 019040.96 19.03439 19040.96 18.93563 19040.96 16.20365 19040.96 033860.15 33.85645 33860.15 33.80103 33860.15 32.3498 33860.15 15.70062
60212.8 60.21072 60212.8 60.17958 60212.8 59.37661 60212.8 52.2071107075.2 107.074 107075.2 107.0565 107075.2 106.6072 107075.2 102.7866190409.6 190.4089 190409.6 190.3991 190409.6 190.1468 190409.6 188.0314
*Assumes a fixed transmitter power
Missile's Minimum Range to Avoid Detection by a Threat SystemSlant R Grnd R Slant R Grnd R Slant R Grnd R Slant R Grnd R
(ft) (10^3 ft) (ft) (10^3 ft) (ft) (10^3 ft) (ft) (10^3 ft)500 2000 10000 30000 Altitude (feet)
8206.4 8.2 8206.4 8.0 8206.4 0.0 8206.4 0.014593.3 14.6 14593.3 14.5 14593.3 10.6 14593.3 0.021822.1 21.8 21822.1 21.7 21822.1 19.4 21822.1 0.025950.9 25.9 25950.9 25.9 25950.9 23.9 25950.9 0.030861.1 30.9 30861.1 30.8 30861.1 29.2 30861.1 7.234153.4 34.1 34153.4 34.1 34153.4 32.7 34153.4 16.338805.7 38.8 38805.7 38.8 38805.7 37.5 38805.7 24.646148.0 46.1 46148.0 46.1 46148.0 45.1 46148.0 35.1
0 20 40 60 80 100 120 140 160 180 2000.001
0.01
0.1
1
10
100
1000
Target Detection Range
500 ftColumn OColumn OColumn O
Ground Range (10^3 ft)
Ta
rge
t R
ad
ar
Cro
ss
Se
cti
on
(m
^2
)
Altitude
0 20 40 60 80 100 120 140 160 180 2000.001
0.01
0.1
1
10
100
1000
Target Detection Range
500 ftColumn OColumn OColumn O
Ground Range (10^3 ft)
Ta
rge
t R
ad
ar
Cro
ss
Se
cti
on
(m
^2
)
Altitude
DynamicsINPUT BLOCK
Variable Name Value Units Other UnitsMissile Time Constant tau_override 2User Input Time Constant Reqd Field user_tau 0.5 sec
Mass Moment of Inertia in Y N/A Iy 94Maximum Angle of Attack N/A alphamax 12 degMaximum Surface Deflection N/A deltamax 15 degMaximum Surface Deflection Rate N/A deltadotmax 360 deg/secCoefficient of Surface Deflection Moment N/A Cmdelta 35.8 1/radianDiameter N/A DDia 0.20 metersNose Length N/A Lnose 0.49 metersRadar Wavelength N/A lamda_mis 0.03 metersRadar Frequency Agility N/A fdf 0.02Dynamic Pressure N/A q 1762.922 psf
N/A Cnalpha 38 /radianFilter Time Constant N/A taufilter 0 sec
Air Density Reqd Field rho 0.000891
Reference Area Reqd Field Sref 0.35Missile Velocity (avg) Reqd Field Vmis 1989.6 ft/secMissile Weight Reqd Field Wmis 500.00 lbsSeeker Lock-on Range Reqd Field Mrange 125 ftTarget Position Offset Reqd Field Targ_offset 3 ft
Gravitational Constant Reqd Field g 32.2Missile Navigation Ratio Reqd Field Nav 4CN Reqd Field C_n 0.99Target Acceleration Reqd Field targ_accel 3 g'sTarget Direction Reqd Field targ_dir 2Target Velocity Reqd Field targ_vel 820 ft/secLauncher Velocity Reqd Field Vlaunch 820 ft/secLaunch Range Reqd Field Rlaunch 60790 ft
Output BlockVariable Name Value Units
Time ConstantsPitch Moment Control Time Constant taucontrol N/A secPiching Moment Control Rate Time Constant taurate N/A secSeeker Dome Error Slope dome_error N/A deg/degSeeker Dome Time Constant taudome N/A secTotal Missile Time Constant taumissile 0.5 sec
Engagement KinematicsHorizontal Turn Radius rad_turn 100895 feetMissile Closing Velocity Vclose 2810 ft/secLauncher Closing Velocity Vclose_launcher 1640 ft/secF-Pole Range Rf_pole 25306 feetF-Pole Range / Launch Range Rf_pole_Rl 0.416Missile Flight Range/Launch Range (Head-On) Rf_Rl_HO 0.708
slugs-ft2
CN-alpha
slugs/ft3
ft2
ft/sec2
Missile Flight Range/Launch Range (Tail-Chase) Rf_Rl_TC 1.701Missile Flight Range (Head-On) HO_Frange 43048 feetMissile Flight Range (Tail-Chase) TC_Frange 103410 feet
Static Target AnalysisExpected Time of Homing tof 0.044 sInitial Heading Error G_naught 0.024 radMaximum Miss Distance Miss_Distance 0.357 feetAcceleration Reqd to Correct Heading Error Acceleration 4292 ft/sec^2 133.3006
Maneuvering Target AnalysisRequired Acceleration Ratio (missile/target) acc_ratio 2Maximum Miss Distance man_miss_dist 3.152 feet
0 2 4 6 8 10 120.0000
0.0500
0.1000
0.1500
0.2000
0.2500
True Missile Minimum Range Against Fixed Targets(axes follow description in text)
Nav Ratio = 3Nav Ratio = 4Nav Ratio = 5Nav Ratio = 6
0 0.2 0.4 0.6 0.8 1 1.20.00
1.00
2.00
3.00
4.00
5.00
6.00
Missile Accel. Reqd to Eliminate Initial Heading Error for Fixed Targets(axes follow description in text)
Nav = 2
Nav = 2.5
Nav = 3
Nav = 4
Nav = 6
0 2 4 6 8 10 120.0000
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
Miss Distance Due to Target Acceleration(axes follow description in text)
Nav Ratio = 3Nav Ratio = 4Nav Ratio = 5Nav Ratio = 6
0 1 2 3 4 5 60
100
200
300
400
500
600
Miss Distance with Target Maneuvering(axes follow description in text)
1 g
2 g
3 g
5 g
Target Accel-eration
0 0.2 0.4 0.6 0.8 1 1.20.00
1.00
2.00
3.00
4.00
5.00
6.00
Missile Accel. Reqd to Eliminate Initial Heading Error for Fixed Targets(axes follow description in text)
Nav = 2
Nav = 2.5
Nav = 3
Nav = 4
Nav = 6
0 1 2 3 4 5 60
100
200
300
400
500
600
Miss Distance with Target Maneuvering(axes follow description in text)
1 g
2 g
3 g
5 g
Target Accel-eration
10
Other UnitsTarget Velocity CalculationsVclose 2809.6 ft/sec
Vclose_launcher 1640 ft/sec
Time Constant Calculations
Time Constant for Pitch Moment Control8.00 inches taucontrol 0.143111
19.20 inches1.181103 inches Time Constant for Picthing Moment Control Rate
taurate 0.083333
Seeker Dome Error Slope Tangent Ogive Assumptiondome_error 0.018233 deg/deg
50.27 Seeker Dome Time Constanttaudome 0.136069
Total Missile Time Constanttaumissile 0.5
Horizontal Turn Radiusrad_turn 100895.1 feet
Static Target Analysis11.51326 mi Missile Time to Target
tof 0.044 sec
Initial Heading ErrorG_naught 0.023995 rad
Other UnitsRequired Missile AccelerationAm*To/(VmGo) 4Acceleration 4292.281 ft/sec^2 133.3 g's
Missile Miss Distance(max-miss dist)/(Vmiss*tof*G_naught)
Nav Ratio Max Coeff4 0.168
Miss_Distance 0.357 feet
Accelerations Against a Maneuvering TargetRequired Missile-to-Target Acceleration Ratio Tau equals zeroacc_ratio 2
in2
Be somewhat pessimistic of the results garnered from this page, in particular. Actual time constant calculations are often very involved, and may not simplify well with these assumptions.
Maximum Miss DistanceNav Ratio Coeff.
4 0.130497Man_miss_dist 3.15 feet
g
0 2 4 6 8 10 120.0000
0.0500
0.1000
0.1500
0.2000
0.2500
True Missile Minimum Range Against Fixed Targets(axes follow description in text)
Nav Ratio = 3Nav Ratio = 4Nav Ratio = 5Nav Ratio = 6
0 0.2 0.4 0.6 0.8 1 1.20.00
1.00
2.00
3.00
4.00
5.00
6.00
Missile Accel. Reqd to Eliminate Initial Heading Error for Fixed Targets(axes follow description in text)
Nav = 2
Nav = 2.5
Nav = 3
Nav = 4
Nav = 6
0 2 4 6 8 10 120.0000
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
Miss Distance Due to Target Acceleration(axes follow description in text)
Nav Ratio = 3Nav Ratio = 4Nav Ratio = 5Nav Ratio = 6
0 1 2 3 4 5 60
100
200
300
400
500
600
Miss Distance with Target Maneuvering(axes follow description in text)
1 g
2 g
3 g
5 g
Target Accel-eration
0 0.2 0.4 0.6 0.8 1 1.20.00
1.00
2.00
3.00
4.00
5.00
6.00
Missile Accel. Reqd to Eliminate Initial Heading Error for Fixed Targets(axes follow description in text)
Nav = 2
Nav = 2.5
Nav = 3
Nav = 4
Nav = 6
0 1 2 3 4 5 60
100
200
300
400
500
600
Miss Distance with Target Maneuvering(axes follow description in text)
1 g
2 g
3 g
5 g
Target Accel-eration
F-Pole Calculationsmissile flight-time 21.63653 sec Non-moving Target
launcher closing dist 35483.91 feet Target Moving Toward MissileLauncher dist at Impact 25306.09 feet Target Moving Away from Missile
Target Moving Orthogonal to MissileRf_pole 25306.09 feetRf_pole_Rl 0.416287
Missile Flight Range/Missile Launch RangeHead-on Rf_Rl_HO 0.708144Tail-Chase Rf_Rl_TC 1.701094Missile Flight Range
HO_Frang 43048.04 feet
TC_Frange 103409.5 feet
Missile Minimum Range Against Fixed Targetstime-of-flight tof/tau Time to correct initial heading error
(sec) Nav = 3 Nav = 4 Nav= 5 Nav = 6 Navigation Ratio0.005 0.01 0.0099 0.0098 0.0098 0.0097 t/to 20.01 0.02 0.0194 0.0192 0.0190 0.0188 0 2
0.025 0.05 0.0464 0.0452 0.0441 0.0429 0.025 20.05 0.1 0.0860 0.0816 0.0774 0.0733 0.05 20.1 0.2 0.1474 0.1321 0.1178 0.1046 0.075 2
0.15 0.3 0.1889 0.1589 0.1320 0.1079 0.1 20.2 0.4 0.2145 0.1680 0.1280 0.0937 0.125 2
0.25 0.5 0.2274 0.1643 0.1121 0.0697 0.15 20.3 0.6 0.2305 0.1515 0.0892 0.0412 0.175 2
0.35 0.7 0.2259 0.1327 0.0628 0.0121 0.2 20.4 0.8 0.2157 0.1102 0.0355 0.0151 0.225 2
0.45 0.9 0.2013 0.0860 0.0090 0.0388 0.25 20.5 1 0.1839 0.0613 0.0153 0.0582 0.275 2
0.55 1.1 0.1648 0.0372 0.0368 0.0731 0.3 20.6 1.2 0.1446 0.0145 0.0549 0.0834 0.325 2
0.65 1.3 0.1240 0.0065 0.0696 0.0894 0.35 20.7 1.4 0.1036 0.0253 0.0809 0.0916 0.375 2
0.75 1.5 0.0837 0.0418 0.0889 0.0905 0.4 20.8 1.6 0.0646 0.0560 0.0939 0.0866 0.425 2
0.85 1.7 0.0466 0.0678 0.0962 0.0805 0.45 20.9 1.8 0.0298 0.0774 0.0961 0.0728 0.475 2
0.95 1.9 0.0142 0.0848 0.0940 0.0638 0.5 21 2 0.0000 0.0902 0.0902 0.0541 0.525 2
Be somewhat pessimistic of the results garnered from this page, in particular. Actual time constant calculations are often very involved, and may not simplify well with these assumptions.
1.05 2.1 0.0129 0.0939 0.0851 0.0441 0.55 21.1 2.2 0.0244 0.0959 0.0789 0.0340 0.575 2
1.15 2.3 0.0346 0.0965 0.0719 0.0241 0.6 21.2 2.4 0.0435 0.0958 0.0644 0.0147 0.625 2
1.25 2.5 0.0513 0.0941 0.0566 0.0059 0.65 21.3 2.6 0.0579 0.0914 0.0487 0.0022 0.675 2
1.35 2.7 0.0635 0.0880 0.0409 0.0095 0.7 21.4 2.8 0.0681 0.0840 0.0331 0.0159 0.725 2
1.45 2.9 0.0718 0.0795 0.0257 0.0215 0.75 21.5 3 0.0747 0.0747 0.0187 0.0261 0.775 2
1.55 3.1 0.0768 0.0696 0.0121 0.0299 0.8 21.6 3.2 0.0783 0.0643 0.0059 0.0329 0.825 2
1.65 3.3 0.0791 0.0590 0.0003 0.0351 0.85 21.7 3.4 0.0794 0.0537 0.0048 0.0366 0.875 2
1.75 3.5 0.0793 0.0484 0.0094 0.0375 0.9 21.8 3.6 0.0787 0.0433 0.0134 0.0377 0.925 2
1.85 3.7 0.0778 0.0383 0.0169 0.0375 0.95 21.9 3.8 0.0765 0.0334 0.0199 0.0367 0.975 2
1.95 3.9 0.0750 0.0288 0.0224 0.0356 1 22 4 0.0733 0.0244 0.0244 0.0342
2.05 4.1 0.0713 0.0203 0.0260 0.03252.1 4.2 0.0693 0.0164 0.0273 0.0306
2.15 4.3 0.0671 0.0127 0.0281 0.02852.2 4.4 0.0648 0.0094 0.0287 0.0263
2.25 4.5 0.0625 0.0062 0.0289 0.02402.3 4.6 0.0601 0.0034 0.0289 0.0217
2.35 4.7 0.0577 0.0008 0.0286 0.01932.4 4.8 0.0553 0.0016 0.0281 0.0171
2.45 4.9 0.0529 0.0037 0.0275 0.01482.5 5 0.0505 0.0056 0.0267 0.0126
2.55 5.1 0.0482 0.0073 0.0257 0.01052.6 5.2 0.0459 0.0088 0.0247 0.0086
2.65 5.3 0.0437 0.0101 0.0236 0.00672.7 5.4 0.0415 0.0112 0.0224 0.0049
2.75 5.5 0.0393 0.0122 0.0212 0.00332.8 5.6 0.0373 0.0130 0.0199 0.0018
2.85 5.7 0.0353 0.0136 0.0187 0.00042.9 5.8 0.0334 0.0142 0.0174 0.0008
2.95 5.9 0.0315 0.0146 0.0161 0.00203 6 0.0297 0.0149 0.0149 0.0030
3.05 6.1 0.0280 0.0151 0.0136 0.00393.1 6.2 0.0264 0.0152 0.0125 0.0046
3.15 6.3 0.0249 0.0152 0.0113 0.00533.2 6.4 0.0234 0.0152 0.0102 0.0058
3.25 6.5 0.0220 0.0151 0.0091 0.00633.3 6.6 0.0207 0.0149 0.0081 0.0067
3.35 6.7 0.0194 0.0147 0.0071 0.00703.4 6.8 0.0182 0.0144 0.0062 0.0072
3.45 6.9 0.0170 0.0142 0.0053 0.00733.5 7 0.0160 0.0138 0.0045 0.0074
0 2 4 6 8 10 120.0000
0.0500
0.1000
0.1500
0.2000
0.2500
True Missile Minimum Range Against Fixed Targets(axes follow description in text)
Nav Ratio = 3Nav Ratio = 4Nav Ratio = 5Nav Ratio = 6
3.55 7.1 0.0149 0.0135 0.0038 0.00743.6 7.2 0.0140 0.0131 0.0031 0.0074
3.65 7.3 0.0131 0.0127 0.0024 0.00733.7 7.4 0.0122 0.0123 0.0018 0.0072
3.75 7.5 0.0114 0.0119 0.0012 0.00703.8 7.6 0.0106 0.0115 0.0007 0.0068
3.85 7.7 0.0099 0.0111 0.0003 0.00663.9 7.8 0.0093 0.0107 0.0002 0.0064
3.95 7.9 0.0086 0.0103 0.0006 0.00624 8 0.0081 0.0098 0.0009 0.0059
4.05 8.1 0.0075 0.0094 0.0012 0.00564.1 8.2 0.0070 0.0090 0.0015 0.0054
4.15 8.3 0.0065 0.0086 0.0017 0.00514.2 8.4 0.0060 0.0082 0.0019 0.0048
4.25 8.5 0.0056 0.0079 0.0021 0.00454.3 8.6 0.0052 0.0075 0.0023 0.0042
4.35 8.7 0.0049 0.0071 0.0024 0.00394.4 8.8 0.0045 0.0068 0.0025 0.0037
4.45 8.9 0.0042 0.0064 0.0026 0.00344.5 9 0.0039 0.0061 0.0026 0.0031
4.55 9.1 0.0036 0.0058 0.0027 0.00294.6 9.2 0.0033 0.0055 0.0027 0.0026
4.65 9.3 0.0031 0.0052 0.0027 0.00244.7 9.4 0.0029 0.0049 0.0027 0.0022
4.75 9.5 0.0027 0.0047 0.0027 0.00204.8 9.6 0.0025 0.0044 0.0027 0.0018
4.85 9.7 0.0023 0.0042 0.0027 0.00164.9 9.8 0.0021 0.0039 0.0027 0.0014
4.95 9.9 0.0020 0.0037 0.0026 0.00125 10 0.0018 0.0035 0.0026 0.0011
5.05 10.1 0.0017 0.0033 0.0025 0.00095.1 10.2 0.0016 0.0031 0.0025 0.0008
PEAK: 0.2305 0.1680 0.1320 0.1079Nav_Ratio: 3 4 5 6
Non-moving Target Calculate Internally
Target Moving Toward Missile User-DefinedTarget Moving Away from MissileTarget Moving Orthogonal to Missile
Missile Miss Distance Against Maneuvering TargetsTime to correct initial heading error
Navigation Ratio tof tof/tau2.5 3 4 6 (sec) Nav=3 Nav=4
2.50 3.00 4.00 6.00 0.005 0.01 0.0000 0.00002.47 2.93 3.80 5.42 0.01 0.02 0.0002 0.00022.44 2.85 3.61 4.89 0.025 0.05 0.0012 0.00122.40 2.78 3.42 4.39 0.05 0.1 0.0045 0.00442.37 2.70 3.24 3.94 0.1 0.2 0.0164 0.01532.34 2.63 3.06 3.52 0.15 0.3 0.0333 0.03002.30 2.55 2.89 3.13 0.2 0.4 0.0536 0.04652.27 2.47 2.72 2.78 0.25 0.5 0.0758 0.06322.24 2.40 2.56 2.46 0.3 0.6 0.0988 0.07902.20 2.33 2.40 2.16 0.35 0.7 0.1217 0.09332.17 2.25 2.25 1.90 0.4 0.8 0.1438 0.10542.13 2.18 2.10 1.66 0.45 0.9 0.1647 0.11532.09 2.10 1.96 1.44 0.5 1 0.1839 0.12262.05 2.03 1.82 1.25 0.55 1.1 0.2014 0.12752.02 1.95 1.69 1.07 0.6 1.2 0.2169 0.13011.98 1.88 1.56 0.92 0.65 1.3 0.2303 0.13051.94 1.80 1.44 0.78 0.7 1.4 0.2417 0.12891.90 1.72 1.32 0.66 0.75 1.5 0.2510 0.12551.85 1.65 1.21 0.55 0.8 1.6 0.2584 0.12061.81 1.58 1.10 0.46 0.85 1.7 0.2640 0.11441.77 1.50 1.00 0.38 0.9 1.8 0.2678 0.10711.72 1.42 0.90 0.31 0.95 1.9 0.2700 0.0990
1.68 1.35 0.81 0.25 1 2 0.2707 0.09021.63 1.28 0.72 0.20 1.05 2.1 0.2700 0.08101.58 1.20 0.64 0.15 1.1 2.2 0.2681 0.07151.53 1.13 0.56 0.12 1.15 2.3 0.2652 0.06191.48 1.05 0.49 0.09 1.2 2.4 0.2613 0.05231.43 0.97 0.42 0.07 1.25 2.5 0.2565 0.04281.37 0.90 0.36 0.05 1.3 2.6 0.2510 0.03351.31 0.83 0.30 0.03 1.35 2.7 0.2450 0.02451.25 0.75 0.25 0.02 1.4 2.8 0.2384 0.01591.19 0.67 0.20 0.02 1.45 2.9 0.2314 0.00771.12 0.60 0.16 0.01 1.5 3 0.2240 0.00001.05 0.53 0.12 0.01 1.55 3.1 0.2165 0.00720.97 0.45 0.09 0.00 1.6 3.2 0.2087 0.01390.88 0.38 0.06 0.00 1.65 3.3 0.2008 0.02010.79 0.30 0.04 0.00 1.7 3.4 0.1929 0.02570.68 0.22 0.02 0.00 1.75 3.5 0.1850 0.03080.56 0.15 0.01 0.00 1.8 3.6 0.1771 0.03540.40 0.08 0.00 0.00 1.85 3.7 0.1692 0.03950.00 0.00 0.00 0.00 1.9 3.8 0.1615 0.0431
1.95 3.9 0.1539 0.04622 4 0.1465 0.0488
2.05 4.1 0.1393 0.05112.1 4.2 0.1323 0.0529
2.15 4.3 0.1254 0.05442.2 4.4 0.1188 0.0555
2.25 4.5 0.1125 0.05622.3 4.6 0.1063 0.0567
2.35 4.7 0.1005 0.05692.4 4.8 0.0948 0.0569
2.45 4.9 0.0894 0.05662.5 5 0.0842 0.0561
2.55 5.1 0.0793 0.05552.6 5.2 0.0746 0.0547
2.65 5.3 0.0701 0.05372.7 5.4 0.0659 0.0527
2.75 5.5 0.0618 0.05152.8 5.6 0.0580 0.0503
2.85 5.7 0.0544 0.04892.9 5.8 0.0509 0.0475
2.95 5.9 0.0477 0.04613 6 0.0446 0.0446
3.05 6.1 0.0417 0.04313.1 6.2 0.0390 0.0416
3.15 6.3 0.0364 0.04013.2 6.4 0.0340 0.0386
3.25 6.5 0.0318 0.03713.3 6.6 0.0296 0.0356
3.35 6.7 0.0276 0.03413.4 6.8 0.0258 0.0326
3.45 6.9 0.0240 0.0312
3.5 7 0.0223 0.02983.55 7.1 0.0208 0.02843.6 7.2 0.0194 0.0271
3.65 7.3 0.0180 0.02583.7 7.4 0.0167 0.0245
3.75 7.5 0.0156 0.02333.8 7.6 0.0145 0.0222
3.85 7.7 0.0134 0.02103.9 7.8 0.0125 0.0199
3.95 7.9 0.0116 0.01894 8 0.0107 0.0179
4.05 8.1 0.0100 0.01694.1 8.2 0.0092 0.0160
4.15 8.3 0.0086 0.01514.2 8.4 0.0079 0.0143
4.25 8.5 0.0074 0.01354.3 8.6 0.0068 0.0127
4.35 8.7 0.0063 0.01204.4 8.8 0.0058 0.0113
4.45 8.9 0.0054 0.01064.5 9 0.0050 0.0100
4.55 9.1 0.0046 0.00944.6 9.2 0.0043 0.0088
4.65 9.3 0.0040 0.00834.7 9.4 0.0037 0.0078
4.75 9.5 0.0034 0.00734.8 9.6 0.0031 0.0069
4.85 9.7 0.0029 0.00644.9 9.8 0.0027 0.0060
4.95 9.9 0.0025 0.00575 10 0.0023 0.0053
5.05 10.1 0.0021 0.00505.1 10.2 0.0019 0.0046
PEAK: 0.2707 0.1305Nav_Ratio: 3 4
Missile Miss Distance Against Maneuvering Targets Miss Distance Against Maneuvering Target
taumissile Target Accel (g's)Nav= 5 Nav=6 (sec) 1 2 3 50.0000 0.0000 0 0 0 0 00.0002 0.0002 0.25 0.26 0.53 0.79 1.310.0011 0.0011 0.5 1.05 2.10 3.15 5.250.0042 0.0041 0.75 2.36 4.73 7.09 11.820.0142 0.0133 1 4.20 8.40 12.61 21.010.0269 0.0241 1.25 6.57 13.13 19.70 32.830.0400 0.0343 1.5 9.45 18.91 28.36 47.270.0521 0.0425 1.75 12.87 25.74 38.61 64.340.0622 0.0480 2 16.81 33.62 50.42 84.040.0699 0.0507 2.25 21.27 42.55 63.82 106.360.0748 0.0505 2.5 26.26 52.53 78.79 131.310.0770 0.0478 2.75 31.78 63.56 95.33 158.890.0766 0.0429 3 37.82 75.64 113.45 189.090.0740 0.0363 3.25 44.38 88.77 133.15 221.920.0694 0.0285 3.5 51.47 102.95 154.42 257.370.0631 0.0198 3.75 59.09 118.18 177.27 295.450.0556 0.0107 4 67.23 134.46 201.70 336.160.0471 0.0016 4.25 75.90 151.80 227.70 379.490.0379 0.0073 4.5 85.09 170.18 255.27 425.450.0284 0.0157 4.75 94.81 189.62 284.42 474.040.0187 0.0234 5 105.05 210.10 315.15 525.250.0092 0.0302
0.0000 0.03610.0088 0.04100.0170 0.04490.0245 0.04780.0314 0.04970.0374 0.05080.0427 0.05090.0472 0.05040.0509 0.04910.0538 0.04720.0560 0.04480.0575 0.04200.0584 0.03880.0587 0.03540.0585 0.03180.0578 0.02810.0567 0.02440.0551 0.02060.0533 0.01690.0512 0.01330.0488 0.00980.0463 0.00640.0436 0.00330.0409 0.00030.0380 0.00240.0351 0.00490.0323 0.00720.0294 0.00930.0265 0.01110.0238 0.01270.0211 0.01400.0184 0.01520.0159 0.01610.0135 0.01690.0112 0.01750.0090 0.01790.0070 0.01820.0050 0.01830.0032 0.01820.0015 0.01810.0000 0.01780.0014 0.01750.0027 0.01710.0039 0.01660.0050 0.01600.0060 0.01540.0068 0.01480.0076 0.01410.0082 0.01340.0088 0.0127
0.0093 0.01190.0097 0.01120.0101 0.01040.0103 0.00970.0105 0.00900.0107 0.00830.0108 0.00760.0108 0.00690.0108 0.00620.0108 0.00560.0107 0.00500.0106 0.00440.0105 0.00390.0103 0.00340.0102 0.00290.0100 0.00240.0097 0.00200.0095 0.00160.0093 0.00120.0090 0.00080.0087 0.00050.0085 0.00020.0082 0.00010.0079 0.00030.0077 0.00060.0074 0.00080.0071 0.00100.0068 0.00110.0066 0.00130.0063 0.00140.0061 0.00150.0058 0.00160.0055 0.00170.0770 0.0509
5 6
Atmospheric Calculations 11
Currently an interpolation scheme is NOT implemented
Altitude Look Up:Alt (ft) 20000a (ft/s) 1036.9 Alt T T Pressurerho (slug/ft^3) 1.267E-03 (Thousand ft) (deg R) (deg F) (psf)Press. (psf) 973.3 0 518.69 59.0 2116.2Press. (psi) 6.759 5 500.9 41.2 1761.0Temp (deg R) 447.4 10 483.1 23.4 1456.0
15 465.2 5.5 1195.020 447.4 -12.3 973.325 429.6 -30.1 786.3
Altitude Look Up: 30 411.9 -47.8 629.7Alt (ft) 30000 35 394.1 -65.6 499.3a (ft/s) 994.8 40 390.0 -69.7 393.1rho (slug/ft^3) 8.907E-04 45 390.0 -69.7 309.5Press. (psf) 629.7 50 390.0 -69.7 243.6Temp (deg R) 411.9 60 390.0 -69.7 151.0
70 390.0 -69.7 93.780 390.0 -69.7 58.190 402.5 -57.2 36.3
100 418.8 -40.9 23.1120 451.4 -8.3 9.8150 500.1 40.4 3.1200 457 -2.7 0.5
Pressure rho a(psi) (slug/ft^3) (ft/s)
14.696 0.00238 1116.412.229 0.002043 1097.110.111 0.001756 1077.48.299 0.001496 1057.46.759 0.001267 1036.95.460 0.001066 1016.14.373 0.0008907 994.83.467 0.0007382 973.12.730 0.0005873 968.12.149 0.0004623 968.11.692 0.0003639 968.11.049 0.0002256 968.10.650 0.0001399 968.10.404 0.00008683 968.10.252 0.00005253 983.50.160 0.00003211 1003.20.068 0.0000127 1041.50.021 0.000003564 1096.30.003 6.061E-07 1047.9