LESSON TOPIC: 4.4 TITLE: TRIM AND DRAFT
Contact periods allotted this LESSON TOPIC:
Classroom: 2.0 Test: 0.0
Trainer: 0.0 Total: 2.0
MEDIA: Classroom lecture with visual media
TERMINAL OBJECTIVES:
6.0 EVALUATE shipboard stability by analyzing weight and moment considerations. (JTI 3.2.1, 6.0, 6.1, 6.2)
ENABLING OBJECTIVES:
6.19 EXPLAIN why trim and loading affect intact stability.
6.20 COMPUTE the impact of longitudinal weight shifts, additions, and removals on the ship's trim and drafts.
6.21 Given a specified loading condition and draft readings, CALCULATE the required movement of solid or liquid loads to bring the ship to within acceptable limits of trim.
6.22 Given a predetermined amount of flooding damage, COMPUTE final trim and drafts.
6.23 DEFINE drag, trim, trimming moment, trimming arm, longitudinal center of flotation, parallel rise, parallel sinkage, and plunging.
6.24 DESCRIBE the movement of longitudinal stability reference points caused by weight shifts, additions, and removals.
LONGITUDINAL STABILITY AND TRIM
Design Waterline (DWL):

The waterline at which the ship is designed to float in the full load condition. Corresponds to a line in the middle of boottopping of the ship. 
Forward Perpendicular (FP): Aft Perpendicular (AP): 
A vertical line drawn at the point of intersection of the DWL and the stem of the ship. Important in the study of longitudinal stability as well as in frame numbering. A vertical line drawn at the point of intersection of the DWL and the stern of the ship. 
Length Between Perpendiculars (LBP): 
Distance from the FP to the AP. Found in the DC Book Part 1(a), and/or in the booklet of general plans. When not found there, use the Length Between Draft Marks (LBD) usually found on the Draft Diagram and Functions of Form. 
Midships Perpendicular (MP): 
A vertical line intersecting the ship's centerline, half the distance between the FP and AP. Symbol 
Longitudinal Center of Flotation (LCF): 
Geometric center of the ship's waterline plane. The ship trims about this point. May be forward or aft of the MP depending on the ship's hull shape at the waterline. 
Center of Flotation Distance: 
Distance from the LCF to the MP. Found using the Draft Diagram and Functions of Form, as a function of displacement. Used to distribute changes of trim between the fwd and aft drafts. 
Center of Buoyancy (LCB): 
The point through which the forces of buoyancy act, longitudinally. 
Drag: 
A design feature where the draft aft is greater than the draft forward. Primarily done to increase propulsion plant effectiveness. 
Trim: 
The difference between the forward and after drafts, in excess of design drag. 
Parallel Rise/Sinkage (PR/PS): 
When weight is removed/added from/to a ship at LCF, the forward and aft drafts will change by the same amount. 
Change in Trim (CT): 
The sum total of the absolute values of the change in forward and after drafts. EXAMPLE: D_{FWD} D_{AFT} Trim Original: 20FT 18FT 2FT b/b Final: 16FT 21FT 5FT b/s Change: 4FT +3FT 7FT b/s 
Trimming Arm (TA): 
The distance from the center of gravity of the weight to the LCF. If the weight is shifted, TA is the distance shifted. 
Trimming Moment (TM): 
Moment about the LCF produced by weight additions, removals, or shifts. , where w is the amount of weight added, removed, or shifted. 
Moment to Trim One Inch (MT1"): 
The moment necessary to produce a change in trim (CT) of one inch. Found using the Draft Diagram and Functions of Form. 
Tons Per Inch Immersion (TPI): 
The number of Long Tons added or removed necessary to produce a change in mean draft of one inch. (in salt water) 
LONGITUDINAL WEIGHT SHIFTS
When a weight is shifted longitudinally (fore 'n' aft) the net effect on a ship is similar to a seesaw, one end goes up and the other goes down. The pivot of the "seesaw" is located at the Longitudinal Center of Flotation (LCF).
To calculate the effect of shifting a weight longitudinally on the ship’s drafts, follow these steps:
1. Calculate the Trimming Moment (TM):
2. Calculate the Change in Trim (CT):
3. Calculate the change in forward draft (Dd_{FWD}):
The + or  sign depends on the location of LCF. If LCF is aft of MP use "+" and if LCF is forward of MP use "".
4. Calculate the change in aft draft (Dd_{AFT}):
NOTE: If the weight was shifted forward, Dd_{FWD} will be positive and Dd_{AFT} will be negative. If the weight was shifted aft, Dd_{AFT} will be positive and Dd_{FWD} will be negative.
Example Problem
The FOWK just completed a transfer of 6500 gallons of diesel fuel (diesel = 322 Gallons/LT). The fuel is now located 135 FT forward of it’s original position. Prior to transfer, the ship’s drafts were 16’9" fwd and 17’3" aft. Design Drag is 0.
LBP is 450 FT, MT1"=825 FTTons/inch and LCF is 24 FT aft of MP. The CHENG wants to know the new drafts and trim.
1. Calculate weight of fuel transferred:
2. Calculate the trimming moment:
3. Calculate the change in trim:
4. Calculate the change in forward draft:
5. Calculate the change in aft draft:
NOTE: Since the weight was shifted forward, the draft change at the bow is positive, and at the stern is negative.
6. Determine the new drafts and trim:
Forward Aft Trim
Original: 16'9.00" 17'3.00" 6.0" b/s
Change: + 1.83"  1.47" 3.3" b/b
Final: 16'10.83" 17'1.53" 2.7" b/s
LONGITUDINAL WEIGHT ADDITIONS AND REMOVALS
When weight is added or removed to/from a ship, the effects on longitudinal stability are evaluated as well. With the weight change, two things will happen:
1. The ship will sink or rise a few inches
2. The ship will trim about the Center of Flotation (LCF)
The easiest way to calculate the draft changes due to a weight addition/removal not located at LCF is to divide the weight change into two steps. First, assume the weight is added at LCF:
The added weight causes the entire ship to sink symmetrically in the water. This is called Parallel Sinkage. If the weight was removed, the ship would rise symmetrically out of the water, called Parallel Rise. To calculate the amount each draft changes due to parallel sinkage/parallel rise (PS/PR) use:
Next, transfer the weight from LCF to it's actual location. Although the weight was never really added at LCF then shifted, the end mathematical result will be the same as when the weight was added directly to it’s actual location.
This step of moving the weight to it’s actual location is identical to a weight shift problem. Again, to determine the change in the ship’s drafts due to trim:
1. Calculate the Trimming Moment (TM):
2. Calculate the Change in Trim (CT):
3. Calculate the change in forward draft (Dd_{FWD}):
The + or  sign depends on the location of LCF. If LCF is aft of MP use "+" and if LCF is forward of MP use "".
4. Calculate the change in aft draft (Dd_{AFT}):
NOTE: If the weight was shifted forward, Dd_{FWD} will be positive and Dd_{AFT} will be negative. If the weight was shifted aft, Dd_{AFT} will be positive and Dd_{FWD} will be negative.
The final step is to calculate the total change in draft forward and draft aft by considering both Parallel Rise/Sinkage and change in trim:
Example Problem
During VERTREP, all JP5 in tanks 53280J and 53440J is transferred. The Liquid Loading Report shows 57 LT in these tanks prior to transfer. The center of gravity of the combined tanks is 146 FT aft of MP. The CHENG wants to know the new drafts and new trim of the ship. Design Drag is 1’6" by stern.
LBP = 408FT MT1" = 775 FTTon/inch TPI = 32.4 LT/inch
Draft_{FWD} = 14’6" Draft_{AFT} = 15’0" LCF = 24FT aft of MP
1. Calculate parallel rise (PR):
2. Determine the Trimming Arm (TA):
3. Calculate the Trimming Moment (TM):
4. Calculate the Change in Trim (CT):
5. Calculate the change in draft forward due to trim (Dd_{FWD}):
6. Calculate the change in draft aft due to trim (Dd_{AFT}):
Since weight was removed aft, this is a forward trimming moment. The forward draft will increase and the stern draft will decrease.
7. Calculate the total change in draft forward (DDRAFT_{FWD}):
8. Calculate the total change in draft aft (DDRAFT_{AFT}):
9. Calculate the final drafts and ship’s trim:
FWD Draft 
AFT Draft 
Trim 

Original: 
14’ 6.00" 
15’ 0.00" 
1’0.00" by the bow 
Change: 
+3.25" 
5.72" 
8.97" by the bow 
New: 
14’ 9.25" 
14’ 6.28" 
1’8.97" by the bow 
EFFECT OF TRIM ON STABILITY
The Draft Diagram & Functions of Form and Cross Curves of Stability are prepared for ships based on the design condition: No Trim. For most surface ships, so long as trim does not become excessive (more than 1% of the length) these curves are still applicable.
RULES OF THUMB FOR TRIM
1. Maximum acceptable Trim is 1% LBP 

2. Follow Liquid Loading Instructions 

3. Watch for Hogging and Sagging Stresses 

PLUNGING
Definition: When the Trimming Moment exceeds the Longitudinal Righting Moment, and the ship sinks by the bow or the stern.
Loss of ships by plunging occurs more often in the merchant or auxiliary type ship than in the combatant type, although some destroyers have been lost in this manner. Merchant ships have much larger compartments, and the flooding of these compartments at the bow or stern trims the ship heavily.
TRIM CALCULATION SHEET
It is often desirable to consider the effects of several weights at once when computing draft changes. The Trim Calculation Sheet is a tabular form used to calculate the net trimming moment created by several weight movements.
DIRECTIONS FOR USE
1. In columns 1 and 2, describe the weight, tank number, flooded compartment, etc. and determine the weight (Long Tons) of each object.
2. Sum total the weights in column 2 to calculate the net weight addition or removal.
3. In column 3, determine the Trimming Arm (TA), the distance from the center of gravity of the weight to the ship’s LCF.
4. In either column 4 or 5, calculate the Trimming Moment by multiplying each weight by it’s Trimming Arm. A weight change causing the bow to sink lower in the water is a forward trimming moment, a weight change causing the stern to sink lower in the water is an aft trimming moment.
5. Sum total the forward trimming moments and aft trimming moments in columns 4 and 5. Take the difference between these totals as the NET Trimming Moment (will either be forward or aft based on the greater column total.)
6. Calculate Parallel Rise or Parallel Sinkage (PR/PS). Divide the net weight addition/removal by Tons per Inch Immersion (TPI, found using Draft Diagram and Functions of Form and ORIGINAL DISPLACEMENT.)
7. Calculate the Change in Trim (CT). Divide the net trimming moment by the Moment to Change Trim by 1" (MT1", found using Draft Diagram and Functions of Form and FINAL DISPLACEMENT.)
8. Calculate the change in draft forward due to trim (Dd_{FWD}) and change in draft aft due to trim (Dd_{AFT}) using the equations. If the net trimming moment was forward, Dd_{FWD} is positive and Dd_{AFT} is negative. If the net trimming moment is aft, Dd_{AFT} is positive and Dd_{FWD} is negative.
9. Fill in the box in the lower right corner by applying all changes to the original conditions.
Example Problem: USS STEPHEN W. GROVES (FFG 29)
Original Drafts: Fwd: 15'0" Aft: 15'3" LBP = 408 FT
1. 200 LT is added 20 FT forward of MP
2. 20 LT is removed 80 FT forward of MP
3. 50 LT is removed 30 FT aft of MP
4. 40 LT is shifted forward 20 FT
FIND: New drafts and new trim
