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# DESCRIBE the relationship between metacentric height and roll period.

EVALUATE shipboard stability by analyzing weight and moment considerations.ENABLING OBJECTIVES:

DESCRIBE the relationship between metacentric height and roll period.
DEFINE floodable length, angle of maximum roll, angle of semi-permanent heel, and reserve dynamic stability.
DESCRIBE the three possible causes for list after damage and the indicators for each.
Given a DC book section II(a), CALCULATE danger angle.
DESCRIBE the survivability design considerations outlined in NAVSEA DDS-079-1 and NAVSEAINST 9096.3(series) which enable the ship to withstand external, dynamic forces and damage.
Given a written summary of damage, a description of the ships behavior and list, EXPLAIN the cause of the list and the procedures necessary to eliminate or reduce the list.
DESCRIBE the intended method of disabling a ship as it applies to: homing influence torpedoes, impact (WWII) torpedoes, anti-ship missiles, influence and contact mines.
Given a ship's beam and average roll period in calm water, use the Roll period equation to CALCULATE the ship's metacentric height.
DRAW a righting moment curve with a heeling moment curve that identifies angle of maximum roll, angle of semi-permanent heel, and reserve dynamic stability remaining.

SITUATION ESTIMATE AFTER DAMAGE
Two possible situations exist following the infliction of damage:
Damage is so extensive that the ship never stops listing, trimming, or settling, and goes down within minutesor
The ship stops heeling, changing trim, and settling shortly after initial damage.
Experience has shown that the loss of ships lasting several hours after damage and then sinking is directly traceable to progressive flooding.
CAUSES OF LOSS1. Floodinga. Bodily Sinkage - The addition of weight (flooding water) has caused the force of gravity to exceed the force of buoyancy.

b. Capsizing - Loss of transverse stability: the inclining moment exceeds the righting moment (IM > RM) and the ship rolls over.
c. Plunging - Loss of longitudinal stability: the trimming moment exceeds the longitudinal righting moment (TM > RM) and the ship sinks by the bow or stern.

2. Breaking Up - Caused by strength member failure
a. Excessive stresses from hull damage or improper distribution of liquid (failure to follow the ships Liquid Loading Instructions (LLI).
b. Violent longitudinal whipping (ex: grounding at high speed, underwater detonation.)
c. Fire: Extreme thermal effects on structural members.
METACENTRIC HEIGHT AND STABILITY
In lesson 4.01 the relationship between Metacentric Height (GM) and righting arms (GZ) was discussed. For small angles of heel (0'-7/10') GZ is proportional to GM. Therefore, GM can be used as a representation of initial righting arms. These basic rules apply:
If GM is large, the ship has large righting arms and will have stiff, fast rolls.
If GM is small, the ship has small righting arms and will have tender, slow rolls.
If GM is very small, the ship is apt to hang at the end of each roll before starting upright.
If GM is slightly negative, the ship will loll (stay heeled at the angle of inclination where righting and upsetting forces are equal) and flop from side to side.
If GM is negative, the ship will capsize when inclined.
SHIPS ROLL PERIOD
The ship's roll period is directly related to the Metacentric Height of your vessel. Should you desire an estimate of your Metacentric Height, the following method works well when underway.
The ship must be making way, approximately 8-10 knots on a relatively calm day. Have the OOD cycle the rudder, from right full to left full or vice versa. Using a stop watch, determine how long it takes to go from 0 inclination to full inclination to starboard, back to 0 inclination, to full inclination to port and back to 0 inclination. This is the ships roll period. Repeat if necessary to ensure that the time is as accurate as possible.
Where:
B = Maximum Beam of the Ship (FT)
T = Period of Roll (Seconds)
GM = Metacentric Height (FT)
LIST IN STABILITYHEEL - A heel is a "temporary" inclination of a ship, caused by outside forces such as winds, waves, or during a ship's turn.
LIST - A list is a "permanent" inclination of a ship, caused by one of the following conditions:
 1. Off-Center Weight (99% of the time) 2. Negative GM (1% of the time)3. Combination of Off-Center Weight and -GM
LIST CAUSED BY OFF-CENTER WEIGHT
Whenever the center of gravity of a ship is moved off centerline, the ship will create an inclining moment. If no external forces are present, the ship will assume a list. This was discussed in section 4.02 where the cosine correction was applied to the static stability curve.
Righting arms are significantly reduced when the center of gravity is off-centerline. This reduction results in the ship having a negative righting arm (upsetting arm) at 0 inclination. Where the corrected curve crosses the horizontal axis, positive righting arms are achieved. This is the angle of list, the ship will roll about this point.
Possible Causes1. Unequal distribution of weight on either side of center line due to loading.2. Shift of weight transversely.
How to Recognize1. Vessel assumes a permanent list to one side only.
2. Vessel has an average roll period about this permanent list.3. If known weight is in excess on one side.
4. If a positive GM is known to exist.
Corrective Measures1. Determine Cause of list first.
2. Shift weight transversely to higher side
3. Add weight to high side or remove weight from low side.
*** NEVER attempt to correct list by the above methods unless you are certain that GM is positive ***
LIST CAUSED BY NEGATIVE GM
When a ship's center of gravity moves vertically upwards and slightly above the Metacenter, the ship will develop a list (or possibly capsize.) The vessel may also "flop" over, developing the same list to the other side.
Possible Causes1. Removal of low weight
2. Addition of high weight (ice, volcanic ash)
3. Moving weight upward
4. Free Surface Effect
5. Free Communication Effect
How to Recognize1. Vessel will not remain upright and will assume a list to either port or starboard.2. Vessel "flops" to port or starboard.
3. Vessel will have a very long, slow roll period about the angle of list.4. A small GM is known to exist plus any of the above.
Corrective Measures1. Eliminate Free Surface and Free Communication Effects.
3. Remove high weight symmetrically.
4. Shift weight down symmetrically.
LIST CAUSED BY OFF-CENTER WEIGHT AND NEGATIVE GM
The vessel's stability is reduced by both an increase in the height of the center of gravity and movement from centerline. A negative GM condition exists, represented by the "uncorrected" curve. An off-center weight, represented by the cosine curve, is added and a larger list develops.
Possible Causes1. A combination of the previous causes of list.How to Recognize1. Vessel will assume a permanent list either port or starboard (vessel will not flop).
2. Very slow roll period about this permanent list.3. The known off-center weight isnt proportional to the ships list.
Corrective Measures1. Correct Negative GM first.a. Eliminate Free Surface and Free Communication Effects.
b. Shift weight down, add weight low, or jettison weight high.
2. Correct for Gravity Off Centerline
a. Add weight to higher side
b. Remove weight from lower side
c. Shift weight to higher side
*** ALWAYS correct Negative GM prior to shifting weights transversely ***FLOODABLE LENGTHBulkhead Deck - The uppermost deck to which the transverse watertight bulkheads extend (usually the Damage Control deck.)
Margin Line - An imaginary waterline located three inches below the Bulkhead Deck.
Floodable Length - The maximum distance within the ship that can be flooded without submerging the margin line.

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FLOFFLOOD FLOODABLE LENGTH (continued)
There are two different forms that Floodable Length is discussed in the Damage Control Book.
1. The Curve of Floodable Length: To use this curve, draw a line parallel to the forward line (60o to vertical) and place it at the baseline of the forward most bulkhead where flooding exists. Project this line up to the Curve of Floodable Length. Draw a line parallel to the aft line (60o to vertical) which intersects the Curve of Floodable Length at the same point. The baseline distance between the forward and after lines is the Floodable Length.
2. A List of Floodable Length Compartment Groups: The Damage Control Book will list all groups of consecutive compartments which constitute Floodable Length. Example, for the FFG-7:
Stem - Frame 100
Frames - 32-140
Frames - 64-180
Frames - 100-212
Frames - 140-250
Frames - 180-292
Frames - 212-328
Frames - 250-368
Frames - 292-Stern
General rule of thumb for Floodable Length:
If the ship's LBP is > 300 FT : 15% of LBP (3 spaces **)
< 300 FT : 2 spaces **
< 100 FT : 1 space **
** A space is the area between two transverse watertight bulkheads from keel to waterline, skin to skin.
Example: For a two compartment ship, flooding any two adjacent spaces will cause the ship to reach its Floodable Length.