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Surface seakeeping experiments with a model of a submarine
Hermanski, Greg; Kim, Stephen
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Surface Seakeeping Experiments with Model of a Submarine.
Greg Hermanski
1), Stephen Kim
2)1)
Institute for Ocean Technology, National Research Council Canada St.John’s, Newfoundland, Canada
2)
Department of National Defence Canada Ottawa, Ontario, Canada
Abstract
Model experiments to investigate the surface
performance of the Canadian Victoria Class submarine, under various environmental and operational conditions, were carried out at the Institute for Ocean Technology of the National Research Council, Canada. The task was initiated by the Canadian Navy in the wake of the HMCS Chicoutimi fire-at-sea on the recommendation of a Naval Board of Inquiry.
The program included systematic experiments to evaluate the seakeeping behaviour of the submarine in environmental and operational conditions selected to support development of guidelines for submarine operators. This included experiments in irregular waves and regular waves, along with roll decay tests.
Environmental and operational variables covered of range of speeds, sea states and vessel headings.
A free running, self-propelled, autopilot-driven, radio controlled model was designed and built to a scale of 1:14.96. The model, suitable for surface operations only, was outfitted with active rudders, fixed forward and after planes, main sail and keel. The model was designed so that the space between the outer body and the pressure hull was subjected to flooding and limited free flow. The external geometry of the model did not include acoustic tiles present on the full-scale boat. The model was instrumented to measure model motions, speed and propeller revolutions, and to monitor presence of water on deck in selected locations. Measurements of the roll responses were the principal targets of the project investigation.
This paper presents a description of the model, its particulars, including the evolution of the design process. Experimental results including roll, pitch and heave responses in regular and irregular waves, and roll decay results are presented. All model information and results meet ITTC requirements for benchmark data.
Keywords
Submarine, surface operation, seakeeping, benchmark data.
Background
In 1998, Canada purchased four conventionally powered diesel-electric Upholder class submarines from
the U.K. Royal Navy. The new submarines replaced the decommissioned Oberon class submarines and are formally designated as the ‘Victoria Class Long Range Patrol Submarine’.
In October 2004 the HMCS Chicoutimi, the last of the four submarines to be commissioned into the Canadian Navy, was crossing the Atlantic on the surface from the U.K. to Canadian Forces Base Halifax. During the transit, the boat experienced heavy seas when water entered the vessel through an opened conning tower hatch inside the sail resulting in a significant amount of seawater to ingress into the submarine. Some
connectors joining the main power cables were immersed causing arcing that started a fire in the electrical space leaving the submarine powerless and without propulsion. The Navy initiated a Board of Inquiry to investigate the accident. During the inquiry it became evident that there was a lack of surface seakeeping performance information that led to a project to investigate the seakeeping attributes of the Victoria Class submarines.
Description of the IOT Ocean Engineering Basin
All experiments were carried out at the IOT Offshore Engineering Basin (OEB). The basin has a working area of 26 m by 65.8 m with a depth that can be varied from 0.1 m to 2.8 m. Waves are generated using 168 individual, computer controlled wet back wavemaker segments, hydraulically activated, fitted around the perimeter of the tank in an “L” configuration. Each segment can be operated in one of three modes of articulation: flapper mode (± 15º), piston mode (± 400 mm) or a combination of both modes. The wavemakers are capable of generating both regular and irregular waves up to 0.5 m significant wave height. Passive wave absorbers are fitted around the other two sides of the tank. The facility has a recirculating water current generation capability with current speed dependent on water depth.
Description of the Submarine Hull
The body of the full-scale submarine includes a pressure hull encompassed by a free-flooding outer body aft and forward of the sail defining the vessel’s external geometry and thus the hydrodynamic characteristics of the submarine. The pressure hull defines hydrostatic
properties of the submarine. The outer body of the submarine is fitted with acoustic tiles to reduce the submarine's acoustic signature. The keel extends the full length of the pressure hull enabling the submarine to bottom safety and dock without the need for a cradle. The appendage configuration consists of stern planes in a cross (+) configuration (two fixed horizontal
stabilizers and two active vertical rudders), retractable bow planes and a main sail that houses a five-man lockout chamber.
The space between the pressure hull and the outer body contains floodable tanks and various equipment including sonars, torpedo tubes, propulsion and rudder system gears, the anchor etc. The permeability of the space varies longitudinally - ranging between 60 and 100 percent. The free flooding spaces are located at the front and aft of the submarine and between the casing and the pressure hull. During surface operations, the aft free flooded spaces are completely filled with water. Since the flooded volume is always under the operational waterline the free flow phenomenon is not significant. The forward spaces are partially filled with water allowing for a limited free flow that might influence pitch response. Estimates of changing water mass and its resultant impact on pitch radius of gyration indicate that the influence on pitch responses is negligible. However the Navy was particularly concerned with the flooding of the space under the casing and resultant influence on the submarine motions during surface operations.
2D Body Model and Experiments
In order to investigate the possible impact of the free flow under the casing on the submarine performance during surface operations, a simplified experimental task was designed. The purpose of the experiments was to determine parameters that could impact free flow under the casing and thus influence boat roll responses, and consequently to determine criteria for the design and fabrication of the seakeeping model of the submarine. The specific goal at this stage was to establish how closely the full-scale free flow
phenomena needed to be simulated on the scaled model.
For these experiments, a 2D body that models the cylindrical mid-body section of the Victoria Class submarine was constructed. The model was designed to capture the basic form of a casing on top of the body with the ability to change freeing port size, and vary permeability under the casing. This 2D model was built to a scale of 1:9.5 (based on beam dimensions). The general arrangement is shown in Fig.1. The 2D model was designed and constructed to allow for three drafts, three flooding volumes (permeability) under the casing, and two freeing port openings. The main dimensions of the model were as follows:
Length (m) = 2.26 Diameter (m) = 0.8
Resultant scale = 9.5 (based on beam, no tiles included)
L/B (D) ratio = 2.83
The main body of the model was an aluminum tube. Two flat removable end pieces were added to make the model a closed vessel. The end plates were bolted on to allow access to the model interior for changing ballast. To reduce possible end effects, the end plates were designed and fabricated with 75mm of extra diameter to prevent around-end flow. The model was outfitted with a keel to better represent the full-scale boat. Two brackets, one each side, were attached to the body (amidships and half of the main body height) to support two relative motion probes. Two soft mooring eyes were fixed at the middle of the end plates to support four mooring lines preventing the model from drifting during wave tests.
The casing skin was made of 1.5mm Lexan sheet. The height of the Lexan frame structure above the centre line of the main body was 135mm. The space under the casing was provided with 3 different inserts to model variation in space’s permeability. Two inserts were made of solid acrylic rods or blocks to fill 20% and 40% of the space for 80% and 60% permeability
respectively. Foam blocks were used for the “dry”, 0% permeability configuration.
There were two sets of casing skin sidepieces, one set higher than the other to allow for the change of freeing port opening. Two openings sizes of freeing port were selected: 15 mm and 28 mm in model scale. The size of openings was determined as the radial (perpendicular) distance between the free end of a sidepiece and the aluminum tube (pressure hull).
The model was configured for 3 different drafts: 1. Draft 788 mm, deepest STC draft equivalent of the full-scale boat standard trim condition. Displacement 1,124.5 kg.
2. Draft 703mm, mid draft DR2. Displacement 1,010.59 kg.
3. Draft 626mm, shallow draft DR3. Displacement 886.97 kg.
The test program included roll decay tests in calm water, and free rolling tests in regular and irregular beam seas, under the “wet” and “dry” conditions. Where the “dry” condition means 0% permeability and no free flow under the casing, and the “wet” conditions indicate 80% and 60% permeability of the space under the casing allowing for the free flow. Only the roll decay tests and results, that affected the seakeeping model concept, are presented in this paper. Examples of roll decay test results are shown in Fig. 2 to Fig. 6. Findings of this preliminary study, that were applied in design of the seakeeping model, indicate that in general terms the free flow phenomenon under the casing needs to be modeled with respect to rate of ingress and egress of the external water under the casing. Examples of roll decay time series, damping ratio and period versus amplitudes for STC draft, 40% permeability under the casing and 40-degree initial heel angle are shown on Fig. 2. The influence of permeability (Fig. 3) can be projected as
not significant, and effects of draft (Fig. 6) are
negligible due to limited free flow occurrence at shallow conditions, other than STC draft. However the size of the free flow ports needs to be modeled as closely as possible to obtain the proper rate of water ingress and egress (Fig. 4 and Fig.5).
Seakeeping Model
The model of the Victoria Class submarine was fabricated to a hull geometry derived from drawings for the Upholder Class at 1:14.9606 scale. The model is free running, self-propelled, and autopilot controlled via wireless link. The Body Plan of the model is shown in Fig.7. To ensure proper roll responses of the model, the combination of the final GM and radii of gyration was selected to obtain target natural roll period for the model scaled down from the full-scale boat.
Findings from the 2D model tests and some practical simplifying assumptions were used in designing and fabricating the seakeeping model. The aft and forward free flow areas were separated from the under-casing free flow area by watertight bulkheads. Additional bulkheads were placed at the forward and aft ends of the pressure hull, Frame 18 and Frame 81, resulting in free flow being localized into the areas forward of Frame 18, aft of Frame 81, and under the casing spaces. The under-casing inflow ports were modeled as a geosim of the full-scale with an estimate of their width at approximately 0.067 m.
There are two primary drafts for the Victoria Class submarine surface operations, the #4 Main Ballast Tank (MBT) Vented, operating condition and the Standard Trim Condition (STC). All seakeeping experiments were conducted at the #4 Main Ballast Tank (MBT) Vented draft. The principal particulars for the full-scale boat and the model at the target draft are outlined in Table1.
Table 1: Full-scale boat and seakeeping model particulars
Model F- S (provided) Length (LOA), m 4.696 70.25 Beam, m 0.508 7.6 FWD Draft, m 0.462 6.909 AFT Draft, m 0.581 8.699 Displacement,
tonnes 0.671 (fresh water)
2281.0 (salt water)
Trim by Stern, deg. 2.01 2.01
Parameters that differ between the boat and model due to modifications in model design:
VCB, m abv. USK 0.290 (4.34 eq. f-s) 4.354
BM, m abv. USK 0.012 (0.18 eq. f-s) n/a
VCG, m abv. USK 0.264 (3.95 eq. f-s) 4.184
GMT, m 0.038 (0.57 eq. f-s) 0.362
LCG, m from
midships 0.088 (1.32 eq. f-s) 1.274
Where USK is defined as Under Side of Keel. The displacement excludes free floodable volumes and all dimensions exclude the presence of acoustic tiles installed on the full-scale hull.
The differences between the equivalent full-scale data (f-s, scaled up from the model) and target full-scale parameters resulted from omission of acoustic tiles from the offset and changes to the model pressure hull shape due to separation of bow and stern free flows from flow under the casing by vertical bulkheads at Frames 20 and 81.
Static/Dynamic Stability
The model was ballasted to the required displacement and draft marks. The ballast mass distribution was arranged to achieve a model natural roll period
equivalent to full-scale period of 8.76 seconds in water. To accomplish this, the “dry” roll radius of gyration (kXX) of the model was set to 0.418B and the transverse metacentric height (GMT) was modelled at 0.572 m full scale.
Appendages
The model was fully appended with sail, stern planes in a cross (+) configuration (fixed aft horizontal planes, two vertical active rudders)and removable bow planes (all NACA 0015 section with the exception of the sail which is a NACA 0018 section).All the lifting surfaces other than the rudders were fixed with zero angle of attack.
Propulsion system
The submarine was fitted with a single screw propulsion system with power provided by a brushless DC motor. A B5 fixed pitch propeller was fabricated specifically for this model. No effort was made to model the full-scale submarine propulsion system characteristics. The propulsion system, including propulsor, was designed and fabricated to produce sufficient thrust to achieve target model speeds during experimentation.
Model construction
The model hull was built in three sections: a main hull lower half, a main hull upper half and a tail section. The joint between the main hull was horizontal and at the elevation of the center of the pressure hull. The aft floodable section was built as one piece and bolted to a bulkhead fixed to the aft end of the bottom hull half. The hull construction was comprised of a laminated sandwich structure consisting of a 0.5 mm thick layer of blue gel coat with two layers of 10 ounce fibreglass cloth on the outside, a layer of 3/8 inch (0.9525 cm) closed cell foam in the center and two layers of 10 ounce fibreglass cloth on the inside. The resin used for this matrix was a 5:1 laminating epoxy resin. The top hull was fitted with two sealable access hatches, one forward and one aft of the sail. These hatches permitted a limited amount of access to electronic components within the hull. Sketch describing the layout of model is given in Fig. 8.
A ctive rudders, operating turning gear, motor control, angular feedback and radio telemetry permitted the rudders to be operated either on autopilot or manual control remotely from shore. Both the upper and lower rudders were linked to insure that they operated as a ganged pair. The model slew rate was design to model the full-scale rudder angle slew rate of 7
degrees/second.
Model marking
The model was painted white and marked with test condition waterline (FWD draft marks located 1.534 m (22.945 m full scale) forward of amidships (aligned with forward sonar mast) and the AFT draft marks located 1.923 m (28.775 m full scale) aft of amidships (aligned with rudder stock)) and model number.
Model Autopilot
To ensure that the model test results were repeatable and consistent between runs, IOT designed a
proportional-derivative (PD) controller with the goal of maintaining a constant heading angle with respect the incident wave direction. System identification techniques were used to obtain a model of the steering dynamics at each of the test speeds using a first-order Nomoto model. There are two objectives to the modeling: first, the model was used to develop the controller gains and secondly for Kalman filtering. The Kalman filter was used to produce noise-free estimates of the vessel’s yaw and yaw rate. The filter also produces estimates of the wave-induced (first-order) motion in yaw, and helps to remove this component from the rudder command signal. The derived system gains are provided in Table 2.
Table 2: Autopilot system gains Forward Speed (knots) Proportional Gain (KP) Differential Gain (KD) 3 2.3932 4.9867 6 1.6903 2.2790 Maximum Speed 0.797 1.0777
It should be noted, that there was no effort to emulate the characteristics of the Victoria Class submarine autopilot, as these attributes were unknown to IOT.
Seakeeping Model Instrumentation
The model was instrumented to measure 6D motions, velocity, speed of propeller, rudder angle, relative motion and water level in selected locations. Wave elevation was measured in the basin.
Model motions were measured with six degrees of freedom using the Crossbow VG700CB Fibre Optic Vertical Gyro (FOG): This unit was fitted on the model longitudinal centreline at a position near the nominal model CG. The Qualisys motion capture and tracking system was used to determine model speed over ground. Array of sonic probes and capacitance probes were used
to measure relative motions, wave elevations and water level at locations along the model hull and in the basin. Rudder angle and shaft speed were measured using magnetic angle and directional sensors. Overall more than 40 data acquisition channels were required for collecting model and environmental information.
Seakeeping Test Program
The model test program includes seakeeping
experiments in regular and irregular waves, drift tests, and roll and pitch decay tests.
Irregular Wave Experiments
Irregular wave experiments were carried out at seven heading angles with respect to the incident wave direction (0, 30, 60, 90, 120, 150 and 180 degrees where 180 degrees is defined as a head sea) at forward speeds of 0 knots (beam seas only), 3 knots, 6 knots and maximum speed (nominally around 13 knots full-scale); 0.059, 0.117, and 0.225 Froude numbers
correspondingly. Experiments were performed in sea state 3 to 6 using a JONSWAP spectrum for fetch-limited seas defined in terms of peak frequency, significant wave height and a gamma factor of 3.3. The sea conditions for these runs are defined as:
Sea state 3, Hs=0.88 m, Tp=7.5 sec, Sea state 4, Hs=1.88 m, Tp=8.8 sec, Sea state 5, Hs=3.25 m, Tp=9.7 sec, Sea state 6, Hs=5.00 m, Tp=12.4 sec.
Regular Wave Experiments
Regular wave experiments were carried out in beam seas only at zero and three knots full scale speeds and for a range of 13 wave length to model lengths ratios: 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 1.0, 1.05, 1.1, 1.2, 1.3, 1.5 and 2.
Roll Decay Tests
Dedicated experiments were carried out in calm water to determine the roll damping characteristics of the submarine hull form. The tests were carried out at zero and all target forward speeds. Since the bow planes are retractable on the Victoria Class, there was an interest in assessing the damping with and without the bow planes in place. The model was excited three times for each condition and the relevant responses were measured.
Results
During the seakeeping experiments, over 500 test runs were conducted. All presented results are projected to full-scale values. The primary goal for the experiments was to provide data for the submarine surface
operational evaluation and for validation of numerical codes applied to simulate performance of the submarine.
Motions in Irregular Waves
The roll responses in irregular seas were the primary interest of the sponsor of the study. Summary results are shown in Fig. 9. The roll angle rms
(root-mean-square) for each sea state (SS3 to SS6), nominal speed (S3, S6 and S14) and heading angle are presented. The most significant responses, as expected, were observed in beam seas and at lower speeds. Increases in speed provided a reduction of roll motions. The roll data were also used to produce contour plots on a polar axis, Fig.13. These polar plots, produced for selected sea states, are provided to submarine operators as operational guidelines.
Summary pitch and heave responses are presented in Fig. 10 and Fig. 11 respectively. Similarly to roll motions the largest responses are observed during operations at low speed and high sea states and increasing boat velocity stabilizes the motions.
Regular Wave Tests
Results of experiments in regular waves (two speeds) are presented in Fig. 12. The RAOs (response amplitude operators) are defined as a ratio of RMS roll motion over the regular wave RMS.
Roll Decay Tests
Examples of roll decay test data are shown in Fig. 14 to Fig. 16. The presented results include zero speed, with and without bow planes, and 3 knots speed with bow planes. The time series peak data was used to calculate log decrements (δ) as the natural log of ratios of two successive amplitudes, and damping ratio (ζ) for all measured amplitudes was computed from formula:
2 2
4
π
δ
δ
ζ
+
=
An identical procedure was used to present roll decay data of the 2D model, Fig. 2.
Uncertainty Analysis
The International Towing Tank Conference (ITTC) recommended ISO-GUM (International Organization for Standardization, Guide to the Expression of Uncertainty in Measurements, ISO 1995) approach was applied to conduct uncertainty analysis of the results.
Type A uncertainty was evaluated based on standard deviations obtained from repeated measurement (six to eight repeats were applied in this project). Type B uncertainty includes quantified sensor quality, calibration processes and precision of instrument installation. The estimate is based on manufacturers’ specifications and previous experience with instruments and model fabrication.
Table 3. Summary of uncertainty analysis
Type A Type B Total Standard
Roll angle, deg. 0.10 2.00 2.0 3.6%
Pitch angle, deg. 0.031 2.00 2.0 18.2%
Heave
displacement, m 0.0005 0.03 0.03 2.2%
Type B uncertainty is the most significant contributor to the total standard uncertainty of angular measurements. In particular, the accuracy of the device used for measurements of dynamic roll and pitch angles is estimated by the manufacturer at 2 degrees rms. Experimental repeatability (Type A uncertainty) is well within projected measuring accuracy.
Conclusions and Observations
In general the project results meet its original objectives by producing good quality data and suitable for benchmark and validation of numerical codes. In addition a few observations were made over the course of the project that affected final design of the model.
Application of the “dry” model for the sea-keeping surface operational evaluation experiments was considered in the initial stages of the project. This was based on an assumption that a simple correction factor will be feasible based on results of the 2D model tests. The presented test results indicate that the behavior of the 2D body is highly nonlinear and derivation of a single correction factor for all experimental
configurations would not be practical. Results of roll decay experiments indicate very different behavior of the “dry” model. The sealed under-casing volume provides significant amount of additional buoyancy, resulting in considerably higher restoring moment and shorter resultant damped rolling period, 3.86-3.9 seconds vs 5.25 - 6 seconds for “wet” model configurations.
The roll decay tests clearly indicate higher damping ratio for the smaller under the casing opening, Figure 4 and Figure 5. Responses to excitation of regular waves confirm marginally larger roll for wider opening (smaller damping). Examination of the relevant time series shows that due to low roll damping for this type of body and high non-linearity of the process, the body has a tendency to respond in its natural frequency rather than at frequency of excitation. This occurs when the exciting wave frequency is near the body natural frequency. The 2D body exhibits the characteristics of a classic lightly damped system. Responses at off-resonance excitation frequencies are low but the system will resonate sharply for near-resonance frequencies or multiples. The speed of onset of resonant rolling appears to be dictated by the size of the casing openings. Small openings delay the entry of water resulting in net buoyancy that excites the resonant rolling relatively quickly. Large openings allow the water to enter the casing quickly and thus buoyancy roll moment is not developed. This results in a smaller roll moment (resulting from dynamic pressure only), which takes a longer time to develop the resonant rolling.
The seakeeping model roll decay experiments indicate expected increase of damping with growing model forward velocity. The variation was found to be well represented by a first-degree polynomial with gradient equal to 0.0085 and y-intercept at 0.0327 for range of
measurements between speeds of 0 and 13 knots. The R2 goodness of fit coefficient between the regression line and observed values is 0.9911.
Impact of bow planes on roll damping at zero forward speed was found to be negligible. The quantitative difference in linear damping is insignificant and is contained within experimental uncertainty.
References
Hermanski, G. (2007), “Victoria Class Submarine, 2D Model Investigation of Free Flow Phenomena”, Institute for Ocean Technology NRC Canada Report TR-2007-12, April 2007.
Thornhill, E., Hermanski, G., “Numerical and Experimental Analysis of Surface Submarine Roll Decay Behaviour”, Journal of Ocean Technology, Vol. 3, No. 1, Jan-Feb-March, 2008, pp.91-100.
Hermanski, G., Cumming, D. (2008), “description of Surface Seakeeping Experiments on Victoria Class Submarine Model IOT769”, Institute for Ocean Technology NRC Canada Report TR-2008-15, December 2008.
Hermanski, G. (2010), “Uncertainty Analysis, Surface Seakeeping Experiments with Model of VCS”, Institute for Ocean Technology NRC Canada Report TR-2010-01, March 2010.
Figures
Fig. 1. 2D Model General Arrangement
Fig. 2: Roll Decay, 2D Model, STC_40, 40 deg.
PERMEABILITY COMPARISON STC_P60_O15 vs STC_P80_O15 0 0.02 0.04 0.06 0.08 0.1 0 5 10 15 20 25 30 Amplitude [deg] D a m p in g R a ti o STC_40_15_10 STC_40_15_20 STC_40_15_30 STC_40_15_40 STC_40_15_50 STC_20_15_10 STC_20_15_20 STC_20_15_30 STC_20_15_40 Expon. (STC_40_15_10) Expon. (STC_40_15_20) Expon. (STC_40_15_30) Expon. (STC_40_15_40) Expon. (STC_40_15_50) Expon. (STC_20_15_10) Expon. (STC_20_15_20) Expon. (STC_20_15_30) Expon. (STC_20_15_40)
Fig. 3: Roll decay, permeability comparison
OPENING COMPARISON STC_P80_O15 vs STC_P80_O30 0 0.02 0.04 0.06 0.08 0.1 0 5 10 15 20 25 30 Amplitude [deg] D a m p in g R a ti o STC_20_15_10 STC_20_15_20 STC_20_15_30 STC_20_15_40 STC_20_30_10 STC_20_30_20 STC_20_30_30 STC_20_30_40 Expon. (STC_20_15_10) Expon. (STC_20_15_20) Expon. (STC_20_15_30) Expon. (STC_20_15_40) Expon. (STC_20_30_10) Expon. (STC_20_30_20) Expon. (STC_20_30_30) Expon. (STC_20_30_40)
Fig. 4: Roll decay, opening comparison, permeability 80%
OPENING COMPARISON STC_P60_O15 vs STC P60_O30 0 0.02 0.04 0.06 0.08 0.1 0 5 10 15 20 25 30 Amplitude [deg] D a m p in g R a ti o STC_40_15_10 STC_40_15_20 STC_40_15_30 STC_40_15_40 STC_40_15_50 STC_40_30_10 STC_40_30_20 STC_40_30_30 STC_40_30_40 Expon. (STC_40_15_10) Expon. (STC_40_15_20) Expon. (STC_40_15_30) Expon. (STC_40_15_40) Expon. (STC_40_15_50) Expon. (STC_40_30_10) Expon. (STC_40_30_20) Expon. (STC_40_30_30) Expon. (STC_40_30_40)
Fig. 5: Roll decay, opening comparison, permeability 60%
DRAFT COMPARISON STC_P80_O15 vs DR2_P80_O15 vs DR3_P80_O15
0 0.02 0.04 0.06 0.08 0.1 0 5 10 15 20 25 30 Amplitude [deg] D a m p in g R a ti o DR2_20_15_10 DR2_20_15_20 DR2_20_15_30 DR2_20_15_40 DR3_20_15_10 DR3_20_15_20 DR3_20_15_30 DR3_20_15_40 DR2_20_15_50 DR3_20_15_50 STC_20_15_10 STC_20_15_20 STC_20_15_30 STC_20_15_40 Ex pon. (DR2_20_15_10) Ex pon. (DR2_20_15_20) Ex pon. (DR2_20_15_30) Ex pon. (DR2_20_15_40) Ex pon. (DR3_20_15_10) Ex pon. (DR3_20_15_20) Ex pon. (DR3_20_15_30) Ex pon. (DR3_20_15_40) Ex pon. (DR2_20_15_50) Ex pon. (DR3_20_15_50) Ex pon. (STC_20_15_10) Ex pon. (STC_20_15_20) Ex pon. (STC_20_15_30) Ex pon. (STC_20_15_40)
Fig. 6: Roll decay, draft comparison
Fig. 7: Submarine body plan
Fig. 8: Seakeeping model layout
ROLL RESPONSES (Irregular Seas)
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 0 30 60 90 120 150 180
HEADING ANGLE [deg]
R O L L A N G L E [ R M S ] SS3_S3 SS4_S3 SS5_S3 SS6_S3 SS3_S6 SS4_S6 SS5_S6 SS3_S14 SS4_S14 Heading 180 deg =
Fig. 9: Roll angle rms
PITCH RESPONSES (Irregular Seas)
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0 30 60 90 120 150 180
HEADING ANGLE [deg]
P IT C H A N G L E [ R M S ] SS3_S3 SS4_S3 SS5_S3 SS6_S3 SS3_S6 SS4_S6 SS5_S6 SS3_S14 SS4_S14 Heading 180 deg =
Fig. 10: Pitch angle rms
HEAVE DISPLACEMENTS (Irregular Seas)
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0 30 60 90 120 150 180
HEADING ANGLE [deg]
H E A V E D IS P L A C E M E N T [ R M S ] SS3_S3 SS4_S3 SS5_S3 SS6_S3 SS3_S6 SS4_S6 SS5_S6 SS3_S14 SS4_S14 Heading 180 deg =
Fig. 11: Heave displacement rms
ROLL AND PITCH ANGLE (Regular Waves, RAO)
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 CIRCULAR FREQUENCY [rd/sec]
R A O [ d e g /m ] Roll_0 Pitch_0 Roll_3 Pitch_3
Fig. 13: Roll angle contours on polar axis
Fig. 14: Roll decay, Speed 3 knots - with bow planes.
Fig. 15: Roll decay, Zero speed - with bow planes
