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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
17-Jan-2023 19:25:19 -0500
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