Remember, in the first article of this series, we had mentioned that the value of GM needs to be obtained at various stages from design to construction of a ship. We had also mentioned that the purpose to obtain the value of this parameter at different stages differs from stage to stage. The first time when the metacentric height of a ship is estimated, is during its initial design stages using the following methods:
The purpose to calculate the GM at this stage of design is to compare it with the value obtained from empirical formulae, and decide on the requirement of iterations in the hull design. For conventional designs, the percentage difference between the two would be within 2 to 3 percent. However, in case of novel designs, the values obtained at this stage is solely reliable, not the ones obtained from empirical calculations. This article will discuss about the other two stages of ship design and construction where evaluation of GM is an absolute necessity and plays a major role in ensuring that the ship is stable, and built as per the requirements of the client. Stability Criteria: A number of criteria that are based on the shape and nature of the stability curve of a ship, are used to evaluate the stability of a ship. Remember, that since we are discussing about intact stability, we will only focus on intact stability criteria, i.e. to evaluate the point where the ship becomes unstable, the values of certain parameters will be obtained from the stability curve pertaining to the least favorable loading condition. Some of the features of the stability curve that are studied here are:
Some of the criteria used to assess stability of a ship are also based on the dynamic stability of the ship. So, what is dynamic stability? Whatever we have discussed in the previous articles on stability, we have only dealt with Static Stability, i.e. stability of a ship when it is static. You could imagine it as if you have photographed a ship that is heeling, and studied its stability for that static condition in the photograph. However, dynamic stability deals with the study of stability over a range of angle of heels on the curve of intact stability. For any given angle of heel, dynamic stability is the measure of the work done in heeling the ship to that angle, very slowly and while maintaining constant displacement. This is measured by the area under the static stability curve upto that angle, as shown in the figure below, where the grey shaded area is the dynamic stability of the ship at 30 degrees of heel. Figure 2: Dynamic Stability of a Surface Ship.So if at every angle of heel, the area under the static stability curve upto that angle is plotted, the curve for dynamic stability is obtained, which is shown in blue. This curve plots the amount of energy that the ship can absorb in order for it to heel upto a certain angle. As per as dynamic stability criterion is concerned, we are more interested in evaluating the Residual Dynamic Stability of the ship in the following conditions:
All the four above cases result in a heeling moment which can be plotted similar to that in Figure 1. The area between the heeling moment curve and the righting moment curve (curve of static stability) is the Residual Dynamic Stability, and is less than the Dynamic Stability in absence of any of these upsetting forces. This value is evaluated for every loading condition and is tallied with a criteria set by governing bodies. There are various international and national governing bodies that have established a set of criteria for ensuring adequacy in stability of ships. Some of these bodies are:
DND, India has set a series of stability criteria that are to be complied with, by all the ships serving for Indian Navy and Indian Coast Guard. Information regarding the same is classified, and hence, out of the scope of this article. Our focus will be on the criteria set for merchant ships that ply on national and international waters. These criteria are laid down by International Maritime Organization (IMO) in The IMO Code of Intact Stability for Merchant Ships. This code specifies the formulae that are used to calculate:
The above four parameters are used to plot the heeling arm curves for each condition. The GM values are calculated by carrying out stability calculations at each loading condition considering reduction in metacentric height due to free surface effect. The results are all plotted on a stability curve. The values obtained from the curve should follow the following stability criteria for all merchant ships:
The criteria mentioned above, are however, only a part of all the criteria mentioned in the code. If any criteria is not complied with, required changes are to be made in the loading conditions or tank capacities, or tank positions, depending on the criteria and which stage of design it is. The Inclining Experiment: An inclining experiment is carried out when the construction of the ship is completed up to a stage when all the components that contribute to the lightship weight have been installed. The primary purposes for carrying out an inclining experiment are:
It is always conducted by the shipbuilder because, at this stage, the shipbuilder must prove to the client that the lightship weight has not exceeded the design value. This is a very important milestone for the shipbuilder because, often, marginal increase in weight is likely to be observed due to various manufacturing constraints. It is due to this reason, a weight margin of approximately 15 to 20 percent is allowed in the technical contact. However, if the difference between the design lightship weight and that calculated during the inclining experiment exceeds weight margin mentioned in the contract, the shipbuilder must pay a penalty for each extra ton. The experiment is carried out by inclining the ship using known weights. The known weight is first shifted to one side of the ship, and the inclination is measured by means of under deck pendulums placed at various longitudinal positions along the center line of the ship. The bobs of the pendulums oscillate on battens with readings marked on them. The length of the pendulums are usually about 10 to 12 meters, and they are submerged in oil or a dense fluid so as to increase damping. When the ship is ready for the experiment, the weight is shifted on the deck in a transverse direction. This causes the ship to list. The ship is first allowed to settle down in this position and the deflection on the battens are measured on all the pendulums. The mean deflection is then calculated and considered as the value to be used for calculations. The same process is repeated by shifting the weight to the opposite side. In some cases, multiple observations are taken using different weights. Figure 3: Inclining Experiment of a Ship.The above figure shows an inclining experiment in which a known weight of ‘w’ tonnes has been shifted by a distance ‘d’. The deflection of the pendulum is read as ‘BC’ on the horizontal batten. As a result of shift of weight on the ship, the center of gravity of the lightship shifts from ‘G’ to ‘G1’. The metacentric height can then be calculated using the following expressions: Where, ‘W’ is the measured mass displacement of the ship; AB is the length of the pendulum used; BC is the mean deflection read on the batten. There are a number of precautions required to be taken in order to attain fairly accurate results, and they are to be ensured by the shipbuilder before the experiment commences:
Though the stability characteristics of a ship can be determined with considerable precision, most authorities and shipbuilders find themselves in a trap while quoting the primary characteristics like metacentric height and righting lever with great accuracy. This is because, a design cannot be replicated to the fullest, in the real world. Hence, a naval architect must be aware of the following reasons that often cause the real-time values to vary from the design values:
All that we have discussed till now is, the stability of a surface ship when it is intact. How is the stability of a ship affected when its hull is damaged? How is a ship designed to be safe even if one or two compartments are completely flooded? These are aspects that fall in the category of Damaged Stability of Surface Ships, which we will be our topic in the next article of this series. Disclaimer: The authors’ views expressed in this article do not necessarily reflect the views of Marine Insight. Data and charts, if used, in the article have been sourced from available information and have not been authenticated by any statutory authority. The author and Marine Insight do not claim it to be accurate nor accept any responsibility for the same. The views constitute only the opinions and do not constitute any guidelines or recommendation on any course of action to be followed by the reader. The article or images cannot be reproduced, copied, shared or used in any form without the permission of the author and Marine Insight. |