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Sample Solution for a Free Surface Correction Problem 

The SS AMERICAN MARINER is ready to bunker with drafts of FWD 15'-05", AFT 21'-03". After all bunkers are on board, soundings indicate the tonnages shown.

Use the white pages of The Stability Data Reference Book to determine the free surface correction.

A. 1.05 feet

Incorrect.

B. 1.15 feet

Correct.

C. 1.25 feet

Incorrect.

D. 1.31 feet

Incorrect.

 

Step 1:

Calculate Mean Draft.

15'-05"fwd + 21'-03" aft = 36'08"

Mean Draft: 36'-08"/2

Mean Draft = 18'04"

Step 2:

Using the Hydrostatic Properties table (Sheet 3) for the SS American Mariner (White Pages), calculate the Total Displacement (S.W. Tons) for the vessel before loading bunkers with a mean draft of 18'04".

The table yields 12,000 tons as the displacement of the vessel at 18'04" mean draft.

 

 

 

 

 

Step 3:

Add up all the bunker totals for each tank. The sum of all bunkers equals 3024.8 tons.

Step 4:

Add the displacement of the vessel before loading the bunkers and the sum of all the bunkers to find the ship's final displacement.

12,000 tons + 3024.8 tons = 15024.8 tons

Step 5:

Refer to the Table for Free Surface Correction and Tank Capacities (Sheet 4) to calculate the free surface moment for each tank. On the S.S. Mariner , a tank is considered FULL if the tank is at least 97% full. Any quantity less than 97% full or an empty tank is considered SLACK.

In the column F.O. Tons under Tank Capacity, the table gives you the capacity of each tank at 97% full. This is the column you will compare your loaded bunkers in each tank with to verify if a tank is considered FULL or SLACK. For example, DB 1 CL is loaded with 48.2 tons of bunkers. The tank capacity at 97% for D.B. 1 CL is 48.2 tons. Therefore, the tank is considered FULL and its free surface correction is 67. Conversely, D.B. 4 CL is loaded with 208.6 tons of bunkers. The tank capacity at 97% for D.B. 4 CL is 224.1 tons. Since 208.6 tons is less than 224.1 tons then D.B. 4 CL is considered SLACK.

Now find the free surface moment for each tank.

Next, find the total sum of free surface moment which equals 17,309 foot tons.

Step 6:

Find the free surface correction in feet by dividing the total free surface moment by the

final displacement of the vessel.

FS(corr) = 17,309 foot tons/15,024.8 tons

FS(corr) = 1.15 feet

 

Last edited on 13-Feb-2016 22:25:34 -0600

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Revised: 13 Feb 2016 22:25:34 -0600 

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See also:

SeaSources online Celestial Navigation Course 

MARYLAND NAUTICAL  Great source for practice charts and study guides

NAVIGATION COURSE

National Oceanic & Atmospheric Administration (NOAA)

The Navigation Center

Chart No. 1 Nautical Chart Symbols Abbreviations and Terms

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Required Subjects for all Deck Licenses

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Sea Service Requirements for Coast Guard Licenses

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