Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014
With such effort going into these aspects of the inclining experiment, it is important that the most accurate method of deriving the as-inclined KG and TCG should be used.
4.2 SETTING A STANDARD
A useful benchmark to use when judging improvements in the accuracy of the inclining experiment workup is the magnitude of the experimental errors to be expected. Unless any improvement is significantly greater than the inherent errors, it is of doubtful value.
For a detailed treatment of these errors, every naval architect should read Shakshober and Montgomery [7].
Figure 2: Armidale Class Patrol Boat (ACPB)
The full locus of the metacentre, the “metacentrique”, as the ship rotates through 360o is shown in Figure 1c. The metacentre moves significantly, even for a wall-sided form. It was Bouguer [3] who first described and named the metacentrique, and he must surely have recognised the inaccuracy which this introduced into the inclining experiment method which he devised.
While the initial movement is relatively slow, it is quite rapid by 45o heel. This may not be a significant problem if a ship is truly wall-sided throughout, but it certainly is for the patrol boat shown in Figure 2. The deadrise of the bottom of this vessel is less than 45o at the waterplane along most of its length, not unlike the box in Figure 1b, where movement of the metacentre is both significant and rapid.
Not only are flare and deadrise problematic, but chines and other knuckles can cause the metacentre to move erratically. There are cases of asymmetric vessels and, for these, the metacentric height differs depending on the direction of heel.
Clearly, any calculation of KG which relies on the assumption of a fixed metacentre will be up against the wall-sided limitations when it comes to delivering consistent, accurate results.
4. ACCURACY 4.1 DERIVATION OF THE LIGHTSHIP
A detailed ship check is undertaken to capture the masses on board which are not part of the lightship and any items not on board which should be included. Tanks are dipped at the beginning of the inclining experiment and any tanks which must remain in use during the experiment are dipped again at the end. These measures ensure that the derivation of the lightship from the as- inclined condition is as accurate as possible.
©2014: The Royal Institution of Naval Architects
At an inclining, all measurements are taken as accurately as possible. Readings of draughts, calibration of inclining masses, measurements
of mass shifts and pendulum
deflections each carry a potential error which will affect the calculated KG.
4.3 EXPERIMENTAL ERRORS
One means of judging the effect of experimental errors is to use the classic inclining Equation 4 to calculate the change in GM0 which would occur when all potential errors are combined.
The potential errors in KG for naval warships, ignoring any detrimental effects of adverse weather or avoidable causes of error, have been investigated. The average potential error over the fleet of RAN warships was found to be in the order of 0.01 m.
5. PROPOSED NEW METHOD
The inclining experiment can be regarded as a practical means of determining a portion of a vessel’s righting arm (GZ) curve over a small range.
5.1 EQUATING HEELING AND RIGHTING ARMS
After each mass shift, the vessel comes to rest so, for the vessel to be in equilibrium, there must be a righting moment of magnitude equal
to the heeling moment
created by the mass movement. Since
displacement remains constant during the
experiment, heeling and righting arms must similarly be of equal magnitude:
Heeling Arm Righting Arm (6)
Unless the vessel is exactly upright, the horizontal distance which an inclining mass moves is less than the slope distance across the deck. The heeling moment at equilibrium after a mass movement is therefore given by:
HeelingMoment cos (7)
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