What is the differences between initial stability and stability art large angles? Range of inclination angle The difference between the small and large angles of heel is due to the fact that at large angles the buoyant force vector does not pass through the metacentre (M). GZ is not equal to GM sinѲ The position of center of floatation M G 2018/2/9
Why do we need to do stability calculations at large angles?
Purposes to do stability calculations at large angles of heel 1. To improve compliance with various stability criteria, international stability regulations and codes for the carriage of movable bulk cargoes, such as grain or logs. 2. To determine the list of the vessel during heavy lift operation。 3. To evaluate and correct conditions of a ship damaged by flooding, mismanaged tanks, cargo shifting, grounding, or the results of free surface effect.
How do we estimate the stability of a vessel at large angles?
Method 1 KN Curve MR = GZ GZ = KN - KH = KN - KG sin
MR = GZ MR= (KN - KH) KN (m)—— The righting lever measured from keel KN = f( ， )，from “KN cross curve for stability” KH = KG sin ， GZ —— Righting Arm， GZ = KN - KH = KN - KG sin
Cross Curves of KN Cross Curves of Stability
Method 2 Assume the height of C. G. Cross curve of stability Ø
Method 3 Assume the position of Metacenter
Curve of Static Stability Angle of heel 0 15 30 45 60 75 90 GZ in meters 0 0. 86 2. 07 2. 45 1. 85 0. 76 -0. 5 These cross curves of stability show that the righting arm (GZ) changes with the change of displacement given the inclination angle of the ship.
• Cross Curves of Stability The results of the righting arm calculations for a ship are plotted as a set of cross curves known as cross curves of stability. These curves are used to determine the length of the righting arm at any angle of inclination for a given displacement.
For the sake of understanding ‘cross curves of stability’ clearly, here is a 3 -D plot of ‘cross curves of stability. ’
static stability curve ‘Curve of static stability’ is a curve of righting arm GZ as a function of angle of inclination for a fixed displacement.
Z (m) tagent 4 maximum GZ 3 GM 2 range of initial stability 1 radian = 57. 3 deg 1 angle of stability 10 20 maximum 30 40 50 range of stability GM= GZ/sinθ = GZ/θ Radians 1 radian = 57. 3° 60 70 Heel angle (deg)
• Influences of movement of G. C on ‘curve of static stability’ 1. Vertical movement (usually due to the correction of G. C position after inclining experiment. ) im GZ KG KG<KG 1 θ
• Influences of movement of G. C on ‘curve of static stability’ 2. Transverse movement (due to the transverse movement of some loose weight) Weight moving from the left to the right
Influence of beam of vessel on stability curve im
4. 2 Influence of freeboard im
Features of static stability curve G B GZ 0 2018/2/9 20 40 60 80 θ
• Analyzing A Curve of Static Stability 1. Initial slope of the curve (GM) 2. Angle of deck edge immersion(E) Point of contraflexure 3. Angle of maximum righting arm (B) 4. The range of stability 5. The angle of vanishing stability MR MH max MH B C A E GM O E 1 max 57. 3 D 2 (°)
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Chapter 6 large angles.ppt