Question From Readers #14: Calculate Cargo To Be Loaded

Find The Cargo To Be Loaded

Find the cargo to be loaded if initial draft aft is 10.873m, Trim Corr. = 14.408, TPC = 38.37 and final draft aft = 10.9m.
Ans. 89.19tons

Solution:

1. Subtract final draft and initial draft.

               10.9 m

             - 10.873 m  

                0.027 m 

2. Convert the 0.027 meter difference into centimeter so that we can apply the TPC.

               0.027 m x 100 cm = 2.7 cm 

                              1 m 

3. Multiply the TPC by 2.7 to get tons of cargo.

              38.37 

             x 2.7    

            103.599 tons     

         -   14.408    trim correction

            89.191 tons of cargo to be loaded  

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Find The Weight Of Sea Water In A Drum

A cylindrical drum, 1.6 meters high has a diameter of 90 cm. Find the weight of sea water it contains if filled to capacity.

Given:

    Height = 1.6 m
Diameter = 90 cm

What is asked:

Weight of sea water it would contain

Solution:

1. Convert first the 90 cm diameter into meter, and then get the radius.

          90 cm ×  1 m      = 0.90 m
                         100 cm

         Radius = Diameter ÷ 2
                     = 0.90 m ÷ 2
                     = 0.45 m

2. We have to solve for the volume of cylindrical drum.

            Volume of cylinder = (πr²) × height
                                             = ( 3.1416 × (0.45 m)² × 1.6 m
                                             = 3.1416 × 0.2025 m² × 1.6 m
                                             = 1.01787 m³

3. We can now proceed to solve for the weight of sea water it would contain.

                                  Weight = Density × Volume
                                              = 1.025 tons/m³ × 1.01787 m^{3
                                              = 1.04 tons}

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Calculating Rope's Diameter

If the circumference of a mooring rope is 250 mm, what is the diameter?

Given:

Rope circumference = 250 mm

What is asked:

Diameter of a rope

Solution:

Circumference = π × Diameter

Circumference = π  ×Diameter 
          π                        π 
Circumference = Diameter
          π
          250 mm  = Diameter
          3.1416
             80 mm = Diameter 

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Calculate How Many Board Feet

You are to load a consignment of lumber. Each piece measure 3-inches thick, 12-inches wide and 16-feet long. There are 30,000 pieces in the shipment. How many board feet would be listed on the Bill of Lading?

Given:

Measurement of each stick: 3 in 12 in 16 ft
Total number of sticks = 30,000 pieces

What is asked:

Number of board feet

Solution:

One board feet is equal to 1 ft lenght × 1 ft width × 1 in height.

1. We have to calculate how many board feet in one stick.

      Board feet = L × W × H  
                                12
                       = 3 × 12 × 16 
                                 12
                       = 48 board feet in one stick

2. Since there are a total of 30,000 pieces of the same kind of stick, so

       30,000 sticks  ×  48 board feet  = 1,440,000 total board feet
                                  1 stick 

                 

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Formula For Sheave Diameter

What is the sheave diameter to be used with a 3 inches manila rope?

Given:

Rope circumference = 3 inches

What is asked:

Sheave diameter

Solution:

This is the formula for solving sheave diameter.

Sheave diameter = 2 × Circumference
                            = 2 × 3 in
                            = 6 inches is the sheave diameter

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Loading Lead And Cotton Cargo

You are to load lead, SF 18 and cotton, SF 78. The available deadweight capacity is 1,600 tons of cargo and cubic capacity is 58,800 cu. ft. Disregarding broken stowage, how much of each cargo should be loaded to make her full and down?

Given:

                        Weight = 1,600 tons
               Hold volume = 58,800 ft³
   Lead stowage factor = 18
Cotton stowage factor = 78

What is asked?

Weight in tons of lead and cotton

Solution:

Weight of cotton = Hold volume - (weight × SF lead)

                                SF of cotton - SF of lead

                          = 58,800 - (1,600 × 18)

                                       78 - 18

                          = 30,000

                                60

                          = 500 tons

 
   Weight of lead = Hold volume - (weight × SF of cotton)
                                SF of cotton - SF of lead
                          = 58,800 - (1,600 × 78)
                                   78 - 18
                          = 1,100 tons

How Much Cargo Remains To Be Loaded

The present draft is 8.20 mtrs fwd and 8.60 mtrs aft. You want to load at your maximum load draft of 8.88 mtrs. If the TPC at this draft is 26, how much cargo remains to be loaded?

Given:

                TPC = 23
        Fwd draft = 8.20 m
          Aft draft = 8.60 m
Maximum draft = 8.88 m

What is asked?

Tons of cargo to be loaded

Solution:

1. We have to solve for the present mean draft by adding forward and aft draft, and then divide the sum by two.

                      Mean draft = (fwd draft + aft draft) ÷ 2

                                        = (8.20 m + 8.60 m) ÷ 2

                                        = 16.80 m ÷ 2

                                        = 8.40 m

2. Subtract the maximum load draft by the present mean draft.

                Maximum draft =   8.88 m 

                      Mean draft = - 8.40 m 

                                             0.48 m

3. Convert 0.48 meters to centimeters so that we could apply the TPC easily.

        0.48 m × 100 cm/m  = 48 cm

                                        × 26 tons per centimeter immersion

                                           1248 tons

At What Temperature Will The Centigrade Scale Be Equal To Fahrenheit Scale?

At what temperature will the centigrade scale be equal to Fahrenheit scale?

Answer: -40°

Solution/Proving:   

      

            We have to convert -40° Celsius to Fahrenheit.

°F = (-40°C × ⁹/₅) + 32
°F = -72 + 32
°F = -40°

And now we have also to convert -40° Fahrenheit to Celsius.

°C = (-40°F – 32) ⁵/₉
°C = -72 × ⁵/₉  
°C = -40°

Celsius to Fahrenheit

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How Many Tons Of Cotton in Bales Having a Stowage Factor of 85

The lower hold of your vessel has a bale capacity of 60,000 cubic feet. How many tons of cotton in bales having a stowage factor of 85 can be stowed in the lower hold assuming a broken stowage of 20%?

Given:
60,000 ft3 - Lower hold bale capacity
 85 ft3/ton- Stowage factor
       20% - Broken stowage

What is asked:
Weight in tons of cotton.

Solution:
This the formula: Weight = (Hold volume x Efficiency)  ÷ Stowage factor

Step 1. We have to solve first for the efficiency.
Efficiency = (100 - Broken Stowage) ÷ 100
               = (100 - 20) ÷ 100
                = 80 ÷ 100
                = 0.80

Step 2. Multiply the efficiency and the hold volume, and then divide it by the stowage factor.

         Weight = (60,000 ft3  x 0.80) ÷ 85 ft3/tons
                    = 48,000 ft3 ÷ 85 ft3/tons
                    = 565 tons is the answer.

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How To Calculate Time To Finish Loading Cargo

You are in the process of loading 465,000 barrels of cargo oil. At 1030, on 5 November, you gauge the vessel and find that you have loaded 203,000 barrels. At 1200, you find that you have loaded 219,000 barrels. If you continue loading at the same rate, you will finish at approximately:

Given:
465,000 bbls- Total cargo to load.
203,000 bbls- Cargo loaded at 1030H 5 November
219,000 bbls- Cargo loaded at 1200H 5 November

What is asked:
Time to finish loading the remaining cargo.

Solution:

Step 1. Get the difference of time and cargo loaded from 1030H to 1200H.
               1200H - 1030H = 1.5 hrs
              219,000 bbls - 203,000 bbls = 16,000 bbls
           
 * We have loaded 16,000 barrels in 1.5 hrs.

Step 2. Solving for the rate of loading.
              16,000 bbls ÷ 1.5 hr = 10,666.67 bbls/hr

Step 3. We have to solve for the remaining cargo to load.
              465,000  bbls - 219,000 bbls = 246,000 bbls

Step 4. Solving for how many hours to load the remaining cargo.
             246,000 barrels ÷ 10,666.67 barrel/hr = 23.06 hrs

Step 5. Solving for the time to finish loading the remaining cargo.
         ***23.06 hrs is equal to 2304H

             1200H   5   November
          + 2304H_____________
            3504H  5  November
          - 24 hr + 1 day________
           1104H  6 November is the final answer.

Time to finish cargo loading

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Safe Working Load Formula (SWL)

The breaking strain of a nylon line is rated at 15,000 kgs. Using a safety factor of 5, what is the safe working load (SWL)?

SOLUTION:

Safe working load (SWL) is equal to the quotient of breaking strength divided by the safety factor.

This is the Safe Working Load formula:

SWL = BREAKING STRENGTH ÷ SAFETY FACTOR
SWL = 15,000 kgs ÷ 5
SWL = 3,000 kgs 

 See this picture.

Safe Working Load Formula

Converting Celsius to Fahrenheit

The thermometer reads 20ºC. Find the equivalent to Fahrenheit scale.

Given:              20ºC

What is asked: Fahrenheit equivalent

Solution:
This the formula to convert Celsius to Fahrenheit scale:  

 F =(^oC x ⁹/₅) + 32

F = (20^oC x ⁹/₅ ) + 32

F = 68º 

The step-by-step solution: 20 x 9 = 180 ÷ 5 = 36 + 32 = 68 degree fahrenheit.

Celsius to Fahrenheit formula

  

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