Internal Assessment (1-31-14)

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


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


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


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:


𝑏

𝑎

𝑏 − 𝑎


(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:


(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


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



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


Panama Canal with relation to time from the year 2000 to 2012 are as follows:


𝑏

𝑎

𝑏 − 𝑎


(2012)

(2000)

(2012) − (2000)

𝑓′(𝑐) =𝐹(2012) − 𝐹(2000)

12

𝑓′(𝑐) =12,857 − 13,653

12

𝑓′(𝑐) =−796



by ship of the Panama Canal with relation to time from the year 2000 to 2012 are as follows:


(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


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


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


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


Northwest Passage with relation to time from the year 2000 to 2012 are as follows:


𝑏

𝑎

𝑏 − 𝑎


(2012)

(2000)

(2012) − (2000)

𝑓′(𝑐) =𝐹(2012) − 𝐹(2000)

12

𝑓′(𝑐) =23 − 6

12

𝑓′(𝑐) =17



by ship of the Northwest Passage with relation to time from the year 2000 to 2012 are as follows:


(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


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


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


Northern Sea Route with relation to time from the year 2010 to 2013 are as follows:


𝑏

𝑎

𝑏 − 𝑎


(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



16

𝑓′(𝑐) =67



by ship of the Northern Sea Route with relation to time from the year 2010 to 2013 are as

follows:


(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


to Time from the Year 2010 to 2013 with a Line Representing the Average Rate of

Change

17

Projection


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



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).

Documents

Internal Assessment (1-31-14)