EP1749739A2 - Method of obtaining vessel stability parameters - Google Patents

Abstract

This process is for carrying out the inclining experiment on ships by means of inclinometers and its fundament is an algorithm developed to be able to use gravitational inclinometers on ships discriminating the component of the signal due to the roll angle, even though the ship is rolling, and in a methodology that its fundament is to consider the equilibrium conditions from a dynamic point of view taking into account the perturbations of the roll torque, distinguishing it from the traditional methodology, based on static consideration of the process. The procedure is materialised in equipment that consists of an original system to calibrate the inclinometer and another system, that allows to register the evolution in time of the measurement, analyse it and establish reliability indexes. The system developed also allows to determine the centre of gravity of the ship by means of a new system independent of the inclining experiment.

Description

• It is to do with a process to obtain the stability parameters of ships, applicable to all types of ships and floating artefacts. From now on, the term ship includes all: ships, vessels, yachts, floating artefacts, semi submergible vehicles, etc.
Technical section
• The invention is related to the ship building field, more specifically with the inclining experiment carried out on ships, necessary to determine the parameters regarding its stability, specifically the initial metacentric height (GM) and the centre of gravity.
State of the art
• Of all the parameters that define the initial stability of a ship, the only one that is not possible to obtain, with the sufficient precision, by theoretical calculations is the vertical position of the centre of gravity. To obtain this parameter an experimental process is carried out with the ship denominated "the inclining experiment".
• The inclining experiment is a test required by the Maritime Authorities with newly built ships (before leaving the ship yard) and with all those ships that have been subjected to any structural alteration. The test is definitive to know all the parameter indicators of the characteristics of the stability of a ship, therefore its importance and is compulsory to carry out.
• The inclining experiment basically consists in subjecting the ship to different known roll torques, generally by moving weights from side to side of the ship, and measuring, for each roll torque, the roll angle adopted by the ship, in each one of the static equilibrium conditions. Also with the test other data is taken (draught marks of the ship when it straitens to obtain, by means of the hydrostatic curves, the displacement and the position of the metacentre, a series of weighs of the ship (magnitude and position), its own, including those that do not form part of its light ship weight, and others; free surfaces etc.). With the information obtained and applying basic hydrostatic laws are obtained the parameters wanted: transversal metacentric height and vertical position of the centre of gravity.
• Logically, due to the nature of the test, while its being carried out no activity can be done on the ship, except that of the inclining experiment itself, and no other people can be on the ship than those dedicated in carrying out the inclining experiment.
• Due to the traditional point of view the test is dealt as a static process, when the weather conditions (wind, waves, etc.) are relatively unfavourable, the inclining experiment can not be carried out.
• Currently the measurement of the roll angle, in the inclining experiment, is carried out, mostly, by pendulums. The use of inclinometers is contemplated in resolution A749 (18) of the International Maritime Organization, (I.M.O.).
• The technical problem presented in the use of pendulums in the measurement of the roll angle is that, in the immense majority of the occasions, the process in which the inclining experiment is carried out is a dynamic process and not a static process. That is, according to the theory in which the traditional methodology is based on, the only roll torque to which the ship is subjected to, is that due to the static torque produced by the different layouts of the weights used in the inclining experiment, notwithstanding, the reality is very different: being the ship out in the open, it is subjected to the action of uncontrolled roll torques provoked by gusts of wind, action of the waves, unexpected tensions of the mooring lines, etc. This causes the ship not to acquire a static roll angle but to oscillate around the different equilibrium positions.
• From the static point of view of the process, the mentioned above is correct, that is, if we represent de evolutions of the roll torque and the roll angles and the pendulum angles, as a function of time, these would be strait horizontal lines and the pendulum angle would coincide, within the error margins of the measurement, with the roll angle. There would also be a biunivocal correspondence between the roll angle (pendulum angle) and the roll torque.
• Never the less, the dynamic point of view of the process of each equilibrium condition of the ship in which the measurements are carried out is a combination of two dynamic systems: the ship being one and the pendulum the other.
• In this case (dynamic), the evolutions of the pendulum angle do not coincide with the roll angle and there is no biunivocal correspondence with the roll torque. That is, in a given instance, the pendulum angle does not coincide with the roll angle which does not coincide with the corresponding roll torque in that instant.
• With the traditional methodology it is presumed that the pendulum oscillates around an equilibrium position which coincides with the roll angle due to the "known" roll torque. The reality is that the equilibrium position mentioned, around which the pendulum oscillates, will fluctuate in accordance with the variations of the roll torque.
• On the other hand, the traditional methodology recommends that the pendulums used be as long as possible with the purpose of obtaining the greatest precision possible in reading the roll angle. This presents problems, in occasions, to find the adequate place for the pendulums on the ship and in the comfort of the observer (an essential factor in the measurement) to take the readings.
• It is important to note that the readings of the pendulum in the dynamic case differ notably from the case when dealing with a static process. In the static case, the pendulum remains in a fixed position and the observer has all the time he needs to carry out the reading. Notwithstanding in the dynamic case, the pendulum is continuously moving, therefore there will be errors associated with the observer.
• In brief, using pendulums, in measuring the roll angle in the inclining experiment presents a number of disadvantages:
• It is a dynamic system and the evolutions of the angle formed with the vertical (which is the measurement given) do not follow the evolutions of the roll angle produced by the uncontrolled roll torques produced during the measurement, therefore introducing errors in the measurement.
  These errors are greater when greater are the uncontrolled roll torqueses reaching a limit where the inclining experiment must be suspended.
• There is no record of the measurement and it is left to the skill of the observer the register of the measurement which introduces a subjective factor leading to errors associated with the observer
• The fact that the pendulums are of great length presents, in occasions, problems to find an adequate place and with the commodity for the observer, an essential factor in the precision of the measurement.
• The use for systems based on inclinometers, instead of pendulums, in the measurement of the roll angle presents basically two advantages and a difficulty in the case of gravitational inclinometers.
• The advantages are:
• The system registers directly the roll angle therefore it eliminates the dynamic system of the pendulum.
• Registers and stores the evolution in time the roll angle during the time the measurement is carried out. The analysis of this register allows determining with more precision the measurement of the roll angle.
• The inclinometer can be classified in two big groups:
• Inertial. They are those that, whether static or dynamic, generate a signal proportional to the inclining angle.
• Gravitational. They are those that take as a reference the acceleration of gravity. In reality they are accelerometers that, in static, generate a signal proportional to the sine of the inclination angle. Never the less in dynamic, they are affected by the accelerations in the direction of the measurement.
• The difficulty, which we referred to previously, in the use of gravitational inclinometers in the measurement of the roll angle is when the ship is oscillating around the equilibrium position, the reading of the inclinometer is affected by the acceleration induced by the roll motion.
• Never the less, the present invention incorporates an algorithm, understood as an ordered and finite set of operations that permit find the solution of a problem, in which, from the register of the gravitational inclinometer, is obtained the component due to the roll angle that the ship adopts in each instant.
• The invention also analyses the temporized evolution of the roll angle and establishes quality indexes of the measurement.
• In the same way it includes an original procedure of calibration/check of the roll angle measurement system with the purpose of giving the necessary reliability to compile with the requirements of the I.M.O.
• Finally, The system is susceptible to be implemented with the connections of an anemometer and a weather vane with the purpose of recording simultaneously with the roll angle, the direction and velocity of the wind, which will allow increase the features of the system, being able to carry out the inclining experiment in weather conditions which, with the traditional methodology, is not done.
Detailed description of the invention
• The present invention refers to a procedure to obtain the parameters of the stability of ships, specially the initial metacentric height (GM) and the position of the centre of gravity, by means of measurements with inclinometers and is carried out in three modes of execution.
• The procedure to carry out the inclining experiment on ships by means of equipment based on the use of inclinometers has its fundament in an algorithm developed to be able to use gravitational inclinometers on ships discriminating the component of the signal due to the roll angle, even though the ship is rolling, and it is a methodology that has its fundament in considering the equilibrium conditions from a dynamic point of view taking into account the perturbations of the roll torque. The procedure is materialized in equipment that has an original system to calibrate the inclinometer and another system that allows to register the evolution in time of the measurement, analyse it and to establish reliability indexes. The developed algorithm also allows determining the centre of gravity of a ship by means of a system independent of the inclining experiment.
• The first method consists in obtaining the stability parameters by carrying out the inclining experiment based on the measurement and register, by means of inclinometers, of the roll angle of the ship in different equilibrium conditions in which are based the inclining experiment, and also in the analysis of the register of the roll angle, which allows to consider the dynamic effects, that are produced in the equilibrium conditions mentioned, due to uncontrolled torques (mainly gusts of wind and waves) and evaluate zones of the register where the reliability of the measurement of the roll angle is greater. This mode of execution is applicable to inertial inclinometers as to gravitational inclinometers since in the case gravitational inclinometers are used an algorithm has been developed which allows to filter the component of the signal from the inclinometer due to the roll angle, eliminating the component due to the rolling motion of the ship.
• The second mode consists in determining the centre of gravity of the ship by means of the analysis of the registers of two gravitational inclinometers situated on the centre line, on the same vertical and at different heights above the base line of the ship.
• The third mode consists in determining the ships roll natural period by means of a procedure based on the spectral analysis of the roll register obtained with the inclinometer. From the roll natural period is determined the ships GM from the formula which relates them: $$\mathit{GM}={\left(\frac{\mathit{K}\mathit{\cdot }\mathit{B}}{{\mathrm{T}}_{\phi }}\right)}^2$$

  

  Being B, the ships breadth, T_φ, the natural period of the ship and K a coefficient which is obtained from some preliminary trials done with the ship.
• Bellow are described the stages the invention is based on. The object procedure of the invention is described in the two modes it is carried out.
• 1^a) Checking, calibrating and setting to zero of the inclinometer. The first stage consists in checking, calibrating and setting to zero the inclinometer and is done on land by means of the following pieces: a coupling of the inclinometer (figure 1), a levelling platform (figure 2) and different calibrated angle generators (figure 3), and following the methodology developed specifically for this purpose. The material which constitute the pieces must be rigid, in deformable and of a very low thermal expansion coefficient, inferior to 2x10^-5 °K^-1, as for example methacrylate. The measurements of the pieces must satisfy the following conditions and there are infinite sets of measurements, maintaining the proportion of the pieces, with which can be built the system of pieces.
  The methodology developed is the following:
  The inclinometer (E) is fixed to the couplings (A) as is represented in figure 1. The coupling is built from a rectangular prism whose top surface (where the inclinometer is placed) and bottom surface are perfectly parallel. At the ends of bottom surface are fitted two cylinders, D, calibrated of 6 mm diameter. The cylinders are parallel and there axes are separated a distance B of 101.56 mm, or multiples. The thickness of the piece, C, will be sufficient to give rigid ness to the piece, at lest, 10 mm.
  On a stable table is placed the piece represented in figure 2, which is a levelling platform (K) and that consists in a horizontal board of perfectly smooth surfaces. The platform rests on the table by means of three screws H,I and J. The screws H and I are separated a distance (F) of, a minimum, of 120 mm and on the top part are some controls to be handled with the hands. Screw J is separated a distance (G) of, a minimum, of 100 mm from the line that connects H and I and is stamped on the platform to allow space for the manoeuvres that are done with the inclinometer.
  With the help of a two dimensional spirit level and the levelling screws, H and I, the platform is levelled with the precision of the spirit level.
  Following, the inclinometer is used with a level of precision of a hundredth of a degree. For this it is placed in the levelling direction (parallel to the line that connects the levelling screws, H and I) and a reading is taken. Then the inclinometer is turned 180° and a second reading is taken. A correction is made with the levelling screws, H and I, looking for the convergence of the two readings. The process is repeated until both readings are the same. At this moment the platform is level in the levelling direction with a precision of a hundredth of a degree and is taken as the zero of the inclinometer.
  With the help of the calibrated angle generators, which are pieces as the reflected in figure 3, placed on the levelling platform and in the levelling direction, with a value of L of 100.00 mm and with different values of M and N, adjusted to the hundredth of a millimetre, angles adjusted to a hundredth of a degree are succeeded, placing the coupling piece of the inclinometer (with the inclinometer), represented in figure 1, as indicated in figure 4. With this the calibration of the inclinometer is checked. If necessary, and with the help of these pieces, the calibration of the inclinometer is carried out.
• 2^a) Register, by means of the inclinometer, of the temporal evolution of the ships roll angle.
  The inclinometer is installed on the ship on the centre line with its sensitive axis in a perpendicular direction to the centre line. Depending on the mode it is carried out you proceed in a different manner.
  In the case that the stability parameters are obtained from the inclining experiment, only one inclinometer is installed which will register the evolutions of the ships roll angle in the different equilibrium conditions in which the inclining experiment is based. It is recommendable that the length of the registers be over ten times the roll natural period of the ship.
  In this case, if the inclinometer used is the gravitational type, the register will be processed by means of an algorithm developed to filter the component of the signal of the inclinometer corresponding to the roll angle. The hypothesis, on which the algorithm is base, is the following:
  • The perturbation accelerations of the signal are due to transversal accelerations induced by gyrations with respect of an axis.
  • The angles that are produced must be such that the difference between the angle (expressed in radians) and the sine of the angle is inferior to the precision established in the measurement.
• In the case of the inclining experiment these conditions are kept since the roll oscillations are very small and are carried out around the longitudinal axis that passes through the ships centre of gravity and the angles that are produced are of an order of 2 degrees.
• To explain the algorithm lets presume that the inclinometer is at a height "h" over the gyration axis and subjected to an irregular oscillating motion, the process is the following:
• 1°) The Fourier transform of the inclinometers register is done.
• 2°) Each harmonic of the Fourier transform is corrected by the following manner: $$\phi \mathrm{=}\frac{\mathrm{g}}{\mathrm{g}\mathrm{+}{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}}\mathrm{C}$$
  
  If h is above the gyration axis. $$\phi \mathrm{=}\frac{\mathrm{g}}{\mathrm{g}-{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}}\mathrm{C}$$
  
  If h is under the gyration axis.
  Being:
  • φ: the roll angle amplitude corresponding to the harmonic
  • g: the gravity acceleration
  • ω: the angular frequency of the harmonic
  • C: the amplitude of the inclinometers signal corresponding to the harmonic
• 3°) All the harmonics and the signal obtained of the corresponding the register of the evolution of the angle in time are added.
  In the case of obtaining the ships centre of gravity by means of the analysis of the registers of two gravitational inclinometers, two gravitational inclinometer are to be installed, on the same vertical and at different heights on the ship, and the temporal evolution of the roll angle of both is to be registered.
  In the second and third mode of execution, the recommended length of the registers is to be of an order of a hundred times that of the ships natural period.
• 3^a) Analysis of the registers obtained.
  The last stage consists in the analysis of the registers of the evolution in time of the roll angle, obtained in the previous stage. Also in this stage, the analysis of the registers is different depending of the mode in carrying out the procedure object of the invention.
  In the case the stability parameters are obtained from the inclining experiment, the analysis consists in determining the zone of the register where the uncontrolled roll torqueses (due to gusts of wind, wavs, etc.) were the minimum. Establishing, in the first place, the sequence of maximum and minimum of the register and the instances where they are produced these maximum and minimum. Then, from the previous relation, is defined a new relation of the ships roll angles, together with the instants they where produced, corresponding to the roll torques that have acted on the ship during the register. Finally doing a statistical analysis of this last relation the optimum zone of the register is defined and with it the roll angle associated to the register which will be the average of the roll angle of the optimum zone of the register and the error associated to the measurement of the roll angle, which will be the mean quadratic error of the roll angles mentioned.
  In the case that the stability parameters are obtained by the second mode of execution of the invention, the analysis of the registers is base on the algorithm developed to "filter" the component of the roll angle of the signals produced by the two gravitational inclinometers.
  In the case that the stability parameters are obtained by the third mode of execution of the invention, the analysis of the registers consists in a procedure based on the Fourier transform.
Description of the figures.
• Figure 1 represents the coupling (A) of the inclinometer (E). The referred coupling is built from a rectangular prism where the top surface (where the inclinometer lies) and the bottom surface are perfectly parallel. At the ends of the bottom surface are fitted two cylinders, D, calibrated with a diameter of 6 mm. The cylinders are parallel and there axis are separated a distance B of 101.56 mm, or multiples. The thickness of the piece, C, will be sufficient to give rigid ness to the piece, at lest, 10 mm.
• Figure 2 represents the levelling platform (K) and consists of a horizontal board with perfectly smooth surfaces. The platform lies on the table on three screws H, I and J. Screws H and I are separated a distance (F) of, a minimum, of 120 mm and the top part has some controls to be handled by hand. Screw J is separated a distance (G) of, a minimum, of 100 mm from the line that connects H and I and is stamped on the platform to allow space for the manoeuvres made with the inclinometer.
• Figure 3 represents the calibrated angle generators, which are U shaped pieces, with a value of L of 100.00 mm, or multiples and with different values of M and N, adjusted to a hundredth of a millimetre, to obtain angles of a hundredth of a degree.
• Figure 4 indicates how to place the different pieces to obtain the calibrated angles to a hundredth of a degree. For this you place, on the stabilizing platform (K), the calibrated angle generator (Ñ) and on this, the coupling piece of the inclinometer (A) (with the inclinometer (E)). The angle the inclinometer in the figure is subjected to is arcsine(N/B). In turning the coupling piece (with the inclinometer (E)) 180°, the angle obtained is - arcsine(N/B). If the coupling piece (A) (with the inclinometer (E)) lies in such a way that the cylinder (D) lays on the side at a distance M, the angles arcsine(N/B) and -arcsine(N/B) are obtained.
1^st Mode in execution of the invention: Inclining experiment.
• The procedure to obtain the stability parameters by means of the invention consists in doing the inclining experiment, but using an inclinometer instead of a pendulum for the measurement of the roll angle. The stages of this execution mode are the following:
  1°) Checking / calibrating and setting to zero of the inclinometer. Its done on dry land before starting the inclining experiment. For this you place the levelling platform (figure 2) on a stable table and, with the help of a two dimensional spirit level, you level. Afterwards the inclinometer is used, which is place in the coupling piece as is shown in figure 1, as precision level, placing the levelling platform in the direction parallel to the levelling screws (H and I of figure 2), taking readings of the inclinometers signal. Later you turn the inclinometer 180° and again reading is taken. If the readings are not the same, the levelling screws are adjusted until the two reading converge. At this moment the inclinometer is in a horizontal position with a precision of a hundredth of a degree and in this position the reading should be "0.00°". If this were not the case, the assigned inclinometer would take that value as "zero".
  Next, and according to the indicated in figure 4, the inclinometer (E) is placed in its coupling piece (A), with the different angle supplied by the calibrated angle generators (N), which, at the same time, are on the levelling platform (K), and the calibration of the inclinometer is checked. In the case it should be necessary, and with the help of these pieces, the inclinometer would be newly calibrated.
  2°) Register, by means of an inclinometer, of the ships roll angle. Once calibrated, the inclinometer is placed anywhere on the ship, the only condition is that of being on the centre line.
  The length of the roll angle registers is established in function of the ships natural period and which will be 10 times greater than the natural period of the ship. Supposing that the ships natural period is around 10 seconds. In that case the length of the register will 2 minutes.
  In the case the inclinometer used is the gravitational type, the coordinates of the point where the inclinometer is placed is written down, also the ships trim, and with the purpose to determine the distance of the mentioned point to the horizontal axis that passes through the ships centre of gravity. Let this distance be called h. As it is obvious, initially the ships centre of gravity is unknown (which is one of the parameters which is intended to be obtained) and, consequently, the value of h is unknown. This problem is solved by means of an iterative process: In the first place an estimated value of the ships centre of gravity is assigned. Next the process is executed obtaining the position of the centre of gravity. The process is repeated with the value of the centre of gravity obtained in the first iteration, etc. The process converges in two iterations.
  In this case, in which the inclinometer used is the gravitational type, an algorithm developed to filter the component of the register of the inclinometers signal corresponding to the roll angle will be used and which consists in:
1. a) Doing the Fourier transform of the inclinometers register.
2. b) To correct each harmonic of the Fourier transform in the following manner: $$\phi \mathrm{=}\frac{\mathrm{g}}{\mathrm{g}\mathrm{+}{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}}\mathrm{C}$$
   
   If h is above the gyration axis. $$\phi \mathrm{=}\frac{\mathrm{g}}{\mathrm{g}-{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}}\mathrm{C}$$
   
   If h is under the gyration axis.
   Being:
   • h: the distance to the horizontal axis that passes through the ships
   • centre of gravity
   • φ: the amplitude of the roll angle corresponding to the harmonic
   • g: the gravity acceleration
   • ω: the angular frequency of the harmonic
   • C: the amplitude of the inclinometers signal corresponding to the harmonic
3. c) All the harmonics and the signal obtained corresponding to the register of the evolution in time of the ships roll angle are added.

3^a) Analysis of the register and obtain the ships stability parameters The following step is to obtain the roll angle. For this is applied the following procedure:
• With the register obtained by the inclinometer, A relation of maximums and minimums is generated with the instances they are produced:

t1	M1
t2	m2
....	....
tn	mn

Where the capital ms indicate the maximums and the lower case ms indicate the minimums and t₁, t₂, ..., in are the instants the maximums and the minimums are produced.
• From this table are eliminated those pares of consecutive maximums and minimums with a time separation of less than 1.5 seconds (filtering harmonics with a period less than 3 seconds).
• From the previous table is constructed a new table whose first element, $\frac{\left({\mathrm{M}}_{\mathrm{1}}\mathrm{+}\mathrm{2}{\mathrm{m}}_{\mathrm{2}}\mathrm{+}{\mathrm{M}}_{\mathrm{3}}\right)}{\mathrm{4}}\mathrm{,}$

corresponds with the second from the old table and the last, $\frac{\left({\mathrm{M}}_{\mathrm{n}\mathrm{-}\mathrm{2}}\mathrm{+}\mathrm{2}{\mathrm{m}}_{\mathrm{n}\mathrm{-}\mathrm{1}}\mathrm{+}{\mathrm{M}}_{\mathrm{n}}\right)}{\mathrm{4}}\mathrm{,}$

with the second last of the old table in the following way:

t1	-
t2	$$\frac{\left({\mathrm{M}}_{\mathrm{1}}\mathrm{+}\mathrm{2}{\mathrm{m}}_{\mathrm{2}}\mathrm{+}{\mathrm{M}}_{\mathrm{3}}\right)}{\mathrm{4}}$$
....	....
tn-1
tn


• If the values of the last table are represented, it can be appreciated the zone of instability of the measurement, those in which have been produced uncontrolled roll torques of a random nature and the most stable zone of the register can be selected. For this a routine is constructed which chooses the continuous zone of a length of one minute whose mean quadratic error of the values contain in the zone is minimum. The average value of the values of that zone will be the value assigned to the roll angle. The quality index will be the mean quadratic error and in the cases in which there is no zone of the register sufficiently stable, it will recommend repeat the measurement.
• The previous routine will allow "control" the uncontrolled roll torques of a random nature (accidental errors), never the less when uniform uncontrolled roll torques are produced (systematic errors), and for example a constant wind against the side of the ship, the previous routine is not capable to detect this error. For this, equipment is implemented with one (or various) anemometer(s) and weather vane(s) to register simultaneously with the roll angle its information. This information allows "control" the systematic errors of the measurement due to the wind.
The rest of the inclining experiment is equivalent to the traditional method: From the points of pares (roll torque, roll angle) and the ships displacement, is constructed the righting arm curve GZ = f(tangent(roll angle)), and, by means of a lineal regression, is determined the ships metacentric height (GMc) in the load condition of the inclining experiment. From the metacentric height and with the help of the hydrostatic curves, is obtained the position of the ships centre of gravity. 2^nd Mode to execute the invention: Determining the height of the centre of gravity of a ship by means of simultaneous registers of two gravitational inclinometers.
• The algorithm developed to "filter" the component of the roll angle for the signals produced by the gravitational inclinometers, can have a second application and that is to determine directly the centre of gravity of a ship.
• For this the two inclinometers are placed on the ship, on the centre line and on the same vertical. When greater is the separation between them, greater will be the precision of the measurement.
• The hypothesis in which is based this procedure is that the roll motion is produced around the (horizontal) longitudinal axis that passes through the ships centre of gravity, or else, with respect to an axis parallel to the one mentioned above from which can be deduced the vertical position of the centre of gravity
• The procedure consists in the following phases:
1. 1°) Checking / calibrating and setting to zero the inclinometers. In this mode of execution of the invention it is very important that the signals generated by the two inclinometer be completely equal when the inclinometers are in the same condition whether static or dynamic. For this it is necessary to carry out, apart of the static calibration, a dynamic calibration consisting in placing the two inclinometers in a mechanical oscillator and adjust the filters of the system so that in the frequency band around the natural period of the ships roll, the signals are completely equal.
2. 2°) Register and processing the signals of the two inclinometers. The signals coming from the two inclinometers are registered during a sufficiently long period of time (around 100 times the natural period of the ships roll). From the registers an optimizing routine is established consisting in the following:
   1. 1) A set is established of KG values (distance of the ships centre of gravity to the ships base line) fixing a minimum KG, a maximum KG and a KG increment.)
   2. 2) For each KG of the previous set an algorithm is applied to the registers C1(t) and C2(t) of the two inclinometers obtaining C1corr(t) and C2corr(t) in the following manner:
      1. a) The Fourier transform of the register C1 (t) y C2(t) is made.
      2. b) Each harmonic of the Fourier transform is corrected in the following way: $${\phi }_{\mathrm{\omega }}1\mathrm{=}\frac{\mathrm{g}}{\mathrm{g}\mathrm{+}{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}1}{\mathrm{C}}_{\mathrm{\omega }}1$$
         
         For the C1 inclinometer. $${\phi }_{\mathrm{\omega }}2\mathrm{=}\frac{\mathrm{g}}{\mathrm{g}\mathrm{+}{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}2}{\mathrm{C}}_{\mathrm{\omega }}2$$
         
         For the C2 inclinometer.
         Being:

         φ_ω1:

         the amplitude of the roll angle corresponding to the C1 inclinometer.

         φ_ω2:

         the amplitude of the roll angle corresponding to the C1 inclinometer.

         g:

         the gravity acceleration.

         ω:

         the angular frequency of the harmonic.

         h1=

         KC1-KG (KC1 is the height of inclinometer 1 above the base line).

         h2=

         KC2-KG (KC2 is the height of inclinometer 2 above the base line).

         C_ω1:

         the amplitude of the inclinometers signal corresponding to the harmonic of the C1 inclinometer.

         C_ω2:

         the amplitude of the inclinometers signal corresponding to the harmonic of the C2 inclinometer.

      3. c) All the harmonics of each inclinometer are added and the signals obtained are C1corr(t) y C2corr(t).
   3. 3) The value of KG is calculated for which the two registers, C1corr(t) and C2corr(t), are equal, that corresponds to the vertical position of the ships centre of gravity.
3^rd Mode to execute the invention: Determining the metacentric height of a ship by means of the calculation of the natural period of the roll obtained from the register of an inclinometer.
• The hypothesis in which this procedure is based is to consider the response in the ships roll as a pass band filter, that is, before a wave spectrum in which the ship is sailing, the roll amplitudes of the harmonics which are in the resonance zone of the ships roll motion will be amplified and those corresponding to the harmonics out side this zone will be dimmed. In such a way that a roll register sufficiently ample is made and with the ship varying its course, with the purpose that there is not any dominant gathering period, will be defined the natural period of the ships roll by means of a statistical spectral analysis of the roll register obtained with the inclinometer.
• The procedure consists of the following phases:
  1°) Checking / calibrating and setting to zero of the inclinometer. On dry land a checking of the signal of the inclinometer will be carried out and, if necessary, a calibration and a setting to zero of it.
  2°) Preliminary trials with the ship. Once calibrated, the inclinometer is placed anywhere on the ship, the only condition is that it be on the centre line. With the object to obtain the coefficient that relates the natural period of the ships roll and its GM, an inclining experiment will be carried out with the ship, to determine its GM, and registers of the ships roll will be taken in different sailing conditions: sailing in sheltered seas at different speeds and in open seas at different speeds, with the purpose of getting the natural period of the ships roll in the different sailing conditions and with it the coefficient that relates natural period of the roll and the GM.
  3°) Register and processing of the signal from the inclinometer. The signal coming from the inclinometer will be registered during a sufficiently long period of time (in the order of 100 times the natural period of the ships roll). From the registers a procedure of statistical spectral analysis is established consisting in the following:
  1) Denominating LP the time a register lasts. If, for example, the natural period of the ships roll is of the order of 10 seconds, it will be presumed that LP is 1000 seconds.
  2) Dividing the main register in samples of size LM and given a time dM. LM and dM will depend on the type of ship and, without any loss of generality, supposing that dM is equal to 20 seconds and LM equal to 300 seconds. The first sample will start in the instant zero and will finish in the instant (300), the second sample will start in the instant dM (20) and will finish in LM+dM (320), and like that successively until reaching the sample that starts in LP (1000) and finishes in LP + LM (1300). With the purpose of giving to all the zone of the register an equal weight, the first LM (300) seconds have been added to the main register.
  3) To each sample from the register is applied the Fourier transform in the following way: A wide rang of periods is defined that contain the possible natural periods of the ships roll defined by Pinit (Lowest period), Pend (highest period) and Pdelta (period increments). For example in the case of a ship whose natural roll periods oscillate between 8 and 20 seconds, Pinit = 5 seconds, Pend = 30 and Pdelta = 0.1 seconds are chosen. To each harmonic from the set of periods included between Pinit and Pend and separated by Pdelta, the Fourier transform is applied on the sample from the register choosing the maximum length that is a multiple of the period on which the Fourier transform is applied.
  Applying this to all the samples a table is obtained like the following one:

  	Sample 1	Sample 2	......	Sample n
  Pinit	A11	A12	......	A1n
  Pinit + Pdelta	A21	A22	......	A2n
  .....	.....	.....	.....	.....
  Pend	Am1	Am2	.....	Amn
  Maximum	M1	M2	......	Mn

  Being A_ij the amplitude corresponding to harmonic i from sample j and M_j the maximum amplitude from sample j.
  From the previous table two spectrums denominated accumulated and normalized are constructed: Accumulated spectrum

  Pinit	(A11+A12+....+A1n)/n
  Pinit + Pdelta	(A21+A22+....+A2n)/n
  .....	.....
  Pend	(Am1+Am2+....+Amn)/n

  Normalized spectrum

  Pinit	(A11/M1+A12/M2+....+A1n/Mn)/n
  Pinit + Pdelta	(A21/M1+A22/M2+....+A2n/Mn)/n
  ..........	..........
  Pend	(Am1/M1+Am2/M2+....+Amn/Mn)/n

  
  In the normalized spectrum all the samples have the same weight, Independently of the magnitude of the roll motion of the sample.
  4) From the study of both spectrums is determined the natural period of the ships roll (T_φ) and the GM is obtained by the formula: $$\mathrm{GM}={\left(\mathrm{K}\mathrm{\cdot }\mathrm{B}\mathrm{/}{\mathrm{T}}_{\phi }\right)}^2$$

  

  Being K the coefficient obtained in the ships trials and B its breadth.

Claims (7)

1. A procedure to obtain the parameters for the stability of ships by measurements with inclinometers characterised because for the measurement of the heeling angle of a ship, in the equilibrium conditions of the inclining experiment, is composed of the following 3 stages:

   1) Checking, calibration and setting to zero of the inclinometer on land.

   2) In the case of using gravitational inclinometers: Filtering the registers of the inclinometer eliminating the component due to the ships rolling motion, and obtaining the evolutions of the heeling angle in the different equilibrium conditions of the inclining experiment.

   3) Analysis of the registers of the heeling angle obtained and the determination of the optimal zones in which the uncontrolled heeling moments have been minimum with the purpose to assign the ships heeling angle, in each equilibrium condition, more precise and also assign the precision of the measurement with the purpose of its validation or its repetition.
2. A procedure to obtain the stability parameters of ships by means of measurements with inclinometers, according to claim 1. characterised because the checking, calibrating and setting to zero procedure of the inclinometer consists in:

   1) Placing the levelling platform (figure 2) on a stable table and, with the help of a two dimensional spirit level, it is levelled.

   2) The inclinometer is then used, which is placed on the coupling piece (figure 1), as a precision level, placing it on the levelling platform in a direction parallel to the levelling screws (H and I in figure 2), reading are taken from the signal from the inclinometer.

   3) Later the inclinometer is turned 180° and reading are again taken. If the two previous readings are not the equal, the levelling screws are adjusted until the two reading converge. In this moment the inclinometer is in a horizontal position with a precision of a hundredth of a degree and the "zero" value is assigned.

   4) Then, with the help of the calibrated angle generators (figure 3), the inclinometer is placed with the different angles that these pieces give (figure 4), and the calibration of the inclinometer is checked. If it were to be necessary, and with the help of these pieces, the inclinometer is again calibrated.
3. A procedure to obtain the stability parameters of ships by means of measurements with inclinometers, according to claim 1. characterised because the filtering of the registers is applied to the case in which gravitational inclinometers are used and consists in an algorithm that filters the signal corresponding to the heeling angle of the signal obtained by the inclinometer.
   The explain the algorithm we presume that the inclinometer is situated at a height "h" above the gyrating axis and subjected to an irregular oscillatory motion

   1°) The Fourier Transform of the inclinometers register is made

   2°) Each harmonic of the Fourier Transform is corrected in the following way: $$\phi \mathrm{=}\frac{\mathrm{g}}{\mathrm{g}+{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}}\mathrm{C}$$

   

   If h is above the gyration axis. $$\phi \mathrm{=}\frac{\mathrm{g}}{\mathrm{g}-{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}}\mathrm{C}$$

   

   If h is under the gyration axis.
   With:

   φ: Amplitude of the heeling angle corresponding to the harmonic.

   g: Gravity acceleration.

   ω: Angular frequency of the harmonic.

   C: Amplitude of the signal from the inclinometer corresponding to the harmonic.

   3°) All the harmonics constituting the signal corresponding to the register of the evolution of the angle in time are added.
4. A procedure to obtain the stability parameters of ships by measurements with inclinometers according to claims 1, characterised because the determination of the heeling angle is carried out by the analysis of the registers of the evolutions of the heeling angle to fix the optimum zones in which the uncontrolled heeling moments have been minimal, with the purpose to assign the heeling angle of the ship, in each equilibrium condition, more precisely and assign also the precision of the measurement.

   1°) The length of the register is established in function of the natural period of the roll of the ship. Around about 20 times the natural period of the roll motion.

   2°) With the obtained register, the relation of maximums and minimums is generated with the instants in which they are produced.

   3°) From this relation, are eliminated those pars of consecutive maximums and minimums separated in time by less than 1.5 seconds (filtering harmonics with a period inferior to 3 seconds).

   4°) From the previous relation a table is built having as first element, $\frac{\left({\mathrm{M}}_{\mathrm{1}}\mathrm{+}\mathrm{2}{\mathrm{m}}_{\mathrm{2}}\mathrm{+}{\mathrm{M}}_{\mathrm{3}}\right)}{\mathrm{4}}\mathrm{,}$

   

   corresponding with the second instant (t₂) of the previous relation and the last, $\frac{\left({\mathrm{M}}_{\mathrm{n}\mathrm{-}\mathrm{2}}\mathrm{+}\mathrm{2}{\mathrm{m}}_{\mathrm{n}\mathrm{-}\mathrm{1}}\mathrm{+}{\mathrm{M}}_{\mathrm{n}}\right)}{\mathrm{4}}\mathrm{,}$

   

   with the second last instant (t_n-1) of the previous relation.

   5°) Selecting, from the representation of the table, the most stable zone of the register. For this, is chosen the continuous zone of the register whose duration is half the time of the register and whose mean quadratic error of the values contained in the zone, are minimum. The average value of the values of this zone will be the value assigned to the heeling angle. The reliability index will be the mean quadratic error and in the cases where there is no zone sufficiently stable of the register, it will recommend to repeat the measurement.

   6°) When uniform uncontrollable heeling moments are produced (systematic errors), for example a constant wind abeam of the ship, the equipment is implemented with one (or various) anemometer(s) and weather vane(s) to register simultaneously with the heeling angle its information and measure the systematic errors of the measurement due to the wind.
5. A procedure to obtain the stability parameters of ships by measurements inclinometers characterised because the determination of the centre of gravity of a ship is carried out by the simultaneous registers of two inclinometers situated on the ship on its centre line and on the same vertical and because it comprehends the following operations:

   1°) Checking / calibrating and setting to zero of the inclinometers. The signals generated by the two inclinometers must be completely identical when the inclinometers are in the same conditions, whether static or dynamic. For this a static calibration and a dynamic calibration is carried out by placing the two inclinometers on a mechanical oscillator and adjusting the filters of the system so that it is within the frequency band around the natural period of the ships roll, the signals are completely identical.

   2°) Register and processing the signals of the two inclinometers. The signals received from the inclinometers during a sufficiently long time (in the order of 100 times the natural period of the ships roll) are registered. From the registers:

   1°) Is established a set of KG values (distance from the ships c.o.g. to the base line) fixing a minimum KG, a maximum KG and increment of the KG.

   2°) For each KG of the previous set is applied the algorithm to the registers C1 (t) and C2(t) from the two inclinometers obtaining C1corr(t) and C2corr(t) in the following way:

   a) The Fourier Transform of the registers C1(t) and C2(t) is done.

   b) Each harmonic of the Fourier Transform has its deviation due to the roll motion and it is corrected in the following way: $${\phi }_{\mathrm{\omega }}1\mathrm{=}\frac{\mathrm{g}}{\mathrm{g}\mathrm{+}{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}1}{\mathrm{C}}_{\mathrm{\omega }}1$$

   

   For the C1 inclinometer $${\phi }_{\mathrm{\omega }}2\mathrm{=}\frac{\mathrm{g}}{\mathrm{g}\mathrm{+}{\mathrm{\omega }}^{\mathrm{2}}\mathrm{h}2}{\mathrm{C}}_{\mathrm{\omega }}2$$

   

   For the C2 inclinometer
   With:

   φ_ω1: Roll angle amplitude corresponding to the harmonic from the C1 inclinometer.

   φ_ω2: Roll angle amplitude corresponding to the harmonic from the C2 inclinometer.

   g: Gravity acceleration.

   ω: Angular frequency of the harmonic.

   h1= KC1-KG (being KC1 the inclinometers height above the base line).

   h2= KC2-KG (being KC2 the inclinometers height above the base line).

   C_ω1: Amplitude of the inclinometers signal corresponding to the C1 inclinometer.

   C_ω2: Amplitude of the inclinometers signal corresponding to the C2 inclinometer.

   c) All the harmonics from each inclinometer are added and the signals obtained are C1corr(t) and C2corr(t).

   3°) The value of the KG is calculated for which the two registers, C1corr(t) y C2corr(t), are equal, which corresponds to the vertical position of the centre of gravity of the ship.
6. A procedure to obtain the stability parameters of ships by means of characterised inclinometers is because the determination of the GM (metacentric height) is carried out from the roll natural period by statistic spectral analysis from the roll register, that comprehends the following operations:

   1°) Checking / calibrating and setting to zero of the inclinometer on land.

   2°) Obtaining the coefficient that relates the roll natural period of the ship with its metacentric height, doing the inclining experiment to determine the metacentric height (GM) and recording registers of the ships roll in different navigation conditions, to obtain the roll natural period of the ship.

   3°) Register and processing of the inclinometers signal. The signal coming from the inclinometer during a sufficiently long enough time (in the order of 100 times the ships natural period) is registered, and from the registers is done a statistic spectral analysis.
7. A procedure to obtain the stability parameters of ships by means of measurements with inclinometers, according to claim 6, characterised by the statistic spectral analysis consisting in:

   1) Dividing the main register into smaller samples and given a specific time, that is established in function of the type of ship.

   2) Each sample of the main register is subjected to a Fourier Transform, over a rang of periods that cover the possible roll natural periods of the ship, and choosing the maximum length of the sample that is a multiple of the period over which is applied the Fourier Transform, obtaining for each sample two spectrums, the normalised (all the samples have the same weight) and the accumulated.

   3) From the study of both spectrums is determined the roll natural period of the ship (T_φ) and the metacetric height (GM) obtained from the formula: $$\mathrm{GM}={\left(\mathrm{K}\mathrm{\cdot }\mathrm{B}\mathrm{/}{\mathrm{T}}_{\phi }\right)}^2$$

   

   Being K the coefficient obtained in the trails carried out with the ship and B its beam.

Images