Astro310_Mission7

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Laboratory Mission 7: Ballistic Missiles

Mission Objective

- Gain a better understanding of ballistic missile trajectories

- Exercise your ability to apply relevant ballistic trajectory equations

- Create an STK scenario to evaluate your answers

- Manually adjust ballistic trajectory initial conditions in order to hit a target location

Resources/RequirementsFor this laboratory mission, you must have;

Successfully installed STK and borrowed a license for a period covering the class in which thismission is to be executed (unless using the computer lab)

Read Appendix E of Understanding Space

Mission Planning

UNDERSTANDINGOFBALLISTICMISSILETRAJECTORIES

1. GEOMETERY OF A BALLISTIC TRAJECTORY: Having read Appendix E of your text,Understanding Space, you should be acquainted with the six initial conditions of a ballistic

trajectory (RBurnout, VBurnout, Burnout, Burnout, LBurnout, lBurnout). It is not clear from the text that theseconditions exist at the point where the missile rocket motor shut offafter a period of thrusting andmaneuvering through the atmosphere. In fact, the text concerns itself only with the second phaseof an ICBM flight. The three phases are the boost, mid-course, and terminal or re-entry phase(Figure 1 illustrates all three). Weve already studied launch velocities and sub phases of theboost phase in Chapter 9.3 of Understanding Space. Because your text makes the assumptionthat the boost and the terminal phases are negligible to the flight path or trajectory, you are not

given this full picture. So the equations you are dealing with assume that 0== and = .At this level of study, this is appropriate.

Last Major Revision byCapt Soberson 5 May 2006


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Figure 1: Ballistic Trajectory Geometry

2 .BALLISTIC MISSILE DEFENSE: The US Missile Defense Agency (http://www.mda.mil) isresponsible for developing the US Ballistic Missile Defense System. The first ballistic missileinterceptor was installed in Fort Greely, Alaska, in July 2004. As of September, 2005, there arenine interceptors deployed in Alaska and Vandenberg AFB, California, providing mid-courseintercept coverage for all 50 states.

This country has struggled with the development of a missile defense for a quarter of a centurybeginning with the Space Defense Initiative (SDI) in the 80s, through the Ballistic Missile DefenseOrganization (BMDO) in the 90s, and now with the Missile Defense Agency (MDA). While aballistic missile (short range, medium range, or intercontinental) is easiest to detect in the boostphase because of the high temperatures generated by the motors, the boost phase is so short thatdetection leading to interception is problematic. Likewise, in the terminal phase, the re-entryvehicle is shrouded in high temperature plasma and is easily observable. This phase is evenshorter than the boost phase and aerodynamic forces complicate interception. Conversely, in themid-course phase, the vehicle is very cold and harder to detect or observe without priorknowledge of the phases initial conditions. With a reliable detection in the boost phase, we canuse the burnout parameters to model the ballistic missiles trajectory--a predictable orbit. Onceweve calculated where the missile will be, we can launch an interceptor before re-entry andneutralize the threat in space.

http://www.mda.mil/http://www.mda.mil/


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APPLYRELEVANTBALLISTICTRAJECTORYEQUATIONS

3 .CALCULATE THE RANGE ANGLE () FOR THE FOLLOWING SCENARIO: Imagine youare the Chief of Safety for a test launch of an Intercontinental Ballistic Missile (ICBM). The launch

site will be Vandenberg Air Force Base (AFB) just north of Los Angeles (Lo=35N, lo=121W).The target is an island in the South Pacific Ocean (Figure 2)Yap Island (Lt=10N, lt=140E).

Figure 2: Yap Island Targeted

a )The contractor planning the test assures you that the test vehicle, which can achieve aburnout velocity (VBurnout) of 7200 m/s, will hit the target based on their calculated initialconditions without error. However, as the Chief of Safety, you must verify their numbers.

Determine what the Range Angle (), Range in km, and Burnout Azimuth (Burnout). Recallfrom Appendix E the equation is:

lCosCosLCosLSinLSinLCos tt += 00

= _____________ or ____________

b) Remember these two answers correspond to the short and the long way around the Earth.Using the shortest path, find the Range and possible launch azimuths.



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090

)(000,10 kmRange =

=Range ___________________ km

=SinCosL

CosSinLSinLCos t

0

0

= _____________ or ____________

c) One of these azimuths is correct for the short path, the other for the long path around theEarth.

4. DRAW THE TRAJECTORYS GROUND TRACK: Using the Polar Map given in Figure 3,draw the ground track for the short path from VAFB to Yap Island. Assume the boost phaseplaces the missile directly above the launch site and the re-entry occurs directly above the target.

Annotate the both the Range Angle ( , centered at the pole) and launch azimuth ( , centeredon your launch site) on your drawing.

Based on your figure, do you expect the launch azimuth to be;

a) 0


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Figure 3: Polar Map

5. DETERMINE THE LAUNCH ELEVATION AND MAXIMUM RANGE: The test vehicleshould obtain a burnout velocity of 7200 m/s at 180 km altitude (RBurnout = 6558 km). What would the

flight path angle ( Burnout) be? Use the method provided in Appendix E. Watch your units!

==

BurnoutBurnoutBurnout

RVQ

2

=BurnoutQ __________________



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=

=

22sin

2sin

2

1 1_

Burnout

BurnoutLOWBurnout

Q

Q

=LOWBurnout_ __________________

=

=

22sin

2sin180

2

1 1_

Burnout

BurnoutHIGHBurnout

Q

Q

=HIGHBurnout_ __________________

Which Burnoutwould you choose and why?

Launch elevation is the angle you point the rocket at launch as measured from thelocal horizontal to the velocity vector. Assuming the angle you launch the rocket is thesame on the pad as it is at burnout, what would your launch elevation angle be?

What would the maximum range be for this ICBM and the elevation angle needed toachieve max range?

=

= Burnout

BurnoutMaximum

Q

QSin

22 1

=Maximum _______________



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=

=

445)( max0_RangeMaxBurnout

=RangeMaxBurnout _)( _______________

6. DETERMINE THE MISSILE TIME OF FLIGHT: To determine the time of flight for ourballistic trajectory, the period of a circular orbit (assuming Q=1) with a radius equal to Rburnout must firstbe calculated. Then the TOF/Pcircular versus Range Angle plot (Figure 4 below or Figure E-6 in

Appendix E of Understanding Space) can be used to determine the flight path angles.

==

3

2 burnoutcircularR

P

Using Figure 4 and the values of Q and range angle, , thatyou calculated in Mission Planning, find

=circularP

TOF____________ or ____________.

=

= circular

circular

PP

TOFTOF _______________(Low trajectory)

or ________________(High Trajectory)

From Figure 4, estimate burnout_Lowand burnout_High.



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Figure 4: TOF/Pcircularversus Range Angle

7. COLLECT OUR DATA FOR THE LAUNCH: Complete the Table 1 with the data youcalculated.

Table 1: Ballistic Trajectory Parameters

PARAMETER DATA STK ENTRYLBurnout Launch Latitude

lBurnout Launch Longitude

LT (Target Latitude) ---

lT (Target Longitude) ---

RBurnout Launch Radius

VBurnout ---

LOWBurnout_Launch Elevation

HIGHBurnout_Launch Elevation

Burnout Launch Azimuth



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8. VELOCITY AT BURNOUT VECTOR: From your skills review, you found that a vectorof magnitude R can be decomposed into its components using the following equations. Find

BurnoutV for the low trajectory and the high trajectory.

Zsin)sin(cosS)cos(cos

sin

sincos

coscos

Zburnout,

Eburnout,

,

BurnoutBurnoutBurnoutBurnout

Burnout

Burnout

BurnoutSburnout

BurnoutBurnout

VEVVV

VV

VV

VV

VV

++=

=

=

==

== S)cos(cosS ,_ lowboBurnoutLowBurnout VV

)sin(cos ,_ == EVEV lowboBurnoutLowBurnout

== ZsinZ ,_ lowboBurnoutLowBurnout VV

=LowBurnoutV _ __________________S+____________________E+_____________________Z

== S)cos(cosS ,_ highboBurnoutHighBurnout VV



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)sin(cos ,_ == EVEV highboBurnoutHighBurnout

== ZsinZ ,_ highboBurnoutHighBurnout VV

=HighBurnoutV _ __________________S+____________________E+_____________________Z

9. From the K: drive, (K:\Campus\DF\DFAS\A310\STK Data Files) copy the Mission 7folderto your hard drive. This folder contains the scenarios you will need in class for MissionExecution.

Mission ExecutionDuring this laboratory mission, you will create a launch facility, a target zone, and the ICBM to matchthe planning scenario. After configuring the scenario, evaluate your calculated answers from missionplanning.

CREATEAN STK SCENARIOTOEVALUATEYOURANSWERS

10. Open the saved scenario file Ballistic_Targeting.scfrom the Mission 7 folder that yousaved in mission planning. This will have two 2-D windows. One is an Equidistant Cylindricalprojection and the other is a polar plot.

11. Create a facility object named VAFB located at Lo=35N, lo=121 W. NOTE: negativevalues are necessary for west longitudes.

a) Check the 2-D map to ensure it was placed where you wanted it to.

12. Create a Target object named Yap_Island using the Object Browser( ) andlocate it at Lt=10N, lt=140E.

a) Check the 2-D map to ensure the Target was placed where you wanted it.

13. Create a Missile object that takes the high trajectory to the target. Remember that weassume the burnout location is directly above the launch site.



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a) Open the missiles Basic/Trajectory property page (Figure 5). Enter the missiles burnoutlatitude (Launch Latitude), burnout longitude (Launch Longitude) and burnout altitude(Rburnout) (Figure 5). NOTE: negative values are necessary for west longitudes.

b) Change the Launch Latitude Geodetic box to read Launch Latitude Geocentricc) Change the Impact Latitude - Geodetic box to read Launch Elevation (Figure 5). This will

generate an error window. Ignore the error and click OK, then set the box to Launch

Elevation again.

d) Enter your HighBurnoutV _ in Fixed Delta V field

Figure 5: Missile Trajectory

e) Enter your HighBurnout_ as your launch elevation and Burnout as your launch azimuth in

the appropriate fieldsf) Click OK.

14. Evaluate your scenarioa) Observe the animated scenario in both of the 2-D windows. You may have to zoom

into the area aroundYap Island in the cylindrical projection using .b) Observe the scenario in a 3-D window. Youll have to open a new one.

Did you hit your target? Explain.

c) Remember that the Earth is spinning eastward. From Chapter 9.3 we know that the

velocity of the launch site is Ekm

LVLaunchSite

sec)cos(4651. 0= . Calculate the launch site

velocity and subtract that value from HighBurnoutV _ to overcome the spin of the Earth to get

the vector Delta V.


35

-121

RBurnout

kmChange to LaunchElevation

Change to Geocentric


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=HighBurnoutV _ _______________S+_______________E+_______________Z

=LaunchSiteV _0_S+_______________E+_0_Z

=V _______________S+_______________E+_______________Z

d) Now calculate the magnitude of the Delta V required to get to the given VBurnout

( ) ( ) ( ) =++= 22

2

ZESVVVV

e) Put this value into the Fixed Delta V

Did you hit your target this time?

15. Manually adjust your launch azimuth (Burnout) and Fixed Delta V ( BurnoutV ) until you do hit the

target and record your new initial conditions that caused a direct hit on Yap Island in Table 2.

Table 2: Initial Conditions to Hit Yap Island High Trajectory

INITIAL CONDITION HIGH TRAJECTORYRBurnoutVBurnout

Burnout

BurnoutLBurnoutl

Burnout



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16. If you have time, try repeating steps through using the low trajectory to the target

Table 3: Initial Conditions to Hit Yap Island Low Trajectory

INITIAL CONDITION LOW TRAJECTORY

RBurnoutVBurnout

Burnout

BurnoutLBurnoutl

Burnout

17. Close the Ballistic_Targeting.scscenario.


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Astro310_Mission7