Changes in Ship's Center of Gravity and Weight Distribution

Changes in Ships Center of Gravity Section 3.2

Center of Mass/Gravity Center of Mass/Gravity (G or CG) The weighted average over area or volume based on given distribution summed such that result is equivalent to the total force applied through a single point Similar to Center of Buoyancy for defining LCG Longitudinal Center of Gravity, x axis TCG Transverse Center of Gravity, y axis KG Vertical Center of Gravity, distance from Keel to Center of Gravity, z axis What can change the Center of Gravity? Add weight Subtract weight Shift (move) weight/change distribution

Important Points F (LCF, TCF) Go (LCG, TCG, KG) Bo (LCB, TCB, KB) So far we ve looked at ships that are in STATIC EQUILIBRIUM: Fx = 0 Fy = 0 Fz = 0 p = 0 BL K CL Now let s take a look at what happens when a weight is added to disturb this equilibrium!

Terminology G = Location of Center of Gravity for whole ship g = Location of Center of Gravity for singular object s= Displacement of ship (LT) w = weight of object placed/removed/shifted G or CG = Center of Gravity LCG = longitudinal Center of Gravity, x axis TCG = transverse center of gravity (left / right), y axis KG (aka VCG) = keel to center of gravity / vertical center of gravity, z axis

Move Weight Change in G A change in weight (either adding, removing or shifting it) causes a change in the location of G, the center of gravity of the ship z-axis Change in VCG (or KG) KGnew y-axis Change in the TCG TCGnew x-axis longitudinal CG (LCG) in x-axis (focus on later in Chapter 3)

Changes in Center of Gravity Z Y

Changes in Center of Gravity 3 Types of Weight Movements 1. Weight Addition 2. Weight Removal 3. Weight Shift = Weight removal + Weight addition Fleet Applications: Food on/off loads Weapons movements Hovering/trim operations Flooding Operational tests Removal of hatches Flooding or pump down of tanks for maintenance Fuel on/off loads Installation / removal of equipment

Weight Additions When a weight is ADDED, the G shifts TOWARD the added weight in line with the G of the ship and the g of the weight

Weight Removals When a weight is REMOVED, the G shifts AWAY from the added weight in line with the G of the ship and the g of the weight

Weight Shift In the case of a weight SHIFT, the G first shifts AWAY from the removed weight . and then TOWARDS the relocated (added) weight

Focus Z-axis Change in KG KGnew

KGNEW Let s first consider a weight added directly over the centerline This will cause the location of the G to move TOWARD the weight Resulting in a change in the VERTICAL distance, or KG

Calculating KGNEW for Weight Addition Use the concept of weighted averages to determine the KGNEW Notice this is g , not G so location from Keel (K) to where weight was added KGnew = + waddx Kg sold + wadd soldx KGold

Calculating KGNEW for Weight Removal It s the same deal for removing a weight, only this time the weight is negative (i.e. removed) This will cause the location of the G to move AWAY FROM the weight KGnew = soldx KGold + (-w) x Kg sold + (-w)

Calculating KGNEW for Weight Shift In a relocation (shift) of a weight, look at it as SUBTRACTING one weight, and ADDING that same weight at a new location.

Calculating KGNEW We can generalize the formula for vertical changes in G by the following: KGnew = sold. KGold + wi. Kgi sold + wi On Equation Sheet (Chapter 3) i represents an infinite number of weight additions/removals all added together. (+w) for weight additions (-w) for weight removals

Focus Y-axis Change in the TCG TCGnew

TCGNEW Imagine this is a slice of the very back of the ship. You are looking in the forward direction: tcg is (-) for Port (on the left) of centerline tcg is (+) for Starboard (on the right) of centerline

Calculating TCGNEW Similarly to KG, we can also calculate for this for transverse (left/right) changes of G to solve for TCGnew this term is w times tcg is for the value of w and/or tcg TCGnew = sold. TCGold + wi. tcgi sold + wi On Equation Sheet (Chapter 3) tcg is (-) for Port of centerline tcg is (+) for Starboard of centerline (+w) for weight additions (-w) for weight removals

Review Change in Z-Axis gives us ____? KGNEW Change in Y-Axis gives us ____? TCGNEW Port (left) of centerline is ____? Negative Starboard (right) of centerline is ____? Positive

Overall Calculation for Change in G Combining Changes in KG and TCG Real world - happens simultaneously Subdivide into 2 axis for easy analysis (z and y axis) Qualitatively determine new location of G (sketch) Determine KGNEW and TCGNEW separately Compare qualitative estimate to quantitative work Putting it all together - this is a change in the ship s _________? List Rotational motion about the x-axis due to weight change

Equation Sheet Familiarity

Problem Solving Technique 1. Draw a Sketch for Qualitative Analysis A. Addition toward, removal away, shift addition then removal 2. Find s (Given or Curves of Form) 3. Write Base Equation 4. Substitute Numerical Values and Calculate 5. Engineering Check on Value vs. Qualitative Analysis

KGNEW Example Problem Given: USS CURTS (FFG-38) floats on an even keel at a draft of 17ft KG = 19.5ft Lpp = 408ft Takes on 150LT of fresh water in a tank 6ft above the keel on the CL Find: New vertical center of gravity (KGNEW) after taking on water

Step 1: Draw a Sketch

Step 2: Find s when floating at 17ft draft Need to utilize Curves of Form s = 147 x 30LT s = 4410LT

Step 3: Write the GENERAL Equation soldx KGold sold + wi KGnew = + wix Kgi

Step 4: Substitute in values into the general equation soldx KGold sold + wi KGnew = + wix Kgi KGnew = 4410LT x 19.5ft + 150LT x 6ft 4410LT + 150LT KGnew = 19.10 ft

Step 5: Engineering Check: Does this answer make sense? YES! The G shifts toward the added weight, lower than the original KG (19.5 ft) KGnew = 19.10 ft

TCGNEW Example Problem 1. Draw a sketch 2. Find s (Given or Curves of Form) 3. Write Base Equation 4. Substitute Numerical Values and Calculate 5. Engineering Check on Value

TCGNEW Example Problem

Questions?