STABILITY AND TRIM

1
STABILITY AND TRIM CALCULATIONS Rolling Period
2

• 1. You are on a vessel that has metacentric
  height of 4 feet and a beam of 50 feet. What can
  you expect the rolling period of the vessel to
  be?
• A. 10.0 s
• B. 10.5 s
• C. 11.0 s
• D. 11.5 s
• 2. You are at the sea on a vessel that has a beam
  of 60 feet, and you calculate the period of roll
  to be 25 seconds. What is the vessels
  metacentric height?
• A. 0.8 ft.
• B. 1.1 ft.
• C. 1.4 ft.
• D. 1.6 ft.

RP .44 B vGM
GM .44 B 2 RP
3

• 3. Your vessel has a displacement of 10,000 tons.
  It is 350 ft. long and has a beam of 55 ft. You
  have timed its full rolling period to be 15.0
  seconds. What is your vessels approximate GM?
• A. 1.18 ft.
• B. 1.83 ft.
• C. 2.60 ft.
• D. 3.36 ft.

GM .44 B 2 RP
4

• 4. Your vessel has a measures 35.0 meters long by
  5.0 meters in 6 seconds. What is the GM?
• A. 0.44
• B. 0.54
• C. 0.33
• D. 0.48
• 5. You are on a vessel that has a metacentric
  height of 0.68 meters and a beam of 5.2 meters.
  What can you expect the rolling period the vessel
  to be?
• A. 7 seconds
• B. 6 seconds
• C. 4 seconds
• D. 5 seconds

GM .797 B 2 RP
RP .797 B vGM
5
VERTICAL SHIFT OF CENTER OF GRAVITY
6

• 1. A vessels light draft displacement is 7400
  tons. The center of gravity at this draft is 21.5
  ft. above the keel. The following weights are
  loaded 450 tons VCG 17 ft. 220 tons VCG 11.6
  ft., 65 tons VCG 7.0 ft. The new CG above the
  keel is
• A. 14.7 ft.
• B. 17.8 ft.
• C. 18.7 ft.
• D. 20.9 ft.

WEIGHT C. G MOMENT
7400 21.5 159100
() 450 17.0 7650
() 220 11.6 2552
() 65 7.0 455
8135 169757
NEW KG MOMENT WT
169757 8135
20.867 FT.
7

• 2. Your present displacement is 15,000 short
  tons. The KG at this displacement is 60 ft. 100
  short tons of casings are added at a VCG of 75
  ft. for an ocean tow. What is the new KG?
• A. 59.09 ft.
• B. 62.09 ft.
• C. 60.09 ft.
• D. 61.09 ft.

WEIGHT KG MOMENT
15,000 60 900,000
() 100 75 () 7,500
15,100 907,500
NEW KG MOMENT WT
907,500 15,100
60.099 FT.
8

• 3. A vessel with displacement of 19,700 LT and a
  KG of 50.96 ft. loads 300 LT of barite into
  P-tanks located 120 ft. above the keel. What is
  the change in KG?
• A. 1.00 ft. upward
• B. 0.79 ft. upward
• C. 1.04 ft. upward
• D. 1.83 ft. upward

WEIGHT KG MOMENT
19,700 50.96 1,003,912
() 300 120 ()36,000
20,000 1,039,912
NEW KG MOMENT WT
1,039,912
20,000 52.00 OLD KG 50.96
(-) 1.04 UPWARD
9

• 4. You have approximately 15 tons of fish on
  deck. What will the shift in the center of
  gravity after you shift the fish to the fish hold
  a vertical distance of 8 feet? Total displacement
  300 tons.
• A. 0.4 ft.
• B. 0.1 ft.
• C. 0.2 ft.
• D. 0.3 ft.

GG W X D ? 15 X 8
300 0.4 FT.
10

• 5. Your ship of 12,000 tons displacement has a
  center of gravity of 21.5 ft. above the keel. You
  run aground and estimate the weight aground is
  2500 tons. The virtual rise in the center of
  gravity is
• A. 1.26 ft.
• B. 5.66 ft.
• C. 3.80 ft.
• D. 4.80 ft.

OLD DISPL. 12,000 X 21.5
258,000 GROUNDED WT (-) 2,500 NEW DISPL.
9,500
NEW KG 258,000
9,500
NEW KG 27.16
OLD KG 21.50 VIRTUAL RISE OF CG 5.66
UPWARD
GG W X D ? 2,500 X
21.5 9,500 5.66 UPWARD
11
INCLINING EXPERIMENT
12

• 1. Sixty tons of cargo are raised with a boom 45
  feet from the centerline. The vessels
  displacement including the weight lifted is
  16,400 tons.The angle of list caused by the
  suspended weight is 1.5. KM is 28.75 ft. and BM
  is 17.25 FT. What is the KG?
• A. 11.65 ft.
• B. 22.46 ft.
• C. 23.15 ft.
• D. 23.82 ft.

GM W X D ? TAN LIST
60 X 45 16,400 TAN 1.5
6.29 FT
KM 28.75 FT. GM 6.29 FT. KG 22.46 FT.
13

• 2. A ship is inclined by moving a weight of 30
  tons a distance of 30 ft. from the center line. A
  28 feet pendulum shows a deflection of 12 inches.
  Displacement including weight moved is 4,000
  tons. KM is 27.64 ft. What is the KG?
• A. 21.34 ft.
• B. 22.06 ft.
• C. 22.76 ft.
• D. 23.21 ft.

14

• INCLINING EXPERIMENT
• GM W X D
• ? Tan LIST
• 30 TONS X 30 FT
• 4,000 TONS X Tan 2.05
• GM 6.29 FT.
• KM 27.64 FT.
• GM - 6.29 FT.
• KG 21.35 FT.

SOHCAHTOA
28
WL1
WL2
1
SIN Ø OPP HYPO 1
28 2.05
15

• 3. A cargo of 75 tons is to be lifted with a boom
  located 50 ft. from the ship centerline. The
  ships displacement including the suspended cargo
  is 6,000 tons and GM is 6 ft. The list of the
  ship with cargo suspended from the boom will be
• A. 5.00O
• B. 5.40O
• C. 5.94O
• D. 6.50O

GM W X D ? TAN LIST TAN LIST
W X D ? X GM
75 X 50 6,000 X 6
5.946
16

• 4. A cargo of 60 tons to be loaded on deck 20
  feet from the ships centerline. The ships
  displacement including the suspended cargo is
  6,000 tons and GM is 2 ft. The list of the ship
  with the cargo suspended from the boom will be
• A. 5.4O
• B. 5.7O
• C. 6.1O
• D. 6.4O

TAN LIST W X D ? X GM
60 X 20
6,000 X 2 5.7
17

• 5. To check stability, a weight of 40 tons is
  lifted with the jumbo boom, whose head is 40 ft.
  from the ships centerline. The clinometer shows
  a list of 6.5O with the weight suspended.
  Displacement including the weight is 16,000 tons.
  The GM while in this condition is
• A. 0.21 ft.
• B. 0.43 ft.
• C. 0.88 ft.
• D. 1.02 ft.

GM W X D ? TAN LIST
40 X 40 16,000 TAN 6.5 0.88
FT.
18

• 6. You are making a heavy lift with the jumbo
  boom. Your vessel displaces 18,000 tons. The
  50-tons weight is on the pier and its center is
  75 feet to starboard of the centerline. The head
  of the boom is 112 feet above the baseline and
  the center of gravity of the lift when stowed on
  the deck will be 56 ft. above the baseline. As
  the jumbo takes the strain the ship lists 3.5O.
  What is the GM when the cargo is stowed?
• A. 3.19 ft.
• B. 3.40 ft.
• C. 3.56 ft.
• D. 3.24 ft.

GG W X D ? 50 X
56 18050 0.156
()3.397 3.553
GM W X D ? TAN LIST
50 X 75 18050 TAN3.5
3.397
19

• 7. A ship of 6,000 tonnes displacement has KM7.3
  meters and KG6.7 meters and is floating upright.
  A weight of 60 tonnes already on board is shifted
  12 meters transversely. Find the resultant list.
• A. 10 00
• B. 1115
• C. 9 15
• D. 1118 30

TAN LIST W X D ? X GM
60 X 12 6,000
X .6 11. 309
11 18 36
KM 7.3 KG 6.7 (-) GM 0.6
20
FREE SURFACE CORRECTION
21
FREE SURFACE CORRN.

• FOR SALT WATER
• F.S.CONST. l b3
• 420

l LENGTH OF THE TANK b BREADTH OF THE TANK
FOR LIQUIDS OTHER THAN SALT WATER F.S.CONST. r
l b3 420
r S.G OF LIQUID IN TANK S.G WHERE VSL.
FLOATS
F.S.CORRN. F.S CONSTANT
?
F.S.CORRN. r l b3
420 ?
432
22

• 1.On the vessel displacing 8,000 tons, what is
  the reduction in metacentric height due to free
  surface when a tank 45 ft. long and 45 ft. wide
  is partially filled with saltwater?
• A. 1.22 ft.
• B. 1.16 ft.
• C. 1.13 ft.
• D. 1.10 ft.

FSC r l b3 420?
(1)(45)(45)3 (420)(8,000)
1.22 ft.
23

• 2. On a vessel of 10,000 tons displacement,
  compute the reduction in metacentric height due
  to free surface in a hold having fresh water on
  the tank top. The hold is 40 ft. long and 50 ft.
  wide. The reduction in GM is
• A. 1.1 ft.
• B. 1.2 ft.
• C. 1.3 ft.
• D. 1.5 ft.

FSC r l b3 420?
24

• 3. What is the reduction in GM due to free
  surface when a tank 60 ft. long and 60 ft. wide
  is partially filled with salt water and is fitted
  with a centerline bulkhead? The vessel has a
  displacement of 10,000 tons.
• A. 0.5 ft.
• B. 0.8 ft.
• C. 1.0 ft.
• D. 1.2 ft.

FSC IS REDUCED BY 75.
FSC r l b3 X .25 420?
25

• 4. A shaft alley divides a vessels cargo hold
  into two tanks, each 25 ft. wide by 50 ft. long.
  Each tank is filled with sea water below the
  level of the shaft alley. The vessels
  displacement is 6,000 tons. What is the reduction
  in Gm due to free surface effect?
• A. 0.56 ft.
• B. 0.58 ft.
• C. 0.62 ft.
• D. 0.66 ft.

FSC r l b3 X 2 420?
26

• 5. A 7,000 ton displacement tankship carries two
  slack tanks of alcohol with a S.G. of 0.8 Each
  tank is 50 long and 30 ft. wide. What is the
  reduction in GM due to free surface with the
  vessel floating in sea water (SG 1.026)?
• A. 0.36 ft.
• B. 0.46 ft.
• C. 0.72 ft.
• D. 0.82 ft.

FSC r l b3 X 2 420?
27

• 6. Determine the free surface constant for fuel
  oil tank 30 ft. long by 40 ft. wide by 15 ft.
  deep. The S.G. of the fuel oil is 0.85 and the
  ship will float in salt water (SG 1.026)
• A. 0.83
• B. 42.7
• C. 3787
• D. 4571
• 7. Determine the free surface correction for
  fuel oil tank 30 ft. long by 40 ft. wide by 15
  ft. deep with free surface constant of 3794. The
  vessel is displacing 7,000 tons in saltwater.
• A. 0.35 ft.
• B. 0.54 ft.
• C. 0.65 ft.
• D. 1.38 ft.

F.S.Const. r l b3 420
F.S.Corrn. F.S.Const ?
28

• 8. A ship of 8,153.75 tonnes displacement has
  KM8 m, KG7.5 and a double bottom tank 15 m x 10
  m x 2 m which is full of salt water ballast. Find
  the new GM if this tank is now pumped out until
  half empty.
• A. 0.225 m
• B. 0.825 m
• C. 1.75 m
• D. 1.45 m
• CHS - VIRTUAL RISE GG1.ppt

29
LET GG1 REPRESENT THE ACTUAL RISE OF G DUE TO
MASS DISCH. THE MASS OF
WATER DISCH.(W) L X B X D X
DENS.
15 X 10 X 1 X 1.025
153.75
TONS

INITIAL KG 7.5 RISE OF g 1.5
6.0
WT CG MOM
8,153.75 7.5 61,153
(-)153.75 1.5 (-) 231
8,000.00 60,922
INITIAL ? 8,153.75 DISCH. (-) 153.75
FINAL ? 8,000.00
GG1 W X D ? 153.75 X 6
8,000 GG1 0.115 M
NKG T.MOM. 60,922 T.WT.
8,000 NKG 7.615 OKG 7.500 GG1 0.115
30
LET G1GV REPRESENTS THE VIRTUAL LOSS OF GM DUE TO
FREE SURFACE. G1GV l b3 12V
15(10)3(1.025)
(12)(8,000) 0.160 M
VIRTUAL LOSS OF GM (G1GV) i X d1 X 1
V d2 n2 i SECOND
MOMENT OF FREE SURFACE ABOUT THE CENTER
LINE. V SHIPS VOL. OF DISPL. d1 DENS.OF
LIQUID IN TANK. d2 DENS.OF WATER WHERE
VSL. IS FLOATING. n NO. OF LONGL. COMPARTMENT
INTO WHICH IS PARTIALLY FILLED WITH
LIQUID.
BUT d1 d2 n 1 G1GV i
V FOR RECTANGULAR WATERPLANE i l
b3 12
31
OLD KM
8.000 M OLD KG 7.500
M OLD GM 0.500 M RISE
OF G DUE DISCH. 0.115 M ( - )
0.385 M VIRTUAL RISE
OF G 0.160 M ( - )
NEW GM 0.225 M
32
FREEBOARD ALLOWANCE
33

• 1. You are loading in a port subject to the
  tropical load line mark and bound for a port
  subject to the summer load line mark. You will
  enter the summer zone after steaming four days.
  You will consume 40 tons of fuel, water, and
  stores per day. The hydrometer reading at the
  loading pier is 1.025 and the average TPI is 53.
  The following data is extracted from the load
  line Certificate
• Freeboard from Deck line Load Line
• Tropical 67 (T)
  5above (s)
• Summer 72 (S)
• Winter 77 (W)
  5 below (s)
• Allowance for fresh water for freeboards 4
• Upper the edge of line at level of center of
  ring.

34

• What is the minimum freeboard required at the
  start of the voyage?
• A. 65 inches
• B. 69 inches
• C. 72 inches
• D. 75 inches

CONSUMPTION 40 TONS/DAY STEAMING
TIME (X) 4 DAYS CONS.FOR 4 DAYS 160 TONS
SUMMER F.B. 72
(-) 3 MIN. F.B.ON DEP 69
CONS. 160 TPI 53 3
35

• 2. You are loading in a port subject to the
  tropical loadline mark and bound for a port
  subject to the summer loadline mark. You will
  enter the summer zone after steaming two days.
  You will consume 28 tons of fuel, water and
  stores per day. The hydrometer reading at the
  loading pier is 1.020 and the average TPI is 55.
  The following data is extracted from the load
  line certificate

36

• Freeboard from Deckline Load Line
• Tropical 69 (T) 7 above (s)
• Summer 76 (S)
• Winter 83 (W) 7
  below (s)
• Allowance for fresh water all freeboards 6
• Upper edge of line at level of center ring.
• What is the minimum freeboard at the start of the
  voyage?
• A. 62 inches
• B. 66 inches
• C. 70 inches
• D. 74 inches

37
CONSUMPTION 28 TONS/DAY STEAMING
TIME (X) 2 DAYS CONS.FOR 2 DAYS 56 TONS
CONS. 56 TPI 55
1.0
A.I FWA X CH.OF DENS 25
6 X 5 25 1.2
BURN OFF/CONS. 1.0 A.I.
1.2 2.2
SUMMER F.B. 76.0 F.B.ON DEP. 73.8
38

69(T)
76(S)
83(W)
TF
F
T
FWA(6)
S
SUMMER
ARR.
W
WNA
TROPICAL
2 DAYS
DEP.
39

• 3. You are loading in a port subject to the
  summer loadline mark and bound for a port subject
  to the winter loadline mark. You will enter the
  winter zone after steaming four days. You will
  consume 35 tons of fuel, water and stores per
  day. The hydrometer reading at the loading pier
  is 1.0083 and the average TPI is 65. The
  following data is extracted from the loadline
  Certificate
• Freeboard from Deckline Load Line
• Tropical 68 (T) 6 above (s)
• Summer 74 (S)
• Winter 80 (W) 6 below (S)
• Allowance for fresh water all freeboards
  5
• Upper edge of line at level of center ring.

40

• What is the minimum freeboard required at he
  start of the voyage?
• A. 74 inches
• B. 78 inches
• C. 80 inches
• D. 86 inches

A.I. FWA X CH.OF DENS.
25 5 X 16.7 25
3.34
CONSUMPTION 35 TONS/DAY STEAMING
TIME (X) 4 DAYS CONS.FOR 4 DAYS 140 TONS

BURN OFF/CONS 2.15
A.I. 3.34
5.49 WINTER F.B. 80.00 DEP.
F.B. 74.51
CONS. 140 TPI 65
2.15
41

• 4. You are loading in a port subject to the
  tropical loadline and bound for a port subject to
  the winter loadline mark. You will enter the
  summer zone after steaming eight days and you
  will enter the winter zone after ten days. You
  will consume 31 tons of fuel, water and stores
  per day. The hydrometer reading at the loading
  pier is 1.016 and the average TPI is 41. The
  following data is extracted from the loadline
  certificate
• Freeboard from deckline Loadline
• Tropical 42 (T) 6 above (s)
• Summer 48 (S)
• Winter 54 (W) 6 below (s)
• Allowance for fresh water all freeboards 5
• Upper edge of the line at the level of center
  ring.

42

• What is the minimum freeboard required at the
  start of the voyage?
• A. 55.0 inches
• B. 49.5 inches
• C. 44.5 inches
• D. 41.0 inches

CONSUMPTION 31 TONS/DAY STEAMING
TIME (X) 10 DAYS CONS.FOR 10 DAYS 310 TONS
CONS. 310 TPI 41
7.56
A.I. FWA X CH.OF DENS.
25 5 x 9 25 1.80
CONSUMPTION 31 TONS/DAY STEAMING
TIME (X) 8 DAYS CONS.FOR 8 DAYS 248 TONS
41(TPI) 6.05
CONS/BURN OFF 7.56
A.I. 1.80
9.36 WINTER F.B. 54.00
F.B.ON DEP. 44.64
CONS./BURN OFF 6.05
A.I. 1.80
7.85 SUMMER F.B. 48.00 F.B. FOR
SUMMER 40.15
43

• 5. You are loading in a port subject to the
  tropical loadline mark and bound for a port
  subject to the winter loadline mark. You will
  enter the summer zone after steaming four days
  and you will enter the winter zone after nine
  days. You will consume 29 tons of fuel, water and
  stores per day. The hydrometer reading at the
  loading pier is 1.008 and the average TPI is 53.
  The following data is extracted from the Load
  Line Certificate.
• Freeboard from Deckline Load Line
• Tropical 75 (T) 8 above (s)
• Summer 83 (S)
• Winter 91 (W) 8 below (S)
• Allowance for fresh water all freeboards 9
• Upper edge of line at the level center ring.

44

• 5. What is the minimum freeboard required at the
  start of the voyage
• A. 72.5 inches
• B. 75.0 inches
• C. 77.0 inches
• D. 80.0 inches

CONSUMPTION 29 TONS/DAY STEAMING
TIME (X) 9 DAYS CONS.FOR 9 DAYS 261 TONS
CONS. 261 TPI 53
4.92
CONSUMPTION 29 TONS/DAY STEAMING TIME
(X) 4 DAYS CONS.FOR 4 DAYS 116 TONS
A.I. FWA X CH.0F DENS.
25 9 X 17 25
6.12
CONS. 116 TPI 53
2.19
A.I.
6.12 CONS/BURN OFF 4.92
11.04 WINTER F.B. 91.00
DEP.F.B. 79.96

A.I. 6.12 CONS/BURN OFF
2.19
8.31 SUMMER F.B
83.00 DEP. F.B./ SUMMER ZONE 74.7
45
ZONE ALLOWANCE

• 1. A tanker loads at a terminal within the
  tropical zone. She will enter the summer zone six
  days after departing the loading port. She will
  burn off 45 tons/day and daily water consumption
  is eight tons. How many tons may she load above
  her summer loadline?
• A. 270 tons
• B. 278 tons
• C. 291 tons
• D. 318 tons

BURN OFF 45 TONS
WATER CONS. 8 TONS
53 TONS/DAY STEAMING TIME (X) 6 DAYS
318 TONS
46

• 2. A vessels tropical loadline is 6 inches above
  her summer loadline. Her TPI is 127 tons. She
  will arrive in the summer zone 8 days after
  departure. She will burn off about 47 tons/day
  and water consumption is 12 tons/day.How many
  tons may she load above her summer loadline if
  she loads in the tropical zone?
• A. 376 tons
• B. 472 tons
• C. 762 tons
• D. 1016 tons

BURN OFF 47 TONS
WATER CONS 12 TONS
59 TONS/DAY STEAMING TIME (X) 8 DAYS
472 TONS
47
THE LOAD LINE MARK
Deck Line
25 mm 1 in.
300 mm 12 in.
540 mm 21 in.
230 mm 9 in.
TF
F
T
L
R
S
230 mm
W
WNA
300 mm
450 mm 18 in.
48

67(T)
72(S)
77(W)
SUMMER
TROPICAL