Center for Aerospace Technology

Contract No. FO86050-02-C-0018 

Sub-Contract No. SRSIS-02-S-0018-002 

RTI Report No. RTI/08360/103-13F 

July 16, 2004 

Titan IV B-30 Downrange Risks 

Final Report 

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Safety Office - 45 SW/SE 

Patrick AFB, FL 32925 

Distribution authorized to US Government agencies and their contractors to protect administrative/ 

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Contract No. FO86050-02-C-0018 RTI Report No. RTI/08360/103-13F 

Sub-Contract No. SRSIS-02-S-0018-002 July 16, 2004 

Titan IV B-30 Downrange Risks 

Final Report 

Prepared by 

Robb T. Laney 

Brenda Wall 

of 

RTI International 

Center for Aerospace Technology 

Florida Office 

Prepared for 

Department of the Air Force 

45th Space Wing (AFSPC) 

Safety Office - 45 SW/SE 

Patrick AFB, FL 32925 

Distribution authorized to US Government agencies and their contractors to protect administrative/ 

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Titan IV B-30 Downrange Risks 5b. GRANT NUMBER 

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14. ABSTRACT

The Titan IV NUS vehicle configuration is described. Downrange risk estimates are based on the B-30 mission. Trajectory data 

was provided for launch from ER Pad 40 with an initial flight azimuth of 48.6°. Estimates are made for Stage 2 and payload 

debris produced by aero-thermal breakup, and casualty areas are computed. Population models for European and Middle 

Eastern nations and surrounding islands are described, along with estimates of sheltering provided by several structure types. 

Using day sheltering assumptions and varying other key parameters, RTI's current estimates of downrange casualty expectation range from a low of 70 x 10-6 to a high of 235 x 10-6. Within that range, the baseline estimates are 145 x 10-6 for day and 

152 x 10-6 for night. 

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Titan IV B-30 Downrange Risks 07/16/2004

Abstract 

The Titan IV NUS (No Upper Stage) vehicle configuration is described. Downrange risk 

estimates are based on the B-30 mission over Europe and the Middle East. Trajectory 

data was provided for launch from ER (Eastern Range) Pad 40 with an initial flight 

azimuth of 48.6°. Estimates are made for Stage 2 and payload debris produced by aerothermal breakup, and casualty areas are computed. Population models for European 

and Middle Eastern nations and surrounding islands are described, along with estimates of sheltering provided by several structure types. 

Hazards are simulated based on two types of failure responses: near trajectory (RTI 

Mode 4) and sustained turn (RTI Mode 5). Baseline risks (casualty expectations) are 

computed for two population sheltering assumptions: day and night. Due to uncertainty associated with various methods and inputs used, sensitivity of results to several 

key assumptions are also investigated. Using day sheltering assumptions and varying 

other key parameters, RTI's current estimates of downrange casualty expectation range 

from a low of 70 x 10-6 to a high of 235 x 10-6. Within that range, the baseline estimates 

are 145 x 10-6 for day and 152 x 10-6 for night. 

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Table of Contents 

1. Introduction ..............................................................................................................................1

2. Vehicle Description..................................................................................................................3

3. Trajectory Description.............................................................................................................4

4. Failure Probabilities.................................................................................................................6

5. Casualty Areas..........................................................................................................................7

5.1 Stage 2 Debris.....................................................................................................................7

5.2 Payload Debris.................................................................................................................10

5.3 Downrange Summary ....................................................................................................13

6. Population Models.................................................................................................................15

6.1 LandScan 2002 .................................................................................................................15

6.1.1 Coverage Details......................................................................................................15

6.1.2 Cell Aggregation......................................................................................................16

6.1.3 Shapefile Creation ...................................................................................................17

6.1.4 Land Area Adjustments .........................................................................................18

6.1.5 Attribute Table.........................................................................................................19

6.1.6 Cells Added by RTI.................................................................................................20

6.2 RTI Sheltering Model......................................................................................................20

6.3 Population Usage for B-30 Analysis .............................................................................21

6.3.1 Mode 4 Computations ............................................................................................21

6.3.2 Mode 5 Computations ............................................................................................21

7. Downrange Risk Estimation.................................................................................................23

7.1 Mode 4 Baseline Risks ....................................................................................................23

7.2 Mode 5 Baseline Risks ....................................................................................................26

7.3 Total Baseline Risks.........................................................................................................32

8. Sensitivity of Risks to Assumptions....................................................................................33

8.1 Sensitivity to Failure Probability ..................................................................................33

8.2 Sensitivity to Response Mode Allocation....................................................................35

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8.3 Sensitivity to Casualty Areas.........................................................................................36

8.3.1 Sensitivity to Breakup Model ................................................................................36

8.3.2 Sensitivity to Post-Impact Effects..........................................................................37

8.4 Sensitivity to Population Counts ..................................................................................38

8.5 Sensitivity to Population Sheltering.............................................................................39

8.6 Sensitivity to Mode 4 Dispersions ................................................................................40

8.7 Sensitivity to Wind Month.............................................................................................41

8.8 Use of Covariance Data ..................................................................................................41

8.9 HACK Version Comparison..........................................................................................42

9. Summary and Conclusions...................................................................................................52

Appendix A: RTI Sheltering Percentages as of 2003 .............................................................. A - 1 

References ................................................................................................................................ R - 1 

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Table of Tables 

Table 1. Event Times for Titan IV B-30 Mission ......................................................................4

Table 2 Titan IV Stage 2 Debris Classes for Downrange Use...................................................9

Table 3. B-30 Payload Debris Classes for Downrange Use – Part 1....................................11

Table 4. B-30 Payload Debris Classes for Downrange Use – Part 2....................................12

Table 5. Debris Model Totals for Downrange Use................................................................13

Table 6. Titan IV B-30 Casualty Areas for Downrange Use.................................................14

Table 7. Population Density Thresholds.................................................................................17

Table 8. Criteria for Adjusting Land Area..............................................................................18

Table 9. Baseline Mode 4 Risks for Titan IV B-30 Mission...................................................25

Table 10. Baseline Mode 5 Risks for Titan IV B-30 Mission.................................................28

Table 11. Day Sheltered Mode 5 Risks by Country...............................................................29

Table 12. Baseline Downrange Risks for Titan IV B-30 Mission .........................................32

Table 13. B-30 Top-Down Failure Probabilities .....................................................................34

Table 14. B-30 Bottom-Up Failure Probabilities.....................................................................35

Table 15. Sensitivity of Downrange Risks to Failure Probability........................................35

Table 16. Sensitivity of Downrange Risks to Response Mode Allocation .........................36

Table 17. Alternative Breakup Models....................................................................................37

Table 18. Sensitivity of Downrange Risks to Breakup Model .............................................37

Table 19. Alternative Post-Impact Assumptions...................................................................38

Table 20. Sensitivity of Downrange Risks to Post-Impact Effects.......................................38

Table 21. Sensitivity of Downrange Risks to Population Counts .......................................39

Table 22. Sensitivity of Downrange Risks to Population Sheltering ..................................39

Table 23. Sensitivity of Downrange Risks to Mode 4 Dispersions .....................................40

Table 24. Sensitivity of Downrange Risks to Wind Month..................................................41

Table 25. Effect of Covariance Data on Downrange Risks...................................................42

Table 26. Debris Class Index and Corresponding Class ID .................................................43

Table 27. Casualty Areas for HACK Version 3......................................................................44

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Table of Figures 

Figure 1. Titan IV NUS Vehicle..................................................................................................3

Figure 2. Vacuum Impact Trace for Titan IV B-30 Mission....................................................5

Figure 3. RTI’s 1 x 1 Degree Version of LandScan ................................................................22

Figure 4. Summary of Mode 4 Corridor for Titan IV B-30 Mission....................................25

Figure 5. Downrange Gate for Titan IV B-30 Mission ..........................................................26

Figure 6. Sample Mode 5 Impacts for Titan IV B-30 Mission ..............................................27

Figure 7. Selected Trends in Mode 5 Simulation Cases........................................................27

Figure 8. Population Exposed to Mode 5 Hazards ...............................................................31

Figure 9. Cumulative Risk for Mode 5 Response – Day Sheltering....................................31

Figure 10. Casualty Areas per Fragment by Debris Class, Part 1 .......................................45

Figure 11. Casualty Areas per Fragment by Debris Class, Part 2 .......................................46

Figure 12. Casualty Areas per Fragment by Debris Class, Part 3 .......................................47

Figure 13. Casualty Areas per Fragment by Debris Class, Part 4 .......................................48

Figure 14. Casualty Areas per Fragment by Roof Type, Part 1...........................................49

Figure 15. Casualty Areas per Fragment by Roof Type, Part 2...........................................50

Figure 16. Casualty Areas per Fragment by Floor Location................................................51

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1. Introduction 

Using information about Stage 2 of the Titan IVB vehicle and a specified payload, RTI 

has developed a fragmentation model, estimated downrange risks associated with 

overflight of Europe and the Middle East, and investigated sensitivities to selected 

parameters and assumptions. Trajectory data were provided for the B-30 mission from 

ER (Eastern Range) Pad 40, with an initial flight azimuth of 48.6 degrees. This work was 

done for, and with selected direction from, ER Wing Safety (45 SW/SE). 

Early in flight while a vehicle is still in or near the launch area, many types of failures 

have the potential to endanger people or property both inside and outside established 

flight safety limits. Later in flight, the nominal impact-point trace may intersect 

downrange landmasses prior to the vehicle achieving orbital conditions. This downrange overflight is often necessary in order to conduct a normal mission. The risk, or 

casualty expectation ( EC), associated with populations on downrange landmasses must 

be estimated to ensure public safety criteria are met. During these overflight periods, 

launch vehicle failures that cause significant divergence from the intended flight track 

have the potential to endanger populations outside a normal overflight corridor. In fact, 

some possibility exists for debris impacts anywhere within the vehicle’s range capability, which is a function of kinetic, potential, and chemical energies. Risks due to such 

failure responses are reduced dramatically as long as a reliable FTS (Flight Termination 

System) is installed and armed. 

Most vehicle malfunctions cause behaviors that lead to impacts within a normal overflight corridor. Termed Mode 4 failure responses by RTI, these near-trajectory behaviors 

result from failures such as a benign engine shutdown, tank rupture, turbine or turbopump failure, pressure rupture or burn-through of a solid rocket motor, premature 

stage separation or ignition, excessive angle of attack during periods of high dynamic 

pressure, or a tumbling turn. It has been estimated that more than three quarters of all 

failures lead to vehicle breakup before the safety officer can send a destruct command.[1] Although most vehicles do not maintain FTS capability beyond a certain point 

in flight, known as the downrange gate, this statistic helps support assumptions made 

regarding the distribution of failure probabilities between Mode 4 and other failure 

responses. 

To simulate the hazards posed by Mode 4 responses, RTI developed a software tool 

called CORIDORE-GIS (Corridor Risk Estimation using a Geographic Information 

System). CORIDORE is hosted in ArcView GIS, a commercial software application from 

ESRI (Environmental Systems Research Institute, Redlands CA). In addition to providing a variety of electronic maps, polygon intersection routines, and a program execution 

environment, ArcView allows for convenient maintenance of population datasets and 

visualization of risk estimation results. 

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In contrast to Mode 4, some malfunctions may cause a vehicle to fly initially in an 

erroneous direction, or after a period of normal flight, execute a sustained turn away 

from the intended flight track. Such behaviors are referred to by RTI as Mode 5 failure 

responses. One response category of this type is modeled by performing a series of 

simulations using randomly generated, fixed directions of thrust; similar behaviors are 

referred to here as random attitude responses. Although this category represents a 

subset of those responses having the potential to yield impacts outside a normal overflight corridor, random attitude simulations can be shown to bound maximum possible 

regions of impact, given that the vehicle has flown nominally for a specified period of 

time.[1] To estimate the hazards posed by Mode 5 failure responses, RTI developed two 

software tools called RAFIP (Random Attitude Failure Impact Points) and RAPIEC 

(Random Attitude Probability of Impact and Expectation of Casualty). Currently, RTI 

assumes that the impact distributions derived from random attitude simulations are 

representative of impact distributions from all Mode 5 response categories. A more 

involved research study would be needed to test the influence of this assumption on 

risk analysis results. 

Once a vehicle is out of the launch area, only Mode 5 failure responses have the 

potential to yield impacts at significant distances from a normal overflight corridor. 

Nevertheless, the nature of Mode 5 density functions is such that impacts are most 

likely inside the corridor, with impact probability decreasing as distance from the 

corridor centerline increases. Mode 5 risks accumulated prior to reaching the downrange gate can usually be minimized by maintaining an FTS capability. Normally, 

Mode 4 risks cannot be significantly mitigated by an FTS, regardless of the gate time 

(i.e., location). For some missions, Mode 4 risks can be somewhat reduced by rotating to 

a slightly different launch azimuth, or performing mid-course steering maneuvers. In 

most cases of launch vehicle ascent, however, some downrange risk is unavoidable. 

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2. Vehicle Description 

The Titan IVB was first launched February 23, 1997. It is a derived configuration of 

Titan IV that features upgraded solid rocket motors (SRMUs), a liquid propellant core 

composed of two stages, and a payload fairing 16.7 feet in diameter. This system can be 

flown with a wide-body Centaur upper stage, IUS (Inertial Upper Stage), or NUS (No 

Upper Stage). 

The B-30 mission will employ the NUS vehicle variant, as shown in Figure 1. Because 

the current analysis deals only with downrange overflight, the vehicle components of 

interest are Stage 2 and a large payload (see Section 5 for weight estimates). Note that 

payload fairing jettison occurs prior to Stage 2 ignition. 

Figure 1. Titan IV NUS Vehicle 

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3. Trajectory Description 

Downrange risk estimates are based on the proposed B-30 mission. Trajectory data were 

provided by Lockheed Martin, via ER Wing Safety, for launch from ER Pad 40 with an 

initial flight azimuth of 48.6 degrees.[2] The nominal trajectory was designed to deliver 

the spacecraft into a parking orbit (after Stage 2 burn) at an inclination of 57.0 degrees, 

with apogee and perigee heights of 383 and 258 nautical miles, respectively. Key event 

times for the B-30 mission are listed in Table 1. 

Table 1. Event Times for Titan IV B-30 Mission 

Event Time (sec)

Stage 0 ignition (SRMU) 

Lift-off 

Begin roll to flight azimuth 

End roll to flight azimuth 

Begin pitch-over 

Begin zero-lift flight 

Begin Stage 0 open-loop pitch rate 

Stage 1 ignition 

TCA jettison 

SRMU separation 

Payload fairing separation 

Stage 1 shutdown command 

Stage 1 shutdown 

Stage 2 ignition 

Step 1 / Stage 2 separation 

Stage 2 shutdown command 

Stage 2 shutdown 

Park orbit injection 

0.000 

0.324 

7.000 

14.000 

15.000 

30.000 

90.000 

131.658 

132.493 

146.417 

180.686 

316.224 

319.409 

319.716 

320.421 

549.818 

549.822 

569.725 

From the supplied trajectory, a Keplerian IIP (Instantaneous Impact Point) was found to 

vanish at 540.851 seconds (to millisecond resolution). This IIP trace crosses into Ireland 

at 461 seconds and exits Oman at 533 seconds, indicating a vacuum dwell time over 

Europe and the Middle East of approximately 72 seconds (note that significant time is 

spent over water). 

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A vacuum impact trace for the nominal B-30 mission azimuth of 48.6 degrees is shown 

in Figure 2; selected time points are provided for reference. The downrange gate for this 

mission is discussed later in this document (see Section 7.2). 

Figure 2. Vacuum Impact Trace for Titan IV B-30 Mission 

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4. Failure Probabilities 

Failure probabilities used for this analysis, including the allocation between Mode 4 and 

Mode 5, were assigned per direction of ER Wing Safety.[3] A baseline failure probability of 

0.02 was assumed for Stage 2, which has a burn time of 230.1 seconds. Assuming Stage 2 

failure probability to be uniformly distributed between ignition and shutdown yields a 

failure rate of 8.692 x 10-5 per second. The baseline split between Mode 4 and Mode 5 was 

assumed to be 95% and 5%, respectively. 

In summary, 

Stage 2 Mode 4 Failure Probability = 0.0190 

Stage 2 Mode 4 Failure Rate = 8.257 x 10-5 /sec 

Stage 2 Mode 5 Failure Probability = 0.0010 

Stage 2 Mode 5 Failure Rate = 0.435 x 10-5 /sec 

Many liquid-propellant motors (e.g., Centaur) have higher failure rates during startup 

than during steady-state operation. It has been suggested that Centaur’s startup transients 

lasts about four seconds following ignition. An investigation into the history of Titan 

Stage 2 revealed that 8 out of 29 failures occurred during startup, including failure to 

ignite.[4] However, none of these were among “representative” configurations; the most 

recent Stage 2 startup failure occurred in 1965. Since Centaur history is not applicable, and 

other information is scant, special steady-state failure rates were not computed. 

Further discussions regarding failure probabilities will be presented later in this document 

(see Section 8.1). 

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5. Casualty Areas 

Downrange risk analysis capabilities have been enhanced through the consideration of 

population sheltering. It has been recognized that most people in downrange areas are 

usually protected, to some unknown degree, by dwellings or other structures. For 

computation of downrange risks, four sheltering categories are considered: open, light, 

medium, and heavy. 

Sheltering categories are used to indicate levels of protection. Structural sheltering 

provides protection from inert debris, primarily through roofing construction and 

materials. Although explosions are not considered in the current study, sheltering also 

provides protection from explosive debris, to a certain extent, through construction and 

materials for both roofing and walls. Examples of light sheltering include typical houses 

and mobile homes in the United States. An example of medium sheltering is the typical 

single or two-story US office building with concrete roof. Examples of heavy sheltering 

are the blockhouses used for launch control at Eastern Range and, for inert debris, the 

lower floors of a multi-story office building. 

Casualty areas for occupants of light, medium, and heavy structures were computed 

using HACK (Hazard Area Computational Kernel), a physics-based, roof penetration 

algorithm developed by ACTA.[5] Casualty areas for people in the open were computed 

using RTI procedures.[6] For baseline risk estimates, all debris were assumed to impact 

on soft surfaces; impacts on hard surfaces were treated in a sensitivity analysis (see 

Section 8.3). On average, soft surfaces were considered more likely than hard surfaces in 

downrange areas. Unsheltered casualty areas were estimated based on the dimensions of 

a fragment, dimensions of a person, impact path angle, and post-impact effects (i.e., 

bounce, splatter, and slide). 

Debris data used for this study was originally documented in an RTI memorandum,[7]

along with a preliminary estimate of total casualty area for people in the open. 

5.1 Stage 2 Debris 

Debris characteristics for Titan IV Stage 2 were provided by Lockheed Martin.[8] This data 

was used as the basis for RTI's Stage 2 debris model, which is listed in Table 2. Casualty 

areas shown in the table are for people in the open assuming impacts on soft surfaces. 

In the table below, risk area refers to a fragment’s projected area at impact. These values 

were calculated based on debris geometry and center of gravity, as provided by Lockheed 

Martin. For example, a side-on impact was assumed for Class S2_01. It became necessary 

to update the dimensions for "Piece #1" to reflect the presence of a payload adaptor.[9] 

Class S2_02 and Class S2_04 are not necessarily expected to stabilize; therefore, impact 

orientation is uncertain. Risk area was calculated as the average of three face areas for 

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Class S2_02, and as a maximum face area for Class S2_04. Due to center of gravity location, 

an end-on impact was assumed for Class S2_03. 

Ballistic coefficients and aerodynamic reference areas for Stage 2 debris are based on drag 

coefficient (CD) versus Mach number curves provided by Lockheed Martin in their initial 

data delivery. Those CD vs. Mach curves were used to create reference CD data tables for 

use in estimating impact locations. It should be noted that the CD vs. Mach curve for 

"Piece #1" does not include effects of the payload (also indicated as space vehicle, or SV) 

adaptor attached to its forward end. 

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Table 2 Titan IV Stage 2 Debris Classes for Downrange Use 

Debris 

Class 

Description No. of

Frags 

Weight

(lb) 

Risk 

Area (ft2) 

Aero Ref

Area (ft2) 

Subsonic 

Beta (psf) 

(M = 0.5) 

Ref 

CD Data 

Table a

Frangibility

S2_01 

SV Adaptor, Fwd Oxidizer Dome, etc. 

1 5,111 215.18 78.54 76.56 CD1 0.2 

S2_02 

Fuel Barrel, Oxidizer Feedline, etc. 

1 1,939 84.76 78.54 37.98 CD2 0.2 

S2

_

03 Engine 1 1,401 25.59 25.59 97.76 CD3 0.2 

S2

_

04 Panels 20 95.8 25.00 25.00 6.39 CD4 0.2 

a Reference CD data table refers to drag vs. Mach curves used in estimating impact locations. Each class has it's own cu

CD1 denotes the table for Class S2_01. 

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5.2 Payload Debris 

Basic debris characteristics for the B-30 payload were provided by Lockheed Martin.[10]

That data was used as the basis for RTI's initial payload debris model, as described in a 

preliminary RTI memorandum.§ As additional data has become available,[11] [12] RTI has 

refined our payload debris model. The updated model now represents classes via two 

distinct methodologies. The first is the same one used for Stage 2 debris; drag data are 

provided as a tabular function of CD vs. Mach number for each class. The second uses a 

single subsonic and a single supersonic CD value for each class. Debris classes for which 

additional data permitted refinement using CD vs. Mach curves are listed in Table 3. 

The remaining debris classes are presented in Table 4. As before, casualty areas shown 

in these tables are for people in the open assuming impacts on soft surfaces. 

The decision to refine a given class by using CD vs. Mach curves was based on two 

primary criteria: 1) fragment shape and dimension data were sufficiently clear, and 

2) subsonic ballistic coefficient was greater than approximately 30 pounds per square 

foot. This value is somewhat arbitrary, but is intended as a reasonable compromise 

between adequately characterizing hazardous fragments and the additional overhead 

incurred by using CD vs. Mach tables. Debris described by Lockheed Martin as "rectangular" were refined if ballistic coefficient was large enough. Debris described as 

"cylindrical" were refined only if diameter was also clearly identified. Consideration of 

diameter versus length is critical in determining appropriate CD vs. Mach curves for 

cylinders. Also of importance is whether a cylinder is circular versus elliptical, or solid 

versus hollow. As no insight on these considerations was provided, RTI assumed all 

cylinders were solid. Any cylinder for which diameter was not clearly identified was 

treated as a tumbling box, which appears to be consistent with assumptions made by 

Lockheed Martin.[13]

"Piece #18" (which would have been Class PL_18) was combined with "Piece #17" 

(which became Class PL_17), as directed by Lockheed Martin.[14] Therefore, a separate 

entry for "Piece #18" does not appear here. This combination made the characteristic 

shape of the resulting, single debris fragment unclear. Hence, a CD vs. Mach curve 

could not be assigned with confidence, even though fragment weight is significant at 

906 pounds. 

Considering the dimensions provided, Class PL_19 and Class PL_20 are both modeled 

as tumbling plates. 

 

§ B. Wall, 3 December 2003, superceded by Reference 7 

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Table 3. B-30 Payload Debris Classes for Downrange Use – Part 1 

Debris 

Class 

Description No. of 

Frags 

Weight 

(lb) 

Risk 

Area (ft2) 

Aero Ref 

Area (ft2) 

Subsonic 

Beta (psf) 

(M = 0.25) 

Ref 

CD Data 

Table a

Frangibility

PL

_

02 rectangular 1 5462 49.33 74.00 98.41 TCUB 0.2 

PL

_

03 rectangular 1 300 9.03 13.55 29.53 TCUB 0.2 

PL

_

08 rectangular 1 460 16.67 25.00 24.53 TCUB 0.2 

PL

_

09 rectangular 1 304 7.06 10.59 38.27 TCUB 0.2 

PL

_

10 rectangular 1 538 9.03 13.55 52.96 TCUB 0.2 

PL

_

11 rectangular 1 488 8.16 12.24 53.16 TCUB 0.2 

PL

_

12 rectangular 2 1410 11.26 16.89 111.29 TCUB 0.2 

PL

_

13 rectangular 1 390 9.30 13.94 37.29 TCUB 0.2 

PL

_

14 rectangular 1 400 8.37 12.55 42.49 TCUB 0.2 

PL

_

15 rectangular 1 544 9.03 13.55 53.55 TCUB 0.2 

PL

_

21 cylindrical 2 688 18.44 1.40 67.31 TCYL21 0.2 

PL

_

24 rectangular 1 275 7.06 10.58 34.65 TCUB 0.2 

PL

_

25 rectangular 1 803 9.54 14.31 74.81 TCUB 0.2 

a Reference CD data table refers to drag vs. Mach curves used in estimating impact locations. TCUB is RTI's standard 

cube while TCYL21 is specifically for a tumbling, solid, right circular cylinder with diameter 16 inches and length 166 

In the above table, risk area refers to a fragment’s projected area at impact. These areas were calculadebris geometry since center of gravity values were not provided by Lockheed Martin. Therefore, it dict impact orientation. Risk area was calculated as the average of three face areas, except for the cyli

for which a side-on impact was assumed. Aerodynamic reference area is, by definition, specific to tgiven debris class. 

For Official Use Only 11 

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Table 4. B-30 Payload Debris Classes for Downrange Use – Part 2 

Debris 

Class 

Description No. of 

Frags 

Weight 

(lb) 

Risk 

Area (ft2) 

LM 

Average 

Area (ft2) 

LM 

Subsonic 

Beta (psf) 

LM 

Supersonic

Beta (psf) 

Frangibility

PL

_

04 cylindrical 1 231 6.02 4.55 101.54 56.41 0.2 

PL

_

05 cylindrical 1 82 1.71 1.21 135.54 75.30 a 0.2 

PL

_

06 cylindrical 1 270 29.58 28.77 18.77 10.43 0.2 

PL

_

07 cylindrical 1 35 7.88 6.00 11.67 6.48 0.2 

PL

_

16 cylindrical 4 97 15.00 7.59 12.78 10.65 0.2 

PL

_

17 rectangular 1 906 21.76 5.93 152.78 127.32 0.2 

PL

_

19 dome 8 38 7.07 10.47 3.63 3.02 0.2 

PL

_

20 rectangular 2 369 209.00 78.18 4.72 3.93 0.2 

PL

_

22 cylindrical 2 83 4.71 3.68 45.11 25.06 0.2 

PL

_

23 cylindrical 2 7 2.25 2.23 6.28 3.49 0.2 

PL

_

26 irregular 1 546 23.57 33.56 16.27 13.56 0.2 

PL

_

27 t-shape 1 738 13.52 15.42 95.72 53.18 0.2 

PL

_

28 rectangular 6 550 40.20 40.15 13.70 11.42 0.2 

PL

_

29 irregular 1 181 4.94 4.47 40.49 33.74 0.2 

a Supersonic beta in LM (Lockheed Martin) data was 56.47 psf. The CD (1.20) used to calculate this value is believ

consistency with other data provided, the CD in question was changed to 0.90, which yields a beta of 75.30 psf. 

As in the previous tables, risk area refers to a fragment’s projected area at impact. These areas weaverage of three face areas for all debris classes listed in this table. For Official Use Only 12 

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5.3 Downrange Summary 

Debris model totals for Stage 2 and the B-30 mission payload are listed below in Table 5. 

As modeled, this collection of inert fragments and components has been grouped into 

31 classes for downrange risk analysis purposes. 

Table 5. Debris Model Totals for Downrange Use 

Component 

No. of 

Frags 

Weight 

(lb)

Risk Area 

(ft2

)

Stage 2 23 10,366 825.53 

Payload 47 22,059 1100.64

Total 70 32,425 1926.2

Based on the debris characteristics presented above, casualty areas were estimated for 

people in the open (assuming impacts on soft surfaces), and for sheltering categories of 

light, medium, and heavy. Resulting values are listed below in Table 6. 

The debris model presented for downrange overflight of B-30 reflects the assumption 

that all liquid propellants leak out or boil off during breakup, leaving only inert weight 

at impact. Due to a current lack of information regarding survivability of debris, ER Wing 

Safety directed RTI to assume all hardware survives to impact with no reduction from

aero-thermal ablation. If re-entry survivability effects were considered, total casualty areas 

might be reduced significantly, depending on the time span for breakup and various 

material properties. 

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Table 6. Titan IV B-30 Casualty Areas for Downrange Use 

Casualty Areas per Fragment (ft2) 

Debris

Class Open (soft) Light Medium Heavy

S2_01 

S2_02 

S2_03 

S2_04 

286.57 

131.54 

70.18 

88.99 

559.95 

231.10 

159.37 

6.86 

543.42 

187.85 

125.52 

0.00 

61.95 

0.00 

24.23 

0.00 

PL_02 

PL_03 

PL_04 

PL_05 

PL_06 

PL_07 

PL_08 

PL_09 

PL_10 

PL_11 

PL_12 

PL_13 

PL_14 

PL_15 

PL_16 

PL_17 

PL_19 

PL_20 

PL_21 

PL_22 

PL_23 

PL_24 

PL_25 

PL_26 

PL_27 

PL_28 

PL_29 

122.20 

31.57 

28.60 

17.60 

80.11 

46.05 

50.10 

25.82 

32.67 

30.84 

56.31 

30.12 

29.20 

32.80 

61.44 

68.73 

46.18 

368.48 

49.41 

19.53 

31.58 

25.30 

39.41 

73.46 

47.71 

106.67 

21.06 

307.78 

37.52 

38.46 

19.15 

46.40 

14.14 

46.64 

37.06 

61.00 

56.24 

122.61 

43.49 

45.81 

61.82 

28.68 

144.84 

0.00 

0.00 

99.01 

30.35 

0.00 

36.11 

85.64 

46.04 

104.00 

47.44 

30.33 

368.13 

13.99 

13.54 

7.78 

10.61 

0.00 

17.75 

13.34 

29.68 

24.95 

92.87 

16.38 

16.99 

30.50 

0.00 

108.26 

0.00 

0.00 

63.66 

8.95 

0.00 

13.00 

60.32 

17.15 

69.45 

12.29 

11.09 

166.76 

0.00 

7.28 

5.33 

0.00 

0.00 

0.00 

4.19 

9.06 

9.02 

45.91 

4.88 

6.12 

9.31 

0.00 

16.87 

0.00 

0.00 

9.05 

0.00 

0.00 

3.82 

12.07 

0.00 

13.55 

0.00 

4.22 

Total 5407.3 3253.3 2104.4 468.6

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6. Population Models 

6.1 LandScan 2002 

RTI has chosen LandScan 2002 Global Population Database, distributed by ORNL (Oak 

Ridge National Laboratory),§ as a reasonable source for population count distributions 

needed to estimate downrange risks.[15] Raw LandScan data has been converted from 

packed binary files to enhanced polygon coverages, which are stored in ArcView shapefile format (see Section 1 for more information on ArcView GIS). This process,[16] which 

results in a series of population cell polygons having multiple sizes, is discussed below 

in more detail. 

LandScan 2002 provides high-resolution population data with a quadrilateral cell size 

of half-minute latitude or longitude (less than one kilometer). Population is based on 

the best available country census counts and is augmented by employing an advanced 

interpolation procedure. Designed by ORNL, this procedure is based on parameters 

such as road locations, terrain slope, land vegetation, night-time lights, and coastlines. 

The LandScan model covers the entire world for a consistent date, and it offers a single, 

reliable data source for trans-continental applications such as overflight risk analysis. 

Originally developed to support emergency response personnel, LandScan provides 

ambient population estimates intended to account for locations such as hotels, factories, 

shopping areas, and highways where population may not be included in official census 

counts. Since time of day for an emergency cannot be anticipated, a reasonable compromise is to estimate ambient population integrated over 24 hours. Future versions of 

LandScan are expected to address distinctions between day and night populations, age 

and gender variations by country, and improved resolution for urban areas. 

6.1.1 Coverage Details 

To accommodate usage of LandScan population counts in current RTI risk analysis 

programs, modifications to raw LandScan data were necessary. Many programs require 

a single polygon coverage to perform intersections and other computations, but the 

original LandScan dataset is partitioned into more than one thousand raster coverages, 

or tiles, each representing 5 x 5 degrees of latitude and longitude. Each tile contains 

360,000 half-minute cells, thus producing a file size well over 20 megabytes when converted to shapefile format. The entire dataset would consume over 20 gigabytes of 

storage space. To reduce this information to a more manageable size, RTI converts the 

LandScan data into a series of multi-res (i.e., multiple resolution) population coverages 

 

§ http://www.ornl.gov/gist/landscan

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by aggregating the half-minute cells according to a fixed schedule, which is based on 

population density. By design, this process maintains reasonable resolution near urban 

concentrations. Land-water boundaries are also identified to maintain reasonable resolution along coastlines. Cells with a known population count of zero are omitted to 

further reduce storage requirements. 

6.1.2 Cell Aggregation 

To reduce the size of LandScan population coverages, raw half-minute grid cells are 

merged based on fixed thresholds for population density. The general aggregation 

process can be illustrated as follows, 

• Fill a 600 x 600 array with population counts from each half-minute cell in a 

5 x 5 degree tile. 

• Sum each 2 x 2 group of population count values to form a series of one-minute 

grid cells. 

• Split the resulting 300 x 300 array into a series of 60 x 60 arrays to preserve onedegree grid boundaries. 

• For each 60 x 60 array, use an independent array to track resulting cell sizes. 

• For each 60 x 60 array, use an independent array to store latitude-longitude 

coordinates for each one-minute grid cell. 

• Test each 2 x 2 group of one-minute cell values to determine if they should be 

summed; if so, the result will be a two-minute grid cell. A group will not be 

summed if, 

1) any of the four densities match criteria (see Table 7) 

2) it contains both a zero and a non-zero count (preserves coastlines) 

3) the largest count is more than three times an average of the four values 

• Similarly, test each 2 x 2 group of 2-minute cell values to determine if they 

should be summed to form a 4-minute grid cell; groups including un-merged, 

1-minute cells should not be tested. 

• Similarly, test each 3 x 3 group of 4-minute cell values to determine if they 

should be summed to form a 12-minute grid cell; groups including un-merged, 

smaller cells should not be tested. 

• Similarly, test each 2 x 2 group of 12-minute cell values to determine if they 

should be summed to form a 24-minute grid cell; groups including un-merged, 

smaller cells should not be tested. 

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• After all 60 x 60 arrays have been processed, re-combine to produce three 

300 x 300 arrays representing one 5 x 5 degree, multi-res tile. 

• Combine data from these three arrays into a text file for input to ArcView. 

Population density thresholds for each cell size are listed in Table 7. These criteria have 

been selected to maintain appropriate resolution for risk analysis purposes, and they 

are based solely on engineering judgment. 

Table 7. Population Density Thresholds 

Cell Size 

(minutes)

Min Pop 

Density

(people/km2)

Max Pop 

Density

(people/km2)

1 180 none

2 60 180

4 20 60

12 5 20

24 0 5

6.1.3 Shapefile Creation 

Each text file representing a 5 x 5 degree, multi-res tile is processed by an RTI script 

hosted in the ArcView environment. This script reads latitude, longitude, cell size, and 

population count, and then creates a polygon object for each multi-res grid cell. The 

script also creates and partially populates an attribute table before calling another RTI 

script to assign names and key codes based on political entities. A polygon coverage 

based on DCW (Digital Chart of the World) was used to determine appropriate identity 

codes and land area estimates for each cell. DCW was published by ESRI (Environmental Systems Research Institute), and it contains detailed polygons that provide a 

reasonable representation of land-water boundaries on a global basis. Generally, DCW 

is partitioned only to the level of individual countries, but first-level administrative 

districts and separate islands are distinguished in selected cases. RTI also used 

polygons from another ESRI coverage (Admin98) to include islands missing from DCW 

and update several obsolete political entities, such as the former Yugoslavia. 

Once a multi-res cell polygon is created, it is intersected with DCW land polygons. If an 

intersection exists, the cell polygon is assigned a GMI (Global Mapping International) 

key code and the lowest level administrative district name that corresponds. If a cell 

intersects more than one land polygon, identification is based on the largest intersection 

area. If a cell has no intersections with land polygons (e.g., is surrounded by water), a 

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search box, which is slightly larger than the cell polygon, is created. The search box is 

then intersected with DCW in order to establish an identity. If needed, a search box will 

be increased in size until an intersection is detected. 

6.1.4 Land Area Adjustments 

Unreasonably large population densities can occur when the intersection of multi-res 

cells and DCW polygons returns very small land areas. Crosschecks in various parts of 

the world using high resolution maps indicate that coastline definitions, as represented 

by DCW polygons, are responsible. With that in mind, logic was introduced to modify 

land area for selected cells based partially on population density. Table 8 lists criteria 

used to make such adjustments. Note that entries are presented in a specific order; the 

first condition met would determine the only modification made for a given cell. 

Table 8. Criteria for Adjusting Land Area 

Criteria Modification

Land Area < 0.01 km2 Land Area = 0.01 km2

Land Area > Cell Area Land Area = Cell Area 

Land Area > 50% of Cell Area None 

(Pop / Land Area) > 8000 Land Area = Cell Area 

(Pop / Land Area) > 1000 & 

Pop < 1000 

Land Area = Pop / 1000 

(always < 1.0 km2

) 

(Pop / Land Area) > 1000 & 

Pop > 1000 

Land Area = linear interpolation between 50% and 

100% of Cell Area based on log10(Pop) between 

log10(1000) = 3.00 and log10(8000) = 3.95 

These adjustments affected 48,730 out of nearly nine million cells, or approximately half 

a percent of all multi-res grid cells. Those with less than 0.01 square kilometers of land 

area accounted for 28,868 of the modified cells. After all multi-res processing, more than 

7400 of the final population cells have a density over 16,000 per square kilometer. These 

cells are located in regions known to be densely populated and appear to be legitimate. 

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6.1.5 Attribute Table 

ArcView uses an attribute table to associate numerical and textual information with 

polygons in a shapefile coverage. Physically, this information is stored in a database file 

using a popular format called DBase IV (e.g., shape_name.dbf). Data fields from RTI’s 

multi-res LandScan coverages are outlined below. 

CELL_ID: 

This field is provided to uniquely identify a multi-res grid cell. Latitude and 

longitude are transformed to integer indices and then converted to text strings. 

The two strings are joined with a period before being stored (e.g., - 89 degrees 

latitude & - 178 degrees longitude yields “120.240”). 

CENT_LAT (+N): 

This field contains the latitude coordinate of a cell's centroid. 

CENT_LON (+E): 

This field contains the longitude coordinate of a cell's centroid. 

CELL_SIZE (min): 

This field contains cell size in minutes of latitude or longitude. 

POP_2002: 

This field contains the aggregated LandScan population count for year 2002. 

SQKM_CELL (km2): 

This field contains cell area in square kilometers. Polygon area was computed in 

ArcView using an equal-area azimuthal projection, which was based on the 

GRS80 ellipsoid. 

SQKM_LAND (km2): 

This field contains the land area of a cell in square kilometers. Land area was 

estimated based on intersections with DCW polygons (see Section 6.1.3). 

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EFF_KEY: 

This field contains an effective key code, which uniquely identifies the political 

entity associated with a cell. Each key code is a text string composed of one to 

three parts that are separated by hyphens. The first part is a country identifier, 

and the second part is a first-level administrative district, if available (e.g., the 

state of Florida would be represented as “USA-FLA”). The third part may be a 

second-level administrative district or any other useful identifier. Total length is 

limited to 17 characters. 

REG_NAME: 

This field contains a human readable region name based on the most specific part 

of a cell’s effective key code. Total length is limited to 35 characters. 

LAND_DIST: 

This field contains a text string describing a cell’s land distribution among DCW 

polygons. Up to three country identifiers are listed, along with a corresponding 

percentage of cell area. The field is left blank if there were no intersections found. 

Total length is limited to 25 characters. 

6.1.6 Cells Added by RTI 

The locations of multi-res LandScan cells were compared to a list of known countries 

and other political entities to ensure adequate coverage. Although there are many 

sources available, the CIA’s World Factbook 2002 [17] was chosen as a baseline source for 

information on political entities. There were a total of twelve entities found to have no 

representation among multi-res population cells. Most of these discrepancies are military bases or research installations having large transient populations. Many population 

counts for foreign military installations are estimated because exact values are difficult 

to obtain from the respective host governments. Nevertheless, RTI added Diego Garcia 

(3502 people), Wake Island (123 people), and Midway Island (39 people) for completeness. One-minute grid cells were created in appropriate locations, and population 

counts were distributed uniformly based on land area in each cell. While the population 

added is very small compared to LandScan’s 2002 world total of 6.23 billion, these three 

islands are sometimes hazarded by launch vehicle overflight. 

6.2 RTI Sheltering Model 

RTI's population sheltering model was originally documented in a report concerning 

only ER launches.[18] Various types of demographic data were used to estimate percentages of populations in four sheltering categories: open, light, medium, and heavy. 

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Based on this information, three sets of sheltering assumptions were developed: one for 

developing third-world nations, a second for more developed nations, and a third for 

industrialized nations. A best-fit assumption set was identified for each country, and 

sheltering percentages were determined for day and night time frames. Percentages by 

country were assumed to apply to each computation cell associated with that country. 

In a later effort, which was documented in an RTI memorandum,[19] these procedures 

were used to extend the model to most of the political entities identified during LandScan processing (see Section 6.1). 

Sheltering percentages for most political entities included in the current model are listed in 

Appendix A. Note that only a subset were used for this analysis. Some administrative

districts, such as U.S. states are not listed separately there.

6.3 Population Usage for B-30 Analysis 

For this study, base year population estimates were updated to an analysis year of 2005. 

Annual growth rates from the CIA’s World Factbook 2002 [17] were applied at a country 

level, although many islands were treated separately. 

6.3.1 Mode 4 Computations 

RTI’s multi-res version of LandScan 2002 is described above in Section 6.1. A subset of 

this model was used as a source of population counts for Mode 4 computations over 

Europe and the Middle East. 

6.3.2 Mode 5 Computations 

LandScan 2002 population counts, obtained from ORNL, were aggregated from raw 

grid cells spanning a half-minute of latitude or longitude to produce 17,034 sixtyminute (i.e., one-degree) cells. RTI added three additional cells covering Diego Garcia, 

Wake Island, and Midway Island (see Section 6.1.6). The 2002 world population represented by RTI's 1 x 1 degree version of LandScan totals 6.23 billion. Updated to reflect 

three years of growth, the 2005 world population totals 6.46 billion. A subset of this 

model was used as a source of population counts for Mode 5 computations. 

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Figure 3. RTI’s 1 x 1 Degree Version of LandScan 

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7. Downrange Risk Estimation 

As described previously, RTI models downrange failure responses (and therefore risks) 

using two methodologies: Mode 4 and Mode 5 (see Section 1). Casualty expectations 

for each mode are estimated separately and then summed. This is appropriate since 

relative likelihood of occurrence has already been included in the failure probabilities 

used. Regardless of response mode, risks are estimated by assuming failure occurs at 

each of a series of time points during upper stage burn. Effects from simulated debris 

impacts are determined based on various models and combined on a probabilistic basis. 

Many assumptions are made to facilitate this process, and they add uncertainty to the 

result, beyond that due to uncertainty associated with input data. Therefore, it is 

important to interpret baseline risk estimates with the assistance of a comprehensive 

sensitivity analysis. Baseline values are intended to be good median estimates that are 

consistent with scope and budget, sometimes conservative, yet reasonable enough to be 

helpful in preparing for launch operations. 

7.1 Mode 4 Baseline Risks 

In order to estimate Mode 4 risks, RTI assumes impact probability (PI) may be modeled 

as the product of a downrange component (PX), a crossrange component (PY), and a 

corridor-specific Mode 4 failure probability (PF4). Due to current modeling limitations, 

PX is assumed to be purely a function of dwell time (based on drag-corrected impacts). 

Dwell time is primarily a function of the upper stage trajectory and aerodynamic 

characteristics of a given debris class. PY is assumed to follow a class-specific Gaussian 

distribution having a time-varying standard deviation.[20] Factors influencing crossrange standard deviation include vehicle performance, potential guidance errors, postfailure behavior, breakup phenomena, and wind profiles. Geographic locations of 

simulated debris impacts determine which people are hazarded versus time. 

CORIDORE (see Section 1) was used to estimate Mode 4 risks over Europe and the 

Middle East. Based on the nominal trajectory, high beta (ballistic coefficient) debris 

classes were found to generate impact traces that enter the west coast of Ireland around 

462 seconds. Likewise, low beta classes were found to generate impact traces that exit 

the south-east coast of Oman around 534 seconds. Simulated debris impacts and associated dispersions were analyzed for assumed failures that bound this time span. 

CORIDORE generates a series of small computation cells over downrange landmasses, 

forming a corridor that envelopes the collection of impact traces for all debris classes 

considered. This process is accomplished such that edges of the corridor extend at least 

four sigma in both crossrange directions (right and left), for all classes. Also, cells are 

sized to be no wider than 40 percent of one sigma for the smallest crossrange dispersion, for all classes. This is done to minimize errors when computing area under the 

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probability density curve. For each computation cell, effective population density is 

determined by intersecting the cell polygon with appropriate population polygons, and 

assuming a uniform density across each. Population counts and casualty areas are both 

tailored based on estimated sheltering percentages (see Section 6.2). The following steps 

are accomplished for each computation cell: 

• find conditional impact probability for one fragment (PX • PY) 

• find conditional fragment casualty probability for each sheltering category 

(multiply by ratio of effective casualty area to cell area) 

• accumulate casualty probabilities for multiple fragments in a class 

• accumulate casualty probabilities across debris classes 

• multiply by PF4 to get an absolute casualty probability 

• find a casualty expectation increment for each sheltering category 

(multiply by product of cell area and effective population density) 

• sum casualty expectation increments for all sheltering categories 

Finally, casualty expectation increments for all computation cells are summed to yield 

an estimate of Mode 4 risk. 

For this study, RTI assumed a combination of immediate breakup at each potential fail 

time and breakup after 90 degrees of tumbling turn. For the tumble cases, end-of-turn 

state vectors were approximated using an RTI software tool called TRAX (Trajectories 

for overflight Risk Analysis), and tumble turn data provided by ER Wing Safety.[21] This 

data includes turn duration, turn angle of the velocity vector, and final speed at 

assumed breakup. TRAX was derived from RTI program TRIAL (Trajectories for Risk 

Investigations At Launch), but it includes a new tumble turn algorithm that is valid for 

downrange overflight use. The cross-track components of debris impact offsets attributable to tumble turns were root-sum-squared with three other dispersion components: 

guidance and performance error, post-breakup wind drift, and estimated effects of 

aerodynamic lift. Due to current modeling limitations, breakup induced components of 

velocity were assumed zero (e.g., low energy breakup). 

The left 3-sigma dispersed trajectory was used to estimate cross-track components of 

debris impact offsets attributable to guidance and performance error. Atmospheric 

properties and wind effects over the region of interest were based on December winds 

from NASA’s Global Reference Atmospheric Model 1999 (GRAM 99). In addition, a 

3-sigma uncertainty factor was applied to obtain wind dispersion components. A recent 

upgrade to RTI’s software supports continuous interpolation of GRAM data as altitude 

and location change. Because current aerodynamic models are based on continuum 

flow assumptions, air density and wind speed were set to zero above an altitude of 

350 thousand feet. Based on engineering judgment, a fixed lift-to-drag ratio of 0.2, and a 

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constant aerodynamic uncertainty of 25 percent, were assumed for all debris classes. 

Cross-track impact offsets attributable to aerodynamic lift were approximated using 

reduced in-track offsets. Based on a limited number of test cases, drag variation was 

reduced by an order of magnitude for this purpose. A more involved research study 

would be needed to improve on that assumption. 

Baseline results for Mode 4 are listed below in Table 9. The first row gives total time to 

transit populated regions, and the second row gives Mode 4 failure probability over 

that time span. Figure 4 shows a representation of the Mode 4 corridor. Each colored 

block in this figure represents the summation of risk increments from hundreds of 

individual computation cells. Casualty expectations for day sheltering are depicted. 

Table 9. Baseline Mode 4 Risks for Titan IV B-30 Mission 

Criteria Result

Transit Time (sec) 72.5 

Failure Probability 5.99 x 10-3

Exposed Population (millions) 128.2 

Casualty Expectation 

Day 142.483 x 10-6

Night 149.366 x 10-6

Figure 4. Summary of Mode 4 Corridor for Titan IV B-30 Mission 

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7.2 Mode 5 Baseline Risks 

The downrange gate time for this analysis (443 sec) was provided by ER Wing Safety,[22]

as shown in Figure 5. Since no FTS is available beyond the gate, this time is a reasonable 

starting point for Mode 5 computations. Once orbit has been achieved, Mode 5 impacts 

are no longer possible. Therefore, Stage 2 shutdown (approximately 550 sec for B-30) is 

a reasonable ending point for Mode 5 computations. Consequently, Mode 5 failures 

were considered from 443 through 550 seconds, a span of 107 seconds. This span was 

divided into 19 failure intervals, and 100,000 random attitude cases were simulated 

from the mid-point of each interval. For each simulation, Stage 2 thrust accelerations 

were included through Stage 2 shutdown, regardless of assumed fail time. 

Impact points for selected failure intervals, identified by mid-point time, are plotted in 

Figure 6. Although 100,000 cases were simulated for each interval, only 20,000 samples 

per interval are plotted in this figure. Impact points corresponding to the assumed gate 

time (shown below for a mid-point time of 446 sec) illustrate the maximum geographic 

extents for Mode 5. 

Panama

Nicaragua

Honduras

Cuba Caribbean

Algeria

Mauritania

Western 

Sahara

Morocco

Mali

Senegal

Gambia

Guinea-Bissau Guinea

Burkina Faso

Azores

Canary Is.

Iceland

Denmark

Ireland

United

Kingdom

Spain

France

Portugal

Belgium

Netherlands

Madeira

Bermuda

100

200

300

400

450 460 470 480 490 443

Gate Time

B-30 Nominal Traj.

Figure 5. Downrange Gate for Titan IV B-30 Mission 

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Figure 6. Sample Mode 5 Impacts for Titan IV B-30 Mission 

0

10

20

30

40

50

60

70

80

90

100

440 450 460 470 480 490 500 510 520 530 540 550

Fail Time MET (sec)

Monte Carlo Cases (%)

Orbital %

Ballistic %

Figure 7. Selected Trends in Mode 5 Simulation Cases 

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The percent of random attitude cases that achieved orbital conditions are plotted above 

in Figure 7. All other cases, which are also plotted, resulted in ballistic impact; none of 

the cases impacted while thrusting. Note that all simulations beyond 547 seconds ended 

in orbit rather than impact. 

Baseline results for Mode 5 are listed below in Table 10. The first row gives the total 

number of simulations performed, and the second row gives Mode 5 failure probability 

over the time span considered. The fourth row gives an average density for all population cells involved. 

Table 10. Baseline Mode 5 Risks for Titan IV B-30 Mission 

Criteria 443 to 550 sec 

Number of Simulations 1,900,000 

Failure Probability 4.65 x 10-4

Exposed Population (millions) 1048.2 

Population Density (/NM2) 230.7

Casualty Expectation 

Day 2.558 x 10-6

Night 2.592 x 10-6

Two countries in Europe (Germany and the United Kingdom) together contribute about 

23 percent of the total Mode 5 risk. Five additional countries (Iran, Ukraine, Turkey, 

Poland, and France) contribute more than five percent each, and approximately 34 percent collectively. Day sheltered risk increments are listed in Table 11 for each political 

entity exposed. Figure 8 presents exposed population as a function of failure time, while 

Figure 9 presents cumulative casualty expectation for day sheltering. 

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Table 11. Day Sheltered Mode 5 Risks by Country 

Country

Casualty

Expectation 

Percent 

Total 

Afghanistan 7.903E-10 0.0

Albania 7.229E-09 0.3

Algeria 8.737E-09 0.3

Armenia 9.915E-09 0.4

Australia 1.827E-13 0.0

Austria 3.153E-08 1.2

Azerbaijan 1.907E-08 0.7

Belarus 2.871E-08 1.1

Belgium 2.069E-08 0.8

Bosnia and Herzegovina 7.480E-09 0.3 

Bulgaria 2.209E-08 0.9

Canada 4.819E-09 0.2

Croatia 1.208E-08 0.5

Cyprus 1.365E-09 0.1

Czech Republic 3.477E-08 1.4 

Denmark 2.327E-08 0.9

Diego Garcia 5.284E-12 0.0 

Djibouti 4.187E-11 0.0

Egypt 6.912E-08 2.7

Eritrea 1.422E-09 0.1

Estonia 1.903E-09 0.1

Ethiopia 5.939E-10 0.0

Faroe Isl 1.554E-10 0.0 

Finland 4.308E-09 0.2

France 1.400E-07 5.5

French Polynesia 4.119E-13 0.0 

Georgia 1.484E-08 0.6

Germany 3.073E-07 12.0

Greece 1.350E-08 0.5

Greenland 2.498E-13 0.0

Hungary 2.900E-08 1.1

Iceland 5.084E-10 0.0

India 6.768E-12 0.0

Iran 1.880E-07 7.3

Iraq 8.764E-08 3.4

Ireland 1.667E-08 0.7

Israel 1.014E-08 0.4

Italy 9.176E-08 3.6

Jersey 4.220E-10 0.0

Jordan 7.555E-09 0.3

Kazakhstan 6.002E-10 0.0

Kuwait 5.098E-09 0.2

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Casualty Percent 

Country Expectation Total 

Latvia 5.670E-09 0.2

Lebanon 6.888E-09 0.3

Libya 3.294E-09 0.1

Lithuania 1.024E-08 0.4

Macedonia 1.558E-09 0.1

Maldives 4.946E-10 0.0

Malta 3.293E-10 0.0

Moldova 1.006E-08 0.4

Montenegro 1.608E-09 0.1

Netherlands 7.331E-08 2.9

New Zealand 2.123E-11 0.0 

Norway 1.104E-08 0.4

Oman 7.964E-09 0.3

Pakistan 1.572E-09 0.1

Poland 1.707E-07 6.7

Portugal 4.325E-09 0.2

Qatar 1.955E-09 0.1

Romania 7.976E-08 3.1

Russia 9.786E-08 3.8

Saudi Arabia 3.090E-08 1.2 

Serbia 2.357E-08 0.9

Slovakia 1.268E-08 0.5

Slovenia 2.578E-09 0.1

Somalia 1.514E-09 0.1

Spain 2.874E-08 1.1

St Pierre and Miguel 2.673E-11 0.0 

Sudan 6.838E-10 0.0

Sweden 2.271E-08 0.9

Switzerland 1.727E-08 0.7

Syria 3.819E-08 1.5

Tunisia 6.600E-09 0.3

Turkey 1.803E-07 7.0

Turkmenistan 2.233E-09 0.1

Ukraine 1.855E-07 7.3

United Arab Emirates 9.062E-09 0.4

United Kingdom 2.700E-07 10.6 

Uzbekistan 9.921E-13 0.0

Yemen 1.372E-08 0.5

Total 2.558E-06 100 

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Titan IV B-30 Mission

Exposed Population

0.00E+00

2.00E+08

4.00E+08

6.00E+08

8.00E+08

1.00E+09

1.20E+09

440 450 460 470 480 490 500 510 520 530 540 550

Mission Elapsed Time (sec)

Exposed Population

Figure 8. Population Exposed to Mode 5 Hazards 

Titan IV B-30 Mission

Casualty Expectation

0.00E+00

5.00E-07

1.00E-06

1.50E-06

2.00E-06

2.50E-06

3.00E-06

440 450 460 470 480 490 500 510 520 530 540 550

Mission Elapsed Time (sec)

Casualty Expectation

Figure 9. Cumulative Risk for Mode 5 Response – Day Sheltering 

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7.3 Total Baseline Risks 

Baseline downrange risks for the Titan IV B-30 mission are listed in Table 12. Including 

all assumptions discussed previously, the Mode 4 and Mode 5 casualty expectations are 

repeated here. Total risks have been rounded to three significant figures as a reminder 

of the uncertainty associated with these results. The totals represent baseline estimates 

for this study. 

Table 12. Baseline Downrange Risks for Titan IV B-30 Mission 

Casualty Expectations 

Failure 

Response Day Night

Mode 4 142.48 x 10-6 149.37 x 10-6

Mode 5 2.56 x 10-6 2.59 x 10-6

Total 145 x 10-6 152 x 10-6

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8. Sensitivity of Risks to Assumptions 

Methods used for this analysis were selected from among several possibilities. As 

acknowledged previously, the relationship between a random attitude, impact density 

function and one based on all possible Mode 5 failure responses is unknown. It is not 

possible, within the scope of this task, to quantify uncertainties in results associated 

with such modeling decisions. However, a general discussion of uncertainty in RTI risk 

estimates is available.[23]

Values used for a number of key parameters associated with the models chosen are 

uncertain. Their influence on risk estimates can be measured by varying values over an 

expected or reasonable range and re-computing. Sensitivity of results to the following 

key parameters is presented in this section: 

• failure probability and response mode allocation 

• casualty areas, both breakup model and post-impact effects 

• population counts 

• sheltering percentages 

• Mode 4 dispersions 

• monthly winds 

Baseline results presented previously have been repeated here for convenience. Sensitivity analyses were performed for Day sheltering only, unless otherwise specified. 

Most of the issues addressed were investigated per direction of ER Wing Safety.

[24]

8.1 Sensitivity to Failure Probability 

As part of this analysis, RTI was tasked by ER Wing Safety to provide estimates for 

failure probabilities, including suggestions for alternate methodologies. RTI's proposed 

Titan IV B-30 failure estimates were documented in an RTI memorandum.[4] That 

information has been used as the basis for sensitivity analyses with respect to failure 

probability. Two possible approaches were presented: top-down and bottom-up. The topdown approach begins with total mission failure probability and allocates it among 

flight phases. Alternatively, the bottom-up approach begins with failure probabilities 

for each flight phase and builds to a total mission failure probability. As compared to 

the baseline probability of a failure during overflight, bottom-up yields a low estimate 

and top-down yields a high estimate. 

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Top-Down Approach

With this approach, an overall mission failure probability of 0.12 is assumed and then 

partitioned among flight phases 0 – 1, 2 - 3, and 4 - 5. The conditional failure probabilities for flight phases 2 and 3 are combined, based on the assumption that Stage 2, in 

this case, has to do the work of typical flight phases 2 and 3. For example, if Stage 1 or 

Stage 2 under-performed, the deficit in energy could possibly be overcome in vehicles 

with a phase 3. Similarly, phases 4 and 5 were combined because the payload, in this 

case, has to do the work typically accomplished by those two phases in Titan configurations with upper stages. Values for the top-down approach are summarized in Table 13.

Table 13. B-30 Top-Down Failure Probabilities 

Parameter Value

Titan overall mission failure probability 0.12 

Conditional failure probability for flight phases 2 - 3 0.27 a

Absolute failure probability for flight phases 2 - 3 0.0324 

Conditional failure probabilities for Mode 4 

 Mode 5 

0.9500 b

0.0500 b

Absolute failure probabilities for: Mode 4 

 Mode 5 

0.0308 

0.0016 

Mode-4 absolute failure rate 

(probability per second) 

(0.0308 / 230.1) 

1.338 x 10-4

Mode-5 absolute failure rate 

(probability per second) 

(0.0016 / 230.1) 

7.0404 x 10-6

a Sum of conditional probabilities for flight phases 2 and 3 

b As directed by ER Wing Safety 

Bottom-Up Approach

With this approach, an enhanced phase 2 conditional probability is used, and the 

phase 3 conditional probability is discarded. Overall mission failure probability is 

effectively reduced from 0.12 to 0.0948. Although not used for this analysis, the conditional probabilities for phases 4 and 5 could be combined into phase 5. Values for the 

bottom-up approach are summarized in Table 14. It should be noted that a more comprehensive bottom-up approach is possible. 

Risk estimates that are based on failure probabilities derived from both bottom-up and 

top-down approaches are listed in Table 15. 

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Table 14. B-30 Bottom-Up Failure Probabilities 

Parameter Value

Titan overall mission failure probability 0.12 

Conditional failure probability for flight phase 2 0.08 a

Absolute failure probability for flight phase 2 0.0096 

Conditional failure probabilities for Mode 4 

 Mode 5 

0.9500 b

0.0500 b

Absolute failure probabilities for: Mode 4 

 Mode 5 

0.0912 

0.0005 

Mode-4 absolute failure rate 

(probability per second) 

(0.0912 / 230.1) 

3.963 x 10-4

Mode-5 absolute failure rate 

(probability per second) 

(0.0005 / 230.1) 

2.086 x 10-6

a Adjusted for Titan configurations with no upper stage 

b As directed by ER Wing Safety 

Table 15. Sensitivity of Downrange Risks to Failure Probability 

Casualty Expectation 

Failure 

Probability Mode 4 Mode 5 Total 

0.0096 (low) 68.39 x 10-6 1.23 x 10-6 69.6 x 10-6

0.0200 (baseline) 142.48 x 10-6 2.56 x 10-6 145.0 x 10-6

0.0324 (high) 230.89 x 10-6 4.14 x 10-6 235.0 x 10-6

8.2 Sensitivity to Response Mode Allocation 

Varying response mode allocation provides insight into risk contributions associated 

with each mode. Total risk is the sum of Mode 4 and Mode 5 values, which are each 

proportional to mode-specific failure probabilities. First, the baseline estimates for each 

mode are adjusted based on updated probability levels. Then, the new estimates for 

each mode are summed to yield a total sensitivity value. Results of this process for 

selected alternate allocations are presented in Table 16. 

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Table 16. Sensitivity of Downrange Risks to Response Mode Allocation 

Casualty Expectation 

Response Mode 

Allocation (M4 - M5) Mode 4 Mode 5 Total 

85% - 15% 127.49 x 10-6 7.67 x 10-6 135.2 x 10-6

90% - 10% 134.98 x 10-6 5.12 x 10-6 140.1 x 10-6

95% - 5% (baseline) 142.48 x 10-6 2.56 x 10-6 145.0 x 10-6

99% - 1% 148.49 x 10-6 0.51 x 10-6 149.0 x 10-6

Intuition would suggest that the relative percentage of Mode 5 failures should be small 

given modern guidance systems and various redundancies. However, launch vehicle 

history can be used to support a range of estimates, some higher than 20 percent.[25]

Baseline and alternate allocations presented here were requested by ER Wing Safety. 

8.3 Sensitivity to Casualty Areas 

Casualty areas depend on extent of vehicle breakup, presence or absence of explosive 

debris, aero-thermal survivability of fragments to impact, population sheltering effects, 

and modeling procedures used. Estimates for occupants of light, medium, and heavy 

sheltering were computed using HACK (Version 2), while those for people in the open 

were computed using RTI procedures (see Section 5). For baseline risk estimates, all 

debris were assumed to impact on soft surfaces, and post-impact effects were included.

Currently, RTI has no way of determining which fragments may be partially or totally 

consumed during re-entry. Therefore, ER Wing Safety directed an assumption that all 

hardware survives to impact, and no sensitivity computations were performed for 

debris survivability. As mentioned previously, all liquid propellants in Stage 2 and the 

payload are assumed to leak out or boil off before impact. If propellants were to remain, 

explosions could occur, thus increasing effective casualty areas. However, RTI believes 

that retention of significant quantities of liquid propellant is implausible. 

8.3.1 Sensitivity to Breakup Model 

Extent of breakup can dramatically influence total casualty areas. RTI's baseline downrange debris model includes 70 fragments, which total an inert weight of 32,425 pounds. 

The Stage 2 portion of this model comprises only 23 pieces with a total weight of 10,366 

pounds. Of these, 20 pieces are small, and the remaining three pieces are much larger. 

In order to conduct a previous quick-look analysis for B-30,[26] RTI assumed a more 

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extensive breakup of Stage 2. This model includes 96 fragments with a total weight of 

9728 pounds, and it has been used for sensitivity purposes in the current study. Due to 

a lack of data regarding the payload, that portion of the baseline model was not 

updated to reflect a more extensive breakup. At the other extreme, if Stage 2 and 

payload each survived intact (with loss of liquid propellants only), there could be as 

few as two components at impact. 

From the above discussion, casualty areas for less extensive breakup were computed 

assuming two intact components that total 32,425 pounds. Casualty areas for more 

extensive breakup were computed assuming 143 fragments that total 31,787 pounds. 

Resulting total casualty areas for four sheltering categories are listed in Table 17. 

Corresponding risk estimates are listed in Table 18. In the third row of each table, note 

that sheltering becomes more effective with a larger number of smaller fragments. 

Table 17. Alternative Breakup Models 

Sheltered Casualty Areas (ft2) 

Breakup 

Model 

Number 

of Frags Open Light Medium Heavy

Two Pieces 2 1433 2283 2474 1520 

Baseline 70 5407 3253 2104 469

Many Pieces 143 9811 2779 1374 434 

Table 18. Sensitivity of Downrange Risks to Breakup Model 

Casualty Expectation 

Breakup 

Model Mode 4 Mode 5 Total 

Two Pieces 108.76 x 10-6 1.87 x 10-6 110.6 x 10-6

Baseline 142.48 x 10-6 2.56 x 10-6 145.0 x 10-6

Many Pieces 141.51 x 10-6 2.60 x 10-6 144.0 x 10-6

8.3.2 Sensitivity to Post-Impact Effects 

Impacts on hard surfaces may be a more reasonable assumption for unsheltered people 

in urban areas. On the other hand, the extent of post-impact effects, as modeled by RTI, 

has been questioned occasionally by other analysts. Consequently, casualty areas for 

people in the open were computed based on hard surfaces to yield a high estimate, and 

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excluding post-impact effects to yield a low estimate. RTI has no way of varying HACK 

computations for people in shelters. Resulting total casualty areas are listed in Table 19, 

and corresponding risk estimates are listed in Table 20. 

Table 19. Alternative Post-Impact Assumptions 

Sheltered Casualty Areas (ft2

) 

Post-Impact 

Effects Open Light Medium Heavy

Off 3630 3253 2104 469

Soft (baseline) 5407 3253 2104 469 

Hard 9594 3253 2104 469

Table 20. Sensitivity of Downrange Risks to Post-Impact Effects 

Casualty Expectation 

Post-Impact 

Effects Mode 4 Mode 5 Total 

Off 134.92 x 10-6 2.41 x 10-6 137.3 x 10-6

Soft (baseline) 142.48 x 10-6 2.56 x 10-6 145.0 x 10-6

Hard 163.74 x 10-6 2.97 x 10-6 166.7 x 10-6

8.4 Sensitivity to Population Counts 

Population counts are uncertain, especially given the movement of refugees in regions 

torn by natural disasters and civil war. In addition, it is typically assumed that population values are for indigenous peoples only, and do not include refugees or tourists. 

Populations for a year of interest (2005 for baseline risks) depend on estimated counts 

for some base year (2002 in this case) and estimated growth rates for subsequent years. 

Growth rates are also uncertain. Therefore, it seems reasonable that population estimates for year 2005 could easily be in error by as much as 20% (high or low). To provide 

further insight, five years of additional growth can be illustrated by updating to year 

2010. Including these adjustments, corresponding risk estimates are listed in Table 21. 

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Table 21. Sensitivity of Downrange Risks to Population Counts 

Population Casualty Expectation 

Year and 

Adjustment Mode 4 Mode 5 Total 

2005 – 20% 113.99 x 10-6 2.10 x 10-6 116.1 x 10-6

2005 (baseline) 142.48 x 10-6 2.56 x 10-6 145.0 x 10-6

2005 + 20% 170.98 x 10-6 3.15 x 10-6 174.1 x 10-6

2010 144.70 x 10-6 2.62 x 10-6 147.3 x 10-6

8.5 Sensitivity to Population Sheltering 

RTI's day and night sheltering percentages are intended as baseline values. Since it is 

difficult to predict the distribution of people among sheltering categories with much 

precision, two additional sheltering scenarios were investigated. To assess sensitivity 

for an upper threshold on effectiveness, RTI created a fictitious sheltering scenario that 

will be referred to here as substantial. Based on engineering judgment, fixed sheltering 

percentages for open, light, medium, and heavy categories were assigned as 0, 50, 30, 

and 20 percent, respectively, for all population cells. To assess sensitivity in the opposite 

sense, an unsheltered scenario, where all people are assumed in the open, was used. Risk 

estimates for substantial and unsheltered scenarios are compared to the baseline results 

for day and night in Table 22. 

Table 22. Sensitivity of Downrange Risks to Population Sheltering 

Casualty Expectation 

Sheltering 

Scenario Mode 4 Mode 5 Total 

Substantial 117.64 x 10-6 2.02 x 10-6 119.7 x 10-6

Day (baseline) 142.48 x 10-6 2.56 x 10-6 145.0 x 10-6

Night (baseline) 149.37 x 10-6 2.59 x 10-6 152.0 x 10-6

Unsheltered 262.30 x 10-6 4.65 x 10-6 266.9 x 10-6

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8.6 Sensitivity to Mode 4 Dispersions 

As discussed in Section 7.1, four dispersion factors were considered for the Mode 4 

portion of this study: guidance and performance (G&P) error, tumbling turn deviations, debris wind drift, and aerodynamic lift effects. Cross-track impact offsets were 

estimated for each debris class based on these dispersion factors. Total impact dispersion for each class was then determined by root-sum-squaring the four components at 

each downrange location of interest. Assuming a Gaussian distribution in the crosstrack direction, each section of the Mode 4 corridor (see Figure 4) was constructed to 

extend at least four sigma for any debris class. It should be noted that relative contributions from each of the four components change with ballistic coefficient (beta). 

To assess sensitivity with respect to Mode 4 dispersions, RTI chose to vary total crosstrack offset by first halving each component of dispersion and then doubling each 

component. Results show the effect of changing all four components simultaneously, as 

presented in rows two and three of Table 23. For this combination of vehicle configuration and mission trajectory, risk appears to increase as Mode 4 dispersions increase; 

however, that trend could reverse for larger multipliers. Each dispersion component 

was also doubled independently to illustrate its relative influence on risk. It can be seen 

in the table below that tumble and lift have little influence for this particular mission 

(e.g., debris characteristics, impact point rates, population distribution, etc.). The negative change for tumble indicates that slightly reducing impact probability near the 

centerline yields more effect than slightly increasing corridor width. 

Table 23. Sensitivity of Downrange Risks to Mode 4 Dispersions 

Casualty Expectation 

Mode 4 

Dispersion Mode 4 Total a % Change

Baseline 142.483 x 10-6 145.04 x 10-6 0.0

Total 0.5x offset 138.084 x 10-6 140.64 x 10-6 -3.0

Total 2.0x offset 151.975 x 10-6 154.53 x 10-6 6.5

G&P 2.0x offset 151.602 x 10-6 154.16 x 10-6 6.3

Tumble 2.0x offset 142.420 x 10-6 144.98 x 10-6 -0.043

Wind 2.0x offset 142.544 x 10-6 145.10 x 10-6 0.042

Lift 2.0x offset 142.485 x 10-6 145.04 x 10-6 < 0.01

a All totals include a constant Mode 5 risk estimate of 2.558 x 10-6. 

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8.7 Sensitivity to Wind Month 

For baseline risk estimates, wind effects over the region of interest were computed 

using December wind data from GRAM 99 (see Section 7.1). To assess sensitivity versus 

seasonal variations, risks were also computed using wind data for October and June. 

These results are presented below in Table 24. Since Mode 5 risk estimates are not a 

function of winds, this sensitivity is applicable to Mode 4 only. 

Table 24. Sensitivity of Downrange Risks to Wind Month 

Casualty Expectation 

Wind 

Month Mode 4 Mode 5 a Total

October 141.63 x 10-6 2.56 x 10-6 144.2 x 10-6

December (baseline) 142.48 x 10-6 2.56 x 10-6 145.0 x 10-6

June 141.66 x 10-6 2.56 x 10-6 144.2 x 10-6

a Monthly wind variations have no effect on Mode 5 risk estimates. 

8.8 Use of Covariance Data 

In an effort separate from this study, RTI investigated B-30 covariance data provided by 

Lockheed Martin.[27] A series of 6 x 6 matrices representing G&P (guidance and performance) error were processed to generate a trajectory (i.e., a collection of state vectors) 

that is similar to the 3-sigma dispersed trajectories typically used for risk estimation 

purposes. Details of this covariance processing are described in an interim RTI memorandum.[28] The alternative G&P trajectory was then used to compute Mode 4 risk 

estimates for comparison to baseline results, as shown in Table 25. 

Covariance data is based on a large number of Monte Carlo simulations, whereas a 

standard 3-sigma trajectory is constructed using a small number of selected simulation 

cases. Since these few cases are usually chosen to model extreme behaviors, it is reasonable to expect that covariance processing should yield smaller G&P dispersions. For the 

B-30 mission, that translates into lower Mode 4 risk estimates. 

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Table 25. Effect of Covariance Data on Downrange Risks 

Casualty Expectation 

G&P 

Trajectory Mode 4 Mode 5 a Total

Left 3-sigma

(baseline) 142.48 x 10-6 2.56 x 10-6 145.0 x 10-6

Covariance

3-sigma 138.67 x 10-6 2.56 x 10-6 141.2 x 10-6

a G&P trajectory variations have no effect on Mode 5 risk estimates. 

8.9 HACK Version Comparison 

RTI first tested and implemented what we refer to as HACK Version 2 (“HACK2”, 

developed by ACTA) in the February to March 2000 time frame. As used for downrange risk analysis, this roof penetration model includes four sheltering categories —

people in the open (assuming impacts on soft surfaces) and people in three structure 

types: light (e.g., a typical house), medium (e.g., a typical office), and heavy (e.g., a 

range blockhouse). RTI has a global population sheltering model that depicts distribution of people into these four categories on a country-level basis (see Section 6.2). Our 

model also includes four distinct population distribution scenarios: day, night, everyone in the open, and substantial sheltering. The latter two scenarios are used for 

sensitivity analysis purposes (see Section 8.5). To estimate baseline casualty areas, RTI 

procedures were used for people in the open (soft), and HACK2 was used for people in 

light, medium, and heavy structures (see Section 5). 

RTI first tested and implemented what we refer to as HACK Version 3 (“HACK3”, also 

developed by ACTA) in the November to December 2003 time frame. This roof penetration model is more complex than HACK2 and includes sixteen sheltering categories—

open (soft), open (hard), and people in fourteen combinations of roof type and location 

by floor: composite laminate (one floor), pre-engineered metal (“pre-metal”; one floor), 

steel (top floor, next floor down = “mid”, and all lower floors = “low”), concrete (top, 

mid, and low), wood (top, mid, and low), and wood with tile (“tile”; top, mid, and low). 

RTI was provided a population sheltering model, developed by ACTA for the B-30 

mission,[29] that depicts distribution of people into these sixteen categories on a countrylevel basis. This model includes two independent sheltering fractions for each category: 

one for urban regions and one for rural regions. In addition, separate parameter sets 

were provided for six distribution scenarios: day summer weekday, day summer weekend, day winter weekday, day winter weekend, night weekday, and night weekend. To 

estimate casualty areas, RTI procedures were used for open (soft) and open (hard) 

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categories, and HACK3 was used for the fourteen structural combinations. It should be 

noted that modifications needed for risk estimation have not yet been made to programs CORIDORE or RAPIEC (see Section 1). 

Casualty areas produced by HACK3, for a single fragment in each debris class, are 

listed in Table 27. The corresponding casualty areas produced by HACK2 were listed 

previously in Table 6 (see Section 5.3). It is interesting to note that the HACK3 responses 

for wood and tile roof types are quite similar for the debris examined in this study. 

Figure 10 presents a visual illustration of casualty areas from both versions of HACK. 

Casualty areas per fragment, for each roof type, are shown in Figure 14 and Figure 15. 

Values corresponding to individual floors have been averaged for each HACK3 roof 

type. Note that effective weighting would not be uniform if population fractions were 

considered. To enhance readability, debris class names were replaced with numeric 

indices in these figures. Debris class index designations are assigned to debris class 

names in Table 26. 

Casualty areas per fragment, for each floor location, are shown in Figure 16. Values corresponding to individual roof types have been averaged for each HACK3 floor location. 

Composite and pre-metal roof types are included in the "Top Only" results. Note that 

light, medium, and heavy structure types do not correspond to specific floors. 

Table 26. Debris Class Index and Corresponding Class ID 

Index Class ID Index Class ID Index Class ID Index Class ID

1 S2_01 9 PL_06 17 PL_14 25 PL_23

2 S2_02 10 PL_07 18 PL_15 26 PL_24

3 S2_03 11 PL_08 19 PL_16 27 PL_25

4 S2_04 12 PL_09 20 PL_17 28 PL_26

5 PL_02 13 PL_10 21 PL_19 29 PL_27

6 PL_03 14 PL_11 22 PL_20 30 PL_28

7 PL_04 15 PL_12 23 PL_21 31 PL_29

8 PL_05 16 PL_13 24 PL_22

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Steel Concrete Wood 

Class 

Open 

(hard) 

Composite Pre- metal Top Mid Low Top Mid Low Mid Low 

S2

_

01 407.91 505.55 689.88 260.49 22.57 406.02 8.02 97.67 540.02 567.32 529.42 

S2

_

02 254.05 160.79 453.64 276.15 34.15 27.75 7.40 0.00 435.53 452.48 438.49 

S2

_

03 144.23 121.47 361.73 166.92 89.21 25.65 81.20 12.56 296.04 316.65 301.59 

S2

_

04 149.43 0.00 0.00 0.00 0.00 0.00 0.00 0.00 11.28 0.00 

PL

_

02 266.71 184.12 475.67 487.28 220.35 344.20 116.85 36.63 369.30 384.15 353.68 

PL

_

03 87.65 21.81 107.44 13.96 5.99 0.00 10.19 0.00 185.43 125.33 35.78 

PL

_

04 27.02 94.83 21.06 8.62 3.93 11.11 2.39 0.00 186.10 113.73 

PL

_

05 37.03 9.53 44.10 6.09 3.82 7.14 1.82 0.00 84.13 85.25 56.10 

PL

_

06 164.52 16.04 185.30 11.29 0.00 0.00 0.00 0.00

Table 27. Casualty Areas for HACK Version 3 

Top

724.77 

0.00

3.38

8.46 0.00

353.86 

0.00

56.80 171.08

8.02 

0.00 202.60 9.27 0.00 

PL

_

07 87.87 11.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 25.79 0.00 0.00 

PL

_

08 119.23 30.71 209.94 20.77 3.18 0.00 12.20 0.00 0.00 226.85 170.45 40.04 

PL

_

09 72.56 22.26 100.69 15.07 8.06 1.56 12.97 0.00 0.00 177.87 150.13 73.88 

PL

_

10 60.45 35.52 132.55 34.16 13.23 5.32 10.88 7.00 0.00 211.62 199.94 173.60 

PL

_

11 57.64 33.07 122.51 30.04 11.64 5.11 10.48 6.20 0.00 203.51 193.53 162.84 

PL

_

12 127.76 99.67 211.96 120.04 89.67 44.89 65.25 17.05 7.28 238.54 246.20 230.24 

PL

_

13 82.19 27.20 117.94 20.05 7.33 1.57 14.09 0.00 0.00 201.50 171.59 96.68 

PL

_

14 72.28 28.11 113.08 21.57 7.89 2.87 12.53 1.63 0.00 199.23 175.69 124.89 

PL

_

15 59.70 35.86 133.24 34.79 13.59 5.47 10.93 7.31 0.00 211.93 200.88 175.47 

PL

_

16 117.30 13.15 3.78 0.00 0.00 0.00 0.00 0.00 0.00 89.06 0.00 0.00 

PL

_

17 156.89 92.59 345.67 136.61 61.17 14.17 55.47 11.75 2.38 292.28 304.53 292.28 

PL

_

19 80.24 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 

PL

_

20 505.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 

PL

_

21 86.55 60.00 271.97 68.54 18.16 3.24 16.82 4.61 0.00 263.96 276.09 254.99 

PL

_

22 55.26 9.79 39.90 13.12 0.00 0.00 0.00 0.00 0.00 108.03 53.87 4.27 

PL

_

23 55.53 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 

PL

_

24 75.99 20.12 98.07 13.46 7.84 0.45 12.15 0.00 0.00 180.16 134.03 51.47 

PL

_

25 78.90 58.63 145.49 60.58 34.07 13.06 18.92 7.03 4.12 222.37 225.78 207.32 

PL

_

26 146.66 32.45 242.71 21.03 0.00 0.00 4.06 0.00 0.00 237.09 152.23 6.04 

PL

_

27 97.69 62.75 233.03 77.11 38.84 10.30 21.55 9.14 2.16 246.72 251.24 237.33 

PL

_

28 197.39 24.07 254.83 10.46 0.00 0.00 0.00 35.23 0.00 279.87 50.60 0.79 

PL

_

29 61.36 15.24 74.00 11.33 7.33 0.00 9.28 0.00 0.00 152.01 110.11 42.49 

Total 9594.2 2264.7 7108.2 2637.3 1188.2 432.5 1257.3 453.8 160.9 8570.2 6007.6 4496.8 

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Figure 10. Casualty Areas per Fragment by Debris Class, Part 1 

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Figure 11. Casualty Areas per Fragment by Debris Class, Part 2 

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Figure 12. Casualty Areas per Fragment by Debris Class, Part 3 

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Figure 13. Casualty Areas per Fragment by Debris Class, Part 4 

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Figure 14. Casualty Areas per Fragment by Roof Type, Part 1 

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Figure 15. Casualty Areas per Fragment by Roof Type, Part 2 

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Figure 16. Casualty Areas per Fragment by Floor Location 

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9. Summary and Conclusions 

A downrange overflight risk analysis has been performed for the Titan IV B-30 mission 

using the methodology described in this document and currently available data. Including all assumptions discussed previously, RTI has estimated baseline total casualty 

expectation as 145 x 10-6 for day sheltering and 152 x 10-6 for night sheltering. The night 

value is larger because the model has more people inside structures at night, and 

simulated debris impacts are, in effect, collapsing at least some portion of the roofs. 

Varying only sheltering assumptions for comparison, total risk was found to increase by 

84 percent (unsheltered) and decrease by 17 percent (substantial) as compared to the baseline value for day sheltering. 

Using day sheltering assumptions and varying other key parameters, RTI's current 

estimates of downrange casualty expectation range from a low of 70 x 10-6 to a high of

235 x 10-6. Both of these extremes result from variations in failure probability. Within 

this range, increasing population count resulted in an estimate of 174 x 10-6, and reducing the extent of simulated breakup resulted in an estimate of 111 x 10-6. Variations in 

several Mode 4 parameters, including wind month, had little effect. It should be noted, 

however, that sensitivity to these parameters could change for other vehicle configurations and mission trajectories. 

Variations in failure probability and population counts have a direct scaling effect on 

downrange risks. This stems from the equations used to estimate casualty expectation 

for both failure response modes considered by RTI. Therefore, it should be expected 

that results will be sensitive to changes in these parameters. 

Risk estimates presented in this study are based on ACTA's HACK2 roof penetration 

model. Casualty areas from their new HACK3 roof penetration model were compared 

to HACK2 results, as discussed in the previous section. For most debris examined, the 

HACK3 model generates a larger casualty area than HACK2. It should be noted that 

RTI has not yet developed an independent population sheltering model which could 

support HACK3 data requirements. 

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuAfghanistan 42.62 47.52 8.28 1.58 5.52 89.51 4Albania 20.97 59.61 16.21 3.21 0.17 85.09 12Algeria 11.75 69.46 16.21 2.58 0.05 85.42 11American-Samoa 10.61 57.09 24.42 7.89 1.42 80.00 13Andorra 7.82 44.73 35.75 11.70 1.72 76.64 16Angola 50.56 40.43 7.52 1.49 6.25 89.56 3Anguilla 9.92 67.50 18.14 4.44 0.01 85.67 11Antarctica 100.00 0.00 0.00 0.00 100.00 0.00 0Antigua and Barbuda 12.13 65.72 17.54 4.61 0.05 85.04 11Argentina 8.25 47.96 27.86 15.93 1.34 77.57 16Armenia 22.85 59.67 14.67 2.81 0.20 85.60 12Aruba 7.03 36.60 45.06 11.31 1.74 75.70 17Ascension Isl 10.65 57.72 21.31 10.32 0.01 84.94 10Australia 8.38 45.96 34.42 11.24 1.64 77.31 16Austria 7.96 45.57 34.07 12.40 1.65 76.87 16Azerbaijan 15.45 65.49 16.00 3.06 0.09 85.43 11Bahamas 10.41 65.98 18.42 5.19 0.02 84.69 11Bahrain 9.07 66.01 19.69 5.23 0.00 85.04 11Baker Isl 10.65 57.72 21.31 10.32 0.01 84.94 10Bangladesh 20.95 62.47 14.52 2.07 0.18 84.82 12Barbados 12.20 64.62 18.13 5.05 0.04 85.56 11Belarus 14.30 66.54 15.89 3.27 0.07 86.59 11Belgium 8.25 47.93 32.81 11.01 1.68 77.19 16Belize 11.10 55.12 25.44 8.34 1.33 80.53 13Benin 39.33 49.62 9.12 1.93 5.33 89.34 5Bermuda 7.98 44.65 36.79 10.58 1.71 76.82 16Bhutan 35.24 52.08 11.50 1.17 0.38 83.55 13Bolivia 16.80 64.03 16.40 2.77 0.12 84.61 12

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuBosnia and Herzegovina 11.42 72.30 14.30 1.98 0.03 87.18 11Botswana 37.81 52.39 8.45 1.35 5.04 89.65 5Bouvet Isl 100.00 0.00 0.00 0.00 100.00 0.00 0Brazil 17.39 60.08 18.17 4.36 0.12 85.01 12Brunei 8.98 46.41 32.20 12.41 1.43 78.15 15Bulgaria 16.90 60.67 17.76 4.67 0.11 86.22 11Burkina Faso 46.10 44.83 7.82 1.25 5.88 89.80 4Burma 28.75 55.08 13.60 2.57 0.29 84.52 12Burundi 44.79 46.45 7.73 1.03 5.73 89.89 4Cambodia 35.06 47.15 15.04 2.75 0.38 83.03 14Cameroon 48.06 41.23 8.54 2.17 6.12 89.04 4Canada 8.00 43.89 36.30 11.81 1.66 76.86 16Canary Isl 15.64 64.75 15.43 4.18 0.09 85.95 11Cape Verde Isl 10.20 71.40 16.33 2.07 0.03 84.87 12Cayman Isl 7.48 39.52 40.95 12.04 1.66 76.28 17Central African Republic 40.40 50.80 7.85 0.95 5.26 89.94 4Chad 42.53 48.08 8.15 1.24 5.55 89.80 4Chesterfield Isl 100.00 0.00 0.00 0.00 100.00 0.00 0Chilcott Isl 100.00 0.00 0.00 0.00 100.00 0.00 0Chile 9.48 50.26 30.15 10.11 1.53 78.60 15China 13.74 53.27 23.92 9.07 1.34 82.91 12Christmas Isl 8.38 45.96 34.42 11.24 1.64 77.31 16Clipperton Isl 100.00 0.00 0.00 0.00 100.00 0.00 0Cocos Isl 8.38 45.96 34.42 11.24 1.64 77.31 16Colombia 15.83 62.71 17.63 3.82 0.10 85.01 12Comoros 48.27 43.71 7.13 0.89 5.97 89.94 4Congo, Democratic Republic 40.88 48.72 8.75 1.65 5.46 89.50 4Congo, Republic 36.00 45.01 12.95 6.04 5.37 87.04 6

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuCook Isl 39.85 46.28 11.27 2.60 5.45 86.39 6Costa Rica 10.00 50.55 29.91 9.54 1.48 79.17 14Cote D’Ivoire 41.37 48.54 8.52 1.57 5.46 89.56 4Croatia 9.23 53.06 28.30 9.41 1.68 78.24 15Cuba 10.28 51.81 28.23 9.67 1.58 79.33 14Cyprus 13.27 61.85 19.35 5.53 0.06 85.34 11Czech Republic 8.28 45.50 34.69 11.53 1.69 77.13 16Denmark 7.96 42.44 36.94 12.66 1.64 76.81 16Diamond and Tregosse 100.00 0.00 0.00 0.00 100.00 0.00 0Diego Garcia 10.65 57.72 21.31 10.32 0.01 84.94 10Djibouti 26.24 57.09 14.58 2.09 0.26 83.73 13Dominica 16.63 63.52 16.71 3.14 0.11 85.60 12Dominican Republic 11.80 66.91 17.77 3.53 0.05 85.23 11East Timor 18.67 63.06 15.45 2.82 0.14 85.18 12Ecuador 14.56 64.36 17.64 3.44 0.09 84.86 12Egypt 15.49 65.47 16.32 2.72 0.10 85.17 12El Salvidor 9.22 74.85 14.86 1.06 0.01 86.01 11Equatorial Guinea 40.88 43.87 10.88 4.37 5.64 88.08 5Eritrea 43.39 47.38 7.94 1.29 5.57 89.72 4Estonia 8.91 45.35 34.44 11.30 1.64 77.79 15Ethiopia 42.31 48.20 8.21 1.28 5.53 89.74 4Europa Isl 10.65 57.72 21.31 10.32 0.01 84.94 10Falkland Isl 17.30 66.80 11.94 3.96 1.46 86.45 8Faroe Isl 13.78 56.37 23.27 6.58 1.47 82.88 11Fiji 47.39 43.45 7.80 1.36 5.89 89.12 4Finland 8.67 46.57 33.61 11.15 1.66 77.57 15France 8.57 48.62 31.97 10.84 1.66 77.53 15French Guiana 12.17 67.33 17.13 3.38 0.05 85.51 11

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuFrench Polynesia 35.75 47.85 12.50 3.90 5.26 86.48 6French Southern 100.00 0.00 0.00 0.00 100.00 0.00 0Gabon 49.18 39.42 8.78 2.62 6.18 88.43 4Gambia 42.63 47.78 8.22 1.37 5.55 89.63 4Gaza Strip 9.95 67.81 18.93 3.31 0.03 83.90 12Georgia 23.56 55.44 16.50 4.50 0.21 85.22 12Germany 8.11 46.08 33.42 12.39 1.65 77.03 16Ghana 41.92 47.88 8.55 1.65 5.49 89.35 4Gibraltar 7.81 44.57 34.39 13.23 1.58 76.80 16Glorioso Isl 10.65 57.72 21.31 10.32 0.01 84.94 10Greece 9.98 52.71 27.93 9.38 1.67 78.94 14Greenland 9.85 64.31 20.37 5.47 0.01 85.34 11Grenada 15.30 61.92 18.37 4.41 0.10 84.07 12Guadeloupe 11.22 70.57 15.56 2.65 0.03 86.41 11Guam 8.23 43.88 35.57 12.31 1.44 77.37 16Guatemala 41.96 46.63 9.29 2.13 5.59 88.83 5Guernsey 8.20 44.54 37.37 9.89 1.78 76.95 16Guinea 44.07 46.62 7.94 1.37 5.64 89.68 4Guinea Bissau 45.01 45.61 7.93 1.45 5.72 89.60 4Guyana 14.70 64.33 17.32 3.65 0.08 85.47 11Haiti 42.67 47.74 8.22 1.37 5.52 89.47 4Heard Isl 100.00 0.00 0.00 0.00 100.00 0.00 0Honduras 14.85 62.74 18.56 3.84 0.09 83.99 12Hong Kong 10.84 50.87 28.17 10.12 1.56 79.84 14Howland Isl 100.00 0.00 0.00 0.00 100.00 0.00 0Hungary 8.88 49.93 30.60 10.59 1.67 77.84 15Iceland 9.64 46.73 32.56 11.07 1.54 78.63 15India 16.38 67.89 14.26 1.47 0.11 85.67 12

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuIndonesia 18.67 63.06 2.82 0.14 85.18 Iran 69.12 16.93 2.69 85.67 11Iraq 39.53 50.37 1.56 5.24 89.52 Ireland 46.14 33.40 11.68 77.76 15Israel 8.43 47.71 10.93 1.56 77.52 Italy 50.98 29.45 10.73 77.78 15Jamaica 14.09 64.04 4.13 0.08 85.12 Jan Mayen 57.72 21.31 10.32 84.94 10

15.45 12

11.26 0.04

8.54 5

8.78 1.58

32.93 15

8.84 1.70

17.74 11

10.65 0.01

Japan 8.09 43.21 35.66 13.04 1.65 76.93 16Jarvis Isl 0.00 0.00 0.00 0Jersey 36.77 44.18 11.43 1.74 76.24 Johnston Atoll 10.65 57.72

100.00 0.00 100.00

7.62 17

21.31 10.32 0.01 84.94 10

Jordan 9.31 71.78 16.48 2.43 0.01 85.39 11Juan De Nova Isl 10.65 57.72 21.31 10.32 0.01 10Kazakhstan 16.22 59.16 5.26 0.10 11Kenya 43.73 7.93 1.31 5.60 89.70 Kiribati 36.78 52.98 9.01 1.23 89.22 5Korea, North 11.51 53.54

84.94 

19.36 84.93

47.03 4

5.03

25.37 9.58 1.44 80.69 13

Korea, South 9.13 47.15 33.04 10.67 1.60 78.09 Kuwait 61.54 21.26 0.01 83.85 11

46.17 42.16 9.15 2.52 88.46 4

Laos 44.55 45.72 1.72 5.69 89.66 4Latvia

15

9.75 7.45

Kyrgyzstan 5.94

8.01

9.47 45.05 31.89 13.59 1.50 78.45

Lebanon 10.33 18.64 4.22 0.02 85.71 11

41.80 49.58 7.65 0.97 5.35 89.88 4

Liberia 40.47 50.27 8.13 1.13 5.30

15

66.81

Lesotho 

89.74 4

Libya 37.68 50.27 5.14 88.62 5Liechtenstein 6.85 32.61 42.83 17.71 1.50 17

9.68 2.37 

75.65

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuLithuania 10.00 48.99 29.91 1.56 78.99 14Luxembourg 7.69 39.37 11.92 1.69 76.48 16

11.10

41.02

Macau 7.06 36.72 41.31 14.91 1.55 75.93 17Macedonia 11.04 69.52 16.42 3.02 Macquarie Isl 100.00 0.00 0.00 100.00 0.00 0Madagascar 46.37 44.01 8.04 1.58 5.90 4Malawi 44.81 46.10

0.03 86.59 11

0.00

89.55

7.84 1.25 5.72 89.76 4

Malaysia 9.59 46.67 12.22 1.35 78.82 15Maldives 71.42 16.74 1.98 0.02 84.83 12Mali 42.31 48.13 8.22 1.34 5.53 89.74

31.53

9.86

4

Malta 8.70 50.07 31.00 77.68 15

7.89 42.84 37.13 12.14 1.67 16

Marshall Isl 41.50 8.38 1.13 5.50 89.74 4

10.23 1.67

Man, Isle of 76.72 

48.99 

Martinique 11.25 68.15 0.03 86.11 11Mauritania 39.21 50.08 9.06 1.65 5.31 5Mauritius 13.15 60.29 20.82 0.06 85.20 11Mayotte 16.28

16.82 3.78 

89.30

5.74

67.14 15.20 1.38 0.12 84.45 12

100.00 0.00 0.00 100.00 0.00 0

Mellish Reef 100.00 0.00 0.00 100.00 0.00 0

10.38 49.97 30.10 9.55 1.43 79.57 14

Micronesia, Federated States 13.40 67.83 16.12 2.64 0.07 McDonald Isl 0.00

0.00 

Mexico 

84.67 12

Midway Isl 10.65 10.32 0.01 84.94 Moldova 17.75 64.82 14.69 2.74 86.04 11Monaco 5.88 26.27 13.49 1.82 74.24 18Mongolia 49.45 9.56 0.68 0.45 83.89 13

57.72 21.31 10

0.12

54.36

40.31

Montenegro 11.26 70.41 15.70 2.63 0.03 87.05Montserrat 13.00 61.77 6.13 0.06 84.72 11

18.92 62.93 15.53 2.62 0.15 84.87 

11

19.10

Morocco 12

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuMozambique 43.50 47.45 7.88 5.58 89.72 4Namibia 47.50 9.38 2.39 5.47 88.94 5Nauru 7.05 33.53 44.88 14.55 76.09 17Navassa Isl 100.00

1.17

40.73 

1.37

0.00 0.00 0.00 100.00 0.00 0

44.88 7.66 1.14 5.82 4

Netherlands 8.29 46.43 33.99 1.67 77.20 16Netherlands Antilles 8.29 33.89 9.91 1.66 77.27 16Nepal 46.32 89.62

11.29

47.91

New Caledonia 34.80 49.39 12.10 3.71 5.12 86.89 6New Zealand 33.86 11.48 1.57 77.86 Nicaragua 17.69 62.47 16.73 3.11 84.29 12Niger 36.96 53.73

8.87 45.79 15

0.13

8.35 0.96 5.01 90.00 4

Nigeria 42.64 46.41 9.20 1.75 5.67 88.86 4Niue 39.85 46.28 11.27 2.60 5.45 86.39 6Norfolk Isl 8.38 34.42 11.24 1.64 77.31 16Northern Mariana Isl 62.44 20.89 6.97 1.67 78.95 14

7.67 38.63 40.32 13.38 1.61 76.48 17

Oman 8.71 69.65 18.52 3.12 0.01 85.04 12Pakistan 41.31 46.66 9.65 2.38 5.56 88.58 Palau, Republic 60.74 32.37 5.71 1.18 6.93 3Palmyra Atoll 10.65 57.72 21.31 10.32

45.96

9.70 

Norway

5

89.57

0.01 84.94 10

Panama 12.83 65.79 17.53 3.85 0.06 85.23 11

14.64 1.65 0.13 84.98 12

Paracel Isl 10.65 57.72 21.31 10.32 84.94 10Paraguay 11.67 56.01 24.66 7.66 1.37 81.04 13Peru 9.85 18.06 3.66 0.02 85.18 11Philippines 19.07 60.56 16.92 3.44 0.15 84.37 12Pitcairn Isl 53.60 40.62 5.36 0.42 6.11 90.00 3Poland 10.44 53.52 26.74 9.30 1.60 14Papua New Guinea 17.60 66.11 

0.01

68.43

79.49

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuPortugal 8.87 46.80 32.50 11.83 1.62 77.80 15Puerto Rico 8.76 51.81 30.08 9.35 1.65 77.82 15Qatar 9.07 71.18 16.93 2.82 0.00 86.62 11Reunion 9.87 70.47 16.74 2.92 0.02 85.76 11Romania 18.98 59.84 17.10 4.08 0.14 86.17 11Russia 9.51 50.14 29.61 10.74 1.61 78.50 15Rwanda 49.47 41.97 7.33 1.23 6.12 89.75 4Samoa 46.04 44.83 7.83 1.30 5.75 89.20 4San Marino 7.49 39.93 37.66 14.93 1.59 76.34 17Sao Tome and Principe 10.99 70.42 16.62 1.97 0.04 84.51 12Saudi Arabia 9.62 70.15 17.57 2.66 0.02 84.88 12Senegal 40.10 50.02 8.54 1.34 5.33 89.56 4Serbia 10.69 72.90 14.63 1.78 0.02 87.44 11Seychelles 10.03 71.72 15.81 2.44 0.02 86.22 11Sierra Leone 41.34 48.85 8.43 1.38 5.44 89.56 4Singapore 9.10 47.12 32.21 11.58 1.61 78.04 15Slovakia 8.65 44.36 34.55 12.44 1.59 77.56 16Slovenia 8.35 47.43 32.17 12.05 1.65 77.28 16Solomon Isl 41.34 48.85 8.43 1.38 5.44 89.56 4Somalia 45.99 43.84 8.41 1.76 5.90 89.27 4South Africa 13.82 66.60 16.63 2.95 0.07 85.52 11S. Georgia and Sandwich Isl 10.65 57.72 21.31 10.32 0.01 84.94 10Spain 8.97 51.69 29.15 10.19 1.70 77.93 15Spratly Isl 10.65 57.72 21.31 10.32 0.01 84.94 10Sri Lanka 15.30 67.39 14.91 2.40 0.09 86.12 11St Helena 10.38 70.92 15.49 3.21 0.02 86.72 11St Kitts and Nevis Isl 11.94 64.45 18.53 5.08 0.04 84.72 11St Lucia 15.95 66.06 15.55 2.44 0.10 85.40 12

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuSt Pierre and Miquel 8.04 45.91 32.05 14.01 1.46 77.18 16St Vincent and Grenada 16.95 59.79 18.46 4.80 0.12 84.31 12Sudan 46.79 43.84 7.86 1.51 5.92 89.65 4Suriname 11.19 69.93 16.30 2.58 0.04 85.84 11Svalbard 7.77 44.74 34.96 12.53 1.66 76.66 16Swaziland 42.45 46.04 9.12 2.39 5.63 89.16 4Sweden 7.94 44.54 35.58 11.94 1.67 76.82 16Switzerland 8.09 42.97 36.10 12.84 1.63 76.96 16Syria 15.24 65.08 16.89 2.79 0.10 84.57 12Taiwan 8.73 46.74 32.29 12.25 1.55 77.75 15Tajikistan 41.48 47.15 9.18 2.19 5.52 88.96 5Tanzania, United Republic 46.36 44.83 7.63 1.18 5.85 89.82 4Thailand 14.32 54.23 23.55 7.90 1.37 83.44 11Togo 41.60 48.49 8.57 1.34 5.50 89.46 4Tokelau 27.81 59.10 12.26 0.84 0.28 84.13 13Tonga 15.86 62.35 18.16 3.64 0.11 84.16 12Trinidad and Tobago 11.71 63.49 19.53 5.27 0.04 85.42 11Tromelin Isl 10.65 57.72 21.31 10.32 0.01 84.94 10Tunisia 12.87 66.95 16.91 3.27 0.06 85.62 11Turkey 10.47 74.74 13.83 0.96 0.02 86.82 11Turkmenistan 41.93 46.07 9.52 2.48 5.57 88.54 5Turks and Caicos Isl 12.14 69.78 15.44 2.64 0.05 85.41 11Tuvalu 17.84 64.28 15.08 2.80 0.13 84.80 12Uganda 11.40 60.27 21.97 6.36 0.04 84.63 11Ukraine 15.56 62.35 17.69 4.40 0.09 86.24 11United Arab Emirates 43.75 46.53 8.36 1.36 5.73 89.68 4United Kingdom 7.81 43.79 36.88 11.52 1.69 76.66 16United States of America 7.94 42.89 36.85 12.32 1.62 76.83 16

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Appendix A: RTI Sheltering Percentages as of 2003 

Day Night

Country Open Light Medium Heavy Open Light MediuUruguay 9.45 50.26 30.84 9.45 1.61 78.48 15Uzbekistan 21.79 56.66 17.54 4.01 0.19 83.95 12Vanuatu 27.78 56.32 13.55 2.35 0.28 83.91 13Venezuela 11.82 64.84 18.89 4.45 0.04 84.93 11Vietnam 25.74 57.35 14.47 2.44 0.24 84.64 12Virgin Isl 9.15 66.58 19.26 5.01 0.00 85.35 11Wake Isl 10.65 57.72 21.31 10.32 0.01 84.94 10Wallis and Futuna 17.35 66.38 14.85 1.42 0.13 84.86 12West Bank 10.34 67.60 18.62 3.44 0.03 84.30 12Western Sahara 36.94 53.31 8.64 1.11 5.06 89.88 5Willis Group 100.00 0.00 0.00 0.00 100.00 0.00 0Yemen 41.65 47.73 8.94 1.68 5.56 89.26 4Zambia 48.44 42.17 7.91 1.48 6.13 89.60 4Zimbabwe 44.66 45.43 8.30 1.61 5.72 89.26 4

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References 

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For Official Use Only R - 1 RTI/08360/103-13F

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For Official Use Only R - 2 RTI/08360/103-13F

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18. J. A. Ward Jr., “Sheltering Percentages for Areas Subject to Overflight from Cape 

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