Method and device for determining a catamaran safety navigation seakeeping criterion parameter and medium

Abstract

One technical solution of this invention is to provide a method for determining seakeeping criterion parameters for safe navigation of a catamaran. Another technical solution of this invention is to provide an electronic device. Yet another technical solution of this invention is to provide a computer-readable storage medium. This invention employs extreme quasi-static analysis, using the ship's stability under extreme motion amplitudes as the verification standard for safe navigation. By calculating ship stability criterion numbers, it determines seakeeping criterions such as roll and pitch for safe navigation of the catamaran. This is used to verify the stability of the catamaran under large motions in extreme sea states and to help designers determine appropriate seakeeping criterion parameters for safe navigation.

Description

Technical Field

[0001] This invention relates to a method, apparatus, and medium for determining seakeeping criterion parameters for safe navigation of catamarans, applicable to stability verification and seakeeping criterion determination of catamarans under extreme sea states. Background Technology

[0002] When ships navigate in rough seas, the significant amplitude of their motion in the waves often impacts their navigational safety. Therefore, the design of various types of ships requires comprehensive consideration of navigational safety and verification of the hull's motion response under high sea states. Taking a conventional monohull surface vessel platform as an example, the criteria for its motion response under high sea states are typically based on various standards (e.g., General Naval Specifications (GJB4000-2000), Practical Handbook for Ship Design, Common Procedures for Seakeeping in the Ship Design Process (STANAG 4154-2000), etc.). These standards provide permissible limits for parameters such as roll and pitch to ensure safe navigation under various sea conditions.

[0003] The current seakeeping standards for safe navigation of surface vessels in my country stipulate that the limits for roll and pitch are set by... Figures 1 to 2 Given, in the figure, Φ 1 / 3 --The average value of the maximum single amplitude of the panning (°); θ 1 / 3 -- The average value of the single amplitude of one-third of the pitch, (°); Δ 1 / 3 --The cube root value of the water displacement, t 1 / 3 g – acceleration due to gravity, taken as 9.8066 m / s² 2 .

[0004] Meanwhile, unless otherwise specified, the maximum allowable roll and pitch values ​​for safe navigation of ships under various navigation conditions in wind and waves should generally comply with the provisions of Table 1.

[0005] Table 1 Maximum Limits for Roll and Pitch of Surface Vessels

[0006]

[0007] In the table, Φmax and θmax are the maximum single amplitude values ​​of roll and pitch, respectively, which are equivalent to the expected values ​​of the maximum values ​​in 2000 swings.

[0008] The aforementioned standards primarily apply to monohull ships. Due to their large length-to-beam ratio, monohull ships exhibit significant differences in lateral and longitudinal stability, particularly with large pitch angles leading to substantial lateral stability loss and a higher risk of capsizing. Therefore, the standards impose significant limitations on the maximum pitch angle. However, catamarans and other special vessel types have much smaller length-to-beam ratios than conventional monohull ships. Furthermore, the presence of connecting bridges allows for a larger waterline area even under large pitch conditions, providing a certain reserve of hull stability and ensuring navigational safety. Consequently, the current seakeeping standards (especially the limits on the maximum pitch angle) are relatively conservative for catamarans and lack sufficient applicability to catamarans and other special vessel types. Summary of the Invention

[0009] The technical problem this invention aims to solve is that current regulations for safe navigation are typically formulated based on monohull vessels, and their seakeeping standards (especially the limits on maximum pitch angle) are relatively conservative for catamarans, lacking applicability to catamarans and other special vessel types. Recent research on the seakeeping of catamarans has mainly focused on resistance performance and longitudinal motion performance in waves, with limited analysis of stability under large pitch conditions. Furthermore, existing seakeeping standards do not consider the influence of catamaran connecting bridges, and there are no specific seakeeping standards for catamarans.

[0010] To address the aforementioned technical problems, one technical solution of the present invention provides a method for determining the seakeeping criterion parameters for safe navigation of a catamaran, characterized by comprising the following steps:

[0011] Step 1: Determine the waterline under extreme conditions;

[0012] Step 2: Calculate the hull roll and pitch restoring arms based on the waterline position under extreme conditions;

[0013] Step 3: Calculate the wind pressure tilting arm based on the waterline position under extreme conditions;

[0014] Step 4: Calculate the stability criterion number under this state based on the calculated restoring arm and wind pressure tilting arm;

[0015] Step 5: Select multiple extreme states, calculate the stability criterion numbers according to steps 1 to 4 above, and determine the seakeeping criterion parameters such as roll angle and pitch angle for safe navigation of the target ship. The selection of extreme states can refer to the target ship model test data or the evaluation data of the parent ship actual ship test.

[0016] Preferably, in step 1, the method for determining the waterline during roll is the same as that for pitch.

[0017] Preferably, in step 2, the calculation of the hull roll and pitch restoring arms adopts the calculation method of large-angle stability.

[0018] Preferably, in step 2, the buoyancy line is set to W0L0, the center of buoyancy is at B0, and after tilting by an angle φ, it floats on the waterline W. φ L φ Floating heart at B φ Its coordinates are y Bφ and z Bφ Then the restoring lever arm is:

[0019]

[0020] In the formula, G represents the location of the ship's center of gravity, and Z represents the distance from the center of gravity to the center of buoyancy B after tilting by an angle φ. φ The perpendicular foot is made at point R, which represents the angle φ after tilting, from the original center of buoyancy B0 to the center of buoyancy B. φ The perpendicular foot is drawn at point E, which represents the perpendicular foot drawn from the ship's center of gravity G to the line segment B0R, and K represents the center of the ship's baseline.

[0021] Preferably, the coordinates of the center of buoyancy are obtained by the following formula:

[0022]

[0023] In the formula, W is an isovolute inclined waterline φ L φ Moment of inertia at the waterline, For drainage volume, It indicates the center of gravity of the ship when it rolls.

[0024] Preferably, in step 2, the calculation of the longitudinal restoring arm of the catamaran under large pitching motion conditions refers to the calculation process of the lateral restoring arm.

[0025] Preferably, in step 3, the wind pressure tilting lever arm is calculated using the following formula:

[0026]

[0027] In the formula: P is the unit calculated wind pressure, A f Z represents the windward area of ​​the ship above the waterline, Z represents the calculated wind force lever arm, and Δ represents the ship's displacement under the calculated conditions.

[0028] Preferably, in step 4, a stability criterion number K applicable to all ships is taken, namely:

[0029]

[0030] In the formula: l q The restoring arm for roll or pitch is calculated in step 2; f The wind pressure tilt arm is calculated in step 3.

[0031] Another technical solution of the present invention is to provide an electronic device, characterized in that it includes a processor, a memory, and a program or instructions stored in the memory and executable on the processor, wherein when the program or instructions are executed by the processor, the steps of the above-described method for determining the seakeeping criterion parameters for safe navigation of catamarans are implemented.

[0032] Another technical solution of the present invention is to provide a computer-readable storage medium, characterized in that it is used to store instructions, which, when executed on a computer, cause the computer to perform the steps of the above-described method for determining the seakeeping criterion parameters for safe navigation of a catamaran.

[0033] This invention employs extreme quasi-static analysis, using the ship's stability under extreme motion amplitudes as the verification standard for safe navigation. By calculating the ship's stability criterion numbers, it determines the seakeeping criterion for safe navigation of catamarans, such as roll and pitch, which is used to verify the stability of catamarans under extreme sea conditions and to help designers determine appropriate safe navigation seakeeping criterion parameters.

[0034] This invention employs extreme quasi-static analysis based on stability to develop a method for determining seakeeping criterion parameters for safe navigation of catamarans. This method is well-suited to the characteristic of catamarans, which, compared to traditional monohull vessels, still possess a greater stability margin under significant motion conditions. By calculating the stability criterion numbers, the upper limit of safe navigation for ships is determined, effectively supplementing existing regulations. This method fully considers the impact of connecting bridges on the stability of catamarans and can be used not only for determining seakeeping criterion parameters for safe navigation of catamarans or multihull vessels with connecting bridges, but also for studying seakeeping criterion parameters for vessels or offshore platforms with special operational requirements. Attached Figure Description

[0035] Figure 1 This illustrates the roll limit curve for surface ships under the most severe navigation conditions.

[0036] Figure 2 This illustrates the pitch limit curve for surface ships under the most severe navigation conditions;

[0037] Figure 3 This diagram illustrates the determination of the waterline position for a catamaran at constant displacement. In the diagram, W0L0 represents the waterline when the ship is upright, ▽0 represents the displacement, and W... φ L φ The waterline at maximum pitch, ▽ φ This represents the displacement at that pitch angle;

[0038] Figure 4 The calculation of the restoring lever arm for large-angle lateral stability is illustrated in the instantaneous state;

[0039] Figure 5 The calculation of the restoring lever arm for longitudinal stability at large tilt angles under instantaneous conditions is illustrated.

[0040] Figure 6 This illustrates the changes in the surface area of ​​the waterline at large trim angles for different ship types.

[0041] Figure 7 The diagram illustrates the change in waterline area of ​​a catamaran when it is trimmed by 25°. Detailed Implementation

[0042] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0043] One aspect of the present invention is to provide a method for determining the seakeeping criterion parameters for safe navigation of a catamaran, comprising the following steps:

[0044] Step 1: Determine the waterline under extreme conditions. Based on the quasi-static principle, at any roll or pitch angle, keeping the displacement constant (▽), determine the waterline position when the buoyancy generated by the ship's underwater displacement volume equals the ship's own weight. Calculate the restoring arm and the wind pressure heeling arm based on this, and then obtain the stability criterion number K to determine whether it meets the stability requirements. The method for determining the waterline during roll is the same as for pitch.

[0045] Step 2: Calculate the restoring arms of the ship's roll and pitch based on the waterline position under extreme conditions. When a ship is in extreme roll and pitch conditions, its trim and heel angles exceed the applicable range of initial metastasis. Therefore, the calculation method for large-angle stability should be used to calculate the restoring arms under such conditions.

[0046] For special ship types such as catamarans, both longitudinal and transverse stability of the hull under extreme conditions should be considered simultaneously, specifically as follows: Figure 4 , Figure 5 As shown.

[0047] A cross section of a ship under instantaneous trim condition, such as Figure 4 As shown, assuming the waterline is W0L0 and the center of buoyancy is at B0, after tilting by an angle φ, it floats on the waterline W. φ L φ Floating heart at B φ Its coordinates are y Bφ and z Bφ Then its restoring lever arm is:

[0048]

[0049] In the formula, G represents the location of the ship's center of gravity, and Z represents the distance from the center of gravity to the center of buoyancy B after tilting by an angle φ.φ The perpendicular foot is made at point R, which represents the angle φ after tilting, from the original center of buoyancy B0 to the center of buoyancy B. φ The perpendicular foot is drawn at point E, which represents the perpendicular foot drawn from the ship's center of gravity G to the line segment B0R, and K represents the center of the ship's baseline.

[0050] The coordinates of the center of buoyancy can be obtained by the following formula:

[0051]

[0052] In the formula, W is an isovolute inclined waterline φ L φ Moment of inertia at the waterline, For drainage volume, It indicates the center of gravity of the ship when it rolls.

[0053] Regarding longitudinal stability, monohull ships, due to their much longer length than their beam, have a longitudinal metacenter height that is significantly larger than their transverse metacenter height, typically on the same order of magnitude as the length. Therefore, longitudinal stability is generally not considered in the design. However, catamarans have a much wider beam, resulting in a much smaller length-to-beam ratio than conventional monohull ships. Consequently, their longitudinal and transverse metacenter heights are roughly on the same order of magnitude. Therefore, while checking their transverse stability, it is also necessary to consider whether their longitudinal stability meets the requirements. The specific calculation of the longitudinal restoring arm of a catamaran under large pitching motion conditions can refer to the calculation process of the transverse restoring arm, such as... Figure 5 As shown.

[0054] Step 3: Calculate the wind pressure tilting arm based on the waterline position under extreme conditions.

[0055] The tilting arm of wind pressure is calculated using the following formula:

[0056]

[0057] Where: P──unit calculated wind pressure, (Pa);

[0058] A f --The windward area of ​​the ship above the waterline, (m²) 2 );

[0059] Z – Calculate the wind force lever arm, which is the vertical distance from the center of the wind-receiving area to the center of buoyancy under the calculated state, (m);

[0060] Δ── Ship displacement under calculated conditions, (t).

[0061] Step 4: Calculate the stability criterion number under this state based on the calculated restoring arm and wind pressure heeling arm. For stability criterion parameters ensuring safe navigation, since this invention considers the stability of the ship under extreme motion amplitudes, only the stability criterion number K applicable to all ships is taken, i.e.:

[0062]

[0063] In the above formula, l q The restoring arm for roll or pitch is calculated in step 2. f The wind pressure tilt arm is calculated in step 3.

[0064] For any extreme case, the ship's stability criterion number K should not be less than 1.

[0065] Step 5: Select multiple extreme conditions and calculate the stability criterion numbers according to steps 1 to 4 above to determine the seakeeping criterion parameters such as roll angle and pitch angle for safe navigation of the target ship. The selection of extreme conditions can refer to the target ship model test data or the evaluation data of the parent ship actual ship test.

[0066] Another aspect of the present invention is to provide an electronic device including a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When executed by the processor, the program or instructions implement the steps of the method for determining the seakeeping criterion parameters for safe navigation of a catamaran as described above. All implementations in the above method embodiments are applicable to the embodiments of this electronic device and can achieve the same technical effects.

[0067] Embodiments of the present invention also provide a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the method for determining the seakeeping criterion parameters for safe navigation of a catamaran as described above. All implementations in the above method embodiments are applicable to the embodiments of this computer-readable storage medium and can achieve the same technical effects.

[0068] The effect of ship pitching on stability shows that the magnitude of the restoring arm is mainly related to the ship's waterplane moment of inertia under different conditions (in the formula of step 2). The magnitude of the waterline moment of inertia is related to the lateral and longitudinal stability radii (BM in step 2), and is in turn closely related to the waterline area. Under conditions of significant pitching, the changes in these parameters reflect the changes in the stability of different ships, thereby affecting the navigation safety of the ship.

[0069] Considering that existing seakeeping standards are typically formulated for monohull vessels, and that catamarans have a more unique hull form with a much smaller length-to-beam ratio, their waterline area and stability radius differ significantly from those of monohull vessels under large pitch angles. Taking a catamaran as an example, we calculated its waterline area and longitudinal and transverse stability radii under upright buoyancy and an extreme pitch angle of 10°. We also compared relevant parameters of a monohull vessel of the same tonnage under an extreme pitch angle of 10°. The hull parameters of the two vessels are shown in Table 2, and the comparison results are shown in Table 3.

[0070] Table 2. Ship type parameters of a catamaran and a monohull of the same tonnage.

[0071]

[0072] Table 3 Comparison of waterline and radius of stability of a catamaran and a monohull of the same tonnage at a 10° pitch angle.

[0073]

[0074] Based on the proportion of waterline parameters change under trim conditions, the waterline area of ​​a catamaran more than doubles due to the ingress of the connecting bridge and part of the main hull, while that of a monohull of the same tonnage decreases by more than 50%. Figure 6 As shown, in terms of lateral and longitudinal stability radii, catamarans show a significant increase compared to upright buoyancy, while monohulls of the same tonnage have a lateral stability radius that decreases by nearly 50% and a longitudinal stability radius that decreases by nearly 90%. This indicates that catamarans are more stable than upright buoyancy under a pitching angle of 10°.

[0075] Based on the above comparisons, and according to the catamaran model tests and actual ship tests, its maximum pitch angle can reach over 25°. Therefore, assuming an extreme pitch angle of 25°, the waterline and stability radius of the catamaran are calculated under this condition, as shown in Table 4.

[0076] Table 4. Changes in waterline and radius of stability of a catamaran under 25° pitching conditions.

[0077]

[0078]

[0079] Based on the proportion of waterline area changes under trim conditions, when the extreme pitch angle reaches 25°, the waterline area of ​​the catamaran is still larger than that in the upright state (approximately 16% increase in the trim condition, and over 50% increase in the trim condition due to the submersion of the bow superstructure). Figure 7 (As shown). In terms of transverse stability radius, the change is not significant between catamaran and upright buoyancy, while that of a monohull of the same tonnage decreases by nearly 50% when pitching by 10°. In terms of longitudinal stability radius, the longitudinal stability radius of the catamaran decreases due to the significant reduction in instantaneous waterline length caused by large pitching motion, but it is still less than the loss of longitudinal stability radius of the monohull when pitching by 10°.

[0080] The above comparison shows that the waterline parameters of a catamaran at a pitch angle of 25° are still better than those of a monohull at 10°. Therefore, it is clearly unreasonable to use the maximum single-amplitude value of 10° as the standard for the pitch angle of a catamaran according to the existing seakeeping specifications for monohulls. Furthermore, by verifying the stability of the catamaran under this condition, it can be shown that the catamaran still has a large margin of stability under extreme pitch motions, as shown in Table 5.

[0081] Table 5. Verification of Stability Criteria for Catamarans under Instantaneous Significant Heeling

[0082]

[0083]

[0084] In the table, the maximum wind pressure for stability verification is P = 500 (V) according to the gust pressure requirement for multihull ship stability in the International High Speed ​​Craft Safety Code 2000. w / 26) 2 Pa calculation, gust wind speed V w The value is taken as 52 m / s.

[0085] Based on the stability verification results above, when the extreme instantaneous pitch angles at the bow and stern of the catamaran reach 25°, its longitudinal and lateral stability criterion numbers are both much greater than 1, indicating that it still has a large stability reserve.

[0086] The above calculations, analysis, and stability checks show that under large pitching conditions, the transverse stability radius of a monohull is significantly reduced. If lateral gusts or other loads occur at this time, the monohull may capsize, posing a significant safety hazard. In contrast, catamarans, under extreme large pitching conditions, considering their smaller length-to-beam ratio and the presence of the connecting bridge between the catamarans entering the water, experience a much smaller loss of waterline area, thus retaining a substantial reserve of stability. Therefore, the maximum permissible pitching limit for safe navigation of catamarans in high winds and waves can be appropriately relaxed.

[0087] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for determining the seakeeping criterion parameters for safe navigation of a catamaran, characterized in that, Includes the following steps: Step 1: Determine the waterline under extreme conditions; Step 2: Calculate the restoring arms of the hull's roll and pitch based on the waterline position under extreme conditions. Let the upright buoyancy line be W0L0, the center of buoyancy be B0, and after a roll angle φ, the hull floats above the waterline W0. φ L φ Floating heart at B φ Its coordinates are y Bφ and z Bφ Then the restoring lever arm is: In the formula, Indicates the location of the ship's center of gravity. This indicates the distance from the center of gravity to the center of buoyancy B after tilting by an angle φ. φ The foot of the foot, This indicates the change in buoyancy from the original center of buoyancy B0 to the center of buoyancy B after tilting by an angle φ. φ The foot of the foot, Indicates the foot of the perpendicular segment from the ship's center of gravity G to B0R. Indicates the center of the hull baseline; In the formula for calculating the restoring arm, the coordinates of the center of buoyancy are obtained by the following formula: In the formula, , W is an isovolute inclined waterline φ L φ Moment of inertia at the waterline, For drainage volume, The center of gravity indicating the ship's rolling position; Step 3: Calculate the wind pressure tilting arm based on the waterline position under extreme conditions; Step 4: Calculate the stability criterion number under this state based on the calculated restoring arm and wind pressure tilting arm; Step 5: Select multiple extreme states, calculate the stability criterion numbers according to steps 1 to 4 above, and determine the seakeeping criterion parameters such as roll angle and pitch angle for safe navigation of the target ship. The selection of extreme states can refer to the target ship model test data or the evaluation data of the parent ship actual ship test.

2. The method for determining the seakeeping criterion parameters for safe navigation of a catamaran as described in claim 1, characterized in that, In step 1, the method for determining the waterline during roll is the same as that for pitch.

3. The method for determining the seakeeping criterion parameters for safe navigation of a catamaran as described in claim 1, characterized in that, In step 2, the calculation of the hull roll and pitch restoring arms adopts the calculation method of large-angle stability.

4. The method for determining the seakeeping criterion parameters for safe navigation of a catamaran as described in claim 1, characterized in that, In step 2, the calculation of the longitudinal restoring arm of the catamaran under large pitching motion conditions is based on the calculation process of the lateral restoring arm.

5. The method for determining the seakeeping criterion parameters for safe navigation of a catamaran as described in claim 1, characterized in that, In step 3, the wind pressure tilting arm is calculated using the following formula: In the formula: P is the unit of calculated wind pressure, A f Z represents the windward area of ​​the ship above the waterline, Z represents the calculated wind force lever arm, and Δ represents the ship's displacement under the calculated conditions.

6. The method for determining the seakeeping criterion parameters for safe navigation of a catamaran as described in claim 1, characterized in that, In step 4, only the stability criterion number K applicable to all ships is used, that is: In the formula: l q The restoring arm for roll or pitch is calculated in step 2; f The wind pressure tilt arm is calculated in step 3.

7. An electronic device, characterized in that, It includes a processor, a memory, and a program or instructions stored in the memory and executable on the processor, which, when executed by the processor, implement the steps of the method for determining the seakeeping criterion parameters for safe navigation of a catamaran as described in claim 1.

8. A computer-readable storage medium, characterized in that, Used to store instructions that, when executed on a computer, cause the computer to perform the steps of the method for determining the seakeeping criterion parameters for safe navigation of a catamaran as described in claim 1.

Images