TJ Trim Stability Booklet Rev F.docx

TRIM AND STABILITY BOOKLET

for the

NOAA SHIP THOMAS JEFFERSON

Contents Page

REVISIONS

Modified hydrostatics properties, draft diagram, trim diagram incidental to tunnel bow thruster & transducer fairing installation.

Modified tank capacity tables incidental to tankage modification.

Modified required GM curve incidental to revised intact stability analysis.

Modified GM change due to filling tanks to suit revised tankage & hydrostatics.

Revised recommended burn/ballast sequence.

Modified loading conditions to suit revised tankage & hydrostatics.

AAA/

EDS

Revised recommended burn/ballast sequence.

Modified tank capacity tables incidental to added HPU tanks.

Modified loading conditions to suit revised tankage.

SSI/JEK

Modified anti-roll tank FSM for salt water

SSI/JEK

GDMW

GDMW

REFERENCES

1. TJ-801-6634641 Rev A, Table of Offsets

2. 085-6980295 Rev E, Tank Capacities and Soundings for the NOAA Ship Thomas Jefferson

3. TJ-079-01 Rev C, Intact Stability Analysis for the NOAA Ship Thomas Jefferson

4. TJ-079-02 Rev C, Damage Stability Analysis for the NOAA Ship Thomas Jefferson

5. Stability Test Data, CDI Marine Co, LLC, 2 October 2017, ABS-stamped on 30 October 2017

DEFINITIONS

(Transverse unless otherwise stated)

above the BL KMt Transverse Metacentric Height above the BL

“a” (aft) or “f” (fwd) of FP LCF Longitudinal Center of Flotation “a” (aft) or “f” (fwd) of FP LCG Longitudinal Center of Gravity “a” (aft) or “f” (fwd) of FP

Atmospheric Administration

starboard draft mark readings T2 Average of the forward port and starboard draft mark readings

PRINCIPAL DIMENSIONS AND PARTICULARS

History

Owner/Operator National Oceanic and Atmospheric Administration (NOAA) 2002 SE Marine Science Drive Newport, Oregon 97365 Particulars of Classification Inspected ABS Load Line, Ocean Service Class Number 9105067

A1, Ⓔ, AMS, ACCU

Statutory Categories

Steel hull Single screw, 8’10” diameter fixed pitch;

Principal Dimensions

Transom - none

(excluding fresh water ballast and anti-roll tank) Boats

Deck Equipment Cranes

Operation on exposed waters is permitted. The Master is cautioned that the route may be further limited by other considerations beyond stability. The ship does not operate with a Certificate of Inspection.

General Arrangements

LIGHT SHIP CHARACTERISTICS AND OTHER WEIGHTS

Deadweight Survey or Inclining Test The most recent Inclining Test was performed at NOAA Marine Operation Center Atlantic, Norfolk, VA on 9 April 2017. This Trim and Stability Booklet incorporates data from the Inclining Experiment Report approved by ABS on 30 October 2017. Any further changes made to the vessel after the date of this Booklet shall void this report. If the vessel undergoes any modifications where large weight changes occur, the vessel shall have a Deadweight Survey or Inclining Experiment done under supervision of the U.S. Coast Guard or American Bureau of Shipping to verify the lightship characteristics.

Light Ship Characteristics

above Baseline Longitudinal, aft of Forward Perpendicular Transverse, starboard of Centerline

Solid Ballast No fixed ballast or other such weight shall be added, removed, altered, and/or relocated without the authorization and supervision of the Cognizant OCMI. At the time of the last Inclining Test, no permanent ballast was included.

Mean Light Operating Condition A maximum of 38 persons may be carried, based on available berths as of the Revision Date of this document. The Master is cautioned that the number of persons carried may be limited by other considerations beyond stability or berthing. The ship does not operate with a Certificate of Inspection.

Icing Any accumulation of ice topside will cause a reduction in metacentric height (GMt) available. An approximation of this loss may be obtained by estimating the average thickness of ice over the exposed areas above the waterline, including masts, crane booms, rails, rigging, etc., as well as bulkheads and decks. Based on USCG guidance, it is assumed that ice on horizontal surfaces will accumulate twice as much as on vertical surfaces. The effect of topside icing on GMt available is shown on page 33, using the example of ice accumulation for the 42 to 66° latitude vertical and horizontal thicknesses. Other thickness will have a proportional effect:

The magnitude of loss in available GMt indicates that significant accumulation of ice can result in a deficient stability condition. Conditions favorable to ice formation should be avoided when possible. When arrival in sheltered waters is not imminent, stability improvement measures should be considered, and ice removal procedures should be initiated early so that substantial amounts do not accumulate.

The table below shows an example of ice accumulation calculations based on consistent thickness across all horizontal and all vertical surfaces. Actual accumulations are not likely to be consistent fore and aft, port to starboard, or waterline to masthead.

TABLES of HYDROSTATICS Specific Gravity = 1.025; moment to trim is based on length between perpendiculars = 190 feet and assumes VCG = 0.

Zero Trim

3 Feet Trim by Stern 3 feet trim over 190 foot LBP = 1.58% trim or 0.905°; damage stability not calculated

VOLUMES

Plans

Capacities and Free Surfaces

Table of Cargo & Storage Spaces Capacity calculated assuming 0.85 Utilization Factor

MAXIMUM ALLOWABLE VCG

The VCG calculated in each condition must be less than the maximum allowable (“Governing”) VCG values listed and plotted below, for the particular LCF draft in sea water. These allowable VCG values have not been corrected for a free surface moment. Therefore, the free surface moment for all tanks must be calculated. See the Operating Instruction for restrictions on tank loading.

Intact The maximum VCGs resulting from the intact stability analysis are presented in the following table and chart. The intact stability is governed by the Weather Criterion at all drafts.

Damaged For the calculation of extent and character of damage, 46 CFR 173.080 categorizes oceanographic research vessels as type Z. The extents of damage for this ship, based on Table 171.080(a) are 15.70 feet longitudinally, 9.00 feet inboard, and upward from the baseline without limit. The standard for passenger vessels carrying 400 or fewer passengers is in 46 CFR 173.075. A one-compartment standard of flooding per 46 CFR 171.070(a) assumes no damage to any main transverse watertight bulkhead. No watertight bulkheads or doors shall be removed, added, or altered without the authorization and supervision of the Cognizant Officer in Charge of Marine Inspection.

Any openings that could allow water to enter the hull or deckhouse shall be kept closed at all times except when actually in use under safe conditions. These include the Main Deck or 01 Level hatches and weather doors to the forecastle and machinery spaces. No downflooding points have been found within 40 degrees of heel.

The vessel is divided into zones by seven main watertight transverse bulkheads at Frames 8, 22, 34, 43, 55, 75, and 87. The damage cases reflect damage to the compartments in each zone according to the following table. The absence of a mark on port compartments just means that the assumed damage to the starboard side does not extend across the ship. Damage to the port side yields an equal or possibly greater margin of safety versus the described cases of the same longitudinal extent.

to Transom

FO 1F (S)

X

FO 1F (P)

FO 1A (S)

X

FO 1A (P)

Bow Thruster Room

X

BLST 4-08-1 (S)

X

BLST 4-08-2 (P)

FO 4-16-1 (S)

X

FO 4-16-2 (P)

Bow Thruster Trunk

X

GSM Stores

X

Ships Stores

X

Chilled Stores

X

Freezer Stores

X

BLST-4-22-0 (CL)

X

Sonar Void

X

Laundry/Exercise

X

Science Stores

X

FO 4-34-1 (S)

X

FO 4-34-2 (P)

C

Lower Dk Fr 34–43

X

Cofferdam 4-43-1

X

Cofferdam 4-43-2

C

FW 3-44-1 (S)

X

FW 3-44-2 (P)

C

Antiroll (C)

X

FO 4-55-3 (S)

X

FO 4-55-4 (P)

Engine Room

X

FO 4-75-3 (S)

X

FO 4-75-4 (P)

Engineer Stores

X

Engineer Workshop

X

FW 2-87-1 (S)

X

FW 2-87-2 (P)

Aft Void (S)

X

Aft Void (P)

Calculations indicate this vessel will have no more than 15 degrees of list under ideal conditions after damage. Damage Case 2 is the limiting damage case at all drafts at zero trim and most drafts at 3’ trim by stern. The following table and figure present the results of the damage stability calculations.

Change in GM by Ballasting This table shows changes in trim and GMt for a range of displacements when ballast (or other fluids) is added. Values are in feet. A positive value means the GMt increases, increasing stability. A negative value means the GMt decreases, reducing stability. VCG, trim and free surface effects are all included in the GMt change.

Change in GM by Adding Weight The following table shows the change in GMt resulting from an addition of 10 long tons at or near the LCF and on centerline, so as not to induce trim or heel. This facilitates estimating the effect on stability of weight changes at various levels, as from additional stores, deck cargo, etc. The change in GMt is proportional for weights other than 10 long tons. When weights are removed, the change is the same as for weights added, but with the sign reversed. Added weight is assumed to have a VCG of 3 feet above the deck at each location cited. Decks noted (CL) have ¼” linear camber (decreased height above baseline) per foot of distance from centerline.

INSTRUCTIONS TO THE MASTER

General This book is designed to help the ship’s Master maintain the satisfactory stability of his vessel for all conditions by heeding the restrictions as outlined below and by following the instructions for determining the ship’s trim and stability contained in the next section. This manual is not intended to replace the judgment of the person in charge, who must use every means at his/her disposal to ensure that the stability of the vessel is adequate to meet the sea and weather conditions encountered.

It is the Master’s responsibility to maintain the vessel in a satisfactory stability condition at all times, meeting the U.S. Coast Guard wind heel and righting energy requirements as well as a one compartment standard of damage stability per 46 CFR Part 170.

Per 46 CFR 196.15-7, after loading and prior to departure and at other times necessary to assure the safety of the vessel, the Master shall determine that the vessel complies with all applicable stability requirements in the vessel’s Trim and Stability Booklet, Stability Letters, Certificate of Inspection, and Load Line Certificate as the case may be. The vessel may not depart until it is in the compliance with applicable stability requirements. The vessel’s draft, trim, and stability must be determined as necessary. The Master must enter an attestation statement in the log verifying that the vessel complies with the applicable stability requirements at the times specified. Any stability calculations made in support of the determinations must be retained on board for the duration of the voyage.

Compliance with the stability criteria does not prevent capsizing regardless of the circumstance or absolve the Master of his responsibilities. The Master shall therefore exercise prudence and good seamanship, with regard to the prevailing circumstances, the season of the year, the weather forecasts, and the navigational zone when determining appropriate vessel loading, speed, or course.

The Master shall make every effort to determine the cause of any list of the vessel before taking corrective action.

Burn/Ballast Sequence and Tank Use Although there are no restrictions on burn sequence, it is recommended that, when operating in a loading condition other than shown on pages 33 through 44, the following sequence be used as a guideline to ensure adequate stability down to a fuel load of about 10%.

Diesel Oil Service Tanks (4-75-1, -2) are maintained 50% full at all times.

Departure Condition:

(1) Burn from DO storage tank 4-55-1 & -2 until empty, empty forward PW tanks first, then use aft PW tanks to adjust any heel, empty ballast 4-22-0 to trim 77.2% fuel, 12.72’ FP depth, 0.36’ aft trim, 0° list

(2) Burn from DO storage tanks 4-16-1 & -2 until empty, empty aft PW tanks, then use mid PW tanks to adjust any heel 52.9% fuel, 11.74’ FP depth, 1.37’ aft trim, 0.04° stbd list

(3) Burn from DO storage tanks 4-75-3 & -4 until empty, use mid PW tanks to adjust any heel 38.7% fuel, 11.97’ FP depth, 0.88’ aft trim, 0° list Time to Refuel! Else,

(4) Burn from DO storage tanks 4-34-1 & -2 until empty, add ballast to 4-75-0 to adjust trim 2.8% fuel, 11.1’ FP depth, 0.84’ aft trim, 0.09° stbd list

(5) Burn from DO day tanks 4-75-1 & -2 to burnout 0% fuel, 11.24’ FP depth, 0.47’ aft trim, 0.67° stbd list Center of Gravity The natural period of roll of a vessel is inversely proportional to the GMt in any particular loading condition. The curve below indicates the approximate relationship between GMt and period of roll for the NOAA Ship Thomas Jefferson, and may be used to estimate the GMt when roll period can be measured. Such measurement should only be made under relatively calm conditions when roll is fairly regular and at constant small amplitude. When measuring roll period, always measure the time for several rolls and divide the time by the number of rolls observed. The period of a complete roll, such as port, starboard, and back to port, must be used with the curve.

Estimating GMt from the roll period is a means of checking only. It is not intended to take the place of the stability calculations described on pages 44 to 49.

Draft and Freeboard The following figure shows the relative location of the forward draft marks, aft draft marks, and reference points used in the displacement calculation above.

Determine Displacement and Trim from Observed Drafts The following procedure describes the method of determining displacement and trim from the observed drafts. Average port and starboard drafts are used to eliminate the effect of heel.

1. Determine the average of the aft port and starboard drafts (T1). The aft draft marks are centered at Frame 94.

2. Determine the average of the forward port and starboard drafts (T2). The forward draft marks are considered centered at Frame 0.

6. Calculate the trim (TRIM) in meters over the 190-foot Length Between Perpendiculars (LBP):

8. Use the Table of Hydrostatics (page 12) to determine the Longitudinal Center of Flotation (LCF) using the Midship draft (TMID) as the Mean Draft (Tm). Intermediate values may be interpolated.

11. Use the Table of Hydrostatics (page 12) to determine the Displacement (DISPL) at the LCF draft. Intermediate values may be interpolated.

Trim shall be minimized. The following graph shows corrections to forward and aft drafts (at the draft marks) for a weight of 10 LT loaded at any location on the vessel.

TRIM TABLE

Example: find the new drafts (at the draft marks) after loading 5 LT centered at Frame 75. Correction in inches = (Weight / 10 LT) * correction from figure.

Aft Marks (Fr 94) (feet) Fwd Marks (FP, Fr 0) (feet)

Notes: When offloading, use the same corrections, but reverse the sign.

VCG vs. Draft Curves Based on the stability criteria and the trim of the vessel, the two important stability parameters, VCG and draft, are plotted against each other and presented in the graphs of Item 5. These graphs indicate for any amidships draft and trim, the corresponding maximum allowable vertical center of gravity (VCG) that the vessel may have. The vessel's actual VCG, corrected for free surface effects, should never be higher than the maximum allowable, taken from the graph at the vessel's mean draft. If the vessel's actual VCG is higher and in the unsafe region of the graph, the vessel may not be able to withstand the effect of wind/wave (or combination of the two) action, or any other heeling force, and thus may capsize.

Loading Conditions Mean Light Operating Condition The Mean Light Operating Condition (MLOC) is a list of weights which remain constant during most vessel operations. These weights are constant load items that are not included in the lightship value. Examples of constant weight items include non-consumable stores. The following table includes both MLOC and Mission Loads, where items marked with an asterisk are estimated to be consumed at the same rate as fuel, i.e. 100% for departure, 50% for mid-voyage, and 10% for arrival.

Moment

Tons feet above BL feet aft of FP feet stbd foot- Long Tons

Launch 3101 (stbd)

Launch 3102 (port)

Workboat TJ-4

Free Surface No more than one centerline or P/S pair of fuel oil storage tanks (excluding service tanks) may be partially filled at one time. If one tank of a P/S pair is full and the other pumped to a minimum content, this need not be considered as a partially full pair of tanks.

When salt water ballast is carried, all ballast tanks that contain liquid should be pressed up whenever possible in order to minimize free surface. During ballasting a reduction in the vessel’s GMt due to slack tank free surface will occur until the tanks are pressed up. This temporary loss of GMt is equal to the salt water Free Surface Moment (FSM) of the tank (or tanks) divided by the vessel’s displacement at the time of ballasting.

Compensating salt water ballast should be introduced and pressed up prior to the drawing of fuel oil to minimize free surface loss and ensure adequate stability at all times. Empty ballast tanks should be pumped periodically to assure a minimum content at all times.

A water tank less than 100% full or a fuel tank less than 95% full shall be considered slack. Miscellaneous oil and dirty tanks less than 98% full shall be considered slack. The vertical FSM for any water tank either empty or 100% full shall be zero. The FSM for those fuel tanks 95% full shall be as calculated. The FSM for those miscellaneous oil and dirty tanks 98% full shall be as calculated.

The vessel is equipped with a roll stabilization tank (included in the vessel trim and stability calculations) with the following characteristics:

The vessel bilges and voids shall be kept pumped to minimum content at all times. Deck freeing ports shall be maintained operable and completely unobstructed at all times.

Shifting of Cargo All deck equipment must be positively secured against shifting before leaving protected waters.

Icing It is recommended that the roll stabilization tank be empty when in icing conditions.

Action Following Damage To maintain the vessel upright after flooding, the heeling forces imposed by wind, wave, and personnel movements must be minimized. The calculations do not specifically account for high winds, heavy seas, or the movement of personnel to one side. The vessel is equipped with five (5) Type III watertight doors located in main transverse watertight bulkheads at Frames 22, 34, 43, 55 and 75. If damage is sustained, these doors shall be closed immediately either remotely or locally. Tank damage may be assessed by use of tank level indicators, physical tank soundings, or visual inspection.

In the event of underwater damage or entry of water through the weather envelope, stability of the vessel will be affected by the consequent flooding of spaces within the vessel. The NOAA Ship Thomas Jefferson is designed to comply with the USCG damage stability criteria with a one compartment standard of flooding.

The response of the vessel to flooding will depend on the intact draft, trim and stability characteristics immediately prior to the incident, and the condition of the tanks, if any, involved in the flooding.

Entry of a significant amount of water into any part of the vessel should be regarded as an emergency situation and appropriate measures should be taken promptly. These would normally include the following:

1. Call for assistance.

2. Alert the vessel personnel to the situation.

3. Close watertight doors. The vessel is equipped with five (5) Type III watertight doors located in MTWBs at Frames 22, 34, 43, 55 and 75. If damage is sustained, these doors shall be closed immediately either remotely or locally.

4. Favor stability in handling the vessel. Head into the wind and sea if possible. Avoid hard turns.

5. Determine the source of the flooding and the spaces affected or likely to be affected.

6. Consider emptying the anti-roll tank to substantially increase the vessel’s stability.

7. Activate the bilge system, emergency generator, and other emergency systems as required.

8. Establish flooding boundaries by shoring or patching to prevent or limit progressive flooding.

In general, further corrective action should be evaluated once trim and list reach a steady state without further increase. The corrective actions must be evaluated depending on the degree of improvement in the vessel’s attitude deemed necessary in the circumstance. For example, if the stern is low in the water, trimming by the head may be considered. If the vessel lists heavily as a result of unsymmetrical flooding list correction may be undertaken.

Trim and list correction should generally be made by shifting liquids already on board rather than by taking on water ballast, which will increase the draft and reduce the reserve buoyancy. When shifting liquids, the following precautions should be observed:

1. DO NOT attempt to correct a list by shifting liquids if any signs of negative GM are present. These signs include:

a. A slow, erratic period of roll

b. Failure to return to upright after rolling to one side, and

c. Listing alternatively to port and starboard

2. If, and only if, it can be positively determined that a list is due to unsymmetrical flooding and that the vessel has a positive GM, list correction by shifting of liquids may be undertaken slowly and cautiously.

3. Take suction from tanks which are already slack rather than tanks which are full. This will minimize the increase in free surface effect.

4. Discharge to tanks which are slack, rather than empty, and preferably to those that are nearly full. Press up into the vent lines.

5. Favor improvements in trim, if possible, when selecting tanks for transfer.

Minor improvements in stability may also be accomplished by lowering moveable weights. For example, cranes, if initially up in the working position, may be lowered to the fully down position. In cases where survival takes precedence over all other considerations, heavy gear may be jettisoned, working from the upper decks down. Jettisoning is a slow and laborious operation and the improvement obtained will usually be small. Therefore it should only be considered in an extreme situation.

Additional Information

STANDARD LOADING CONDITIONS

Lightship

Mean Light Operating Condition

Standard Mission — Full Load Departure from Port

Standard Mission — Mid-Voyage

Standard Mission — Arrival

Standard Mission – Extreme Full Load

Standard Mission — Mid-Voyage with Icing

INSTRUCTIONS FOR CALCULATING OTHER LOADING CONDITIONS

The following procedure has been used in solving the examples on pages 34 to 44 and shall be utilized to calculate the vessel’s displacement, centers of gravity, drafts, and trim for any condition of loading. Blank loading forms are included on pages 50 to 52.

Instructions for Computing Vessel Trim and Stability

1. A typical condition is calculated by determining the amount and location of cargo on board, liquids in tanks, and stores. For this booklet the reference point is the intersection of a vertical line through the Forward Perpendicular (FP), the Center Line (CL), and the molded Baseline (BL). The FP is at Frame 0. The VCG is referenced from the BL (positive up), the LCG is referenced from the FP (positive aft), and the TCG is referenced from the CL (positive starboard).

2. Calculate the Tank Loading by first locating the Tank Load Worksheet (page 51). Tank loading is a volumetric fraction and may be determined for each tank from its sounding and table in reference (2), the Tank Capacities & Soundings document. Determine the loading fraction (percent full) for each tank on board. Use the Tank Capacity Table on pages 15-16 to establish the weight of liquid in each tank at 100% capacity, VCG, LCG, and TCG. The weight of the liquid in each tank is calculated by multiplying the loading fraction by the weight of liquid in the tank at 100% capacity. Enter the calculated weight of each tank liquid in the Weight Column of the Tank Load Worksheet. The VCG, LCG, and TCG for each tank in the Tank Capacity Table is already entered in the Worksheet for tanks loaded to their maximum recommended levels, which is a conservative assumption for VCG calculations. If more accuracy is desired, these values may be replaced by ones found in reference (2) for tank loading less than maximum.

Weight in tank = Loading fraction x Weight at 100% tank capacity

Calculate the vertical, longitudinal, and transverse moments by multiplying the weight of the liquid in the tank by the center of gravity.

Vmom = Weight x VCG Lmom = Weight x LCG Tmom = Weight x TCG

The table to the right is a reference to the specific gravity and specific volume used for liquids on board.

Gravity Specific Volume gallons/LT

Enter the vertical Free Surface Moment (FSM) in the FSM Column of the Tank Load Worksheet. The FSM shall be calculated according to the following notes:

· There is no FSM for tanks that are empty or 100% full.

· A water tank less than 100% full or a fuel tank less than 95% full shall be considered slack. Potable water tanks shall be considered to be slack at all times. Miscellaneous oil, waste, and fuel day tanks shall always be considered slack. The FSM of each slack tank shall be determined from the “Max” FSM Column of the Tank Capacity Table (pages 15-16).

· The FSM for those fuel tanks 95% full shall be as indicated in the “At Usable Fraction” FSM Column of the Tank Capacity Table (page 15-16). The FSM for those miscellaneous oil and dirty tanks 98% full shall be as indicated in the “Max” FSM Column of the Tank Capacity Table.

· The total FSM for each type of liquid carried shall not be less than the values in the following table.

foot-LT Remarks

Sum the FSM Column. The minimum total FSM for any loading condition shall be 2907 foot-LT when the Roll Stabilization Tank is used. The minimum total FSM for any loading condition shall be 1244 foot-LT when the Roll Stabilization Tank is empty. Substitute the specified minimum FSM value for the total FSM if the specified minimum FSM value is greater than the total FSM tabulated.

Sum the Weight and Moment Columns to obtain the subtotal for each type of tank. Divide the subtotaled moments by the subtotaled weights to determine the centroid of the tank type. Copy the Weight, Vmom, Lmom, Tmom, and FSM of the total tank load to the Summary Loading Sheet.

VCG = Σ Vmom / Σ Weight LCG = Σ Lmom / Σ Weight TCG = Σ Tmom / Σ Weight 3.

4. Calculate the Mission Load by first locating the Mission Load Worksheet (page 52). Mission loads consist of solid items not included in the Mean Light Operating Condition (MLOC). These loads should include Mission Loads and Expendables such as:

a.

b. Crew and effects

c. Rescue and work boat

d. Working deck disposable loads

e. Van loads

f. Scientific stores

g. Fishing gear

h. Consumable stores and provisions

i. Miscellaneous Cargo

j. Any other items not included on the Tank Load Worksheet or the MLOC.

The Mission Load Worksheet contains typical mission loads with a column indicating the maximum reference weight. If the typical mission loads are on board, enter Y (yes) in the first column and enter the weight of the load in the Weight Column. There are extra lines to include weights not already present on the worksheet. Enter these weights, VCGs, LCGs, and TCGs. The Mission Loads shall be calculated according to the following notes:

· All variable non-tank loads aboard the vessel are to be recorded on the Mission Loads Worksheet. Note that constant vessel loads such as constant stores are already included in the MLOC weight and should not be entered in the Mission Loads Worksheet. See page 29 for the list of MLOC weights.

To aid in determining the VCG of loads, the deck heights above the baseline are as follows:

The General Arrangements included on pages 6 to 8 will also aid in determining centers of Load Items.

The moments are calculated by multiplying the object weight by the center of gravity.

Vmom = Weight x VCG Lmom = Weight x LCG Tmom = Weight x TCG

Once the list is complete and the moments have been calculated, sum the Weight and Moment Columns. Divide each moment subtotal by the weight subtotal to determine the centroid of the Total Mission Load Weight. Copy the Total Mission Load Weight, Vmom, Lmom, and Tmom to the Summary Loading Sheet.

VCG = Σ Vmom / Σ Weight LCG = Σ Lmom / Σ Weight TCG = Σ Tmom / Σ Weight 5.

6. Use the Summary Load Worksheet (page 51) to determine the vessel load condition displacement and center of gravity. Enter the weight, Vmom, Lmom, Tmom, and FSM values for the Tank Load and the Mission Load. The Icing weight should be determined based on the guidance on page 10. Calculate the vertical, longitudinal, and transverse moments by multiplying the ice weight by the center of gravity.

Vmom = Weight x VCG Lmom = Weight x LCG Tmom = Weight x TCG

The Total Deadweight is calculated by summing the Tank Load, Mission Load, MLOC, and Icing Load. The Total Deadweight centroid is calculated by summing the moments and dividing by the total weight. The Lightship characteristics are already included on the Worksheet. To calculate the Total Displacement (DISPL), sum the weights of the Total Deadweight and Lightship. The centroid is calculated by dividing the moment subtotals by the total weight.

VCG = Σ Vmom / Σ Weight LCG = Σ Lmom / Σ Weight TCG = Σ Tmom / Σ Weight 7.

8. Determine the trim at the existing vessel condition. Use the Tables of Hydrostatics (pages 11-12) to determine the Mean Molded Salt Water Draft (Tm), Longitudinal Center of Buoyancy (LCB), Longitudinal Metacentric Height (KML), and Longitudinal Center of Flotation (LCF) by interpolating these values for the Total Displacement. The Trimming Lever (TL) is calculated by subtracting the LCB from the LCG and may be positive or negative. Next calculate the Moment to alter Trim One Inch (MTI) by multiplying the difference of the Vertical Center of Gravity (VCG) and the Longitudinal Metacentric Height by the Displacement and dividing by twelve times the Length between Perpendiculars (LBP). The Trim (TRIM) in feet is calculated by multiplying the Displacement by the Trimming Lever and dividing by twelve times the Moment to alter Trim One Inch. A positive answer is a trim by the stern, and a negative answer is a trim by the bow.

TL = LCG – LCB

MTI = (KML – VCG) * DISPL / (12 * LBP)

TRIM = (DISPL x TL) / (12 * MTI) LBP = 190 feet

9. The trim should not exceed 3.0 feet by the stern (+) or 1.0 foot by the bow (-). If changes to the trim are required, the Trim Table on page 28 can be used to quickly determine the effects of weight changes. Note that the movement of any weight will require the stability to be re-calculated and re-checked.

10. Determine the expected average drafts at the forward perpendicular (TFP), aft perpendicular (TAP), forward draft mark (TFM) and aft draft mark (TAM).

TFP = Tm – (TRIM / LBP * LCF)

TAP = TFP + TRIM

TFM = Tm – [ TRIM / LBP * (LCF ) ] TAM = Tm – [ TRIM / LBP * (LCF – 190) ]

11. Determine the stability of the vessel. The Free Surface Correction (FSC) is calculated by dividing the Total FSM by the Displacement. The Transverse Metacentric Height (GMt) is the value of the VCG subtracted from the Metacentric Height (KMt). The Available GMt (GMavail) is a measure of the stability of the vessel and is obtained by subtracting the Free Surface Correction from the Transverse Metacentric Height. The Required GMt (GMreq) is interpolated from the Required GMt Curve (page 20).

FSC = Total FSM / DISPL GMt = KMt – VCG GMavail = GMt – FSC The resulting Available GMt value must be greater than the Required GMt curve on page 21, for the particular mean draft.

GMavail > GMreq

12. Determine the heel at the existing vessel condition. The Moment to alter Heel One Degree (MH1) is calculated by multiplying π/180 (or 0.01745) times the Available GM times the Displacement. To determine the heel, the total Transverse Moment (Tmom) is divided by the Moment to alter Heel One Degree. Heel can be positive or negative. A positive answer indicates heel to starboard, and a negative answer indicates heel to port. This heel calculation method uses GM corrected with the USCG free surface moment correction; therefore, it provides a conservative estimate of heel.

MH1 = 0.01745 x GMavail x DISPL HEEL = Total Tmom / MH1

13. Blank Loading Condition pages 50 to 52 are provided for calculating a particular condition not found within this Trim and Stability Booklet.

BLANK FORMS

Summary Load Worksheet

Tank Load Worksheet

Mission Load Worksheet

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