Hydrostatics Buoyancy & Subdivision Heel & Trim Stability

HydrostaticsHydrostatics

Buoyancy & Subdivision

Heel & Trim

Stability

Stuff Floats … why?Stuff Floats … why?

A 30” pine 2x4 (240 cu. In.) weighs approximately 4.44 lbs (density ≈ .0185 lb/in3)

The downward force (weight) is considered to act through the Center of Gravity, G, of the object

G

Stuff Floats … why?Stuff Floats … why?

4.44 lbs of sea water (density ≈ .037 lb/in3) occupies only 120 cu.in.

Thus our pine 2x4 need only be half submerged to displace its weight

The upward Buoyant Force (equal to the weight displaced) is considered to act through the Center of Buoyancy, B.

GB

Some stuff doesn’t … Some stuff doesn’t … why?why? A 2.5 cu.ft. steel

anvil weighs 1200 lbs …

and would displace 2.5 cu. Ft. of water (161 lbs)

The upward Buoyant Force (equal to the weight displaced) would not support the weight

1 sq. ft. of one-inch thick steel plate weighs about 40 lbs.

But some big, steel stuff does But some big, steel stuff does float …float …

| 1 ft | 40 lbs.

Consider a box 500 ft long, 80 ft wide & 40 ft deep made from “40 lb” steel plate:

80 ft40 ft

500 ft

But some big, steel stuff does But some big, steel stuff does float …float … This box weighs: [ 2(80x40) + 2(40x500) + (80x500) ] x 40 lbs

= 3,456,000 lbs = 1543 Long Tons

(1 Long Ton = 2240 lbs)

40 lb.

40 x 500

80 x 40 80 x 500

35 cu. ft. of seawater weighs 1 Long Ton Our “barge” displaces 1543 x 35

= 54,000 cu.ft of sea water

40 x 500

80 x 40 80 x 500


40 lb.

54,000 cu. ft. of seawater would fill a hole 80 ft wide, 500 ft long And only 1.35 ft deep ! The draft of our vessel is only 1.35 ft!


To displace 80 x 500 x 20 ft (800,000 cu.ft)

We can carry another 746,000/35 = 21,314 Tons of cargo( a total displacement of 22,857 Tons)

Draft, T= 20 ft


If the hull were breached … the internal volume would no longer be contributing

to the displacement (lost buoyancy), only the steel shell itself ...

and the steel weight is greater than the volume (of water) it displaces.

FloodingFlooding

By partitioning the vessel into (longitudinally) water tight compartments ,,,

a breach of one compartment only loses the buoyancy due to the volume of that compartment

If there is sufficient reserve buoyancy from the remaining compartments the vessel will remain afloat (at a deeper draft).

FloodingFlooding

lost buoyancylost buoyancy

regained buoyancy

lost buoyancy

FloodingFlooding

lost buoyancy

Flooding forward or aft is particularly critical Buoyancy must be regained before a second

becomes flooded “over the top” of the watertight partition

If not …

lost buoyancy

FloodingFlooding

lost buoyancy

Flooding forward or aft is particularly critical Buoyancy must be regained before a second

becomes flooded “over the top” of the watertight partition

If not … How can we prevent this?

FloodingFlooding Construct smaller subdivisions fore & aft A breach at an extreme end then results in less lost

buoyancy.. And the vessel remains afloat. How do we determine the size (length) of watertight

compartments?

Floodable length is amount of ship length (centered at the ordinate) which may be flooded without the waterline rising above the margin line.

The Floodable Length The Floodable Length CurveCurve

FL (ft)

In the previous example, flooding of any single compartment will not cause the ship to founder

This is a single compartment vessel If the floodable length everywhere spans two compartments,

we have a two compartment vessel Empire State VI is a single compartment vessel The Titanic was a four compartment vessel.

Floodable Length Floodable Length Notes:Notes:

0 trim (even keel) means same drafts fore & aft B is directly under G (but not necessarily amidships) If a weight is shifted longitudinally (say, aft) G

moves proportionately and a trim moment is produced

TrimTrim

Da= 30 ft Df= 30 ft

G

B

w

LCG

LCB

Trimming moment causes ship to submerge at the stern shifting B aft to equilibrium point under G

Note that trimming axis is not amidships but about a point on the original water plane called the center of floatation

The ship is now trimmed “2 ft by the stern”

TrimTrim

Da= 30.8 ft Df= 28.8 ft

G

B

w

B

Da – Df = 30.8 – 28.8 = 2 ft

LCFF

The mean draft is the draft at F (still 30 ft.) not the average of Da & Df

The change in drafts (+.8 at the stern & -1.2 at the bow) are not equal but determined by the location of F

LCF, mean draft, and (0 trim) LCB are determined by the shape of the hull and change with displacement

Trim notes:Trim notes:

Da= 30.8 ft Df= 28.8 ft

G

B

Da – Df = 30.8 – 28.8 = 2 ft

F

HeelHeel Heel, or angle

of heel, is the amount of tipping to one side

Heel is measured in degrees

There are many causes of heel

HeelHeel A permanent

heel results if G is not on the centerline

A heel due to an off-center G is called a list

A list may be corrected by shifting fuel, ballast or FW to the high side

w

G

B

G

B

HeelHeel When a ship rolls, it

takes on various angles of heel

If a ship has a list, rolling is centered about the listing angle

Stability is concerned with the ship’s ability to return to its equilibrium position

Stability & Stability & EquilibriumEquilibrium

Equilibrium is a state of balance. In the upright position, with B vertically aligned with G, a vessel is in equilibrium. Equilibrium may be either stable or unstable

Stability is the tendency to return to equilibrium if disturbed Positive stability is the

tendency to return to the original (stable) equilibrium position after being disturbed

Negative stability is the tendency to move toward another equilibrium position when disturbed

Initial StabilityInitial Stability With G on the

centerline, as a ship rolls B moves outboard & up

For small angles of heel, the locus of B is a circular arc with its center at M, the metacenter

G

B B B

M

Initial Initial StabilityStability KB & KM the location of B and M with respect to the keel K are functions of the underwater shape of the hull and may be calculated for any given displacement (draft)

KG depends on the arrangements of weights within the vessel and must be recalculated each time the vessel is loaded

G

B

M

K

Initial Initial StabilityStability

The Metacentric Radius, BM, fixed by the location of B and M with respect to the keel K, is also a function of the underwater shape of the hull and may be calculated for any given displacement (draft)

GM depends on the location of G (arrangements of weights within the vessel)

Thus shifting weights within the vessel affects G and GM, but not M and B

G

B

M

K

BM

GM

KM

KG

KB


As the ship heels, the upward buoyant force is aligned through B’ &M, but not G

The distance between the lines of action of B and the vessel weight (through G) is the Righting Arm, GZ

This action of two opposite & equal forces, separated by distance GZ is the Righting moment x GZ

Since GZ = GM sin , the Righting Moment at any angle of heal is proportional to GM

The Righting Moment acts to return the ship to the vertical, equilibrium position

B

M

K

B’

ZG


In the unlikely (and unsafe) condition where G is located above M (negative GM) …

Any disturbance results in similar, parallel forces creating a moment, but …

In this case the moment tends to further heel the ship.

This is an example of negative stability, and the vessel will heel to some other, non-upright, equilibrium position—maybe even capsizing

GM then, is a measure of initial stability.

B

M

K

B’

ZG

15o 30o 45o 60o 75o 90o 105o Heel,

Large Angle Stability: Large Angle Stability: (Uncorrected) (Uncorrected) Static Stability CurveStatic Stability Curve – – GZ vs. Heel plotted for some assumed GZ vs. Heel plotted for some assumed KG (must be “corrected” for actual KG)KG (must be “corrected” for actual KG)

2 ft

4 ft

6 ft

8 ftGZ—Righting Arm

GZ≈GM sin

Maximum Righting Arm

Range of Stability

Initial Slope = GM

15o 30o 45o 60o 75o 90o 105o Heel,

Large Angle Large Angle Stability:Stability:

2 ft

4 ft

6 ft

8 ftGZ

M

G

G

G

K

Uncorrected KG

■Raising G increases KG, reduces GM (less stable)

■Lowering G, decreases KG, increases GM (more stable)

uncorr GM

smaller GM

larger GM

15o 30o 45o 60o 75o 90o 105o Heel,

Large Angle Large Angle Stability:Stability:

2 ft

4 ft

6 ft

8 ftGZ

M

G

G

G

K

■As the GM increases, so does the Maximum Righting Arm

■..and so does the Range of Stability

Additional GM notes:Additional GM notes:

Since GM is a measure of initial stability, there is a recommended minimum GM at each draft, but …

Rolling period is inversely proportional to GM Thus a large GM, though more stable, results in

short, quick rolls – the ship is said to be stiff And a small GM yields longer, gentile rolls – the

ship is said to be tender.

■■■■■■■■■■■■■■■■

Roll Period, T Roll Period, T ∝Beam ∝Beam /√GM/√GM

Tankers tend to have a low center of gravity and large KM (large GM), little freeboard and are stiff.

Passenger ships, with large freeboard are designed to be tender for comfort.

Impaired StabilityImpaired Stability Reduction of GM by addition of topside

weight (e.g., icing) Flooding

Solid Flooding (lost buoyancy Partial Flooding (free surface effect) Flooding “in communication with the sea”

(worst case: lost buoyancy + free surface + communication effects)

Grounding Upward grounding force reduces GM and stability Structural damage from impact or severe bending

stress can cause flooding

■■■■■■■■■

G

M

K

■■■■■■■■■MG’

Impaired StabilityImpaired Stability Upon grounding, only only

partpart of the vessel’s weight is supported by the Buoyancy force

The rest is support by a Ground Force, P

This results in a virtual rise of G (to G’)

If G’ rises above the metacenter M, there is negative stability

The ship will certainly heel and maybe capsize

Initial Displ, 0

Grounded Displ, 1

G’

Ground Force, P = 0 – 1

P

B

0

Documents

Hydrostatics Buoyancy & Subdivision Heel & Trim Stability