International Conference on Fast Sea Transportation FAST'2005, June 2005, Sl.Petersburg, Russia
SIMULATIONS AND F U L L - S C A L E T R I A L S F O R A HSC L I N K E D B Y
W A V E - H E I G H T M E A S U R E M E N T S
Karl Garme and Jakob Kuttenkeuler
Division of Naval Systems, Royal Institute of Technology, K T H Teknikringen 8, SE-100 44 Stockholm, Sweden
A B S T R A C T
A set of full-scale sea trials with a planing craft, M'as performed in coastal conditions measuring motions and accelerations. The primaiy objective of the trials M>as to investigate the seakeeping characteristics at moderate sea conditions. Sea state was measured using an in-house developed directional M'm>e measurement system presented in the paper. The wa\'e buoy is tailored for localized sea trials in coastai waters and verified by a
M>a\'e-wire installation at an off shore lighthouse. The sea trial data is used to investigate correlation with a
2-dimensional time-domain strip model for planing hull in head seas. The potential theoiy based simulation model uses a pre-calcul ation scheme for added mass and hydrostatic coefficients. The equation of motion is up-dated at each time step fi-om the pre-calculated data with reference to the local instantaneous draught and the solution catches the non-linear behavior of the planing hull. The simulations show generally good correlation with experiments although the study concludes that the accelerations are somewhat under estimated and sometimes veiy sensitive to the variation in forward speed. This response sensitivity' stresses the importance of localized wave measurements when full-scale experiments are made.
I N T R O D U C T I O N
The operability of high-performance craft, e.g. patrol craft for police, navy or cost guard, is often specified with respect to sea state and forward speed. The question may be rised how such specifications are followed up with the obvious difficulties to know the sea state. In the fiiture, onboard measurement systems might register the directional spectrum of the sea. Attempts have been made using radar technique, but the most common way is to approximate the wave height by the eye believing that what the skilled seaman sees is the significant wave height with an acceptable accuracy.
Investigations and predictions of structural loads or seakeeping characteristics for high speed craft aim at describing the situation of the real ship in a true seaway. Prediction methods, semi-empirical or theoretical, are normally validated with respect to model test data but the difference between the ship at sea and a model experiment is more than just the scale. The ship condition is always approximate and its shape, appendices, propulsion and maneuvering systems differ from the modeled. Still, the perhaps most uncertain factor when comparing computations and a fiill-scale situation is the wave enviromnent. This is not necessarily because of the difficulties to model the wind generated sea states, but due to the fact that the conditions at sea not easily lend themselves to be determined. This is definitely the case in costal condfions and in shallow waters as the
Baltic where the wave conditions change rapidly and thus standard spectrum formulations might not give a good description of the waves. This partly explanains why firll-scale validation of computational tools is rarely seen in the literature. Another reason is of com-se the high cost for full-scale trials. Nevertheless, it is striking how many full-scale investigations actually are made and how seldom the wave conditions are measured, even though the investigations often are specified with reference to a sea state.
Garme & Rosén (2003) review comparisons of computational results produced by an early version of the simulation model used in the present study, with full-scale measurement data. A t those sea trials, (Rosén 1998), the ship itself was used as wave buoy and a reasonable picture of the wave system was obtained. Later the division of Naval Systems K T H , have participated in full-scale trials with naval vessels and the need for a simple system for localized wave height measurements has become obvious. For this reason a portable wave buoy system with du'ectional capacity has been developed. In the present paper the buoy and its validation is described together with a full-scale investigation where the buoy was used. The wave buoy data have been used to create wave models as input to the time-domain model for simulation of planing craft. With the wave model linking simulations and fiall-scale measurements some comparisons between simuladons and
measurements have been performed and are reviewed and discussed in the paper.
1. T H E SHIP AND I N S T R U M E N T A T I O N The present investigation was performed using a Swedish multipuipose light transportation HSC for coastal conditions. The body plan is shown in Fig. 1 and main particulars in Table 1.
////in
Fig. 1: Body plan. Table 1: Main particulars.
Displacement 44 ton
LOA 22.6 m
Mean draught 1.0 m
Trim (bow up) 1.1 deg
Beam 5.4 m
LCG 7.8 m
The ship was instrumented for registration of rigid body motion and accelerations and data was stored on a standard PC. Ship position, speed and course were measui-ed using global positioning system GPS. Ship fixed vertical accelerations were measured using two bulkhead-mounted linear accelerometers (Brilel & Kjear 4507) at the center line and about 8 meters apart. Accelerations were sampled and stored at 1000 Hz. Boat motions were measured using a gyro enhanced motion sensor 3DM-GX1, Microstrain Inc (2004), including 3 linear accelerometers, 3 magnetometers and 3 rate gyroscopes, mounted near the ship center o f gravity. The motion sensor was sampled at about 76 Hz.
2. W A V E M E A S U R E M E N T S
During the trials the sea state was measured using the in-house developed wave gauge system Biding.
Buling is a small portable research buoy with a
displacement of about 3 kg that is tailored to support localized sea trials such as the present. The development has been driven by the need for detailed and unbiased characterization of the local sea state at, or at least near, the position of the trials. Hence, some of the more dominating design objectives has been robusmess, extreme light weight and low cost using mostly off-the-shelf components. Another important objective has been the capability of launch and recovery from any boat in any coastal sea state at the location of the trials. The use as a research tool also
dictated detailed tune series data output for later post processing rather than on-board analysis, data reduction and telemeti-ic deliveiy of significant values. The system, shown in Fig. 2, consists o f the buoy itself, the mooring system, a recovery system and analysis software.
Fig. 2: The Buling system M'ith mooring. The gauge buoy is a 0 0.23 m half spherical carbon-fiber/epoxy composite container with a threaded transparent lid. Mooring is achieved using an anchor, a secondary buoy which is connected to the gauge buoy by a floating rope and a 3 m long steel chain. This mooring configuration assures low horizontal physical constraints on the gauge buoy which is especially important for the directional analysis. The mooring also enable easy recovery even in rough sea through hooking of the floatmg rope by the use o f a heaving-line.
The motion of the gauge buoy is measured using 9 temperature compensated sensors, 3 accelerometers, 3 magnetometers and 3 rate gyroscope sensors in a common housing, Microstrain Inc. (2004). A l l conditioned signals are logged at a rate of about 50 Hz and stored on a solid state flash memory m a standard palm-top computer. Both sensors and logger are powered by two rechargeable Li-Polymer batteries with low magnetic signatures. Filtering of measured gauge data is done using discrete fourier decomposition of the time signals. Further data reduction uses both peak identification techniques in the time domain and spectral analysis. The calculation of the directional wave spectrum is based on the iterated maximum likelihood method accorduig to Pawka (1983) and Benoit (1993) implemented in a computational package, Johnsson (2004).
The magnetometer data enables direct transformation of accelerometer and rate data from the buoy fixed reference system to the earth fixed reference system. This means that the influence of roll and pitch seakeeping characteristics of the buoy disappear. Naturally, the dynamic characteristic in the heave direction is still critical. Further, Billing is designed for use in both open water and coastal measurements in the archipelago where fairly short wave fetch and thus shorter wave periods are dominating. To ensure adequate measui'ements a study of the buoy
seakeeping characteristics was performed by Dedovic (2005). The analytical heave transfer fianction is shown in Fig. 3. The curve shows that the buoy follows wave components with periods down to 2 seconds with negligible distortion. The heave natural fi-equency was also experimentally verified to 1.4 Hz which corresponds well with the peak in the analytical transfer function.
A number of dry laboratory tests of the buoy sensors, signal conditioning and analysis, were perfonned subjected to both harmonic and irregular motion although not reported here. Further, a set of verifying buoy measurements at sea was performed using earth fixed reference wave height measurements from a capacitive wke gauge mounted on a free standing light house. This non-directional reference gauge was mounted hanging from a 5 meter horizontal cantilever beam mounted on the side of the 0 3.5 m light house foundation and rigged to log gauge data continuously. A t 5 occasions at various sea states Billing was placed near the reference gauge for comparative data collection during typically 500 wave encounters. A summary of the results for five measurements is given in Table 2 where significant wave height is denoted H, 3 and mean period between zero-crossings 71. A maximum discrepancy of about 5% is seen for both wave height and period.
Table 2: Buling and reference gauge comparison.
Buling Reference gauge
Hi/3 [m 1 2.5 0.52 2.6 0.53 2 4.1 1.25 4.0 1.32 3 3.5 0.82 3.7 0.83 4 2.9 0.51 2.9 0.50 5 2.4 0.38 2.5 0.40
In the present study no directional buoy data was used since the validation of the directional capacity is still ongoing. However, results from sea trials are promising and a dfrectional wave spectrum plot from a measurement in dominating wave direction 152° is shown in Fig. 4. 1 6 -L'l • 1.3 • DB OA -j l 1 1 1 i I D 0.5 1 1.5 2 25 FrfcqjEfic^ [Hz]
Fig. 3: Wave buoy heave transfer function.
Directional spectmm eslimaled using If/LM method 10"
m ^ s / d e g
Fig. 4: Directional spectrum with a dominating wa\'e
direction of 152°.
3. S I M U L A T I O N O F T H E P L A N I N G C R A F T The simulation model is developed at the division of Naval Systems, K T H . It is a 2-dimensional time-domain strip approach to model the planing hull in head seas. The hydrodynamic force calculations are based on the concept of added mass. The added mass coefficients are pre-calculated for all sections, strips, and determined for an incident velocity of unity and for a number of draughts. The pre-calculation scheme means that the hydi^odynamic problem is solved only once which minimizes the computational time when performing the simulation. The relative velocity between the hull section and the incident water is along with the local section draught determined during the tune-stepping procedure. This data together with the pre-calculated data defuies the coefficients in the equation of motions that becomes time dependent and the solution catches the non-linear behavior of the planing craft in waves. The simulation model is described in Garme (2004).
The simulation model follows the tradition from Zarnick (1978) and later Keuning (1994) and Akers (1999) but is different on some points, for instance on the load distribution m the near-transom area. It is generally known that a strictly 2-dimensional load calculation leads to a too small trim angle for a hull planing in cahn water. This has, starting with Zarnick (1978), been treated by a correction o f the hydrostatic part of the lift force and pitch moment. Garme (2005) suggests a coiTection of the aft end of the complete load distribution so that the load is zero at the transom and successively increasing alongships until it after a distance reaches the level of the 2-dimensional distribution, see Fig. 5.
Fig. 5: Definition of the distance, a, of load reduction
and the principal load distribution of a planing craft in calm water.
The correction is semi-emphical and has been determined basically refening to the calm water experiments of Fridsma (1969). The distance of load reduction, a, is expressed as,
— ^ = 0.34 (1)
BC,
where B is the craft beam and C,, is the beam Froude number. As shown in Ganne (2005) the agreement between simulations and the Fridsma (1969) results is increased both conceming calm water and planing in regular waves. Successftil comparisons were also made between simulations and corresponding model experiment series, see Garme (2005). This time-domain comparison was achieved by creating a wave-height measurement based wave model using the method by Garme & Hua (1999). The simulation model is considered verified for prismatic planing hulls with high (C^>2) constant forward speed heading long-crested waves.
The wave model used for the simulations is a superposition of linear deep water wave components described by potential theory. The wave surface is described as,
N
where the first factor is to avoid transient disturbances in the initial stage of the simulation. The constants a,„ k„ and w,, denote component amplitude, wave number and angular frequency respectively and 7„ is a randomly chosen component phase shift between 0 and n. The number of regular wave components are denoted A^.
When a time-domain wave model is made based on a wave spectrum, S(w), is the energy canying part of the frequency domain divided in N parts and the corresponding component amplitudes are expressed as,
where co\, is the discrete frequencies ranging from
Aco to NAco stepped with the constant value Am. Each
component value co„ in the wave model is randomly chosen in the interval
(to'„-^y^)<m„<[ai\,+^y^) (4)
to avoid periodicity among the components that could lead to a too low degi'ee of frregularity. The component wave number follows from the dispersion relation. With the component constants determined, the water surface and velocities are analytically known for all instances and positions and the local draught and water particle velocities can be determined along the hull.
Ll this particular investigation the irregular wave models were developed from wave-height time series. The buoy motion time series were ti'ansformed to energy specti'a by FFT analysis and then re-composed to time-continuous irregular time series in terms of component constants according to the above sketched scheme. In the present study where wave buoy time signals from measurements in the actual test area were available this is an effective and rational way of obtaining a relevant wave model. Even so, one should be observant on that in coastal conditions veiy local changes in wave characteristics can be found caused by changes in wind characteristics and water depths. The water depths ranged between 15-30m. h i such conditions the use of standard wave spectrums formulated for hilly developed conditions with infinite water depth is very doubtful.
To ftirther illustrate this the five buoy measurements that foiTn the basis for the simulations are summarized in Table 3. The measurements were made during 30-60 minutes and comprised 450-900 wave peaks. Measurements 1 and 2 where made within a time period of 2 hours at fairly constant wind conditions. Measurements 3-5 where made within 4 hours again in fafrly constant wind conditions but with old decaying crossing sea almost orthogonal to the new wind generated sea. It was during the tiials evident that ocular estimations o f wave height is a very um'eliable technique.
Table 3: Summaiy of wave measurements.
1 2 ' 3 4 5 r , [ s ] 3.1 3.5 4.4 4.0 3.8 H,3\m} 0.74 0.93 1.45 1.19 1.08
4. S I M U L A T I O N S AND T E S T S 5. R E S U L T S AND C O N C L U S I O N S The prime objective of the hall-scale trials was to
investigate the ship motional responses at the present wave conditions. Further, the study also gave an opportunity to approach simulation of a full-scale situation and perfonn comparisons between calculations and measurements.
A l l in all, 5 runs in head seas o f about 15 minutes each were performed. The ship fomard speed was approximately 10, 18 and 24 knots, corresponding to beam Froude numbers o f C,,=0.7, 1.3 and 1.7, of which all are less than 2 which is the lowest speed for which the simulation model is verified. Nevertheless, it is clear from Garme (2005) that the limit Cv=2 is high enough but C,,= 1.33 is a too low speed and that the limiting value is unknown, besides the fact that there is not an absolute limit rather a gradually decrease in accuracy for lower speeds. The highest speeds at the trials were around 24 knots, i.e. Cv=1.7 which is here considered high enough to expect acceptable accuracy. Of course it should be kept in mind that the calculations are made at the lower speed limit of the model validity.
The ship forward speed over ground, measured by GPS, varies during a run about ± 1 knot. In the simulations however the ship moves at constant speed through the waves. The importance of this difference is not obvious and w i l l be discussed later but in order to catch the speed influence on the responses a set o f simulations of each trial run is made with forward speed about 1 knot above and below the mean speed ofthe full-scale ship.
The pre-calculation is made on the geometry as shown in Fig. 1. The pitch radius of gyration is assumed to be 25% o f the overall length which might be on the large side since the ship was fafrly lightly loaded and with most bunker close to the CG.
The forward speed and wave measurement characteristics around the time o f the two studied head sea runs, in the following referred to as Case I and Case II, are shown in Table 4.
Table 4: The runs suitable to simulate.
Case I Casell
Full-scale speed: Full-scale speed:
23.2±1 kn 23.9±1.2kn
Measured waves: Measured waves:
Hi/3=0.74 & 0.93 m H i / 3 = I . 1 9 & 1.08 m
T,=3.1 & 3.5 s T,=4.0 & 3.8 s
Comments: Comments:
relatively long crested intersecting wave systems waves, large local variations with distinctly different main in the test area wave direction, head sea was
defined relative to the dominating wave system
Simulation of the ship running in calm water at speeds o f 23 and 25 knots resulted in a steady state running attitude o f 3.6° and 3.9° respectively and a dynamic lift at CG of 0.09 and 0.13 m. Further, the hull was simulated in regular waves and the natural period of pitch and heave motion was identified to approximately 2.7 s. Accordmg to hydrostatic calculations the bow-up trim at rest was 1.2° which corresponds well with the experimental value and confirms the LCG.
The motion measurement unit was unable to measure static angles which mean that the running attitude was not measured and that the pitch time series show the hull pitch motion around an unknown mean. The simulation on the other hand deliver motional output relative to an inertial frame o f reference following the path of the ship at constant speed and the pitch oscillates around the mean running attitude.
The compared quantities fi'om the simulated and meastu'ed data of the two runs, Case I and II, were ship fixed vertical acceleration at the position of the accelerometers (1.2 and 9 mette ahead of the CG), pitch motion around the mean ruiming attitude and the angular velocity of the pitch.
For both computed and measured time-series the peak values were identified and used to determine fraction mean values, and fitted to a Weibull-disttibution in order to study expected maximum levels. The comparison shown in the following figures uses the
most probable largest value during 1 hour in the sea
state.
Figures 6 and 7 summarize the results o f the comparison. For Case I simulations have been performed with wave models based on wave measurement 1 and 2 and for Case II simulations were made at sea states corresponding to wave measurements 4 and 5. In both cases it was difficult to estimate which measurement was the most representative for the sea condition that the ship experienced. The measurement results are therefore indicated in Fig. 6 and 7 as a band rangfrig the variation o f significant wave height. Sunulations were made with forward speed about a knot above and below the mean measured speed over ground.
_ i MeasuremenI A Simjlation E O G + l k n • Simulation S 0 G - 1 k r • . 5 D.G U.7 D B 0.9 1 1.1 1.2 1.3 1.-i 1.-i MeasuremenI A Sirnvilation S Ü G + l k n T Simulation S O G - l k n O.B as 0 7 D.B 0 9 1 1.1 1.2 1 3 H , „ [ m l
Fig. 6: Accelerations at mid ship and at bow. The
most probable largest value to occur during 1 hour in the sea state.
• MeasuremEnl Simulaiion S O G + l k n Simulaiion S O G - l k n 0.6 0 7 O.a O.S 1 1.1 1.2 1.3 \i H , „ | m l ^ Measurement A Simulation S Ü G + 1 kn T Simulation S O G - l k n 0.6 O.B 0.7 OB 0.9 1 1.1 1.2 1.3 1.4 1.5 H , „ | m l
Fig. 7: Pitch and pitch rate. The most probable
largest value to occur during 1 hour in the sea state. BoM'-down is defined as positive pitch.
It can be concluded that the simulations of the two runs, with the wave height measurement based wave models, show results in fair agreement with the measurements. For Case I is the simulated variation of foiward speed hardly influencing the results. The pitch motion and rate is in good agreement with the measurement but the accelerations are under estimated. In Case If on the other hand, where the wave height is larger and all responses more pronounced, the simulated acceleration is very sensitive to the variation in speed. The step between 23 to 25 knots is almost doubling the acceleration levels whereas the pitch and pitch rate levels are almost constant. This dramatic change in acceleration is explained by the fact that the larger acceleration levels origins from the impact situation which is very sensitive to the relative velocity and simply does not seem to occur as frequently at the lower speed. This is illustrated in Fig. 8 where the chosen sequences characterize the difference between the two simulations. A t the higher speed the impacts are more distinct at an otherwise similar situation. Also for
Case II the pitch and pitch rate responses are m level
with the measurements and the accelerations are under estimated. C a s e 2, Forward EpeBi123 kn BB3 B90 B91 692 B33 694 B95 B9B B97 698 l i m e Is) C a s e 2 , Forward speed 25 kn 630 631 B32 633 634 635 63B 637 630 B39 64D time [s]
Fig. 8: Example of the ship fonvard speed influence
The speed sensitivity for the impact acceleration addresses a weak point in modeling of planing craft in waves. The acceleration is a veiy important quantity with respect to structural design, as well as human comfort and safety and thus cmcial to model correctly. Besides the speed the runnmg attitude affects the acceleration and this too is difficuh to model. In the present simulation model the forward speed is constant and the transom-load correction is chosen with respect to model experiments towed with constant velocity. The propulsion system of the f i i l l -scale ship influences the ixinning attitude and the self-propelled ship has a surge velocity that influences the impact occasions. The performance may increase i f the simulation model would be flirther developed to include the surge degi'ee of freedom and equipped with a propulsion model.
R E F E R E N C E S
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Hulls in the Vertical Plane, paper presented at
SNAME New England Section Meeting, April 29. 2. Benoit M . , 1993, Practical Comparative
Performance Sun>ey of Methods Used for Estimating Directional Wa\'e Spectra From Heave-Pitch-Roll Data, Proc. 23rd ICCE, ASCE, pp. 62-75.
3. Dedovic S., 2005, Motion Behavior Analysis of a
Half-Spherical Wave Buoy, MSc thesis, Technical
report, K T H , Naval Systems, http://www.ave.kth.se. 4. Fridsma G., 1969, A Systematic Study of the
Rough-Water Performance of Planing Boats,
Davidson Laboratoiy report 1275.
5. Garme K. & Hua J., 1999, A Method to Analyse
Seakeeping Model Measurements in Time Domain,
9th Int. Offshore and Polar Engineering Conference ISOPE'99.
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Simulations and Full-Scale Trials on Planing Craft in Waves, International Shipbuilding Progress, Vol. 50,
no 3.
7. Garme K., 2005, Improved Time Domain
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Int. Shipbuild. Prog.
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SPectra Toolbox for Matlab, Coastal Oceanography
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Fast Monohulls in Head Waves, Thesis Technische
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10. Microstrain inc., Williston, VT, USA, 2004,
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Manual.
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