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# DESCRIBE the inclining experiment, including its mathematical basis, range of validity, and common causes for inaccuracies

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

For the MOB-D-6-SF Righting Ship drill:
a. STATE the purpose of the drill.
b. DESCRIBE the procedure for conducting the drill.
c. STATE the requirements for conducting the drill.
d. DESCRIBE how to employ the DCTT to evaluate the drill.
DESCRIBE the inclining experiment, including its mathematical basis, range of validity, and common causes for inaccuracies.
Given a change in a ship's weight distribution, CALCULATE the resulting list using the moment to heel one degree (MH1) equation.
Given a ship's list, CALCULATE the necessary transverse moment to correct the list, using the moment to heel one degree (MH1) equation.

DEFINITIONS

Roll: The action of a vessel involving a recurrent motion, usually caused by wave action.
Heel: Semi-permanent angle of inclination caused by external forces, such as high speed turns, beam winds, and seas.
List: Permanent angle of inclination, caused by:

 Ship�s Center of Gravity transversely shifted from centerline. 2. Negative Metacentric Height (-GM) 3. Combination of Gravity off-centerline and -GM

MOMENT TO HEEL 1o EQUATION
When a ship experiences an Inclining Moment (IM) the vessel will list or heel until the Righting Moment (RM) is equal to the Inclining Moment (RM = IM). The Inclining Moment is simply a force acting through some distance.

This is only true when the ship has a negligible heel or list.

As the vessel inclines, the distance between the forces changes.

A relationship can be developed to solve for the distance between forces for all angles of heel. Using an expanded drawing of the triangle from the above diagram:

Using the cosine equation to solve for the distance X:

Therefore:

A Righting Moment is created by the ship to keep itself upright. In this case, the force is equal to the ship's displacement (WF) and the distance is the ship's righting arm (GZ) at each particular angle of heel.
The Righting Arm (GZ) changes with inclination of the ship. Using the relationship derived in Unit 4.01 for small angles of heel:
NOTE: This relationship holds true for angles less than 7�-10�

Therefore:

The initial premise was that RM = IM:

Transferring cos q to the right:

Choosing a specific angle, the moment (w x d) required to create that list or heel can be found. Using 1o:
tan 1o = 0.01746
Therefore:
This formula is valid for angles less than 10o due to movement of the metacenter. To check this formula for all inclinations less than 10o, a comparison between the MH10o and 10 times MH1o is made.
-vs-

and

There is a 0.0017 difference over the 10 range. This error is negligible. The list equation can now be used.

Example
Your ship has a 1.5o list to starboard. There are 50 LT of spare parts sitting on the starboard side. The CHENG wants to know how far to transfer the spare parts to correct the list.
 Step 1: Calculate MH1o: Step 2: Use the list equation to solve for distance: or
Example
Your ship has a 2.8� list to port. The CO wants it corrected. There are 3,200 gallons of fuel in the port wing tank (DFM 322 Gal/LT). The starboard wing tank is empty. Correct the list using the fuel and a set of 5 forklifts (8 LT each). The forklifts may only be moved 15 FT to starboard before hitting the bulkhead. How long will it take to correct the list?
 WO = 4200 LT KM = 23.5 FT KG = 19.75 FT

Step 1: Calculate MH1�:

Step 2: Calculate the amount of list corrected by shifting fuel:

or
Step 3: So far, we have corrected 1.27o of the 2.8o list. Using the forklifts, we will correct for the remaining 1.53o list.

or

Step 4: Finally, calculate how long it takes to transfer 3,200 gallons of fuel when the pump capacity is 150 gallons per minute.

Assuming it takes less than 21.33 minutes to move 5 forklifts, this is the time required to correct the list.
INCLINING EXPERIMENT
The inclining experiment is completed upon commissioning and following each major overhaul. It is performed to obtain accurately the vertical height of the ship�s center of gravity above the keel (KGo). Details of the procedures and requirements are spelled out in Section 4, NSTM 079 volume 1, Damage Control Stability and Buoyancy.

Who will get involved:
1. Ship�s Damage Control Assistant
2. NAVSEA / Engineering Logistics Center
3. F/O and Water King
4. Yard Naval Architect
5. SUPSHIP / Cutter Type Desk
6. Pendulum Riggers
7. CHENG
8. Except for necessary watches, ship�s force is put ashore

Procedures:
The naval shipyard or building yard at which the inclining experiment is to be performed will issue a memorandum to the ship outlining the necessary work to be done by ship�s force and by the yard to prepare the ship for inclining.

 1. Liquid load will be in accordance with the memorandum. 2. Inventory of all consumables to be made by ship�s force and inclining party. 3. Inclining weights are placed on centerline. 4. Freeboard is measured, and a photo of the drafts is taken. 5. Salinity of saltwater is measured. 8. Pendulums set up forward, midships, and aft. 9. Weights are moved off-centerline. 10.Inclination of the ship measured.
Measurements are taken for several weight movements both port and starboard. The Naval Architect then uses the following equation:
Where:
w = Inclining Weights (LT)
d = Athwartships Distance Weights Were Moved (FT)
WF = Displacement of Ship (LT, with Inclining Weights)
tan q = Movement of Pendulum  Length of Pendulum
The inclining experiment measures GM accurately, and since the ship�s drafts are known, KM can be found on the Draft Diagram and Functions of Form. KG is then found using KG = KM - GM.

USS/USCG_________________________ DATE _______________
PURPOSE: TO TRAIN THE DAMAGE CONTROL ORGANIZATION IN CORRECTING A LIST.
REQUIREMENTS: CONDITION ONE WITH DAMAGE CONTROL MATERIAL CONDITION ZEBRA SET. LIQUID LOADING MAY BE VARIED TO PUT AN ACTUAL LIST OR TRIM ON THE SHIP IF DESIRED.
PREREQUISITES: 1. ONE OR MORE TANKS OR COMPARTMENTS ARE SIMULATED FLOODED/OPEN TO THE SEA.
2. FLOODING BOUNDARIES HAVE BEEN SET.
3. FLOODING IS UNDER CONTROL.
4. EMERGENCY PATCHING, PLUGGING AND SHORING HAS BEEN COMPLETED.
5. CORRECTION OF THE SHIPS LIST OR TRIM AND SHORING ORDERED.
LIMITS OF THE DRILL:
1. ONLY COUNTER FLOODING OR SHIFTING OF THE LIQUID LOAD IS AUTHORIZED AS CORRECTIVE ACTION.
1. PROPER DISSEMINATION OF INFORMATION AND REPORTS. 15________
1. FLOODING EFFECTS AND LIQUID LOAD DIAGRAM.
3. FUEL OIL TRANSFER BILL.
A. FUEL OIL TANK SEQUENCE TABLES.
4. COUNTER FLOODING BILL.
5. FLOODING EFFECTS BILL.
B. COMPLETENESS AND CORRECTNESS OF DC MESSAGES. 5
1. COMPLETE SET OF DAMAGE CONTROL WRITTEN MESSAGES.
2. USE OF STANDARD PHONE TALKER PROCEDURES.
C. INFORMATION TO THE CAPTAIN 5
1. EXTENT OF DAMAGE.
2. CORRECTIVE MEASURES TAKEN/PLANNED.
2. ACTION OF REPAIR PARTY TO DETERMINE THE EXTENT OF FLOODING AND LIQUID LOAD AT START OF PROBLEM. 15 __________________
A. PREPARATION OF THE INVESTIGATORS 5
1. INVESTIGATION KIT COMPLETE
2. FAMILIARIZATION WITH ASSIGNED AREAS.
3. CORRECTIONS OF INVESTIGATION TECHNIQUES.
B. WAS THE REPAIR PARTY AWARE OF THE LIQUID LEVELS PRIOR TO CASUALTY?
C. WAS THE REPAIR PARTY OFFICER KNOWLEDGEABLE OF THE SHIP'S STABILITY AND SUBDIVISION CHARACTERISTICS?
3. ABILITY OF THE DAMAGE CONTROL PERSONNEL TO COMPUTE EFFECT OF DAMAGE AND TO DETERMINE MEANS OF COUNTERFLOODING OR SHIFTING THE LIQUID LOAD TO CORRECT THE LIST OR TRIM.
40 _________________
A. THE ABILITY TO DECIPHER THE FLOODING EFFECTS AND LIQUID LOAD DIAGRAM AND USE FLOODING EFFECT BILL. 10
B. KNOWLEDGE OF PUMPING OR SLUICING LIQUIDS ACROSS THE SHIP.
10
C. KNOWLEDGE OF PROCEDURES TO COUNTER FLOOD. 5
D. UNDERSTANDING THE CONSEQUENCES OF CONTAMINATION. 5
E. UNDERSTANDING THE FUEL OIL TANK SEQUENCE TABLES. 5
F. UNDERSTANDING THE EFFECTS OF DEWATERING/FLOODING SOLID/PARTIAL FLOODED COMPARTMENTS ABOVE CENTER OF GRAVITY. 5
4. ACTION OF THE REPAIR PARTY IN COUNTER FLOODING AND SHIFTING OF LIQUID LOAD. 30 ____________
A. THE ABILITY TO IDENTIFY AND LOCATE SELECTED SYSTEM CONTROL VALVES. 10
B. KNOWLEDGE OF THE INSTALLED SYSTEMS 10
1. FUEL OIL TRANSFER SYSTEM.
2. DRAINAGE SYSTEM.
3. FLOODING AND BALLASTING SYSTEMS.
4. PUMP CAPACITIES.
C. HANDLING OF SELF-INFLICTED DAMAGES 10
1. LACK OF SYSTEM MAINTENANCE (PMS)
2. FAILURE TO PROPERLY OPERATE CONTROLS.
3. INSUFFICIENT OR IMPROPER DC CLASSIFICATIONS.

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