Clearance

Gerald Desmond Bridge Shipping Traffic

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Objective: Given real situational data, the student will be able to calculate the possibility of a ship’s passage underneath the Gerald Desmond bridge in the Port of Long Beach.

Purpose:

• Proficiency on Algebra standards • Proficiency on tests and quizzes 2

Algebra 1 Content Standards 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers… where applicable. 25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements. 25.1 Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions. 25.2 Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step. 3

The Port of Long Beach

Gerald Desmond Bridge

Bridge Background

Structural Type: Arch bridge / suspended deck Function/usage: Road bridge connects the Ports of Long Beach and Los Angeles with the I-710. Span: 5,134 Ft. Built: 1968 (replacing the previous pontoon bridge) Length: 1,053 feet long Highest point: 250 feet **** 157 feet of clearance above the water 5

The Challenge •

The primary channel leading to the majority of offloading docks in the interior of the Port of Long Beach is spanned by the Gerald Desmond Bridge.

•

The bridge was originally built (in 1968) with plenty of clearance for shipping vessels to pass underneath.

•

Today ships are being built larger and larger…and the ability for ships to pass underneath is becoming impossible for some ships. 6

The Challenge

Today we will calculate whether a ship can pass under the Gerald Desmond bridge given the ship’s dimensions.

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A typical ship’s dimensions: Length – bow to stern Width – widest part of the ship Depth – height of the hull taken from the lowest part under the water 9

A typical ship’s dimensions: Length – bow to stern Width – widest part of the ship Depth – height of the hull TEUs – amount of 20 foot containers the ship holds

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The height of the ship’s tower

What is still needed to determine the total height of the ship? Length – bow to stern Width – widest part of the ship Depth – height of the hull TEUs – amount of 20 foot containers the ship holds

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Let’s look at the height of the hull. Length – bow to stern Width – widest part of the ship Depth – height of the hull TEUs – amount of 20 foot containers the ship holds

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Depth – height of the hull It has two parts: Under the water Over the water 13

Depth – height of the hull It has two parts: Under the water ≈ tower height Over the water 14

Depth – height of the hull It has two parts: Under the water ≈ tower height Over the water 15

Therefore, the depth given is approximately equal to the hull over the water plus the height of the tower. 16

Length – bow to stern Width – widest part of the ship Depth – height of the hull over water plus height of tower TEUs – amount of 20 foot containers the ship holds

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Length – bow to stern Width – widest part of the ship Depth – height of the hull over water plus height of tower TEUs –TEUs amount – what of 20isfoot a TEU? containers the ship holds

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What is a TEU? Twenty Equivalent Units.

8.6 feet

20 feet

8 feet

Two of them make up the load on a standard semi truck:

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Now that we know the typical dimensions of a ship,

Length – bow to stern Width – widest part of the ship Depth – height of the hull over water plus height of tower TEUs – amount of 20 foot containers the ship holds Let’s calculate whether a ship can pass under the Gerald Desmond bridge. 20

Vessel # 1 Ship Length Width Depth TEUs

Hanjin Amsterdam 279 meters 40 meters s i n 14 meters e v i g n 5,618 atio the

e t m r a l o f u c n l i a t c a h o ? t t W h d g e i d e e h e l n a tot

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Vessel # 1 Ship Hanjin Amsterdam Length 279 meters Width 40 meters Depth 14 meters TEUs 5,618 or how many rows of TEUs

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5 TEUs 14 meters

What is the height of a TEU?

8.6 feet 20 feet

8 feet

What is the total height of the stacked TEUs?

5 TEUs 8.6 feet = 43 feet 1 1 TEU 24

43 feet 14 meters

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We now have feet and meters. We cannot combine unlike terms, so….. Convert depth from meters to feet: 14 meters 3.28 feet = 45.9 1 1 meter feet Depth of the hull 45.9 feet

+

Height of the stacked cargo 43 feet

= 26

Depth of the hull 45.9 feet

+

Height of the stacked cargo 43 feet

=

88.9 feet Will it clear the Gerald Desmond Bridge which has 157 feet of clearance?

YES!

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Vessel # 2 Ship Length Width Depth TEUs

Neptune Amber 231 meters 32.2 meters 12.5 meters 2,314

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Vessel # 2

6 TEUs Depth

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What is the height of a TEU?

8.6 feet 20 feet

8 feet

What is the total height of the stacked TEUs?

6 TEUs 8.6 feet = 51.6 feet 1 1 TEU 30

51.6 feet

12.5 meters

We now have feet and meters. We cannot combine unlike terms, so… Convert depth from meters to feet: 12.5 3.28 feet = 41 feet meters 1 meter 1 Depth of Height of the the hull stacked cargo 41 feet

+

51.6 feet

=

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Depth of the hull 41 feet

+

Height of the stacked cargo 51.6 feet

=

92.6 feet Will it clear the Gerald Desmond Bridge which has 157 feet of clearance?

YES!

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Check for Understanding Thumbs up or down: 1)To determine whether a ship will pass under a bridge, the length of the ship is needed. 2)When calculating the total height of the TEUs, the number of TEUs stacked above the ship’s rail must be counted. 34

Vessel # 3 Your Turn: Ship Length Width Depth TEUs

Zim Atlantic 253.7 m 32.2 m 19.2 m 3,429

Work out the problem in your notes. Put the total height on your white board. 35

19.2 meters

8 TEUs

8.6 feet 20 feet

8 feet

What is the total height of the stacked TEUs?

8 TEUs 8.6 feet = 68.8 feet 1 1 TEU 37

19.2 meters

68.8 feet

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We now have feet and meters. We cannot combine unlike terms, so….. Convert depth from meters to feet: 19.2 3.28 feet = 63 feet meters 1 meter 1 Depth of Height of the the hull stacked cargo 63 feet

+

68.8 feet

=

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Depth of the hull 63 feet

+

Height of the stacked cargo 68.8 feet

=

131.8 feet Will it clear the Gerald Desmond Bridge which has 157 feet of clearance?

YES!

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Vessel # 4 Your turn again: Ship Length Width Depth TEUs

MSC Texas Majuro 321 m 42.8 m 20.2 m 8,238

Work out the problem in your notes. Put the total height on your white board. 41

8 TEUs

20.2 meters

We now have feet and meters. We cannot combine unlike terms, so… Convert depth from meters to feet: 20.2 3.28 feet = 66.3 meters 1 meter feet 1 Depth of Height of the the hull stacked cargo 66.3 feet

+

68.8 feet

=

43

68.8 feet

20.2 meters

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Depth of the hull 66.3 feet

+

Height of the stacked cargo 68.8 feet

=

135.1 feet Will it clear the Gerald Desmond Bridge which has 157 feet of clearance?

YES!...but it is getting pretty tight…

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Vessel # 5 This is one of the largest vessels currently in existence:

Length Width Depth TEUs

320 m 41 m 29 m 7 high above rail

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8.6 feet 20 feet

8 feet

What is the total height of the stacked TEUs?

7 TEUs 8.6 feet = 60.2 feet 1 1 TEU 47

We now have feet and meters. We cannot combine unlike terms, so… Convert depth from meters to feet: 29 meters 3.28 feet = 95.1 feet 1 1 meter Depth of the hull 95.1 feet

+

Height of the stacked cargo 60.2 feet

= 48

Depth of the hull 95.1 feet

+

Height of the stacked cargo 60.2 feet

=

155.3 feet Will it clear the Gerald Desmond Bridge? At 157 feet of clearance… Eeeeeking by! Is it worth the risk?

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Check for Understanding Think, pair, share: 1)Think: What is one thing that was different about this example (vessel #5)? 2)Pair: Take turns telling your partner what was different. 3)Share: One person will be called on to share with the group. 50

Vessel # 6 Your turn: This is another very large vessel:

Length Width Depth TEUs

Work out the problem in your notes. Put the total height on your white board.

327 m 41.8 m 32.2 m 6 high above rail

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8.6 feet 20 feet

8 feet

What is the total height of the stacked TEUs?

6 TEUs 8.6 feet = 51.6 feet 1 1 TEU 52

We now have feet and meters. We cannot combine unlike terms, so… Convert depth from meters to feet: 32.2 3.28 feet = 105.6 meters 1 meter feet 1 Depth of Height of the the hull stacked cargo

+

105.6 feet

51.6 feet

=

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Depth of the hull

+

105.6 feet

Height of the stacked cargo 51.6 feet

=

157.2 feet Will it clear the Gerald Desmond Bridge? At 157 feet of clearance…

NO!

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Vessel # 7 The last two vessels barely passed under the bridge. Let’s try an even bigger ship. Ship Length Width Depth TEUs

OOCL Long Beach SX Class Vessel 323.2 m 43 m 38.8 m 8,000 + 7 high above rail 55

8.6 feet 20 feet

8 feet

What is the total height of the stacked TEUs?

7 TEUs 8.6 feet = 60.2 feet 1 1 TEU 56

Let’s calculate one of the largest vessels currently in existence: Convert depth from meters to feet: 39 meters 3.28 feet = 127.3 1 1 meter feet Depth of the hull

+

127.3 feet

Height of the stacked cargo 60.2 feet

= 57

Depth of the hull

+

Height of the stacked cargo

127.9 feet

60.2 feet

=

188.1 feet Will it clear the Gerald Desmond Bridge? At 157 feet of clearance…

NO!

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Summary • In your notes, list the steps used today to determine whether or not a ship will be able to pass under a bridge. • Check your list with your partner. • Add any steps to your list that you fell are missing. 59

Further Learning Discussion and written summary for and their effect on the passage of ships under the Gerald Desmond Bridge http://www.saltwatertides.com/cgi-local/california.cgi •

See “Tide Table Handout” or go to above website for real time information Extreme low tide: -1.1 feet Extreme high tide: 7.2 feet 60

Tide Changes http://www.saltwatertides.com/cgi-local/california.cgi

Extreme Low Tide: -1.1 feet Extreme High Tide: 7.2 feet How would high tide affect the passage of vessels under the Gerald Desmond Bridge? High Tide would shorten the clearance by 7.2 feet…to 149.8 ft.

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Tide Changes http://www.saltwatertides.com/cgi-local/california.cgi

Extreme Low Tide: -1.1 feet Extreme High Tide: 7.2 feet Which vessels would be affected? Make a table to support your claim. Click to see a sample table

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Tide Changes Vessel #

Height in feet

Passage under bridge (157 feet)

Height added Effect of to tide in feet passage

Vessel #1

92.6

yes

99.8

same

Vessel #2

114.7

yes

121.9

same

Vessel #3

131.8

yes

139

same

Vessel #4

135.1

yes

142.3

same

Vessel #5

155.3

yes

162.5

will not pass

Vessel #6

157.2

no

164.4

same

Vessel #7

188.1

no

195.3

same

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Tide Changes http://www.saltwatertides.com/cgi-local/california.cgi

Extreme Low Tide: -1.1 feet Extreme High Tide: 7.2 feet Which vessels would be affected? Vessel 5 would be affected where is was not before. Write a statement in your notes describing the effect of high tide on ships passing under a bridge. 64

Tide Changes http://www.saltwatertides.com/cgi-local/california.cgi

Extreme Low Tide: -1.1 feet Extreme High Tide: 7.2 feet How would low tide affect the passage of vessels under the Gerald Desmond Bridge? Which vessels do you imagine would be most affected? Why?

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Answers Will Vary… Low tide would change the depth of the water. The heaviest vessels would be most affected because they sit further below the water line than a lighter ship.

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