A vessel in this context means a ship, a drilling rig, a hotel platform, or the like, the stability of which should be determined to ensure its safety. The stability of a vessel depends on its geometry as well as the amount and distribut¬ ion of its load. This means that the stability of a vessel is not constant and, thus, cannot be established once for all.

The stability of a vessel is expressed by its so called meta- centric height, that is defined and explained inter alia in B.Baxter: "Naval Architecture" , the English University's Press Ltd.

Extensive theoretical work has been done as regards stability requirements for drilling rigs and the like. In this connect¬ ion we refer to E. Numata, .H. Michelet and McClure: "Assessment of stability requirements for semisubmergable units", and Frank S. Chou: "Minimization scheme for the motion and forces of an ocean platform in random seas" .

Drilling rigs often are provided with stabilizing devices, and we refer to Norwegian Patent No. 128 811 in this connection.

Norwegian Patent No. 141 363 shows a semisubmergable support¬ ing platform provided with ballast weights moving on rails to dampen or rapidly to balance roll or pitch of the platform.

Irrespective of the platform or ship construction, determin¬ ation of its meta.centre height is an important parameter for determining the stability of a vessel.

The etacetre height of a vessel, in principle, can be determined indirectly by computing the metacentre height from the geometry of a ship or a drilling rig, and by

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computing the xαetacentre height, e.g. from the load that is introduced and its distribution on a ship, or from the distribution and weight of equipment taken on board a drill- g ing rig or the like. To this end, special computer programs have been developed, but this method involves uncertainties. It may, thus, be necessary to supplement such determinations with a more or less direct determination of the metacentre height by the aid of inclining experiments. 0

In an inclining experiment the vessel is made to incline by the aid of a known load and the inclining angle is determined. From the known load and the observed inclining angle the meta¬ centre height is calculated. 5

Figure 1 is a diagrammatical view of a vessel that has been made to incline by a known load w resulting in an inclining angle α. From the inclining angle α , the applied inclining moment (w-y) , and the displacement of the vessel, the stabi¬ 0 lity GM = the metacentric height, can be calculated accord¬ ing to the following expression:

GM = M δg V tg(α) 5 where

GM = metacentric height in the inclining direction

M = applied inclining angle _Q = inclining angle δ = density of water g = acceleration of weight

Vo = volume of displacement

The localization of the center of gravity (VCG) over keel kg is then determined with the expression:

kG = kM - GM

wherein

y = moment arm w = inclining weight

W = weight of the vessel Applied moment: M = w (tons) y(m)

kM can be found in calculated graphs or tables, so called hydrostatic tables/graphs.

The methods presently used involve extensive and time consum¬ ing book keeping of variable weights, localization of load, filling of tanks, calculation of correction factors due to free surfaces, etc. The main drawbacks of the present method are:

The uncertainty represented by such manual bookkeeping. Mis¬ calculations cannot be excluded, and it is difficult to calculate the weight of many different loads, etc. Possible errors may be difficult to discover, and if they accumulate, the answer may become more and more dubious.

Another disadvantage of the present manner of carrying out an inclining experiment is that it has to be made in fair weather and in calm waters.

Also, it is necessary that activities on board, like ordinary work, movement of the crew, consumption of fuel and fresh water, etc. must be minimized during the actual experiment.

It appears, inter alia from Robert L. Cornell: "Rethinking the inclining experiment" (Ocean Industry, May 1983) that the classical inclining experiment has certain drawbacks. It is, for instance, stated that inaccurate inclining experiments may hazard the safety of semisubmergable drilling rigs.

Out of consideration for the safety there is a need for an

improved method for determining the stability of a vessel, which method permits said determination to be carried out, e.g. on a drilling rig during normal operation, and to be _c carried out under the prevailing weather conditions.

According to the present method it is, thus, possible to determine the stability of a vessel during normal operation on board, under the prevailing weather conditions, which 0 means that it is not necessary to tow a vessel to calm waters in order to be able to carry out an inclining experi¬ ment.

According to the present method the inclining experiment is carried out by applying a varying inclining load to the 5 vessel or a drilling rig. The vessel is, thus, made to turn e.g. with an expected inclining angle α = approx. 0,5 . An enforced inclination of this kind may e. g. be achieved by pumping a liquid with a known rate of volume from one tank to another, preferably involving tanks that are located 0 symmetrically to the centreline of the vessel.

The tanks used for this purpose may be existing ballast tanks in the vessel, or they may be mobile tanks or 5 containers suitably arranged on oppsite sides of the centre¬ line about which centreline the vessel is to be inclined.

Such tanks or containers may e.g. be flexible containers

3 having a volume capacity in the order of 20 m , depending in the dimensions of the vessel. Said containers may be 0 connected with a pipeline and a pumping means having a known and adjustable capacity. Sea water may be used as the liquid to be pumped into said tanks.

A cyclic inclining moment may also be brought about, e.g. by 5 moving a load from one side of the vessel to the other, i.e. by the aid of a movable ballast means, based on the principle shown in Norwegian Patent No. 141 363. According to said Patent Specification a movable ballast means is used to dampen or rapidly to balance roll or pich movement of a platform.

Another possibility of enforcing a controlled inclination of the vessel is to move known loads by the aid of cranes in such a manner that the applied inclination moment is always knovm. Generally, it will, however, be practical to transfer ballast water from one tank to another, since most drilling rigs are already provided with systems permitting such transference from one ballast tank to another. Systems of this kind are well known in patent literature.

Figure 2 illustrates the principle of the new method, the inclining moment beeing applied dynamically with a known period, and not statically as in the conventional inclining method. For a drilling rig, as shown in Figure 2, this may, as mentioned above, be carried out by pumping water between two tanks, so as to make the drilling rig "turn" about an imaginary centre line. As mentioned, the inclination moment may be applied in any desired manner, provided that the quantity of the moment is always known.

In Figure 2 the application of the inclination moment is shown as a triangularfunction, however, said moment may ra¬ ther be applied as a sinus function or a square function.

The application of the inclination moment as a square function, may e.g. be carried out by a crane lifting and lowering a mass that is floating on the water, lifting it clear of the water surface and then lowering it in accordance with a predetermined cycle.

A platform in the open sea generally being in motion due to wind, waves, mass transport on board the platform, etc. the observed inclination angle resulting from the applied inclin¬ ation moment will to a certain degree be masked by the "natural" frequencies of the rig. If the period of the applied moment is longer than the oscillation period of the "natural frequencies of" the rig, however, it is possible to filter off the natural frequencies of the rig and other noise. Due to the fact that the inclination moment is dynamically

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applied, the inclination angle and consequently GM is sta¬ tistically calculable.

With the method according to the invention it is, thus, poss¬ ible to calibrate/controll the stability data used, e.g. on board a rig. The determination can be carried out in the field of operation without any necessity of disturbing the ordinary working routines.

If equipment for determining the stability according to the present invention is permanently installed on board a rig, the stability may be determined when required, especially during adverse climatic conditions, e.g. when a rig is ice-covered. Ice-covering of a rig will imply that an unknown weight of ice covers the rig. The effect on the rig of this ice is difficult to assertain, but the stability of the rig can easily be determined by the aid of the present method the metacentre height being measured directly even where an unknovm number of tons of ice is present as a load. Additionally it is possible to determine how much ice weighs down a vessel at any given time. This may be done, e. g. by comparing data received from the method according to the pre¬ sent invention before ice covering with data determined from the vessel with ice covering.

As mentioned above, the metacentre height is determined by the aid of the equation shown above, comprising, among others the varable M, which is the applied inclining moment, and the inclining angle α resulting from said inclining moment. A first approximation to be assumed is that ^α i ^{= kM} i ^{+ F} i wherein α. is the inclination angle resulting from the applied moment M. , F. = measuring noise, ΣF. being expected to be equal to o, and the quotient k being statistically de- terminable in a known manner.

It will appear from the following that the applied moment is relatively easy to determine, whereas the inclining angle α

being in the order of 0,5°, is easily masked by the "natural frequency" of the rig, that can be considerable and up to 3-4 in relation to α. Statistical measuring of the inclinat- ion will, thus, be dominated by the natural frequency of the rig. Additionally, slowly varying forces, e.g. current and wind, will cause statistical measuring errors and result in an uncertain determination of the metacentre height. By the method according to the present invention,applying an oscillating inclining moment to the rig and determining the inclining angle as a function of that, by the aid of titrat- ion and statistical methods for parameter estimation, the metacetre height is calculated. The period of the oscillat¬ ing inclinating moment must be longer than characteristic natural frequency periods of the platform. In parctical use, this means that the oscillating inclination moment is applied with a period of 20-100 minutes, which is consider¬ ably longer than the natural frequency period of a rig, typically being 30-40 seconds.

The determination of a parameter, as for instance the inclination angle, being superimposed on a statistically arbitrary error is made much mention of in the literature. In this regard, it is referred to e.g. A. Papoules: "Prob¬ ability, random variables and stochastic processes" (McGrave- Hill) , W.B. Dav/enport Jr: "Probability and random processes, and introduction for applied scientists and engineers" (McGrave-Hill) , Otnes and Enochson: "Digital time serious analysis" (John Wiley et Sons, 1972), and Eykhoff: "System identification" (John Wiley et Sons, 1977), and especially: "A Theoretical Analysis of Recursive Identification Methods", Aut atica Vol. 14, 78, 1978.

Now, the present method will be more closely described with reference to Figure 3, diagrammatically showing a system for carrying out the method.

In the Figure two ballast tanks are marked 1 and 2. 3 and 4 show the level indicators.

Two flowmeters are designated 5 and 6. 13 is a reversible pump. 7 is a microcomputer, 8 is an entry keyboard for the microcomputer, 9 represents a depth recorder indicating the draught of the vessel, 10 is an angle gauge, 11 also indic¬ ates an entry of possible environmental data, like wind force and wind direction, wave height and wave direction, anchor cable forces, water depth, etc., which data may be obtained by measuring and may be included in the calculations. 0

12 is a pump control unit, and 14, 15, and 16 are a display, a printer, and a magnetic tape station respectively.

The system operates as follows: A variabel moment M is 5 applied to, e.g. a platform to incline said platform to an angle α. In the shown embodiment said moment is applied by pumping water from tank 1 into tank 2 , said tanks 1 and 2 being arranged so that such a transport of water will provide an inklining moment. Moment M being applied at any given time _Q is continuously included in the calculation, the moved volume of water being measured by level indicators 3 and 4 and/or by flowmeters 5 and 6. Microcomputer 7 calculates the volume of water and multiplies it by the moment arm, so that the applied moment is always knovm. The moment arm and other 5 constants of the vessel in question are entered via keyboard 8, which is also the manual operation means of the system. In an actual experiment the density of water and the acceleration of the weight (g) are entered = constant values. The displace¬ ment (V) is obtained by the aid of the draught of the vessel, Q determined by the aid of the depth recorder and calculated in microcomputer 7. The instantaneous angle α. of the vessel is measured by angle gauge 10 , which may be a servo-inclino¬ meter. By letting the microcomputer filter the observed angul¬ ar travel and make the statistical calculations, the inclining 5 angle α. due to the applied moment M. is obtained and is then used in the equation shown above to calculate the stability GM.

Computer 7 also controls the reversible pump 13 via pump

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control unit 12. Also, computer 7 makes all necessary calcul¬ ations and presents the results on display 14 or printer 15. If desired, the provided dada are also stored on magnetic tape for up-dating later.

Due to the inherent statistical nature of the determination the effect of arbitrary errors the expected mean value of which is zero, will decrease with the number of measurements forming the basis of the determination of the metacentre height.

Normally all physical test data will be burdened with a certai test error or uncertainty, and practical experiments have e. g. shown that the determination of the level in a ballast tank shows an uncertainty of approximately + 3,8%, the de¬ termination of the inclination angle shows an error of - 2%. The determination of displacement shows an error of approx. - 0,8%. Despite the above mentioned uncertainties of the "separate determinations" it was found that the statistical uncertainty as to determination of the metacentre height is in the order of - 4%.

As will appear from the above mentioned the present method permits determination of the stability of a vessel expressed in the metacentre height, with high accuracy and in an easy and simple manner during ordinary operating conditions, and in such a manner that the determination itself does not to any significant degree influence e. g. the normal operating conditions of a drilling rig.

As stated above, the above described method is based on the following model: α. = kM. + F.. In practice this model has prooved to be satisfactory. However, this model may, if necess¬ ary, be made more precice by introducing more measurable varables the expected value of which differ from zero, e.g. the tension of anchor cables, wind conditions, current conditions, etc.

The inclination angle then may, for instance, be expressed: α. = kM.+k-,X, .+k_X ₂ . +F. , wherein X, . , ^x _? i ^{/ etc} * ^are measurable quantities, and k„ , k., are associated quotients. Estimates of k-, , k ₂ , k ₃ , etc. may be made in a known manner by multiple regression analysis . The net effect of the applied inclination moment can, thus, be determined.

The invention also relates to a transportable system for carrying out the present method, mainly comprising the components shown in Figure 3. The ballast tanks 1 and 2 of the system are transportable and may be arranged on a vessel in such a manner that the desired inclination moment is achieved, e.g. by filling the ballast tanks with water in a manner analogical to the description with reference to Figure 3. The amount of ballast water in said tanks may be determined as mentioned before, or they kan be placed on platforms provided with weighing cells . In the last mentioned case an uncertainty of measurement will be introduced due to acceleration forces that will influence the weighing results because of the natural movement of the platform. This mea¬ suring error, however, will be averaged out during the experiment period. For the sake of convenience, such trans¬ portable ballast tanks may consist of a flexible material, e.g. a plastic covered textile, in the shape of a bag having connecting means for supply hoses or the like. The transport¬ able ballast tanks may also be, e.g. folding cylinders having an approximately constant cross section so that the amount of liquid in each tank can be determined by the level of the liquid in the tank.

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