Systems-Based Analysis of a Ship Borne Approach for the Detection of
Fissile Material Concealed in Cargo Containers
by
Brett P. Broderick
B.S. Electrical Engineering (2001)
Texas A&M University
Submitted to the Department of Nuclear Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Nuclear Engineering
at the
Massachusetts Institute of Technology
September 2004
@ 2004 Massachusetts Institute of Technology
All rights reserved
I
Cerified
Signatureof Author .............
.............
Department of Nuclear Engineering
August 31, 2004
Certifiedb
..........
. .K.i
--
Richard C. Lanza
Senior Research Scientist in Nuclear Engineering
n
Thesis Supervisor
Readby.........
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Michael J. Driscoll
Professor Emeritus of Nuclear Engineering
zAd .
,
Thesis Reader
Accepted
by................................................... ...
Jeffery A. Coderre
Chairman, Department Committee on Graduate Students
MASSACHUSETTS S~iirTL
OF TECHNOLOGY
OCT 1 12005
.IBRARIES
ARCHie .
Systems-Based Analysis of a Ship Borne Approach for the Detection of Fissile
Material Concealed in Cargo Containers
By
Brett P. Broderick
Submitted to the Department of Nuclear Engineering On August 31, 2004 in Partial Fulfillment
of the Requirements for the Degree of Master of Science in Nuclear Engineering
Abstract
The international maritime container trade, which imports an average of 19,000
largely uninspected cargo containers to United States ports each day, has been identified
as a potential avenue of attack for nuclear terrorism. Currently envisioned and deployed
defensive measures that seek to detect and interdict concealed fissile material once
containers have already reached a U.S. port do not adequately protect against nuclear
threats due to the unique power and range of nuclear weapon effects. This thesis
describes and examines a novel "ship-based" approach to container-borne fissile material
detection where suites of radiation detectors with imaging capabilities are enclosed in
standard, non-descript cargo containers and shipped in limited numbers aboard
commercial containerships. Outfitted with communication hardware, these dedicated
containerized units could provide crucial advance detection and notification of an
inbound nuclear threat while the danger is still safely removed from U.S. shores.
Attributes of the container shipping trade that would impact the performance and
viability of the proposed ship-based approach were identified and investigated. Average
available count times, based on the duration of shipping voyages, for container imports to
representative ports on the east and west coasts of the U.S. where found to be 19.2 days
and 13.3. days, respectively. These long count times will enhance the ability of the shipbased approach to confidently detect heavily shielded and well-concealed fissile material.
A distribution for the average distributed density of commercial cargo, which affects
radiation attenuation between the source and detectors, was also derived and found to
have a favorably low mean value of 0.198 g/cm3 .
The coverage efficiency (i.e. the number of containerized units required to
provide detection coverage over a given percentage of a reference vessel) variations
associated with prospective modes of deployment were also investigated using Matlabbased computer simulations. Evaluated deployment strategies ranged from fully random
placement of detection units to completely constrained optimal placement. Despite
holding important advantages in terms of stealth, random deployment was found to
require an average of between 2.2 to 3.3 times more detectors than optimal deployment,
depending on the desired level of detection coverage. This result suggests that some
combination of random and constrained deployment might yield an optimized balance
between stealth and coverage efficiency. This analysis also identified significant
efficiency and deployment flexibility benefits associated with units that could detect
sources at ranges equal to, or greater than, 70 ft (21.3 m).
Overall, no results were obtained that seriously challenged the potential efficacy
and viability of the proposed ship-based approach.
Thesis Supervisor: Richard C. Lanza
Title: Senior Research Scientist in Nuclear Engineering
2
Acknowledgments
I would first like to thank my research advisor, Dr. Richard Lanza. His patient guidance
and continuous stream of ideas were extremely helpful throughout this effort. I would
also like to thank Professor Emeritus Michael Driscoll for agreeing to serve as my thesis
reader. His insightful comments were invaluable to this thesis.
I owe an enormous debt of gratitude to Shawn Gallagher who first conceived of the topic
about which I wrote. Without his selfless collaboration and intellectual ingenuity this
thesis literally would not have been possible.
I would also like to thank Dr. Richard Wagner for his valuable feedback and continued
support.
The Federal government and the fine people at the U.S. Defense Nuclear Facilities Safety
Board provided financial support for this academic enterprise.
Rachel Batista was very helpful in making this thesis sound more like English, in
addition to generally making life more pleasant around the office.
Antonio Damato was gracious enough to share his cultural sophistication and his Matlab
expertise with an ugly American.
Finally, I'd like to thank Michael Pope for his many contributions and for sharing his
proficiency in a number of areas, not the least of which was his extensive knowledge and
appreciation of scientific jargon.
3
Table of Contents
Abstract ..........
.................................................................
Acknowledgments .
...
.......................
Table of Contents......................................
.......
Table of Figures..........................................................
List of Tables............................................
1 Nuclear Terrorism Threat .....................
1.1 Objectives and Organization of Thesis .......
1.2 Introduction
.........
2
................................. 4
.............................
.......................................
................ .....
....
................
....................
.........
1.3 Threat Dynamics..............................................................
1.4 Container Scenario Development...
.....................
..........
Fissile Material Detection.................
.............................................
2.1 Fissile Material Characteristics........................................................
2.1.1 HEU Radiation Signature ..................
....................
2.1.2 Pu Radiation Signature .
.........................................................
2.1.3
23 3 U Radiation
2
Signature ............................
8
11
11
11..
12
15
20
20
24
30
33
2.2
3
Detection Techniques ......................................
............................. 34
2.2.1 Active Detection .............................................................
34
2.2.1.1 Induced Fission .........
.........
.........
.................................
34
2.2.1.2 Radiography
...........................................
35
2.2.2 Passive Detection ................................................................
37
Detection Schemes ...................
4...................0.............
3.1 Current Approaches ..................................................................
40
3.1.1
3.2
4
Customs-Based..................
.............................
3.1.2 Smart Containers ................................................................
Ship-Based Approach ........
...................
3.2.1 Attributes ...................
3.2.1.1 Sensitivity ...................
.......................................
3.2.1.2 Stealth .................................
3.2.1.3 Standoff ....................................................................
3.2.2 External Uncertainties ............................................................
Shipping and Cargo Analysis ..
....
40
41
42
4...................2.............
43
44
44
45
........................................................... 47
4.1
4.2
Container Shipping Overview ........
.....
............................................
47
Count Time ...................
4...................9............
4.2.1 Distance Between Ports ...................
....................
50
4.2.2 Vessel Speeds
.
.......
................ 65
4.2.3 Voyage Times ......
........
........
...............................................
68
4.3 Vessel Container Capacities .......................
....................................75
4.4 Cargo Density ..
...........
...................... 77
5 Deployment Simulator
.................
81
5.1 Introduction ..............................................................................
81
5.2 Model Development .....................................................................
83
5.2.1 Assumptions........
...
5.2.2 Input/Output
.....
..
......
.........
5.2.3Algorithm
..... .. ......
4
.........
...
.........
.....
83
......................85
..........
85........
5.2.4 Validation and Verification......................................................
89
Random Deployment ........................
. .......................................... 91
Constrained Deployment..............................................................
114
5.3
5.4
5.5
Centerline Deployment .
......................
........................................
5.6 Deployment Comparison. ......................
......................................
5.7 Total Detector Estimates ...................
......................................
6 Summary, Conclusion, Recommendations . ......
.........................................
6.1 Summary...
...............................................................................
6.2 Conclusions ...............................................................................
6.3 Recommendations for Future Work...................................................
References..........................................................................................
Appendix A .........................................................................................
Appendix B
. ...................
5
126
139
141
143
144
147
149
152
156
174
Table of Figures
Figure 2-1. High resolution HEU spectrum ..........
..........
.............................
25
Figure 2-2. Dominant regions for different photon interactions .............................
26
Figure 2-3. Thorium series ................................................................
28
Figure 2-4. Photon interaction cross-sections for aluminum and lead......................
36
Figure 2-5. Schematic representation of source detection through
intervening material ................................................................
38
Figure 4-1. Map of upper North America showing selected ports ...........................
52
Figure 4-2. Map of the United States, Central America, and the Caribbean
showing selected ports .
....................................................
53
Figure 4-3. Map of Africa showing selected ports ............................................
54
Figure 4-4. Map of Europe showing selected ports ...........................................
55
Figure 4-5. Map of the Middle East and India showing selected ports .....................
56
Figure 4-6. Map of the Far East showing selected ports ......................................
57
Figure 4-7. Map of Australia showing selected ports.........................................
58
Figure 4-8. Vessel speed CDF ..................
67
.................................
Figure 4-9. Vessel capacity CDF ...............................................................
76
Figure 4-10. Cargo distributed density, Pdist, CDF .............................................
80
Figure 5-1. Container orientation for simulation..............................................
86
Figure 5-2. Cube bounding the detection sphere ..............................................
87
Figure 5-3. Coverage vs. Detectors plot for the 1440 TEU array [Random] .............
102
Figure 5-4. Coverage vs. Detectors plot for the 2496 TEU array [Random]...........
103
Figure 5-5. Coverage vs. Detectors plot for the 3600 TEU array [Random]...........
103
Figure 5-6. Coverage vs. Detectors plot for the 4800 TEU array [Random]...........
104
6
Figure 5-7. Coverage vs. Detectors plot for the 6460 TEU array [Random] .............
104
Figure 5-8. Graphical determination of detectors required for various
coverage levels...........................................
..........................105
Figure 5-9. Required Detectors vs. Range for the 1440 TEU array [Random] ..........
109
Figure 5-10. Required Detectors vs. Range for the 2496 TEU array [Random] ..........
109
Figure 5-11. Required Detectors vs. Range for the 3600 TEU array [Random] .......... 110
Figure 5-12. Required Detectors vs. Range for the 4800 TEU array [Random] ..........
110
Figure 5-13. Required Detectors vs. Range for the 6460 TEU array [Random] ..........
111
Figure 5-14. Required Detectors (with 45 ft. range) vs. Array Capacity [Random]...... 112
Figure 5-15. Required Detectors (with 55 ft. range) vs. Array Capacity [Random]...... 1 12
Figure 5-16. Required Detectors (with 65 ft. range) vs. Array Capacity [Random]......
1 13
Figure 5-17. Required Det ectors (with 75 ft. range) vs. Array Capacity [Random]......
1 13
Figure 5-18. Required Det ectors (with 85 ft. range) vs. Array Capacity [Random]......1 14
Figure 5-19. Coverage vs. Detectors plot for the 1440 TEU array [Constrained]........ 122
Figure 5-20. Coverage vs. Detectors plot for the 2496 TEU;array [Constrained] ......... 123
Figure 5-21. Coverage vs. Detectors plot for the 3600 TEU;array [Constrained] ......... 123
Figure 5-22. Coverage vs. Detectors plot for the 4800 TEU; array [Constrained]......... 124
Figure 5-23. Coverage vs. Detectors plot for the 6460 TEU; array [Constrained] ........ 124
Figure 5-24. Coverage vs. Detectors plot for the 1440 TEU array [Centerline] .......... 135
Figure 5-25. Coverage vs. Detectors plot for the 2496 TEU array [Centerline] .......... 136
Figure 5-26. Coverage vs. Detectors plot for the 3600 TEU array [Centerline] .......... 136
Figure 5-27. Coverage vs. Detectors plot for the 4800 TEU array [Centerline] .......... 137
Figure 5-28. Coverage vs. Detectors plot for the 6460 TEU array [Centerline] .......... 137
7
List of Tables
Table 2-1. Densities of common weapons-grade fissile materials .........
.............. 23
Table 2-2. Ratios of MFPs in selected materials to HEU ...................................
Table 2-3.
208 T1 gamma
lines and branching ratios ...................
23
.........................
28
Table 2-4. Decay rates for selected gamma emissions from plutonium
anditsdaughters
......... ......... ........
........................ 31
Table 4-1. Containerized cargo volume by U.S. port (CY 2003) ...........................
48
Table 4-2. Foreign container import data (CY 2003) ........................................
49
Table 4-3. Nautical distances from selected ports to New York
and Los Angeles .................................................................
61
Table 4-4. Vessel database capacity benchmark results ......................................
66
Table 4-5. Vessel speed statistics ...............................................................
68
Table 4-6. Voyage times from selected ports to New York and Los Angeles ............. 69
Table 4-7. Mean voyage times to New York and Los Angeles .............................
74
Table 4-8. Vessel capacity statistics ..........
76
........................................
Table 4-9. Average distributed density, Pdist, values for imported cargo ...................
79
Table 5-1. Properties of the OR operator ......................................................
88
Table 5-2. Spherical volume error ..............................................................
91
Table 5-3. Reference array dimensions ......................................................
92
Table 5-4. Mean fractional coverage results for variable run sizes .........................
93
Table 5-5. Random deployment simulation results .........................................
94
Table 5-6. Estimated number of detectors needed for various scenarios [Random]....106
Table 5-7. Double assignment probabilities for 20' and 40' containers [Random].....108
Table 5-8. Constrained deployment simulation results ......................................
8
116
Table 5-9. Estimated number of detectors needed for various scenarios
125
[Constrained] ....................................................................
Table 5-10. Centerline deployment simulation results .........
..
.........
.. 127
Table 5-11. Estimated number of detectors needed for various scenarios
..........
[Centerline]
............................................................ 138
Table 5-12. Random vs. Centerline deployment comparison ................................
140
Table 5-13. Average R/C values.................................................................
141
Table 5-14. U.S. port calls by vessel capacity.................................................
141
Table 5-15. Total detector estimates ...........................................................
143
Table 6-1. Results summary for deployment environment analyses......................
145
Table 6-2. Random deployment results summary ............................................
146
Table 6-3. Centerline deployment results summary.........................................
146
9
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10
Chapter 1: Nuclear Terrorism Threat
1.1 Objectives and Organization of Thesis
The objective of this thesis is to describe and analyze a novel "ship-based" approach,
proposed by Gallagher at the Massachusetts Institute of Technology (MIT), for the
detection of fissile material concealed in waterborne cargo containers.
The need for new
thinking will be established by investigating the nature of the threat posed by
unconventional nuclear attack and nuclear terrorism and then highlighting the critical
shortcomings of currently deployed approaches that seek to address this threat. The
attributes and advantages of the ship-based approach will then be examined in the context
of the threat and compared to existing detection and interdiction methodologies. Once a
case for the promise and utility of the proposed approach has been presented, analysis
will be performed to remove or constrain important remaining uncertainties related the to
potential efficacy and viability of a ship-based fissile material detection regime.
1.2 Introduction
The specter of nuclear weapons has loomed large over the Earth since their
dramatic introduction to the world in 1945. The nature of the threat that these weapons
pose to the United States, however, has evolved over time. The end of the Cold War
brought with it a relaxation of the conventional nuclear threat stemming from blast
hardened silos dotting the land, strategic bombers roaming the skies, and ballistic missile
submarines prowling the seas. Yet, the dissolution of the Soviet Union and the
ascendance of transnational terrorism has brought with it a new challenge for the nuclear
age, that of devising and implementing effective strategies to prevent the acquisition and
deployment of nuclear weapons by individuals and organizations who are not restrained
by the same means that had deterred nuclear catastrophes for more than half a century.
Although the dynamics of the threat have changed, what remains constant is the
understanding that the detonation of a single nuclear device on American soil would have
11
profound and lasting impacts on this country and the world, the scale and breadth of
which are difficult to comprehend.
1.3 Threat Dynamics
The September
11
th attacks clearly demonstrated that transnational terrorist
organizations have supplanted state-based actors as the primary (or at least most
immediate) threat to the security of the United States. To strengthen our homeland
security posture and develop more effective strategies to defend against attack, including
those involving unconventional weapons, we must seek to understand how the emergence
of this new adversary alters the nature of threats faced by the United States. The
transnational terrorist organizations we must combat today are not only fundamentally
different than the state-based adversary faced during the Cold War, they are also
markedly different from terrorist organizations that have been encountered in decades
past. Some critical differences, at least as they pertain to the threat of nuclear attack, can
be generally described in terms of deterability, material access, and motivation.
Nuclear aggression during the Cold War was deterred through the doctrine of
mutually assured destruction. This conventional means of deterrence was effective
because the primary belligerents were state-based actors having well-defined borders
with citizens and national assets to protect. Both the United States and the Soviet Union
developed nuclear arsenals massive enough, and deployment platforms and delivery
systems diverse enough, that any offensive nuclear strike was sure to be met with a
devastating retaliatory counterattack [Knorr, 1985]. Therefore, the motivation to unleash
nuclear weapons to destroy the enemy was checked by the understanding that a decisive
blow could not be struck without the assurance of a crippling reprisal. However, unlike
states, transnational terrorist organizations, in general, are highly mobile, have no
delineated territorial borders, and no populace to defend. Without fixed targets to be held
in jeopardy of counter-attack, a terrorist organization can hope to deliver a devastating
blow without the prospect (or at least the assurance) of immediate annihilation.
12
Therefore, a transnational terrorist adversary contemplating a nuclear attack remains
undeterred by conventional means.
Unlike a large state-based actor, a terrorist organization is unlikely to have open
access to a military-industrial infrastructure dedicated to the production of fissile material
and the design and assembly of nuclear weapons. Numerous barriers, both physical and
political, have been erected by international institutions to inhibit the flow of fissile
material from established nuclear states, which are susceptible to conventional means of
deterrence, to undeterred terrorist organizations [Bunn et. al, 2003]. As such, even highly
motivated, well financed terrorist groups will likely find gaining access to fissile material
the most difficult and daunting aspect of initiating a nuclear attack. The difficulty
associated with the procurement or acquisition of fissile material, and the resulting
scarcity of the commodity, has important implications for how an attack might be
planned and executed.
In the past, terrorist organizations used attacks primarily in an attempt to achieve
political objectives [NCT, 2000]. With this political motivation, it was thought that
terrorist organizations would eschew attacks that claimed large numbers of civilian lives,
because such an act would promote public outcry, inspire widespread condemnation of
the perpetrators and ultimately weaken support for their cause [Hoffman, 1995]. The
transnational terrorist organizations threatening the United States today, however, are
increasingly found to have at their core fanatical religious and ideological, rather than
purely political, motivations [Laqueur, 1998]. With radical religious ideology serving as
the basis, attacks are no longer carried out with the express purpose of meeting political
ends. Instead, they are executed to destroy infidels and punish the enemies of God/Allah.
As such, religiously inspired terrorist organizations now tend to view attacks that cause
mass casualties as desirable rather than taboo [Morgan, 2004]. This motivational shift
was summed up succinctly by former CIA director James Woolsey who said, "Today's
terrorists don't want a seat at the table, they want to destroy the table and everyone sitting
at it." [NCT, 2000]
13
Another key to understanding the threat posed by unconventional nuclear attack is
to appreciate the unique destructive capabilities of nuclear weapons. Although they are
often grouped alongside chemical and biological weapons under the generic banner of
weapons of mass destruction (WMD), nuclear weapons stand markedly apart even from
their other WMD brethren. The totality of destruction that can be wrought, together with
the massive spatial and instantaneous temporal scales over which their effects are
unleashed, combine to make the gravity of threats posed by nuclear weapons wholly
unique. Unlike chemical and biological agents that inflict harm by specifically targeting
and damaging human biological functions, nuclear weapons destroy in a much more
indiscriminate manner. With their combined thermal, blast, and radiation effects, nuclear
weapons inflict their damage on all forms of matter in their vicinity, including people,
buildings, and economically vital infrastructure. These effects can be devastating even at
distances far removed from the location of the actual detonation. Finally, the primary
effects of a nuclear detonation are all experienced more or less instantaneously and
simultaneously, and without warning. As such, there is no time for affected populations
to evacuate or seek refuge once a nuclear weapon has been actuated.
Given the destructive potential of nuclear weapons, the motivation and stated
desire of transnational terrorist organizations to obtain and use these weapons, and the
ineffectiveness of conventional means to deter terrorist-mounted nuclear attacks, it is
unacceptable to rely solely on existing barriers meant to prevent unauthorized parties
from gaining access to fissile material or assembled weapons. Realizing that no
individual barrier or safeguard is going to provide perfectly reliable protection, we must
develop multiple, redundant and diverse layers of protection that can impede or disrupt
all phases of attack from fissile material procurement to final operational deployment.
One important step in effectively implementing this type of defense-in-depth protection
philosophy is to identify and assess potential avenues of attack that could be used by a
terrorist adversary that had somehow managed to obtain fissile material. The
vulnerabilities of each potential avenue of attack should then be evaluated so that
deficiencies can be identified and remediated.
14
1.4 Container Scenario Development
One potentially vulnerable avenue of attack flows through US seaports where an
average ofjust over 19,000 cargo containers arrive by ship each day [MARAD(1), 2004],
any one of which could be used by an adversary to conceal fissile material or an
assembled nuclear device. Only about 4% of these incoming cargo containers currently
undergo any type of physical inspection [Lok, 2004]. The vulnerability associated with
thousands of opaque, largely uninspected, and loosely controlled cargo containers
arriving on U.S. shores everyday is compounded by the proximity of major seaports to
large metropolitan population centers. As a result of this collocation, a weapon arriving
in a major U.S. port is often already in range to cause massive casualties, regardless of
the intended ultimate target of the device. Despite security concerns, seaports and the
international container shipping trade are critical to sustaining modern global commerce
and to maintaining a healthy U.S. economy. The transaction of international commerce
requires an open architecture, where containerized goods can move freely and efficiently
between countries and across borders. Therefore a critical and urgent challenge remains
to develop and implement protective measures that can enhance the U.S. security posture
with respect to seaports and incoming containers of foreign origin, without unduly
burdening the free flow of commerce.
As a first step in meeting the challenge of successfully addressing port and cargo
container related vulnerabilities, a conservative threat scenario will be developed based
on carefully chosen and logically defended assumptions. Scenario development will
frame the problem, allowing helpful insights to be drawn. The resulting product will then
provide a means to evaluate the efficacy and highlight weaknesses of potential solutions.
The overarching assumption used in scenario development is that a rational,
determined adversary would always seek to maximize the probability of a successful
attack. (Despite fanatical religious ideologies, transnational terrorist organizations have
repeatedly proven themselves rational in the context of operational planning,
coordination and execution.) As discussed later, in detail, the following propositions are
15
some logical implications of the "rational enemy assumption" as applied to a
transnational terrorist adversary: 1) if an enemy somehow procures fissile material, they
will seek to weaponize it (if not already in the form of a functional nuclear weapon) and
use it; 2) an enemy will seek to weaponize unassembled fissile material prior to container
shipment to the U.S.; and 3) an enemy may provide some means (e.g. booby-trapping or
remote detonation capability) to thwart the successful interdiction and neutralization of a
deployed (i.e. shipped) weapon.
The assertion that a transnational terrorist organization, having obtained fissile
material, will weaponize it and attempt to use it is perhaps the most easily justified of the
preceding discussion. A number of leading figures in transnational terrorist organizations
(including al Qaeda) have openly professed their desire to obtain nuclear weapons and
there have been several well-documented attempts to purchase fissile material [Lee,
2003]. Additionally, these groups have demonstrated the motivation and ability to carry
out well planned, large-scale attacks that result in mass civilian casualties. Finally, as
noted previously, highly mobile, borderless terrorist organizations are not stymied by
conventional means of deterrence based on the threat of massive retaliation. Given the
vigor with which fissile material procurement has been pursued, the repeatedly
demonstrated willingness to employ ever more lethal tactics to carry out high-casualty
attacks, and the undeterred nature of the adversary, it is reasonable, and certainly
conservative, to posit that if a sufficient quantity of fissile material is obtained, a terrorist
organization would seek to assemble it into a weapon and use it for an attack.
The belief that an enemy would seek to ship a functional weapon to the U.S., as
opposed to unassembled fissile material, follows from the rational enemy assumption for
the following two reasons. First, to maximize the probability of a successful attack, an
adversary that had obtained unassembled fissile material would clearly want to avoid
disruption or detection during the device assembly process. Unfettered weapon assembly
and preparation would presumably be far easier to achieve abroad, in a location of the
terrorists' choosing, where they could enjoy a substantially stronger and more secure
support network, in addition to a less menacing intelligence gathering and law
16
enforcement presence than would be encountered in the United States. Second, a rational
adversary would seek to ship a functioning weapon rather than attempt to smuggle
unassembled fissile material into the U.S. to create the possibility that some degree of
operational success (i.e. a nuclear detonation causing significant casualties and physical
damage) could still be achieved even in the event that the device was somehow detected
or discovered prior to reaching its intended target. There is no such possibility of limited
success if the fissile material has not been weaponized prior to shipment.
The assertion that an adversary would seek to implement countermeasures such as
"booby traps" or remote detonation provisions to guard against interdiction and
disarmament prior to detonation can also be defended using the rational enemy
assumption. "Booby-traps" are defined here as a feature or features intended to trigger
detonation of the device if certain perturbations, such as mechanical or radiation probing,
are experienced. A remote detonation capability would give an adversary the opportunity
to detonate a detected weapon before it could be isolated and rendered safe. Despite the
technological difficulty of implementing such features, the presence of countermeasures
to guard against interdiction cannot be ruled out since the rational-enemy assumption
dictates that an adversary would aggressively seek to ensure detonation once the weapon
was deployed. The desire to ensure detonation, using any available means, would only
be amplified by the extremely limited availability of fissile material and the extraordinary
efforts that were likely required to obtain it. Even if the device did not reach its intended
target, a nuclear explosion impacting any Western port or territory would presumably be
a marginally successful outcome for a terrorist organization.
Finally, to accept the rational enemy assumption but to reject the possibility of
countermeasures being present requires the assumption that an enemy is not capable, for
whatever reason, of implementing them. However, the fact that we concern ourselves
with screening cargo containers for fissile material in the first place implies that we are
willing to accept that an enemy possesses a level of sophistication high enough to
procure, transport, (possibly) assemble and deploy a nuclear weapon, all without being
detected or exposed by any military, law enforcement or intelligence gathering
17
organization. It seems, therefore, wholly irrational to then assume that the same enemy is
not sophisticated enough to devise and implement effective countermeasures.
Consistent with the assumptions discussed in the previous paragraphs, we now
postulate a scenario in which a functional nuclear weapon is concealed in a standard, full
sized (40' long, 8' wide and 8.5' high) cargo container and deployed from a foreign
location aboard a transoceanic container vessel that is due to call on a major United
States seaport that is in or adjacent to a large urban population center (e.g. New York
City or Los Angeles). We conservatively assume that the weapon is surrounded with
some level of shielding appropriate for the fissile material used in the weapon (i.e. high
atomic number material for uranium or both low and high atomic number material for
plutonium). We further assume that the device has been outfitted with counterinterdiction features, including a remote detonation capability and booby-traps that
trigger the weapon in the event that certain mechanical or radiation insults are
experienced.
We consider the above scenario (referred to hereafter as "the container scenario")
to be conservative and bounding. As such, it is assumed that an approach that can defeat
this extremely challenging scenario can similarly defeat any number of less conservative,
less challenging scenarios. We further believe that the highly conservative nature of the
container scenario is appropriate considering the extraordinarily dire consequences of a
successful nuclear attack on U.S. soil and the fact that none of the (admittedly)
improbable elements of the scenario can be confidently excluded as incredible.
Using the postulated container scenario we can now make a number of useful
observations regarding the capabilities that will be required to successfully address the
specific vulnerabilities associated with the commercial maritime container trade as an
avenue for nuclear attack. First, it is clear that the only way to ensure adequate protection
from this threat is to keep the weapon (or the container concealing the weapon) from ever
reaching U.S. shores. To do this, not only must the weapon be detected prior to the
threat-bearing vessel reaching a U.S. port of call, but the presence of this threat must also
18
be communicated to appropriate parties in time for an effective response to be mobilized
prior to port entry. Additionally, the initial threat detection must be made in a manner
that accounts for the possibility that countermeasures may be present, which could
function the weapon if intrusive perturbations are experienced.
The ultimate success criterion for any defensive measure (or measures) in
defeating the container scenario or any other postulated nuclear attack is not the detection
of the device; it is the ability to prevent a nuclear detonation that physically impacts the
United States. Detecting the weapon is a necessary but not sufficient step toward
defeating this threat. Stated differently, the deployment of a defensive measure that
detects incoming fissile material with perfect effectiveness and reliability (even if this
were possible) fails to adequately protect against the threat of nuclear attack if the
weapon isn't detected until it is already in range to impact the United States (e.g. in a
U.S. port).
19
Chapter 2: Fissile Material Detection
2.1 Fissile Material Characteristics
It is clear both intuitively and from the earlier discussion of the container scenario
that no nuclear attack will be thwarted if the concealed weapon is never detected. As
such, it is useful to investigate the common properties of fissile material and the various
ways in which these properties can be exploited to remotely detect the presence of this
material without the luxury of having physical access to the inside of each cargo
container.
In the current context, a nuclide is defined as fissile if it can undergo neutroninduced fission with the absorption of a neutron of any energy. The ability to fission
readily when interacting with neutrons of any energy regime makes fissile isotopes
critically important in producing and sustaining the fission chain reactions that give
nuclear weapons their explosive power. For the purposes of this analysis, fissile
materials will be generally defined as materials containing fissile isotopes in sufficient
quantities to make them suitable for use in nuclear weapons. Although nuclear weapons
can theoretically be constructed using more exotic materials, such as neptunium or
americium [Albright et. al, 1999], the following discussion will focus on materials that
contain the fissile isotopes 239pu, 235U, and 233 U.
Natural uranium has an isotopic composition of 99.28% (by weight) 238 U, 0.72%
235 U, and 0.0055%
235 U
234U.Uranium is considered enriched if the abundance of the fissile
constituent is artificially increased above its naturally occurring level. Uranium that
is greater than 20%
235 U
is classified as highly enriched. The 20% cutoff corresponds to
the minimum enrichment, as identified by the International Atomic Energy Agency
(IAEA), required for materials that can be used in nuclear weapons [IAEA, 2001].
Unlike the fissile 235U isotope, 238U can only be made to fission with neutrons exceeding
a threshold energy of approximately 1 MeV [Krane, 1988]. This threshold makes
20
uranium with a high 238U content unsuitable for creating and sustaining chain reactions
because not all neutrons produced during a given generation of fissions will exceed the
238U energy threshold
and be available to create subsequent fission events. The
population of neutrons energetic enough to fission 238U would be further decreased as
neutrons undergo inelastic scattering events that transfer some of their energy to the
nuclei with which they interact. As a result, the highly enriched uranium (HEU) used in
nuclear weapons typically has an enrichment of greater than 90% 235U [Bunn et. al,
1997].
Plutonium, unlike uranium, is not a naturally occurring element and must be
produced artificially. Fissile
239 Pu is
typically bred in a nuclear reactor through the
following transmutation chain and then chemically separated.
238 U
(n,y)>239 U
>239
2d
23.5m
Weapons grade plutonium is rich in the fissile
defined as containing less than 7% of the
Np
P
65 >239
23 9 Pu isotope
24 0 Pu isotope
P
56.5h
(again above 90%) and is
[DOE, 1994], which is considered
a contaminant by weapons designers. Reactor grade plutonium also contains 239Pu,but is
defined as containing greater than 7% 240pul . Each type of plutonium also contains
varying amounts of other plutonium isotopes including 238 Pu,24 1pu, and
242pu.
Although
weapons grade plutonium (as the name implies) is vastly preferable for use in fabricating
a nuclear weapon, reactor grade plutonium can also be used to produce an explosive that
delivers a nuclear yield2 [Mark et. al, 1987]. For this reason, and because a terrorist
organization is unlikely to be picky if an opportunity to obtain this material avails itself,
reactor grade plutonium has been included in the discussion, despite the added weapon
design and assembly difficulties associated with its use.
' Plutonium containing between 7 and 18% 2 4 0 Pu is sometimes referred to as fuel grade.
2 In 1977 the United States declassified
the existence of an underground test conducted in 1962 where a
nuclear device fabricated with reactor grade plutonium was successfully detonated.
21
233U is not
a constituent of naturally occurring uranium and, like plutonium, must
be produced artificially. This fissile nuclide is bred from thorium in nuclear reactors
through the following transmutation chain.
232
Th
(n,)
233
Th 22.3-
233
Pa
6
27.0d
>233
U
Uranium bred and chemically separated from thorium blankets is contaminated with
varying amounts of 232U. 233U is not nearly as popular as
2 35 U
and
239 Pu for
use in
nuclear weapons (no country is publicly known to have produced weapons using 233U
[NTI, 2003]) because of radiation dose concerns arising from the 232U contaminant.
However, this material is very capable of producing a nuclear explosion, evidenced by a
bare sphere critical mass3 smaller than that of 235 U [NERAC, 2000]. Currently, the
worldwide availability of 233 U is rather small compared to other fissile materials that are
likely being coveted by terrorist organizations. However, a number of countries, most
notably India (already a nuclear weapon state), are considering the use of a 233Uproducing thorium fuel cycle for nuclear power generation [Gopalakrishnan, 2002].
Despite their many physical, chemical, and metallurgical differences, fissile
materials have a number of common traits that can be used as a basis for detection. One
characteristic that is obviously shared by all fissile materials is that they can be made to
fission. When fissile materials are bombarded with neutrons of any energy or gamma
rays above a threshold energy4 , fission (or so-called photo-fission in the case of gamma
bombardment) will occur and neutrons and prompt gamma rays will be released
immediately as a result of the fission event, followed by delayed gamma rays (and
occasionally delayed neutrons) emitted by subsequent decay and de-excitation of the
fission products. Unlike the heavy ionized fragments created during fission and the beta
particles that are typically emitted as these fission products decay toward stability,
neutrons and gammas are uncharged. Due to their lack of electronic charge, these
particles do not undergo Coulomb interactions with the atomic electrons of the matter
3 The bare sphere critical masses of 233U and 235U are 16.4 kg and 47.9 kg, respectively.
4For 235U and 239 Pu, the photo-fission threshold energy is about 5.3 MeV [Fetter(l), 1990]
22
through which they pass so they can travel a relatively long distance before and between
interactions. The long-range nature (relative to other forms of nuclear radiation) of
neutrons and gammas makes them particularly well suited to the task of detecting fissile
material at a distance using conventional equipment and well-understood methods.
Another useful characteristic shared by all fissile materials is that they have high
densities, and are able to readily absorb gamma rays and neutrons. Densities of some
common weapons-grade fissile materials are shown in Table 2-1 [Mark et. al, 1987].
Table 2-1: Densities of common weapons-grade fissile materials
HEU
(94% U-235)
Weapons Grade Pu
delta phase
alpha phase
18.7 g/cmA3
19.86 g/cmA3
15.6 g/cm^3
One way to quantify how effectively a material can absorb a particular type of radiation
is to define the mean free path of that radiation in the material. The mean free path is the
average distance traveled between interactions. Since each interaction creates the
opportunity for scattering or absorption, a short mean free path, or equivalently, more
average interactions per unit length, indicates that the material is effective in absorbing or
shielding that particular radiation. Table 2-1 below shows the mean free path ratios
between HEU and a number of other materials for neutrons and gamma rays of several
different energy regimes [Fetter(l), 1990].
Table 2-2: Ratios of MFPs in selected materials to HEU
Gamma Rays
Neutrons
Ratio of MFP in element to that in HEU
Al
Fe
W
Pb
Energy
MeV
C
0.4
10
100
22
23
56
19
16
27
thermal
50
240
24
40
70
0.001
10
3.0
2.2
16
2.4
2.2
1.5
1.6
0.94
4.1
1.5
6.7
4.3
5.5
1.4
1.1
1.1
2.0
1.8
1.7
Ratios in Table 2-1 greater than unity indicate a larger mean free path in the reference
material than in HEU. Plutonium with its similar density, atomic number, and ability to
23
fission (even with thermal neutrons) would produce comparably small mean free paths
for gamma rays and neutrons at energies tabulated above.
Fissile materials are also radioactive. However, since each type of fissile material
has a distinct isotopic composition, which in turn gives rise to distinct populations of
decay progeny, each of the materials produce intrinsic radiation signatures that can differ
in terms of character and intensity. The characteristic emission signatures for each type
of fissile material will now be identified and discussed separately in the context of how
they can be used to facilitate remote detection.
2.1.1HEURadiationSignature
The isotopic composition of a radioactive material determines both the nature and
energy of the radiation emitted. Therefore to begin discussing the radiation signature of
HEU, the general composition of this material must first be revisited in greater detail.
The primary constituents of HEU are the naturally occurring
2 3 8 U, 235U,
and
2 34 U
isotopes. To produce weapons-usable material, some means of enrichment (e.g. gaseous
diffusion or centrifuge enrichment) must be employed to artificially raise the relative
abundance of the fissile 235U isotope to well above its natural level of 0.72%. Because
most means of enrichment exploit the fractional mass differences between isotopes, the
trace amount of 2 34 U found in natural uranium is also preferentially enriched along with
235U
due to its comparatively low atomic mass. If none of the material used as input, or
feedstock, to the enrichment process had ever been irradiated in a nuclear reactor, than
the naturally occurring nuclides listed above would be the only uranium isotopes present
in the resulting HEU. However, if even a minute fraction of the enrichment feedstock
had been irradiated (and subsequently reprocessed), the HEU output would likely be
contaminated with small amounts of the non-naturally occurring 232U,
236U,
and 237U
isotopes [Peurrung, 1998].
As the
23 5U, 23 8U,
and 234U isotopes (as well as the
23 2 U, 23 6U,
and
2 37 U
contaminants that may be present) begin down their long decay chains toward stable
24
nuclides, alpha and beta particles are emitted as individual nuclei decay. While these
short-range, charged particles are generally unhelpful for remote detection, the longrange characteristic photons that often accompany these decays can be usefully exploited.
The gamma rays emitted as the excited daughter nuclei created during alpha or beta
decay transition to lower excited states or their ground states, give rise to a rich and
complex spectrum of photons that can penetrate surrounding material and be detected at a
physically removed location. Since gamma ray energies are determined by the
characteristics of the emitting nucleus, peaks in the measured spectrum can be used to
unambiguously identify the presence of specific isotopes. The HEU spectrum, as
measured using a high resolution, high purity germanium (HPGe) detector, is shown in
I
Figure 2-1 [Gosnell,
2000].
I ____...
.-
i
. I
tx10 6
lx10
5
lx10 4
1x10
3
O0
O
U)
Z0
U
z
lx10 2
1x10
1
x10O o
lx10
-1
0
500
1000
1500
2000
2500
3000
Energy (keV)
Figure 2-1: High resolution HEU spectrum
As indicated by the magnified region of Figure 2-1, the characteristic gamma
lines emitted by 235 U are concentrated at the low energy end of the spectrum. The most
intense of the 59 discrete lines emitted by 23 5 U is at 186 keV and the most energetic line
emitted with a reasonably high intensity is at 205 keV. Unfortunately, these photons are
25
not highly penetrating because most types of matter have large linear attenuation
coefficients in this energy regime, with a particularly large contribution from the photonabsorbing photoelectric process. Figure 2-2 shows the dominant regions for various
types of photon interactions as functions of the atomic number of the transmission
medium [Evans, 1955].
§
0
N
0.01
0.05
0.1
0.5
1
E. (MeV)
5
10
50
100
Figure 2-2: Dominant regions for different photon interactions
As a result of the high probability of photoelectric interaction, which results in the loss of
the photon in the process, dense matter shields low energy gamma lines emitted by
235 U
very efficiently. In uranium the mean free path of 200 keV gamma rays is 0.5 mm, so a
significant fraction of these low energy photons are subject to self-absorption within the
HEU from with they originate [Fetter(2), 1990].
The most notable contribution to the HEU spectrum stemming from residual 238U
is the 1001 keV line arising from the isomeric transition of
234 mPathat
is created through
the following series of decays.
a
4.5 Gy
>234
Th
d
24.3d
>234m
Pa
Although this line is highly penetrating and emitted with reasonably high intensity, the
use of gamma rays that arise from 238U (or its daughters) for fissile material detection
26
purposes is inherently problematic. This is due in part to the fact that the presence of
238
U doesn't necessarily indicate the presence of HEU. Additionally, the ubiquitous
nature of the 238U isotope, particularly in terrestrial settings, produces a significant
amount of nuisance background that can confound detection efforts.
Because gamma lines emitted by 235U are intense but not highly penetrating and
lines emitted by
23 8U
(and its daughters) are less than ideal for fissile material detection,
gamma emissions stemming from the decay of 232 U and its daughter products can prove
extremely useful for remote detection applications.
232U is produced
primarily through
the following reactions in a nuclear reactor [Peurrung, 1998].
(1)
(2)
(3)
235U
U
'234
a
704My
a
246ky
235 U
>230
Th
Np a-
238U (n,2n) >237 U
231
Th 25.5h
V
(n,y) >237
>236 PU a
>237
(n)
231
25.5h
Th (r)
(n,y)>236 U
236m
(4)
231
>232
Np
U
232
Pa (ny)
>231
> 237
>
6.8
Pa
Np
31.4h
>232
>232
U
Pa 31 .4h
>232
U
n,2n) >
2
U
,2 ) >236m
6.8d
Np
'1
-
22.5h
>236 PU a >232 U
2.9y
The reactions shown above (particularly the first two listed) are the most significant
pathways by which 232U is produced in a reactor, provided that actinide impurities arising
from previous irradiations have been removed from the initial fuel prior to loading
[Perrung, 1998]. If present in HEU, 232U will decay through a long chain of successive
alpha and beta decays through the so-called thorium series depicted below in Figure 2-3
[Krane, 1988].
27
Figure 2-3: Thorium series
The thorium series is shown in detail because several of the distant daughter products of
23 2
U emit high energy, highly penetrating gamma lines that can significantly enhance the
distance at which HEU can be remotely detected. Of the daughter products found in the
thorium series, the one with the most utility for detection is 208 T1. The beta decay of
208T1
to stable 208 Pb is accompanied by one or more high-energy photons emitted as the
daughter nucleus de-excites. Table 2-2 shows the energies of the most intense gamma
ray lines produced by
208T1 decay,
as well as the branching ratios of these lines [Fetter(3),
1990].
Table 2-3: 208TI gamma lines and branching ratios
Gamma Energy
Branching Ratio
(keV)
(% per decay)
583.0
860.3
86.0
12.0
1620.7
1.51
2614.4
99.79
28
Because of their significant branching ratios and highly penetrating nature, the 583 and
2615 keV
208 T1 gamma
lines can be particularly useful in detecting HEU that is
contaminated with the 232U parent nuclide, even if 232 U is found in concentrations less
than 1 ppb [Fetter(1), 1990]. The prominence of these two peaks in the HEU spectrum
can be seen in Figure 2-1. The 2615 keV photon is especially noteworthy because photon
interaction cross-sections at this energy are generally quite low, which allows this gamma
line to be powerfully penetrating and quite long range. Also, as shown in Figure 2-2 the
Compton scattering process dominates the overall interaction cross-section at 2615 keV,
so even when an interaction does take place, the photon will most likely be scattered
(albeit losing some energy in the process) instead of absorbed. Additionally, in general,
the background rate in this high-energy region of the spectrum is fairly low, so a source
that emits gammas in this regime can usually be detected more easily than a low energy
gamma emitter. Unfortunately, as the thorium series in Figure 2-3 demonstrates,
not the only potential source of 20 8T1 and its 2615 keV decay photon.
2 32 Th,
232U
is
an isotope
that represents greater than 99% of naturally occurring thorium and is 3 times more
abundant in the earth's crust than natural uranium [WNA, 2003], also decays down to
208Tl and can
produce a very strong background signal, which inhibits confident detection
of HEU.
Like many other extremely heavy isotopes,
238 U
and
23 4 U can
undergo
spontaneous fission. In general, spontaneous fission is more likely in nuclides with even
numbers of protons and neutrons and becomes increasingly important as atomic number
increases. However, it does not seriously compete with alpha emission as the dominant
decay process until atomic mass increases above about 250 [Krane, 1988]. As a result,
238U and 234U both
have partial half-lives for spontaneous fission that are significantly
longer than their total half-lives. (Partial half-lives are defined as the time necessary for
half of the nuclei in a given sample to decay if only a single specified decay process were
allowed to occur.) 2 38 U has a partial half life for spontaneous fission of 8.20x1015 yr
versus a total half life of 4.468x 109yr and 2 34 U has a spontaneous fission half life of
2.04x1016 yr versus a total half life of 2.455x10 5 yr [Fetter(4), 1990].
29
Several other processes contribute to neutron generation in HEU. One is the
production of neutrons through (a,n) reactions that can occur when light element
impurities (e.g. carbon and oxygen) in the material interact with alpha particles emitted
by the uranium nuclides and their daughter products [Fetter(2), 1990]. The other process
influencing the neutron population in HEU is the multiplication that occurs when an
existing neutron induces fission in the fissile material thereby releasing additional
neutrons. The degree of multiplication is strongly dependant on the geometry of the
material.
Despite the effects of multiplication and the neutron production that could occur
due to (a,n) reactions in light element contaminated material, spontaneous fission events
in 238Uand 234 U occur infrequently enough that the intrinsic neutron signature of HEU is
very small and essentially undetectable for the remote detection application of interest.
2.1.2 Plutonium Radiation Signature
Both weapons grade and reactor grade plutonium contain essentially the same
plutonium
isotopes ( 238pu,
2 39
Pu,
1
240pU, 24 pu
and
24 2
Pu) but in different concentrations.
Weapons grade plutonium is typically composed of greater than 93% 239Pu,around 6%
24 0
Pu, and small quantities (less than 1%) of
238
Pu, 241pu,
and 2 42pu [Fetter(1), 1990].
Reactor grade plutonium, a material that does not have uniquely specified isotopics, has
been produced and separated from higher burnup fuel than weapons grade plutonium,
giving it a lower concentration of 239 Pu and higher relative concentrations of the 238 Pu,
240pu, 241pu, and 242 Pu isotopes [Mark, 1990].
All of the plutonium isotopes identified above are radioactive, and just as in the
case with HEU, the alpha and beta decays undergone by these isotopes and their daughter
products are accompanied by the emission of one or more characteristic photons. The
most prominent gamma lines in the plutonium spectrum arise from the decay of 239pu,
and the decay of the 24 1pu isotope's daughter product.
239 Pu is
an alpha emitter with a
half-life of 2.41 lx105 yr. The two most intense gamma lines arising from the 239 Pu alpha
30
decay are at 375 and 414 keV with branching ratios (% per decay) of 0.00158 and
0.00151 respectively [Fetter(3), 1990]. The most energetic line emitted by 2 39 Pu with a
24 1 Pu has
useful intensity is at 769 keV, and has a branching ratio of 0.000011.
of 14.35 yr and beta decays to
24 1
Am
a half-life
99.9976% of the time [Oetting, 1968]. The
24 1 Am
daughter then alpha decays with a 432.2 yr half-life emitting gammas at 662, 721.96 and
722.70 keV with respective branching ratios of 0.00036, 0.00006 and 0.00013 [Fetter(3),
1990]. The peak energies of the later two photons are exceedingly difficult to resolve,
using even high-quality semiconductor detectors, because the peak energies are so close
together. As such, the counts from these two photons can be aggregated into one peak
centered at approximately 722.5 keV, with a combined branching ratio of 0.00019. Table
2-4 shows the decay rates of the gamma emissions discussed above5 [Fetter(3), 1990].
Table 2-4: Decay rates for selected gamma emissions from plutonium and its daughters
Parent Isotope
Gamma Energy
(keV)
Decay Rate
(g x s)^-1
Pu-239
Pu-239
Pu-239
Pu-241
Pu-241
375
414
769
662
722.5
36300
34600
252
174000
92000
In the case of weapons grade plutonium, the
239 Pu and 241 Am
gamma lines
identified above can be fairly helpful for remote detection due to their reasonable
intensity and good penetrating power in most materials. Since reactor grade plutonium
has a significantly higher concentration of both 241pu and
241Am, the highly
penetrating
662 and (averaged) 722.5 keV can become quite intense. Consequently these gamma
lines can be extremely helpful in remotely detecting reactor grade material.
It should also be noted that because
2 39 Pu and 2 4 1 Am are
not naturally occurring
isotopes, the detection of plutonium using the gamma lines discussed above does not
suffer from the same problems associated with natural background that can complicate
HEU detection. However, 241Am is used in commercial products such as smoke detectors
5 Decay rates in Table 2-4 assume 10-year-old plutonium (i.e. 10 years of decay time starting with I g of
the pure parent nuclides).
31
and the popular radiation source 13 7Cs, emits a gamma ray at 661 keV, which is
essentially indistinguishable from the 662 keV line emitted by
spectral peak overlap with
137 Cs could
2 41 Am.
Although the
frustrate unambiguous identification of 241Am, the
unexpected detection of this line emanating from a cargo container would still
presumably be of intense interest due to the potential use of 137Cs (particularly in its
powdery chloride form [Stone, 2002]) in a radiological dispersion device.
A potentially more important aspect of plutonium's intrinsic radiation signature,
in terms of remote detection, is neutron emission. Plutonium has a high rate of internal
neutron generation due largely to the spontaneous fissioning of its nuclei. All of the
plutonium nuclides present in weapons grade and reactor grade materials undergo
spontaneous fission more readily (i.e. they have shorter spontaneous fission partial half
lives) than
2 38 U
[Fetter(4), 1990]. The 238pu, 240pu, and
2 42 Pu nuclides,
with their even
number of protons and neutrons, are particularly active contributors to the neutron
population with relatively short spontaneous fission partial half lives of 4.77x101°,
1.31 x10,
and 6.84x10 10 years respectively [Fetter(4), 1990].
As is the case with HEU, alpha particles interacting with light element impurities
can cause (a,n) reactions, giving rise to another potentially important neutron production
mechanism. However, reactions of the (a,n) variety are more significant in plutonium
than HEU because the dramatically higher alpha activity in plutonium creates more
opportunity for these reactions to occur. Likewise, neutron multiplication can also play a
more significant role in plutonium because more spontaneous fission and (a,n) neutrons
are present to begin the multiplication process by inducing fission.
There is also some evidence to suggest that a significantly enhanced high-energy
(above 1.6 MeV) gamma flux can be observed in the vicinity of plutonium-based nuclear
weapons [Baryshevsky et. al, 1994]. These energetic photons would most likely be the
result of radiative capture reactions occurring as materials in the surrounding chemical
high explosive absorb neutrons emitted by the plutonium. Due to the low natural
32
background flux in this energy regime, these highly penetrating gamma rays could prove
quite useful for remote detection.
2.1.3
23 3 U Radiation
Signature
The isotopic composition of uranium that is chemically separated from thorium
targets irradiated in a reactor varies depending on the reactor type and burnup. Although
the relative concentrations may vary, all uranium produced from thorium irradiation will
be contaminated with 232 U produced primarily through the following reaction chains.
232Th (n,2n) >231
232Th
(n,y) >233
Th
fl >231 Pa (ny) >232 Pa A3- >232 U
Th A-
>233
Pa
-
>233 U (n,2n)>232 U
The limiting reactions for both 232 U production mechanisms are the (n,2n) reactions that
have threshold neutron energies of around 6 MeV. As a result, uranium bred in reactors
with relatively large neutron populations in the high-energy (i.e. > 6 MeV) portion of the
spectrum will typically be contaminated with higher levels of 232U.
232U contamination
also increases with burnup [Kang, 2001].
As noted above for HEU,
2 32 U, with
its 69.8 yr half-life and its
2 08T1 progeny
can be
very helpful for remote detection even at 232U contamination levels on the order of 100
ppt. In contrast to the minute concentrations of 232U that can be found in contaminated
HEU, 233U is considered to be "clean" if it has levels of
ppm. [Kang, 2001].
2 32 U contamination
The intense radiation field given off by the
23 2U
less than 1
decay chain is the
root of radiation protection concerns that have kept 233U from being pursued by states as
the basis for nuclear weapons production. This intense, high-energy radiation will also
help to facilitate fairly straightforward remote detection of concealed 233 U.
33
2.2 Detection Techniques
Detection techniques that seek to exploit the common properties of fissile material
discussed in the previous section can be generally categorized as either active or passive.
Active methods involve the application of external radiation sources to induce fission
events in fissile material that may be present or to take photon transmission
measurements that can indicate the presence and location of dense materials. Passive
techniques do not probe with radiation, but instead measure the intrinsic radiation emitted
by the fissile material to achieve detection. Methods using both active and passive
techniques will now be discussed in additional detail and their applicability to the
postulated container scenario will be assessed.
2.2.1 Active Detection
There are a number of disparate detection methods that fall under the category of
active techniques. The commonality between these methods is that they all employ some
dedicated photon or neutron source to bombard an object or material with intense
radiation to measure its response. In some cases the response of interest is the induced
radiation emitted by the object or material being interrogated and in other cases the
measured response is the amount of radiation that is effectively transmitted through (or
absorbed in) the test object. Methods concerned with stimulating radiation in fissile
material using external radiation sources will be referred to here as induced fission
techniques and methods that measure radiation transmission will be referred to as
radiography.
2.2.1.1InducedFission
As discussed earlier, fissile materials can be made to fission with neutrons of any
energy and by gamma rays above certain nuclide-specific threshold energies. Fission
events are accompanied by the emission of about 7 prompt gamma rays and anywhere
between 2 to 5 prompt neutrons depending on the isotope undergoing fission and the type
34
and energy of the particle that induced the event [Fetter(4), 1990]. Induced fission
techniques interrogate an object with intense beams of radiation and detect evidence of
induced fission in the form of prompt neutrons and/or gammas.
Induced fission techniques have a number of attractive attributes. The intense
probing radiation can penetrate significant amounts of intervening material such that even
well-shielded fissile material can normally be detected. Additionally, by artificially
inducing a strong signal that is unique to the class of materials that are being screened
for, induced fission techniques require a much smaller detection time than other methods,
particularly those that are passive in nature. Disadvantages associated with this method
include radiation protection concerns for workers and bystanders stemming from the use
of intense and energetic radiation sources. An additional concern for methods that would
employ neutrons as probing radiation arises from the possible activation of benign
materials in the test object.
In terms of suitability to the container scenario, induced fission techniques are not
a particularly desirable option. Although the ability to detect fissile material despite
shielding is an important virtue of this method, the insult to the device arising from the
bombardment of probing radiation is a critical drawback. A booby-trap provision, such
as the one postulated by the container scenario, could be triggered by intense radiation
resulting in detonation of the weapon.
2.2.1.2 Radiography
As photons pass through material they can interact with surrounding matter
through a number of different processes. The most notable of these photon interactions
are photoelectric absorption, Compton scattering, and (if the photon has an energy greater
than 1.022 MeV) pair production. Examples of photon interaction cross-sections for
aluminum and lead, illustrating the energy dependence of the three primary interaction
processes, are shown in Figure 2-4 [Krane, 1988].
35
I
I
E
I
0.01
0.1
1
10
0.01
MeV
0.1
1
10
MeV
Figure 2-4: Photon interaction cross-sections for aluminum and lead
The denser the material being traversed by a photon, the more matter is available
to cause these interactions per unit length traveled. As such, a test object with unknown
contents can be exposed to a beam of photons with a known intensity and transmission
measurements can be carried out to detect the presence of particularly dense material,
which could indicate the presence of either fissile material or shielding. Sophisticated
radiographic techniques can image the contents of an unknown test object using the
contrast provided by the varying linear attenuation coefficients of different materials.
These contrast images can be used to indicate both the presence and geometry of
suspicious dense material.
An advantage of radiography is that it can provide visual insights into the contents
of sealed, opaque containers without requiring them to be physically opened. The
sensitivity to very dense materials could also easily detect the presence of engineered
shielding. However, high densities are not unique to fissile materials or shielding that is
being used to conceal a nuclear weapon. As such, this method (and other more exotic
36
radiographic methods including those using muons) could be prone to high false alarm
rates that could create a potentially costly commercial choke point. Additionally, the
bombardment of high-energy photons can damage some radiation-sensitive types of
commercial cargo, such as photographic film.
Evaluated in terms of the container scenario, radiography warrants an assessment
similar to that of induced fission techniques. The ability to readily detect the presence of
material that could be used as shielding is desirable (although unlike induced fission
methods, radiography cannot unambiguously detect the presence of fissile material
behind potential shielding). However, the overall desirability of this technique, at least
with respect to the postulated container scenario, is severely limited by the fact that the
bombardment of a booby-trapped nuclear device with intense external radiation could
trigger the weapon.
2.2.2PassiveDetection
Whereas active techniques use externally applied radiation to exploit common
properties of fissile material related to fissionability and density, passive techniques focus
on the intrinsic radiation that is emitted in varying forms by all fissile material as a means
of detection. Using large static arrays of gamma and neutron detectors to obtain gross
count measurements can identify the presence of a radiation source. This technique
cannot, however, discriminate between fissile material and any other type of radiation
emitting material. More advanced techniques using gamma spectroscopy can be used to
detect and identify individual types of fissile material.
By relying on intrinsic radiation emitted by fissile material instead of radiation
induced by powerful external sources, passive techniques are non-invasive and do not
present radiation protection concerns. However, the intrinsic signal emitted by fissile
material is significantly less intense than the signal that can be artificially induced using
active methods. In general, the number of counts detected from an isotropic point source
can be expressed as follows,
37
SAet -'ii
(1)
where
is
the
intensity
A
of
apoint
source,
is2thedetector
areanormal
totheincident
where S is the intensity of a point source, A is the detector area normal to the incident
radiation, e is the detector efficiency, t is count time, r is the linear distance between the
source and the detector, /u is the linear attenuation coefficient of a given intervening
material, and ris the thickness of a given intervening material. The situation described
by Eq. (1) is shown schematically in Figure 2-5.
Apt
Ad
|t----
T2
r
Figure 2-5: Schematic representation of source detection through intervening material
Assuming that the detector or detectors will be placed as close to the source as the
situation permits and that detectors with efficiencies as high as feasible were employed,
Eq. (1) shows that the only remaining options for increasing the magnitude of the
detected signal are to increase the effective detector area or increase the count time. As a
result, either large detectors, arrays of detectors, long count times or some combination
thereof are likely to be required to make a confident detection of fissile material using
passive techniques. An additional difficulty encountered using passive detection methods
arises from the relative ease with which the low energy characteristic gamma emissions
from some types of fissile material (most notably HEU with very limited or no 232U
contamination) can be shielded by dense materials. Shielding can cause already weak
intrinsic signals to become even weaker and can be a serious obstacle to confident
detection.
38
Assessed against the container scenario, passive techniques have the critical
advantage of not perturbing radiation-sensitive booby-traps in the course of detection.
The trade-off for this desirable attribute is the potential for significantly longer count
times if the weakly penetrating intrinsic radiation from fissile material is to be detected
despite the presence of intentional shielding. Increased count times may or may not be
tolerable.
39
Chapter 3: Detection Schemes
3.1 Current Approaches
The preceding section discussed general methods for detecting concealed fissile
material without consideration for how and where within the international container
shipping architecture these techniques could be implemented. Identifying suitable
deployment strategies for selected detection techniques is often complicated by the
potentially competing interests of enhancing security and preserving the free flow of
commerce. A number of deployment approaches seeking to strike a balance between
security and commerce have been envisioned or even implemented. Some of the more
prominent approaches that have been proposed or realized to date will now be discussed
in terms of their abilities to address the conservative postulated threat.
3.1.1 Customs-Based Approach
The vast majority of detection schemes that are currently deployed or slated for
deployment, can be generally characterized as customs-based approaches. These
approaches strive to integrate detection systems using either active or passive techniques
into existing infrastructure elements at U.S. ports. Examples include outfitting cranes
that transfer containers from cargo vessels onto shore with passive large-area detectors,
processing incoming containers through inspection facilities where they are subjected to
active interrogation, or using mobile detection units to scan containers with photons for
signs of fissile material. The development of in-port detection regimes, such as the
examples cited above, represents a natural extension of conventional strategies based on
the customs model for finding and seizing contraband as the material is coming into the
country. Nuclear weapons, however, are utterly unlike conventional forms of contraband
due to the power and range of their effects. As such, when an attack is mounted by a
rational and determined adversary, the discovery of a nuclear weapon in a major U.S.
port simply cannot ensure protection from the device's destructive power and reach.
40
3.1.2 "Smart" Containers
Another approach that has been vigorously discussed recently is the deployment
of so-called "smart" containers. This approach would retrofit containers used for
maritime commerce with small radiation detectors to sense the presence of concealed
fissile material. Aside from the extremely daunting logistical challenges that would be
presented by installing, maintaining, and mentoring detection equipment in the
approximately 11 million [WSC, 2003] cargo containers in circulation worldwide, there
are a number of critical limitations associated with this approach. First, the detectors
employed in "smart" containers would be very susceptible to tampering. It is the sender
who loads and seals the cargo container prior to shipment, so if a "smart container"
approach was adopted and it was well known that each container was outfitted with a
small detector or detectors, the enemy would have ample opportunity to disable or defeat
the detection devices given their unlimited access to the container prior to shipment.
Even if an enemy did not successfully defeat the detector or if sensors in neighboring
containers detected radiation, the presence of a threat would still not be known until the
container entered port unless the alarm could be communicated in a quasi-real time
fashion. Equipping all containers with detectors that can transmit alarm information
would most likely render the "smart" container approach cost prohibitive. Therefore, like
customs-based approaches, "smart" containers would not identify the presence of a
nuclear weapon until it has already reached a U.S. port, which is not adequately
protective when faced with a sophisticated and determined adversary.
These and other current approaches that subscribe to the conventional notion that
threats can be successfully detected and interdicted as they enter the country (in this case
when the threat has come ashore in port) are critically flawed because they do not take
into account the unique destructive dimensions of the nuclear threat they seek to address.
Even if they make detections with perfectly reliability, these approaches and any others
that propose to look for fissile material in containers that have already entered port cannot
ensure that a nuclear detonation that physically impacts the United States can be
41
prevented. Therefore, with respect to the challenges posed by the threat of containerborne nuclear attack, these approaches do not meet the ultimate success criterion.
3.2 Ship-Based Approach
3.2.1 Attributes
The primary drawbacks of the approaches discussed above relate to the critical
issue of how and where defensive measures are to be deployed. For conventional
contraband, shipping ports are logical locations to field inspection and detection
capabilities because they represent choke points where many elements (i.e. containers) of
a generally diffuse threat (i.e. container borne contraband) come together. Domestic
ports are also convenient deployment nodes because, unlike foreign ports and
commercially owned property, the U.S. government has wide access to the facilities and
infrastructure. To ensure protection from the effects of nuclear weapons, however, the
threat must be interdicted prior to reaching, or even coming into range of, U.S. shores.
Large ocean-going container vessels represent another choke point where many
cargo containers, each representing a potential threat, come together en route to the
United States. If the presence of a concealed nuclear weapon could be detected and
communicated while the ship carrying it was still at sea, a defensive response could be
mounted while the threat was still safely removed from U.S. shores. The U.S.
government cannot unilaterally deploy and maintain control over detection equipment
deployed on the actual vessels themselves since they are the property and dominion of
private concerns. However, akin to the terrorists who may seek to exploit it as an avenue
of attack, the U.S. government does have access to the open architecture of international
maritime commerce that allows any party to ship containers to and from just about any
destination aboard these ships.
Therefore, Gallagher at MIT has proposed an approach whereby suites of
commercial off the shelf (COTS) gamma and neutron detectors are mounted inside
42
standard, non-descript cargo containers. These dedicated units could then be shipped
clandestinely using existing commercial channels where they would be deployed
alongside potentially threat-bearing containers aboard vessels sailing for U.S. ports. On
board the container ship, the detection units will be able to utilize passive neutron
counting and imaging-enhanced gamma spectroscopy techniques to detect and potentially
identify any threat-related nuclear signature being emitted from nearby containers with a
count time constrained only by the duration of the voyage. The containerized detection
units would also be outfitted with a transmission capability such that the presence of
potential threats could be communicated as they were detected and prior to entering U.S.
ports. The primary advantages of this "ship-based approach" can be summarized as
sensitivity, stealth, and most importantly, standoff.
3.2.1.1 Sensitivity
Characteristics of the ship-based deployment environment and the containerized
detection units themselves combine to promote good detection sensitivity. Standard fullsized cargo containers, which would be used to house detectors, have dimensions
measuring 40' in length, 8' in width and 8.5' in height. The 2720 ft3 interior volume of
these containers provides ample space to mount neutron detection equipment and arrays
of gamma detectors that can be configured to present a large effective area when viewed
from any incident direction. Additionally, the long transoceanic voyages required to ship
containers from many foreign ports of call to U.S. shores provide extremely long count
times. From most foreign ports, count times of a week or more would be available.
Referring back to Eq. (1), it is clear that a large detector area and very long count
times will enhance signal strength and help to offset the unknown and variable distance to
the fissile source. However, the signal strength defined in Eq. (1) is not the only relevant
factor in confidently detecting the presence of fissile material. Background radiation
being emitted by benign sources can mimic or obscure the emissions from a genuine
threat. Two particularly problematic contributors of background radiation are cosmic ray
induced neutrons and naturally occurring radionuclides. Cosmic rays, composed
43
primarily of energetic protons and alpha particles, produce neutrons predominantly
through spallation interactions with matter [Frank et. al, 2000]. The distributed neutron
background flux at an interface between air and iron (e.g. on the deck of a containership)
has been found to be approximately 12 times greater than the background flux at an
interface between air and ground [O'Brien, et. al, 1978]. This distributed neutron
background enhancement, sometimes referred to as the "Ship Effect", is the result of a
massive object composed of dense material (e.g. iron) serving as an effective medium for
the production of cosmic ray-induced neutrons. Naturally occurring uranium and thorium
can also frustrate detection efforts because these radioactive materials and their daughter
products produce characteristic gamma emissions that are identical in energy to those
emitted by some fissile materials of interest. Unlike many terrestrial settings, the
uranium and thorium concentrations of seawater are small at 3.3 p.g/L [Turekian, 1976]
and 9.2 ng/L [Emsley, 1998] respectively, and these concentrations are not expected to
fluctuate substantially. Therefore the background sources likely to interfere with shipbased fissile material detection are diffuse uranium and thorium impurities in the ship's
structural steel and distributed benign sources in commercial containers. Imaging
techniques provide a means for identifying localization of incident radiation. As a result,
threatening point-like sources can be distinguished from the benign distributed
background sources described above.
3.2.1.2 Stealth
The nondescript nature of the containerized ship-based detection systems allows
these units to operate surreptitiously. The stealth afforded by these sealed, containerized
units will frustrate attempts by adversaries to disable or defeat the embedded detection
equipment. Additionally, while the exact number and location of the detection units
would not be obvious to an enemy, the knowledge that they are operationally deployed
may produce sufficient uncertainty regarding mission success to dissuade the enemy from
using this means of delivery. This could achieve an important degree of deterrence.
3.2.1.3 Standoff
44
The most important advantage of the ship-based approach is the physical location
of the material when a positive detection is made and communicated. Instead of
identifying the presence of concealed fissile material once it has already entered the
country, a ship-based approach could detect the presence of a threat while the container
was still safely removed from American shores. The warning time provided by a
transmitter equipped, ship-based detection system would allow protective measures to be
taken to ensure that a minimum level of standoff distance between the container vessel
and the United States coastline could be established and maintained. Not only would
early warning prevent a concealed weapon from ever becoming a threat to the American
homeland, it would also ensure that responders had the greatest possible degree of
flexibility in how to safely contain and neutralize the threat.
3.2.2External Uncertainties
It is difficult to overstate the critical advantages of a system that uses COTS
equipment and well understood techniques to provide advance detection and notification
of an incoming container borne nuclear threat. However, before the effectiveness,
reliability, and practicality of this conceptual approach can be persuasively demonstrated,
a number of important remaining uncertainties must be investigated and resolved. Some
of these uncertainties involve aspects of design and performance verification concerned
with elements internal to the containerized detection units. Other uncertainties are
external to the detection units and relate to facets of the international shipping trade and
characteristics of the deployment environment. A concerted effort is underway to
remove or constrain these uncertainties and to produce defensible assessments of the
efficacy and viability of the ship-based approach. Research and development activities
supporting this effort have been roughly divided along the lines of whether they address
uncertainties that are internal or external to the detection units. The remainder of this
thesis will address some of the more pressing external uncertainties. These uncertainties
include the count times available on container voyages originating from different regions
of the world, the number of detection units needed to adequately cover a vessel of a given
45
size, and the number of detection units needed for a fully deployed system. Internal
uncertainties are being investigated by Gallagher at MIT and are outside the scope of this
thesis. Some important internal issues that are explicitly excluded are detection suite
design and quantification of internal performance parameters such as the expected
maximum distance (or range) at which a detection unit will be able to confidently and
reliably detect fissile sources under realistic conditions. Although concerns internal to
the detection unit will not be addressed here, there is an extremely high degree of
coordination and collaboration between the two functional areas and as work is produced
on one track it is immediately fed into ongoing activities on the parallel track.
46
Chapter 4: Container Shipping and Cargo Analysis
Some important uncertainties associated with a ship-based detection regime
cannot be meaningfully addressed and resolved outside the context of the international
container trade and its attendant infrastructure, equipment, and cargo diversity. The
following analysis seeks to gain insights into relevant external uncertainties by examining
the imported container traffic at U.S. ports and deconstructing it terms of where the
containers came from, how far containers traveled to get here, what kinds of vessels (with
respect to container capacity and speed) were used to transport them, and what are the
relevant material properties of the cargo found within them.
4.1 Container Shipping Overview
In 2003, commercial vessels of all types, including tankers, bulk material carriers,
vehicle transports, and containerships, made 56,759 calls at U.S. ports [MARAD(1),
2004]. Containerships accounted for 17,271 (31.7%) of these calls with 1,025 separate
vessels importing over 13,900,000 containers, measured in twenty-foot equivalent units6
(TEUs). In the same year, containerships averaged about 17 calls per vessel and had an
average nominal capacity of 3,144 TEU. Table 4-1 shows the volume of imported and
exported containers that are processed through the top 30 U.S. ports in 2003
[MARAD(2), 2004].
6 Cargo containers come in lengths of 20', 40', and 45'. For the sake of normalization, TEU is the standard
measure for container statistics even though 40' containers are the most commonly used. A TEU is
nominally defined as a 20' x 8' x 8' container. A standard 40' container therefore counts as 2 TEU.
47
Table 4-1: Containerized cargo volume by U.S. port (CY 2003)
Rank
Port
Export
Total
(TEU x 1000) (TEU x 1000)
1022
4664
Import
I
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Los Angeles
Long Beach
New York
Charleston SC
Savannah
Norfolk
Oakland
Houston
Tacoma
Seattle
Miami
Port Everglades
Baltimore
New Orleans
Portland OR
Wilmington
DE
San Juan
Gulfport MS
West Palm Beach
Jacksonville
Philadelphia
Boston
Newport News
Chester PA
Wilmington NC
3091
723
2803
1250
1124
1093
1064
933
838
529
529
460
815
764
423
307
237
210
595
633
517
450
594
486
428
187
192
115
139
147
98
63
29
39
166
71
108
106
34
113
72
103
9
34
42
95
58
48
195
185
179
140
93
80
San Diego
53
9
50
41
37
23
20
25
21148
147
32
28
28
72
72
44
44
44
28
21
19
18
I
23
7312
141
77
21289
7389
-
721
483
337
329
336
236
931
(TEU x 1000)
3642
2368
1965
548
Freeport TX
Richmond VA
Honolulu
Port Bienville MS
Total (Top 30)
All Other Ports
Grand Total
I
-
2
13837
62
13899
-
Table 4-2 shows the origin and volume of containers imported in 2003 from the top 25
U.S. containerized cargo trading partners [MARAD(3), 2004].
48
Table 4-2: Foreign container import data (CY 2003)
Country
of Origin
China
Total Trade
Imports
(TEU x 1000) (TEU x 1000)
4447
5656
Hong Kong
Japan
Taiwan
Korea
1292
722
651
469
Germany
467
650
Italy
Brazil
Thailand
United Kingdom
Belgium
Indonesia
Netherlands
India
473
388
378
206
156
261
225
253
602
533
496
429
392
391
390
389
Malaysia
239
299
France
Honduras
Guatemala
Spain
Costa Rica
Philippines
Dominican Republic
Australia
Turkey
Chile
Total
All Others
Grand Total
195
152
156
158
166
141
98
78
114
135
12019
1880
13899
280
275
268
246
245
221
216
210
196
190
17637
3650
21287
1619
1603
946
898
4.2 Count Time
The amount of available count time is a critical factor in determining the efficacy
of the proposed ship-based approach. Count times for ship-based detection are
constrained only by the duration of the containership voyage. The voyage time between
any two ports is determined primarily by the total nautical distance between the ports of
interest and the average speed of the vessel. The following focuses on nautical distances
between ports and vessel speeds separately and then combines the results of these
analyses to derive defensible count time estimates for container shipments originating
anywhere in the world.
49
4.2.1 DistanceBetween Ports
The nautical distance a vessel travels between a foreign port and a given U.S. port
is dominated by the location of the originating port and world geography (i.e. intervening
land masses). This distance, however, can also be heavily influenced by the number of
intermediate calls made between the ports of interest and by the size of the containership.
Many international shipping lines offer regularly scheduled service routes that call on
multiple ports en route to the United States. These additional port calls add distance to
the overall voyage and each call results in some idle time while the ship is berthed during
the container discharge and loading process. The size of containerships is relevant to the
travel distance because some important navigational short cuts have physical dimensions
that limit the size of vessels that can safely access them. The most important of these
size-limited navigational conveniences for containerships is the Panama Canal, which has
a 32.2 m maximum width restriction [Ircha, 2002]. Vessels with a beam width exceeding
this dimension (i.e. vessels that can fit more than 13 containers across the weather deck)
cannot transit the canal and must instead sail around the tip of South America. Despite
the additional voyage distances, economies of scale associated with larger, higher
capacity vessels drove many international shipping companies to build containerships
with deck widths that exceed 32.2 m [Wijnolst, 1999]. These so-called "Post-Panamax"
vessels, with capacities greater than 4,000 TEU, now account for 30% of the worldwide
containership fleet, by capacity [Tozer, 2003].
Several important assumptions were made prior to carrying out distance to port
calculations that would ultimately serve as input to count time estimates. First, New
York was selected as a representative destination for the east coast of the United States
and Los Angeles was chosen as a representative west coast destination port. In addition
to being the largest U.S. ports on their respective coasts, these ports were chosen because
their proximity to large urban population centers with vast cultural and economic
significance presumably makes them especially attractive targets for attack. Another
assumption was that all voyages made from foreign ports to the reference ports (i.e. New
50
York and Los Angeles) were direct, with no intermediate calls. This assumption was
made to ensure conservatism, since intervening port calls add time and distance to the
voyage. Finally, it was assumed that the originating port used in a nuclear attack (i.e. the
port from which a fully functional device is operationally deployed to the United States)
could be anywhere in the world.
A total of 133 foreign ports were included in the distance analysis. An effort was
made to select a set of foreign ports that provided reasonably comprehensive coverage of
the world's navigable coastlines when taken as a whole. Therefore, some ports were
selected for inclusion because of their prominence in the international container trade
(e.g. Singapore and Hong Kong), and others were chosen to fill in geographical gaps. By
providing quasi-continuous coastal coverage, the distance from any port not included in
this analysis can be reasonably approximated by interpolation. Figures 4-1 through 4-8
show the geographic locations [Hammond, 1999] of the selected ports by region.
51
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Map Number
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Country
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Canada
Figure 4-1: Map of upper North America showing selected ports
52
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Map Number
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Port
Havana
Kingston
Port au Prince
Santo Domingo
Fort de France
Tampico
Belize City
Puerto Barrios
Puerto Cortes
Limon
Panama
Puntarenas
Corinto
Acajutla
Champerico
Acapulco
Mazatlan
Cartagena
Maracaibo
Country
Cuba
Jamaica
Haiti
Dom. Rep.
Martinique
Mexico
Belize
Guatemala
Honduras
Costa Rica
Panama
Costa Rica
Nicaragua
El Salvador
Guatemala
Mexico
Mexico
Colombia
Venezuela
Map Number
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Port
Georgetown
Paramaribo
Natal
Salvador
Rio de Janeiro
Porto Alegre
Monte Video
Buenos Aires
Bahia Blanca
Comodoro Rivadavia
Puenta Arenas
Puerto Montt
Valparaiso
Antofagasta
Mollendo
Callao
Guayaquil
Esmeraldes
Buenaventura
Country
French Guyana
Suriname
Brazil
Brazil
Brazil
Brazil
Uruguay
Argentina
Argentina
Argentina
Chile
Chile
Chile
Chile
Peru
Peru
Ecuador
Ecuador
Colombia
Figure 4-2: Map of the United States, Central America and the Caribbean
showing selected ports
53
Africa
Map Number
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
Port
Port Said
Tunis
Banghazi
Algiers
Casablanca
Las Palmas
Dakar
Freetown
Lagos
Boma
Luanda
Cape Town
Durban
Beira
Dar Es Salaam
Mombasa
Mogadishu
Djibouti
Tamatave
Figure 4-3: Map of Africa showing selected ports
54
Country
Eygpt
Tunisia
Libya
Algeria
Morocco
Canary Islands
Senegal
Sierra Leone
Nigeria
Congo
Angola
South Africa
South Africa
Mozambique
Tanzania
Kenya
Somalia
Djibouti
Madagiascar
Europe
Map Number
60
Port
Batumi
Country
Georgia
Map Number
77
61
62
63
64
65
66
67
68
69
70
71
72
Odessa
Constanza
Varna
Istanbul
Piraeus
Durres
Split
Koper
La Spezia
Barcelona
Lisbon
Coruna
Ukraine
Romania
Bulgaria
Turkey
Greece
Albania
Croatia
Slovenia
Italy
Spain
Portugal
Spain
73
Bordeaux
74
75
76
Le Havre
Southampton
Dublin
Port
Zeebrugge
Country
Belgium
78
79
80
81
82
83
84
85
86
87
88
89
Antwerp
Rotterdam
Hamburg
Copenhagen
Gdynia
Klaipeda
Oslo
Stockholm
Helsinki
St. Petersburg
Riga
Tallinn
Belgium
Netherlands
Germany
Denmark
Poland
Lithuania
Norway
Sweden
Finland
Russia
Latvia
Estonia
France
90
Murmansk
Russia
France
England
Ireland
91
92
Arkhangelsk
Reykjavik
Russia
Iceland
Figure 4-4: Map of Europe showing selected ports
55
Middle East / Indi
I
Map Number
93
94
95
96
97
98
99
100
101
102
I
Port
Calcutta
Madras
Colombo
Bombay
Karachi
Bandar Abbas
Bushehr
Abu Dhabi
Umm Said
Mina Raysut
Manama
103
104
Ad Damman
105
Mina al Ahmadi
106
107
Aden
Rabigh
108
109
Eilat
Haifa
Beirut
Al Latakia
Al Basrah
110
111
112
Country
India
India
Sri Lanka
India
Pakistan
Iran
Iran
U.A.E.
Qatar
Oman
Bahrain
Saudi Arabia
Kuwait
Yemen
Saudi Arabia
Israel
Israel
Lebanon
Syria
IraqI
Figure 4-5: Map of the Middle East and India showing selected ports
56
~~~~~~~~~~~~~~~~~~~~~~~~~~~
.
9-~
~'
~sv~lrrarar
Wnrt~
i
-9,
i
A -
FarEast
Map Number
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
i;·
I'BE r·i:*tSi
`!·
·i':?$ P"·`S-;:
i..kii:2
I:·lr.
t
:·".!
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r··:·:···
-·
t;
·
";
i:
r2,·
';;1
`·j
·
.·'·
..
ii..
I*
Port
Vladivostok
Yokohama
Weonsan
Busan
Nampo
Tianjin
Shanghai
Kaohsiung
Hong Kong
Manilla
Ho Chi Minh
Selat Lombok
Jakarta
Singapore
Port Kelang
Bangkok
Chittagong
Figure 4-6: Map of the Far East showing selected ports
57
Country
Russia
Japan
North Korea
South Korea
North Korea
China
China
Tiawan
China
Philippines
Vietnam
Indonesia
Indonesia
Singapore
Malaysia
Thailand
Bangladesh
"'
,.B
~Lombo
al
NAURU
se /
Si
,
CaN
ak
ag
-
.
JvI
,
Chritmas
.
t.
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..
\
....
-
.· _,
.
.:
..
.
,·
·
..
....
......
Xt...
i
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e St.Isabledonl
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.no,
.~..
,,
.;
...
:;
....
··
·.,
Sl~
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I"my
r
s
,
Thri
Kings
,nae
¶j '
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e.
T~dac.-
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ia * djl
K
Australia
Map Number
bISouth
A
Port
ttttttUttttttSttttt
130
Brisbane
131
Port Moresby
132
133
Port Darwin
Freemantle
-
ttttttttttttttttttt
Country
Australia
Papua New Guinea
Australia
Australia
Figure 4-7: Map of Australia showing selected ports
58
ZEALA/N
G wo'3
Tomltnia
.
I
.
E y
I
The nautical distances between the two U.S. reference ports and the 133 selected
foreign ports shown above were calculated using information tabulated in "Publication
151 - Distance Between Ports" (referred to hereafter as DBP) prepared by the National
Imagery and Mapping Agency [NIMA, 2001]. Information on over 1400 worldwide
ports is compiled in this document and all published distances are based on accepted
maritime routes and charted nautical sailing lanes. Because of the impracticality of
listing distances between every possible combination of these ports, distance calculations
using this document typically have to be carried out in several intermediate steps using
specified "junction points". The DBP identifies 25 junction points where international
shipping routes converge and through which ships pass when sailing from one major
maritime area to another (e.g. the Strait of Gibraltar or the Cape of Good Hope).
Distances between any two tabulated world ports can then be calculated by summing the
distances to, and between, these junction points. Some voyage distances vary
considerably depending on whether the Panama Canal can be transited. Because a
significant fraction of the international containership fleet is Post-Panamax, distances
between a given foreign port and the two U.S. reference ports were calculated with and
without access to the Panama Canal. When the two distances differed depending on
canal access, the following expression was used to calculate a weighted average,
Dvg = 0.3 Dos_,,anamax+ 0. 7Dpanaax
(2)
where Dpost Panamax is the voyage distance without access to the Panama Canal and
Dpanaa,,is the distance with access. The weighting factors were chosen because 30% of
the current fleet (by capacity) is Post-Panamax and the balance is not. Therefore, a
container heading to the U.S. should have a 0.3 probability of being on a ship that can't
gain access to the Panama Canal and a 0.7 probability of being on a ship that can.
Distances from the 133 foreign ports to New York and Los Angeles in nautical
miles 7 are shown in Table 4-3. The Panamax, Post-Panamax and weighted average
7 1 nautical mile = 1.15 statute miles = 1.85 km
59
distances are captured for each foreign port to the 2 U.S. reference ports. Highlighted
cells illustrate the shorter of the voyage distances between the two reference ports.
60
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4.2.2 Vessel Speed
The diverse fleet of international containerships has a broad spectrum of nominal
cruising speeds. Although point estimates, such as mean values, can be used to convey
information about large and diverse data sets, the character of a wide spectrum of values
is better and more completely captured by a statistical distribution. To develop an
appropriate and representative distribution, a containership database was created using
publicly available Lloyd's Register information provided online by large commercial
shipping lines and U.S. ports. This database was populated with nominal speed (in
knots8) and/or container capacity (in TEU) data for 1,734 commercial container vessels.
Information on both capacity and speed could not be found for every vessel included in
the database so there are 1,184 vessel speed entries and 1,706 vessel capacity entries.
The full database can be found in Appendix A. No size threshold was initially imposed
to exclude any vessel from the database, however, since the subject of interest is
international shipping, some screening criterion had to be devised to bar small domestic
feeder ships from further consideration. In its annual breakdown of commercial shipping
statistics the Maritime Administration (MARAD) of the Department of Transportation
imposes a vessel size threshold of 10,000 deadweight tons9 [MARAD(1), 2004]. This
threshold was adopted as a screening criterion for the containership database to facilitate
fair comparison with the MARAD statistical abstract and was found heuristically to
correspond to vessels with a capacity of roughly 715 TEU. The screened database
contained speed information for 910 vessels and capacity data for 1,313 vessels. For
comparison, MARAD reported that 1,025 containerships called on U.S. ports in 2003.
The speed and capacity information contained in the database were assumed to be
reasonably representative of vessels importing containers to U.S. ports for the following
reasons. All information used to populate the database was available through U.S. ports
or major container shipping lines that service the U.S. Additionally, the size of the data
sets for speed and capacity are comparable to, or exceed, the total number of
8
1 knot = 1 nautical mile/hour = 1.85 km/hour
9 Deadweight tonnage is the amount of cargo, fuels, water, stores, and crew that a vessel can carry when
fully loaded. It is measured in long tons (1 long ton = 2,240 lbs.).
65
containerships that called on U.S. ports in all of 2003. However, to obtain some
benchmark of how well the vessel information in the database comported with the
containership fleet that actually serviced U.S. ports in 2003, the mean capacity of
(screened) database vessels was compared to the actual mean capacity reported by
MARAD. The results are shown in Table 4-4 below.
Table 4-4: Vessel database capacity benchmark results
Mean Capacity (TEU)
MARAD
Database
3144
3047
Error (%)
3.085
Although this benchmark used only a single parameter (because it was the only value that
invited straightforward comparison), the excellent agreement between the database and
the MARAD data suggests that conclusions drawn using the vessel database will be
reasonably representative of the actual containership fleet servicing the U.S.
To extract meaningful statistical information from the 910 nominal vessel speeds
tabulated in the containership database, a cumulative distribution function (CDF) was
constructed. A CDF is a statistical distribution that relates the value of a parameter to the
probability that the given parameter value, or a lesser value, will be observed. In this
case, the CDF gives the probability that a containership calling on a U.S. port will have a
nominal speed equal to or less than any given value.
To construct a CDF, the raw vessel speed data from the screened containership
database was first sorted into ascending order. Then the frequency of each distinct
nominal speed was computed by simply counting how many times a given speed was
.
(3)
observed in the database. The probability, or relative frequency, of each nominal speed
was then calculated using the following general expression,
P
=
nn,
Zn,
66
where Pi is the probability of the ith value, and ni is the frequency of the ith value. The
CDF was then found using the following general formula,
(4)
F
o
where F[xi] is the discrete CDF value for the ithelement. In this case, xi represents each
distinct nominal vessel speed. Figure 4-9 is a plot of the vessel speed CDF with the 25 th ,
5 0 th, 7 5 th, 9 5 t
h
,
and 9 9th percentilevalues identifiedgraphically.
Vessel Speed - Cumulative Distribution Function
(N = 910 Vessels)
1.00
0.90
0.80
0.70
0.60
u.
0.50
0.40
0.30
0.20
0.10
0.00
10.0
15.0
20.0
25.0
30.0
Nominal
Speed(knots)
Figure 4-8: Vessel speed CDF
The mean, median, and mode values of the nominal speed from the screened
containership database are shown in Table 4-5 along with interpolated numerical values
of the 2 5 th,
7 5 th 9 5 th,
and 99th percentiles.
67
Table 4-5: Vessel speed statistics
MEDIAN
MEAN
MODE
Speed (knots)
21.43
21.29
21.00
25TH
75TH
95TH
99TH
18.88
23.86
25.77
26.33
4.2.3 Voyage Times
The distance and speed analyses performed in the previous sections can now be
used to generate estimated non-stop voyage times for the 133 foreign ports. Weighted
average distances between foreign ports and the U.S. reference ports were used to
calculate voyage times to account for the additional expanse that must be traveled by
Post-Panamax vessels on some routes. Also, acknowledging the inherent variability of
vessel speeds, voyage times were calculated using both the expected, or mean, value of
21.29 knots and the conservative 9 5 th percentile value of 25.77 knots. Voyage times, in
days, were found using the following expression,
T
voyage
D
=D
g
(5)
(5)
24 * V
where Tvoyageis the voyage time (in days), Davgis the weighted average distance between
the ports of interest (in n.m.) and vx is the mean or 9 5 th percentile vessel speed (in knots).
Table 4-6 shows calculated voyage times, by region.
68
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Highlighted cells in Table 4-6 illustrate whether the voyage is shorter between the
given foreign port and New York or Los Angeles. The highlighted 9 5 th percentile voyage
time represents a conservative lower bound for the amount of count time that will be
available if an attack is mounted from this port. Count times for non-stop voyages from
almost any port in the world to New York or Los Angeles can now be approximated by
interpolating between the tabulated values shown in Table 4-6.
The information above is useful for determining the minimum count time
available for a container shipment being deployed from a particular port or region of the
world. However, it cannot be used directly to give an accurate measure of the expected,
or average, count time that would be available on incoming containerships. This is
because containers are not uniformly imported to the U.S. from all parts of the globe. To
derive a reasonable estimate of how much count time will actually be available on
average, the voyage times from ports that ship more containers to the U.S. must be given
higher relative weightings. The information in Table 4-2 documenting the volume of
container imports broken down by country can be used to assign weighting factors. Since
the 25 countries listed in Table 4-2 make up 86.5% of the total containerized imports to
the United States, using voyage times from ports located in these countries alone should
yield a reasonable estimate. Using this approximation, weighting factors were then
calculated as follows,
nTEU
E
(6)
'nTEU
where Wi is the weighting factor for the ith country in Table 4-2 and nTEUiis the number
of imported containers from the ithcountry (in TEU). Distances from the countries listed
in Table 4-2 to the U.S. reference ports were obtained using information from the
distance analysis presented above. Each country of interest has at least one port listed in
Table 4-3. For countries with multiple ports listed in Table 4-3, the arithmetic mean of
the port distances from that country was used to establish a single representative distance.
73
Voyage times from the countries in Table 4-2 were then calculated using the mean vessel
speed of 21.29 knots (because an expected value was being sought). The appropriate
weighting factors were then applied to the voyage times for each country to find expected
count time values for ships calling on New York and Los Angeles. Results are shown in
Table 4-7.
Table 4-7: Mean voyage times to New York and Los Angeles
LosAngeles
NewYork
Imports Weighting
(TEUx 1000) Factor Avg. Distance(n.m.) Time [Mean](days) Avg.Distance(n.m.) Time [Mean](days)
China
4447
0.36997
11991
23.5
6057
11.9
23.4
6380
12.5
1292
0.10749
11981
HongKong
9.5
0.06007
11371
22.3
4839
Japan
722
Taiwan
651
0.05416
11774
23.0
6011
11.8
Italy
473
0.03935
4067
8.0
9643
18.9
Korea
469
0.03902
11771
23.0
5374
10.5
18.9
3654
7.2
9661
Germany
467
0.03885
Brazil
388
0.03228
4413
8.6
7366
14.4
Thailand
378
0.03145
13257
25.9
7775
15.2
Indonesia
261
0.02171
12042
23.6
8392
16.4
India
253
0.02105
11730
23.0
9758
19.1
Malaysia
239
0.01988
12160
23.8
8087
15.8
Netherlands
225
0.01872
3391
6.6
9402
18.4
6.2
9181
18.0
206
0.01714
3169
UnitedKingdom
France
195
0.01622
3211
6.3
9167
17.9
CostaRica
166
0.01381
3537
6.9
4243
8.3
Spain
158
0.01314
3314
6.5
9183
18.0
Belgium
156
0.01298
3358
6.6
9365
18.3
Guatemala
156
0.01298
1804
3.5
6546
12.8
Honduras
152
0.01265
1764
3.5
6535
12.8
12.8
0.01173
13543
26.5
6530
Philippines
141
Chile
135
0.01123
6073
11.9
5135
10.0
Turkey
114
0.00948
4997
9.8
10471
20.5
DominicanRepublic
98
0.00815
1489
2.9
6290
12.3
Australia
78
0.00649
11321
22.2
7271
14.2
Total
12020
1
WeightedAvg.
=
13.3
Country
The mean count times available for vessels calling on New York and Los Angeles are on
the order of 2 weeks. This represents a significant amount of time to make a confident
detection of fissile material. Finally, even though the average count times shown above
were calculated using mean vessel speeds, the assumption that all voyages are non-stop
still makes these numbers reasonably conservative.
74
4.3 Vessel Container Capacities
Modem containerships vary considerably in size, with the largest vessels in the
current fleet able to carry over 8,000 TEU [MacGregor, 2003]. The number of detection
units needed to provide adequate coverage of a given vessel will depend on the
dimensions of that particular vessel's container array and the number of commercial
containers being transported. Therefore, to gauge the number of containerized detections
units that will be necessary to implement a comprehensive ship-based detection regime, a
container capacity distribution must be derived for the commercial fleet.
Information from the containership database that was discussed in the vessel
speed section was used to construct a similar CDF for container capacity. The screened
database contained 1,313 capacity entries ranging from 724 TEU to 8,200 TEU. The
CDF development process used for vessel speed was employed again for container
capacity. The general formulae shown in Eqs. (3) and (4) were used, with the frequency
of each distinct container capacity serving as n in Eq. (3) and container capacity (in TEU)
being represented by x in Eq. (4). The resulting capacity CDF is shown in Figure 4-9,
with the 25t h, 50th , 75t h , 95t h , and
9 9 th
percentile values illustrated graphically.
75
Vessel Capactiy - Cumulative Distribution Function
(N = 1313 Vessels)
0.9
0.8
0.7
k
In
.o
0
0
U.
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1000
2000
3000
4000
5000
Capacity(TEU)
6000
7000
8000
Figure 4-9: Vessel capacity CDF
The mean, median, and mode values of the container capacity from the screened
containership database are shown in Table 4-8 along with interpolated numerical values
of the
2 5th, 7 5 th, 9 5 th,
and
9 9 th
percentiles.
Table 4-8: Vessel capacity statistics
Capacity (TEU)
2722
3047
4300
MEDIAN
MEAN
MODE
25TH
75TH
95TH
99TH
1666
4173
6204
6782
76
9000
The container capacity CDF generated here will be used in subsequent analysis to
develop defensible estimates for the total number of containerized detection units that
will be needed for a fully implemented system.
4.4 Cargo Density
For a ship-based approach to be effective, the signal emitted by concealed fissile
material must be strong enough to be confidently distinguished from natural background
fluctuations by a passive detection unit some distance removed from the source. The
signal will be attenuated by intentional shielding that is likely to be present in the
container bearing the weapon and by the commercial cargo in containers that are oriented
between the source and detector. The maximum amount of intentional shielding is
constrained by the physical dimensions of the container and the 32-ton weight restriction
imposed by international shippers [Lok, 2004]. Although they still allow for a very
substantial amount of intentional shielding, the space and weight constraints do bound the
problem and worst-case signal attenuation can be calculated. What is less
straightforward is the extent to which the intervening commercial cargo will attenuate the
signal.
Density is a cargo parameter that is helpful when trying to accurately model
radiation transport through intervening commercial material. One way to obtain a rough
but useful measure of the density of imported cargo material is to assume that the
contents of a container (and the mass of the contents) are equally distributed throughout
the volume of the container. This "distributed density" (in g/cm3 ) can then be found
using the following expression,
m
(7)
Pdist =
VOlcontainer
where m is the total mass of the cargo,
VOlcontainer
is the interior volume of the container.
Although the homogeneous distribution of mass throughout the container is clearly
77
unphysical, it can be a helpful measure for benchmarking computer simulations. When
simulations are run where representative types of cargo (e.g. furniture, electronics,
clothing, etc.) have been explicitly modeled, it is important to know how the aggregate
distributed density of the modeled cargo compares with the average distributed density of
actual imported cargo (i.e. is the model more, less, or similarly attenuating as actual
cargo). A simple method for obtaining a point estimate of the average distributed density
of actual imported cargo is given by,
mtot
(8)
Pdist TEU
VOITEU
where mtotis the total tonnage of a large sample of imported containers, nTEUis the
number of imported containers, and VOlTEU
is the interior volume of a TEU. Using
imported cargo data for calendar year 2001 (the most recent year for which MARAD
reported total tonnage information) as the large container sample, mtot, nTEU, and VOITEU
are 80,725 metric tons (MT), 11,268 TEU, and 1360 ft2 respectively [MARAD, 2002].
Converting these values into appropriate units and plugging into Eq. (3) gives an average
distributed density of 0.1977 g/cm3 . However, a single point estimate of the average
distributed density is less instructive than a distribution that reflects the relative
probabilities of a range of distributed densities.
The 2001 data for container imports at the top 25 U.S. ports was used construct an
average distributed density CDF. Table 4-9 below shows mtot,nTEuand the calculated
average densities for the top 25 ports [MARAD, 2002].
78
Table 4-9: Average distributed density, Pdist,values for imported cargo
Port
n TEU
m tot
(TEU x 1000) (MT x 1000) Avg Density (glcc)
Los Angeles
2614
16221
0.1712
Long Beach
2376
14355
0.1667
New York
1588
12758
0.2217
Charleston
612
4890
0.2204
Seattle
500
2993
0.1652
Norfolk
454
3556
0.2161
Savannah
431
2998
0.1919
Oakland
419
3058
0.2014
Houston
381
3656
0.2647
Tacoma
356
2111
0.1636
Miami
347
3120
0.2481
Baltimore
178
1942
0.3010
PT Everglades
171
1235
0.1993
San Juan
108
1006
0.2570
Wilmington (DE)
103
965
0.2585
New Orleans
86
891
0.2858
Gulfport
74
599
0.2233
Philadelphia
71
913
0.3548
Boston
51
445
0.2407
Portland
47
350
0.2055
Wilmington (NC)
37
232
0.1730
Chester (PA)
31
316
0.2812
Ponce
30
332
0.3053
W Palm Beach
27
195
0.1993
Jacksonville
25
210
0.2318
All Other
153
1379
0.2487
Total
11268
80725
0.1977
By specifying mtot and nTEu for 26 separate sample populations (i.e. the top 25 ports and
the lumped data for all others) this data can be used to construct an approximate CDF.
The same CDF derivation procedure outlined earlier is used here with the tabulated
values of nTEuserving as the frequency of the given average distributed density value.
The resulting CDF is plotted in Figure 4-10.
79
Dist. Density - Cumulative Distribution Function
1
1
0.9
0.8
0.7
7 0.6
' I 0.5
U. 0.4
0.3
0.2
0.1
0
0.15
0.2
0.25
0.3
0.35
Dist. Density (g/cmA3)
Figure 4-10: Cargo distributed density, Pdist,CDF
Ideally the mass of every individual imported cargo container would be known so that an
exact CDF for Pdist could be derived.
In this case, however, the data points used to
construct the CDF were themselves already point estimates of larger data sets. Although
some useful information about the character of the original data is lost when a single
point estimate is used to represent a population of data, these point estimates encapsulate
the most important aggregated attributes of the original data. Therefore, even though it is
based on aggregated point estimates instead of exhaustive raw data, the approximate
average distributed density CDF is still a useful measure of the probability that the
distributed density of a cargo container will exceed a given value.
80
Chapter 5: Deployment Simulation
5.1 Introduction
The fact that the proposed ship-based approach would deploy containerized
detection units aboard commercial containerships has been discussed, but the manner in
which these units would be deployed (i.e. how they are loaded onto the ship and
distributed throughout the vessel's container array) has not been addressed. Ideally, the
detection units could be loaded in a manner that simultaneously allowed completely
clandestine deployment and maximum detection coverage with the minimum number of
units. If this could be accomplished, total system costs would be minimized and
adversaries would be kept utterly unaware of the number and location of deployed
detection units that could interrupt or thwart their efforts. In reality, however, there is a
trade-off between the precision with which one can dictate or predict the placement of the
detection units and the covert nature of the deployment process. Specifying exactly
where or how certain cargo containers are to be loaded into the container array can
optimize the amount of the containership covered per detection unit, but it could also
provide enemies with valuable information about the defensive measures being employed
against them. This fundamental trade-off leads to a potential clash between coverage
efficiency and stealth.
A computer-based deployment simulator was created using Matlab to help inform
the process of striking an appropriate balance between coverage efficiency and stealth.
This simulator was used to quantify the coverage efficiency gains that could be reaped by
adopting increasingly constrained (and consequently less stealthy) deployment strategies.
Three strategies were investigated, including a random deployment where units could be
placed anywhere in the container array, a partially constrained deployment where units
were randomly placed anywhere except a specified exclusion zone one container deep
around the surface of the array, and a fully constrained deployment where units could
only be placed along a row down the length of the array. Hereafter, these strategies are
referred to as random, constrained, and centerline deployment, respectively.
81
An extremely important remaining uncertainty (that is outside the scope of this
thesis) is the effective detection range of a deployed unit. The effective range is the
maximum distance at which a unit is expected to reliably detect the presence of fissile
material when deployed amongst commercial containers with realistic and representative
cargo. Once a reasonable estimate for the effective range is obtained, it is a
straightforward problem to determine the expected detection coverage provided by
centerline deployment. The relative ease of calculating centerline coverage stems from
the highly constrained nature of this deployment strategy, which uniquely determines the
spatial distribution of detection units for any given container array. The spatial
distributions arising from the other two strategies, however, are determined either totally
or partially by chance. Mean attributes, such as expected detection coverage, of systems
with this stochastic character are often difficult or impossible to derive analytically and
instead lend themselves to Monte Carlo analysis.
Monte Carlo techniques use random numbers to sample distributions for
parameters to be used in a calculation, or calculations, of interest. The calculation is then
carried out a large number of times with each iteration using different randomly sampled
parameter values. The large population of outputs from the calculation of interest can
then be statically analyzed to gain meaningful insights. The speed with which modem
digital computers can carry out large numbers of computations makes Monte Carlo
analysis a very powerful tool for solving complex problems.
Detection coverage calculations for container arrays of arbitrary sizes were
carried out using Monte Carlo methods for both random and constrained deployment.
Random numbers were used to sample the uniform distributions representing Cartesian
coordinates that determined the placement location of a given detection unit within the
container array. Once a given number of detection units with a specified detection range
were randomly distributed throughout a container array with known dimensions, the
detection coverage calculation could be carried out for this geometry. The output was
then logged and the entire detector placement and coverage calculation process was
82
carried out again until the output population was large enough to yield good statistics.
Expected values, along with corresponding standard deviations, for random and
constrained deployment could then be determined through statistical analysis.
5.2 Model Development
The deployment simulator was programmed in Matlab and takes advantage of the
ease with which the Matlab environment can create and manipulate n-dimensional
matrices. The entire container array of a hypothetical vessel is modeled in matrix space
with each cubic foot of actual volume represented by an individual element in a 3dimensional matrix. Detection units are then distributed through the container array in a
manner consistent with the constraints of the scenario (i.e. random, constrained, or
centerline) being studied. With the geometry of the problem now uniquely specified, the
fractional volume of the actual container array that would be effectively covered by the
detectors in the generated configuration can be calculated using a few simple matrix
operations in Matlab. If Monte Carlo analysis were being used, as would be the case for
random and constrained deployment, this process of detector placement and fractional
coverage calculation would be repeated many times.
5.2.1 Assumptions
Key assumptions will be identified, and explained before a detailed treatment of
the simulator's algorithm and mechanics is offered. First, it was assumed that all
container arrays were continuous rectangular prisms. This is an approximation given that
large vessels often have container arrays that taper below deck (to accommodate hull
dimensions) and some discontinuity created by the ship's superstructure. These effects
were not explicitly modeled because the degree of tapering and the location and
magnitude of superstructure discontinuities vary depending on the size and design of the
containership and cannot be meaningfully generalized.
83
Since the detection suite is not necessarily confined to the center of a
containerized unit, it was also assumed that detectors could be centered at any (nonconstrained) location in the container array and not limited solely to coordinates that
corresponded to the midpoints of containers. This assumption simplifies calculation but
was made primarily to conserve computation time. It was noted that this assumption
could lead to the non-physical situation of two or more detectors being randomly
assigned to the volume corresponding to a single container. The probability of any two
detectors being randomly assigned to the same (TEU) 0° container volume is represented
by the following expression,
p=
1 fnl(xyz-i) = (xyz-1)!
(xyz)(
i-
xyz
- ' (xyz
-
(9
n)!
where x, y, and z are the number of unconstrained TEUs arrayed in the respective x, y,
and z directions and n is the number of detectors being deployed. In general, the
probability of 2 detectors being assigned to the same container volume increases as n
increases and as the total number of TEUs (i.e. [xyz]) decreases. The effects of this
"double-assignment" will be examined in more detail in subsequent sections.
Another important assumption is that deployed units provide coverage of a
perfectly spherical volume with a radius determined by the effective detection range.
(Estimates for the effective detection range are being developed by Gallagher at MIT and
are still evolving as design decisions and improvements are made, so a series of range
values were assumed as part of a parameter study). This is an approximation of a realworld setting, where shielding effects manifested by the specific loading and cargo
characteristics of surrounding commercial containers and the threat container itself would
render the effective detection volume non-spherical. It is further assumed that fissile
material located anywhere within the idealized coverage sphere will be detected with
equal probability. In reality, a source close to the detector will be more easily detected
'0The probability that any two detectors will be assigned to the same 40' container can also be found using
Eq. (9) by substituting (xyz/2) for each (xyz) term.
84
than one at the outer edge of the sphere (along the same line of sight) as a result of
shielding by intervening materials and the inverse square nature of detector solid angles.
This assumption was deemed acceptable because the definition of the effective detection
range is the expected maximum distance at which a source can be confidently and
reliably detected with a given count time under realistic conditions. Also, by not
considering or crediting the enhanced ease of detection afforded by source proximity and
detection sphere overlap, the analysis gains a measure of conservatism.
5.2.2Input/Output
The Matlab-based deployment simulator accepted user-defined inputs for
container array dimensions (length, width, and height in TEUs), the number of detectors
to be distributed through the array, the effective detection range (in ft.) and the number of
runs to be completed for Monte Carlo analysis. Output for Monte Carlo calculations
were statistics (mean, median, standard deviation, minimum, and maximum values) that
described the set of fractional detection coverages calculated for each run, or iteration, of
the simulation. Output for the deterministic centerline analysis consisted of a fractional
detection coverage corresponding to the evaluated scenario.
5.2.3 Algorithm
The simulation of each deployment strategy (i.e. random, constrained, and
centerline) used the same algorithm to generate a virtual container array and then
calculate the fractional volume that was "covered" by deployed detectors. Differences in
random, constrained, and centerline deployment simulation were limited primarily to the
manner in which the detectors were placed into (or distributed through) the virtual array.
For clarity, the algorithm will be explained in its entirety using random deployment as an
example. Differences in the detector placement step for constrained and centerline
deployment will then be identified and discussed. The actual Matlab codes used to
simulate each type of deployment are found in Appendix B.
85
The simulation began by creating a matrix representation of the physical space to
be modeled by employing user inputs that defined the desired container array dimensions.
The inputs specify array dimensions in terms of how many (TEU) containers are to be
aligned along the length, width, and height of the array. Figure 5-1 shows the assumed
orientation of the containers along the 3 Cartesian axes.
20'
I'l
(height)
I
8'
I
Y
(width)
I"
z
0ength)
Figure 5-1: Container orientation for simulation
A 3-dimensional matrix was then constructed in which each cubic foot of physical space
in the user-specified container array was represented by a matrix element with an initial
value of 0. This "geometry matrix" had dimensions [(x*8),(y*8),(z*20)], where x, y, and
z were the user inputs for the number of containers along the respective height, width,
and length of the array and the scaler multipliers are the corresponding height, width, and
length dimensions of (TEU) containers in feet.
Detector placement was the next step in simulation. For random deployment,
Matlab's random number generator was used to assign arbitrary coordinates (referred to
here as dx, dy, and dz) to fix the center-point of an emplaced detector. Once dx, dy, and
dz had been identified, a new null matrix, referred to hereafter as the "detector matrix",
was created. The detector matrix was of the same dimensions as the geometry matrix and
the element at (dx,dy,dz) representing the emplaced detector was assigned a value of 1.
86
Next the coverage sphere associated with the emplaced detector was generated.
An approximated sphere can be created within a 3-dimensional matrix by serially
evaluating individual elements to determine the linear distance between the given
element and the emplaced detector using the following expression,
D= (i dx)2+(j -dy)2+(k -dz)2
(10)
where i,j, and k are the respective x, y, and z coordinates of the matrix element being
evaluated. If this distance is greater than the effective detection radius, R, then the
element under evaluation is outside the detection sphere and the value of that element
remains 0. If the distance is less than or equal to R, the element in question is within the
detection sphere and its value in the detector matrix is changed to 1. To save
computation time, only matrix elements inside a cube centered at (dx, dy, dz) with sides
measuring 2R were evaluated using Eq. (10). This cube bounding the detection sphere is
shown (2-dimensionally) in Figure 5-2.
2R
I
2R
(dx4yjdz)
2R
Figure 5-2: Cube bounding the detection sphere
Once the entire coverage sphere, represented by elements with a value of 1, had
been generated, an element-by-element comparison of the detector matrix and the
geometry matrix was performed using the logical OR operator, whose properties are
shown in Table 5-1.
87
Table 5-1: Properties of the OR operator
x (OR)Y
0
X
O
Y
0
0
1
1
1
0
1
1
1
1
The matrix resulting from this operation becomes the updated geometry matrix. The
process of detector placement is then repeated and a new detector matrix is created. The
new detector matrix is then compared to the updated geometry matrix, again using the
logical OR operator, and the result becomes the new geometry matrix. Each time the
geometry matrix is updated, the OR operation imprints it with another coverage sphere.
The OR operator is used in lieu of matrix addition to avoid overlapping coverage regions
being double counted in the final fractional coverage calculation.
The process of emplacing detectors, creating detector matrices, and updating the
geometry matrix continues until the user specified number of detectors has been
deployed. At this point, the geometry matrix holds the placement and coverage
information of every detector, in addition to information defining the overall dimensions
of the simulated container array. An element of the geometry matrix with a value of 1
represents physical space that is within the effective detection range of an emplaced
detector, and is therefore "covered". Matlab can then sum the values of all the elements
in the geometry matrix to find the volume covered by deployed detectors. The coverage
volume, represented by the summation of the geometry matrix, can then be divided by the
total number of elements in the geometry matrix, which represents the total volume of the
simulated container array, to find the fractional coverage volume. The fractional
coverage volume calculation is shown symbolically as follows,
V
Vtotal
88
(11)
where F is the fractional coverage volume, Vcovis the volume of the array that is
"covered" by deployed detectors, and Vtotalis the total volume of the array.
This entire process is repeated until the user-defined number of fractional
coverage volume outputs has been generated. At the end of each run, the calculated
fractional coverage value is added to an output vector. Once the vector has been fully
populated, Matlab performs statistical analysis on the output data and returns the mean,
median, standard deviation, minimum and maximum values for the fractional coverage.
Detector placement for constrained and centerline deployment is the only major
difference from the simulation process described above. Matlab's random number
generator is also used to determine coordinates for detector placement in constrained
deployment simulations. However, before a detector matrix is generated reflecting a
given placement location, the coordinates are checked to ensure that the detector is not
being placed in physical space that would be in a container that is along the surface of the
array (i.e. the first or last [TEU] container in any row, column, or span of the array). If
the prospective placement coordinates fall in this exclusion zone, then they are discarded
and new sets of random numbers are generated until coordinates are obtained that satisfy
the constraints. When coordinates are found that do not place the detector in the
exclusion zone, a detector matrix is generated and the element representing the placement
coordinates is given a value of 1. For deterministic centerline deployment calculations,
detector placement is determined by the user inputs concerning the geometry of the
container array and the number of detectors to be deployed.
5.2.4 Validation and Verification
During development, a 2-dimensional version of the each simulation code was
created to facilitate validation and debugging. Once the 2-dimensional models were
found to work as expected with high confidence, they were scaled up to the full 3-
dimensional simulations of interest. Prior to actual data collection, the output from 3dimensional test simulations, starting with small scale runs (i.e. modestly sized arrays
89
with a small number of deployed detectors) and concluding with a limited number of
larger scale runs, were extensively checked against hand calculations.
This validation and verification process also sought to ensure that reality was
being modeled with reasonable accuracy. One problem with representing physical space,
and especially spherical regions of space, with elements of 3-dimensional matrices is the
discretization error introduced by the non-continuous nature of matrix space. To provide
reasonably high fidelity models of coverage spheres, each matrix element represented 1
cubic foot. For reference, at this resolution, it takes 2720 matrix elements to model the
interior of one full sized 40' cargo container. To check the error introduced by
discretization, the calculated volume values for spheres generated in matrix space were
compared to the theoretical volume (in ft3 ) given by the following formula,
4
V = '-r
3
where r is the radius of the sphere (in ft). Table 5-2 shows the discretization error
observed for spheres of varying radii.
90
(12)
Table 5-2: Spherical volume error
Radius (ft)
45
Simulation (ftA3) Theoretical (ftA3)
381615
381703.5
Error (%)
0.0232
50
523305
523598.8
0.0561
55
60
65
696507
904089
1149651
696910
904778.7
1150346.5
0.0578
0.0762
0.0605
70
75
1436385
1767063
1436755
1767145.9
0.0258
0.0047
80
85
2143641
2571711
2144660.6
2572440.8
0.0475
0.0284
The errors tabulated above are quite small, so the volume underestimation caused by the
discrete nature of matrix space will not significantly impact the accuracy of the fractional
coverage values output by the simulations.
5.3 Random Deployment
A deployment methodology where containerized detection units are randomly
loaded onto containerships is vastly preferable in terms of both logistics and stealth. By
imposing no constraints on the placement of these units, there is no opportunity for an
adversary to identify their presence due to abnormal or preferential treatment during the
loading process. Therefore, the enemy is not afforded an opportunity to study and probe
the defense posture prior to attack or the opportunity to take compensatory action during
an attack. The logistics of random deployment are also favorable in that the detection
units can be simply delivered to the embarkation port or commercial shipper and then
monitored from afar without the need for further direct involvement.
Despite these important advantages, randomly placed detection units can lead to
highly inefficient container array geometries due to spatial clustering of units or
deployment on or near the fringes of the array. Due to the possibility of poor container
array geometries, additional units must be deployed to ensure that an adequate level of
detection coverage will be provided. Simulation was carried out in an attempt to better
quantify the effects of placement randomization on coverage efficiency (i.e. the fractional
coverage provided by a given number of detection units) and to estimate the number of
91
units that would be required for different levels of coverage for containerships of a given
size.
The simulation explained in Section 5.2.3 calls for the specification of container
array dimensions, effective detection range, number of deployed detectors, and number of
runs as inputs. Five standard container array geometries were selected for use throughout
this analysis to facilitate comparison between the deployment strategies. The dimensions
of these "reference arrays" are shown in Table 5-3.
Table 5-3: Reference array dimensions
Reference Array Dimensions
Capacity
Height (cont)
Width (cont)
Length (cont)
(TEU)
8
8
10
10
10
9
12
12
15
17
20
26
30
32
38
1440
2496
3600
4800
6460
Reference arrays shown above were selected to provide a representative sample of the
capacities and array geometries of the contemporary containership fleet.
Gallagher at MIT is currently investigating the effective detection range.
Preliminary analysis and modeling suggests that the range may be somewhere around 65
ft. Using this uncertain estimate as a point of departure, detection ranges spanning from
45 ft. to 85 ft. (in 5 ft. increments) were studied.
To determine the appropriate number of iterations to obtain high confidence
results with good statistics, a sample simulation was run using 1, 5, 10, 50, 100, 200, 500
and 1000 iterations. Results of the test, which used 15 detectors with 65 ft. ranges
randomly deployed within the 4800 TEU reference array, are shown in Table 5-4.
92
Table 5-4: Mean fractional coverage results for variable run sizes
Runs
Mean
Std Dev
1
0.7133
0
5
0.7308
0.0646
10
0.7750
0.0922
50
0.7577
0.0673
100
0.7522
0.0566
200
0.7523
0.0584
500
0.7566
0.0583
1000
0.7553
0.0587
Table 5-4 shows that the mean fractional coverage begins to converge at around 50
iterations and the standard deviation has been reduced to the extent practicable by the
100th run. These results are similar to those obtained for cases using different test
parameters. As a result, 200 was chosen to be the standard number of iterations used in
the simulation of each scenario. This number of runs was large enough to provide high
confidence results with good statistics, but small enough to make efficient use of limited
computational resources.
Simulations were carried out as follows. Starting with the smallest reference
array, the shortest effective detection range was held fixed and the number of deployed
units was varied until a distribution of outputs with mean fractional detection coverage
values having a nominal span of at least 0.75 to 0.95 was obtained. Then 5 ft. was added
to the effective detection range input and the process was carried out again. Once this
had been completed for each 5 ft. increment of effective detection range from 45 ft to 85
ft. the next reference array was selected and the entire process began anew. Inputs and
output statistics for each simulated scenario are shown in Table 5-5.
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To distill the information captured in Table 5-5 for easier inspection and analysis, Figures
5-2 through 5-6 show plots that relate the mean values of fractional coverage volume, as
defined in Eq. (1 1), to the number of deployed detectors for each reference array.
Coverage vs. Detectors (1440 TEU)
0.9
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Numberof RandomlyDeployedDetectors
Figure 5-3: Coverage vs. Detectors plot for the 1440 TEU array [Random]
102
40
Coverage vs. Detectors (2496 TEU)
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Numberof RandomlyDeployedDetectors
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Figure 5-4: Coverage vs. Detectors plot for the 2496 TEU array [Random]
Coverage vs. Detectors (3600 TEU)
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,,f"VI·"ir·
· ;··-.
40
30
50
Numberof RandomlyDeployedDetectors
60
1:
i·l
· h'.
70
Figure 5-5: Coverage vs. Detectors plot for the 3600 TEU array [Random]
103
80
*R_45
*R.50
R_55
I R_60
XR_65
*R_70
+R_75
- R_80
- R 85
Coverage vs. Detectors (4800 TEU)
0.9
0
E
*R_45
R_50
R_55
o
'
R_60
x R65
* R70
+R_75
& 0.7
U.
-R80
- R 85
0.6
0.5
0
10
20
30
50
40
60
70
80
100
90
Numberof RandomlyDeployedDetectors
.4,~~~~
Figure 5-6: Coverage vs. Detectors plot for the 4800 TEU array [Random]
Coverage vs. Detectors (6460 TEU)
-
0.9
-+
:C
x
· ;,
+ ~~
U;·I·
,·.
e 0.8
CD
E
0
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00
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Number~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;
Deployed:Deetr
of~.Randoml
/.i i ~,
0.4
0
20
40
80
60
Number of Randomly Deployed Detectors
100
120
Figure 5-7: Coverage vs. Detectors plot for the 6460 TEU array [Random]
104
140
It is unclear what minimum acceptable level of detection coverage is appropriate,
given the reality that it will not always be possible to provide 100% coverage of every
containership and that attempting to do so will likely prove to be cost prohibitive.
Acknowledging this uncertainty, all subsequent analysis will measure the system against
three potential choices for minimum acceptable coverage. These three levels are 75%,
85%, and 95%.
To identify the number of detectors with a given range that are required to
provide 75%, 85%, and 95% coverage for each of the 5 reference arrays, the mean
fractional coverages for each simulated scenario were plotted and graphical techniques
were employed. Figure 5-7 shows an example using the 1440 TEU reference array and
detectors with a 65 ft. effective range (error bars represent +/- 1 standard deviation).
1440 TEU (Range = 65 ft)
I
0.8
cm
0.6
o
0.4
0.2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Detectors
Figure 5-8: Graphical determination of detectors required for various coverage levels
For the example case illustrated in Figure 5-7, it was estimated that 75%, 85%, and 95%
fractional detection coverage could be provided with 6, 8, and 14 detectors, respectively.
105
Results of these graphical analyses showing the estimated number of detectors needed to
provide various levels of coverage for each scenario are listed in Table 5-6.
Table 5-6: Estimated number of detectors needed for various scenarios [Random]
Reference Array Capacity (TEU)
Random Deployment
Coverage
(ft)
Range (ft) Range
Coverage
45
50
55
60
65
70
75
80
85
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
1440
2496
3600
4800
6460
13
19
32
11
15
25
9
12
19
7
10
15
6
8
14
5
7
11
5
6
10
4
6
9
4
5
8
21
31
50
17
23
39
13
19
30
11
15
25
9
12
21
8
11
18
7
9
15
6
8
14
5
8
12
30
40
69
22
31
53
18
25
41
15
20
34
12
17
27
10
14
23
9
12
19
8
10
17
7
9
15
37
52
88
29
40
69
23
31
53
18
26
43
15
20
34
13
18
29
11
15
24
9
13
21
8
11
19
59
68
117
37
52
88
30
41
70
24
33
55
20
27
45
16
22
38
14
18
31
12
17
29
10
15
25
One clear trend observed in the Figures above (particularly 5-2 through 5-6) are
the diminishing returns in coverage afforded by the deployment of each additional
detector, especially in the high coverage region (i.e. above around 0.80). It takes the
addition of considerably more detectors to get from 85% to 95% coverage than it took to
get from 75% to 85%. Using the scenario where detectors with a 65 ft. range were
deployed in the 6460 TEU reference array as an example, it took 7 additional detectors to
go from 75% to 85% coverage and 18 additional detectors to go from 85% to 95%.
106
The primary cause of this phenomenon is the fact that random deployment does
not promise uniform distribution of detectors throughout a container array. As a result,
randomized placement will unavoidably give rise to some well-covered regions with
significant coverage overlap and some sparsely covered regions with little to no detection
coverage. Detectors cannot be preferentially deployed to uncovered or inadequately
covered areas. Therefore, to enhance the fractional coverage area with additional
detectors, one must rely on the capricious nature of random placement to fortuitously
deploy added units to sparsely covered regions. Inefficiencies associated with this
process lead to the diminishing marginal returns observed in the simulation results. The
extent to which random deployment is less efficient than optimal centerline deployment
will be discussed in a later section.
Although the mechanism discussed above is the primary determinant, there is
another factor at work in the deployment simulation that artificially magnifies the
diminishing returns effect. Given that the simulation used for this analysis assumed that
the center point of detectors could be placed at any point in space within the container
array, there is a non-negligible probability, given by Eq. (9), that 2 detectors could be
randomly assigned to the space that corresponds to a single container. The probability of
this "double assignment" increases as the number of deployed detectors increases. Since
double assignment is an inefficient distribution of detectors, it could make a small
contribution to the diminishing returns effect. Table 5-7 shows the probability that any 2
detectors will be randomly assigned to the same 20' and 40' container volumes for a
sampling of simulated scenarios.
107
Table 5-7: Double assignment probabilities for 20' and 40' containers [Random]
Capacity
Detectors
Double Assign.
Double Assign.
Capacity
Detectors
Double Assign.
Double Assign.
1440
1440
1440
1440
1440
1440
1440
1440
2496
2496
2496
2496
2496
2496
2496
2496
2496
2496
3600
3600
3600
3600
3600
3600
3600
3
5
10
15
20
25
30
35
3
5
10
15
20
25
30
39
47
52
3
5
10
20
30
40
50
0.002
0.007
0.031
0.071
0.124
0.189
0.262
0.341
0.001
0.004
0.018
0.041
0.074
0.114
0.161
0.258
0.353
0.414
0.001
0.003
0.012
0.052
0.114
0.195
0.290
0.004
0.014
0.061
0.137
0.234
0.344
0.458
0.568
0.002
0.008
0.036
0.081
0.142
0.215
0.296
0.451
0.584
0.660
0.002
0.006
0.025
0.101
0.216
0.354
0.497
3600
3600
4800
4800
4800
4800
4800
4800
4800
4800
4800
4800
6460
6460
6460
6460
6460
6460
6460
6460
6460
6460
6460
6460
6460
60
70
5
10
20
30
40
50
60
70
80
90
5
10
20
30
40
50
60
70
80
90
100
110
120
0.390
0.491
0.002
0.009
0.039
0.087
0.150
0.226
0.310
0.397
0.484
0.568
0.002
0.007
0.029
0.065
0.114
0.173
0.240
0.313
0.388
0.464
0.537
0.607
0.671
0.630
0.743
0.004
0.019
0.076
0.166
0.279
0.402
0.525
0.638
0.736
0.816
0.003
0.014
0.057
0.126
0.215
0.317
0.424
0.529
0.627
0.714
0.787
0.847
0.893
Table 5-7 shows the probability that any two detectors will be assigned to a single
container becomes quite large as the number of deployed detectors gets large and in some
extreme cases, double assignment is almost assured. Since this inefficient double
assignment is non-physical, the fractional detection coverage output by the simulation
will be marginally underestimated and the diminishing returns effect will be slightly
exaggerated.
Another notable feature of the results captured in Table 5-6 is the strong relation
between the number of detectors needed to provide a given fractional coverage level and
the effective detection range of the deployed units. This dependence is illustrated in
Figures 5-8 through 5-12 where the estimated number of detectors required for 75%,
85%, and 95% coverage are plotted against detection range for each of the 5 reference
arrays.
108
Detectors vs Range (1440 TEU)
100
0
0
0
Q
* Cov 0.75
* Cov 0.85
10
Cov_0.95
1
40
50
60
70
90
80
Range (ft)
Figure 5-9: Required Detectors vs. Range for the 1440 TEU array [Random]
Detectors vs. Range (2496 TEU)
*.'.'
100
-
I; (.Cov
.ek 0.75
U
..
10- ..
....
;,-,
0
40
50
60
70
80
..
..
Cov
0.85
I
Coy_0.95
90
Range (ft)
Figure 5-10: Required Detectors vs. Range for the 2496 TEU array [Random]
109
Detectors vs. Range (3600 TEU)
100
0
E
.o
* Cov 0.75
* Cov 0.85
10
0
Cov_0.95
03
4-I
1
40
50
60
70
90
80
Range (ft)
Figure 5-11: Required Detectors vs. Range for the 3600 TEU array [Random]
Detectors vs. Range (4800 TEU)
100
I * Cov 0.75
mr
10
,
*Cov
0.85
Cov_0.95
1
'I
40
'
50
I
60
I
70
80
90
Range (ft)
Figure 5-12: Required Detectors vs. Range for the 4800 TEU array [Random]
110
Detectors vs. Range (6460 TEU)
1000
p
100
a
10
* Cov 0.75
* Cov 0.85
Cov_0.95
1
40
50
60
70
80
90
Range (ff)
Figure 5-13: Required Detectors vs. Range for the 6460 TEU array [Random]
The pronounced "range effect" illustrated in Figures 5-8 through 5-12 can be
explained by the relation between the effective detection range and the volume of
coverage provided by a detection unit. Equation (12) shows that the volume of the
idealized detection sphere increases as the cube of the effective detection radius.
Therefore, the volume of a detection sphere created by a detector with an 85 ft. radius is
6.74 times greater than that of a detector with a 45 ft. radius. By covering a significantly
larger detection volume per unit, fewer long-range detectors are needed, on average, to
provide a given fractional coverage.
Finally, although the 6460 TEU reference array represents a larger container
capacity than the 95 th percentile vessel in the current fleet, it is likely that the trend to
build and deploy larger and larger containerships will continue in the coming years until
capacities exceed 10000 TEU [Ircha, 2002]. Figures 5-13 through 5-17 plot the number
of detectors needed for given coverage levels versus vessel capacity for a representative
sampling of ranges.
111
Detectors vs. Capacity (Range = 45 ft)
,
,
140
120
100
,
* Cov 0.75
80
· Coy 0.85
* Cov_0.85
60
Cov_0.95
40
20
0
0
2000
4000
6000
8000
Capacity (TEU)
Figure 5-14: Required Detectors (with 45 ft. range) vs. Array Capacity [Random]
-
Detectors vs. Capacity (Range = 55 ft)
80
70
60
50
.
-. . ...
.
4
....
...
.
; i ;RtJI
Cov
40
2010
- ;
-
830
u
O
Cov_0.85
C _0.95
I
.. ..
.r
:
. .
. . .
..
0.75
.
-
0
2000
4000
6000
8000
0
2000
4000
6000
8000
Capacity (TEU)
Figure 5-15: Required Detectors (with 55 ft. range) vs. Array Capacity [Random]
112
Detectors vs. Capacity (Range = 65 ft)
mA
50
45
40
35
E 30
* Cov 0.75
O 25
aCov 0.85
* Cov_0.85
a 20
Cov_0.95
15
10
5
Nv
2000
O
4000
6000
8000
Capacity (TEU)
Figure 5-16: Required Detectors (with 65 ft. range) vs. Array Capacity [Random]
Detectors vs. Capacity (Range = 75 ft)
35 -
E
15
20
-0000
":
2
"'
:
(T)Cov
|
*Cov 0.75
·
0.85
Cov 0.95
5
0
0
2000
4000
6000
8000
Capacity (TEU)
Figure 5-17: Required Detectors (with 75 ft. range) vs. Array Capacity [Random]
113
Detectors vs. Capacity (Range = 85 ft)
30
25
20
0
U
* Cov 0.75
* Cov 0.85
15
Cov_0.95
a lO
0
0
2000
4000
6000
8000
Capacity (TEU)
Figure 5-18: Required Detectors (with 85 ft. range) vs. Array Capacity [Random]
Figures 5-13 through 5-17 show relationships between the number of required
detectors and vessel container capacities that are linear to a very good approximation.
This linearity could be used in the future to estimate the number of detectors needed to
provide coverage of proposed vessels with capacities exceeding those of containerships
in the fleet today.
5.4 Constrained Deployment
Deviation from random deployment could challenge and potentially comprise the
desired surreptitious nature of the ship-based approach and invite serious logistical
difficulties. However, given the coverage inefficiencies that are an unavoidable
consequence of completely random deployment, the constrained deployment strategy was
investigated to determine the efficiency gains that could be reaped by imposing minimum
loading constraints. In an effort to limit the undesirable and inefficient situation in which
detectors are placed close to the edge or surface of the container array, the constrained
114
deployment simulation explicitly barred the assignment of detectors to space that
corresponded to the first or last (TEU) container in any row, column, or span of the array.
It is unclear whether even this limited constraint would be possible to impose in practice.
Constrained deployment simulation was carried out in the same manner as
described above for random deployment. The only modification to the simulation
schedule was the exclusion of scenarios with detectors having 45 ft. and 85 ft. effective
ranges. Limited computing resources necessitated the tailoring of the simulation
schedule and the excised scenarios were the most computationally intensive 1 . Table 5-8
shows the output statistics for constrained simulations.
" 45 ft. range scenarios were intensive due to the large number of detectors that had to be deployed to
achieve desired fractional coverages. 85 ft. range scenarios were intensive because of the large number of
computations required to construct their detection spheres.
115
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For ease of inspection, the mean fractional coverage volumes for each scenario and
reference array are plotted in Figures 5-18 through 5-22.
Coverage vs. Detectors (1440 TEU)
1
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20
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Numberof Detectors
Figure 5-19: Coverage vs. Detectors plot for the 1440 TEU array [Constrained]
122
Coverage vs. Detectors (2496 TEU)
0.9
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Numberof Detectors
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Figure 5-20: Coverage vs. Detectors plot for the 2496 TEU array [Constrained]
Coverage vs. Detectors (3600 TEU)
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10
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30
40
50
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Numberof Detectors
Figure 5-21: Coverage vs. Detectors plot for the 3600 TEU array [Constrained]
123
Coverage vs. Detectors (4800 TEU)
0.9
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Numberof Detectors
Figure 5-22: Coverage vs. Detectors plot for the 4800 TEU array [Constrained]
Coverage vs. Detectors (6460 TEU)
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Figure 5-23: Coverage vs. Detectors plot for the 6460 TEU array [Constrained]
124
The number of detectors needed to provide 75%, 85%, and 95% coverage for
each scenario were estimated in the same manner as described in the previous section and
results are shown in Table 5-9.
Table 5-9: Estimated number of detectors needed for various scenarios [Constrained]
Constrained
Depl
ent
1440
2496
3600
4800
6460
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
9
12
21
7
10
18
6
8
15
14
20
38
12
16
28
9
13
23
20
28
51
16
21
39
12
18
31
25
35
65
20
28
50
15
23
40
33
48
86
26
37
65
21
29
51
0.75
5
8
11
13
18
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0.85
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7
11
5
7
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4
6
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8
10
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7
9
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25
9
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8
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32
11
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10
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43
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9
14
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35
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4
5
6
8
7
10
9
11
11
15
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9
13
15
20
26
Range (ft) Coverage
50
55
60
65
70
75
80
Capacity (TEU)
When the numbers tabulated above for constrained deployment are compared to
the random deployment results shown in Table 5-7, the differences are not particularly
striking. Surprisingly, very little is gained in terms of coverage efficiency by
constraining placement in containers along the surface of the array. It appears, that by
excluding placement in such a large volume fraction of the total container array, that
inefficient overlapping was promoted in the center. This seems to have offset efficiency
gains that were realized by limiting coverage volume "losses" at the surface of the array.
Double assignment effects also played a larger role in the constrained simulation because
the (xyz) term in Eq. (9) was smaller due to the imposed placement constraint.
125
5.5 Centerline Deployment
Centerline deployment, where detectors are optimally distributed along the length
of the middle row and column of the container array, is the least secure of the examined
deployment strategies, in terms of concealing the location of detection units. It is also
dubious as to whether this approach would be logistically feasible in practice. However,
the completely constrained nature of this strategy does afford extremely efficient
utilization of detector coverage. As a result, this deployment approach is useful for
establishing a lower bound for the number of detectors that would be needed to cover a
vessel with a given capacity. This lower bound can also be used to quantify the coverage
efficiency losses resulting from full randomization.
Since the imposed constraints dictate that detectors could only be placed along the
centerline of the reference arrays, the geometry of each scenario was uniquely specified
so only one calculation (as opposed to multi-run Monte Carlo analysis) was needed to
determine the coverage. For the purposes of these calculations, the centerline of each
array was assumed to consist of 40' containers to more accurately model arrays
encountered aboard actual containerships. It was further assumed that detectors were
only placed in the center of these full-sized containers. The first scenario for each
reference array would place a detector in each of the available full containers along the
centerline. The next scenario would place detectors in every other container, then every
third container, and so on. Sometimes using placement patterns of this fashion did not
uniquely specify the arrangement of detectors. For example, if detectors are to be placed
in every third full sized container and there are 15 containers along the length of the
centerline, then the desired placement pattern can be realized with an equal number of
detectors when the pattern is begun with a detector in the first, second, or third container
in the line. Whenever there were degrees of freedom associated with which container to
place the first detector in, the coverage for each available geometry was calculated and
the arrangement with the highest coverage was used. The results of these calculations
are shown in Table 5-10.
126
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134
For ease of inspection, the fractional coverage volumes provided by selected detector
loading patterns 1 2 in each reference array are plotted in Figures 5-23 through 5-27.
Coverage vs. Detectors (1440 TEU)
..
1.0
i
.·
lj
··
··
ii.
...· · li·'
··
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-R 85
-i
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a
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·-1
-- i·
0.3
1
2
3
4
5
6
7
8
9
10
11
Numberof Centerline
DeployedDetectors
Figure 5-24: Coverage vs. Detectors plot for the 1440 TEU array [Centerline]
12 When two or more loading patterns resulted in the same number of detectors being deployed, only the
result from the pattern with the highest fractional coverage was plotted.
135
R_-70
-- R_75
'·
Ila
R_45
R_50
R_55
-RR_60
i
.;·1..,.
j
---
't;',·r
i·
Coverage vs. Detectors (2496 TEU)
1.0
0.9
0.8
E
0
-e-- R_45
0.7
-- R50
Ol
R_55
- R60
R65
o 0.6
-* 0.5
R-70
-- R75
-R80
iL
I 0.4
R-85
R
0.3
0.2
0.1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Numberof CenterlineDeployedDetectors
Figure 5-25: Coverage vs. Detectors plot for the 2496 TEU array [Centerline]
Coverage vs. Detectors (3600 TEU)
r·:
1.0
y·
0.9
:(::·
·
:·
0.8
-:L
E
-e-- R_45
-- R_50
R_55
"R_60
--- R65
-- R_70
> 0.7
'::-"T:·.r: r·'-i;. -·. -· -. ·
0
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4
5
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-.
:
7
8
9
10
13
14
Numberof CenterlineDeployedDetectors
Figure 5-26: Coverage vs. Detectors plot for the 3600 TEU array [Centerline]
136
w
Coverage vs. Detectors (4800 TEU)
1.0
0.9
0.8
E
0.7
-eR_45
- R50
o 0.6
I- R60
e
o0
R-55
0
R-65
R70
I--R 75
R-80
-- R 85
U.
0
-
--
0.4
0.3
0.2
0.1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Numberof CenterlineDeployedDetectors
Figure 5-27: Coverage vs. Detectors plot for the 4800 TEU array [Centerline]
Coverage vs. Detectors (6460 TEU)
1.0
-·:·
·;··?.
0.9
I·
·-L;
.i-·
`··
`I
i
-·I-··'
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E
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0.5
irbi_.
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0.0
3
4
5
6
7
8
9
10
11
12
13
14
15
Numberof CenterlineDeployedDetectors
16
17
18
19
20
Figure 5-28: Coverage vs. Detectors plot for the 6460 TEU array [Centerline]
137
-- R85
The number of centerline deployed detectors needed to provide 75%, 85%, and
95% coverage for each evaluated range and reference array are shown in Table 5-11.
Table 5-11: Estimated number of detectors needed for various scenarios [Centerline]
Centerline
Depi
Range (ft)
45
50
55
60
oment
Coverage
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
Reference Array Capacity (TEU)
1440
2496
3600
4800
6460
5
7
10
5
5
7
4
5
5
4
4
5
3
10
N/A
N/A
6
9
N/A
6
6
10
5
6
7
5
N/A
N/A
N/A
8
13
N/A
7
8
N/A
5
6
9
5
N/A
N/A
N/A
N/A
N/A
N/A
12
N/A
N/A
7
12
N/A
6
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
12
N/A
N/A
8
65
0.85
4
5
5
7
15
70
0.95
0.75
0.85
0.95
0.75
4
3
4
4
3
6
4
5
5
4
7
4
5
6
4
14
4
6
8
4
N/A
7
8
19
6
75
0.85
3
5
4
5
7
0.95
0.75
0.85
0.95
0.75
0.85
0.95
4
2
3
3
2
3
3
5
3
4
5
3
4
4
5
4
4
5
3
4
4
7
4
5
7
4
4
5
9
5
6
8
5
5
6
80
85
Depending on the effective range of the detection unit, there are some levels of
coverage for certain reference arrays that cannot be achieved through the use of detectors
deployed exclusively along the centerline (denoted in Table 5-11 as N/A). However, in
cases where the range is sufficient to provide desirable coverage using only centerline
deployment, the deployment efficiency resulting from the preferential placement
attendant to this approach allows high levels of coverage to be achieved with a significant
economy of detection units.
138
5.6 Deployment Comparison
The most germane comparison that can be drawn between the deployment
strategies examined in the previous sections is to contrast the number of detectors
required by each method to achieve given levels of fractional coverage when faced with
identical range and array capacity scenarios. Since constrained deployment was not
found to hold any significant efficiency advantages over random deployment (despite its
stealth and logistical disadvantages), only random and centerline deployment will be
considered in the following analysis.
Table 5-12 shows the number of detectors required for each scenario using both
random and centerline deployment. It also tabulates the ratio of randomly deployed
detectors to centerline deployed detectors for each case so that a measure of the
efficiency cost of randomization can be obtained.
139
Table 5-12: Random vs. Centerline deployment comparison
Random vs.
Reference
Centerline
Ranae ftl Coveraae
.I
-- '113
0.75
0.75
45
0.85
0.95
I
50
32
IZn A,
IIIf
v. I'~ '" E
0.85
0.95
I
I
55
I
I
60
65
70
75
80
85
U.
7
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1440
R
C IR/C
5D2,-I
13
5 2.6
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15
5
25
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39
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59
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6460
C
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9
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40
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50
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Array Capac
3600
R
C IR/C
30
2496
R
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21 10 2.1
31
15 1.8
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5
3
1.7
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4
2.0
10
4
2.5
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4
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7
4
1.8
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5
2.8
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6
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22
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11
5
4
3
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1.7
18
7
5
4
3.6
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23
9
6
4
3.8
2.3
29
11
8
4
3.6
2.8
38
14
19
6
2.0
2.3
0.85
6
3
2.0
9
5
1.8
12
4
15
5
3.0
18
7
2.6
0.95
0.75
0.85
0.95
10
4
6
9
4
2
3
3
2.5
2.0
2.0
3.0
15
6
8
14
5
3
4
5
3.0
2.0
2.0
2.8
19
8
10
17
5
4
4
5
24
9
13
21
7
4
5
7
3.4
2.3
2.6
3.0
31
12
17
29
9
5
6
8
3.4
2.4
2.8
3.6
3.0
3.8
2.0
2.5
3.4
2.3
0.75
4
2
2.0
5
3
1.7
7
3
2.3
8
4
2.0 10
5
2.0
0.85
0.95
5
8
3
3
1.7
2.7
8
12
4
4
2.0
3.0
9
15
4
4
2.3
3.8
11
19
4
5
2.8
3.8
15
25
5
6
3.0
4.2
Comparisons between random and centerline deployment could be rendered moot
if the centerline strategy is definitively judged to be logistically infeasible or if it is
determined to be an unacceptable compromise of the stealth characteristics that are so
important to the ship based approach. Additionally, centerline deployment, by itself,
would presumably stop receiving serious consideration if the effective detection range is
found to be too low to provide the minimum acceptable detection coverage for all vessels
of interest. That said, Table 5-12 clearly illustrates the efficiency gains realized through
centerline deployment. Table 5-13 shows the average random to centerline, R/C, values
for the three analyzed fractional coverage volume targets.
140
Table 5-13: Average R/C values
Fractional Coverage Volume
R/C
0.75
0.85
0.95
2.249
2.531
3.306
As Table 5-13 illustrates, the efficiency advantage enjoyed by centerline deploy
increases as the desired level of coverage increases. This stems from the diminishing
marginal returns phenomenon associated with random deployment. Unlike the random
case, when additional detectors are deployed along the centerline to achieve a higher
level of fractional detection coverage they will preferentially "fill in" uncovered or
sparsely covered areas of the container array. Therefore, marginal returns are greater
when employing the centerline approach and as a greater number of detectors are added
to provide higher levels of coverage this amplifies the efficiency advantages over random
deployment.
5.7 Total Detector Estimates
To estimate the total number of detectors required to field a comprehensive
system (i.e. to cover every inbound commercial containership) the data compiled in the
previous sections must be combined with information from the shipping industry and
U.S. ports. If all classes of containerships called on U.S. ports with uniform frequency
then the capacity distribution derived in Chapter 4 could be used directly to determine the
total number of detectors. Some types of container vessels, however, make more port
calls than others, so these vessels should receive a higher importance weighting in the
analysis. Table 5-14 shows the relative frequency of calls at U.S. ports broken down by
vessel size (i.e. container capacity) [MARAD, 2000] and the number of calls that these
vessel classes would make out of the CY 2003 call total of 17287 [MARAD(1), 2004].
Table 5-14: U.S. port calls by vessel capacity
Relative Freq.
Calls
<2000
0.3491
6035
Vessel Capacity (TEU)
2001-3000 3001-4000 4001-5000
0.2853
0.2129
0.1147
4932
3680
1983
141
>5000
0.038
657
Total
1
17287
Since one of the reference arrays described in the previous analysis fits
approximately in the middle of each of the capacity bins shown in Table 5-14, the
number of detectors found to be required to cover a given reference array can be
considered roughly representative of the entire binned vessel class. Estimates for the
total number of detectors needed for comprehensive deployment can now be made using
the following expression,
(13)
DetTotal =
Avgclv
i
where Avgc/vis the average number of calls made per vessel, Ci is the number of calls for
a given vessel class, and Deti is the number of detectors required for a given vessel class.
In 2003, the average number of calls made by containerships was 17 [MARAD(1), 2004].
Since the detection units have no inland destination and are intended solely for
deployment aboard containerships, once they are discharged from a given vessel they can
be redeployed with minimal downtime. Downtime that could be required for
maintenance and calibration is not considered. For the purposes of this analysis, it is
assumed that turn-around can occur immediately, so the discharged detection unit can be
shipped out (i.e. transported back to a foreign port where it can be deployed for its
intended purpose) without delay. It should be noted that the export leg of the detection
unit's voyage could be used to perform performance reliability tests and to monitor for
the unlikely event that a fissile or radiological source was being smuggled out of the
United States, for use abroad. Stops between foreign ports on the export leg could also
be used to monitor for radioactive material movement abroad, which could discourage or
thwart international smuggling attempts and augment the ability of other nations to
defend against nuclear or radiological attack.
Eq. (13) was applied to the results from the random and centerline deployment
simulations and estimates for the total number of detectors that would be necessary using
either deployment strategy are shown in Table 5-15.
142
Table 5-15: Total detector estimates
Total Detector
II
I Estimoatea
Fatimtnt
-- 7 ---
I Rnna
,
,-
..
45
fft
nvarnna
0.75
0.85
0.95
I
GaI%
23798
33091
55589
0.75
18412
25384
43112
0.75
0.85
0.95
7
14705
20385
33211
4O.x4
0.85
16539
0.95
27079
0.75
0.85
0.95
0.75
9861
13378
22612
8395
0.85
11657
4962
0.95
0.75
18957
7578
5837
3790
75
0.85
0.95
0.75
9784
16012
6406
4235
5117
3106
80
0.85
8789
3906
0.95
14507
4724
0.75
0.85
5706
7907
2890
3751
0.95
12751
3906
55
60
65
70
85
I
l ll 1
0.85
0.95
50
I
Deployment Strategy
DAnrm
__.,
I
_
_
__
_
4607
5349
3828
Table 5-15 shows that if only purely random or purely centerline deployment strategies
are being considered, the option space is limited if the effective detection range of the
containerized units is less than 70 ft. An additional advantage to units with effective
ranges equal to or greater than 70 ft is the significant reduction in the number of detectors
required to provide any of the evaluated fractional coverage volumes. Table 5-15 also
demonstrates the reduction in detection units required for full deployment if the fractional
coverage volume is chosen to be less than 95%.
143
Chapter 6: Summary, Conclusions, and Recommended Future Work
6.1 Summary
The rise of highly mobile, religiously motivated transnational terrorist
organizations that are not restrained by conventional means of deterrence has changed the
dynamics of the threat that nuclear weapons pose to the United States. The international
commercial container trade that delivers over 19,000 cargo containers to U.S. ports every
day is one possible avenue that could be exploited by a terrorist organization to mount an
unconventional nuclear attack. Due to the unique power and range of nuclear weapons,
defensive measures that have been envisioned or deployed that would not detect threats
until they come ashore at U.S. ports do not provide adequate protection against attacks
that are planned and executed by rational, determined adversaries.
We propose a new ship-based approach to fissile material detection where large
effective area, commercial off the shelf, radiation detectors, enhanced with imaging
capabilities, are enclosed in standard, non-descript cargo containers and shipped
alongside commercial containers. When deployed in limited numbers aboard commercial
vessels the detection units would passively measure any nuclear signature emitted by
nearby containers with count times limited only by the duration of the voyage. By
outfitting the dedicated detection units with communication hardware, identification and
notification of a potential threat could be made while the danger was still safely removed
from U.S. shores.
To better characterize the feasibility of the proposed ship-based approach,
"external" uncertainties associated with the deployment environment and potential modes
of deployment were investigated. Characteristics of the deployment environment that
were evaluated included the count times that would be available on container import
voyages terminating at U.S. ports, the container capacities of the vessel fleet that ply the
international container trade, and the average densities of cargo being imported to the
U.S. Table 6-1 summarizes the salient results of these analyses.
144
Table 6-1: Results summary for deployment environment analyses
Vessel Capacity Avg. Density*
Count Time (days)
(TEU)
(q/cmA3)
To NY
To LA
Mean
3047
0.1977
19.2
13.3
Median
2722
0.1708
19.1
13.3
25th
75th
1666
4173
0.1664
0.2208
21.7
17.2
15.1
11.9
95th
99th
6204
6782
0.2620
0.2998
15.9
15.6
11
10.8
* 0.1977 g/cm3 corresponds to 15.23 metric tons / 40'container
To study different potential modes of deployment, a Matlab-based simulator was
developed. The simulator was used to evaluate and compare detection coverage
efficiencies for fully random detector deployment, partially constrained deployment
where containerized detection units could not be placed along the surface of container
array, and fully constrained deployment where detectors could only be placed along the
centerline of the array. Partially constrained deployment was not found to have any
particularly desirable attributes. The number of detection units required to provide
various degrees of coverage for random and centerline deployment are summarized in
Tables 6-2 and 6-3 respectively. Coverage is defined as the fractional volume of a
vessel's container array that is within the effective detection range of one of the deployed
containerized detection units. The effective detection range is the expected maximum
distance at which a source can be confidently and reliably detected in a given count time,
under realistic conditions.
145
Table 6-2: Random deployment results summary
-
Reference ArravCaoacitv(TEUI
-
Random Deployment
Range(ft) Coverage
0.75
45
0.85
0.95
0.75
50
0.85
0.95
0.75
55
0.85
0.95
0.75
60
0.85
0.95
0.75
65
0.85
0.95
0.75
70
0.85
0.95
0.75
75
0.85
0.95
0.75
80
0.85
0.95
0.75
85
0.85
0.95
1440
2496
3600
4800
6460
13
19
32
11
15
25
9
12
19
7
10
15
6
8
14
5
7
11
5
6
10
4
6
9
4
5
8
21
31
50
17
23
39
13
19
30
11
15
25
9
12
21
8
11
18
7
9
15
6
8
14
5
8
12
30
40
69
22
31
53
18
25
41
15
20
34
12
17
27
10
14
23
9
12
19
8
10
17
7
9
15
37
52
88
29
40
69
23
31
53
18
26
43
15
20
34
13
18
29
11
15
24
9
13
21
8
11
19
59
68
117
37
52
88
30
41
70
24
33
55
20
27
45
16
22
38
14
18
31
12
17
29
10
15
25
TotalDetectors
23798
33091
55589
18412
25384
43112
14705
20385
33211
11951
16539
27079
9861
13378
22612
8395
11657
18957
7578
9784
16012
6406
8789
14507
5706
7907
12751
Table 6-3: Centerline deployment results summary
I
eployment I
ICenterl-neDeployment
45
50
55
60
65
70
75
80
85
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
__ntene
..
1440
5
7
10
5
5
7
4
5
5
4
4
5
3
4
4
3
4
4
3
3
4
2
3
3
2
3
3
ReferenceArrayCapacity(TEU)
.
I
.
I
2496
3600
4800
10
N/A
N/A
6
9
N/A
6
6
10
5
6
7
5
5
6
4
5
5
4
5
5
3
4
5
3
4
4
N/A
N/A
N/A
8
13
N/A
7
8
N/A
5
6
9
5
5
7
4
5
6
4
4
5
4
4
5
3
4
4
146
N/A
N/A
N/A
N/A
N/A
N/A
12
N/A
N/A
7
12
N/A
6
7
14
4
6
8
4
5
7
4
5
7
4
4
5
6460
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
12
N/A
N/A
8
15
N/A
7
8
19
6
7
9
5
6
8
5
5
6
5349
3828
4962
6837
3790
4235
5117
3106
3906
4724
2890
3751
3906
Tables 6-2 and 6-3 show that the geometrically optimal centerline deployment provides
significantly more efficient detection coverage than the stealthier and more logistically
appealing random deployment. The efficiency advantage of centerline deployment is
evidenced by the finding that an average of 2.249, 2.53 1, and 3.306 times more randomly
deployed detection units are required to provide 75%, 85%, and 95% fractional
coverages, respectively, for vessels with a given container array. The preceding tables
also demonstrate the considerable benefit to developing detection units with an effective
detection range equal to, or greater than, 70 ft. Units with ranges at or exceeding 70 ft.
will yield maximum flexibility in terms of deployment options and will significantly
reduce the number of units required to cover a given vessel and to field a comprehensive
ship-based detector network.
6.2 Conclusions
Since this work was performed as one element of an integrated effort, not all of
the calculations and evaluations documented in this thesis may carry significant relevance
and meaning when viewed alone. These results will be combined with, and serve as
input to, ongoing work being conducted by Gallagher at MIT on system design and
performance modeling. The end product of this continuing effort will yield crucial
information regarding the expected performance of the detection units and the overall
efficacy of the ship-based approach. Despite the essentially unfinished nature of system
development, there are a number of notable conclusions that can be drawn strictly from
the analysis presented and discussed in this document.
First, and perhaps most importantly, none of the results obtained in the preceding
analyses serve to discredit the overall feasibility of the ship-based approach. A
primary objective of this thesis was to assess the practical viability of this new
detection methodology and nothing was discovered that suggested the ship-based
approach could not be viable and effective if prudent design and deployment
decisions are made.
147
Mean count time estimates for the representative East Coast and West Coast ports
were particularly encouraging. With an average of 19.2 days and 13.3 days of
available count time for voyages to New York and Los Angeles respectively, the
ship-based detection units will have a lengthy window of opportunity to passively
detect incoming fissile material and communicate warning to responders while the
threat is still safely at sea.
The results of deployment simulation highlighted the effective detection range of
containerized units as being especially important to promoting and ensuring the
viability of the ship-based approach. Special consideration should be paid to
maximizing this parameter during upcoming design and optimization activities.
Design decisions that increase the expected detection range at the expense of unit
costs should be vigorously examined in light of the dramatic reductions in per
vessel and total detectors required as effective range was increased. The observed
relationship between the required number of detectors and the effective range
suggests that while unit costs may increase as range enhancing features are
incorporated, the total system costs could fall as less detectors are required on the
whole.
Simulation also helped to quantify the efficiency costs associated with random
deployment. While a purely random deployment strategy is very desirable from
both stealth and logistical standpoints, the use of this approach necessitates the
deployment of 2.2 to 3.3 times more detectors (depending on the fractional
coverage target) than the less covert strategy of deploying detection units only
along the ship's centerline. This inefficiency could become quite costly.
Therefore, some combination of random and centerline deployment may prove to
be the most attractive strategy. In such a "hybrid" deployment scenario, if even a
small number of detectors could be deployed along or near the array's centerline
with the remaining detectors randomly distributed, an important degree of stealth
would be preserved by the random component and a helpful boost in efficiency
will be afforded by the centerline component.
148
6.3 Recommendations for Future Work
The deployment strategies described and modeled in this thesis were selected to
represent archetypal cases useful in studying the fundamental trade-off between
deployment stealth and coverage efficiency. Random deployment is at one end of the
spectrum, being the stealthiest approach, but having less than optimal efficiency.
Centerline deployment (i.e. fully constrained placement of detectors along the ship's
centerline) resides at the opposite end of the spectrum, affording optimal efficiency, but
being among the least covert of any potential strategies. Simulations documented in
Chapter 5 provide some quantitative insights into the trade-offs involved when going
from one end of the deployment spectrum to the other. This analysis, however, was
somewhat divorced from important practical considerations that arise from the common
practices and capabilities of the international shipping trade. For instance, it is unclear
whether centerline deployment would be logistically feasible in practice. Therefore, a
clear priority for any future deployment analysis should be to conduct more in-depth
consultations with individuals possessing intimate knowledge of the shipping trade
(particularly the loading and discharging of containerships) to better understand what
types of placement constraints are and are not practicable. This practical knowledge is
essential to understanding the true performance capabilities of a ship-based system and to
developing an effective deployment strategy that can be reliably implemented in the real
world.
Future deployment modeling conducted either to refine the results of this analysis
or to study alternative deployment strategies could employ an enhanced version of the
Monte Carlo simulation codes used to produce the results presented in this thesis.
Simulation codes used in this analysis (and documented in Appendix B) assumed that
detectors could be placed anywhere within a container being used as a dedicated
detection unit. This assumption saved considerable computation time but also created the
opportunity for unphysical situations (e.g. multiple detectors in a single container) to
arise that underestimated the actual performance of the ensemble of deployed detectors.
149
Reality would be more accurately modeled if the locations where detectors could be
randomly placed were limited to the centerpoints of simulated containers. Output
distortions caused by double-assignment situations would be eliminated with this
modification. Additionally, by imposing a minimum separation distance between
detectors (i.e. the distance separating the centers of adjacent containers) better overall
distribution should be observed. Therefore, the enhanced simulation would be expected
to show better and more realistic coverage efficiencies than the results shown above.
Another assumption used in deployment modeling that warrants further attention
is the geometry of the coverage volume provided by deployed detectors. In the preceding
analysis, this volume was represented by a perfect sphere centered at a detector and
having a radius equal to the effective detection range of the unit. A focus of future efforts
should be to investigate factors that morph or distort this idealized sphere. This includes
better characterization of important radiation transport phenomena, such as the effects of
potential radiation streaming through tiny openings, or "pinholes", in commercial cargo
packed in containers. More thorough understanding of these mechanisms can lead to
more realistic and appropriate coverage patterns that can be incorporated in future
performance and deployment models.
Another useful extension of the work presented above would be to model a
number of different hybrid deployment scenarios where some detectors were placed
along the ship's centerline (assuming this mode of deployment is found to be practicable)
and the balance were randomly distributed. By performing parameter studies, an optimal
ratio or mix of centerline to random detectors may be identified. The results from this
optimized hybrid deployment could then be compared to the results of pure random and
pure centerline deployment.
Some of the results presented and discussed in this thesis have direct and
important implications for the on going design and performance assessment activities
being conducted by Gallagher at MIT. One outcome with direct bearing on the
continuing design process is the pronounced benefit of detectors that can achieve
150
effective detection ranges equal to, or greater than, 70 feet. Results of the parameter
study undertaken as part of the deployment simulation demonstrated that significant gains
in coverage efficiency and deployment flexibility were realized when detection units had
effective ranges of 70 ft or higher. These findings strongly suggest that any available
means to augment the detection range of the containerized detection suite should be
investigated and seriously considered. Even design features that enhance range while
increasing unit costs should be considered since the eventual reduction in the number of
longer-range detectors required to provide a given degree of coverage may ultimately
offset the unit cost increases.
Finally, while computer simulations are very instructive in guiding the design
process and estimating the performance of the proposed ship-based containerized
detection units, there is a limit to what can be confidently demonstrated on the strength of
computer modeling alone. Therefore, at the earliest practical juncture, a full-scale
prototype of a containerized unit, complete with a full detection suite, should be built and
vigorously tested in environments as close to those that would be realistically
encountered as possible.
151
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155
Appendix A
156
Vessel name
Capacity
Speed
Vessel name
Yun Long
A.P. Moller
6600
(knots)
24.6
Agnete Maersk
Albert Maersk
Alva Maersk
Amersham
Axel Maersk
Caroline Maersk
Carsten Maersk
Cecilie Maersk
Charlotte Maersk
Chastine Maersk
Chesham
Christian Maersk
Claes Maersk
1100
1100
1100
658
18.0
18.0
18.0
14.8
6600
6600
6600
24.6
24.6
24.6
Zhao Gang No.1
Zhao Qing He
Zhen He
Zhen Wu
1750
19.0
Zhi Shan 1
6600
6600
658
24.6
24.6
Zhong Hang 608
(TEU)
-
Clara Maersk
1550
1750
1550
Clementine Maersk
Clifford Maersk
Columbine Maersk
Cornelia Maersk
Cornelius Maersk
6600
6600
6600
6600
Denham
658
4300
4300
4300
4300
4300
2840
2840
2840
2840
6000
6000
6000
6000
6000
3700
3700
3700
3700
Dirch Maersk
Glasgow Maersk
Gosport Maersk
Grasmere Maersk
Greenwich Maersk
Jens Maersk
Jeppesen Maersk
Johannes Maersk
Josephine Maersk
Karen Maersk
Kate Maersk
Katrine Maersk
Kirsten Maersk
Knud Maersk
Laura Maersk
Laust Maersk
Leda Maersk
Lexa Maersk
Lica Maersk
Luna Maersk
Madison Maersk
Maersk Aberdeen
Maersk Ahram
Maersk Antwerp
Maersk Arun
Maersk Atlantic
Maersk Avon
Maersk Carolina
Maersk Gairloch
6600
Zeus
Zhong Hang 905
Zhong Hang 909
Zhong Hang 912
Zhong Hang 913
Zhong Hang 915
Zhong Hang 916
Zhong Hang 917
Zhong Hang 919
Zhong Hang 920
24.6
24.6
24.6
24.6
14.8
24.2
24.2
24.2
24.2
24.2
22.4
22.5
22.5
23.0
24.6
24.6
24.6
1100
1100
1100
1100
1100
1100
18.0
18.0
18.0
18.0
18.0
18.0
4300
4300
24,20
24.2
Speed
(TEU)
(knots)
12.0
83
345
2728
72
16.5
3801
108
36
36
80
80
80
60
104
104
120
22.5
96
118
118
118
4215
22.0
1668
15.5
Zhu Chuan 992
Zhu Hai 203
ZIM Adriatic
ZIM America
42
ZIM Asia
ZIM Barcelona
72
2810
19.0
3029
3429
3429
4992
21.0
21.7
21.7
24.0
4992
3029
3429
2998
2606
3429
3005
2810
24.0
21.0
21.7
21.0
21.0
21.7
20.0
19.0
3029
3429
21.0
21.7
3029
3029
3429
3029
21.0
21.0
21.7
21.0
ZIM Buenos Aires
ZIM California
ZIM Canada
ZIM China
ZIM Dalian
ZIM Eilat I
ZIM Europa
ZIM Florida
ZIM Haifa I
ZIM Hong Kong
ZIM Iberia
ZIM Israel
ZIM Italia
ZIM Jamaica
ZIM Japan
ZIM Keelung
ZIM Korea
ZIM Mediterranean
ZIM New York
ZIM Pacific
157
12.6
20.5
Zhong He
Zhuang He
ZIM Atlantic
24.6
3700
4300
II
Zhong Hang 901
Zhong Hang 903
14.8
18.9
19.0
18.9
24.6
24.6
24.7
27.7
24.7
24.7
25.0
25.0
23.5
3700
Yu Quan Shan
Yu Xi Quan
Capacity
19.5
2810
19.0
3029
21.0
24.0
24.0
21.0
4992
3429
Maersk Gateshead
Maersk Georgia
Maersk Gironde
Maersk Missouri
Maersk Virginia
Magleby Maersk
Majestic Maersk
Marchen Maersk
Maren Maersk
Margrethe Maersk
Marie Maersk
Marit Maersk
Marstal Maersk
Mathilde Maersk
Mayview Maersk
Mc-Kinney Maersk
Mette Maersk
Munkebo Maersk
Nele Maersk
Nexoe Maersk
Nicolai Maersk
Nikoline Maersk
Nora Maersk
Nysted Maersk
Regina Maersk
Sea-Land Champion
Sea-Land Charger
Sea-Land Comet
Sea-Land Eagle
Sea-Land Freedom
Sea-Land Intrepid
Sea-Land Lightning
Sea-Land Mariner
Sea-Land Mercury
Sea-Land Meteor
Sea-Land Pride
Sea-Land Racer
Sea-Land Value
Sally Maersk
Sine Maersk
Skagen Maersk
Sofie Maersk
Soroe Maersk
Sovereign Maersk
Susan Maersk
Svend Maersk
Svendborg Maersk
Taasinge Maersk
Thies Maersk
Thomas Maersk
Thuroe Maersk
Tinglev Maersk
4300
4300
4300
4300
4300
4300
4300
4300
4300
4300
4300
4300
4000
4300
4300
4300
4300
4000
2200
2200
2200
2200
2200
2026
6000
3733
3733
3733
3733
2344
3733
3733
2344
3733
3733
3918
3733
3612
6600
6600
6600
6600
6600
6600
6600
6600
6600
1750
1350
1500
1350
1500
24.0
24.2
24.2
24.3
24.0
23.5
23.5
23.0
23.0
ZIM Panama
ZIM Piraeus
ZIM Ravenna I
ZIM Shanghai
ZIM Shenzhen
ZIM Singapore I
ZIM USA
ZIM Venezia II
ZIM Virginia
23.0
Zi Ya He
23.5
23.0
24.5
23.0
23.5
23.5
23.0
24.5
21,80
21,80
21,80
21,80
21,80
21.8
24.6
24.0
24.0
24.0
24.0
20.3
24.0
24.0
20.3
24.0
24.0
21.0
24.0
21.0
24.6
24.6
24.6
24.6
24.6
24.6
24.6
24.6
24.6
19.0
Hyundai Republic
Hyundai Kingdom
Hyundai National
Hyundai Dominion
Hyundai Patriot
Hyundai Independence
Hyundai Liberty
Hyundai Discovery
Hyundai Freedom
Hyundai Fortune
Hyundai General
Hyundai Highness
Hyundai Admiral
18.6
18.9
18.6
18.9
Hyundai Baron
Hyundai Commandore
Hyundai Duke
Hyundai Emporer
Hyundai Federal
Hyundai Explorer
Hyundai Poineer
Hyundai Frontier
Hyundai Commander
Hyundai Vladivostok
Hyundai Future
Hyundai Stride
Hyundai Advance
Hyundai Sprinter
Hyundai Progress
Hyundai Highway
Hyundai Bridge
Hyundai Primorskiy
Hyundai Infinity
Hyundai Nobility
Suzuran
Asian Zephyr
Cape Canet
Doris Waluff
Saturn
Star Eagle
Star Evanger
Star Evviva
Star Florida
158
4992
5000
2998
4992
2633
2474
3429
2682
4992
764
6479
6479
6479
6479
6479
5551
5551
5551
5551
5551
5551
5551
4411
4411
4411
4411
4411
4411
3014
3014
3014
3014
2174
2174
2174
2174
2174
2174
2174
2174
628
2241
2241
1177
1032
834
1203
1129
24.0
21.0
24.0
21.0
21.0
21.7
21.0
24.0
19.2
26.4
26.4
26.4
26.4
26.4
25.6
25.6
25.6
25.6
25.6
25.6
25.6
25.1
25.1
25.1
25.1
25.1
25.1
21.7
21.7
21.7
21.7
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
15.8
23.0
23.0
18.1
18.5
18.0
19.5
18.5
15.0
15.0
15.0
15.0
Tobias Maersk
Torben Maerks
Tove Maersk
Trein Maersk
Troense Maersk
Achim
1300
1300
1350
1300
1350
ACX Dahlia
ACX Hibiscus
ACX Lily
ACX Magnolia
ACX Marguerite
ACX Marigold
1430
1430
1250
1480
1467
ACX Primrose
820
ACX Raffiesia
1430
Agios Dimitrios I
Akashi Bridge
Akinada Bridge
Alexandria
3428
3456
5600
400
2199
3209
2199
Al Mariyah
Alva Star
Al Wajba
Ambassador Bridge
America Senator
Anan Bhum
An Rong 1
Aotea
Apollon
I
181
18.0
18.0
18.6
18.0
18.6
15.5
19.5
19.5
19.0
19.5
19.0
19.0
19.5
19.5
18.5
23.0
25.0
17.5
21.0
21.5
2661
993
116
1842
1566
16.5
21.0
Star Fraser
Star Fuji
Star Geiranger
Star Gran
Star Grindanger
Star Grip
Star Hidra
Star Hoyanger
Star Ikebana
Star Inventana
Star Isoldana
Star Istind
Star Isfjord
Star Ismene
Adeline Delmas
Africa
Alpana
Astrid
Blandine Delmas
Bougainville
Caroline Delmas
Delmas Acacia
Delmas Aloe
Delmas Blosseville
Delmas Cartier
Delmas Casablanca
Delmas Charcot
937
1935
1664
574
937
1730
937
676
676
1202
1728
518
1706
1740
15.0
15.0
15.0
15.0
15.0
15.0
16.0
16.0
17.0
17.0
17.0
17.0
17.0
17.0
13.5
18.0
20.0
13.5
13.5
13.5
18.5
18.5
19.0
20.0
15.5
19.6
Arafura
Aramac
2432
2732
Delmas Forbin
Delmas Fjacaranda
Aris I
1810
357
1032
14.3
18.5
2258
20.0
3100
3100
18.0
18.0
18.0
18.0
18.0
Delmas Kenya
Delmas Kerguelen
Delmas Mascareignes
Delmas Sycamore
Delmas Tourville
Delphine Delmas
Eax Sanctity
1158
1740
1466
789
1730
937
940
13.5
Elisa Delmas
20.3
Kaduna
Kamina
1614
1614
1614
1935
582
511
1113
Kwanza
4355
Asian Glory
Asian Gyro
Astoria Bridge
Atlantic Cartier
Atlantic Companion
Atlantic Compass
Atlantic Concert
Atlantic Conveyor
Australia Bridge
3100
3100
3110
2400
Bai Yun He
1674
Baltrum Trader
2470
456
Banga Bijoy
Banga Biraj
Banga Birol
Banga Bodor
Banga Bonik
Banga Borak
Banga Borat
Banga Lanka
Bao Zhong 23
Bao Zhong 68
Barcelona Bridge
Flora Delmas
Gaby Delmas
Giorgia
Heide
20.0
21.0
669
606
510
500
510
846
538
66
140
3965
23.1
159
676
La Bourdonnais
Laura Delmas
Lauren
Lucie Delmas
4473
2150
4473
Madagascar
1346
Marie Delmas
Mirella
Mol Horizon
2207
2152
21.0
18.5
17.0
20.5
18.5
18.0
20.0
20.3
20.3
18.0
15.5
15.3
16.5
19.0
1600
1113
19.0
23.0
19.0
22.6
19.0
16.5
Bay Bridge
2257
20.0
Beauty River
Berlin Senator
Mol Karina
1932
17.5
3007
21.0
15.5
Nicolas Delmas
Paraguay
Parana
Patricia Delmas
9.0
Ponl Mahe
14.5
16.0
Bimba
1
Bin Cheng
Bin Dong Shan
Bing He
Blue Moon
Bonn Express
Bonvoy 88
Bo Shi Ji 386
Bosporus Bridge
BPW 2031
Bremen Bridge
Bremen Senator
Bunga Mas Empat
Bu Yi He
Cai Yun He
California Luna
California Senator
Camilla Rickmers
74
724
78
1696
3400
21.0
Rejane Delmas
Reunion
Rokia Delmas
Roland Delmas
Romain Delmas
Rosa Delmas
Roxanne Delmas
Saint Roch
Santa Barbara I
Santa Margherita
Sassandra
1432
19.0
St Pauli
2916
2850
22.0
Trave Trader
CSAV Shanghai
Copiapo
614
2803
279
45
3210
22.8
11.5
24.0
350
5576
1730
135
1728
1510
20.0
Cap Colville
Cap Delgado
2442
21.5
Cape Campbell
Cape Canaveral
Cape Canet
834
356
590
Cape Coldbek
834
Cape Cook
Caraka JN3-9
Caraka JN319
Carinthia
Caroline Schulte
834
18.5
16.0
18.5
18.5
18.5
10.0
10.0
2824
2532
CEC Mayflower
CEC Morning
Centre Point 28
Chang An 104
650
650
80
104
Chang Jiang Bridge
3456
Chang Sheng 301
Chang Xing 108
Chang Xing 208
Chao He
Chao Shan He
74
Cherokee Bridge
Chesapeak Bridge
Chesapeak Bay Bridge
Chicago Bridge
Chiswick Bridge
Chuan He
Chun He
Concord
Concord Bridge
Conti Arabian
128
24.0
21.0
20.2
20.2
48
1322
836
4226
4226
3400
5576
5600
5446
1322
1452
24.5
24.5
21.0
25.0
25.0
22.5
3308
1742
1895
4355
411
1608
2214
2074
IGA
Sea Puma
IZU
2205
Alice Rickmers
Donna Schulte
1900
2256
CSAV Livorno
CCNI Ancud
1878
1816
1878
1829
Ankara
Arnis
Berulan
Cabo Creus
3482
23.0
Cap Aguilar
Cap Blanco
Cap Bonavista
1466
18.5
Cap Carmel
160
5278
3308
3308
2578
3590
1613
Alianca Urca
16.0
1113
1104
1684
1364
2524
2450
2456
Alianca Macarena
Alianca Sao Paulo
Alianca Shanghai
Alianca Singapore
17.2
17.0
2129
Ikoma
Alianca Hong Kong
Alianca Ipanema
48
1935
CSAV Callao
CSAV Shenzhen
Buxfavourite
CSAV Barcelona
CSAV Genova
Alianca Bahia
Alianca Brasil
Alianca Europa
24.0
770
2207
1613
1613
2460
2045
2045
2468
2233
2233
2524
2442
2456
1151
1388
1208
907
2524
1740
2154
2442
2542
22.6
18.0
17.5
16.5
18.0
16.0
17.0
17.0
16.0
15.5
17.0
19.2
20.0
19.0
14.0
21.0
Conti Cartagena
2432
20.0
Conti Jork
Conti Valencia
Cosco Antwerp
Cosco Atlantic
Cap Castillo
2442
1597
18.0
Cap Colorado
2305
5446
2054
21.0
24.5
21.4
22.2
24.5
24.5
24.5
Cap Colville
Cap Cortes
1510
1510
1651
Cosco Cape Town
Cosco Felixstowe
Cosco Hamburg
5446
5446
Cosco Hong Kong
Cosco Kiku
5446
542
Cosco New York
Cosco Norfolk
Cosco Qingdao
2728
3330
5446
24.5
Cosco Ran
542
1164
18.0
18.7
5446
24.5
Cosco Redsea
Cosco Rotterdam
Cosco Sakura
Cosco Sao Paulo
Cosco Shanghai
Cosco Singapore
Cosco Tianjin
542
5446
Da Qing He
Daxin
5446
5752
96
3801
1932
764
588
Delaware Bridge
4452
CRC No. 1
Da He
Dainty River
Diman
II
Donau Bridge
Dong He
Dong Rong
Dong Xu
Dong Yun 009
Dong Yun 030
Dong Yun 556
Dubai
Duburg
1822
18.0
17.5
22.0
Cap Ortegal
Cap Pasado
Cap Pilar
Cap Polonio
Cap Reinga
Cap Roca
18.0
Cap San Antonio
Cap San Augustin
Cap San Lorenzo
22.2
24.5
24.5
26.3
Cap San Marco
Cap San Nicolas
Cap San Raphael
24.0
Cap Velas
Cap Vilano
Cap Vincent
Castor
City of Glasgow
City of Hamburg
18.5
19.2
15.6
19.0
4038
2761
58
83
36
Cap Domingo
Cap Ferrato
Cap Finisterre
Cap Frio
Cap Lobos
Cap Norte
City of Istanbul
City of Manchester
City of Tunis
Columbian Express
Columbus Australia
Columbus Canada
Columbus China
18.5
9.5
24
96
2199
Columbus Florida
1464
1704
21.0
Eagle Strength
E Cheng
Elbe Bridge
725
680
17.0
18.3
Elisabeth Schulte
Empress Dragon
2532
3494
Empress Heaven
Empress Phoenix
3494
3494
Empress Sea
En Hui
En Yuan
Ever Able
3494
24.5
21.9
21.0
21.0
21.0
21.0
Columbus Victoria
Columbus Waikato
Copacabana
Courier
Damaskus
88
88
1164
1164
1164
4211
20.5
20.5
20.5
25.0
Eagle Express
Ever Ally
Ever Apex
Ever Dainty
Flamengo
Independente
Intrepido
Kairo
Kapitan Kurov
Karthago
Leblon
Mekhanik Kalyuzhniy
Santa Felicita
Santa Fiorenza
Santa Francesca
161
2100
2478
2023
2456
1645
2468
2442
1550
1581
2023
1651
2640
3739
3739
3739
3739
3739
3739
1709
1742
1835
1129
956
2228
1232
300
1709
752
2062
1215
2524
1651
1229
1837
1402
1452
1645
1254
1138
1138
1709
1250
1354
1157
1167
2169
2169
2169
Ever Delight
Ever Deluxe
Ever Diadem
Ever Diamond
Ever Dynamic
Ever Gaining
Ever Gallant
Ever Garden
Ever Gather
Ever General
Ever Genius
Ever Gentle
Ever Gentry
Ever Gifted
Ever Given
Ever Glowing
Ever Golden
Ever Goods
Ever Govern
Ever Growth
Ever Guest
Ever Guide
Ever Uberty
Ever Ultra
Ever Union
Ever Unique
Ever Unison
Ever United
4211
4211
4211
4211
4211
3428
25.0
25.0
25.0
25.0
25.0
21.7
22.1
2728
2728
3428
2868
2868
2868
2728
3428
2868
3428
2868
2728
3428
2390
5364
5625
21.7
20.5
20.7
21.3
21.3
21.3
21.0
22.2
21.9
21.3
22.2
21.3
22.5
22.2
22.0
25.0
Santa Isabella
Santos Express
Sea Tiger
Stoja
Tausala Samoa
Uranus
Vernuda
Westmed
II
Bruarfoss
Dettifoss
Godafoss
Manafoss
Selfoss
Skogafoss
Heinrich S
1894
21.0
I
26.7
Ever Pearl
Ever Urban
Ever Useful
Fair Wind 18
Fair Wind 28
5652
120
120
25.0
Ever Reach
Ever Refine
Ever Renown
Faith I
3428
Fang Gang 1001
Fang Gang 3
Fang Gang 6
Fei He
Fei Yun He
Feng Da 328
54
32
18.5
8.0
Ever Racer
Feng Guang 2
Feng Shun 8
Feng Yun He
Fo Hang 906
1432
60
19.0
France
Franconia
Franklin Strait
4158
946
518
23.1
Fu Feng
Fu Feng Shan
Fu Gang 811
132
132
96
52
96
Fu Gang 812
Fu Gang 815
Ever Repute
Ever Result
Ever Reward
Ever Right
Ever Round
Ever Royal
20.2
7.0
Ever Unific
Ever Unity
Green Modest
Green Moral
Hansa Africa
Hansa India
208
21.0
Athena
Ever Gleamy
Ever Grade
Ever Peace
1702
16
80
416
2474
17.6
17.5
Caribbean Sea
8.0
14.0
724
1457
1457
518
724
657
Conti Barcelona
Dimitra II
23.0
1181
1555
25.0
25.0
45
3764
703
Agiasofia
Angeln
5364
5364
5364
5652
5652
Ever Uranus
703
1116
1835
Global Rio
Birk
Cala Paestum
5364
2400
2532
2562
657
17.0
1645
3681
1597
1894
21.0
24.0
2728
2728
1618
1618
4229
4229
4229
4229
4229
4229
4229
4229
4229
4229
5652
5652
951
951
18.0
21.0
20.5
20.5
19.3
19.3
23.0
23.0
23.2
23.2
23.2
23.2
23.2
23.0
23.0
23.0
25.0
25.0
15.5
15.5
20.0
Hatsu Ethic
LT Going
15.5
Pelopensian Pride
3424
3424
6332
2728
3428
Poseidon VII
1894
21.0
Rhoneborg
1643
UNI Accord
UNI Ahead
UNI Ardent
1164
1164
1164
17.5
18.7
18.7
18.7
162
23.5
22.8
24.5
20.5
18.0
Fu Gang 816
Fu Gang 818
Fu Tai
Gallant Wave
Ganta Bhum
Gao Cheng
Gao He
96
96
63
1510
1094
724
2761
10.0
18.0
18.0
15.6
18.5
Gao Yao Gang No. 1
Genoa Bridge
George Washington Bridge
Gigi
Gihock
Gijoo
Gikim
Gileong
36
5600
9.0
25.0
21.5
152
504
152
276
597
Gi Lian
396
235
278
11.0
14.0
11.0
10.5
14.0
12.0
12.5
15.0
11.0
13.5
11.0
11.0
8.0
18.0
Gimeng
Ginter Star
Giseng
Gisiang
Gisoon
Giswee
Global 3
Glory D
Golden Cloud
191
384
191
202
100
946
5610
Great Pride
Guang Da Lun
Guang Liong Lun
538
Guang Xing Lun
Guan Hang 109
Guan Hang 238
Guan Hang 278
Guan Hang 362
Guan Hang 393
Gulf Bridge
Guo Dian 1001
Haifenglianfa
Hai Feng Shan
Hakone
Han Bo 1 Hao
Han Bo 2 Hao
Han Da
Hang Feng
Ha Ni He
Han Jiang He
Hanjin Amsterdam
Hanjin Athens
Hanjin Barcelona
Hanjin Basel
Hanjin Beijing
AnnaJ
Cape Falcon
Castor
Chesapeak Bay
City of Cape Town
24.4
City of Stuttgart
Colombo Bay
Columbus New Zealand
Delaware Bay
Endeavor
Endurance
Enterprise
Genua Express
Heemskerck
208
14.2
45
45
45
64
60
10.0
60
84
45
9.0
1984
106
19.0
358
283
13.5
11.5
Heide J
Ijsseldijk
Jervis Bay
Karin B
Luetjenburg
Marivia
Mercosul Palometa
Mercosul Pescada
Mercosul Uruguay
Merkur Lake
1864
66
66
51
10.0
140
3400
422
5618
5618
4024
5753
5302
Vlaherna
Vladivostok
Kapitan Afanasyev
Fesco Voyager
Amsteldiep
APL Manaus
Argana
Argonaut
Astor
Aynur Urkmez
Baltimar Boreas
Beliz Urkmez
618
Golden Gate Bridge
Golden Star
UNI Assent
UNI Forever
UNI Fortune
UNI Oasis
UNI Onward
UNI Order
UNI Orient
UNI Phoenix
21.0
17.5
26.3
26.3
24.0
26.3
26.4
163
1164
978
953
1170
1278
1170
1182
1618
1555
1748
1748
1684
446
198
1016
353
1236
1129
580
256
580
1200
446
2411
3126
1900
4224
4112
2411
1928
1928
1928
2157
3230
202
301
4224
350
3510
2082
Mount Ida
1512
1730
740
1012
724
Nedlloyd Africa
Nedlloyd America
Nedlloyd Asia
Nedlloyd Clarence
Nedlloyd Clement
Nedlloyd Europa
Nedlloyd Hong Kong
3604
3604
3604
2515
2470
3604
4169
18.7
16.5
16.5
15.6
14.8
15.6
14.8
18.7
17.6
18.5
18.5
20.0
Hanjin Bremen
2692
Hanjin Brussels
5618
5447
5752
Hanjin Cairo
Hanjin Chicago
Hanjin Colombo
Hanjin Copenhagen
Hanjin Elisabeth
Hanjin Felixstowe
Hanjin Geneva
Hanjin Gothenburg
Hanjin Hamburg
Hanjin Helsinki
Hanjin Kaohsiung
Hanjin Kelung
Hanjin Lisbon
Hanjin London
Hanjin Los Angeles
Hanjin Madrid
Hanjin Malta
Hanjin Marseilles
Hanjin Nagoya
Hanjin New York
Hanjin Osaka
Hanjin Oslo
Hanjin Ottawa
Hanjin Paris
Hanjin Pennsylvania
Hanjin Philadelphia
Hanjin Phoenix
Hanjin Portland
Hanjin Praha
Hanjin Pretoria
Hanjin Rome
Hanjin San Francisco
Hanjin Savannah
Hanjin Shanghai
Hanjin Singapore
Hanjin Taipei
Hanjin Tokyo
Hanjin Valencia
Hanjin Vancouver
Hanjin Vienna
Hanjin Washington
Hanjin Wilmington
Han Long
Hansa Stavanger
Hanseduo
Han Shui He
Han Tao He
Han Zhong He
Hao Sheng 101
Happy Island
4024
5618
2846
2692
5752
5447
2692
5447
2692
2668
5752
5306
4024
5752
4024
4024
4024
4038
4024
5308
5618
5302
4389
4389
4389
4024
4389
4389
5308
4024
4038
4024
2666
5447
4024
4024
2692
22.0
26.3
25.9
26.3
24.0
26.3
21.0
21.0
26.3
24.0
21.0
24.2
21.0
22.0
26.3
26.4
24.0
26.3
24.0
Nedlloyd Honshu
Nedlloyd Oceania
Newport Bay
Olivia
Oriental Bay
P&O Nedlloyd Abidjan
P&O Nedlloyd Acapulco
P&O Nedlloyd Accra
P&O Nedlloyd Aconcagua
P&O Nedlloyd Adelaide
P&O Nedlloyd Adriana
P&O Nedlloyd Agulhas
P&O Nedlloyd Algoa
P&O Nedlloyd Altiplano
P&O Nedlloyd Andes
P&O Nedlloyd Antisana
P&O Nedlloyd Apapa
P&O Nedlloyd Araucania
P&O Nedlloyd Atacama
24.0
P&O Nedlloyd Bantam
24.0
22.0
24.0
26.0
26.3
P&O Nedlloyd Barentsz
P&O Nedlloyd Barossa Valley
P&O Nedlloyd Beirut
P&O Nedlloyd Botany
P&O Nedlloyd Brisbane
26.4
P&O Nedlloyd Brunel
24.3
24.3
24.3
24.0
24.3
24.3
26.4
P&O Nedlloyd Buenos Aires
P&O Nedlloyd Cagliari
P&O Nedlloyd Calypso
P&O Nedlloyd Caracas
P&O Nedlloyd Caribbean
P&O Nedlloyd Cesme
P&O Nedlloyd Chania
24.1
P&O Nedlloyd Christine
22.0
24.0
22.0
25.9
24.0
P&O Nedlloyd Chusan
P&O Nedlloyd Cobra
P&O Nedlloyd Cook
P&O Nedlloyd Curacao
P&O Nedlloyd Damietta
24.0
P&O Nedlloyd Dejima
21.0
P&O Nedlloyd Drake
5752
26.3
P&O Nedlloyd Dubai
5302
4024
52
26.4
24.0
P&O Nedlloyd Encounter
P&O Nedlloyd Houston
500
422
422
422
96
400
4181
3604
4224
1452
4180
2506
2556
2506
2556
3005
2556
2506
2506
2556
2556
2556
2506
1102
2556
3430
5468
2602
1717
4112
2686
2080
1779
970
1730
4253
4253
1022
1012
856
3430
4038
6802
1012
3607
3430
5468
2732
4112
1779
10.0
P&O Nedlloyd Houtman
6802
20.0
16.0
P&O Nedlloyd Hudson
P&O Nedlloyd Hunter Valley
5468
17.5
P&O Nedlloyd Inca
17.5
P&O Nedlloyd Juliana
17.5
P&O Nedlloyd Kowloon
2478
923
2556
6690
6690
P&O Nedlloyd Los Angeles
1548
P&O Nedlloyd Kobe
15.0
164
Hatsu Eagle
Hatsu Elite
Hatsu Envoy
Hatsu Excel
Hatsu Pride
Hatsu Prima
Heidelberg Express
Henry Hudson Bridge
Hera
Hermes
III
Hong Kong Senator
Hong Yun He
Honor River
Hope
Howrah Bridge
Hsh Ubin
Hua Chang Hai 16
Hua Hang 229
Huai Ji He
Huai Lai He
Hua Lun 1
Hua Tai He
Hua Yun He
Hui Long 7
Hui Xin Hang 508
Humber Bridge
Humen Bridge
Hunsa Bhum
Hu Tuo He
6332
6332
6332
6332
1618
1618
3468
24.5
24.5
24.5
24.5
P&O Nedlloyd Magellan
P&O Nedlloyd Mahe
P&O Nedlloyd Mairangi
P&O Nedlloyd Malindi
18.7
P&O Nedlloyd Marita
P&O nedlloyd Maxima
2556
2556
22.0
21.5
P&O Nedlloyd Mercator
P&O Nedlloyd Muisca
5468
1102
2728
18.5
P&O Nedlloyd Nina
2014
21.3
20.0
P&O Nedlloyd Obock
P&O Nedlloyd Olinda
P&O Nedlloyd Palliser
384
3430
16.5
P&O Nedlloyd Panama
21.0
20.0
P&O Nedlloyd Pantanal
P&O Nedlloyd Pinta
1926
2850
1700
1932
3480
2257
2097
17.0
P&O Nedlloyd Regina
P&O Nedlloyd Remuera
P&O Nedlloyd Rotterdam
150
36
424
724
100
1216
1700
16.9
17.3
P&O Nedlloyd Salsa
P&O Nedlloyd Samba
P&O Nedlloyd San Francisco
24.8
20.0
P&O Nedlloyd Seattle
P&O Nedlloyd Shackleton
5642
1104
4112
1116
4112
3014
2474
2394
2556
4112
6690
2061
1742
1716
3450
6802
2169
6690
6802
154.0
P&O Nedlloyd Singapore
60.0
21.0
21.0
P&O Nedlloyd Southampton
P&O Nedlloyd Stuyvesant
P&O Nedlloyd Surat
18.0
19.2
P&O Nedlloyd Susana
P&O Nedlloyd Taranaki
2556
20.5
20.5
P&O Nedlloyd Tasman
P&O Nedlloyd Tema
P&O Nedlloyd Teslin
5468
16.0
14.5
19.8
P&O Nedlloyd Thekwini
P&O Nedlloyd Torres
P&O Nedlloyd Trinidad
1055
5642
384
25.0
19.5
P&O Nedlloyd Valentina
P&O Nedlloyd Vera Cruz
2556
14.5
P&O Nedlloyd Vespucci
3400
21.0
P&O Nedlloyd Xiamen
Peninsula Bay
8.5
Providence Bay
Jin He
36
52
5446
Jin Long Jiang
71
Jin Sheng
386
1432
120
5551
802
3456
3008
1094
764
Hyundai Challenger
Hyundai Innovator
3014
Ibn Sina
2850
Indonesian Star
1203
3014
Intra Bhum
Jade Trader
James River Bride
Japan Senator
Jaru Bhum
Ji Hai Xiang
Jing Po He
Jin Hai Feng
Jin Hai Yan
Jing Yun He
Jun Chuan 9
Jupiter Bridge
Jurong Bauhinia
Kaido
Kai Fa
Kai Yue
1122
5610
2661
640
96
450
90
8.5
Repulse Bay
23.0
10.0
18.0
19.0
San Lorezo I
Santa Federica
Shenzhen Bay
Singapore Bay
Stadt Kiel
25.9
Sydney Express
16.5
15.0
Tai Chuang
Ulsnis
Volkers
Providence
113
165
3430
1270
1511
2556
1779
5642
2986
4180
4224
4224
1512
2169
4224
4224
373
4112
1034
1388
374
1624
Kasuga
1
2450
Khaled Ibn Al Waleed
Kota benar
Kota Bintang
Ksh Kusu
Kuoyu
Kwong Ta No. 8
Lan Shi 10
2211
Lausanne
2826
Lian Fa 66
Lian Fa 67
Lian Feng
Liao He
Lilium
Ling Chang He
Ling Quan He
Ling Yun He
Lin Hai 103
Lions Gate Bridge
London Senator
Long Beach Bridge
Long He
Long Lun 103
LT Garland
LT Genova
LT Giant
LT Grand
LT Greet
LT Guard
LT Lloydiana
LT Pearl
LT Popular
LT Power
LT Trieste
LT Ulysees
LT Unica
LT Unicorn
LT Unity
LT Universo
LT Ursula
LT Usodimare
LT Utile
Lu He
Lumoso Express
Lunar River
Luo Ba He
Luo He
Lu Sheng
Lykes Ambassador
Lykes Deliverer
Lykes Discoverer
Lykes Explorer
764
476
1674
1169
132
64
Karukera
Anterpen Express
Tokyo Express
Bremen Express
Rotterdam Express
17.0
15.0
17.5
18.0
Kuala Lumpur Express
16.1
New York Express
Singapore Express
Kobe Express
Dusseldorf Express
London Express
Hannover Express
Leverkusen Express
Dresden Express
Hoechst Express
Ludwigshafen Express
1702
54
20.3
Essen Express
5610
2850
5576
25.0
725
52
18.9
10.0
Stuttgart Express
Paris Express
Busan Express
San Francisco Express
Bankok Express
Los Angeles Express
3428
2987
2728
2728
2728
2868
21.0
21.0
Berlin Express
Hong Kong Express
17.5
2511
1618
1566
1618
20.0
Hamburg Express
Shanghai Express
Santiago Express
Humboldt Express
Frankfurt Express
Abu Dhabi
Al Abdali
24.0
140
140
1234
387
377
672
2820
5652
4948
5652
5652
5346
5652
4948
5652
5446
12.0
17.7
15.0
12.5
25.0
20.5
17.5
19.3
21.0
18.7
17.5
Al Farahidi
Alnoof
Asir
25.0
25.0
25.0
25.0
25.0
Deira
Fowairet
19.5
21.0
1234
127
18.3
3266
11.5
3026
3026
18.8
18.8
166
7506
7506
7506
7506
2181
2181
3430
3800
3800
3800
3800
3800
Al Ihsa'a
1665
1718
AL Manakh
2199
Hammurabi
Hanjin Berlin
4051
6732
PONL Beirut
Port Said Senator
Najran
Al Sabahia
MSC Brasilia
MSC Carla
MSC Germany
MSC Levina
MSC Maria Laura
MSC Pretoria
138
494
3400
6732
3800
3800
3800
3800
3800
3074
3022
2708
2900
2557
2829
2199
5302
2199
AlMutanabbi
25.0
25.0
24.5
1624
4890
4890
4890
4890
4890
4890
4890
4612
4612
4612
4639
4639
4639
4639
4639
4639
4639
4639
6732
6732
24.0
24.0
24.0
24.0
24.0
24.0
24.0
24.0
24.0
24.0
23.0
23.0
23.0
23.0
23.0
23.0
23.0
23.0
25.6
25.6
25.6
25.6
25.0
25.0
25.0
25.0
18.0
18.0
23.0
Lykes Hero
Lykes Innovator
Lykes Liberator
Lykes Motivator
Lykes Navigator
Lykes Pathfinder
Mackinac Bridge
Maersk Doha
Maersk Norfolk
3026
2808
3026
2954
3026
2280
2875
4158
2300
Man Fu
72
Manhattan Bridge
Maple River
Mare Balticum
Mare Doricum
Mare Lycium
Mare Thracium
Margret Knueppel
Mathu Bhum
Matsuko
Med Taipei
Mentor
Mercury Bridge
Merkur Bay
Methi Bhum
Mild Lin
Mild Star
Mild Sun
Mild Union
Min Feng
Ming America
Ming Asia
Ming Bamboo
Ming Cheng
Ming Cosmos
2157
1054
1054
3900
Ming Longevity
Ming North
Ming Ocean
Ming Orchid
Ming Pine
Ming Plum
Ming South
Ming West
Ming Zenith
Min He
Min Su
Min Tai No.2
Min Tai No.4
Min Tai No.5
18.8
21.7
18.8
19.8
21.5
CMA-CGM Eiffel
18.0
17.5
17.5
Norasia Enterprise
CMA-CGM Vernet
CMA-CGM Vega
24.0
21.0
CMA-CGM Neptune
564
2550
294
20.7
5551
25.9
23.0
928
17.0
15.5
15.0
15.0
14.0
422
422
443
308
3494
3604
5551
724
5551
3502
3604
5551
1984
3502
1984
5551
5551
5551
Qatari Ibn Al Fuja'a
Norasia Valparaiso
22.4
16.0
17.0
746
Canmar Bravery
Canmar Endurance
Canada Senator
Canmar Glory
Canmar Triumph
Canmar Valour
Canmar Victory
Al Mirqab
20.0
532
1080
Ming Cypress
Ming East
Ming Europe
Ming Green
21.0
22.0
CMA-CGM Mercure
DAL Kalahari
DAL Madagascar
Karonga
OOCL Hamburg
21.0
OOCL Long Beach
OOCL Ningbo
OOCL Qingdao
OOCL Rotterdam
OOCL Shenzhen
OOCL Chicago
OOCL San Francisco
OOCL Netherlands
OOCL Singapore
OOCL America
OOCL Britain
OOCL California
OOCL China
21.2
21.2
25.9
15.6
25.9
25.9
24.0
21.2
25.9
OOCL Hong Kong
OOCL Friendship
OOCL Fair
OOCL Fidelity
OOCL Freedom
OOCL Envoy
OOCL Exporter
OOCL Montreal
19.0
24.0
19.0
25.9
25.9
25.9
OOCL Belgium
MV Helgafell
MV Arnafell
3502
3502
3052
24.0
MV Skaftafell
MS Jokulfell
2761
144
106
140
18.5
24.0
24.0
MV Regina J
MV Kurske
MV Adele J
MV Carina
MV Virtsu
80
MV Dirhami
167
1737
1952
2017
1074
1061
1061
1053
2199
2199
4100
3900
4444
3538
3900
4369
4365
3177
1730
1191
8063
8063
8063
8063
8063
8063
5714
5714
5390
5390
5344
5344
5344
5344
5344
3218
3161
3161
3161
2544
2544
4402
2808
703
703
364
140
395
266
202
202
266
266
16.5
16.5
15.5
13.8
15.0
13.0
12.5
12.5
14.0
14.0
Min Tai No.6
Min Yun He
Mol Glory
Mol Triumph
mol Wellington
Montreal Senator
MSC New Plymouth
Na Xi He
Nevelsk
New Blessing
Newpac Cirrus
Newpac Cumulus
Newport Bridge
Nicolas Delamus
Nithi Bhum
Noble River
Nordseas
Nordstrand
Nordsun
Norfolk Express
Normandie Bridge
Northern Fortune
Northern Virtue
NYK Prosperity
OOCL Atlantic
72
1432
19.0
2400
2400
20.6
1600
18.0
3400
270
706
650
650
21.0
12.5
16.5
20.2
20.2
3456
2207
23.0
21.8
ACX Cosmos
ACX Hokuto
ACX Lilac
ACX Sakura
ACX Swan
Angela J
928
969
1400
17.0
15.0
20.0
California Jupiter
California Mercury
Cape Charles
2280
20.0
Cape May
1158
3607
17.0
23.5
23.0
19.3
Commodore
1899
2987
3607
3161
OOCL Harmony
OOCL Japan
OOCL Japan
5344
2762
Oriental Bright
1001
Orient Brilliancy
OSG Argosy
Oxford
545
2880
2500
P&O Nedkowlown
2890
2890
2890
2890
2720
2890
Pac Bali
Pac Banda
Pac Bintan
306
314
306
728
2661
2661
Panagia Tinou
Patmos Senator
Conti Malaga
Hotaka Maru
Ipanema
Iris
Iwaki
Iwashiro
Kaedi
Kaga
22.0
22.5
23.5
20.5
20.5
22.0
23.0
22.0
Kamakura
Katsuragi
Kitano
17.0
15.0
NYK Andromeda
NYK Antares
NYK Aphrodite
NYK Apollo
NYK Aquarius
NYK Argus
21.5
21.5
21.5
21.5
22.0
21.5
NYK Artemis
NYK Athena
NYK Canopus
NYK Castor
NYK Fantasia
NYK Freesia
NYK Kai
NYK Leo
NYK Libra
NYK Lodestar
NYK Lynx
NYK Lyra
16.3
18.0
18.0
22.0
916
725
2661
ACX Cherry
Hansa Constitution
279
P&O Nedlloyd Auckland
P&O Nedlloyd Genoa
P&O Nedlloyd Jakarta
P&O Nedlloyd Marseille
P&O Nedlloyd Newark
P&O Nedlloyd Sydney
Pan He
MV Marienborg
23.8
821
6690
Pancaran Sinar
Libra New York
Ocean Trader
Libra Buenos Aires
1174
1550
OOCL Europe
OOCL Faith
OOCL Fortune
Pacific Envoy
Pacific Senator
Palermo Senator
22.0
MV Kalana
MV Muuga
CMA-CGM Rodin
16.0
16.8
18.0
168
266
266
2602
2526
1608
2470
1684
1048
1048
338
1430
1350
484
260
2841
2990
2829
2826
2764
2432
2760
1939
1613
2113
1613
1613
2020
3618
3611
3609
3618
6141
6141
6200
6200
6238
6238
6200
6200
6135
6135
2532
3468
3618
NYK Pegasus
NYK Phoenix
6200
6200
6200
6200
6200
6200
6238
NYK Pride
2641
14.0
13.0
21.5
21.7
21.0
22.0
19.0
Peking Senator
Penang Senator
4545
4545
23.7
23.7
Pira Bhum
628
15.5
Pohang Senator
Ponl Nelson
Portland Senator
Portugal Senator
4545
23.7
Potomac Bridge
Precious River
Pretty Lake
Pretty Ripple
Pretty River
Pretty Sea
Pretty Wave
Progress 3
Pudong Senator
Pugwash Senator
Pu He
Punjab Senator
Pusan Senator
Qian Jin 303
Qian Jin 310
Qian Yuan Shan
Quin Yun He
Qing Yun No.2
Qui He
Qi Yun He
1600
4545
4545
3965
969
420
420
1932
316
316
126
4545
4545
2716
4545
4545
16
36
137
1702
30
1318
1432
Rainbow Bridge
23.7
23.7
23.1
15.0
14.0
18.5
15.9
14.0
7.0
23.7
23.7
18.0
23.7
23.7
Victory
15.5
19.1
21.5
628
Ratstor
Reestborg
Resourceful
516
558
100
15.5
16.0
17.5
16.0
3681
23.0
23.0
River Aquamarine
River Crystal
River Elegance
River Wisdom
65
542
22.5
Rong Feng
524
14.5
Rotterdam Bridge
5576
Rui Yun He
1702
25.0
21.0
Saipan Winner
428
3482
San Pedro Bridge
Santa Elena
Santa Giovanna
Santiago
Savannah
Sea Breeze
Seabright
Sea Dragon
Seto Bridge
1664
Athlete F
Baltic Tern
18.0
18.0
25.2
2157
3802
3802
14.5
21.5
21.5
17.5
19.0
2000
2868
21.0
261
517
12.5
15.0
424
2310
23.0
1
America Feeder
Angelica Schulte
ANL Australia
ANL Bass Trader
ANL Emblem
ANL Explorer
ANL Pacific
ANL Progress
Anne Catharina
APL Cyprine
Aron
Asturia
20.3
9.0
Ratha Bhum
Rhein Bridge
Rialto Bridge
Ri Feng
NYK Procyon
NYK Sirius
NYK Springtide
NYK Starlight
Provider
Sagar
Sakura
Sandra Azul
Sandra Blanca
Santa Barbara
Santa Cruz
Santa Monica
Sanuki
Satsuki
Settsu
Shima
Shion
Soga
Sophia Britannia
Sumida
Sumire
169
1782
1005
4931
4895
4895
2893
2918
2905
1157
1181
1152
1152
1122
1091
3618
1100
1181
3066
584
366
2668
642
3300
2266
4250
910
298
5016
17.5
15.3
19.0
16.0
22.5
21.0
23.3
19.0
12.5
22.5
333
13.5
2202
369
357
20.0
Banjaard
Barrier
Burak Bayraktar
Cap Canaille
550
133
15.0
13.5
14.5
17.0
16.0
16.0
Cap Melville
2532
21.5
Carola
Cervantes
1107
538
Cimil
426
City of Lisbon
City of Oporto
700
700
2811
18.5
15.5
13.5
16.5
16.5
CMA CGM Aegean
CMA CGM Alabama
CMA CGM Alger
CMA CGM Amazonia
CMA CGM Arno
CMA CGM Balzac
15.1
4895
6135
2893
2918
912
860
2758
678
405
22.0
21.5
1668
17.0
15.0
19.5
6447
25.9
Sha He
Shamrock
Shang Cheng
Shanghai Bridge
Shanghai Senator
1234
18.3
CMA CGM Baudelaire
350
724
5576
6447
16.0
CMA CGM Belem
1162
17.0
15.5
25.0
CMA CGM Bellini
CMA CGM Berlioz
24.5
18.0
CMA CGM Bizet
5700
6627
6627
3538
San He
Sheng He
2661
3801
725
Shi Gang 233
45
Shi Gang 388
75
Shimanami
450
Shi Tai 3 Hao
Shuang Feng Shan
Sinar Bali
Sinar Bangka
Sinar Batam
Sinar Bintan
Sinar Bontang
Sinar Java
Sinar Lombok
Sinar Salju
Sinar Solo
Sinar Sunda
Sinar Surya
Sing Ping
Siri Bhum
Sky Light
Sky River
Sky Success
Song Cheng
Song He
Song Yun He
Star River
Steamers Prudence
St Petersburg Mariner
Su Da
Suez Canal Bridge
Sui Da 3
Sui Jian Hang JI 129
Sui Jian Hang JI 131
Sui Jian Hang 133
Sui Shun 101
Sui Shun Hang 28
Sui Shun Hang 32
Sui Sun 77
Sui Wu 501
Sui Xing 3
Sui Yue 2 Hao
Sun Hop Lee
Synthesis No.28
22.0
18.0
CMA CGM Capella
CMA CGM Caribbean
CMA CGM Chardin
CMA CGM Chopin
CMA CGM Claudel
CMA CGM Colombie
CMA CGM Condor
CMA CGM Constellation
CMA CGM Debussy
CMA CGM Eygpt
CMA CGM Elbe
CMA CGM Emerald
CMA CGM Energy
CMA CGM Falcon
CMA CGM Force
CMA CGM Fort St Georges
CMA CGM Fort St Louis
11.0
15.0
90
140
1060
1054
1556
1054
1054
1146
816
197
1060
1556
1556
18.5
96
550
14.5
746
1960
617
724
1688
1432
494
779
3005
288
5608
18.0
18.0
18.5
18.0
18.0
17.0
18.0
16.0
18.0
18.5
CMA CGM Fort St Pierre
CMA CGM St Marie
CMA CGM Greece
16.5
CMA CGM Hispaniola
23.0
CMA CGM Hudson
14.0
15.5
15.5
19.0
19.2
17.5
20.0
14.0
25.0
CMA CGM Hugo
CMA CGM Impala
CMA CGM Kalamata
CMA CGM Kingston
CMA CGM Kiwi
CMA CGM Komodo
CMA CGM La Bourdonnais
CMA CGM Latour
CMA CGM Lea
CMA CGM Licorne
CMA CGM Maghreb
CMA CGM Makassar
36
45
45
45
9.0
9.0
7.5
CMA CGM Manet
100
45
45
48
24
36
CMA CGM Marmara
CMA CGM Matisse
CMA CGM Mozart
CMA CGM Normandie
CMA CGM Okapi
CMA CGM Oran
CMA CGM Papagayo
CMA CGM Pasteur
CMA CGM Potomac
CMA CGM Puccini
CMA CGM Puget
CMA CGM Puma
9.0
39
124
96
Tai Hang 302
Tai Heng 8
42
Takeko
564
51
10.0
9.5
20.7
170
25.9
25.9
25.9
22.5
516
15.5
3300
5700
2602
2113
22.5
24.5
21.5
20.0
1354
19.5
22.5
3359
6627
2811
2917
2458
2438
2432
2438
2260
2260
2260
2260
2824
25.9
22.0
22.0
21.0
20.5
21.0
20.5
21.5
21.5
21.5
21.5
24.0
1367
1668
17.8
19.5
8200
24.5
1726
19.6
2917
4250
22.0
23.3
20.0
22.0
1730
2917
1684
18.0
2272
21.5
541
1728
20.0
580
2917
2272
2811
2262
5700
4688
1708
352
1354
2023
1645
5700
4404
1716
15.0
17.0
22.0
21.5
22.0
20.5
24.5
24.0
19.8
13.0
19.5
19.0
19.5
24.5
24.0
21.8
Teng He
3764
Teng Yun He
1702
TMM Campeche
3032
TMM Yucatan
Tong Jie
Tong Wei
Tower Bridge
Trade Eternity
3200
Trade Freda
Trade Hallie
Trade Harvest
Trade Selene
Trade Tesia
Trade Worlder
Trisk
Tsing Ma Bridge
Twadika
Umeko
UNI Active
UNI Adroit
UNI Ample
UNI Angel
UNI Arise
UNI Aspire
UNI Assure
UNI Chart
UNI Concert
UNI Concord
UNI Corona
UNI Crown
UNI Forward
UNI Pacific
UNI Patriot
UNI Perfect
UNI Popular
UNI Premier
UNI Probity
UNI Promote
UNI Prosper
UNI Prudent
UNI Ahead
UNI Phoenix
22.0
20.2
20.5
21.6
80
75
2140
2480
4038
4038
2227
2480
4038
442
204
5610
267
564
1164
1164
1164
1164
1164
998
998
998
998
998
956
1618
1618
1618
1618
1618
1618
1618
1618
1618
20.6
19.0
24.0
24.0
20.0
19.0
24.0
25.0
12.5
20.7
18.7
18.7
18.7
18.7
18.7
18.7
18.7
17.0
17.0
17.0
17.0
17.0
16.5
18.7
18.7
18.0
18.0
18.0
18.0
18.0
18.0
18.7
18.7
18.7
15.0
19.6
CMA CGM Rabat
CMA CGM Ravel
CMA CGM Rio Para
511
15.3
2478
5700
370
2986
2732
2917
21.7
24.5
CMA CGM Strauss
5700
24.5
CMA CGM Tage
CMA CGM Tatiana
CMA CGM Tucano
CMA CGM Turkey
CMA CGM Ukraine
CMA CGM Utrillo
CMA CGM Verdi
CMA CGM Verlaine
CMA CGM Virginia
CMA CGM Vivaldi
CMA CGM Voltaire
CMA CGM Wagner
CMA CGM Wallaby
CMA CGM Yantian
1645
19.5
18.5
Corona
Denizhan Bayraktar
Doerte
Dollart Trader
Dutch Runner
Enforcer
Engiadina
Er Caen
Er Calais
Er Camargue
Er Cannes
Er Sydney
Euro Storm
Fas Damman
Fas Gulf
Fas Provence
Fas Var
3482
Wang Foong 18
Wang Foong 9
228
130
WanHai 215
Indamex Godavari
Ingo J
500
Jan D
784
5551
25.9
1118
1020
23.0
19.2
17.0
2500
21.6
Gascogne
Holger
Iduna
Indamex Delaware
171
17.5
25.8
CMA CGM Romania
CMA CGM Rossini
CMA CGM Santiago
CMA CGM Sapphire
CMA CGM Seagull
CMA CGM Seine
CMA CGM Skikda
CMA CGM Springbok
CMA CGM St Laurent
CMA CGM St Martin
Van Xuan
Vega Diamond
Venus Bridge
Victoria Bridge
Victoria Strait
VN Sapphire
Wadi Alrayan
594
976
6712
516
1608
1162
1162
822
2008
2811
2824
2262
5700
6456
2811
8200
6456
5700
1684
4250
372
470
448
1608
221
750
2824
2556
2556
2556
2556
3359
686
847
1102
581
601
558
508
325
2890
3607
202
440
15.3
21.5
22.5
22.0
16.0
21.0
17.0
17.0
21.5
22.0
24.0
20.5
24.5
25.8
22.0
24.5
25.8
24.5
20.0
23.3
15.5
15.0
15.5
21.0
12.5
18.0
24.0
21.5
21.5
21.5
21.5
22.5
17.6
17.5
20.0
15.5
14.3
17.5
15.0
14.5
21.8
23.5
11.5
14.0
WanHai 262
1240
Wan Hai 266
Wan Hai 301
Wan Hai 302
Wan Hai 303
Wan Hai 305
Wan Hai 307
Wan He
2496
2496
2496
Washington Senator
Wehr Bille
Wehr Havel
Wei Xing
Welcome
Well Grace
Well Union
Westerhever
Wide Tech 23
Wide Tech 33
Wing Hing NO.18
Wing Lee No.1
Wing On 838
World D
Xetha Bhum
XHSJ 0288
Xiang Da
Xiang Dan
Xiang He
Xiang Kun
Xiang Lain
Xiang Peng
Xiang Qian
Xiang Tan Huo 0029
Xiang Xing
Xiang Yun He
Xi Bo He
Xie Hang 1
Xie Hang 12
Xie Hang 198
Xie Hang 2
Xie Hang 28
Xie Hang 313
Xie Hang 88
Xie Hang 9
Xing He
Xin Hai Run
Xin Hui He
Xin Hui JI 12
Xin
Xin
Xin
Xin
Hui
Hui
Hui
Hui
JI
JI
JI
JI
13
15
16
19
Xin Hui J 20
2496
2496
2496
5446
2850
2546
2526
65
437
132
124
1572
72
100
120
120
120
934
1080
64
200
200
1686
582
200
576
582
392
316
1702
3400
21.0
22.0
22.0
22.0
22.0
22.0
22.0
22.5
19.8
22.0
10.0
14.0
96
80
96
1328
612
836
10
36
48
48
16
12
Madeleine Rickmers
Margaretha
Maria Schulte
Neva
Nicola
Nordmed
Northern Dignity
Orient Aishwarya
Pacheco
Priwall
Promoter N
20.0
17.0
12.0
12.0
14.5
15.0
12.0
15.0
15.0
Rahana
Renate Schulte
Rigena
Rybno
Sadan Bayraktar
Saipan Carrier
Saipan Harvester
Saipan Voyager
Sea Explorer
Sieltor
Stella J
Sunshine
II
Sylvette
14.0
20.3
21.0
10.0
868
366
263
847
2478
3607
21.7
23.8
1020
300
17.0
13.5
2480
20.0
756
1122
1354
1810
261
596
602
576
13.5
18.5
19.5
17.0
12.5
15.0
14.0
14.0
14.0
15.0
15.5
16.0
13.5
17.5
12.0
701
384
516
520
347
844
132
4030
Ville De Mars
Ville De Mijo
2954
21.5
601
3961
4031
3961
23.7
23.8
23.7
4030
23.7
3961
23.7
22.0
9.0
9.0
9.0
9.0
Andalusia
Safmarine Cotonou
Alicantia
Safmarine Maluti
Safmarine Cameroun
Safmarine Concord
Safmarine Asia
Safmarine Europe
Safmarine Lobito
Safmarine Soyo
8.0
Elise D
172
847
1728
17.0
17.5
17.5
19.6
18.5
15.3
12.5
17.5
Ville D'Antares
Ville D'Aquarius
Ville De Dubai
Xiang Ling
17.6
15.5
16.5
8.0
678
657
VD Mina Qaboos
Ville De Mimosa
Ville De Tanya
Ville De Taurus
Ville De Virgo
Ville D'Orion
Westerland
Wotan
36
36
120
60
45
Janina
Kappel N
Karina
3961
847
23.7
23.7
17.5
14.3
2764
297
210
2262
21.5
1737
19.5
2262
2063
2096
21.5
21.5
21.0
1799
1972
1972
17.5
17.5
17.5
14.5
15.0
14.5
428
428
428
12.5
12.5
Xin Hui JI 22
Xin Hui JI 23
Xin Hui JI 3
Xin Hui JI 5
Xin Hui JI 9
Xin Tong 16
Xiu Shan
Yang Jiang He
Yang Xian 8
Yan He
Yantra Bhum
Yellow Sea
Yin He
YM Athens
YM Bremens
YM Earth
YM Fountain
YM Genova II
YM Great
YM March
YM Milano
YM Napoli
12
8.0
36
16
16
36
24
66
8.0
8.0
8.0
16.5
54
725
1080
3681
1328
16.8
17.0
16.5
5618
5576
26.3
1620
5551
1400
5576
5576
19.7
25.9
YM New york
4038
25.0
25.0
22.0
22.4
22.2
YM Pearl River I
YM People
1464
1620
18.0
19.7
YM Savannah
4038
22.2
YM Sky
1620
5551
YM Success
YM Tacoma
YM Wealth
YM Wilmington
YM Yantian
Yokohama Senator
2800
3359
3456
5551
4038
3916
4545
Yongyue No.6
Young Liberty
631
1295
12.0
17.0
Yuan He
Yu Chang 2
3764
24.0
Yue An Yun 05
Yue Feng 902
Yue Feng 903
Yue Hai 1028
Yue He
Yu Feng
Yu Gu He
Yu He
Yun Bao
Yun He
3101
3101
3101
3101
Safmarine Letaba
2080
20.5
20.5
20.5
20.5
21.0
20.0
22.2
Safmarine Mgeni
1730
Safmarine Kei
2474
LT Grace
LT Greet
LT Garland
LT Glamor
LT Usodimare
LT Unica
LT Universo
MV R.J. Pfeiffer
MV Mahimahi
MV Mokihana
MV Manoa
MV Manukai
S.S. Maui
17.0
45
118
72
60
60
96
5446
14.5
13.0
15.0
15.5
15.5
14.0
14.0
14.0
14.0
15.5
15.0
15.5
16.5
Safmarine Igoli
Safmarine Ibhayi
Safmarine Ikapa
19.7
764
140
428
640
925
519
525
925
414
414
414
448
390
523
510
Pongola
Safmarine Zambezi
Safmarine Tugela
Maersk Dakar
25.9
24.0
25.9
22.2
22.5
23.7
Yong Ding He
Yong Feng
Yong Hang 9
Safemarine Gabon
Theofano
Safmarine Bioko
Safmarine Onne
Safmarine Houston
Safmarine Douala
Safmarine Evagelia
Safmarine Meroula
Safmarine Congo
Elizabeth
Portlink Caravel
Portlink Pacer
Sven Oltmann
SA Winterberg
Maersk Constantia
SA Sederberg
SA Helderberg
S.S. Chief Gadao
S.S. Lurline
S.S. Kauai
S.S. Lihue
S.S. Ewa
S.S. Matsonia
24.7
65
3400
20.0
1686
98
14.5
5446
24.5
Independent Trader
Independent Venture
Independent Endeavor
Independent Action
173
797
18.0
2496
2063
2106
3152
2732
2732
2728
2728
3428
3428
5652
5652
5652
2229
2824
2824
2824
2600
2600
21.7
21.5
21.0
22.0
22.5
22.5
20.5
20.5
20.7
20.7
25.0
25.0
25.0
23.0
23.0
23.0
23.0
22.5
22.5
21.0
21.5
22.5
21.0
21.0
21.5
1981
1379
1626
1979
2015
1712
1208
1468
1452
1388
17.5
18.5
19.0
17.5
Appendix B
174
%Random Deployment Simulation
function cov = cov_3d(X,Y,Z,r,num det,N)
%
%
%
%
%
%
X: Height of container array (in TEUs)
Y: Width of container array (in TEUs)
Z: Length of container array (in TEUs)
r: Effective detection range (in feet)
num_det: Number of detectors to be deployed
N: Number of runs
tic
x = 8 * X; % Conversion from TEUs to feet
y = 8 * Y; % Conversion from TEUs to feet
z = 20 * Z; % Conversion from TEUs to feet
for 1 =
:N % Number of runs loop
% Constructs initial geometry matrix
DO = logical(zeros(x,y,z));
count
= 1;
% Generates random number vector
pos = rand(1,3);
while count < (numdet
% Number of detectors loop
+ 1)
% Constructs a new detector matrix
D1 = logical(zeros(x,y,z));
pos = rand(1,3);
%
%
%
%
%
dx = ceil(pos(l)*x);
dy = ceil(pos(2)*y);
dz = ceil(pos(3)*z);
Dl(dx,dy,dz)
=
1;
% x-axis loop
for i = dx-r:dx+r
if
((i < 1)
I
Fixes the x-coordinate of the detector
Fixes the y-coordinate of the detector
Fixes the z-coordinate of the detector
Establishes the detector's center-point
in the detector matrix
(i > x))
% Ensures
detector
matrices
& geometry
% remain equi-dimensional
continue
end
% y-axis loop
for j = dy-r:dy+r
if
((j < 1)
I (j > y))
% Dimension
control
continue
end
% z-axis loop
for k = dz-r:dz+r
if
((k <
1)
I (k > z))
% Dimension
control
continue
end
if sqrt((i-dx)^2+(j-dy)^2+(k-dz)^2)
175
<=
r
%
%
%
%
Checks whether
element is within
the detection
sphere
Dl(i,j,k) = 1;
% Fills in the detector matrix
end
end
end
end
% Current geometry matrix and detector matrix are 'OR'ed together
DO = DO
D1;
count = count + 1;
end.
det cov = sum(sum(sum(D0)));
cov(l) = det_cov/(x*y*z);
% Sums the number of elements within detection spheres
% Calculates fractional coverage volume and writes it
% to an output vector
end
cov = coy'
mean cov = mean(cov)
mediancov = median(cov)
stdcov = std(cov)
min cov = min(cov)
max cov = max(cov)
% Statistical analysis of full output vector
% Statistical analysis of full output vector
%
toc
176
% Constrained Deployment Simulator
function cov = new_3d(X,Y,Z,r,num_det,N)
%
%
%
%
%
%
X: Height of container array
Y: Width of container array
Z: Length of container array
r: Effective detection range
num_det: Number of detectors
N: Number of runs
(in TEUs)
(in TEUs)
(in TEUs)
(in feet)
to be deployed
tic
x = 8 * X; % Conversion from TEUs to feet
y = 8 * Y; % Conversion from TEUs to feet
z = 20 * Z; % Conversion from TEUs to feet
for
1 =-
:N
DO = logical(zeros(x,y,z));
count
% Constructs initial geometry matrix
= 1;
% Generates random number vector
pos = rand(1,20);
while count < (numdet
+ 1)
% Number of detectors loop
D1 = logical(zeros(x,y,z)); % Constructs a new detector matrix
pos = rand(l,20);
rnd cnt = 1;
x switch = 0;
%
y_switch = 0;
% Initializes constraint test variables
z switch
%
= 0;
while x switch < 1
dx_test = ceil(pos(rnd_cnt)*x);
if
((dx_test
> 8) & (dx_test
%
%
%
Checks
dx = dx test;
< (x-7)))
%
satisfies constraints
if x-coordinate
rndcnt = rndcnt +1;
%
x switch = 1;
%
else
rnd cnt = rnd cnt + 1;
end
end
while y_switch < 1
dy_test = ceil(pos(rnd_cnt)*y);
if
((dy_test
> 8) & (dy test
%
%
< (y-7)))
dy = dy_test;
rnd cnt = rnd cnt + 1;
y_switch = 1;
else
rndcnt = rnd cnt + 1;
177
%
Checks
%
%
%
satisfies constraints
if y-coordinate
end
end
while
z switch
< 1
dz_test = ceil(pos(rnd_cnt)*z);
if
> 20) & (dz test < (z-19)))
((dztest
dz = dz test;
%
%
Checks if z-coordinate
satisfies constraints
rnd cnt = rnd cnt + 1;
z switch
= 1;
else
rnd cnt = rndcnt
+ 1;
end
end
Dl(dx,dy,dz) = 1;
% Establishs detector center-point
% in the detector matrix
% x-axis loop
% Dimension control
for i = dx-r:dx+r
if
((i
< 1)
))
I (i >
continue
end
for j = dy-r:dy+r
if ((j < 1)
(
))
% y-axis loop
% Dimension control
I (k > z))
% z-axis loop
% Dimension control
>
continue
end
for k = dz-r:dz+r
if
((k
< 1)
continue
end
if sqrt((i-dx)^2+(j-dy)^2+(k-dz)
2)
<= r
% Checks whether
% element is within
% the detection
% sphere
Dl(i,j,k)
% Fills in the detector matrix
= 1;
end
end
end
end
% Current geometry matrix and detector matrix are 'OR'ed together
DO = DO
D1;
count = count + 1;
rnd cnt = 1;
178
end
det_cov = sum(sum(sum(DO)));
cov(l)
= det_cov/(x*y*z);
% Sums the number of elements within detection spheres
% Calculates fractional coverage volume and writes it
% to an output vector
end
File = strcat(num2str(X), '',num2str(Y) , ',num2str(Z),'
), ' ',num2str(N))
meancov = mean(cov)
median cov = median(cov)
stdcov = std(cov)
min cov = min(cov)
',num2str(r),' ',num2str(numdet
% Statistical analysis of full output vector
max cov = max(cov)
toc
179
% Centerline Deployment Simulator
function cov = centerline(X,Y,Z,r,det_start,det_step,det_stop)
tic
x = 8 * X; % Conversion from TEUs to feet
y = 8 * Y; % Conversion from TEUs to feet
z = 20 * Z; % Conversion from TEUs to feet
DO = logical(zeros(x,y,z));
% Constructs initial geometry matrix
for det = det_start : det_step : det_stop
% Detector placement loop
D1 = logical (zeros(x,y,z));
% Constructs a new detector matrix
dx = ?;
% 1440 TEU -> dx = 28
%
%
%
%
dy = ?;
2496
3600
4800
6460
TEU
TEU
TEU
TEU
->
->
->
->
dx
dx
dx
dx
=
=
=
=
36
36
36
36
% 1440 TEU -> dy = 36
%
%
%
%
2496
3600
4800
6460
TEU
TEU
TEU
TEU
->
->
->
->
dy
dy
dy
dy
=
=
=
=
44
44
60
68
dz = det
% Places detectors along the length
Dl(dx,dy,dz) = 1;
% Fixes center-point of detector in
% the detector matrix
for i = dx-r:dx+r
if
((i <
1)
I
% x-axis loop
(i > x))
% Dimension
control
continue
end
for
j = dy-r:dy+r
((j < 1)
(j
continue
end
% y-axis loop
if
>
y))
% Dimension
for k = dz-r:dz+r
if
((k
< 1)
I
cont:rol
% z-axis
(k > z))
% Dimension
cont: rol
continue
end
if sqrt((i-dx)^2+(j-dy)A2+(k-dz)A2)
<= r
% Checks whether
% element is within
% the detection
% sphere
180
Dl(i,j,k) = 1;
% Fills in the detector matrix
end
end
end
end
DO = DO
Dl;
% Current geometry matrix and detector matrix are 'OR'ed together
end
= sum(sum(sum(DO)));
detco
co = det_cov/(x*y*z);
cov
% Sums the number of elements within detection spheres
% Calculates fractional coverage volume
% Outputs fractional coverage volume
toc
181
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