Chapter 6: Ship Stability and Trim. From my Book Principles and practice of Marine Engineering. Er.Praveen Kr Tyagi Chief Engineer (Asso-RINA-ENGLAND).
Chapter 6: Ship Stability and Trim
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6.1 Introduction
Ship stability is a fundamental aspect of naval architecture, ensuring that a vessel remains upright and returns to an upright position after being tilted by external forces like waves or wind. This chapter covers the basic principles of stability, center of gravity, buoyancy, metacentric height, types of equilibrium, and trim.
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6.2 Definitions and Key Concepts
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6.3 Conditions for Stability
Stable Equilibrium: M is above G
Unstable Equilibrium: G is above M
Neutral Equilibrium: M coincides with G
Stability condition:
GM = BM - BG > 0
(I = second moment of area, V = displaced volume)
Diagram 6.1: Stable, Unstable, and Neutral Equilibrium Conditions
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6.4 Types of Stability
Righting Arm (GZ):
GZ = GM \cdot \sin(\theta)
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6.5 Factors Affecting Stability
6.2: Effect of Free Surface and Cargo Shifting on Stability
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6.6 Stability Curves (GZ Curves)
These curves plot righting arm (GZ) vs. heel angle and help evaluate how much a ship resists heeling.
Diagram 6.3: GZ Curve with Key Points Marked
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6.7 Angle of Loll and Listing
Listing: Permanent heel due to uneven loading or damage
Loll: Heel occurs because GM < 0, leading to instability in calm water
Angle of Loll is dangerous because small external forces can capsize the vessel.
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6.8 Trim and Longitudinal Stability
Trim refers to the difference in draft forward and aft:
\text{Trim} = \text{Draft Aft} - \text{Draft Forward}
Longitudinal Center of Gravity (LCG) and Longitudinal Center of Buoyancy (LCB) are key in trim analysis.
If LCG > LCB, ship trims by stern
If LCG < LCB, ship trims by bow
Moment to Change Trim by 1 cm (MCT 1cm):
\text{MCT}_{1cm} = \frac{W \times d}{\text{Trim change in cm}}
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6.9 Use of Ballast and Anti-Heeling Systems
Ballast Systems adjust the draft and trim by moving water in tanks.
Anti-Heeling Systems use pumps or tanks to balance the ship during cargo operations or weather conditions.
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6.10 Practical Stability Guidelines
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6.11 Sample Calculation: Metacentric Height
Given:
Moment of Inertia (I) = 8000 m⁴
Volume Displaced (V) = 2000 m³
BG = 1.2 m
BM = \frac{I}{V} = \frac{8000}{2000} = 4.0\,m
GM = BM - BG = 4.0 - 1.2 = 2.8,m ]
Since GM > 0, the ship is stable.
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6.12 Summary
Stability is crucial to safe and efficient ship operation. A firm grasp of hydrostatics, forces, and trim allows engineers to anticipate and correct dangerous conditions like listing or capsizing.
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