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ZOOM User Manual - Trajectory Solution

1. variables dat delv_losses dat in the ECF and ECI frames results of ZOOM s optimization procedure showing initial and final values of the variables being optimized initial and final values of the scaled objective and constraint functions scale factors and history of the iterative procedure list of variables being optimized effects of perturbations of the variables on the objective and constraint functions and other factors all viewable via the GUI control variable values for each iteration of the optimization procedure time histories of the ideal delta velocity and delta velocity losses 1 INTRODUCTION An Intercept Spacecraft or RV mission has at least three additional output files output5 dat time histories target position and velocity components in the NED frame target altitude geodetic latitude and longitude target ground range from launch site target states dat time histories of the target s position and velocity in the ECF and ECI frames target drag dat time history of the target s post launch drag deceleration significant only for missions where the target descends to low altitude There are sometimes as many as three other files in the output subfolder for an Intercept Spacecraft or RV mission tgtElem dat time histories of the target s osculating conic elements prior to the displayed pre launch ground track This file is created whenever a plot of the target s
2. 1 INTRODUCTION ZOOM is a computer program for the conceptual design and analysis of rockets and their missions in the vicinity of a single central body such as the earth The program incorporates insights and methods that were employed during America s developments of the Saturn V moon rocket and the Space Shuttle It is important to note that in some places in this manual the term earth is used where it would have been more appropriate to use the term central body You have the flexibility to modify the default gravitational dimensional atmospheric and rotational parameters and so define a central body other than the earth ZOOM can be operated via its graphical user interface GUI with a touch screen interface as well as with a mouse keyboard interface The program has been checked out with Windows XP Windows 7 and Windows 8 1 operating systems However with Windows 8 1 a program has stopped working error sometimes occurs apparently at random times As far as is known the Windows 8 1 related error has never been encountered on computers with Windows XP or Windows 7 operating systems And constructive results can often be obtained on a computer with the Windows 8 1 operating system before the stopped working error is encountered ZOOM s optimization procedure was created in the early 1970 s and enhanced over a subsequent period of 35 years The procedure uses the Simplex algorithm in a novel and powerful way that has
3. deltav etc refer to changes in We W s Total ideal delta velocity m s 8693 inertial speed which are scalar quantities Gravity Loss m s 622 Aerodynamic Loss m s 6459 When the Mission Summary window is Steering Dose mss 843 accessed from the Mission Synopsis Thrust Loss mzs 132 window there is no DeltaV Summary marcai Speed anaa G95 button in the window because the delta velocity information is provided in the Computational Error m s 1 70274E 04 Mission Synopsis window But when the Mission Summary window is accessed Except for the Computational Error the values have from the Solution Window there is a been rounded to the nearest whole number DeltaV Summary button in the o The Inertial Speed Gain is the computed difference window s top right corner Clicking this between the rocket s final inertial speed and its button produces the Rocket Inertial inertial speed at launch Speed Summary consisting of the z following elements The Computational Error is the difference between the Inertial Speed Gain and the Total Ideal Delta Velocity minus losses The magnitude of this error is a measure Total ideal delta velocity which is of the rocket motion computational inaccuracy calculated by integrating the rocket s total vacuum thrust mass ratio over the entire trajectory When there is no strap on booster this total ideal delta velocity will be equal to the sum of the core ideal
4. ES140817 ES141206 ES150303 ES150312 ES150407 01140722 01140801 01140808 01140808 01140808 01140808 01140808 01140902 01150215 01150216 01150222 01150227 01150302 01150306 The target s initial state will be set equal to the rocket s burnout state from the mission selected below Shuttle Max Range Reentry 65 AOA amp 9 5 BTUps AHR Limits Shuttle Min Heat Reentry Fixed End State 65 AOA amp 9 5 BTUps AHR Limit Topol ICBM Huntsville Target Lift Drag Model for Stage 2 500 kW AHR I Max Payload to Given Altitude FPA Heading and Speed Shuttle Max Range Reentry 65 AOA amp 9 5 BTUps AHR Limits 9 stages Shuttle Max Range Reentry 65 AOA amp 9 5 BTUps AHR Limits 9 stages Shuttle Max Range Reentry 65 AOA amp 9 5 BTUps AHR Limits 9 stages Shuttle Max Range Reentry 65 AOA amp 9 5 BTUps AHR Limits 9 stages Topol ICBM Huntsville Target Lift Drag Model for Stage 2 500 kW AHR I Max Payload 120 Nmi 4SSME F1SOB 2J2X stg 2 ballistic 22 AOA amp 1 7 SLS2 maxPL stdET Sssme SOB throtDown up issme 7OMT to 120 Nmi 3 SSME SOB min launch wt Air Launch Payload 13500 Ib Min Init Mass Lift Drag Model AOA and AHF Ascent to Geosynchronous Orbit 3 Stages SOB minimum initial mass Max Payload to 120 Nmi 3SSME F1SOB 1 J2X 01 normal g limit 21 d SA 507 to 100 Nmi Limits on Thrusts and Propellants SLS1 maxPL stdET Sssme SOB throtDown up issme SLS2 maxPL stdET Sssme SOB throtDown u
5. Effects of 20 Variable Perturbations on Scaled Functions functions are listed near the top of 12345678 9 1011 the window and are numbered to turn angle 3 allowed by the box size history over initial avg turn rate 3 a A a i the course of the optimization Strap on Burn Time procedure s iterations Such a large change indicates that the variable ee _ Toggle Mode _ Toggle Mode a may not yet have gotten close to its optimum value nn ae ane relate them to the mosaic columns launch azimuth 8 32 i core initiel 1 rien Metric units are included in the angle step 1 12 2 function names as a reminder that a a tona the numerical values internal to the initial avg turn rate 1 1 32 1 8 cnea sian deere 121 as sets program and values of the scale core initial T W 2 0 1 128 factors are based on Metric units angle step 2 A The variables are identified in the post thrust coast time 2 column of buttons to the left of the ore ies dalta vat 15 mosaic A variable s button title is a colored red if the variable changed angle step 3 more than 50 of the maximum The first listed function is the objective The name begins either with the abbreviation max or min indicating that it is to be maximized or minimized The other listed functions are constraints either equations or inequalities The name of an inequality constraint begins with the abbreviation lim indic
6. NAVIGATION BUTTONS The row of buttons at the bottom of the Mission Selection window are the navigation buttons that you use to navigate back and forth between the program s primary windows The navigation buttons and their corresponding destination windows are 3 MISSION SELECTION Navigation Button Destination Window Mission Type First List or ReZOOM Mission Selection Synopsis Mission Synopsis Mission Mission Definition Conditions Launch and In Flight Conditions Stack Rocket Stage Stack Countdown Launch Preparation CHOICE OF UNITS Click the Toggle Units button to alternate between Metric and English units for display and data entry A new mission s data will be saved in the chosen units When you choose an existing mission as a template changing the units for your new mission will not affect the original template mission The Mission Selection and Mission Synopsis windows are the only windows where you can choose change the units DELETE SELECTED MISSION You can remove a mission from the mission selection list via the Delete button This action moves the mission subfolder from the DATA folder to the Trash folder in the ZOOM Program Directory The operating system s file management application_can be used off line to empty the Trash folder EDIT SELECTED MISSION S CORE NAME You can edit the selected mission s core name by clicking the Rename button The core name will appear in an e
7. Stage Diameter Height of Primary Inert Mass Height of Propellant Tank Height of Adjunct Inert Mass or Payload and Total Stage Height Although it is not affected by the sizing parameters the Stage Propellant Load can be calculated from the other parameters already defined for the stage and it is displayed in the Sizing Factors for Stage window 68 22 LAUNCH PREPARATION The Launch Preparation window is used to 1 name the mission 2 write a mission description 3 specify optimizer precision and output parameters 4 preview the first guess trajectory and 5 initiate a fly out or quasi optimization procedure 2 NAMING THE MISSION FOLDER Launch Preparation aun The default core name for the mission is that of the selected template mission except if Mission minimize initial mass from Scratch is selected in which case the default PAESANA SAANA core name will be blank To change the default core name you must type the new core name in the Mission Folder Core Name box replacing the template name The program will Optimizer Precision and Parameters Output Parameters automatically add a two Name the New Mission Folder Enter or Edit Mission Description character mission type ID and the current date to Mission Folder Core Name 90 Characters Maximum Rendezvous 120 N Mi SOB Lift Drag Aero amp AOA Limit for Stage 2 the core name to create the mission folder s
8. The default model keeps the speed of sound at the higher altitudes constant at the 90 km value Between geopotential altitudes of 90 km and 700 km the default atmospheric pressure and density are gotten by interpolation in fifteen point tables of their logarithms versus geopotential altitude These fifteen points were selected from the over 400 points in the 1962 reference document s tables By tabling logarithms of density and pressure it is feasible to cover the substantial altitude range with only fifteen points without introducing significant error For geopotential altitudes above 700 km the default pressure and density are gotten by extrapolation from the fifteen point tables At these altitudes and even much lower altitudes the very thin atmosphere is highly variable and the extremely small densities and pressures in the model are at best gross approximations of reality at any given time EXPONENTIAL ATMOSPHERIC MODEL The CHANGE to Exponential Model button activates the display of an Exponential Model button that when clicked displays a window where you can enter the parameter values for an exponential atmospheric model This atmospheric model is described in the Exponential Atmospheric Model section CHARACTERIZATION OF THE CENTRAL BODY MODEL In the Mission Definition window the Central Body Model will be characterized by one of three phrases 1 Earth Standard 2 Earth Modified or 3 User Defined
9. Angle Step Turn Angle and Initial Average Turn Rate The steering law can be enhanced by adding two other parameters Maneuver Delay which provides for a delay before the maneuver starts and Maneuver Plane Roll which provides a degree of freedom that is needed for flight in three dimensions Maneuver Delay is the delay between a stage s start i e its rocket motor ignition and the start of its maneuver However if the rocket has not left the launch rail by the end of this delay the maneuver will start when the rocket leaves the launch rail Before starting its maneuver the rocket holds constant attitude in the central body frame Maneuver Plane Roll is the angle between the stage s reference plane and the stage s maneuver plane The first stage s reference plane is the vertical plane defined by the Launch Azimuth and the reference plane s defining normal unit vector lies in the local horizontal plane rotated 90 degrees from the launch azimuth The reference plane for each subsequent stage is the previous stage s maneuver plane The maneuver plane is determined at stage initiation The rocket s longitudinal axis is at the intersection of the reference and maneuver planes and is the axis of rotation for the Maneuver Plane Roll angle A positive Maneuver Plane Roll angle means that rotation from the reference plane to the maneuver plane is clockwise when viewed from the rocket s rear During a stage s bur
10. ETE RE in s a4 p Metric units wind speed is expressed in meters per second m s and altitude is expressed in kilometers km In English units wind speed is expressed in feet per second ft s and altitude is expressed in nautical miles Nmi ma Wind Speed is the plot s abscissa variable and Altitude is the plot s ordinate variable The altitude units are shown in the window s top bar The Azimuth of Wind Vector i e azimuth of the wind velocity is expressed in degrees An azimuth of 90 degrees indicates that the wind is blowing from west 20 0 30 0 40 0 to east Wind Speed m s p CHANGING THE AZIMUTH RETURN Restore Default Wind Zero Wind OF THE WIND VECTOR To change the azimuth of the wind vector you specify the desired value deg in the small box near the top of the window CHANGING THE NUMBER OF POINTS IN THE WIND PROFILE You can change the number of points defining the wind profile by specifying a value in the Points box and clicking the update button If the number of points is increased the new points will be added at altitudes higher than that of the original highest altitude point and the default wind speed value of the new points will match that of the original highest altitude 36 12 WIND MODEL point If the number of points is decreased from the original value the higher altitude points will be deleted The number of points cannot exceed 15 M
11. If a constraint is imposed it is advisable to Vary the core ideal delta velocity to make a feasible solution more likely The message Propellant Constraint Determined by Base Stage of Mated Group will be displayed in the Configure Tandem Stage windows of all stages in a mated group except that of the base stage AERODYNAMIC FORCE MODEL BUTTON The parenthetical suffix in the button s title indicates whether the current aerodynamic force model uses normal axial coefficients NA or lift drag coefficients LD Clicking the Aerodynamic Force Model button opens a window from which you can define the stage s aerodynamic force model The aerodynamic force models are discussed in the Aerodynamic Force Models section NORMALIZED THRUST PROFILE BUTTON The symbol at the end of the Normalized Thrust Profile button s title indicates that a time varying normalized vacuum thrust profile is currently defined The symbol at the end of the button s title indicates that the vacuum thrust is currently declared to be constant You can click the button to open a window where you can define a normalized vacuum thrust profile The average value of the vacuum thrust is determined by the stage s core initial thrust weight ratio and the rocket s mass at the time of the stage s thrust initiation The normalized thrust profile is discussed in the Normalized Thrust Profile section STAGE SIZING FACTORS BUTTON Clicking the Stage Sizing Facto
12. If you do not alter the default model in any way it will be characterized as Earth Standard If you alter the Reference Julian date Corresponding Greenwich hour angle or a zonal harmonic coefficient and or if you only slightly change the Body s sidereal rotation rate Gravitational constant Equatorial radius and or Polar radius the central body model will be characterized as Earth Modified If you significantly change the Body s sidereal rotation rate Gravitational constant Equatorial radius or Polar radius and or if you opt to use the exponential atmospheric model the central body model will be characterized User Defined 29 10 EXPONENTIAL ATMOSPHERIC MODEL xi The default parameter values for the exponential Units Expressed in this Window are Always Metric atmospheric model produce an approximation of the 1962 earth standard atmospheric sea level pressure N m 2 101325 model The molecular scale mean molecular weight of air 28 9644 temperature is the air temperature at sea level molecular scale temperature deg K 288 15 adiabatic index of air The program calculates the central body s average radius m 6367469 exponential atmospheric variables as functions of Romie altitude h and the central body s average radius ravg as follows Geopotential altitude hg h ravg ravg h Pressure P p0 exp g0 MO hg R Tm Density M
13. L Post Thrust Coast Time 0 000 sec FIXED relevant stage is colored bi linear tangent steering normally and the other Time constant 0 000 sec 1 stages in the drawing are Stage Diameter 8 415 m FIXED grayed out Propellant Stage Total Height 3 107 m mass is colored red primary inert mass is colored dark gray and adjunct inert mass if any RETURN Copy All Data to Clipboard and Return is colored brown The values of variable parameters which can be constrained will be accompanied by a designation that indicates whether the constraint was applied If a variable parameter was unconstrained the designation free will be displayed If a variable parameter had a maximum limit placed on it and was constrained by the limit the designation On Limit will be displayed If the optimum value of the parameter was below the specified limit the designation Below Limit will be displayed If the parameter was constrained to have an exact value the designation FIXED will be displayed 17 5 MISSION SUMMARY Propellant Load is the tandem stage s total propellant mass before and at the instant of the stage s rocket motor ignition A tandem stage s propellant is always used to completion Primary Inert Mass is the stage s total mass minus the propellant mass and minus any adjunct inert mass e g payload The program calculates the primary inert mass from the stage s propellant load and Propellant Mass Fraction
14. Positive values for the rocket s heading and flight path angles indicate a turn right from true north in the local horizontal plane turn up Euler angle sequence for the rocket velocity The rocket is symmetric with respect to its pitch plane The rocket rolls automatically to keep its pitch plane in the plane defined by the rocket s relative velocity and longitudinal axis The rocket thrusts along its longitudinal axis so both the thrust and aerodynamic forces remain in the rocket s pitch plane for the duration of the flight Except in one case the speed flight path angle and heading angle are based on rocket velocity in a central body fixed frame The exceptional case is the Achieve Specified State mission with the Inertial reference In this case these variables are based on the rocket s inertial velocity 82 27 PLOT SELECTION AERODYNAMIC LIFT AND NORMAL ACCELERATIONS The Aerodynamic Lift acceleration is normal to rocket velocity w r t the air and will usually be a little less than the Aerodynamic Normal acceleration normal to the rocket centerline The aerodynamic lift and normal forces are affected by the wind COCKPIT VIEW PLAYBACK Clicking Cockpit View Playback opens a window where the rocket flight can be played back from the perspective of a viewer who follows immediately behind the rocket in a vertical plane in the North East Down NED frame and looking forward along the rocket long axis Blu
15. SOB throtDown up issme i ROCKET BURNOUT CONIC GMT Epoch Year 2010 Month 4 Day 5 Hour 9 Minute 10 Second 48 387 Osculating Conic Elements perigee altitude km 222 216475 apogee altitude km 222 263426 inclination deg 28 3655123 right ascension deg 21 4311377 argument of perigee deg 158 884577 true anomaly deg 44 798825 RETURN Copy to Clipboard and Return 20 6 MISSION DEFINITION Intercept Spacecraft or RV 6 MISSION DEFINITION Intercept Spacecraft or RV The format of the Mission Definition window depends on the selected mission type Intercept Spacecraft or RV Inject into Conic or Achieve Specified State GB Z00M Rocket Trajectory Optimization ml x Mission Definition _ourr Intercept Spacecraft or RV CENTRAL BODY MODEL The option to define the Central Body Model is Central Body Model Earth Standard View or Change Model provided in the Mission Definition windows of all three RENDEZVOUS Change to IMPACT mission types The default Se model is Earth Standard garaa Clicking the View or Change I Maximize Payload l Minimize Flight Ti i occas E E a Model button opens a window I Minimize Aero Heating where the parameters defining the central body s rotation Target s Epoch and Osculating Conic Elements g ravity dimensions and Edit Target Data Below or Get Target Data from Existing Mission atmosphere ool be changed see the s
16. Thrust kN 10 traces of tandem core stages are light blue The thrust trace of a strap on booster is brown Step reductions in a tandem stage s thrust indicate that it has been step throttled to stay within a limit on axial acceleration When a strap on booster burns out and is discarded it is possible that a tandem stage which had been previously throttled down will step throttle back up to as high as its maximum allowable thrust The Thrusts plot is the only plot that shows the time history of a strap on booster quantity 2500 2000 p 1500 1000 500 HA TIME SLICE 0 100 200 300 400 500 600 Time sec In all of the post launch time history Slice 0 to 536 231 sec VIEW Slice Show Events plots the abscissa variable Time is the time after rocket launch expressed in seconds A time Slice can be expanded to fill the graph s horizontal dimension This is done by entering a start time and end time in the Slice boxes and clicking the VIEW Slice button to zoom in on that portion of the plot defined by the slice Full scale can be restored by entering zero in the first Slice box and a large number in the second Slice box In an Intercept Spacecraft or RV mission s pre launch time histories of the target s altitude and aerodynamic drag the abscissa variable is time with respect to launch expressed in minutes negative values After viewing a
17. __ 63 0 m 325 Fixed Nozzle Exit Dia m AUTO FIX Booster Diameter m AUTO FIX B25 Fixed m m m kg 28 6473345 7 1511239 F 35 7984583 f Update SOB 1082771 82 xi If the SOB being modeled consists of two or more parallel burning motors these must be converted into a single motor equivalent The individual motors can be dissimilar but their normalized thrust profiles and burn times must be equal If parallel burning motors have identical propellant mass fractions vacuum specific impulses and propellant densities the corresponding parameters of the single motor equivalent will have the same values If the individual motors are dissimilar the formulae in Appendix B of the User Manual can be used to calculate the single motor equivalent values from the individual values The rocket nozzle exit diameter of any single motor equivalent is equal to the RSS of the rocket nozzle exit diameters of the parallel motors whether these motors be identical or dissimilar The SOB ignites at t 0 when the first tandem stage rocket motor ignites If the SOB burns out at t Burn Time before the end of the first real tandem stage the SOB inert mass is immediately discarded If the SOB is still burning at the end of the first real tandem stage it is discarded along with the inert mass of the first real tandem stage In this case the discarded SOB mass will
18. as expeditiously as possible During the optimization iterations the box size is constrained to remain between the specified Minimum and Maximum values A small Minimum less than unity is usually recommended If the box size becomes too large the solution may jump out of the quasi linear region that the optimizer is working in The default Maximum box size is 128 Larger values will allow greater changes in the trajectory on each iteration but there is a risk of greater changes producing an aberrant trajectory PERTURBATIONS You can specify how much each variable will be perturbed by the optimization procedure to determine the variable s effect on the objective and constraint functions There are three launch related perturbations a payload perturbation used when the objective is Maximize Payload eight tandem stage perturbations and two strap on booster perturbations the strap on booster perturbations are not displayed if the rocket has no strap on booster The maximum amount that any free variable can be varied on an iteration of the optimization procedure is equal to the product of that variable s perturbation value and the box size There is only one perturbation value for each of the eight stage dependent free variables This means for example that the core ideal delta velocities of all the tandem stages for which this variable is free will be perturbed by the same amount Clicking the Restore Defaults but
19. expressed as an actual amount and as a O 10 20 30 40 50 60 70 80 percentage of the maximum possible Iteration change allowed by the box size history The final value attained by the variable is aa also displayed 01 Slice o to 30 86 28 EFFECTS A variable change plot indicates whether or not a variable is likely to have attained or approached its optimum value A variable may remain on either the plus or minus limit defined by the box size for the duration of the optimization procedure This indicates that the variable is probably not close to its optimum value A variable may start out on a limit but may begin to swing back and forth between limits before the optimization procedure is complete This variable may be close to its optimum value A variable may swing back and forth but at lower amplitudes than the limits This variable may be close to or at its optimum value A variable may reach a point where it does not swing back and forth at all but rather remains virtually constant which is indicated by a zero value in the plot This variable may also be close to or at its optimum value CONCLUSIONS DRAWN FROM THE VARIABLE CHANGE HISTORIES Even though its variable change plot indicates that a variable has not reached its optimum value a substantial further change in the variable may not produce a significant improvement in the objective The objective may simply be insensitive to the v
20. free to be optimized the Vary button should be checked 55 17 AERODYNAMIC FORCE MODELS A tandem stage s aerodynamic force model defines the aerodynamics for the entire rocket when the stage is at the bottom of the airborne stack Whether or not the stage is mated is of no consequence An attached strap on booster SOB could pose a problem in some cases The aerodynamic force models of tandem stages that are active while the SOB is attached must incorporate the aerodynamic effects of the SOB An SOB that is still burning at the end of the first real stage poses no problem for the aerodynamic modeling because the SOB inert mass and unburned propellant are discarded when the first real stage ends However in most cases an SOB will burn out before the end of the first real stage Then unless SOB burn out coincides with the end of a stage in a mated group there is no way to properly simulate the effect of the discarded SOB mass on the rocket s aerodynamics Fortunately SOB mass will usually be discarded at a time when the aerodynamic forces are small For each stage you can choose from two aerodynamic force models 1 Normal Axial Force Model defined by normal and axial force coefficient data that are expressed as functions of Mach number These data are displayed by the GUI in graphical and tabular forms and can be edited in either form The normal axial aerodynamic data are recorded in the rocket dat input file 2 Lif
21. heating rate do not result in the imposition of unnecessary constraints The heating rate at the final time will also produce a constraint if the value is more than 80 of the specified limit If the heating rate at the start of the trajectory exceeds the specified limit a pop up window informs you that the specified limit should be increased DEFINING THE WIND A wind speed vs altitude profile and a wind azimuth can be defined or edited by clicking the Define a wind profile or Edit the wind profile button If a wind profile has been defined the message A wind profile has been defined will be displayed Otherwise the message There is no wind will be displayed The wind model and its editing are explained in the Wind Model section In the special case where a user defined central body has no atmosphere i e the specified sea level pressure is zero the option of defining a wind profile will not appear in the Launch and In Flight Conditions window and the program will set the wind speed to zero EXCESSIVE TIME LAPSE BETWEEN TARGET EPOCH AND LAUNCH TIME Intercept Spacecraft or RV mission only If you proceed to the Launch Preparation window with a Launch GMT that is more than 30 days past the target s epoch a pop up window will warn you that the target epoch may be too old to provide an accurate target state for the mission and you will be given the option to adjust the target epoch and associated state or the
22. increase from left to right in the data records When an independent variable s value is equal to or less than the preceding value the program will assume that the preceding value is the last value in the data record and the number of tabled points will be defined accordingly Linear interpolation is used to extract values of the dependent variables There is no extrapolation when the value of an independent variable falls outside the range of its tabled values Data lines for the independent and dependent variables in a group are not separated by blank lines However a blank line must separate one group from another Other places where a single blank line must appear are 1 after 2 after the ang units line and 3 after the sref or refdia line If there is no sref or refdia line a single blank line must separate the ang units line from the following mach line 64 20 NORMALIZED THRUST PROFILE 20 NORMALIZED THRUST PROFILE The vacuum thrust s time variance is defined by a normalized profile with a unity maximum value and duration The program scales the normalized profile by the average vacuum thrust and burn time to obtain the actual vacuum thrust profile The default normalized profile is a horizontal line representing a constant vacuum thrust Average vacuum thrusts are specified in the tandem stage and strap on booster configuration windows 1 2 1 0 0 8 0 6 0 4 0 2 0 0 RETURN EE
23. is a useful feature since all three coefficients share the same Mach number sequence To change the location of a point on the selected curve the point is first selected by placing the mouse cursor near the point and clicking the mouse s right button the selected point s symbol will change from an open circle to a solid disc Then the mouse cursor is placed at the desired new location for the point and the mouse s left button is clicked If VAR has been selected the point will move to the new location If there is a horizontal component in the movement of the point i e the Mach number is changed for that point the corresponding points on the other two curves will have their Mach numbers changed as well there being only one Mach number table for the three aerodynamic coefficients However if FIX has been selected the point will move only vertically attaining the indicated location insofar as the coefficient value is concerned but retaining the same Mach number In this case the other two curves will not be altered when points on the selected curve are relocated VIEWING A DATA SLICE In the Slice boxes under the graph you can input beginning and ending Mach numbers and click the VIEW Slice button to stretch the Mach Number axis This zooming is helpful in distinguishing individual points when they are crowded together To regain the total view enter 0 in the left box and a large number in the right box and click the VI
24. is modeled separately as a single motor equivalent booster that is attached to the rocket s first real tandem stage which is either a single tandem stage or a mated group of tandem stages that includes the first tandem stage MATED STAGES The mating of tandem stages allows a simulated single stage to be represented by two or more dummy stages thus providing more thrust and steering variables for the stage 45 16 CONFIGURE TANDEM STAGE A tandem stage will be mated to the stage above it if you check the Mate to Next Stage box A mated group of two or more tandem stages can be created in this way The primary inert mass does not include Adjunct Inert Mass of a mated stage will not be discarded until the last stage in the mated group ends Then the primary inert masses of all stages in the group will be discarded simultaneously A stage ends at rocket engine burnout unless there is a post thrust coast In that case the stage ends when the post thrust coast ends The diameters of all stages in a mated group are automatically set equal to the diameter of the lowest base stage in the group Mated stages are indicated by special markings in the Rocket Stage Stack window and in the rocket drawing ADJUNCT INERT MASS A propelled tandem stage s total mass is the sum of its propellant mass primary inert mass and adjunct inert mass the top stage s adjunct inert mass is termed Payload Mass Unlike the primary inert mass
25. launch time However you are not required to make any adjustments 34 11 LAUNCH AND IN FLIGHT CONDITIONS If you proceed to the Launch Preparation window with a Launch GMT that is more than 10 days past the target s epoch a pop up window will advise you that the program will automatically advance the target epoch so that the epoch is only 10 days before the Launch GMT The program will numerically integrate the target s motion equations from the original specified target epoch to a time that is 10 days before the rocket s specified nominal launch time thus re defining the epoch The 10 day buffer is provided so that if the rocket s launch time is substantially reduced during the optimization procedure it will remain later than the target epoch The program will not allow a rocket launch time that is earlier than the target epoch 35 12 WIND MODEL The wind data are initially displayed in graphical form At the top right of the graphical display window is the View TABLE button which changes the display to a tabular form At the top of the tabular display window is the Return to PLOT button which toggles back to the graphical display You can create or modify wind data in either window Altitude km xj Wind speed is expressed as a function of altitude and Wind Speed vs Altitude View TABLE the azimuth of the wind vector is assumed to be the same at all altitudes In A th of Wind Vect d Point update P
26. pre launch ground track is activated opportunities dat list of possible launch opportunities during launch window based on target s ground track and the launch point latlong dat time histories during launch window of target s latitude longitude altitude and slant range from launch site to target VIEWING THE DATA FILES Most input and output data files can be viewed in their raw forms via the GUI and copied to the keyboard buffer when a mission is examined via Mission Synopsis It is normally not necessary to access the files off line using the operating system s file management application If the files are examined off line CARE MUST BE TAKEN TO NOT ALTER THEM And none of the files should be selected by the operating system s file management application when the program is being executed 2 FIRST WINDOW 2 FIRST WINDOW Select Mission Type ra i Click the bubble for your chosen mission type ZOOM a Achieve Specified State b Inject into Conic c Intercept Spacecraft or RV Version 1512 Check for Upgrade Conceptual Design and Analysis of Rockets and Their Missions A A Mission Selection window l will be displayed from which you can select an existing mission for a template or start your mission from scratch Depending on mission type you will be able to choose one of several objectives which include maximum payload minimum initial mass minimum flight time maxi
27. responds to a 180 degree angle of attack command in the central body frame If the stage has a non zero time constant the actual angle of attack will usually deviate from 180 degrees Because the angle of attack is a function of the rocket s velocity w r t the air a non zero wind will affect the rocket s attitude retro ballistic steering goes into effect at the start of the stage The steering command remains in effect throughout the stage during both the thrust and post thrust coast if any This steering method should never be used for a first stage when there is a launch rail i e Launch Rail Length gt 0 because the rocket would never be able to leave the rail An example of retro ballistic steering is a de orbit maneuver that causes the rocket to descend from an orbit about a central body to a specified starting point for a final descent to the central body s surface With retro ballistic steering there will be no aerodynamic normal g s FIXED YAW AND PITCH STEERING fixed yaw and pitch steering will command the rocket stage to attain and hold a specified fixed attitude in the central body frame while the rocket stage thrusts The user must specify the yaw and pitch angle values that define the fixed attitude The fixed attitude command can continue during any post thrust coast period if the maintain steering option is chosen If the stage has a non zero time constant the rocket s actual attitud
28. the new points are set equal to the original final value of normalized thrust If the number of points is decreased from the original value a number of end points are deleted The addition or deletion of points will cause a shift of the other points because the data are re scaled to the normalized time interval zero to unity 65 20 NORMALIZED THRUST PROFILE MODIFYING THE DATA The tabular data are modified by entering the desired numbers in the appropriate boxes When you return to the plot window the data is automatically normalized The plot data are modified using the mouse To change the location of a plotted point first select the point by placing the mouse cursor near the point and clicking the mouse s right button the selected point s symbol will change from an open circle to a closed disc Then position the mouse cursor at the desired new location for the point and click the mouse s left button A point cannot be moved horizontally by an amount that would pass adjacent points ENTERING TYPICAL PROFILE OR RESTORING THE DEFAULT You can enter a typical vacuum thrust profile or restore the default constant profile by clicking either the Typical Profile button or the Constant Thrust button You can then modify the profile as desired 66 21 STAGE SIZING FACTORS When you click the Stage Sizing Factors button in a stage s Configure Tandem Stage window the Sizing Factors for Stage window opens If the stage i
29. the rocket s final position measured in the ECF frame When Inertial is the chosen reference frame this mission objective becomes Maximize Central Angle where the central angle is the angle between the rocket s initial and final position vectors in the ECI frame When Central Body Fixed is the chosen reference frame Ground Range and Longitude are two of the end state variables that can be specified by you When Inertial is the chosen reference frame these two variables become Central Angle and Right Ascension Central Angle was defined in the preceding paragraph Right Ascension an angle differs from Longitude in that the reference is the Vernal Equinox an inertial vector for all practical purposes instead of the Prime Meridian SPECIFY THE END STATE Each FREE SET button toggles between a FREE condition where the end state variable is unconstrained and a SET condition where the rocket must achieve the specified set value for the end state variable Any combination of the seven end state variables can be FREE or SET except that the program will not allow Ground Range Latitude and Longitude in the Central Body Fixed frame or Central Angle Latitude and Right Ascension in the Inertial frame to all be SET The settings of any two of these three variables will determine the value of the third 27 9 CENTRAL BODY MODEL 5 xj The central body s d
30. thrust provides the specified core initial thrust weight ratio By toggling the opt max fix button you can impose an explicit constraint on the vacuum thrust If you toggle the button to MAXIMUM you can enter a maximum allowable value for the vacuum thrust If you toggle the button to EXACT you can enter a specific value During its optimization procedure the program will adjust the free variables so that the imposed constraint on vacuum thrust is satisfied If a constraint is imposed it is advisable to Vary the core initial thrust weight ratio to make a feasible solution more likely If you toggle the button to OPTIMUM no constraint will be imposed on the vacuum thrust If the vacuum thrust is to remain constant or is to be throttled down in steps so as to keep the rocket s axial acceleration within a specified limit then the name Vacuum Thrust is displayed If a constraint is imposed the specified value of the vacuum thrust is the starting value The axial acceleration limit and throttle specifications are discussed in a following paragraph If a time varying profile has been defined for the vacuum thrust then the name Average Vacuum Thrust is displayed If a constraint is imposed the specified value of the vacuum thrust is the average value of the time varying profile With such a profile there can be no throttling The time varying thrust profile specifications are discussed in the section Normalized Thrust Profil
31. time slice in these plots full scale is restored by entering a large negative number in the first Slice box and a zero in the second Slice box SHOW EVENTS Clicking the Show Events button in a post launch time history plot window will mark the rocket s tandem stage burnout and staging points A burnout point is indicated by a small solid disc and a staging point where inert mass is dropped is indicated by a larger open circle If the stage is mated to the following stage the marks are light gray in color Otherwise the marks are dark blue When burnout and staging occur simultaneously the small solid disc is perfectly centered in the larger open circle When the Show Events button is clicked the button title will change to Hide Events Clicking the Hide Events button will remove the burnout and staging marks from the plots 80 GM 51151110 Rendezvous 120 N Mi SOB Lift Drag Aero amp AOA Limit for Stage 2 Aerodynamic Normal Acceleration g s 14 42 I Stage Limit 1 0 0200 2 0 1200 3 None 10 08 06 04 eee aa aaa a ca a a a 350 100 1 300 RETURN Slice 0 200 250 Time sec sec VIEW Slice to 465 545 400 Motor Burnout End of Stage 450 500 Hide Events x 27 PLOT SELECTION SHOW LIMITS Clicking the Show Limits button which appears in some post launch time history win
32. vertical location of the drawn horizon depends only on the rocket s pitch angle Effects on the horizon of the rocket s heading flight path angle range and altitude are not included When the pitch angle is zero the horizon is centered on the rocket When the pitch angle is ninety degrees the horizon is near the bottom of the graphic and when the pitch angle is minus ninety degrees the horizon is at the top of the graphic Before playback starts the total flight time is displayed in hours minutes seconds and the default Flight Segment starts at time zero and ends at the total flight time you can redefine the Flight Segment During playback the time from launch and the playback speed are displayed When a playback is completed the display remains fixed at the final condition If you then click one of the Playback Duration buttons the display will reset to the time zero condition A second click of the button will restart the playback 84 28 EFFECTS ajx You can click the Effects button to see a mosaic depiction of the effects EFFECTS Metric Units Angles in Radi Scale Fact P P Metric Units Angles in Radians earen OF Variable perturbations on the Objective and Constraint Functions values of scaled objective and 2 x position m 7 Z velocity m s sss constraint functions 3 y position m 8 si qBar KN m 2 4 z position m lim i noel 2 2 Seen E E sul The objective and constraint
33. will independently vary the SOB s RETURN average vacuum thrust and burn time as it seeks to determine the quasi optimum solution for the mission OTHER SOB PARAMETERS The SOB s performance parameters Vacuum Specific Impulse and Propellant Mass Fraction and the sizing parameters Propellant Density and Inert Mass Density have the same meanings as their counterparts for the tandem stages a tandem stage s propellant density is termed Propellant Bulk Density and its inert mass density is termed Density of Primary Inert Mass 44 EE Z00M Rocket Trajectory Optimization 5 xj Configure Tandem Stage 2 M Mate to Next Stage Adjunct Inert Mass kg REMOVE Propulsion System Core Ideal Delta Velocity m s 4125 Vary Core Initial Thrust Weight Ratio Vary Vacuum Specific Impulse sec Propellant Mass Fraction Rocket Nozzle Exit Diameter m auto fix 4 876 Fixed Vacuum Thrust kN opt max fix EXACT opt max fix 942000 MAXIMUM Mated Group Total Propellant Mass kg Aerodynamic Force Model LD Normalized Thrust Profile Stage Sizing Factors Time Constant s Maneuver Delay s fo E vary Maneuver Plane Roll deg Vary Angle Step deg Vary Steering bi linear tangent change steering Turn Angle deg 23 56 Vary Initial Average Turn Rate Vary Normal G Limit Free Set Axial G Limit Free Set Throttle Fraction Times Post Thrust Coast Time sec vary
34. 5 28 EFFECTS 89 APPENDIX A APPENDIX A COORDINATE REFERENCE FRAMES SPIN AXIS CENTRAL BODY X NORTH Y EAST RO PRIME MERIDIAN LAUNCH SITE Z DOWN EQUATOR North East Down NED Computational Reference Frame Calculations of the rocket s and target s flight mechanics are done in a north east down NED reference frame that is fixed to the central body with origin at the launch site The launch site location is defined by inputs for its longitude w geodetic latitude 0 and altitude above sea level Another north east down frame a local frame with origin at the rocket instead of the launch site is the reference for the rocket s pitch angle yaw angle heading angle and flight path angle 90 APPENDIX A APPENDIX A CONTINUED Z SPIN AXIS CENTRAL BODY PRIME MERIDIAN EQUATOR Central Body Fixed ECF Reference Frame The ECF reference frame is fixed to the central body with origin at the center of the central body A transformation from the NED frame into the ECF frame is done for the calculation of the rocket s and target s gravitational acceleration geodetic latitude longitude and altitude 91 APPENDIX A APPENDIX A CONTINUED Z SPIN AXIS CENTRAL BODY PRIME MERIDIAN VERNAL EQUINOX DIRECTION EQUATOR Inertial ECI Reference Frame The ECI reference frame is an inertial i e non rotating frame with origin at the cent
35. 8 MISSION DEFINITION Achieve Specified State between these two choices Your choice of reference frame affects 1 definition of the rocket s final velocity 2 whether Ground Range or Central Angle will be available as an objective or end state constraint and 3 whether Longitude or Right Ascension will be available as an end state constraint When the Central Body Fixed frame is chosen the rocket s end state Speed Flight Path Angle and Heading are defined by the rocket s velocity relative to the central body which is usually a rotating body and therefore not an inertial reference When the Inertial frame is chosen these three variables are defined by the rocket s inertial velocity For either reference frame Flight Path Angle is the angle between the chosen velocity and the local horizontal plane i e horizontal plane at the rocket s location and is positive when the velocity vector is above the horizontal plane Heading is the angle between the chosen velocity s projection onto the local horizontal plane and a vector in the plane that points in the true north direction Heading is positive when the chosen velocity s horizontal projection has an eastward component When Central Body Fixed is the chosen reference frame one of the mission objectives is Maximize Ground Range This range is an approximation of the great circle distance along the central body s surface between the launch site and
36. During Coast M Maintain Steering I Zero Relative AOA Zero Inertial AOA RETURN M Ride Normal G Limit This is the Base Stage of a Mated Group 16 CONFIGURE TANDEM STAGE The tandem stage model has only one rocket engine If the actual stage being modeled has two or more parallel burning engines they must be converted into a single engine equivalent This can be done only if the engines normalized thrust profiles and burn times are identical If parallel burning engines have identical propellant mass fractions vacuum specific impulses and propellant bulk densities the corresponding parameters of the single engine equivalent will have those same values Any throttling sequence is valid when the single engine equivalent represents identical parallel engines If the parallel rocket engines are dissimilar a single engine equivalent can still be defined provided that any throttling of the thrust is the same percentage wise for each engine Formulae to convert the parameter values of dissimilar parallel rocket engines into the parameter values of a single engine equivalent are presented in Appendix B of the User Manual The rocket nozzle exit diameter of a single engine equivalent of parallel engines is equal to the RSS of the rocket nozzle exit diameters of the parallel engines whether these engines are identical or dissimilar A strap on booster SOB is not one of the parallel burning engines The SOB
37. E FLIGHT TIME Stage Flight Time applies only to an unpropelled stage It is the stage s total flight time HOW TO MODEL A TANDEM STAGE OF FIXED DESIGN In some analyses a tandem stage will have already been designed having a fixed primary inert mass and a maximum or exact propellant load Such a fixed design stage can be modeled by setting the Propellant Mass Fraction to unity and setting the Adjunct Inert Mass equal to the stage s fixed design total inert mass This will allow the program s optimization procedure to reduce the propellant mass assuming liquid propellant below tank capacity without changing the inert mass The top stage s Payload Mass must be set to the sum of the actual payload and the stage s fixed design inert mass If the rocket s payload is varied maximized by the optimization procedure the resultant actual payload will be the difference between the resultant Payload Mass and the fixed design inert mass If the mission objective is to Maximize Payload and if all of the rocket s stages including strap on booster if any are fixed design stages the rocket s initial mass must be unconstrained FREE The Vacuum Thrust or Average Vacuum Thrust of a fixed design stage is by definition fixed EXACT and the stage s Propellant Mass is either fixed EXACT or limited MAXIMUM to a maximum value The Core Initial Thrust Weight Ratio of a fixed design stage should be
38. EW Slice button COPYING NORMAL AXIAL DATA TO THE NEXT STAGE If the Copy Aero to Next Stage button is clicked and the next stage has a normal axial aerodynamic force model the normal axial aerodynamic data are copied to the next stage overwriting the data already there This option is particularly handy when a mission is being designed from scratch or when replicating aerodynamic data for stages in a mated group However it is not required that stages in a mated group have the same aerodynamic characteristics 59 18 NORMAL AXIAL AERODYNAMIC FORCE MODEL RESTORING THE DEFAULT NORMAL AXIAL DATA You can replace the displayed normal axial aerodynamic data with the default normal axial data by clicking the Restore Default Aero button The replaced data cannot be recovered For scratch missions the default data will be displayed initially 60 19 LIFT DRAG AERODYNAMIC FORCE MODEL 19 LIFT DRAG AERODYNAMIC FORCE MODEL gt The Lift aerodynamic force Fl is perpendicular to the rocket s relative velocity i e velocity w r t the air and the drag aerodynamic force Fd is anti parallel to the rocket s relative velocity These forces are calculated as functions of the lift and drag coefficients Cl and Cd aerodynamic reference area Aref and dynamic pressure qBar Fl qBar Aref Cl Fd qBar Aref Cd Aref is calculated from the reference diameter refdia Aref 0 25 pi refd
39. In cases where an axial acceleration constraint must be satisfied explicitly it is advisable to Vary the stage s initial thrust to weight ratio POST THRUST COAST TIME Post Thrust Coast Time can be specified for each propelled stage It can either be fixed at the specified value or varied Vary by the optimization procedure This parameter is not relevant for an unpropelled stage and is replaced by Stage Flight Time With the bi linear tangent inertial hold and fixed yaw and pitch steering options there is a During Coast provision to choose how the rocket will be steered during the post thrust coast period By checking the appropriate box you can choose to Maintain Steering i e use the same steering formula as that used during the burn or have the rocket transition to either Zero Relative AOA or Zero Inertial AOA zero angle of attack in either the central body or inertial frame With the Zero Relative AOA option a wind will affect the rocket s attitude If the Post Thrust Coast Time is fixed at zero the stage will end at rocket motor burnout and the During Coast option will be irrelevant the program will automatically set it to Maintain Steering 54 16 CONFIGURE TANDEM STAGE With ballistic or retro ballistic steering there is no During Coast option The rocket will fly with zero or 180 degree relative angle of attack for the duration of the stage STAG
40. In such a case there is a CONTINUE button at the window s bottom left corner Clicking this button will display the variable perturbation effects that could not be displayed initially In rare cases where there is an unusually large number of variables more than one continuation may be required to see all of the effects SCALE FACTORS The objective and constraint functions are scaled to make them approximately all apples Clicking the Scale Factors button at the top right of the Effects window produces a display of the scale factors for the mission In the program the physical values of the functions in Metric units are multiplied by the associated scale factors to obtain the scaled functional values 88 Scale Factors for Objective and Constraint Functions x Metric Units Angles in Radians These scale factors are multiplied by the corresponding objective and constraint functional values expressed in the indicated units to get the scaled values used by the optimization algorithm and for calculation of the composite constraint satisfaction error Function max payload kg x position m y position m z position m x velocity m s y velocity m s z velocity m s lim initial mass kg lim qBar a kN m 2 10 lim qBar b kN m 2 11 lim axial accel 1 g 1 2 3 4 3 6 7 8 9 Scale Factor 0 03919387 1 19230E 03 1 19230E 03 1 19230E 03 1 1 2 1 23495E 03 5 56758305 5 56758305 735 4987
41. ME burning at 109 ZOOM Stage 2 5 SSME burning at 65 ZOOM Stage 3 5 SSME burning at 109 Second stage modeled as a single ZOOM stage ZOOM Stage 4 1 SSME burning at 109 Strap On boosters SOB single engine equivalent with thrust and Isp of Shuttle SRB s SAVE Description and RETURN The mission names displayed in the Trash Folder window are listed in order of their creation dates and have the prefixes that define the mission type and the year month day creation dates To move a mission from the Trash folder and restore it to the DATA folder you select the mission via a mouse click and then click the RESTORE Selected Mission button The Mission Description button opens a window where you can view alter and or define a description of the mission You can type ina new description or edit a description that is already in the text box The text will wrap horizontally and you can start new paragraphs with the keyboard s ENTER key The display of the rocket drawing enhances the comprehension of the mission description The Mission Description window is also accessible from the Mission Synopsis and Launch Preparation windows 4 MISSION SYNOPSIS The Mission Synopsis window provides salient information about the selected mission and contains buttons that activate windows where detailed data and plots are displayed EE Z00M Rocket Trajectory Optimization The missi
42. Normalized Vacuum Thrust Normalized Thrust Profile for Stage 2 View TABLE Points update Constant Thrust Typical Profile 0 0 0 2 0 4 0 6 0 8 1 0 Normalized Burn Time _Copy Profile to Next Stage NUMBER OF POINTS IN THE TABLES x When the Normalized Thrust Profile button is clicked in the Configure Tandem Stage window the Normalized Thrust Profile window appears When the Thrust Profile button is clicked in the Configure Strap on Booster window an almost identical Normalized Thrust Profile window appears but without the Copy Profile to Next Stage button The normalized thrust profile is initially displayed as a plot At the top right of the plot window is a View TABLE button which changes the display to the tabular form At the top of the tabular window is a Return to PLOT button which changes the display back to the plot window You can create or modify data in either window In the plot window for a tandem stage other than the top stage a click of the Copy Profile to Next Stage button will cause the normalized vacuum thrust profile to be copied to the next stage in the tandem stack You can vary the number of points in the plot and table by entering a value in the Points box and clicking the update button The number of points cannot exceed 20 If the number of points is increased the new points are added at the end of the profile and the default values for
43. O P R Tm Speed of Sound sqrt gamma R Tm MO where PO sea level pressure N m 2 g0 mass to force conversion factor m s 2 9 80665 MO mean molecular weight of air dimensionless R universal gas constant J kg deg K 8314 32 Tm molecular scale temperature deg K gamma adiabatic index of air dimensionless The default exponential atmospheric model approximates the default earth atmospheric model for geopotential altitudes below 90 km But the constant molecular scale temperature of the exponential model will cause differences especially in the speed of sound which will not vary with altitude 30 11 LAUNCH AND IN FLIGHT CONDITIONS 11 LAUNCH AND IN FLIGHT CONDITIONS By definition the rocket s launch occurs at time 0 when the rocket s first tandem stage ignites The Launch GMT Launch Azimuth and Launch Elevation can either be fixed or varied by the program if the corresponding Vary radio button is checked The other parameter values remain fixed at their specified values Intercept Spacecraft or RV ear re ani Fal Launch GMT path 6 ee Vary Change to Launch Window Estimation of Launch GMT and Azimuth Launch Azimuth lt 86 7965488 Vary Launch Elevation deg Vary Launch Speed mn booo Launch Rail Length m Launch Latitude deg Launch Longitude deg 82 Launch Altitude m Initial Mass kg FREE MAX SET FREE Maximum Qbar kN
44. ODIFYING THE WIND DATA On the tabular display the data are modified by entering the desired numbers in the Altitude and Wind Speed boxes On the graphical display the individual points on the wind speed vs altitude curve are marked with small circles To change the location of a point the point is first selected by placing the mouse cursor near the point and clicking the mouse s right button the selected point s symbol will change from an open circle to a closed disc Then the mouse cursor is placed at the desired new location for the point and the mouse s left button is clicked The selected point will move to the new location If you wish to move a point outside the graph area you can simply move it to the edge of the area and the area will automatically expand INSTANTLY CHANGING THE WIND PROFILE You can replace the displayed wind profile with either the default wind profile or with a zero wind speed profile by clicking the Restore Default Wind or Zero Wind button A replaced user supplied wind profile cannot be recovered 37 13 AERODYNAMIC HEATING RATE MODEL 13 AERODYNAMIC HEATING RATE MODEL 5 5 gt 5 gt 5 gt Clicking the MODEL button in the Launch and In Flight Conditions window produces a window where the aerodynamic heating rate model parameters can be specified o x Aerodynamic heating can be a serious problem at hypersonic speeds An Aerodynamic Heating Rate Model approximati
45. ON DEFINITION Intercept Spacecraft or RV mass will remain fixed at the value specified in the top stage s Configure Tandem Stage window TARGET S EPOCH AND OSCULATING CONIC ELEMENTS The GMT year month day hour minute and second constitute the epoch of the target s six osculating conic elements The conic s size and shape are determined by Perigee Altitude and Apogee Altitude or alternatively by Semilatus Rectum and Eccentricity The SLR Ecc and Apo Per buttons toggle between these two element sets The Semilatus Rectum Eccentricity set is the more general of the two and can be used for elliptical parabolic or hyperbolic conics The Apogee Altitude Perigee Altitude set can only be used for elliptical conics The target s apogee and perigee altitudes are referenced to the central body s equatorial radius It is important to remember than these conic elements are osculating elements and not mean elements The program converts the input osculating conic elements to the target s six state variables position and velocity in a central body centered inertial frame You can enter each orbital element value in the box provided or you can click the Get Target Data from Existing Mission button to display a list of all the existing Inject into Conic and Achieve Specified State missions that are in the DATA folder ZOOM Rocket Trajectory Optimization x ES140721 ES140721 ES140721 ES140808
46. S Offline you can create lift drag aerodynamic data files and place them in the Aerodynamic File Library naming them as you choose Or you can modify and rename lift drag files that are already in the library You can also delete lift drag files from the library The Aerodynamic File Library resides in the ZOOM Program Directory When you first opt to use the lift drag aerodynamic force model for a stage you must assign to that stage via the GUI a lift drag data file from the Aerodynamic File Library The assigned file is actually a copy and is automatically stored in the mission subfolder with a 61 19 LIFT DRAG AERODYNAMIC FORCE MODEL generic stage dependent file name e g Ldfile_2 dat Neither the original library file nor its name is altered Once a lift drag data file has been assigned to a stage you can view and edit the file via the GUI After viewing or editing the file you can click the Copy Data to Clipboard button to extract the data for off line use Lift Drag Aerodynamic Data Lift Drag Aerodynamic Data for Stage 2 Read Only AN EXAMPLE LIFT DRAG AERODYNAMIC DATA FILE Sti len units alt units ang units sref H H mach altitude alphamd 0 0 0 0 0 0 0 0 0 eo0000000 6 O 6 6 0 6 6 6 6 eo00000000 COrFOOPPH eoo0ooOoOKFOKY mach altitude clo clalpha RETURN Copy Data to Clipboard When returning from editing a lift drag data fi
47. Trajectory plot uses an inertial reference plane to define the abscissa variable The inertial reference plane is defined by the rocket s radius vectors at the 81 27 PLOT SELECTION Attitude km Flight Time 415 sec position and target s position for a Intercept Spacecraft or RV mission is projected into this plane and the central angle between the launch site vector and this projection is used to determine the abscissa variable For all Inject Into Conic and Intercept Spacecraft or RV missions and for Achieve Specified State missions with the Central Body Fixed reference frame the abscissa variable is Ground Range in Inertial Plane For an Achieve Specified State mission with the Inertial reference frame the abscissa variable is Inertial Central Angle 1000 500 0 500 Ground Range in Inertial Plane km ANGLE DEFINITIONS The rocket s angle of attack always the total angle of attack is based on the rocket s velocity with respect to the atmosphere Therefore the angle of attack depends on the wind The rocket s yaw pitch and roll angles as well as heading and flight path angles are referenced to the local north east down NED frame with origin at the rocket Positive values for the rocket s yaw pitch and roll angles indicate a yaw right from true north in the local horizontal plane pitch up roll clockwise Euler angle sequence for the rocket centerline
48. ZOOM User Manual Version 1512 03 December 2015 ZOOM is a product of Trajectory Solution Huntsville Alabama http trajectorysolution com trajectorysolution bellsouth net NOTE The Graphical User Interface images in this manual generally do not apply to the same mission TABLE OF CONTENTS Page Numbers in Brackets Oo ON DMN KRWYN NNNNNNNNNKPKRPRP HRB BBB AONAURKRWNHHROWWAN ADU KRWNH OO INTRODUCTION 1 FIRST WINDOW 6 MISSION SELECTION 7 MISSION SYNOPSIS 10 MISSION SUMMARY 15 MISSION DEFINITION Intercept Spacecraft Or RV 21 MISSION DEFINITION Inject Into Conic 24 MISSION DEFINITION Achieve Specified State 26 CENTRAL BODY MODEL 28 EXPONENTIAL ATMOSPHERIC MODEL 30 LAUNCH AND IN FLIGHT CONDITIONS 31 WIND MODEL 36 AERODYNAMIC HEATING RATE MODEL 38 ROCKET STAGE STACK 39 CONFIGURE STRAP ON BOOSTER 42 CONFIGURE TANDEM STAGE 45 AERODYNAMIC FORCE MODELS 56 NORMAL AXIAL AERODYNAMIC FORCE MODEL 58 LIFT DRAG AERODYNAMIC FORCE MODEL 61 NORMALIZED THRUST PROFILE 65 STAGE SIZING FACTORS 67 LAUNCH PREPARATION 69 OPTIMIZER PARAMETERS 71 PRECISION AND OUTPUT PARAMETERS 73 RECOMMENDED SOLUTION PROCEDURE 74 SOLUTION WINDOW 77 PLOT SELECTION 79 EFFECTS 85 APPENDIX A COORDINATE REFERENCE FRAMES 90 APPENDIX B PARAMETERS FOR SINGLE ENGINE EQUIVALENT ROCKET MOTOR 93 TABLE OF CONTENTS
49. a free argument of perigee has resulted in an erratic perhaps divergent solution procedure This problem is not common but may occur in some cases especially when the destination conic has a small non zero eccentricity If you specify a value for the conic s right ascension and you later indicate in the Launch and In Flight Conditions window that the launch GMT is to be varied the program will wait until it has found the quasi optimum solution disregarding the constraint on right ascension and will then calculate the launch GMT that produces the desired right ascension 25 8 MISSION DEFINITION Achieve Specified State 8 MISSION DEFINITION Achieve Specified State The format of the Mission Definition window depends on the selected mission type Intercept Spacecraft or RV Inject into Conic or Achieve Specified State Zax CENTRAL BODY MODEL Mission Definition _ourr The option to define the Central Body Model is provided in the Mission Definition windows of all three mission types The Central Body Model Earth Standard _Viewor Change Mode default model is Earth Choose the Mission Objective Standard Clicking the View or Change Model button opens a Achieve Specified State Maximize Payload M Minimize Initial Mass Minimize Flight Time l Maximize Ground Range window where the parameters Maximize Altitude l Maximize Speed a 1 Minimize Aero Heating defining the ce
50. aft or RV Inject into Conic or Achieve Specified State ixi CENTRAL BODY MODEL Mission Definition _ourr The option to define the Central Body Model is provided in the Mission Central Body Model Earth Standard View or Change Model Definition windows of all three mission types The default model is Earth Standard Choose the Mission Objective Clicking the View or Change Model button opens a window Inject into Conic Maximize Payload 7 Minimize Initial Mass I Minimize Flight Time I Minimize Aero Heating where the parameters defining the central body s rotation Osculating Elements of Destination Conic gravity dimensions and atmosphere can be changed see the section on Central Perigee Altitude km 222 2400064 SLR Ecc Apogee Altitude km 222 2400064 Body Model Argmt of Perigee deg FREE SET TIED If only small adjustments are made to the central body s Right Ascension deg FREE SET rotation gravity and or dimension parameters the model will be labeled Earth Modified If any of these List Mission Conditions Stack Countdown parameters are changed significantly or if the 1962 earth standard atmospheric model is replaced by an exponential atmospheric model the Central Body Model will be labeled User Defined Inclination deg FREE SET CHOOSE THE MISSION OBJECTIVE You can select one of four mission objectives for the Inject into Conic mission Unless the objectiv
51. ally be necessary to use the Preview procedure repeatedly adjusting these two variables along with other variables that affect the rocket trajectory before attempting to obtain a quasi optimum solution The Preview procedure is discussed in the Launch Preparation section CONSTRAINT ON THE ROCKET S INITIAL MASS When the objective is something other than Minimize Initial Mass a FREE MAX SET button can toggle between three kinds of initial mass constraints 1 FREE i e unconstrained 2 MAXIMUM and 3 EXACT For the MAXIMUM and EXACT options a box is provided for entry of the rocket s Initial Mass either a maximum limit or an exact value When the objective is Minimize Initial Mass the message Initial Mass is To Be Minimized is displayed and there is no provision for entry of an initial mass value MAXIMUM QBAR Maximum Qbar is the maximum allowable dynamic pressure Qbar on the rocket The FREE SET button toggles between a FREE unconstrained condition and a maximum limit SET If the maximum limit option is chosen a box is provided for entry of the maximum allowable Qbar and an optional Ascent restriction is provided If the Ascent box is checked the Maximum Qbar constraint applies only while the rocket is ascending Otherwise the constraint applies for the rocket s entire flight The dynamic pressure is calculated as Qbar 0 5 rho V 2 where rho is the local atmospheric density and V
52. alues of Time to Start Output and Time to End Output put no restriction on the output interval The default Integration Steps Between Records is unity which means that the output records will be written to files after every numerical integration step It is advantageous to guard against creating extraordinarily large output data files However it is likely that the maximum data default values of the Data Output Controls will be acceptable for the great majority of missions 73 25 RECOMMENDED SOLUTION PROCEDURE 25 RECOMMENDED SOLUTION PROCEDURE 5 5 5 After choosing the mission type and selecting a template mission from the list in the Mission Selection window you should usually proceed through the GUI s main sequential windows in the order indicated by the navigation buttons Synopsis Mission Conditions Stack and Countdown It is not required that you visit any particular window and it is only necessary to visit those windows where input data need to be specified or changed For a Mission from Scratch though it is recommended that you methodically visit all the windows In the Mission Synopsis window and the windows that branch from it you can familiarize yourself with the template mission before proceeding to the other windows to specify or modify the input data In each of the main sequential windows there are buttons that open other windows where essential input data are re
53. are mated can be readily Flight Path Angle 0 03331 deg Speed 7348 253 m s recognized for their buttons touch Rocket Final Conditions in Central Body Frame Osculating Conic Elements at Injection Perigee Altitude 222 237 km specified Stages constrained to have Apogee Altitude 222 243 km specified Inclination 28 37332 deg the same burn time will coma 9 00000 dem have red buttons Stages Argument of Latitude 114 25017 deg constrained to have the same propellant mass will RETURN Data is Copied Into Clipboard STAGES SOB 2 3 al have green buttons Labels such as On Limit FIXED Below Limit and free are associated with certain variables as reminders of constraints that either were or were not imposed on the mission DATA DISPLAYED TOWARD THE BOTTOM OF THE WINDOW For an Inject into Conic mission the rocket s osculating conic elements at the conic injection point i e at the final time are displayed near the bottom of the window The Argument of Latitude is the sum of the Argument of Perigee and True Anomaly For an Intercept Spacecraft or RV mission the final state of the rocket relative to the spacecraft or RV is displayed near the bottom of the window This state is defined by the Relative Speed Relative Direction and miss distance The Relative Speed is the rocket s speed relative to the spacecraft or RV at the final time and it will be very small
54. ariable or the coordinated changes in other variables may keep the objective from improving significantly On each iteration of the optimization procedure the objective and constraints are approximated as linear functions of the variables Because there will usually be more variables than constraints and because of the linear approximations some of the variables will want to change as much as the limits allow on any given iteration These variables may overshoot their optimum values and attempt to compensate on the next iteration so that they bang back and forth between the limits This behavior is of little practical consequence and is a small price to pay for the robustness of the optimization procedure Because the objective can be insensitive to coordinated changes in the variables there are innumerable quasi optimum solutions with values for the objective that are practically the same as the truly optimum value MOSAIC COLOR CODE DISPLAY MODE The mosaic depicting the effects of variable perturbations has four display modes You can click the Toggle Mode button to toggle from one mode to the next The Color Code mode default is probably the most useful In this mode the changes produced by the variable perturbations are divided into eight color coded bins based on the magnitudes of the changes The mosaic of colored squares indicates these magnitudes for all combinations of variable perturbations and changes in the objective and
55. ating that the quantity is not to exceed a specified limit If the quantity does not reach the limit during the solution procedure the color of the displayed name will be light gray instead of black If a constraint is stage dependent a bracketed number indicates the stage i e 1 2 etc Changes in a scaled function caused by all the variable perturbations are shown in the function s mosaic column Changes in all the scaled functions caused by the perturbation of a variable are shown in the variable s mosaic row CONSTRAINTS ON QBAR AND AERODYNAMIC HEATING RATE Constraints on maximum dynamic pressure qBar and aerodynamic heating rate apply to the entire flight but these quantities may have more than one peak The intervals within which these peaks occur are identified by the program and separate constraints are applied to these intervals The constraints names will indicate the intervals by letters preceded by a dash such as lim qBar a lim qBar b etc or such as lim aero heat rate a lim aero heat rate b etc 85 28 EFFECTS CONSTRAINTS ON BURN TIME AND PROPELLANT MATCHES Burn time match and propellant match constraints are named match burn time and match propellant with suffixes a b etc as required by the number of constraints The number of burn time match or propellant match constraints will be one less than the number of stages or mated groups that have been designat
56. ation procedure x 27 64 DIFFICULTIES THAT MAY ARISE Iteration p If the optimization procedure displays the OPTIMIZATION FAILED message you should click the ReZOOM button to return to the Mission Selection window from which you can navigate to the various other windows to analyze the probable cause s of the program s failure to find a solution It may be that some constraint is overly restrictive given the variables that are free to be optimized Or it may be that the initial box size is too small given the sizes of the initial constraint satisfaction errors produced by the first trajectory Non linear relationships between constraints and variables can pose difficulties for any optimization procedure ZOOM s procedure is unusually robust and for most cases where a reasonable first guess trajectory has been established there will be convergence to a quasi optimum solution or at least to a solution that satisfies the mission constraints However there are cases where convergence will be difficult In difficult cases the user may have to make adjustments such as fixing certain variables that had been free or freeing certain variables that had been fixed 75 25 RECOMMENDED SOLUTION PROCEDURE A hypothetical example of a difficult convergence is an Inject into Conic mission with the Maximize Payload objective a variable Core Initial Thrust Weight Ratio T W for the first stage a restrictive Normal G Limit to be rid
57. ber of Iterations Solution Error Tolerance Box Size Minimum Initial Maximum and the perturbation magnitudes for the free variables BD cece Geenaions a Number of Iterations is the Number of Iterations number of times the program will generate a set of perturbed trajectories use the Simplex Box Size Minimum Initial Maximum algorithm and adjust the free variables in attempting to partarnaiores eee obtain a quasi optimum solution to your mission The Number of Launch Time 0 sec Iterations must be at least 2 Launch Azimuth 0 deg and cannot exceed 999 If it Launch Etayetion deg turns out that your specified Payless Mass kg number of iterations was Id al Delta Velocity ixe insufficient for the optimization Initial Thrust Weight 2 000E 04 procedure to achieve a quasi Maneuver Delay 0 02 sec optimum solution you can Maneuver Plane Roll Angle 0 02 deg OPTIMIZE More to repeat the Angle Step deg optimization procedure as many Turn Angle 4 000E 04 deg times as necessary Initial Avg Turn Rate 2 000E 04 Post Thrust Coast Time fo 05 sec SOB Thrust 20 kN SOB Burn Time 5 000E 03 sec Solution Error Tolerance 001 04 Oia 1 0 SOLUTION ERROR TOLERANCE Solution Error Tolerance is one NOTE Only three significant figures of a perturbation value will be saved of four options 001 01 0 1 i ae EER and 1 0 The Solution Er
58. ble number of stages is nine If a stage is inserted in a stack that already has nine stages the top stage will be pushed out of the stack and the payload will be assigned to the stage that has been pushed up to the top of the stack Also if the top stage in the stack is deleted the payload will be assigned to the new top stage DELETING OR INSERTING A STRAP ON BOOSTER The rocket has a strap on booster SOB when the button at the bottom of the stack is titled Configure Strap On Booster Otherwise the button is titled Add Strap On Booster Clicking this button at the bottom of the stack regardless of its title opens a window where you can configure the SOB When there is an SOB in the stack there is a Delete button to the right of the Configure Strap On Booster button that when clicked deletes the SOB INTER STAGE CONSTRAINTS There are two kinds of inter stage constraints Burn Time Match and Propellant Match Two or more stages can be constrained to have the same burn time or the same propellant mass the values of these variables being determined by the program s optimization procedure The colors of the Configure Tandem Stage buttons indicate the stages that have been constrained to have matching burn times red or matching propellant masses green When you click the Burn Time Match or Propellant Match button a small window is displayed where you can check boxes to define which stages are to have matchin
59. cept Spacecraft or RV mission has three additional output files that contain data related to the target For some of the accessible files short explanations of file contents are provided by clicking the adjacent buttons SUMMARY EFFECTS AND PLOTS Clicking the Summary Effects and Plots buttons open windows that contain a wealth of useful data which are described in detail in the Mission Summary Effects and Plots sections 14 5 MISSION SUMMARY The Mission Summary window displays an overall summary of the mission solution E 01150319 SLS2 maxPL stdET 5ssme SOB throtDown up issme l6lxi The data in the u pper pa rt lets of the window including the aa Rocket s Final Conditions in Mission Type Pil ecovinnad ante Central Body Frame data Mission Objective maximize payload are displayed for all three i susie mission types and are Flight Time 649 842 sec basically self explanatory Gayicall Gen 745081 68 kg free _ 629m Additional data which is Launch GMT ymdhms 2010 4 5 0 0 0 0000 FIXED different for each mission Launch Azimuth 449 16834 deg free type IS displayed toward Launch Elevation 90 00000 deg FIXED the bottom of the window along with buttons for the rocket s tandem stages and Ground Range from Launch 2288 298 km strap on booster SOB if 1 Altitude 226 267 km Geodetic Latitude 25 82144 deg any Tandem stages that Longitude 57 57037 deg Heading 103 23981 deg
60. constraint functions The color scale is displayed to the right of the mosaic The Color Code mode is the only mode where the absolute values of the changes in the scaled objective and constraint functions are indicated The ideal range for a scaled function s change on a given iteration lies between 1 2 and 2 indicated by the green color in the Color Code mode However this ideal is usually not attained by more than a fraction of the changes In some cases all of the scaled functions may be insensitive to the perturbation of a particular variable at least in the vicinity of the solution However it is not always advisable to increase the magnitude of such a perturbation When deciding whether to increase the magnitude of a perturbation you should remember that the limit on the variable s change on any given iteration is the product of the 87 28 EFFECTS perturbation value and the box size And you should remember that the magnitude of a stage dependent perturbation will apply to all of the tandem stages The mosaic s Color Code mode can be used to identify variable perturbations with magnitudes too large or small so that these perturbations can be adjusted before ReZOOMing in an attempt to achieve a quasi optimum solution or improve on a solution already obtained MOSAIC GRAY SCALE DISPLAY MODES The other three display modes which use gray scales display normalized brightness to indicate the relative magnitudes of the c
61. de any adjunct inert mass or payload lengths Propellant Bulk Density is the average density of the rocket stage s propellants It can affect the stage diameter when the aspect ratio sizing option is chosen and thus possibly affect the aerodynamic force on the stage Otherwise Propellant Bulk Density only affects the stage length in the rocket drawing Density of Primary Inert Mass is the average density of the stage s primary inert mass It too can affect the stage diameter when the aspect ratio sizing option is chosen and thus possibly affect the aerodynamic force on the stage Otherwise Density of Primary Inert Mass only affects the stage length in the rocket drawing Density of Adjunct Inert Mass is the average density of the adjunct inert mass If the stage has no adjunct inert mass this factor will not appear in the stage sizing window For the top stage this factor always appears and is labeled Density of Payload Density of Adjunct Inert Mass only affects the stage length in the rocket drawing 67 21 STAGE SIZING FACTORS The stage being sized is colored normally in the accompanying rocket drawing The other rocket stages are colored light gray When you click the Update Stage button the rocket drawing is updated to reflect any changes you have made to the sizing factors Some parameters that are affected by the sizing factors are displayed in the Sizing Factors for Stage window These include the
62. delta velocities of all the rocket s tandem stages The Total ideal delta velocity is the gain in the rocket s inertial speed that would be obtained if there were no losses Return Gravity Loss Aerodynamic Loss Steering Loss and Thrust Loss are delta velocity losses due to gravity aerodynamics steering and thrust These losses are independently calculated by the numerical integration of their effects on the rocket s acceleration There is a more detailed discussion of the delta velocity losses in the Mission Synopsis section The rocket s Inertial Speed Gain is calculated by subtracting its final inertial speed from its inertial speed at launch all of these quantities have been rounded to the nearest whole 16 5 MISSION SUMMARY number for display If perfect accuracy were achieved in the computations of the rocket s motion and the various delta velocity losses the inertial speed gain would be exactly equal to the Total ideal delta velocity minus the losses The amount by which these quantities do not agree is displayed as the Computational Error In all observed cases thus far this error has been very small and therefore of no concern TANDEM STAGE SUMMARY Clicking one of the tandem stage buttons produces a window showing a data summary for that stage The mission subfolder s name is displayed in the window s top bar If the stage is the base stage of a mated group data associated with the grou
63. den and no constraint on the initial mass of the rocket In such a case depending on mission details the optimization procedure may continually reduce the first stage s core initial T W toward unity The combination of a very low T W e g 1 1 or less and the restrictive Normal G Limit e g 0 005 g can make the trajectory very sensitive to the slightest variation in the turn angles and angular rates of the stages that must ride the normal g limit As the program iterates the convergence may at first appear robust only to suddenly produce an aberrant trajectory thus ending the iterative procedure and displaying the message OPTIMIZATION FAILED Another difficulty may arise in certain circumstances when a strap on booster is attached Substantial nonlinear results of the variable perturbations may occur if the burnout times of the booster and a tandem stage nearly coincide This may result in erratic swings of the Composite Error during the iterative solution procedure One way to solve this problem is to fix the strap on booster s burn time and or the first tandem stage s core ideal delta velocity at values so that the burnout times are measurably different If the fixed values are appropriate the optimality of the solution should not be affected significantly In some Inject into Conic cases where the target orbit is only slightly eccentric and the argument of perigee is free there may be some convergence difficulty In s
64. ditable text box Only the core name can be edited The mission type and date prefix will remain unchanged Rename Mission Mission Type Intercept Spacecraft or RV Core Name Rendezvous in 200 x 400 Nmi Orbit Min Initial Mass Cancel OK RETURN A TRASHED MISSION TO THE DATA FOLDER 3 MISSION SELECTION Clicking the View TRASH button will display a list of all missions of the chosen type that are in the Trash folder LIE ix NOTE The Windows file management application e g Windows Explorer File Explorer etc can be used to move trashed missions from the TRASH Folder to the Windows Recycle Bin Trashed Missions of Type Intercept Spacecraft or RV Select a Trashed Mission to Restore to the DATA Folder i Return RESTORE Selected Mission MISSION DESCRIPTION Enter or Edit Mission Description 01150306 SLS2 maxPL stdET 5ssme SOB throtDown up 1ssme Mission Description Two LOX LH2 stages using SSME engines augmented with the SST s Strap On Boosters Ascent to 120 N Mi Circular Orbit Maximum Payload over 145 metric tons Unconstrained liftoff weight optimum approx 2396 metric tons LOX LH2 stage diameters equal to that of SST External Tank 8 415 m Propellant load of first stage 1082882 kg compared to the 735601 kg of the SST s standard external tank Propellant load of upper stage 143362 kg First stage modeled as three mated ZOOM stages ZOOM Stage 1 5 SS
65. dows will produce a display of any imposed in flight limits These limits apply to total angle of attack dynamic pressure aerodynamic normal g s axial g s and aerodynamic heating rate When the Show Limits button is clicked the button name will change to Hide Limits Clicking the Hide Limits button will remove the limits display from the plots PLOT SCALING Except for the ground track plots the ordinate label and units are displayed above the grid in the plot windows Scaling is indicated in the units notation For example km 10 means that a plotted value of 15 represents 150 km Ground Tracks Flight Time 405 sec LONGITUDE DEG 85 80 75 70 35 OB 51140607 Rendezvous 35 x 160 Nmi min flight time 2Stg SOB Lift Drag Model for St 30 25 LATITUDE DEG 20 oO Launch Site POST LAUNCH ANIMATED PLOTS The post launch Ground Track and Vertical Plane Trajectory plots are traced out over time i e animated with the time scale determined so that the traces are completed in a few seconds of real time For the Intercept Spacecraft or RV mission the post launch ground tracks and vertical plane trajectories of both the rocket blue and target red are traced Flight time is shown above the grid in the post launch Ground Track and Vertical Plane Trajectory plot windows VERTICAL PLANE TRAJECTORY PLOT The Vertical Plane
66. e The net thrust Thr of the tandem stage is calculated from the vacuum thrust Thrv atmospheric pressure Prs and area of the rocket nozzle s exit plane Ae Thr Thrv Prs Ae The nozzle s exit plane area is conceptualized as circular and is calculated from the Rocket Nozzle Exit Diameter CONSTRAINT ON PROPELLANT MASS The stage s propellant mass is determined by the core ideal delta velocity specific impulse and the rocket s core stage mass at the time of the stage s thrust initiation If the stage is not mated to the previous stage or if the stage is the base stage in a mated group an opt max fix button will be displayed By toggling this button you can impose an explicit constraint on the propellant mass If you toggle the button to MAXIMUM you can enter a maximum allowable value for the propellant mass If you toggle the button to EXACT you can enter a specific value If the stage is the base stage in a mated group a constraint on propellant mass will apply to the sum of propellant masses of all stages in the mated group The reason for this is that a mated group of stages is usually considered to be a single real stage The message Mated Group Total will be displayed under the specified propellant mass to emphasize this fact 48 16 CONFIGURE TANDEM STAGE During its optimization procedure the program will adjust the free variables so that any constraint imposed on propellant mass is satisfied
67. e and light brown colors represent the sky and ground EE s1150508 Rendezvous 120 N Hi 508 Lift Drag Aero amp AOA Limit for Stage 2 oix You can play back the entire flight or you can define a Flight Segment to be played back In either case you can select one READY TO PLAYBACK of four playback durations ee clock times 10 sec 20 sec aoe 40 sec or real time Depending 871 1901 193 on your selection and the length of the flight segment the playback can be fast motion slow motion or real time RANGE km 0 SPEED m s 0 FPA PIT The rocket s pitch angle PIT flight path angle FPA yaw 751 1 901 1105 angle YAW roll angle 751 1 901 1105 heading HED angle of attack AOA ground range RANGE oe speed and altitude ALT are ALT km continually updated during the playback All displayed Playback Duration Sec 10 40 Real Time Flight Segment 474 623 quantities are defined in the NED frame The roll angle is based on a yaw pitch roll Euler angle sequence The rocket drawing includes a tail and opposing wings so that the rocket s roll angle will be evident in the drawing When the roll angle is zero the tail points upward The roll angle is continually calculated to keep the rocket s relative velocity in the rocket s pitch plane which contains the drawn tail The tandem stage is drawn as two concentric circles the inner circle representing the periphery of the roc
68. e is Maximize Payload the payload mass will remain fixed at the value specified in the top stage s Configure Tandem Stage window OSCULATING ELEMENTS OF DESTINATION CONIC The conic to be achieved by the rocket is defined by osculating elements The size and shape of the conic are determined by the first two elements which must be specified and can be expressed in one of two forms 1 apogee and perigee altitudes or 2 semilatus rectum and eccentricity The SLR Ecc and Apo Per buttons toggle between these two element sets The Semilatus Rectum Eccentricity set is the more general of the two and can be used for elliptical parabolic or hyperbolic conics The Apogee Altitude Perigee Altitude set can only be used for elliptical conics The apogee and perigee altitudes are referenced to the central 24 7 MISSION DEFINITION Inject into Conic body s equatorial radius It is important to remember than these conic elements are osculating elements and not mean elements By clicking the FREE SET toggle buttons the destination conic s inclination and or right ascension i e right ascension of the conic s ascending node can be specified SET or left FREE for the program to optimize The argument of perigee s FREE SET TIED toggle button has a third state TIED which constrains the injection to occur at perigee and thus ties the argument of perigee to that constraint This third option is useful in cases where
69. e maximum aerodynamic heating rate that the rocket is allowed to experience during the flight The FREE SET button toggles between a FREE unconstrained condition and a maximum limit SET If the maximum limit is chosen a box is provided for entry of the maximum allowable aerodynamic heating rate The aerodynamic heating rate expressed as BTU s or kW is numerically integrated over the rocket s flight to produce the aerodynamic heat load expressed as BTU or kJ Minimization of this heat load Minimize Aero Heating is a mission objective option for all three mission types The aerodynamic heating rate model is a simple one that can be an adequate approximation for several kinds of aerodynamic heating depending on the values specified for the model s parameters Clicking the MODEL button produces a window where values for the model parameters can be specified The model is explained in the Aerodynamic Heating Rate Model section For some missions such as the atmospheric reentry of a spacecraft there may be several peaks in the aerodynamic heating rate during reentry The program identifies the time intervals in which significant peaks occur and the optimization algorithm imposes a separate constraint for each of these intervals The intervals are re defined on each iteration of the optimization procedure Only peak values that exceed 80 of the specified limit are considered This restriction is applied so that small peaks in the
70. e rocket s centerline and has a constant velocity equal to the rocket s initial velocity After the first stage rocket motor ignites at t 0 the rocket s axial acceleration will free it from the launch rail s lateral constraint when the rocket has traveled a distance relative to the rail equal to the specified Launch Rail Length 31 11 LAUNCH AND IN FLIGHT CONDITIONS LAUNCH POSITION The launch position of the rocket is defined by its Launch Latitude geodetic Launch Longitude and Launch Altitude above local sea level LAUNCH PARAMETERS THAT CAN BE OPTIMIZED For some missions you will want to click the Vary radio button that allows the program to vary the launch GMT from its specified initial value as the program seeks the quasi optinum solution You may also want to click one or both of the Vary radio buttons that allow the launch azimuth and elevation to be varied from their specified initial values If the launch GMT is not varied it may be difficult for the program to achieve a solution for an Intercept Spacecraft or RV mission or for one of the other two mission types if the Right Ascension of the destination orbit is fixed for the Achieve Specified State mission this constraint only applies when the Inertial reference frame is chosen If you have fixed the Launch GMT for an Intercept Spacecraft or RV mission or if you have fixed both the Launch GMT and the Right Asce
71. e will lag the command as governed by the time constant The fixed yaw and pitch steering command goes into effect at the start of the stage unless the rocket is still on the launch rail In that case the command goes into effect the instant the rocket leaves the launch rail With fixed yaw and pitch steering no limit on aerodynamic normal g s can be imposed so any aerodynamic normal g s that may occur must be accepted 52 16 CONFIGURE TANDEM STAGE NORMAL G LIMIT Normal G Limit is a constraint on the rocket s aerodynamic normal acceleration expressed in g s One g equals 9 80665 m s 2 This constraint only applies when the bi linear tangent steering option is chosen By toggling the Free Set button you may either leave this acceleration unconstrained Free or set a limit on it There are two methods of imposing the limit 1 If the Ride Normal G Limit box is not checked the rocket s steering is determined at all times by the bi linear tangent steering formula The normal g limit is treated as an inequality constraint by the optimizer and during its iterations the program adjusts the steering parameters so that the maximum normal acceleration does not exceed the specified Normal G Limit if this is possible 2 If the Ride Normal G Limit box is checked and the normal acceleration reaches the Normal G Limit the rocket s steering command is continually adjusted so that the rocket rides t
72. ection on Central 1 GMT Year Perigee Altitude km 222 237645 SLR Ecc Body Model Month Apogee Altitude km Day Inclination deg 28 36496 If only small adjustments are Hour Right Ascension deg 21 50854 made to the central body s Minute Arg of Perigee deg rotation gravity and or Sarona True Anomaly deg 115 26582 dimension parameters the model will be labeled Earth Target Ballistic Coefficient kg m 2 Modified If any of these parameters are changed List Mission Conditions Stack Countdown significantly or if the 1962 earth standard atmospheric model is replaced by an exponential atmospheric model the Central Body Model will be labeled User Defined RENDEZVOUS OR IMPACT The kind of intercept must be specified either a rendezvous or an impact A rendezvous requires that the rocket match the spacecraft s or RV s position and velocity at the final time An impact requires only a position match at the final time The desired kind of intercept can be specified by clicking the Change to IMPACT or Change to RENDEZVOUS button causing the designation IMPACT or RENDEZVOUS to be displayed CHOOSE THE MISSION OBJECTIVE With the RENDEZVOUS option there are five choices for the mission objective With the IMPACT option there are two additional choices for mission objective Maximize Closing Speed and Minimize Closing Speed Unless the objective is Maximize Payload the payload 21 6 MISSI
73. ed as functions of the normal and axial force coefficients Cn and Ca aerodynamic reference area Aref and dynamic pressure qBar Fn qBar Aref Cn Fa qBar Aref Ca Aref is calculated from the reference diameter refdia Aref 0 25 pi refdia 2 Dynamic pressure qBar is calculated from the air density rho and the rocket s speed w r t the air vrel qBar 0 5 rho vrel 2 Cn is proportional to the angle of attack alpha Cn Cna alpha where Cna is a function of Mach number There are two Ca coefficients Ca on the power on coefficient which applies when the rocket motor is thrusting and Ca off the power off coefficient which applies when the rocket is coasting Both Ca coefficients are functions of Mach number xj The normal axial aerodynamic data are initially displayed in graphical Aerodynamic Data for Stage 1 Points 18 update _TABLES form At the top right of the graphical display window is a TABLES button which changes the display to a tabular form At the top of the tabular display window is a PLOTS button which toggles back to the graphical display You can create or modify the aerodynamic data in either window All three aerodynamic coefficients are functions of the same Mach number sequence The Ca on plot is colored red the Ca off plot blue and the Cna plot black POINTS You can vary the number of plotted or tabled points by specifying a va
74. ed by a six digit yymmdd mission creation date automatically assigned by the program The six digit date is followed by a space and then by the mission s core name that you supply When the DATA folder is opened via the operating system s file management application the mission subfolder names look like these examples ES120824 One Stg Max Speed to Given FPA and Altitude 01120621 Three Stg 100 x 600 Nmi Thrust Profile for All Stages S1120622 Rendezvous in Sun Sync Orbit Min Initial Mass When mission subfolder names are listed in the Mission Selection window the two letter prefixes are not shown and the dates appear as suffixes of the form 14Apr09 Each mission s data files are stored in its mission subfolder You have access via the Data Files button in the Mission Synopsis window to view the essential data in these files INPUT DATA FILES Each mission regardless of type always has the following eight input data files earth dat parameters of the central body mDescrip dat a user supplied descriptive narrative mission dat rocket dat wind dat optimizer dat precision dat units dat 1 INTRODUCTION mission definition data file format of depends on the mission type rocket definition data characterization of the wind if any optimization control parameters computational precision control indicating either Metric or English units For each stage using the Lift Drag aerodyna
75. ed to have the same burn time or propellant mass CONSTRAINT VIOLATION INDICATIONS If a scaled constraint is not satisfied within the error tolerance Solution Error Tolerance in the Optimizer Parameters window one or more asterisks will appear beside its name The number of asterisks indicates the magnitude of the error greater than tolerance TN greater than 10 x tolerance greater than 100 x tolerance greater than 1000 x tolerance CHANGE HISTORIES OF THE VARIABLES On each iteration the maximum amount that the optimization procedure can change a variable is equal to that variable s perturbation magnitude multiplied by the box size refer to the Optimizer Parameters section The perturbation magnitude should not be Change 0 0084625 75 of Allowed Value 1 520474 great enough to allow an unreasonably TUE TSEC DEE eae IE u Erta Tee large change in the variable on a single iteration Clicking a variable s button in the Effects window displays a plot of the variable s change history during the iterative solution procedure O1 The variable s change on each iteration is plotted against the iteration number Upper and lower boundaries on the change are indicated by light gray lines on the plot These boundaries are defined by the box size which is adjusted by the optimization algorithm during the iterative procedure The variable s total change is shown at the top of the plot W MANAA
76. efault parameter values for the Central Body Model rotation rate gravitation and dimensions are those of Units Expressed in this Window are Always Metric a typical earth model a 1 close approximation of the DEFAULT parameters are BLACK Standard Earth Model WGS84 model Click the User edited parameters are RED g Edit Parameters button to edit any of these model Reference Julian date 2433282 5 parameters Click the Corresponding Greenwich hour angle rad 1 7466477 Restore Defaults button to Body s sidereal rotation rate rad sec 7 2921158553E 05 restore the default values Gravitational constant m 3 sec 2 398600441500000 i g i J2 zonal harmonic coefficient 1 082636E 03 The Reference Julian date J3 zonal harmonic coefficient 2 53240E 06 its Corresponding J4 zonal harmonic coefficient 1 61930E 06 Greenwich hour angle and the Body s sidereal rotation rate are used to calculate the Greenwich hour angle for any given Julian date The Reference Julian date default value 2433282 5 ATMOSPHERE Earth US Standard 1962 CHANGE to Exponential Model corresponds to 0 hours January 1 1950 RETURN The Greenwich hour angle is the angle in the central body s equatorial plane between the prime meridian and the vernal equinox The hour angle increases as the central body rotates The Body s sidereal rotation rate is the rate of change of the Greenwich hour angle Equatorial radius m 6378137 Po
77. equality constraint is exceeded such as maximum dynamic pressure or maximum propellant the excess is included in the Composite Error The Change in Performance is the percentage improvement in the mission objective since the start of the iterative optimization procedure A negative value indicates a percentage decline in the mission objective Iteration 40 Iteration 40 After the program has completed its iterations the Solution Window will be accessible until you click the ReZOOM button to return to the Mission Selection window Before that you can click the Summary Effects and Plots buttons to view the details of the mission solution You may wish to click the OPTIMIZE More button to initiate another optimization procedure and perhaps improve the performance further If you do click the OPTIMIZE More button a 77 26 SOLUTION WINDOW pop up window will afford you the option of adjusting Optimizer Parameters and or Precision and Output Parameters before the optimization procedure commences If you choose to adjust the optimizer parameters an EFFECTS button in the Optimizer Parameters window enables you to examine the effects of the various perturbations before deciding how to adjust the perturbation values When the optimization procedure is completed one of the following four messages will be displayed a QUASI OPTIMUM SOLUTION which is not always a guarantee that no further impro
78. er of the central body and an X axis that points in the direction of the vernal equinox The central body fixed ECF frame is related to the ECI frame by the Greenwich hour angle Wy The ECI frame is needed for Specify End State missions where the Inertial option is chosen The default parameter values from which the Greenwich hour angle is calculated are for the earth and are defined in the Central Body Model section of this manual Strictly speaking the ECI frame would be truly inertial only if the central body moved at constant velocity Centrifugal and coriolis accelerations due to curvature in the central body s path as well as any linear acceleration of the central body are assumed to be negligible and are not included in calculations of rocket and target motion 3 The terms vernal equinox Greenwich hour angle and prime meridian are usually associated with the earth However in this manual these terms can refer to an inertial vector angle and reference meridian in any central body s equatorial plane 4 Flight mechanics computations are performed in the NED reference frame which is fixed to the central body with origin at the rocket launch site Centrifugal and coriolis accelerations due to rotation of the central body about its spin axis are included in the calculations of rocket and target motions 92 APPENDIX B APPENDIX B PARAMETERS FOR SINGLE ENGINE EQUIVALENT ROCKET MOTOR The key para
79. f propellant adjunct inert mass and primary inert mass will determine the volumes that combined with the stage diameter will define the heights of the stage s primary inert mass propellant and adjunct inert mass in the rocket drawing Maximum Vacuum Thrust is one of three names that may be displayed in the stage summary display The other two alternatives are Constant Vacuum Thrust and Average Vacuum Thrust Maximum indicates that an optional normalized time varying thrust profile was NOT chosen for the stage but that the stage was allowed to throttle in finite steps Constant would likewise indicate that a normalized time varying profile was NOT chosen but it would also indicate that the stage was NOT allowed to throttle Average would indicate that a normalized time varying thrust profile WAS chosen Throttling of a time varying profile is not allowed If a limit constraint was placed on the vacuum thrust but the quasi optimum solution s value was less than the limit the designation Below Limit will be displayed If the solution s value equals the limit the designation On Limit will be displayed If an exact value was specified for the vacuum thrust the designation FIXED will be displayed If no constraint was placed on the vacuum thrust the designation free will be displayed Diameter of Nozzle Exit is the diameter of the rocket nozzle s exit plane The exit plane area calculated from this diameter is m
80. f the initial to average angular turn rates during the maneuver It is always a positive value The program limits the ratio to values between 0 01 and 100 to avoid excessively abrupt angular motion J In general the bi linear tangent i steering formula cannot produce a steering angle that is linear w r t 90 time The Initial Average Turn Rate that produces the most linear 40 steering angle w r t time is equal to a the sine of the turn angle divided by the turn angle expressed in radians Z ad For a turn angle of 60 degrees an O Initial Average Turn Rate of 0 827 E 20 produces the most linear steering 2 angle w r t time 10 0 0 50 100 150 200 TIME SEC Effect on Steering of Initial Average Turn Rate Example INERTIAL HOLD STEERING inertial hold steering keeps the rocket s attitude constant in an inertial frame This inertial attitude is determined by the Maneuver Plane Roll and Angle Step parameters these are the same two parameters that initialize the rocket s attitude when bi linear tangent steering is used Although these two parameters define an attitude change in the central body frame the resultant inertial attitude is the one that the rocket maintains The inertial attitude command goes into effect at the start of the stage unless the rocket is still on the launch rail In that case the command goes into effect the instant the rocket leaves the launch rail A non ze
81. ficient is a very large unrealistic value which will insure that there is no significant drag deceleration Reentry vehicles similar to the Apollo spacecraft tend to have ballistic coefficients in the range 250 500 kg m Calculation of Target Motion The target s motion is calculated by numerically integrating time derivatives of the target s state variables in the ECI frame using the same integration algorithm as that used for the rocket s motion a fixed step fourth order Runge Kutta algorithm with the Gill correction The time derivatives are functions of the accelerations due to gravity and to aerodynamic drag if significant The target s aerodynamic lift is assumed to be zero If the target conic s eccentricity is less than 0 9 and the aerodynamic drag on the target is negligible the numerical integration step size is fixed at 1 200 of the orbital period For more eccentric exo atmospheric conics the integration step size is fixed at 30 seconds These step sizes will produce very accurate target motion in the absence of significant aerodynamic drag When the target experiences significant aerodynamic drag the numerical integration step size is automatically reduced by an empirical algorithm to maintain accuracy 23 7 MISSION DEFINITION Inject into Conic 7 MISSION DEFINITION Inject into Conic The format of the Mission Definition window depends on the selected mission type Intercept Spacecr
82. found quasi optimum solutions for a wide variety of trajectory optimization problems The modeled rocket s tandem stages are defined by core ideal delta velocities propellant mass fractions and core thrust to weight ratios From these quantities ZOOM calculates the propellant loads inert masses and thrusts The rocket is treated as a point mass with three degrees of freedom The rocket is symmetric with respect to its pitch plane The rocket rolls automatically to keep its pitch plane in the plane defined by the rocket s relative velocity and longitudinal axis The rocket thrusts along its longitudinal axis so both the thrust and aerodynamic forces remain in the rocket s pitch plane for the duration of the flight You can opt to specify the thrusts and or propellant loads of one or more of the rocket s tandem stages or you can set maximum limits on the quantities The program treats these specifications as constraint equations or inequalities and satisfies them during its iterative optimization procedure The thrust and or burn time of a strap on booster can be fixed or optimized within maximum limits If the thrust and burn time are both optimized they can be optimized independently within the specified limits or their optimization can be constrained to keep the strap on booster s propellant at a specified value 1 The Simplex algorithm was created by George B Dantzig Ph D in the 1930 s to solve linear programming problems and ha
83. four messages will be displayed a QUASI OPTIMUM SOLUTION which is not always a guarantee that no further improvement in performance can be achieved b SOLUTION Satisfies Constraints which although not judged to be quasi optimum may sometimes be arbitrarily close to it c CONSTRAINTS ARE NOT SATISFIED which may sometimes occur for an acceptable trajectory one that just barely fails to satisfy all constraint error tolerances d OPTIMIZATION FAILED which means that no combination of free variable values can be found that satisfies all of the mission constraints 6 Unless the OPTIMIZATION FAILED message is displayed examine the solution results via the Summary Effects and Plots buttons When viewing the effects of the variable perturbations make a mental note of any needed adjustments to the perturbation values After returning to the Solution Window click the OPTIMIZE More button A pop up window will offer the option to adjust Optimizer Parameters and or Precision and Output Parameters before repeating the optimization procedure Whether or not you opt to adjust the parameters you will eventually click an OPTIMIZE button to repeat the optimization procedure Change in Performance 64 7 Repeat Step 6 until the Change in Performance 27 0 01 graph in the Solution Window shows no significant i increase in performance i e improvement of 0 objective during the optimiz
84. ft Aerodynamic Normal Lift Drag Ratio target s pre launch ground track Mach Number Axial Acceleration Wind Speed Aerodynamic Heating Rate is traced over an appropriate time interval which depends on the ne Te nee ons target s conic elements and the time interval between the epoch of the target conic and the launch GMT The symbol in the a plot s button title indicates that Target s Pre Launch Ground Track the plot is animated i e traced Orbital Period approx 102 min 13 sec out overa specific real time Time Period of Graph approx 306 min 41 sec 90 interval EE 51140607 Rendezvous in Sun Sync Orbit Min Initial Mass Also for the Intercept Spacecraft or RV mission only time histories of the target s post launch aerodynamic drag and speed are provided and the Altitudes plot shows the post launch altitude history for both the rocket and target All plotted altitudes are Latitude deg eee ee AM O ele 90 20 1150 altitudes above the ground track ee O Launch Site point on the central body s surface The color red is used for Maximum drag lt 10 micro G s 54 min before launch at 864 km altitude approx the target plots and blue is used 1 for the rocket plots Of the plots showing post launch results all except the Vertical Plane Trajectories and Ground Tracks are time histories 79 27 PLOT SELECTION 2 In Rocket Thrust plots the thrust Rocket
85. full 7 yout omz name No two missions can have the same full name but they can have the same core name Intercept Spacecraft or RV List Mission Conditions Stack Countdown If you attempt to give your new mission a core name already possessed by an existing mission of the same type and creation date you will be given the options to overwrite and replace the existing mission or to change the name of your new mission If your new core name matches the core name of an existing mission of the same type but with an earlier creation date you will be advised of this and given the option to use the name anyway or to change it The earlier mission will not be affected ENTER OR EDIT MISSION DESCRIPTION Clicking the Enter or Edit Mission Description button opens a window where you can view alter and or define a description of the mission The Mission Description can also be accessed and edited from the Mission Synopsis and Mission Selection windows More detail on the mission description is provided in the Mission Selection section 69 22 LAUNCH PREPARATION PREVIEW TRAJECTORY When you click the PREVIEW button the first guess trajectory will be generated and the Plot Selection window will appear so that you can view various plots that define the rocket performance and trajectory You return from viewing the plots to the Rocket Stage Stack window You can then navigate to view and adjust any of the
86. g burn times or propellant masses The same combination of stages cannot be constrained to have both matching burn times and matching propellant masses Burn time Match Constraint x Propellant Match Constraint 14 ROCKET STAGE STACK An unmated stage or a mated group of stages is an entity The rocket stage stack must have at least two entities for an inter stage constraint to be imposed Imposition of an inter stage constraint may prevent a feasible solution if the constrained stages core ideal delta velocities core initial thrust weight ratios or propellant masses are fixed 41 15 CONFIGURE STRAP ON BOOSTER 15 CONFIGURE STRAP ON BOOSTER The strap on booster if any is attached to the first real tandem stage an unmated tandem stage or a mated group of tandem stages is termed a real tandem stage Clicking the Configure Strap on Booster or Add Strap on Booster button in the Rocket Stage Stack window opens a window where the strap on booster SOB can be configured Average Vacuum Thrust kN Vacuum Thrust Limit kN Thrust Profile Burn Time sec Burn Time Limit sec Vacuum Specific Impulse sec Propellant Mass Fraction Propellant Density kg m 3 Inert Mass Density kg m 3 Height of Inert Mass Height of Propellant Total Booster Height Booster Propellant Load RETURN 23035 Configure Strap On Booster Single Motor Equivalent Vary 25000 VARIABLE Vary
87. ge Stack window is where you define the rocket configuration The stack can consist of as many as nine tandem stages plus a strap on booster that is attached to the first tandem stage or to a mated group that includes the first tandem stage Stages can be deleted from or inserted into the stack A stage s DE ZOOM Rocket Trajectory Optimization oj xi presence is indicated by its ESEESE Paaa Configure Tandem Stage Inject into Conic button Enumerate and Configure the Rocket Stages _ 62 5 m MATED STAGES Mated stages are indicated in the graphic by linkage lines and the label MATED Whether or not a stage is mated to the a stage above it is determined when you Configure Tandem Stage 4 Configure Tandem Stage 3 Insert Above on a configure that stage see Configure Tandem Stage 2 Insert Above the Confi gure Tandem Configure Tandem Stage 1 Insert Above Stage section Configure Strap On Booster DELETING OR INSERTING Inter Stage Constraints Bum Time Match _ Propellant Match A TANDEM STAGE A tandem stage is deleted List Mission Conditions stack Countdown by clicking the Delete button to the right of the ___ _ _e C _ _e_C _rkr er _ stage s Configure Tandem Stage button Any stages above the deleted stage will drop to close the gap and will be renumbered A tandem stage is inserted by clicking the Insert Above button to the right of the
88. hanges The three gray scale modes differ in the method of normalization In the Normalize Cells mode the greatest change in the entire mosaic of changes has the maximum brightness and the brightnesses of all other cells in the mosaic are scaled according to how their changes compare to the greatest change In the Normalize Columns mode the greatest change in each mosaic column has the maximum brightness and the brightnesses of all other cells in the column are scaled according to how their changes compare to the greatest change in that column Of the three gray scale modes the Normalize Columns mode is probably the most useful indicating which variable has the greatest effect on each function In the Normalize Rows mode the greatest change in each mosaic row has the maximum brightness and the brightnesses of all other cells in the row are scaled according to how their changes compare to the greatest change in that row There are two brightness scales for the gray scale modes Linear and Log Base 10 The Toggle Scale button allows you to toggle between these two scales The Log Base 10 scale accentuates the smaller changes many of which may be invisible with the Linear scale DISPLAYING THE EFFECTS OF A LARGE NUMBER OF VARIABLES If the computer screen doesn t have enough vertical pixels to support the display of all rows in the Effects mosaic some of the variable perturbation effects cannot be displayed initially
89. he limit to attain your specified value When the optimizer iterations are complete a pop up window will inform you if the number of iterations was insufficient If you then choose to Optimize More the program will continue to adjust the Normal G Limit toward your specified value as it continues its iterations However if you ReZOOM or QUIT the program then the normal g limit that was imposed by the optimization procedure on its final iteration will be recorded as the Normal G Limit for your mission AXIAL G LIMIT Axial G Limit is a constraint on the rocket s sensible axial acceleration along the rocket s centerline This axial acceleration is caused by the rocket s propulsive thrust and by the aerodynamic axial force a negative value By toggling the Free Set button you can either 53 16 CONFIGURE TANDEM STAGE place no constraint on the axial g s or you can specify a maximum limit If you specify a limit for a case where the thrust is not a time varying profile you can also specify a Throttle Fraction and a Times that the rocket engine can be step throttled when the maximum limit on axial acceleration is reached The Axial G Limit is not relevant for an unpropelled stage Throttle Fraction is the vacuum thrust reduction expressed as a fraction of the maximum vacuum thrust making it easy to simulate the shutting down of one or more identical parallel rocket engines when the axial acceleration limi
90. he SOB s sea level thrust on earth is 85 of its vacuum thrust However the calculated nozzle exit diameter will not be allowed to exceed to 95 of the SOB diameter SOB DIAMETER An option to specify FIX the SOB s Diameter Booster Diameter or let the program automatically AUTO estimate the diameter is provided by an AUTO FIX button With the automatic estimation option the program will calculate an SOB diameter consistent with an aspect ratio height diameter of 6 4 an arbitrary but realistic value AERODYNAMIC EFFECTS OF THE STRAP ON BOOSTER There is no provision for modeling the SOB aerodynamics directly The aerodynamic effects of the SOB must be incorporated into the aerodynamic characteristics of the tandem stage s comprising the rocket s first real tandem stage If the SOB is discarded before the end of the first real tandem stage there is no provision for directly modeling the effect on the aerodynamics However if the first real stage is configured as a mated group the end of one of the mated stages could be made to virtually coincide with the burnout and discarding of the SOB Since the aerodynamics of each stage in the mated group are independently modeled the effect on aerodynamics of the discarding of the SOB could thus be closely approximated 43 15 CONFIGURE STRAP ON BOOSTER In most cases the dynamic pressure when an SOB is discarded is relatively small and neglecting to adjust the aerodynamic mode
91. he accuracy of the integration depends Time to Start Output sec P on the Numerical Integration Step Sizes Time to End Output sec chosen for the stages burn and coast periods Default values of 2 seconds for burn and 8 seconds for coast will be sufficient for many cases and can be RETURN increased in some cases without significant loss of accuracy However integration step sizes that are too large are probably the most common reason for bad results in rocket trajectory computations and for many missions smaller step sizes will be needed For a given mission you may want to experiment in order to determine step sizes that are sufficiently small for accuracy but not unnecessarily small so as to substantially increase computation time Integration Steps Between Records The program checks the step sizes for the tandem stage burn periods and warns you if a specified step size is too large for high accuracy considering the rocket thrust acceleration When the rocket is coasting and diving at high speed in the atmosphere the program will automatically reduce the integration step size if necessary to prevent integration instability For the more ordinary coast periods there is no check on the integration step sizes you specify for the Coast periods DATA OUTPUT CONTROLS You can specify the interval within which output is to be recorded and you can specify the number of integration steps between output records The default v
92. he limit until the unadjusted steering command does not cause a violation of the limit In this way the limit is implicitly satisfied and an inequality constraint is not required by the optimizer If the Time Constant is non zero the rocket can only approximately ride the normal g limit Also if a stage s aerodynamic model is Lift Drag and if the clO parameter is nonzero it may not be possible to satisfy the normal g constraint because the total angle of attack cannot be negative In such a case the rocket s steering will be adjusted to obtain the total angle of attack that produces the minimum possible normal aerodynamic acceleration The Ride Normal G Limit option is often preferred It produces no additional inequality constraints for the optimizer and in most cases it will produce a more optimal result However even a small change in the limit will usually produce a big change in the trajectory In order to prevent a solution failure due to the strong effect of a newly imposed ridden normal g limit the optimizer will incrementally apply your specified limit if the template mission s achieved maximum normal g for the stage is greater than your specified limit The initially imposed limit will equal the maximum normal g achieved by the template mission On each optimizer iteration the imposed limit will be reduced by no more than 1 and you must specify a sufficient number of iterations in the Optimizer Parameters window for t
93. ia 2 Dynamic pressure qBar is calculated from the air density rho and the rocket s speed w r t the air vrel qBar 0 5 rho vrel 2 The lift coefficient is a function of total angle of attack alpha Cl clO clalpha alpha where the parameters cl0 and clalpha are tabled as functions of Mach number and optionally altitude Because the total angle of attack alpha can never be negative it may sometimes be impossible to satisfy a constraint on normal aerodynamic acceleration when clO is nonzero In such a case where the option to ride the constraint boundary has been chosen the rocket s steering will be adjusted to obtain the total angle of attack that produces the minimum possible normal aerodynamic acceleration The drag coefficient is modeled as a quadratic function of the angle of attack variation from its minimum drag value alphamd Cd cdmin k clalpha alpha alphamd 2 where the minimum drag values of cd and alpha cdmin and alphamd and the drag due to lift parameter k are tabled as functions of Mach number and optionally altitude There are actually two different cdmin tables one for the power on thrust condition and the other for the power off coast condition The two different cdmin s are named cdmin on and cdmin off The tabular lift drag data are contained in an aerodynamic data file that has been assigned to the stage CREATING MODIFYING AND USING THE LIFT DRAG DATA FILE
94. include unburned propellant NOTE A tandem stage can have a coast period after its burn If a tandem stage s coast period is not zero the stage ends when its coast period ends Otherwise the stage ends when its rocket motor burns out 42 15 CONFIGURE STRAP ON BOOSTER OPTIMIZING THE THRUST AND OR BURN TIME By clicking the appropriate Vary radio buttons you can opt to let the program vary the SOB s Average Vacuum Thrust as constrained by the Vacuum Thrust Limit and or vary the Burn Time as constrained by the Burn Time Limit Limits on SOB thrust and burn time are implicitly enforced so that explicit inequality constraints for the optimization algorithm are not needed TIME VARYING THRUST PROFILE Clicking the Thrust Profile button opens a window where you can define a normalized vacuum thrust profile for the SOB This process is described in the Normalized Thrust Profile section If a time varying profile is specified the word VARIABLE will appear beside the Thrust Profile button If a constant vacuum thrust is specified the word CONSTANT will appear beside the Thrust Profile button ROCKET NOZZLE EXIT DIAMETER An option to specify FIX the SOB s rocket nozzle exit diameter Nozzle Exit Dia or let the program automatically AUTO estimate the diameter is provided by an AUTO FIX button If the automatic estimation option is chosen the program will calculate a nozzle exit diameter such that t
95. is the rocket s speed relative to the air For some missions there may be more than one peak in the dynamic pressure The program identifies the time intervals in which significant peaks occur and the optimization algorithm imposes a separate constraint for each of these intervals The intervals are re defined on each iteration of the optimization procedure Only peak values that exceed 80 of the specified limit are considered This restriction is applied so that small peaks in the dynamic pressure do not result in the imposition of unnecessary constraints The dynamic pressure at the final time will also produce a constraint if the value is more than 80 of the specified limit If the dynamic pressure at the start of the trajectory exceeds the specified limit a pop up window informs you that the specified limit should be increased MINIMUM ALTITUDE Minimum Altitude is the minimum altitude allowed AFTER the rocket has once begun to descend The FREE SET button toggles between a FREE unconstrained condition and a minimum limit SET If the minimum limit option is chosen a box is provided for entry of the minimum allowable altitude The minimum altitude constraint can be helpful in cases where the rocket would otherwise dip too far into the atmosphere and experience aerodynamic forces of such magnitude as to prevent a solution 33 11 LAUNCH AND IN FLIGHT CONDITIONS MAXIMUM AERODYNAMIC HEATING RATE Maximum Aero Heat Rate is th
96. ise constant vacuum thrust if step throttled If the stage has a time varying vacuum thrust profile the ratio of average thrust to initial weight Core Avg Thrust Init Weight 46 16 CONFIGURE TANDEM STAGE Ratio is specified In either case the weight term is the total weight of all inflight tandem stages the weight of a strap on booster is not included in this total The thrust value in the ratio is the stage s net thrust equal to the vacuum thrust minus the product of atmospheric pressure and rocket nozzle exit plane area The program uses the initial thrust to weight ratio to calculate the stage s vacuum thrust and propellant mass flow rate which is equal to the vacuum thrust divided by the vacuum exhaust velocity which itself is the product of the Vacuum Specific Impulse and the mass to force conversion factor gO 9 80665 m s 2 in Metric units VACUUM SPECIFIC IMPULSE Vacuum Specific Impulse Isp is the constant ratio of the stage s vacuum thrust to the propellant weight flow rate It has the dimension of time and is expressed in seconds The payload delivery capability of the rocket is sensitive to this parameter The stage s propellant mass mProp is calculated from this parameter and the Core Ideal Delta Velocity deltav mProp m0 1 exp deltav gO Isp where mO is the total mass of the rocket s inflight tandem stages at the beginning of the stage and gO is the mass to force conve
97. ket nozzle When the rocket is thrusting the area of the inner circle is red in color Otherwise this area is light gray The stage number is displayed in the center of the circle If a single engine equivalent strap on booster is attached it is drawn as two boosters attached on opposite sides of the tandem stage Each booster is depicted by two concentric 83 27 PLOT SELECTION circles the inner circle representing the periphery of the booster s rocket nozzle A strap on booster is always thrusting while attached so the boosters inner circle areas are always red The strap on boosters disappear instantly when they burn out Any significant aerodynamic force on the rocket is depicted by a red aura that surrounds the tandem stage The diameter of this circular aura indicates the magnitude of the acceleration caused by the aerodynamic force If all of the aerodynamic force is drag the circular aura is centered about the rocket s long axis If there is significant aerodynamic lift the aura is displaced toward the center of aerodynamic pressure on the tandem stage s surface The amount of this displacement is proportional to the lift drag ratio but is limited so that the outer boundary of the aura does not intrude into the tandem stage The center of pressure will always be opposite the drawn tail on the rocket s body At the drawing s ground sky interface horizon are bumps or hills that move horizontally when the rocket is yawing The
98. l for this situation may not significantly affect the rocket s performance STRAP ON BOOSTER DRAWING In the drawing of a rocket with an SOB two individual strap on motors are always shown The scaled diameters of these two individual motors are each equal to the single motor equivalent s Booster Diameter divided by the square root of 2 UPDATE THE SOB DRAWING AND DATA Clicking the Update SOB button will cause the program to update the SOB drawing as well as the dependent data displayed toward the bottom of the Configure Strap On Booster window The displayed dependent data include Height of Inert Mass Height of Propellant Total Booster Height and Booster Propellant Load CONSTRAINING THE BOOSTER S PROPELLANT MASS When you return from the Configure Strap On Booster window and you have opted to vary both the SOB s Average Vacuum Thrust and Burn Time a pop up window will offer you the option of keeping the SOB propellant mass at its current value BE Ganson ance Genel propellant mass at its current value You have chosen to optimize the strap on booster s variations in average vacuum thrust vacuum thrust and burn time The current value for and burn time will be coordinated the booster s propellant mass is 1082771 824 kg during the program s optimization procedure so that the SOB propellant r Keep this propellant mass at its current value mass remains constant If you do not check the box the program
99. lar radius m 6356752 Restore Defaults EDIT Parameters In ZOOM this sidereal rotation rate is also used to calculate the rocket s coriolis and centrifugal accelerations in the central body s rotating coordinate system This use of the sidereal rotation rate is acceptable because the vernal equinox is very nearly an inertial reference direction For the earth the difference between the sidereal rotation rate and the inertial rotation rate is less than 1 x 10 rad sec The parameters defining the central body s gravity model and dimensions are always displayed in Metric units in the Central Body Model window Gravitational acceleration is calculated using the same equations as those presented in Orbital Mechanics with Matlab a section of the Matlab Programmer s toolbox DEFAULT ATMOSPHERIC MODEL The default atmospheric model is derived from the reference U S Standard Atmosphere 1962 National Aeronautics and Space Administration United States Air Force United States Weather Bureau December 1962 Washington D C 28 9 CENTRAL BODY MODEL The default model defines the atmospheric pressure and density up to a geopotential altitude of 700 km Below 90 km the molecular scale temperature expressed as a piecewise linear function of geopotential altitude is used to calculate the atmospheric pressure density and speed of sound The 1962 standard doesn t define the speed of sound for geopotential altitudes above 90 km
100. le you are presented with the option to give the edited file a unique name and copy it to the Aerodynamic File Library 62 19 LIFT DRAG AERODYNAMIC FORCE MODEL Save to Aerodynamic File Library 3 If the edited LD file is to be copied to the Aerodynamic File Library a unique file name must first be provided in the text box below Modify Template to Define File Name EXAMPLE LIFT DRAG AERODYNAMIC FILE RETURN Without Copying Copy Edited File to Aerodynamic File Library FORMAT OF THE LIFT DRAG DATA FILES Lift drag aerodynamic data files are plain text files A fixed width font should be used when creating lift drag files off line and the text editor s word wrap option should be disabled Each record line should be entered with the ENTER or RETURN key Each lift drag aerodynamic data file begins with an unformatted header section consisting of any number of lines This section can be used to explain the origin of the lift drag data and to define the nature of the aerodynamic configuration represented by the data The header s first line is the file s Descriptor and is an essential element in the file The Descriptor is displayed in the Aerodynamic Force Model window to identify the lift drag file that is assigned to the stage The Descriptor is used instead of the file name because the file name once the file is assigned is generic and conveys no information The starting point of the lift drag ae
101. llant mass fraction of the single engine equivalent is readily calculated from the inert mass fraction 1 A o l 4 The propellant bulk density of the single engine equivalent of n parallel rocket motors is 3 VAC i l Isp p ii VAC 5 py i 1P sp l It is seen in equation 5 that if all the parallel rocket motors have the same propellant bulk density then the single engine equivalent will also have that same propellant bulk density In order for the single engine equivalent to be a valid model the three parameters must maintain constant values and all of its inert mass must be discarded at the staging point When an axial acceleration limit is reached the thrust of the single engine equivalent will be throttled in accord with the specification of the throttle fraction and the number of times that throttling is allowed If the single engine equivalent represents parallel rocket motors having the same specific impulse propellant mass fraction and propellant bulk density the 94 APPENDIX B APPENDIX B CONTINUED throttling can validly simulate the shutdown of one or more engines a partial step throttling of one or more engines or the approximate continuous throttling of one or more engines If the parallel rocket motors are dissimilar throttling of the single engine equivalent can only represent a proportional throttling of all the engines whether step or approximately continuous This restric
102. lue Mach Number in the Points box and clicking the ws z update button The number of CNA ice o o 12 ice __ or E m f bina points cannot exceed 25 RETURN Restore Default Aero If the number of points is increased the new points are added at higher Mach numbers than the highest Mach 58 o 2 40 60 8 0 10 0 12 0 14 0 18 NORMAL AXIAL AERODYNAMIC FORCE MODEL number in the original data and the default values for the new points are equal to the original values at the original highest Mach number If the number of points is decreased from the original value the higher Mach number points will be deleted MODIFYING THE NORMAL AXIAL DATA On the tabular display the data are modified by entering the desired numbers in the appropriate boxes On the graphical display a curve is selected by clicking the appropriate button CA ON CA OFF or CNA The individual points on the selected curve are marked with small circles The default initial selection is the CA ON red curve the power on axial force coefficient To the right of the Mach Number axis label on the graphical display is a small toggle button that when clicked will toggle between VAR and FIX When VAR is selected both the value of the selected coefficient and its Mach number can be modified if the Mach number is modified the modification will affect the other two plots When FIX is selected only the coefficient value can be modified This
103. m 2 FREE SET M Ascent Minimum Altitude km FREE SET FREE kW FREE SET MODEL A wind profile has been defined Edit the wind profile List Mission conditions Stack Maximum Aero Heat Rate i Countdown DE Z00M Rocket Trajectory Optimization iol x seston Launch and In Flight Conditions _ourr LAUNCH WINDOW OPTION For an Intercept Spacecraft or RV mission only there is an optional provision to let the program estimate the best Launch GMT and Launch Azimuth to achieve the intercept You exercise this option by clicking the Change to Launch Window Estimation of Launch GMT and Azimuth button which only appears in the Launch and In Flight Conditions window for an Intercept Spacecraft or RV mission This option is discussed in detail in a following paragraph LAUNCH ATTITUDE AND VELOCITY The rocket s attitude and velocity at launch are expressed in the central body fixed frame NED frame with origin at the launch site The attitude of the rocket s centerline is defined by a two angle Euler sequence a positive Launch Azimuth measured clockwise from true north looking from above in the horizontal plane followed by a positive Launch Elevation measured upward from the horizontal plane The Launch Speed of the rocket if any is in the direction of the rocket s centerline LAUNCH RAIL If there is a launch rail Launch Rail Length gt 0 it is aligned with th
104. meter values constants for a single engine equivalent rocket motor can be calculated so as to represent a number of parallel burning individual rocket motors The key parameters are 1 vacuum specific impulse Isp 2 propellant mass fraction A and 3 propellant bulk density p The vacuum specific impulse of the single engine equivalent of n parallel rocket motors is n T i VAC Pnr 1 g VAC i l lsp Where the subscript i identifies an individual rocket motor and TVAC is the average vacuum l thrust of rocket motor i It is seen in equation 1 that if all the parallel rocket motors have the same specific impulse then the single engine equivalent will also have that same specific impulse It is convenient to convert the propellant mass fractions 4 into what are called inert mass fractions Oe J 1 J Bs l cae 2 l NOTE If the vacuum thrusts of the individual rocket motors are time varying the motors must have identical normalized vacuum thrust profiles in order to be represented by a single engine equivalent 93 APPENDIX B APPENDIX B CONTINUED The inert mass fraction of the single engine equivalent can then be calculated as a SIT IA VAG It is seen in equation 3 that if all the parallel rocket motors have the same inert mass fraction and the same specific impulse then the single engine equivalent will also have that same inert mass fraction The prope
105. mic force model the mission subfolder also includes a Lift Drag file with a generic name e g LDfile_1 dat LDfile_2 dat etc OUTPUT DATA FILES Each mission s output data files are contained in an output subfolder within the mission subfolder All missions have the following twelve output data files summary dat outputO dat outputi1 dat output2 dat output3 dat output4 dat rocket conic dat essential data describing the solution format depends on mission type event timeline and other data time histories of rocket trajectory variables in a central body fixed frame primarily time histories of forces accelerations propellant remaining dynamic pressure and Mach number time histories of gravitational acceleration in both the ECF and NED frames atmospheric density pressure and sound speed Mach number redundant and wind speed primarily time histories of the rocket s position and velocity components in the NED frame and of the acceleration coriolis and centrifugal due to the frame s angular velocity also expressed in the NED frame the epoch osculating elements and orbital period of the rocket s conic at burnout The orbital period in this file is that which would apply if the central body s atmosphere or surface were not encountered rocket states dat primarily time histories of the rocket s position and velocity components solution dat effects dat
106. mission The recommended procedure for creating a new mission is described in the Recommended Solution Procedure section Section 24 CONTENTS OF THE ZOOM PROGRAM DIRECTORY All files needed for the operation of ZOOM are in the ZOOM Program Directory which contains the folders Aerodynamic File Library DATA Help and Trash and the files salflibc dll and ZOOM exe the program executable file The default salflibc dll file is intended for use with Windows operating systems newer than Windows XP For Windows XP and earlier operating systems this file should be replaced with the salflibc dll file in the DLL XP folder that is included in the ZOOM Folder The Aerodynamic File Library folder contains any Lift Drag aerodynamic data files which have been created off line or which have been named and copied to the folder using the GUI Normal Axial aerodynamic data are included in the rocket dat files in the mission 1 INTRODUCTION subfolders Each mission uses one of the two kinds of aerodynamic models Normal Axial the default linear model or Lift Drag a higher fidelity model The DATA folder contains the mission subfolders for all missions that have been defined and solved The folder also contains two small files 1 bkgrndColors dat which defines the two window background colors that distinguish missions having Metric and English units and 2 unitsOut_default dat which identifies the unit
107. mission and rocket data and repeat the preview This iterative preview adjust method is handy for insuring that the initial trajectory in the optimization procedure is a reasonable one NOTE When the PREVIEW button is clicked a new mission folder is created and you will not be allowed to navigate all the way back to the Mission Selection Window FLY OUT OR OPTIMIZE When you click the Fly Out or OPTIMIZE button The Solution Window appears the new mission is calculated and mission output data are recorded in the mission subfolder The Fly Out button generates the nominal trajectory i e first guess trajectory and the neighboring trajectories that result from individual perturbations of the free variables From these trajectories the effects of the variable perturbations on the objective and constraint functions are defined The first guess trajectory is the same trajectory that was generated by the last preview if there was a preview When you click the OPTIMIZE button the program varies the free variables in an iterative optimization procedure generating a series of nominal trajectories iterations until the procedure succeeds or fails to obtain a quasi optimum solution for the new mission 70 23 OPTIMIZER PARAMETERS Any time before you click the Fly Out or OPTIMIZE button you can view and change the Optimizer Parameters by clicking the Optimizer Parameters button These parameters include Num
108. mum range etc and you will be able to define your mission constraints INFO buttons appear in many of the GUI windows These buttons display the text of the relevant section in the User Manual and thus provide contextual help information Click the COLORS button to choose window background colors You can pick different background colors for missions based on Metric and English units to help distinguish them The COLORS button only appears in this window Click the QUIT button to immediately quit and close the program This button also appears in several other windows Click the Developer s Statement button for a link to the developer s website and for the developer s email address Links are also provided for three Children s hospitals and a suggestion is made for donations to one of these or to a charity of your choice There is no obligation to donate however The ZOOM program is available for you to use as you please free of charge GB Z00M Rocket Trajectory Optimization 3 MISSION SELECTION Mission Selection Mission Type Intercept Spacecraft or RV Select an archived mission to examine or to use as a template for a new mission Chronological List Newest First Change to Alphabetical List Mission from Scratch Rendezvous 120 N Mi SOB Lift Drag Aero amp AOA Limit for Stage 2 13Mar15 Impact RV at Low Altitude Minimum Closing Speed 12Mar15 Rendezvous in Sun Sync Orbit Min Initial Mas
109. n This mission data will now have been saved in a mission subfolder in the DATA folder 4 In the Solution Window click the Effects button to see the effects of the variable perturbations on the scaled objective and constraint functions The magnitudes of these effects will indicate whether some of the perturbation values should perhaps be increased or decreased 5 Return to the Solution Window and click the OPTIMIZE button A pop up window will offer the option to adjust Optimizer Parameters and or Precision and Output Parameters If in Step 4 you determined that some perturbation values need adjustment click the Adjust Parameters button in the pop up window to open the Optimizer Parameters window In this presentation of the window there is an EFFECTS button which allows you to look again at the mosaic of the perturbation effects You can open and return from the Effects window as many times as necessary as you adjust perturbation values that produced unusually large or 74 25 RECOMMENDED SOLUTION PROCEDURE small effects When you finish the adjustments if any click either the Adjust Precision and Output Parameters button to adjust those parameters or click the OPTIMIZE button to initiate the iterative optimization procedure If you decided to adjust Precision and Output Parameters you can then click the OPTIMIZE button in that window When the optimization procedure is completed one of the following
110. n and coast periods the maneuver plane can be visualized as translating with the rocket its orientation fixed with respect to the central body The rocket centerline remains in the maneuver plane unless the riding of a Normal G Limit requires it to leave the plane Angle Step is a discontinuity in the steering angle at the start of the maneuver It is symbolized by dThetaO in the bi linear tangent steering formula dTheta dThetaO atan bt 1 ct where dTheta is the angular change of the rocket centerline in the maneuver plane since the start of the maneuver and t is the time lapse since the start of the maneuver The constants b and c are calculated from the remaining two steering parameters and from the maneuver duration which is a function of various other conditions Turn Angle is the total angle to be turned by the rocket s centerline in the maneuver plane excluding the initial Angle Step It is the final value of the arc tangent term in the bi linear tangent steering formula Positive values of Turn Angle and Angle Step satisfy the vectorial right hand rule with respect to the maneuver plane s defining normal unit vector The specified value for Turn Angle must not exceed plus or minus 89 99999 deg The program 50 16 CONFIGURE TANDEM STAGE insures that these limits are observed in order to prevent discontinuities at plus or minus 90 degrees Initial Average Turn Rate is the ratio o
111. nct inert masses brown and payload brown A stage s primary inert mass is determined by the propellant mass fraction and propellant mass It does not include the fixed adjunct inert mass if any or payload i e the adjunct inert mass of the top stage Yellow connecting rectangles identify mated tandem stages The drawing s dimensions are determined by the propellant loads propellant bulk densities stage diameters primary inert mass densities and the masses and densities of adjunct inert masses and payload The drawing is scaled to a specific vertical dimension in the window and the height of the rocket is indicated The gray rectangle beside the rocket is an abstract depiction of a person six feet tall When there is a strap on booster single engine equivalent it is depicted in the drawing as two strap on rocket motors one on each side of the tandem stack The scaled diameter of each strap on motor is equal to the scaled diameter of the single engine equivalent strap on booster divided by the square root of 2 The height of the strap on motors is determined by this diameter and the strap on booster s burn time thrust vacuum specific impulse 10 4 MISSION SYNOPSIS propellant density and inert mass density The spaces occupied by each strap on motor s propellant and inert mass are indicated in the drawing by the colors red and gray respectively Not included in the drawing are important details such as interstage struct
112. ndividual tandem stages and strap on booster if any to the Total Ideal Deltav 11 4 MISSION SYNOPSIS DELTAV LOSSES The actual change in the rocket s inertial speed over the course of its flight is equal to the Total Ideal Deltav minus four deltav losses Gravity Loss Aerodynamic Loss Steering Loss and Thrust Loss Gravity Loss is the integration over time of the component of gravitational acceleration that is anti parallel to the rocket s inertial velocity Aerodynamic Loss is the integration over time of the component of aerodynamic acceleration that is anti parallel to the rocket s inertial velocity Steering Loss is the integration over time of the difference between the total vacuum thrust acceleration and the component of vacuum thrust acceleration that is parallel to the rocket s inertial velocity This loss occurs because the thrust vector rocket centerline is not generally aligned with the inertial velocity and therefore has a component that does not contribute to an increase in inertial speed Thrust Loss is caused by atmospheric pressure at the rocket nozzles exit planes which reduces the thrust from its ideal value in a vacuum The product of atmospheric pressure and total rocket nozzle exit plane area divided by the rocket s mass can be thought of as an acceleration that is anti parallel to the rocket centerline The integration over time of the component of this acceleration that is a
113. nsion for one of the other mission types a warning window will pop up and you will be given the opportunity to vary the Launch GMT or to free up the Right Ascension if you so desire PROGRAM ESTIMATION OF LAUNCH GMT AND AZIMUTH For an Intercept Spacecraft or RV mission only clicking the Change to Launch Window Estimation of Launch GMT and Azimuth button opens a window where you can define a launch window and constrain the intercept geometry ix The program estimates the rocket s launch time and launch azimuth based on the Define the Launch Window and Intercept Condition mission objective This option is usually essential for missions being defined from scratch You can yyyy mm dd hh mm revert to the manual GMT of Target Epoch 2010 4 5 0 11 specification of launch GMT The program will estimate the launch GMT and azimuth EE SEES k le Es and azimuth by clicking the 8 Change to User Launch Window Duration hrs Specification of Launch GMT I Intercept While Target is Ascending in Latitude oT Azimuth aoe Ang I Intercept While Target is Descending in Latitude wil appear in the Laune I No Constraint on Intercept Point and In Flight Conditions window when a launch window has been defined RETURN to Launch and In Flight Conditions The program s estimates of Launch GMT and Launch 32 11 LAUNCH AND IN FLIGHT CONDITIONS Azimuth are very helpful but are inaccurate and it will usu
114. nti parallel to the rocket s inertial velocity produces the thrust loss In some cases a gravitational or aerodynamic acceleration may have enough positive projection onto the rocket s inertial velocity to produce a velocity gain negative loss in that category INERTIAL SPEED GAIN AND COMPUTATIONAL ERROR The difference between the final and initial magnitudes of the rocket s inertial velocity is the Inertial Speed Gain and should be equal to the Total Ideal Deltav minus the deltav losses Because the numerical integrations to define rocket motion and to obtain the losses are not perfectly accurate there will be some error in this comparison This Computational Error should always be a very small fraction of the Total Ideal Deltav It is calculated when a solution is obtained and is recorded in the outputO dat file in the mission s output subfolder UNITS A toggle button provides the means for you to select either METRIC or ENGLISH units for the displayed data This capability to change the units is provided only in this window and in the Mission Selection window 12 4 MISSION SYNOPSIS MISSION DESCRIPTION Clicking the Mission Description button opens a window where you can view alter and or define a description of the mission The mission description can also be accessed and edited from the Mission Selection and Launch Preparation windows More detail on the mission description is provided in the Mi
115. ntral body S rotation gravity dimensions Reference Frame Central Body Fixed Change and atmosphere can be changed see the section on Central Desired End State Body Model s d FREE SET 7 ae If only small adjustments are Flight Path Angle FREE SET made to the central body s Heading FREE SET rotation gravity and or Altitude FREE SET dimension parameters the model will be labeled Earth Modified If any of these parameters are changed Longitude FREE SET significantly or if the 1962 earth standard atmospheric model is replaced by an exponential atmospheric model the Central Body Model will be labeled User Defined Ground Range FREE SET Latitude FREE SET List Mission Conditions Stack Countdown CHOOSE THE MISSION OBJECTIVE An Achieve Specified State mission affords you a wide selection of end states and mission objectives For example this mission type can be used to define performance envelopes of maneuvering surface to air missiles surface to surface ballistic missiles and unconventional rockets such as ramp launched lifting bodies Unless the objective is Maximize Payload the payload mass will remain fixed at the value specified in the top stage s Configure Tandem Stage window REFERENCE FRAME With an Achieve Specified State mission only you can choose to define certain conditions in one of two reference frames Central Body Fixed or Inertial The Change button toggles 26
116. objective is changed But on the optimizer s last 12 iterations if SIMPLEX continues to solve the linearized problem the box size is methodically reduced in steps toward the Minimum Box Size This programmed reduction in the box size is meant to reduce the solution s Composite Error so that it satisfies the Solution Error Tolerance 78 27 PLOT SELECTION The PLOT SELECTION window is displayed when the Plots button Animated plots are indicated by in the Mission Synopsis window or Solution Window is clicked or when a Preview trajectory is Target PRE Launch Flight generated Ground Track Altitude Aerodynamic Drag 1150508 Rendezvous 120 N Mi SOB Lift Drag Aero AOA Limit for Stage 2 For an Intercept Spacecraft or 1 H A Li Rocket and Target POST Launch Flight RV MISSION plots of the target S Speed Flight Path and Heading Angles are in Central Body Fixed frame pre la unch grou nd track a Ititude Target Aerodynamic Drag Target Speed an d ae rod yn am ic d ra g are provided For Achieve Specified Vertical Plane Trajectories Ground Tracks Altitudes State and Inject Into Conic missions these plots have no B eel eee meaning and therefore are not Yaw Pitch Roll Angle of Attack Dynamic Pressure provided Rocket Total Mass Thrusts Propellant Left in Tandem Stage When the pre launch Ground Track button is clicked the Aerodynamic Drag Aerodynamic Li
117. on for any one of several kinds of aerodynamic heating rates The aerodynamic heating rate model has three parameters convective at stagnation point all of which are constants Values of these parameters radiative etc is provided by the can be entered or edited in the text boxes below following equation which was taken The model description is provided by the INFO button from A Survey of Hypersonic Aerodynamics and Aero thermodynamics Scale Factor C Metric Units for Planetary Reentry Capsules by Sane annt Hs Chester Ong R D Braun and banian Taa S M Ruffin Georgia Institute of k e Technology AHR C rho N VAM Where rho is the local air density and V is the speed of the body with respect to the air The parameters in the equation scale factor C air density exponent N and speed exponent M are constants their values being determined by experimentation and or theoretical analysis Exponents N and M are dimensionless The dimensions of C depend on the values of M and N Units of the variables and default values of the parameters are given in the following table TAE English Metric AHR BTU s kW rho Ibm ft 3 kg m 3 V ft s m s C 5 9188 E 10 5 5100 E 9 N 0 5 0 5 M 3 0 3 0 The values in the table for C N and M are default values that produce a stagnation convective heating rate at hypersonic speeds for a space shuttle type reentry vehicle 38 14 ROCKET STAGE STACK The Rocket Sta
118. on name and type are Mission Synopsis i displayed near the top of the window followed by the mission SLS2 PL stdET 5 SOB throtD up 1 06Mar15 A A MAAE EA ESEE EA objective and its resultant value Mission Type Inject into Conic If the mission objective is Maximize Payload then the 1 1 H 1 Number of Iterations 40 Solution Error 1 5E 03 rocket S MAXIMAT payload and A quasi optimum solution was obtained Initial Mass values are displayed If the mission Total Ideal Deltav m s 9241 objective is not Maximize _Stage Contributions Payload then the objective and Gravity Loss m s 914 Payload values are displayed Aerodynamic Loss m s 27 Steering Loss m s 901 Thrust Loss m s 37 The kind of solution is displayed Inertial Speed Gain m s 7362 whether it Isa simple fly out a Computation Error m s 9 98650E 08 quasi optimum solution ora l solution that satisfied or failed to METRIC Units _ Toggle to English Units satisfy the mission constraints Mission Description Data Files The displa ea Solution Emor E l y uti rror I SIEMA the average of the scaled absolute values of violations of List Synopsis Mission Conditions Stack Countdown the specified constraints maximum payload kg 145092 Initial Mass kg 2395706 ROCKET DRAWING The scaled drawing of the rocket s tandem stage stack illustrates the spaces occupied by the propellants red primary inert masses gray adju
119. p 1issme SLS2 maxPL stdET Sssme SOB throtDown up issme SLS1 maxPL stdET Sssme SOB throtDown up 1ssme SLS2 maxPL stdET 5ssme SOB throtDown up issme Air Launch Payload 13500 lb Min Init Mass Lift Drag Model AOA and AHR SLS2 maxPL stdET Sssme SOB throtDown up 1ssme y Cancel Copy Rocket Burnout Data into Target Initial State From this list of existing missions you can select a mission and click the Copy Rocket Burnout Data into Target Initial State button The rocket s burnout state from the selected mission expressed in terms of GMT and osculating conic elements will automatically be written into the appropriate data boxes in the Mission Definition window If you do opt to define the target s initial state by getting data from an existing mission you will then have the option to let the program automatically set the rocket s launch GMT to the selected target s epoch In any event you will be able to specify or change the launch GMT when you proceed to the Launch and In Flight Conditions window In any case the rocket s launch GMT cannot be earlier than the target s epoch 22 6 MISSION DEFINITION Intercept Spacecraft or RV TARGET BALLISTIC COEFFICIENT A ballistic coefficient constant must be specified for the target This coefficient is equal to the mass of the target divided by the product of its aerodynamic reference area and drag coefficient assumed to be a constant The default ballistic coef
120. p as a whole is displayed near the top of the window These group data will include Propellant Load of Group Total Inert Mass of Group and Total height of Group If the mated group includes the rocket s top stage the total inert mass of the group will include the payload z In some cases the tandem Tandem Stage 1 BASE STAGE of Mated Group stage may be a single i engine equivalent that GROUP DATA Propellant Load of Group 735601 18 kg On Limit represents a number of Total Inert Mass of Group 63965 32 kg a Total Height of Group 46 284 m parallel burning stages In Propellant Load 49379 87 ko such a case all values Primary Inert Mass 4293 90 kg 62 9 m displayed in the tandem Adjunct Inert Mass 0 00 kag 7 stage summary window are Ideal Delta Velocity 96 291 m s FIXED Vacuum Specific Impulse 454 400 sec those of the single engine Propellant Mass Fraction 0 920000 equivalent The relationship Propellant Bulk Density 357 21173 ko m 3 i minea anit Mass DEn RE 124 24756 cat ens between parallel burning stages and their single Maximum Vacuum Thrust 11375 001 KN On Limit Throttleable in Steps engine equivalent IS defined Diameter of Nozzle Exit 5 374 m FIXED in Appendix B of the User Core T W Ratio at Ign ion 0 82266 g free Core T W sat i a E EBON 0 87784 G Manual Time of Ignition 0 000 sec m Rocket Mass at Ignition 2396081 15 kg In the rocket drawing the Burn Time 19 344 sec
121. quired From the Launch Preparation window you can opt to OPTIMIZE without first doing a PREVIEW or Fly Out This short cut saves time but should only be used when you are confident that the first guess values for the free variables and the fixed values of the other variables will not cause the optimization procedure to fail Such failure may sometimes result in a loss of user input data After reaching the Launch Preparation window and verifying that the Optimizer Parameters and Precision and Output Parameters seem appropriate the following procedure is recommended 1 Give the mission a core name 2 Click the PREVIEW button The first guess trajectory will be generated and graphical plots will be presented If the plotted data show an unacceptable trajectory for instance one that hits the ground navigate from the Plot Selection window to the appropriate windows to adjust relevant mission definition inputs launch and in flight conditions inputs and or various stage configuration inputs Repeat the preview adjustment procedure as many times as required to get a reasonable first guess trajectory Then return to the Launch Preparation window 3 Click the Fly Out button The program will re generate the last trajectory obtained in step 2 generate the set of perturbed trajectories display the Solution Window and record all data associated with the trajectory rocket and mission configuratio
122. refdia or for the aerodynamic reference area sref In those cases the displayed value for the aerodynamic reference diameter cannot be changed in the Aerodynamic Force Model window Instead you must edit the lift drag aerodynamic data file via the View and Edit Data button to change the aerodynamic reference diameter 56 17 AERODYNAMIC FORCE MODELS GB Aerodynamic Force Model l0 x Cet Bj x Stage 1 Aerodynamic Force Model BS Stage 2 Aerodynamic Force Model Angle of Attack Limit deg No Limit Specify a Limit Angle of Attack Limit deg 14 Remove Limit Aerodynamic Ref Dia m Max Stack Diameter Specify Fixed Value Aerodynamic Ref Dia m 7 1510195 Fixed Setto Max Stack Diameter Normal Axial Force Model View and Edit Data Lift Drag Force Model View and Edit Data In Rocket dat File p Descriptor EXPERIMENTAL LIFT DRAG AERODYNAMIC FILE FOR CHECKOUT Replace Model with Lift Drag Model from the Aerodynamic File Library Switch to LIFT DRAG Force Model Switch to Normal Axial Force Model RETURN RETURN With the lift drag model a Descriptor is displayed The descriptor is the first non blank record line in the stage s lift drag aerodynamic data file With either the normal axial or lift drag model you can view and edit the aerodynamic data by clicking the View and Edit Data button and you can switch from one model kind to the other by clicking
123. ro Time Constant will prevent an instant change in the rocket s attitude when the inertial attitude command goes into effect The rocket will maintain the inertial attitude during the rocket motor burn If Maintain Steering is the designated During Coast steering option the rocket will continue to maintain the inertial attitude during the coast period With inertial hold steering no limit on aerodynamic normal g s can be imposed so any aerodynamic normal g s that may occur must be accepted 51 16 CONFIGURE TANDEM STAGE BALLISTIC STEERING ballistic steering does not use any steering parameters The rocket simply responds to a zero angle of attack command in the central body frame If the stage has a non zero time constant the actual angle of attack will usually deviate from zero Because the angle of attack is a function of the rocket s velocity w r t the air a non zero wind will affect the rocket s attitude The ballistic steering command goes into effect at the start of the stage unless the rocket is still on the launch rail In that case the command goes into effect the instant the rocket leaves the launch rail the steering command remains in effect throughout the stage during both the thrust and post thrust coast if any With ballistic steering there will be no aerodynamic normal g s RETRO BALLISTIC STEERING retro ballistic steering does not use any steering parameters The rocket simply
124. rodynamic data file s formatted section is indicated by three slash characters in columns 1 3 Specific variable names must be present in the formatted section of the file All letters in these names must be lower case The first field in each formatted line has a width of 9 characters All subsequent fields in each formatted line have a width of 8 characters All text and data entries must be right justified in their fields Single blank lines are required at specific places in the formatted section of the file as shown in the illustration of the Lift Drag Aerodynamic Data window in the Lift Drag Aerodynamic Force Model section of the User manual Units must be specified for length len units altitude alt units and angle ang units The data values in the file are based on these unit specifications The length unit must be either feet ft or meters m The length unit applies to the aerodynamic reference metric whether it be the reference area sref or reference diameter refdia The altitude unit must be either feet ft kilometers km or nautical miles nmi The angle unit must be either degrees deg or radians rad The angle unit applies to the angle of attack at minimum drag alphamd and to the derivative of the lift coefficient with respect to angle of attack clalpha The specification of an aerodynamic reference metric sref or refdia i
125. ror is the average of the scaled absolute values of violations of the specified constraints The scale factors are calculated by the program and are displayed in the Scale Factors for Objective and Constraint Functions window which is discussed in the EFFECTS section The scaled individual constraint satisfaction errors are contained in the solution dat file which can be accessed from the Mission Synopsis window by clicking the Data Files button and then the SOLUTION DAT button The default Solution Error Tolerance is 0 1 a tolerance that will usually produce an accurate satisfaction of mission constraints in most cases For difficult missions with many non linearities a greater tolerance may be acceptable depending on your requirements 71 23 OPTIMIZER PARAMETERS BOX SIZE Box Size Minimum Initial Maximum are the minimum initial and maximum values of the box size which is the limit on free variable adjustments during the iterations of the optimization procedure For example a box size value of 128 means that on a single iteration a free variable can be adjusted no more than 128 times as much plus or minus as that free variable is perturbed to calculate its effects on the objective and constraint functions The specified Initial value for box size is used for the first iteration The box size is thereafter automatically adjusted as the iterations proceed so as to obtain the quasi optimum solution
126. rs button opens a window where you can define factors that affect the diameter and heights of the various stage components These factors are discussed in the Stage Sizing Factors section TIME CONSTANT The Time Constant defines the first order lag between the attitude defined by the stage s steering formula and the actual attitude achieved by the rocket The default time constant is zero STEERING OPTIONS The rocket is conceptualized to be symmetric with respect to its pitch plane The rocket rolls automatically about its longitudinal axis so that its pitch plane contains the rocket s relative velocity The angle of attack must be non negative The rocket s attitude will deviate from the steering method s formula if a deviation is required to keep the angle of attack non negative or is required to satisfy a constraint on normal acceleration The rocket always thrusts along its longitudinal axis and the thrust and aerodynamic forces are always in the 49 16 CONFIGURE TANDEM STAGE rocket s pitch plane By clicking the change steering button you can toggle among five steering methods 1 bi linear tangent 2 inertial hold 3 ballistic 4 retro ballistic and 5 fixed yaw and pitch BI LINEAR TANGENT STEERING bi linear tangent steering is a quasi optimum steering law for a two dimensional trajectory under certain conditions It has three independent parameters which can be expressed in readily visualized forms
127. rsion factor The mO value does NOT include the mass of any strap on booster that may be attached to the stage PROPELLANT MASS FRACTION Propellant Mass Fraction is the ratio of the stage s propellant mass to the sum of its propellant mass and primary inert mass The program calculates the stage s primary inert mass mPI from the propellant mass fraction PMF and propellant mass mProp mPI 1 PMF mProp PMF ROCKET NOZZLE EXIT DIAMETER Rocket Nozzle Exit Diameter is either specified Fixed by you or automatically calculated by the program Auto Calculated based on a typical ratio 0 85 of sea level thrust on earth to vacuum thrust However the automatically calculated nozzle exit diameter is not allowed to exceed 0 95 of the stage diameter The auto fix button toggles between the fixed and automatically calculated options The product of nozzle exit plane area and ambient atmospheric pressure is subtracted from the vacuum thrust to define the net thrust of the rocket engine CONSTRAINT ON VACUUM THRUST The stage s vacuum thrust is calculated from the stage s core initial thrust weight ratio and the rocket s core stage mass at the time of the stage s thrust initiation The core stage mass is calculated from various other variables and parameters Thrust reduction caused by 47 16 CONFIGURE TANDEM STAGE atmospheric pressure is taken into account in the calculation of the vacuum thrust so that the net
128. s 11Mari5 Rendezvous in 200 x 400 Nmi Orbit Min Initial Mass 11Mar15 Rendezvous in 200 x 400 Nmi Orbit Min Initial Mass New Miss Dist Calc 10Mar15 Impact RV at Low Altitude Minimum Closing Speed New Miss Dist Calc limit late qbar 10Mar1 Impact RV at Low Altitude Minimum Closing Speed New Miss Dist Calc 10Mari5 Rendezvous with Target on Hyperbolic Escape Conic 08Aug14 Rendezvous in Sun Sync Orbit Min Initial Mass 07Jun14 Rendezvous in 200 x 400 Nmi Orbit Min Initial Mass 07Jun14 Rendezvous 35 x 160 Nmi min flight time 2Stg SOB Lift Drag Model for Stage 2 07Jun14 Rendezvous 35 x 160 Nmi 2Stg max Payload 07Jun14 Rendezvous 120 N Mi SOB Lift Drag Aero amp AOA Limit for Stage 2 07Jun14 Intercept Incoming Target on Parabolic Conic Maximum Altitude 07Jun14 Impact RV at Maximum Altitude 07Jun14 Impact RV at Low Altitude Minimum Closing Speed 07Jun14 Impact RV at Low Altitude Maximum Closing Speed 07Jun14 Impact in Sun Sync Orbit Minimum Flight Time 07Jun14 Impact in GPS Orbit Maximum Payload 07Jun14 3 MISSION SELECTION The Mission Selection window is activated when you click one of the mission type bubbles in ZOOM s First window Clicking the Mission Type button returns you to the First window Access to the Mission Selection window from windows other than the First window is via the List button The Mission Selection window i
129. s Metric or English chosen for the last mission solved by the program The Help folder contains the plain text files that comprise the contextual help information The content of the appropriate file is displayed by the GUI when an INFO button is clicked Although it is not encouraged you may modify these plain text files to make the explanations clearer to you as you gain experience using the program If you do modify a file you should use a plain text application such as Notepad and the word wrap option should be deactivated Each line of text should be ended by clicking the keyboard s Enter or Return key And the length of each line should be kept within the maximum line length observed in the original file so that the entire line can be seen in the GUI s displayed window The Trash folder contains the mission subfolders that have been deleted via Delete in the Mission Selection window The Trash folder should be periodically emptied off line into the Windows Recycle Bin using the operating system s file management application e g Windows Explorer File Explorer etc MISSION SUBFOLDERS Each mission s data are saved in a subfolder within the DATA folder The mission subfolder names begin with a two letter prefix that identifies the mission type ES for Achieve Specified State missions OI for Inject into Conic missions and SI for Intercept Spacecraft or RV missions These two letters are follow
130. s discarded There are five options for a stage s steering method bi linear tangent inertial hold ballistic retro ballistic and fixed yaw and pitch These five steering methods are explained in the Configure Tandem Stage section 19 5 MISSION SUMMARY Time Constant is the time constant of a first order lag between the rocket attitude as defined by the steering formula and the attitude actually attained by the rocket Stage Diameter is the diameter of the cylindrical tandem stage Stage Total Height is the total height of the stage including adjunct inert mass or payload Stage Height w o Adjunct Inert Mass or w o Payload is the height of the propellant and primary inert mass It is this height that is used in the calculation of an unmated stage s aspect ratio height diameter The aspect ratio of a mated stage is not relevant The aspect ratio of a mated group is calculated by dividing the sum of the heights of the stages in the group not including adjunct inert masses or payload by the stage diameter same for all stages in the group ROCKET BURNOUT CONIC In the top stage s summary window there is a Burnout Conic button Clicking this button opens a small window that displays the GMT epoch and osculating conic elements of the rocket s state when the top stage s rocket motor burns out The conic elements are based on the selected central body model SLS2 maxPL stdET 5ssme
131. s an unpropelled stage the only sizing factors are the stage diameter and density of the stage mass If the unpropelled stage is a dummy stage with zero Stage Mass the density is meaningless and does not appear in the sizing factors window The following discussion applies only to propelled stages WW ifthe seceis unmaiedor is the base stage ina mated group you have two options for sizing the stage Checking the Aspect Ratio box and specifying a stage aspect Sizing Factors for Stage 1 M Aspect Ratio l Diameter m 5 69 2m for mated group Propellant Bulk Density kg m 3 500 000316 Density of Primary Inert Mass kg m 3 222 222364 Density of Adjunct Inert Mass kg m 3 350 003425 ratio or checking the Diameter box and Stage Diameter m 7 166147 specifying a stage Height of Primary Inert Mass m 1 2523355 Diameter Height of Propellant Tank m 5 0093421 If the stage is in a mated Height of Adjunct Inert Mass m 0 0141675 eal group but is not the Total Stage Height m 6 2758451 group s base stage its Stage Propellant Load kg 101021 141 Update Stage diameter will be the same as that of the base stage and the message Stage _revunn Diameter determined by Base Stage of Mated Group will appear in the sizing factors window The Aspect Ratio is the ratio of the stage s or mated group s length to its diameter The length in the ratio does not inclu
132. s optional If the line with the aerodynamic reference metric is not present in the file you must define the 63 19 LIFT DRAG AERODYNAMIC FORCE MODEL aerodynamic reference diameter in the space provided in the Aerodynamic Force Model window The six dependent variables in the lift drag aerodynamic model are separated into three groups Group 1 three dependent variables alphamd total angle of attack for minimum drag cdmin on power on drag coefficient at minimum drag angle of attack cdmin off power off drag coefficient at minimum drag angle of attack Group 2 two dependent variables clO lift coefficient at zero angle of attack clalpha derivative of lift coefficient w r t total angle of attack Group 3 one dependent variable k drag due to lift coefficient In each group the dependent variables are functions of Mach number and optionally altitude All variables in a group share the same Mach number and optionally altitude tables If a group has no altitude line the program will know that the dependent variables in the group are functions only of mach In each data group there can be no more than 100 Mach number points and no more than 100 altitude points Each data value is defined by a maximum of eight characters digits There can be no more than 32768 characters in a lift drag aerodynamic data file including the header section The tabular mach and altitude values must
133. s proven to be unusually robust and effective in this application 1 INTRODUCTION REFERENCE FRAMES Rocket motion is computed in a central body fixed frame with origin at the launch site The three orthogonal axes of this right handed frame are pointed north east and down along the plumb line This frame is termed the north east down frame abbreviated NED For an Intercept Satellite or RV mission the target motion is computed in an earth centered inertial frame abbreviated ECI Some computations are done in an earth centered earth fixed frame abbreviated ECF Various output data are also expressed in this frame The NED ECI and ECF frames are defined in Appendix A GRAPHICAL USER INTERFACE ZOOM s graphical user interface GUI facilitates the creation of new missions and the examination of completed missions Navigation among the GUI s primary sequential windows is done via navigation buttons at the bottoms of the windows These buttons and their associated destination windows are Navigation Button Destination Window Mission Type First window List or ReZOOM Mission Selection Synopsis Mission Synopsis Mission Mission Definition Conditions Launch and In Flight Conditions Stack Rocket Stage Stack Countdown Launch Preparation The navigation buttons are arranged in a single row at the bottom of the primary sequential windows The buttons are positioned left to right in the usual order for creating a new
134. s the only window from which you can access the First window and the Mission Synopsis window All existing missions of the chosen type that are in the Data folder are listed in this window A so called Mission from Scratch is included at the top of the list If you don t want to use an existing mission as a template for a new mission you can select the Mission from Scratch You select a mission from the list by left clicking it Mission Description _Deiete Rename METRIC Toggle Units View TRASH Mission Type List Synopsis Mission Conditions Stack Countdown By default the missions are listed in inverse chronological order according to their creation dates most recent first To get an alphabetical listing you click Change to Alphabetical List The alphabetical ordering is defined by the ASCII sequence where numerals precede letters and upper case letters precede lower case letters You can return to the inverse chronological listing by clicking the Change to Chronological List button which will appear when the alphabetical list is displayed The displayed names differ from the names of the files in the DATA folder in that the mission type indicator ES OI or SI has been removed and the six digit creation date has been moved to the end of the name and reformatted in a day month year sequence e g 07Jun14 The name as listed but excluding the date suffix is defined as the mission s core name
135. see the following definition of Propellant Mass Fraction If the stage is a lower stage in a mated group it s primary inert mass is not discarded until the end of the last stage in the mated group Otherwise the primary inert mass is discarded at the instant the stage ends The stage ends when its post thrust coast period if any ends If there is no post thrust coast period the stage ends when its thrust terminates rocket motor burnout Adjunct Inert Mass is inert mass that has a fixed value unaffected by the propellant mass The adjunct inert mass of any stage other than the top stage in the stack is discarded at the end of the stage even if the stage is mated to a following stage The adjunct inert mass of the rocket s top stage is called Payload Ideal Delta Velocity is the tandem stage s actual contribution to the rocket s total ideal delta velocity If a strap on booster is attached at any time during a stage s burn the displayed Ideal Delta Velocity will be somewhat less than the Core Ideal Delta Velocity that is displayed in the stage s Configure Tandem Stage window because the Core Ideal Delta Velocity does not take into account the mass of the strap on booster Vacuum Specific Impulse is the ratio of the rocket engine s vacuum thrust to its propellant weight flow rate Multiplying this specific impulse by the mass to weight conversion factor gO 9 80665 m s s in Metric units produces
136. ssion Selection section DATA FILES Clicking the Data Files button opens a window with a mosaic of buttons for the display of various data files associated with the selected mission The files reside in the mission s subfolder 51150313 Rendezvous 120 N Mi SOB Lift Drag Aero amp AOA Limit for Stage 2 Rocket Conic Earth Output0 and Solution data were recorded in Metric Units All other data for this mission were recorded in English units The EARTH DAT file defines the central body Earth or otherwise INPUT DATA ROCKET DAT EARTH DAT OPTIMIZER DAT PRECISTON DAT OUTPUT DATA OUTPUT DAT Ideal Delta Velocity and Losses OUTPUTS DAT TARGET STATES DAT TARGET DRAG DAT RETURN When a particular data file button is clicked the entire file is displayed in a text box with vertical and horizontal scroll bars as needed The displayed file cannot be edited but can be copied to the clipboard keyboard buffer with the click of a button For each of the three mission types the accessible files include six input data files and ten output data files Additionally for each rocket stage having a lift drag aerodynamic model as opposed to a normal axial aerodynamic model there is an additional lift drag aerodynamic model file This kind of file will have a generic name such as Ldfile_2 dat where the numeral in the file name refers to the tandem stage 13 4 MISSION SYNOPSIS An Inter
137. stage above which the new stage is to be inserted Any stages that were already above this stage will be pushed upward and renumbered When you click the Insert Above button a pop up window will require you to specify one of two kinds of insertions 1 NEW stage in which case the values for some of the inserted stage s parameters will be set equal to those of the stage below but the core ideal delta velocity of the inserted stage will be set to a negligible default value and all variable parameters will be fixed The default settings for the inserted stage are such that the rocket s performance should not be significantly altered You must change the default parameter values of the inserted stage to suit your requirements 2 SPLIT stage in which case the inserted stage will be mated to the stage below it and the core ideal delta velocity of the stage below will initially be split equally between that stage and the inserted stage The steering parameters of the mated stages and the core initial T W 39 14 ROCKET STAGE STACK ratio of the inserted stage will be initially calculated by the program so that the two mated stages i e the split stage will usually perform at the outset approximately like the original stage However the split stage may perform somewhat differently if the original stage would have reached an axial acceleration limit or if the original stage s turn angle were substantially nonlinear The maximum allowa
138. t Drag Force Model defined by lift and drag force coefficient data that are expressed as functions of Mach number and optionally altitude These data files originate as formatted files in the Aerodynamic File Library within the ZOOM Program Directory When one of these files is assigned to a tandem stage it is automatically copied into the mission subfolder with a generic name identifying the stage number e g LDFile_2 dat In the Configure Tandem Stage window the parenthetical suffix NA or LD in the title of the Aerodynamic Force Model button indicates whether the current model is normal axial or lift drag Clicking the button opens the Aerodynamic Force Model window The Aerodynamic Force Model windows are somewhat different for the normal axial and lift drag models But in both windows you can toggle a button to either specify an Angle of Attack Limit or leave the angle of attack unconstrained No Limit With the normal axial model you can toggle a button to either specify the aerodynamic reference diameter Aerodynamic Ref Dia or let this diameter be automatically set to the maximum diameter of the in flight stack Max Stack Diameter With the lift drag model you can toggle the aerodynamic reference diameter in the same way as with the normal axial model unless there is a record in the lift drag aerodynamic data file for the aerodynamic reference diameter
139. t is reached e g a throttle fraction of 0 2 could represent the shutting down of one of five engines This step throttling can occur more than once during the stage burn to keep axial acceleration within the limit but it cannot occur more than Times You are not permitted to specify a combination of values for Throttle Fraction and Times that could result in the vacuum thrust being throttled down to zero If Throttle Fraction is very small e g 01 and Times is sufficient the thrust will be repeatedly throttled in small steps when the maximum limit is repeatedly reached and the axial acceleration will remain near the limit for some time thus approximating a continuously throttled engine and a riding of the axial acceleration limit If the axial acceleration constraint can be satisfied by the throttling of rocket engine thrust the constraint is said to be satisfied implicitly However if the specified value for Throttle Fraction is zero i e no throttling is allowed or if the engine has been throttled the maximum number of times in an attempt to keep axial acceleration within the limit then the limit on axial acceleration will be treated as an inequality constraint to be satisfied explicitly by the optimization procedure If the thrust has a time varying profile there is no option to step throttle and a constraint on axial acceleration must be handled explicitly by the program s optimization procedure
140. tempt to move the window or click a mouse button x If you exercised the OPTIMIZE option the optimization algorithm will begin its iterations A drawing of the OPTIMIZATION CUMPEETED __69 2m rocket s initial configuration will Gansin Egualpas o be displayed and the number Inequalities 4 i A I D i eni of Constraint Equations Inequalities and free I QUASI OPTIMUM SOLUTION Va iables ill be displa ed ri wi i yed minimum initial mass kg 858996 2 Composite error 0 01624 View the solution s data by clicking the AS the program s optimization SUMMARY EFFECTS and PLOTS buttons iterations proceed the rocket ReZOOM to initiate a new session i i drawing will be continually After ReZOOMing you can EXAMINE the fi mission and access the raw Data Files updated to reflect adjustments from the Mission Synopsis window to stage propellant loads primary inert masses and payload the payload will be adjusted only for a mission with the Maximize Payload Composite Error amp Box Size Change in Performance objective Three plots will be 000 P 0 37 traced out Composite Error red Box Size gray and Change in Performance blue Iteration 40 Composite error is the average of the scaled absolute ReZOOM OPTIMIZE More Summary Effects Pios aun values of violations of the specified constraints such as the errors in conic elements or miss distance components If an in
141. the Switch to Force Model button x When you switch from a normal axial Select a File for Lift Drag Model model to a lift drag model a list of the aerodynamic data files in the Check Out Aero File air launch double CLA 2 t Aerodynamic File Library is displayed Check Out Aero File tt Dickmanns Reentry Aero Model a nd you m ust select one of these fi les EXAMPLE LIFT DRAG AERODYNAMIC FILE EDITED First Result Reentry Aero Model Afterward you can edit the file as you LD Aero Model with a More Negative CLO mye LD Aero Model with Negative CLO choose Once you have established a lift Modified Reentry Aerodynamic model a Space Shuttle Reentry Aerodynamic Model drag aerodynamic model you have the Special LD File symmetric Tentative File for Micro Rocket Orbit Injection option to replace the lift drag data file with another lift drag data file in the Aerodynamic File Library The aerodynamic force models are discussed in detail in the Normal Axial Cancel SELECT Lit Drag File Aerodynamic Force Model and Lift Drag Aerodynamic Force Model sections 57 18 NORMAL AXIAL AERODYNAMIC FORCE MODEL 18 NORMAL AXIAL AERODYNAMIC FORCE MODEL gt The normal aerodynamic force Fn is perpendicular to the rocket s longitudinal axis and the axial aerodynamic force Fa is anti parallel to the rocket s longitudinal axis These forces are calculat
142. the rocket engine s exhaust velocity Propellant Mass Fraction aka lambda prime is the ratio of the rocket stage s propellant mass to the stage s total mass excluding any adjunct inert mass or payload Propellant Mass Fraction Propellant Load Propellant Load Primary Inert Mass Propellant mass fractions of stages with liquid propellant rocket engines and high specific impulse propellants are typically greater than 0 9 Solid rocket motors typically have lower propellant mass fractions but usually greater than 0 8 Propellant Bulk Density is simply the average density of the stage s propellant s It has no effect on the program s calculation of the rocket trajectory but it does affect the dimensions of the rocket drawing For the top stage which carries the payload and other stages that carry adjunct inert masses the Payload Density or Adjunct Inert Mass Density will be displayed These values have no effect on the program s calculation of the rocket trajectory but they do affect the dimensions of the rocket drawing Primary Inert Mass Density is the average density of the rocket s primary inert mass It also has no effect on the program s calculation of the rocket trajectory but it does affect the dimensions of the rocket drawing 18 5 MISSION SUMMARY In specifying the density values you should remember that average densities are called for These average densities combined with the masses o
143. tion can be seen in the forms of equations 1 3 and 5 In all of these equations the vacuum thrusts of the individual parallel motors are positioned so that if each motor is throttled by the same percentage there will be no effect on the parameter being calculated It is helpful to recognize that equations 1 3 and 5 are homogenous with regard to the vacuum thrusts of the parallel rocket motors Therefore the equations can be evaluated without assigning the actual thrust values It is only necessary to assign relative values to the thrusts For example TVAC could be arbitrarily assigned the value 1 0 Then if TVAC is known to be twice as large as TAC it can be assigned the value 2 0 etc If all the thrust 1 values in the equations are thus normalized the values calculated from the equations do not change Equation 5 is also homogeneous with regard to the ratio of thrust to specific impulse This ratio is proportional to propellant flow rate propellant consumption rate 6 If a partial step throttling of the single engine equivalent is to be interpreted as the shutdown of one or more parallel rocket motors it should be noted that simulation fidelity may be slightly affected because the thrust force due to atmospheric pressure at the rocket nozzle s exit plane will remain 95
144. ton will restore the default perturbation values The default values have been selected to produce good results in many cases but you may often want to adjust the values based on how the objective and constraint functions are affected by the perturbations The effects of the perturbations on the objective and constraint functions are displayed in the EFFECTS window which can be accessed from either the Solution Window or from the Mission Synopsis window Only the first three significant figures of a perturbation value will be saved 72 24 PRECISION AND OUTPUT PARAMETERS 24 PRECISION AND OUTPUT PARAMETERS Any time before you click the Fly Out or OPTIMIZE button you can view and change the Precision and Output Parameters by clicking the Precision and Output Parameters button x A fourth order fixed step Runge Kutta numerical integration algorithm is used to Precision and Output Parameters integrate the ordinary differential equations defining the rocket s kinematics Numerical Integration Step Sizes seconds The integration algorithm includes a Gill correction and has been shown to be more accurate than the standard fourth order Runge Kutta algorithm for these kinds of differential equations step sizes must be between 001 and 999 9 seconds for Stage 1 Burn Coast for Stage 2 Burn Coast for Stage 3 Burn Coast NUMERICAL INTEGRATION STEP SIZES Data Output Controls 3 j T
145. uch a case in the Mission Definition window you may try toggling the FREE SET TIED button until the Perigee Injection option is indicated This will locate the conic s argument of perigee so that the rocket injects at perigee a constraint that may or may not improve convergence efficiency In most cases the additional constraint of perigee injection will not significantly affect the performance For some difficult or improperly defined missions the program may crash There are several kinds of crashes The worst kind is when the program freezes because of an unending computational loop or some other reason In a case like this the only reasonable recourse is to open the operating system s Task Manager display the list of active processes select the ZOOM exe 32 process and click the end process button This will stop and close the program 76 26 SOLUTION WINDOW After you click the Fly Out or OPTIMIZE button in the Launch Preparation window the Solution Window will be displayed and will remain while the program performs the required calculations Even a Fly Out will require a little time to complete because the program not only generates the nominal trajectory but it also generates a trajectory for each of the free variable perturbations so that the effects of the perturbations on the objective and constraint functions can be determined Until the program has completed its calculations you should not at
146. ultiplied by the local atmospheric pressure and the result is subtracted from the rocket s vacuum thrust to obtain the net thrust Core T W Ratio at Ignition is equal to the tandem stage s net thrust divided by the mass of the tandem stage stack at the start of the stage i e at rocket motor ignition The stage s achieved T W will be less than the displayed core value if there is an attached strap on booster The tandem stage s net thrust includes the reduction due to atmospheric pressure on the rocket nozzle s exit plane area Core T W Ratio at Burnout is defined like its ignition counterpart but at the instant the tandem stage s thrust becomes zero i e rocket motor burnout Time of Ignition is the time of the tandem stage rocket motor s thrust initiation with respect to launch time t 0 This time of ignition defines the start of the stage For the first stage it is the launch time t 0 For an upper stage it coincides with the end of the previous stage Rocket Mass at Ignition is the total mass of the rocket at the time of ignition including any attached strap on booster Burn Time is the total burn time of the stage s rocket motor The time of rocket motor burnout is equal to the time of ignition plus the burn time Post Thrust Coast Time is the time between rocket motor burnout and the end of the stage During this time there is no thrust At the end of the coast the stage inert mass i
147. ures fairings thicknesses of propellant tanks and outer skins These omissions combined with assumed values for payload densities and inert mass densities relegate the drawing to only a rough approximation of an actual rocket s size and shape The rocket drawing also appears in several other windows NUMBER OF ITERATIONS For all kinds of solutions except a Fly Out the title of a Number of Iterations button shows how many iterations were made by the program s solution procedure in an attempt to obtain a quasi optimum solution Clicking this button will display plots of the Composite Error aka Solution Error Box Size and Change in Performance i e improvement in the objective for each iteration of the program s solution procedure GB History of Optimizer Iterations Composite Error amp Box Size Change in Performance Iteration 100 0 01 Iteration The parameters of the solution procedure are explained in detail in the Solution Window section TOTAL IDEAL DELTAV The Total Ideal Deltav of the mission is the change in the rocket s speed in an inertial reference frame that would occur if a the rocket flew in a vacuum b the thrust remained aligned with the rocket s inertial velocity and c there were no gravity The total ideal delta velocity includes the contribution of a strap on booster if any Clicking the Stage Contributions button displays the deltav contributions of the i
148. vement in performance can be achieved b SOLUTION Satisfies Constraints which although not judged to be quasi optimum may sometimes be arbitrarily close to it c CONSTRAINTS ARE NOT SATISFIED which may sometimes occur for an acceptable trajectory one that just barely fails to satisfy all constraint error tolerances d OPTIMIZATION FAILED which means that no combination of free variable values can be found that satisfies all of the mission constraints Refer to the Recommended Solution Procedure section for a discussion of the recommended procedure for obtaining a quasi optimum solution for the mission THE OPTIMIZATION METHOD The quasi optimum solution is gotten with a parameter optimization method that uses the SIMPLEX algorithm often used to solve linear programming problems On each iteration of the optimization procedure the free variables are perturbed one at a time to find their effects on the objective and constraints The program then forms a canonical set of linear equations that include the objective and constraints expressed as linear functions of transformed non negative variables and other expressions that keep the variables within a box The SIMPLEX algorithm is then exercised to calculate constrained optimal adjustments to the free variables keeping them within the box The program adjusts the box size on each iteration based on how good the linear approximations appear to be and on how much the
149. when the rendezvous option has been chosen zero relative speed is ideal The Relative Speed can be substantial when the impact i e no rendezvous option has been chosen The Relative Direction is the total angle between the inertial velocities of the rocket and spacecraft or RV at the final time For a head on impact the Relative Direction is 180 degrees When the velocities are aligned the Relative Direction is zero The miss distance is the distance between rocket and target at the final time 15 5 MISSION SUMMARY For an Achieve Specified State mission the rocket s final conditions in the central body centered inertial frame i e the ECI frame is displayed near the bottom of the window Right Ascension is the angle in the equatorial plane between the vernal equinox and the projection of the rocket s final radius vector into the equatorial plane It can be thought of as an inertial longitude where the reference is the vernal equinox instead of the prime meridian Central Angle is the total angle in the inertial frame between the rocket s initial and final radius vectors Heading and Flight Path Angle define the direction of the rocket s final inertial velocity in the local north east down frame with origin at the rocket Speed is the magnitude of the rocket s final inertial velocity ROCKET INERTIAL SPEED SUMMARY NOTE In keeping with conventional usage the terms delta velocity
150. which is proportional to the stage s propellant mass the Adjunct Inert Mass is a fixed constant The adjunct inert mass is discarded when the stage ends whether or not the stage is mated to the stage above it The Adjunct Inert Mass of an unpropelled stage is simply called Stage Mass STAGE MASS Stage Mass applies only to an unpropelled stage It is the unpropelled stage s total mass and is treated just like a propelled stage s Adjunct Inert Mass UNPROPELLED STAGE Clicking the REMOVE Propulsion System button will remove from the display the parameters related to propulsion and the stage will be treated as an Unpropelled Stage An ADD Propulsion System button will then be displayed in the reformatted window to allow restoration of the propulsion related parameters CORE IDEAL DELTA VELOCITY Core Ideal Delta Velocity is the change in inertial speed of the rocket that would be produced by the tandem stage s propulsive thrust in a vacuum if a there were no strap on booster b the thrust remained co aligned with the inertial velocity and c there were no other forces acting on the rocket If you check the associated Vary button the program will optimize this variable starting with the specified value Otherwise the variable will remain fixed at the specified value CORE INITIAL THRUST WEIGHT RATIO Core Initial Thrust Weight Ratio is specified for a stage with constant vacuum thrust or piecew

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