View
40
Download
1
Category
Preview:
Citation preview
Internal Assessment
Modelling the Transit of Select Shipping Waterways from 2000 Through 2013 and Projecting
the Transit of Select Shipping Waterways from Present Day Through 2020
Name: Adam Costa
Date: 2/5/2014
Period: 5
Subject: Mathematics
Candidate Number: 000534-0009
1
Introduction
With an ever more connected and globalized world, the need for efficient and sustainable
transportation infrastructure has become ever more vital to the satisfaction of international
consumer demand and persistence of international economies.
Transport of cargo by sea is one of the methods of international transport that are used most
often, due to the cost effectiveness of transporting cargo by sea, in comparison to the lofty
expenses of transporting cargo by air.
With the aging shipping waterways of the past no longer being able to accommodate the ever
going size of ships and the frequency of transits today, as well as the opening of more viable and
preferable alternatives to aged waterways, the projection of the usage of major shipping
waterways around the world would be indispensable when it comes to what investments
companies should make, when referencing by what routes they would like their products to be
shipped. Projecting the usage of major shipping waterways would allow companies to select
shipping routes that would be increasingly efficient, thus reducing expense to ship a product to
the consumer, ultimately reducing the price of the product to the consumer. My explorations in
everyday life have led me to uncover the conflicts between the major shipping waterways around
the world and has spurred me to investigate what is to come of the future of the shipping industry
and, with how influential cargo transportation by sea is to the world today, how society, world
economies, and my life will be in the near future.
Modelling the Transit of Select Shipping Waterways
The timespans used for the following sets of information were decided upon with the intention of
setting timespans that all waterways had sufficient data for. Additionally, another reason for the
selection of these set timespans is because the turn of the century was a time when the age and
inadequacies of older canals and the possibility of alternatives to traditional waterways began to
be earnestly considered.
2
Suez Canal
Tabular Representation of the Transits by Ship of the Suez Canal with Relation to Time from the
Year 2000 to 2012
Time in
Years
Transits
by Ship
2000 14,142
2001 13,986
2002 13,447
2003 15,667
2004 16,850
2005 18,224
2006 18,664
2007 20,384
2008 21,415
2009 17,228
2010 17,993
2011 17,799
2012 17,225
Data Analysis
It is evident that there is a fluctuating but ever increasing flow of transits of the Suez Canal over
this 12-year period. However, more recently, it is evident that the rate at which ships transit the
Suez Canal on a yearly basis is rather low, with reference to rates of transit of prior years, and
0
5000
10000
15000
20000
25000
1998 2000 2002 2004 2006 2008 2010 2012 2014
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Suez Canal with Relation to Time
from the Year 2000 to 2012
3
the rate has reached a point of a gradual decrease in the amount of transits of the Suez Canal.
Additionally, the Suez Canal represents 8% of world trade.
Panama Canal
Tabular Representation of the Transits by Ship of the Panama Canal with Relation to Time from
the Year 2000 to 2012
Time in
Years
Transits
by Ship
2000 13,653
2001 13,492
2002 13,185
2003 13,154
2004 12,621
2005 12,573
2006 13,040
2007 13,174
2008 13,126
2009 12,892
2010 12,662
2011 12,987
2012 12,857
12400
12600
12800
13000
13200
13400
13600
13800
1998 2000 2002 2004 2006 2008 2010 2012 2014
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Panama Canal with Relation to
Time from the Year 2000 to 2012
4
Data Analysis
It is evident that there is a fluctuating but ever decreasing flow of transits of the Panama Canal
over this 12-year period. However, it is important to acknowledge the rapid increase in transits of
the Panama Canal leading up to 2007, with yet another spike in transits of the canal leading up to
2011. Additionally, the Panama Canal represents 5% of world trade.
Northwest Passage
0
5
10
15
20
25
1998 2000 2002 2004 2006 2008 2010 2012 2014
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Northwest Passage with Relation
to Time from the Year 2000 to 2012
5
Tabular Representation of the Transits by Ship of the Northwest Passage with Relation to Time
from the Year 2000 to 2012
Time in
Years
Transits
by Ship
2000 6
2001 5
2002 5
2003 8
2004 2
2005 5
2006 3
2007 5
2008 7
2009 13
2010 11
2011 17
2012 23
Data Analysis
It is evident that there is a fluctuating but ever increasing flow of transits of the Northwest
Passage over this 12-year period. Furthermore, more recently, it is evident that the rate at which
ships transit the Northwest Passage is on a steep and steady incline. It is important to
acknowledge the essentially steady increase in the rate of transits of the Northwest Passage
between 2006 and 2012.
6
Northern Sea Route
Tabular Representation of the Transits by Ship of the Northern Sea Route with Relation to Time
from the Year 2010 to 2013
Data Analysis
It is evident that there is a rapid increase of transits of the Northern Sea Route over this 4-year
period. It is important to note the massive increase in the transit of the route from 2010 to 2011
and 2012 to 2013.
Projecting the Transit of Select Shipping Waterways
Given that the Mean Value Theorem states that, “For any function that is continuous on [a, b]
and differentiable on (a, b) there exists some c in the interval (a, b) such that the secant joining
the endpoints of the interval [a, b] is parallel to the tangent at c,” the formula for the Mean Value
Theorem could be used, and, in the instance of this investigation, is used, to determine the trend
of change of the amount of transits by ship through the aforementioned international waterways;
thus, allowing the transits by ship of these waterways to be more accurately projected.
0
10
20
30
40
50
60
70
80
2009.5 2010 2010.5 2011 2011.5 2012 2012.5 2013 2013.5
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Northern Sea Route with Relation
to Time from the Year 2010 to 2013
Time in
Years
Transits
by Ship
2010 4
2011 41
2012 46
2013 71
7
The formula for the Mean Value Theorem is as follows:
𝑓′(𝑐) =∫ 𝑓(𝑥)𝑑𝑥
𝑏
𝑎
𝑏 − 𝑎
The formula for the Slop-Intercept Form is also utilized for this development of the projections
for the selected waterways. The Slope-Intercept Form is as follows:
𝑦 = 𝑚𝑥 + 𝑏
Suez Canal
Calculations for the determination of the average rate of change for the transits by ship of the
Suez Canal with relation to time from the year 2000 to 2012 are as follows:
𝑓′(𝑐) =∫ 𝑓(𝑥)𝑑𝑥
𝑏
𝑎
𝑏 − 𝑎
𝑓′(𝑐) =∫ 𝑓(𝑥)𝑑𝑥
(2012)
(2000)
(2012) − (2000)
𝑓′(𝑐) =𝐹(2012) − 𝐹(2000)
12
𝑓′(𝑐) =17,225 − 14,142
12
𝑓′(𝑐) =3,083
12 𝑠ℎ𝑖𝑝𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
Calculations for the determination of the function for the average rate of change for the transits
by ship of the Suez Canal with relation to time from the year 2000 to 2012 are as follows:
𝑦 = 𝑚𝑥 + 𝑏
(14,142) = (3,083
12) ∙ (2000) + 𝑏
14,142 = (6,166,000
12) 𝑥 + 𝑏
𝑏 = 14,142 − (513,833 + (1
3))
𝑏 = −499,691 − (1
3)
8
𝑦 = (3,083
12) 𝑥 − (499,691 + (
1
3))
Projection
Based upon previously mentioned evidence for the average change of the amount of ships
transiting the Suez Canal, I believe the transits of the Suez Canal from 2012 to 2020 will be as
follows, if the rate of transits continue at this generalized pace, which is based upon the value of
𝑓′(𝑐) for the Suez Canal:
0
5000
10000
15000
20000
25000
1998 2000 2002 2004 2006 2008 2010 2012 2014
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Suez Canal with Relation to Time
from the Year 2000 to 2012 with a Line Representing the Average Rate of Change
9
Data Analysis
My explanation for this shallow increase in transits of the Suez Canal over the next 6 years lies
in the innovations in alternate sources of energy and the nationalization of energy production.
The United States has recently constructed a pipe line that allows natural gas to be more readily
available for usage as a fuel for electrical production and heating purposes; thus, reducing the
United States’ reliance on foreign fuel. The current administrations in the United States, United
Kingdom, Germany, and several other nations have increasingly invested in renewable sources
of usable energy; thus, reducing these countries reliance on foreign fuels. The Suez Canal is the
gateway where the Persian Gulf oil producing nations send the majority of their oil shipments
through. With a reduction in foreign demand for Persian Gulf oil, decreased oil shipments are
sent through the Suez Canal, and the shallow increase in transits of the Suez Canal results.
0
5000
10000
15000
20000
25000
1995 2000 2005 2010 2015 2020 2025
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Suez Canal with Relation to Time
from the Year 2000 to 2020
10
Tabular Representation of the Transits by Ship of the Suez Canal with Relation to Time from the
Year 2000 to 2020
Time in
Years
Transits
by Ship
2000 14142
2001 13986
2002 13447
2003 15667
2004 16850
2005 18224
2006 18664
2007 20384
2008 21415
2009 17228
2010 17993
2011 17799
2012 17225
2013 17482
2014 17739
2015 17996
2016 18253
2017 18510
2018 18767
2019 19024
2020 19281
11
Panama Canal
Calculations for the determination of the average rate of change for the transits by ship of the
Panama Canal with relation to time from the year 2000 to 2012 are as follows:
𝑓′(𝑐) =∫ 𝑓(𝑥)𝑑𝑥
𝑏
𝑎
𝑏 − 𝑎
𝑓′(𝑐) =∫ 𝑓(𝑥)𝑑𝑥
(2012)
(2000)
(2012) − (2000)
𝑓′(𝑐) =𝐹(2012) − 𝐹(2000)
12
𝑓′(𝑐) =12,857 − 13,653
12
𝑓′(𝑐) =−796
12 𝑠ℎ𝑖𝑝𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
Calculations for the determination of the function for the average rate of change for the transits
by ship of the Panama Canal with relation to time from the year 2000 to 2012 are as follows:
𝑦 = 𝑚𝑥 + 𝑏
(13,653) = (−796
12) ∙ (2000) + 𝑏
13,653 = (−1,592,000
12) + 𝑏
𝑏 = 13,653 − (−132,666 − (2
3))
𝑏 = 146,319 + (2
3)
𝑦 = (−796
12) 𝑥 + (146,319 + (
2
3))
12
Projection
Based upon previously mentioned evidence for the average change of the amount of ships
transiting the Panama Canal, I believe the transits of the Panama Canal from 2012 to 2020 will
be as follows, if the rate of transits continue at this generalized pace, which is based upon the
value of 𝑓′(𝑐) for the Panama Canal:
12400
12600
12800
13000
13200
13400
13600
13800
1998 2000 2002 2004 2006 2008 2010 2012 2014
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Panama Canal with Relation to
Time from the Year 2000 to 2012 with a Line Representing the Average Rate of Change
12200
12400
12600
12800
13000
13200
13400
13600
13800
1995 2000 2005 2010 2015 2020 2025
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Panama Canal with Relation to
Time from the Year 2000 to 2020
13
Data Analysis
My explanation for the rather steep declination of transits through the Panama Canal is best
found in the Panama Canal’s inability to comfortably welcome today’s ships. The Panama Canal
has gone through a series of minor renovations and dredging operations in order to accommodate
the increasing size of ships that transit the Panama Canal, but the canal was originally designed
to facilitate ships of a far smaller scale, in comparison to today’s Panamax ships. The Panama
Canal is currently unable to accommodate 37% of the world’s ships and that number will be
increasingly rising into the next decade, as companies continue to strive to cut costs off of the
bottom-line, by shipping their products in ships of sizes that have yet to be conceived.
Northwest Passage
Calculations for the determination of the average rate of change for the transits by ship of the
Northwest Passage with relation to time from the year 2000 to 2012 are as follows:
𝑓′(𝑐) =∫ 𝑓(𝑥)𝑑𝑥
𝑏
𝑎
𝑏 − 𝑎
𝑓′(𝑐) =∫ 𝑓(𝑥)𝑑𝑥
(2012)
(2000)
(2012) − (2000)
𝑓′(𝑐) =𝐹(2012) − 𝐹(2000)
12
𝑓′(𝑐) =23 − 6
12
𝑓′(𝑐) =17
12 𝑠ℎ𝑖𝑝𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
Calculations for the determination of the function for the average rate of change for the transits
by ship of the Northwest Passage with relation to time from the year 2000 to 2012 are as follows:
𝑦 = 𝑚𝑥 + 𝑏
(6) = (17
12) ∙ (2000) + 𝑏
6 = (17,000
12) + 𝑏
𝑏 = 6 − (1,416 + (2
3))
14
𝑏 = −1,410 − (2
3)
𝑦 = (17
12) 𝑥 − (1,410 + (
2
3))
Projection
Based upon previously mentioned evidence for the average change of the amount of ships
transiting the Northwest Passage, I believe the transits of the Northwest Passage from 2012 to
2020 will be as follows, if the rate of transits continue at this generalized pace, which is based
upon the value of 𝑓′(𝑐) for the Northwest Passage:
0
5
10
15
20
25
1998 2000 2002 2004 2006 2008 2010 2012 2014
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Northwest Passage with Relation
to Time from the Year 2000 to 2012 with a Line Representing the Average Rate of
Change
15
Data Analysis
My explanation for the respectable increase of transits of the Northwest Passage lies in the
increasingly receding arctic ice sheets for greater periods of time during the spring and summer
seasons of the northern hemisphere, which allow transits of the passage for greater lengths of
time. I also attribute this increase in transits to the benefit of the amount of time this passage
removes from the transportation of goods from Northern Europe, Canada, and the Northern
United States to Eastern Russia, the Koreas, Japan, and Eastern China and vice-versa.
Northern Sea Route
Calculations for the determination of the average rate of change for the transits by ship of the
Northern Sea Route with relation to time from the year 2010 to 2013 are as follows:
𝑓′(𝑐) =∫ 𝑓(𝑥)𝑑𝑥
𝑏
𝑎
𝑏 − 𝑎
𝑓′(𝑐) =∫ 𝑓(𝑥)𝑑𝑥
(2013)
(2010)
(2013) − (2010)
𝑓′(𝑐) =𝐹(2013) − 𝐹(2010)
4
𝑓′(𝑐) =71 − 4
4
0
5
10
15
20
25
30
35
1995 2000 2005 2010 2015 2020 2025
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Northwest Passage with Relation
to Time from the Year 2000 to 2020
16
𝑓′(𝑐) =67
4 𝑠ℎ𝑖𝑝𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
Calculations for the determination of the function for the average rate of change for the transits
by ship of the Northern Sea Route with relation to time from the year 2010 to 2013 are as
follows:
𝑦 = 𝑚𝑥 + 𝑏
(4) = (67
4) ∙ (2010) + 𝑏
4 = (134,670
4) + 𝑏
𝑏 = 4 − (33,667 + (1
2))
𝑏 = −33,663 − (1
2)
𝑦 = (67
4) 𝑥 − (33,663 + (
1
2))
0
20
40
60
80
2009.5 2010 2010.5 2011 2011.5 2012 2012.5 2013 2013.5
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Northern Sea Route with Relation
to Time from the Year 2010 to 2013 with a Line Representing the Average Rate of
Change
17
Projection
Based upon previously mentioned evidence for the average change of the amount of ships
transiting the Northern Sea Route, I believe the transits of the Northern Sea Route from 2012 to
2020 will be as follows, if the rate of transits continue at this generalized pace, which is based
upon the value of 𝑓′(𝑐) for the Northern Sea Route:
Data Analysis
My explanation for the respectable increase in transits of the Northern Sea Route lies in the
increasing receding artic ice sheets for greater periods of time during the spring and summer
seasons of the northern hemisphere, which allow transits of the route of greater lengths of time. I
also attribute this incease in transits to the increased infrastructure, personel, and equipment
being constructed and positioned along the route to accommodate increased water traffic, making
the route more attractive to companies wishing to cut off time for the transporation of their goods
from Eastern Aisa to Northern Europe and vice-versa, because the security of their goods is more
ensured.
Conclusion
Considerations
It is important to acknowledge the major renovation of the Panama Canal that is scheduled to be
completed in 2015. This expansion project is focused on the construction of new lanes, locks,
0
50
100
150
200
2008 2010 2012 2014 2016 2018 2020 2022
Tran
sits
by
Ship
Time in Years
Graphical Representation of the Transits by Ship of the Northern Sea Route with Relation
to Time from the Year 2010 to 2020
18
widen passages, and accommodating larger post-Panamax ships. This expansion will allow for
the 37% of the ships that the Panama Canal could not previously accommodate to proceed
through the canal unhindered, making the Panama Canal more attractive to companies with
larger ships, and increasing the frequency of transits of the Panama Canal.
Furthermore, it is important to note that the Northwest Passage has passages that are shallower
than the N.A.S.A. satellite images of receding arctic ice could detect, making some parts of the
Northwest Passage impassable by larger cargo ships. Additionally, specialists have noted that the
possibility of cargo ships being able to transit the Northwest Passage unaided by ice-breaker
ships is not expected to occur at the current rate of ice sheet recession by 2020. The previously
mention point is also the case with the Northern Sea Route: ice-breaker or ships strengthened
against ice are necessary for passage until potentially 2020.
Moreover, land-bridge methods of transit are becoming increasingly preferable to companies,
because of the efficiency and convenience of transit to the destinations of their goods, as opposed
to the circumnavigation of ships around continents and the construction of billion currency
waterways through landmasses for the convenience of ship transit.
It is important to acknowledge the possible outcomes of the completion of the following sets of
infrastructure in the near future:
Israel Sea-Rail Infrastructure
This proposed plan, known as the Red-Med Rail, by the Israeli Prime Minister, Benjamin
Netanyahu , was purposed in 2012 as an alternative to ships transiting the Suez Canal when the
canal is unable to assume all of the ships requesting transit of the canal. This was purposed
during the Egyptian Arab Spring Uprising where the operational integrity of the Suez Canal
during internal turmoil was increasingly questioned. The proposition was not intended to directly
compete with shipments through the Suez Canal but to assist in keeping cargo steadily flowing
when the Suez Canal is unable to facilitate the shipping overflow. However, it is important to
acknowledge that this alternative to the Suez Canal has the great potential to compete with the
Suez Canal for Middle Eastern shipping dominance, especially with the great interest India and
China are showing in this venture and if the proper funds are devoted to the project. It is
expected to run from Eliat on the coast of the Red Sea to Tel Aviv on the Mediterranean Sea. It
is expected to be completed 5 years after to start of its construction.
Nicaragua Canal
A canal through the isthmus of Nicaragua has been considered for the past century but earnest
consideration has not arisen until 2012, where the Nicaraguan government and the Hong Kong-
based private enterprise H.N.K.D. signed a memorandum confirming H.N.K.D.’s commitment to
the financing and construction of the Nicaragua Canal. In January 2014 H.N.K.D. announced
that the construction of the canal would begin December 2014. This canal is intended to be a
19
complementary route to the Panama Canal. However, it is important to acknowledge the
potential for this route to challenge and surpass the transit frequency of the Panama Canal, as
increased east-west trade and ship sizes will cause congestion of the Panama Canal with its
inability to accommodate current and future ships. With the previously mentioned reality in
mind, the shipping volume served by the Nicaragua Canal is expected to increase 240% from its
completion into 2030.
Summation
Evidently the world of maritime goods transportation is a competitive and foreseeably
increasingly influential reality. Many drastic and forever-changing alterations to the world of
maritime trade, and to our day-to-day lives, will be occurring within the ever-so-near future. As
previously observed with the models, projections, and considerations of major maritime
waterways and infrastructure of the past and upcoming future, it is indisputable that the
waterways of the past are declining in usage and are being exchanged for alternative and more
lucrative methods, modes, and means of transportation. For international consumers and major
exporting companies, this matter is beneficial, since companies cut costs on transportation and
consumers save money on the products they wish to purchase, if the companies pass on the
financial benefits of their logistic decisions to their customers.
Further Investigation
In further investigations, it would be interesting to explore how the establishment of waterways,
such as the Panama Canal and Suez Canal, have influenced the rate of industrial, economic, and
social development of countries where these waterways have been established (Examples: Egypt
and Panama) and countries that benefit from the existence of these waterways (Examples: China,
India, the United States of America, and Saudi Arabia to name a few).
20
Bibiliography
Andrea Thompson, Extra Sunshine Blamed for Part of Arctic Meltdown Foxnews,
Friday, December 14, 2007
http://arcticecon.wordpress.com/category/transit/northern-sea-route/
http://hknd-group.com/trends-in-global-shipping-trade-demand-a-new-canal/
http://northwestpassage2013.blogspot.com/2013/05/transits-of-northwest-passage-to-end-
of.html
http://www.arctic-lio.com/nsr_transits
http://www.marinelink.com/news/northern-transits-clicks349471.aspx
http://www.panama-travel-guide.com/Panama-Canal.html
http://www.pbs.org/wgbh/americanexperience/features/timeline/panama/2/
http://www.reuters.com/article/2012/01/29/us-israel-railway-idUSTRE80S0KC20120129
http://www.suezcanal.gov.eg/TRstat.aspx?reportId=3
http://www.thehindu.com/news/national/india-keen-to-participate-in-israeli-redmed-
project/article2891580.ece
Nicaragua signs memorandum with Chinese company to build a canal between two
oceans", Inside Costa rica, 2012-09-10.
"Promotora china de canal interoceanico de Nicaragua de US$40mn es 100% privada"
[Chinese promoter of Nicaragua’s US$4b interoceanic canal is 100% private], BN
Americas (in Castilan).
Recommended