Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014 BACK AGAINST THE WALL
R J Dunworth, Department of Defence, Navy Engineering Division, Australia (DOI No: 10.3940/rina.ijsct.2014.b2.163) SUMMARY
An inclining experiment is the established method used to determine the vertical centre of gravity of a ship. At the same time, the other lightship properties can be found — displacement and the longitudinal and transverse centres of gravity. Only in exceptional circumstances will the traditional method of calculating KG deliver a completely accurate value due to the dependence on wall-sided theory. Although the result may be acceptable for large vessels which tend to be wall sided (or nearly so) at the inclining waterplane, there can be significant error on small vessels which typically have more shape in that region. The problem is discussed and the magnitude of potential error is investigated. An alternative calculation method is proposed, with validity demonstrated by calculation and example. The method overcomes the drawbacks of the classic calculations and allows the evaluation of KG and TCG of any hull form, inclined to any angle of heel or trim. This paper expands on a previous paper, Up Against the Wall, by the author [1].
NOMENCLATURE
Displacement of the system (ship plus inclining masses) (t)
BM0 Height of the transverse metacentre above the centre of buoyancy (m)
d Distance of inclining mass shift (m)
Angle of heel (degrees) GG’ Shift of centre of gravity (m) GM0
Transverse metacentric height when upright (m)
GZ Righting arm (m) HZ Heeling arm (m) HZ0 Heeling arm when upright (m) KG
Height of vertical centre of gravity above baseline (m)
KGI Estimated height of vertical centre of gravity above the origin, in global coordinates, with inclining masses in their initial position (m)
KGL Estimated height of vertical centre of gravity above baseline, in local (ship) coordinates, with inclining masses in their initial position (m)
KM0 Height of transverse metacentre above baseline (m)
KN Righting arm about the origin (m) KN0 Righting arm about the origin when upright (m)
Density (t/m3)
TCB0 Transverse centre of buoyancy when upright (m)
TCG Transverse centre of gravity (m) TCG0 Estimated transverse centre of gravity when in upright equilibrium (m)
TCGI Estimated transverse centre of gravity of the system with inclining masses in their initial position (m)
w Inclining mass (t) 1.
The concept proposed in
mathematics at INTRODUCTION
of an inclining experiment was first 1697 by
Hoste [2], a professor of the Royal Naval College in Toulon, France, but it was nearly fifty years before a practical ©2014: The Royal Institution of Naval Architects method of conducting an inclining experiment was described in 1746 by Bouguer [3].
The first inclining was conducted two years later at the Brest naval shipyard on the 74-gun ship Intrépide by Clairin-Deslauriers [4]. At that time, the French navy was fighting in the War of the Austrian Succession and had recently suffered defeats by the British in the first and second battles of Cape Finisterre. Gaining an advantage through the ability to carry more sail was of great importance to the navy. Metacentric height GM0 was used to determine a ship’s stiffness and, hence, the sail-carrying capacity.
The traditional calculation associated with an inclining experiment led directly to a value of GM0 and, as this was the primary measure of
stability, it was not
necessary to know the position of KG itself until the development of the concept of GZ by Atwood and Vial de Clairbois [5] in 1798. By that time, Bouguer’s calculation method was well established and continues to be used to this day.
The Australian Department of Defence requires regular inclining experiments on Royal Australian Navy (RAN) vessels to monitor the growth in displacement and KG which is
a common phenomenon on naval ships.
Communication, navigation and armament equipment increase with time and tend to be placed high up.
Conversely, when heavy machinery low down in the ship is upgraded, it is often replaced with more efficient, lighter equipment.
Without compensation, these effects almost guarantee that KG will rise over time. Growth must be captured and updated regularly in the stability information provided to ships.
For the RAN, stability is managed by comparison of a load condition’s KG with a curve of limiting KG. If KG has been over-estimated, then unnecessary operational restrictions may result but, if KG has been under- estimated, then the vessel may be at risk if it encounters
B-99
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80 |
Page 81 |
Page 82 |
Page 83 |
Page 84 |
Page 85 |
Page 86 |
Page 87 |
Page 88