Date 2013 Author D e y z e n , A.F.J, v a n
TUDelft
Address Delft U n i v e r s i t y of T e c h n o l o g y Ship H y d r o m e c h a n i c s and S t r u c t u r e s L a b o r a t o r y Mekelweg 2 , 2628 CD D e l f tDelft University of Technology
Improving the operability of planning monohulls
sailing in head seas using automated proactive control
of the thrust - Proof of concept.
by
A . F . J , van Deyzen
Report No. 1897-P 2013
Proceedings of the 12'" I n t e r n a t i o n a l C o n f e r e n c e on Fast Sea T r a n s p o r t a t i o n , F A S T 2 0 1 3 , A m s t e r d a m , The N e t h e r l a n d s .
FINAL SCIENTIFIC PROGRAM
Monday 2 December9:30 Registration 10:15 Opening Conference
10:30 Keynote irJ.L. Gelling Damen Shipyards 11:00 Keynote R. Bogaard KNRM
11:30 Coffee break
12:00 Keynote prof. Ir. J. Hopman Delft University of Technology 12:30 Keynote mr T. Eiiis - Specialised Vessel Sen/Ices
13:00 Lunch
14:00 Session 1A New Concepts Session 1B Seal^eeping 1 P44 Gelling P29 Grigoropoulos P06On/ieto P13 Stojanovic P32Shahraki P15 Peterson 15:30 Coffee break
16:00 Session 2A Seakeeping 2 Session 2 8 Wash P35 Olausson P41 Pinkster P37 Alien P09 Kuroda 17:00 Opening Reception at the Maritime Museum
Tuesday 3 December
9:30 Session 3A Stmctural Design 1 P05 Benson
P11 W u P45 Misiriis
11:00 Coffee break
11:30 Session 4A Structural Design 2 P24 Schiere
P27 den Besten P12 Tuitman
13:00 Lunch
14:00 Excursions
Session 3B Hullform design / Hydrodynamics P31 Paryshev P04 Rosenthal P20 Diez Session 48 Seakeeping 3 P26 Walree P14 Ahmadian P18 Ommani Wednesday 4 December
9:30 Session 5A Hydrodynamic Loads P08 Fine
P34 Varyukhin P38 Serebryakov
11:00 Coffee break
11:30 Session 6A Calm Water Resistance P07 Kinaci P22 Fossati P40 Scherer 13:00 Lunch 14:00 Session 7A CFD 1 P I 6 Kobayashi P17Tahara P I 9 Chen
18:30 Conference dinner at the Maritime Museum
Session 5B Seakeeping 4 P33 Davidson P48 Tascon P25 Castro Feliciano
Session 68 Motion Control 1 P28 Rijkens
P42 Deyzen P21 Yengejeh
Session 78 Dynamic Stability P01 De Jong P39 Sadat Hosseini P30 Castiglioni Thursday 5 December 9:30 Session 8A Hydrodynamics P36 Dogan P02 Gontsova P10 Lliopoulos 11:00 Coffee break 11:30 Session 8A Hydrodynamics P43 Cleijsen (Rijkens) P46 Zangle 12:30 Conference Closing 13:00 Lunch Session 88 Propulsion P03 Dang P23 Eslamdoost P49 Caponetto
IMPROVING T H E O P E R A B I L I T Y O F PLANING MONOHULLS SAILING IN HEAD
SEAS USING AUTOMATED P R O A C T I V E CONTROL O F T H E THRUST - PROOF OF
CONCEPT
A . F . J , van Deyzen, Ship Hydromechanics and Structures, D e l f t University o f Technology, The Netherlands
S U M M A R Y
The main limiting factor f o r operability for planing monohulls in head seas is the occurrence o f large vertical peak accelerations. To improve the operability a reduction o f the vertical accelerations is required. A solution f o r increasing the operability o f planing monohulls sailing in head seas may be found in proactive control o f the thrust.
This paper presents a proof o f concept f o r proactive control o f the forward speed, also defined as automated proactive thrust control. M o d e l tests have been carried out in the towing tank o f D e l f t University o f Technology. The speed o f the towing carriage was continuously determined using the outcome o f real-time response predictions. The magnitude o f the predicted vertical peak accelerations was used to determine the speed. The results o f these model tests showed that proactive control o f the forward speed based on predicted vertical peak accelerations is possible. The vertical accelerations can be kept within a predefined bandwidth.
N O M E N C L A T U R E R O M A N
Vertical accel. at the bow ( m / s ' )
AZcG Vertical accel. at the CG ( m / s ^ )
Boa Beam over all ( m m )
Beam waterline ( m m )
c Phase velocity ( m / s )
Cg Group velocity ( m / s )
hy Mass moment o f inertia ( k g m ' )
kyy Radius o f gyration ( m m )
LCG Longitudinal position C G ( m m )
Toa Length over all ( m m )
I'probe Distance wave probe- model ( m )
Lul Length waterline ( m m )
m mass o f model ( k g ) r Water elevation ( c m ) la Wave amplitude ( c m ) T D r a f t ( m m ) Deceleration w i n d o w ( s ) T ^ env
Period env. bichrom. wave ( s )
h Time interval ( s )
T Prediction window ( s )
Sample time during run ( s )
VCG Vertical position C G ( m m )
Vs Speed towing carriage ( m / s )
Vsa Initial speed during model tests ( m / s ) 11' Vertical orbital velocity ( m / s )
X Position towing carriage ( m )
G R E E K
M Total time-lag ( s ) Ate Calculation time ( s ) At,c Reaction time towing carriage ( s )
V Volume o f displacement ( d m ^ )
1. I N T R O D U C T I O N
The demand to sail at high forward speeds i n both calm water and i n a seaway remains high. For various patrol, search and rescue or military operations attaining high forward speeds is essential. Ships used for such mission purposes are often planing monohulls. I n head and bow quartering seas, the main factor for voluntary speed reduction is the occurrence o f large vertical peak accelerations [ 1 ] . Results o f f u l l scale measurements showed that a professional crew reacts to extremes rather than to the significant or 'average' values [2,3]. The occurrence o f large vertical peak accelerations imposes limits to the operability o f planing monohulls sailing i n head seas.
A challenge for designers o f fast monohulls is to explore different possibilities to increase the operability o f small, planing monohulls sailing i n head seas. The motion and acceleration levels increase w i t h decreasing ship size and increasing speed. To achieve an improvement o f the operability a reduction o f the vertical accelerations is required.
Operators on board o f small, planing boats apply so-called thrust control to avoid unacceptably large vertical peak acceleration during a trip. They temporary reduce
the forward speed before impact (proactive control) i f they anticipate that the next vertical peak acceleration might be unacceptably large. Results o f f u l l scale measurements showed that i f helmsmen are free to influence the thrust, a higher average forward speed is attained during the trial compared to a trial where the operator had to choose a constant throttle opening before the start o f the trial [4,5]. This suggests that thrust control may be a very effective way o f increasing the operability o f small, planing monohulls.
Proactive control o f the forward speed, also defmed as automated proactive thrust control, on a planing boat sailing in head seas (surge, heave and pitch) is presented in this study. Vertical peak accelerations have a very short duration. Unacceptably large vertical peak accelerations have a low frequency o f occurrence; not all wave encounters result i n an unacceptably large vertical peak acceleration (the response o f a planing monohull sailing in head seas can be considered to be nonlinear to the amplitude o f the incoming wave [ 1 ] ) . These two aspects are the incentive f o r a proactive control system. For automated proactive thrust control the f o l l o w i n g three components are essential [ 5 ] :
- A shipboard wave measurement system that provides a sufficiently accurate description o f the incoming wave(s) over the next f e w seconds;
- A computational model that predicts the response (especially the vertical peak accelerations) o f the ship based on the measured incoming wave faster than real-time;
- A stable control system that determines the thrust continuously and i f necessary applies the necessary amount o f thrust reduction i n time;
It has been assumed that the waves used f o r predicting the response can be measured by state-of-the-art techniques (laser, radar, lidar) in the near future. Real-time wave measurements from an object moving in waves and its transformation i n time to the ship's location are still very much state-of-the-art (see f o r example [7,8,9]). The development o f a shipboard wave measurement system for this specific purpose becomes more relevant when it has been proven that using proactive control the vertical acceleration level can be reduced on board o f a planing monohull sailing in head seas.
The first step is to proof the concept o f proactive control o f the forward speed. What makes automated proactive thrust control unique is the fact that the control is based on predicted vertical peak accelerations. The magnitude o f the predicted vertical peak acceleration determines the amount o f thrust reduction. The response o f the ship f o r the next f e w seconds needs to be predicted real-time while sailing. Due to the high relative velocity between the ship and the incoming waves the response needs to be predicted faster than real-time.
A proof o f concept is presented in this paper. The aim o f this study is to p r o o f that proactive control based on predicted vertical peak accelerations is possible. The
control scheme, presented i n [5,6], has been implemented in model experiments i n order to study the scheme i n a more realistic setting. M o d e l tests o f a planing monohull in regular and bichromatic waves are carried out. The water elevation i n front o f the towing carriage is measured continuously and provides the required wave input for the response predictions. The predictions are carried out real-time during a run. The forward speed is adjusted based on outcome o f the response predictions (the predicted vertical peak accelerations). The proactive control system should adjust the speed in order to keep the vertical accelerations w i t h i n a predefined bandwidth. Section 2 o f this paper explains the implementation o f the control scheme. Section 3 presents the experimental setup. Section 4 presents the results o f the model tests. Time-traces o f the measured water elevation, the speed o f the towing carriage and the measured and predicted vertical peak accelerations are depicted. I n Section 5 conclusions are drawn and recommendations are given. 2. I M P L E M E N T A T I O N P R O A C T I V E C O N T R O L
S C H E M E
Figure I depicts an overview o f the proactive control system in the test setup. The dashed frame represents the control system. The elements outside the frame are elements in the real w o r l d . The control strategy is that the response should be predicted for a certain time interval, called the prediction w i n d o w (7},„.), dependent on the control setting. The control setting i n this case is the speed o f the towing carriage (the model is f i x e d to the carriage).
The computational model that w i l l be used for the response predictions is the model developed by Zarnick [10] and Keuning [ 1 ] . I t is based on strip theory and has little calculation time. The CPU time depends on the number o f stations i n which the hull is divided and the time step used for the calculations, but generally speaking it is much faster than real-time. Moreover, this model is able to predict the short vertical peak accelerations.
lnrtan(^r^eouI h c * v « a n d pitch
motion
current eft sired forward speed
Simulation
nrwdel pr*Jict«d motion respcfise f n d c t t d venkal peak aeceterilion: ( l H e s A ( 2 > « f t > r o x . equal, or O l g r e a t e i than criterion? p - > < f a } ^ > - ^ | inert a i « V.
Figure 1: Overview proactive control system during model tests
A bandwidth i n which the vertical accelerations are considered acceptable is defined and used to determine i f speed reductions is required. A t the start o f the test the towing carriage accelerates to an initial forward speed. On time /, the response w i l l be predicted f o r the duration o f the prediction w i n d o w using the computational model for this initial forward speed. I f the predicted vertical
acceleration falls i n between the lower and upper limit o f a predefined bandwidth for the vertical accelerations, the speed used for the prediction may be maintained. I f the predicted vertical acceleration was smaller than the lower limit, speed increase is possible. I f it exceeds the upper limit, speed reduction is necessary. I f an alteration o f the speed is required, the next response prediction w i l l be carried out using the altered desired forward speed. The response predictions are performed sequentially (see Figure 2). The time interval between two predictions (tp) is equal to the calculation time f o r the predictions (Ate). The time interval between two predictions is therefore not constant. The time interval available f o r speed reduction is due to the calculation time always smaller than the prediction window: 7rf„.<7^„,-A/c..
Tpw
tp=Atc Tnw
ti+1 - I 1— t+2 ti+3
time instant
+
peak
Figure 2: Time line with respect to response predictions during model tests
3. E X P E R I M E N T S
3.1 E X P E R I M E N T A L SETUP
The experiments were carried out i n the towing tank o f the Ship Hydromechanics Laboratory o f the D e l f t University o f Technology. The towing tank has a total length o f 142 m and a w i d t h o f 4.25 m. The water depth during the experiments was equal to 2.34 m. The towing tank is fitted w i t h a hydraulically actuated flap type wave generator.
Figure 3 depicts a sketch o f the experimental setup. The model was fitted underneath the towing carriage using a strut. The stmt could move frictionless i n a guide bearing. It was fixed to the model using a support hinge. The model was free to heave and pitch, but it was fixed in all other directions. A guide bearing at the stern prevented the model to yaw.
the carriage. A l o w forward speed implied more measurement time for the given length o f the towing tank. Moreover, since these model tests, where the speed o f the carriage is controlled real-time during the tests, is a new concept, it was preferred to limit the speed due to safety reasons. The design speed o f the S A R boat o f the A r i e Visser class is 35 kts, which is equivalent to 4.5 m/s on model scale.
The used ship was the S A R boat o f the A r i e Visser class (see Figure 4). The model was ballasted to a typical weight, mass moment o f inertia, longitudinal and vertical location o f the centre o f gravity. Table 1 presents these values on model scale. Figure 5 depicts a photo o f the model beneath the carriage.
Table 1: Main particulars of Arie Visser Description Symbol U n i t V a l u e
Length over all ^oa m m 1175
Length between perp. Lpp m m 906
Beam over all Boa m m 381
Beam over waterline BSMI mm 259
D r a f t T m m 68.5
Displacement V d m ' 7.4
Long. Pos. CG w.r.t. app LCG m m 380 Vert. Pos. CG w.r.t. app VCG m m 102
Radius o f gyration kyy m m 303
Mass moment o f inertia lyy k g m ' 0.6794
guidtbtirlng
Figure 3: Experimental setup
A scale o f I / I 6 was chosen, leading to a model length o f 1.18 m (18.8 m on f u l l scale). The time scale, using Froude law o f similitude, was equal to 1/4. The resistance was not o f interest during these tests, so a large model was not required. A small scale limits the speed o f
Figure 4: Dutch SAR boat of Arie Visser class (Photo K N R M - Arie van Dijk)
The initial speed o f the towing carriage was equal to 4 m/s. Once the towing carriage attained a constant forward speed, the proactive control system was activated. Based on the predicted vertical peak accelerations the speed was reduced. I n case o f a bichromatic wave the speed was also increased again, once the wave amplitude started to decrease. The minimum speed was set to 1.75 m/s. This implies a speed range o f 7 to 16 m/s (13.6 to 31.1 kts) on f u l l scale, well in the middle to high speed range o f the S A R boat o f the Arie Visser class.
The bandwidth, between which the control system should keep the vertical accelerations, was chosen to be -17.5 to -12.5 m/s' (the z-axis is defmed positive downwards). The accelerations are independent o f the chosen scale when using Froude law o f similitude.
3.2 D E C E L E R A T I O N T O W I N G C A R R I A G E
The towing carriage at the D e l f t University o f Technology is able to attain a maximum speed o f 7 m/s. The maximum deceleration o f the carriage is -I.O m/s'. This is, however, the absolute maximum deceleration. Using a maximum deceleration o f -0.8 m/s' the risk o f damaging the engines on the carriage has been reduced to an acceptable level. The towing carriage has its o w n speed control system. I f the desired forward speed has been altered, its control system w i l l see to it that the speed changes to the new desired speed.
Deceleration tests were carried out to determine the path o f the deceleration. I t was found that the maximum deceleration cannot be attained instantly. A time-lag between the moment that the chosen speed reduction has been communicated with the control system o f the carriage and the start o f the deceleration exists. Figure 6 depicts the path o f the speed o f the carriage, once the desired forward speed has been changed. The time the towing carriage needs to react has been defmed as A/,c. The total time-lag before between the start o f a response prediction and the start o f a speed reduction is therefore equal to: At = At, + A/^.
The forward speed changes gradually. I t shows a S-shape. The reaction time o f the carriage is typically 0.4 to 0.5 s. I f sufficient time is available the deceleration reaches its maximum value o f -0.8 m/s'. The average deceleration is therefore less than the maximum value. I f an aheration o f the forward speed is required the change o f desired forward speed goes in steps o f 0.25 m/s. A speed step o f 0.25 m/s is considered an optimum between a sufficiently small discretization o f the speed reduction and a sufficiently large speed reduction. For larger speed steps the discretization o f the speed may become too coarse. Where the magnitude o f the predicted vertical peak accelerations is larger than the upper l i m i t o f the predefined bandwidth for the current desired forward speed, it might j u m p below the lower l i m h f o r the reduced forward speed. The speed o f the towing carriage might start to oscillate.
For smaller speed steps the deceleration becomes limited (see Figure 7). Here the signal the control system receives is in steps o f 0.25 m/s. As a result, the average deceleration has been decreased. Each prediction takes about 0.3 to 0.5 s. The resulting average deceleration (including reaction time o f the carriage) is i n the order o f magnitude o f -0.40 to -0.45 m/s'. For smaller speed steps this w i l l be decreased even further.
Figure 6: Maximum deceleration towing carriage
Atte
jci ^- ,
O
desired Vs
Figure 7: Deceleration towing carriage using proactive control
3.3 M E A S U R E D Q U A N T I T I E S
During the tests the f o l l o w i n g quantities were measured: - Travelled distance Irom the starting point;
- Forward speed;
- Heave and pitch displacement;
- Vertical accelerations at the centre o f gravity and the bow;
- Water elevation in front o f the model;
The motions were measured i n an earth fixed coordinate system with the x-axis lying at the centre o f gravity o f the ship at zero forward speed, pointing in the direction o f the forward speed (see Figure 3). The z- axis is pointing down, implying a positive pitch bow up and negative vertical peak accelerations.
The travelled distance was measured by counting the pulses given by the measurement wheel on the carriage. The forward speed was read fi-om the control system o f the towing carriage. The sample rate was 5 H z . The
heave and pitch motion were measured using an optical measurement system, called Krypton. I R LEDs were positioned on the model to enable optical motion tracking w i t h a dedicated I R camera system. The sample rate was 200 Hz. The heave and pitch velocity were derived from their measured displacements.
The vertical accelerations were measured using accelerometers. One was positioned at the lengthwise position o f the centre o f gravity, at the same height as the hinge (29 m m below the centre o f gravity). The other was positioned at the bow. This was at 855 m m f r o m the stern at the same height as the centre o f gravity. This is equal to 87% o f the total length, measured from the aft. The vertical accelerations were measured at a frequency o f 99 H z and filtered at 40 Hz. The vertical peak accelerations were measured body fixed. Upward vertical peak accelerations appear as negative peak values due to the z-axis pointing downwards.
The wave probe was mounted at the f r o n t o f the towing carriage, at 6.38 m from the centre o f gravity o f the model. This wave height meter was a servo controlled instrument, capable to measure wave heights with high accuracy and frequency. This wave probe was selected f o r its capability to measure the water elevation at high forward speeds.
The mechanical part consisted o f a guided rod at the end o f which a needle was mounted. A n electronic circuit detected the contact o f the needle w i t h the water surface. A servo motor moved the rod up and down. The electronic circuit controlled the servo motor in such a way that the needle was i n continuous contact w i t h the water surface. I n this way the needle followed the wave profile. The sample frequency was equal to 15 Hz. Note that a wave crest has a negative value due to the z-axis pointing downwards.
A computer mounted on the carriage acted both as a measurement and control computer. For a response prediction the incoming wave and the instantaneous heave and pitch displacement and velocity were input f o r the computational model. On /, s, the data acquisition card o f the computer received the current pulse o f the measurement wheel and the data o f the wave probe, the speed o f the carriage and the heave and pitch displacements measured by the K r y p t o n f o r the past 3 s at a sample rate o f 200 H z .
The heave and pitch velocity were derived from the displacements. B y taking the average over the last 10 samples the instantaneous heave and pitch displacement and velocity on /, s were approximated. The position was determined using the current pulse. The hindcast data o f the water elevation was converted to time dependent snapshots o f the wave profile and the vertical orbital velocity, as explained i n the f o l l o w i n g section. The response was predicted f o r the duration o f the prediction w i n d o w using the current desired forward speed. I f the response predictions implied a speed i n - or decrease the computer communicates the new desired forward speed w i t h the control system o f the t o w i n g carriage. The measured vertical accelerations were not used f o r the
response predictions. They were used f o r comparison after the run.
The fime step was equal to 0.01 s. The peak value was found by averaging the values belonging to the neighbouring samples o f the maximum value found. This yielded a peak width o f 0.02 s. The corresponding calculation time varied between 0.3 and 0.5 s.
3.4 W A V E P R E D I C T I O N M E T H O D
During a test run the water elevation has been measured at a certain distance i n front o f the model. A wave probe has been mounted on the towing carriage at distance
Lprobe from the centre o f gravity o f the ship.
During the tests the time-trace o f the measured water elevation has been used to derive time dependent snapshots o f the wave profile. These snapshots are used to determine to sectional submergence o f the cross sections defined i n the computational model.
Figure 8 depicts a time-space plot o f the model o f the ship and the wave probe. The water elevation has been measured including its moment in fime and position i n the towing tank (r(x(t),t)). A regular wave w i t h a constant amplitude propagates w i t h the phase velocity. Each time a response prediction is carried out (on /,), the last s o f the measurement o f the water elevation, the position o f the model and the corresponding time instant it was measured are used to derive the water elevafion at and i n front o f the current position o f the model. This yields n measured water elevations (depending on the sample rate and duration). Each measured water elevation is translated i n time and space using the phase velocity:
XccOJ+Lprobe-cOHn). whcrc c=g/co m/s (assuming deep
water). The wave celerity is determined using the wave frequency that has been provided to the wave f l a p . This is i n fact an input parameter.
Ts Tp,i
Figure 8: Wave prediction method
Time instant /„ represents the time instant that the water elevation was measured; time instant /, to ti+Tp„ represents the time f o r which the response w i l l be predicted. The measured hindcast data o f the water elevation can now be used to derive snapshots f o r the duration o f the prediction w i n d o w (see Figure 8).
The duration for w h i c h the response can be predicted is dependent on the current forward speed, the phase velocity and the distance between the wave probe and the foremost section on the ship. The duration o f the prediction window is equal to:
L'probe
~Vs + c
The computational model also requires an input for the orbital velocity at the undisturbed water line. The orbital velocity has been found taking the derivation in time o f the time-trace o f the measured water elevation. The water elevation has been measured at approximately the encounter frequency.
A sine fit has been created o f the water elevation. The derivation o f the sine fit over the time-trace o f the water elevation yields a time dependent expression for the orbital velocity:
rmit) =
sin(6Jeit -I- £ i ) + sinCwezt -I- £ 2 )
dr
wix(t),t)= — ^
r„iöj cos(c(Jeit + £1) -frjijW cos(a)e2t -I- E2)
The wave frequency was determined using the expression for the encounter frequency:
— w ' + 0) - We - 0 a
The position o f the vertical orbital velocities is equal to the position o f the corresponding water elevation. Using the same translation i n time and space as explained above 'snapshots' o f the vertical orbital velocity at the current position o f the model can be found.
3.5 TEST P R O G R A M
Two sets o f model tests were carried out:
- Model tests in regular waves to check the implementation o f the control scheme (see Figure 1); - Model tests showing that i n case o f a bichromatic wave
the speed is adjusted according to the i n - and decrease o f the vertical peak accelerations;
The control system cannot react on individual peaks. The deceleration o f the carriage is too small. Instead, the control system reacts on the slowly increasing and decreasing vertical accelerations rather than individual peaks. I t follows the change o f wave amplitude.
Model tests in regular waves at a constant forward speed have been carried out first i n order to choose adequate wave frequencies f o r the tests w i t h proactive control. Comparison between measured vertical accelerations (filtered at 20 H z ) and calculated ones (time step equal to 0.01 s) showed that the vertical peak accelerations were sufficiently accurately predicted f o r wave frequencies between 5.0 and 6.0 rad/s, but f o r lower frequencies
(co<5.0 rad/s) the peaks were significantly overestimated by the computational model.
The chosen wave frequency range was therefore 5.0, 5.5 and 6.0 rad/s f o r the tests i n regular waves. The wave amplitude was 4 cm. The mean wave frequency o f the bichromatic waves was 5.5 rad/s. The wave amplitude increased from 2 to 4 cm and 3 to 5 cm. T w o different durafions o f the envelope were chosen: 62.8 and 125.7 s (dco equal to 0.10 and 0.05 rad/s). It is expected that f o r a short duration o f the envelope the peaks might exceed the bandwidth due to the limited deceleration capacity o f the carriage. For the longer wave envelope it is expected that the peaks can be kept between the predefined bandwidth. 4. R E S U L T S
4.1 M O D E L TESTS I N R E G U L A R W A V E S
Figure 9, Figure 10 and Figure I I show the measured water elevation (translated to the CG o f the model), the speed o f the carriage and the vertical peak accelerations at the bow for the experiments i n regular waves. The predicted vertical peak accelerations are displayed as green triangles. These figures show that only after 5 s after the control system had been activated, the speed was reduced. A f t e r 3 s the data required f o r a response prediction was available. The wave prediction method required hindcast data o f the water elevation. The first time-lag was considerably larger than the time-lags throughout the rest o f the run (approximately 1.5 s). A d d i n g the reaction time o f the towing carriage the start o f the speed reduction was at approximately 5 s after the control and measurement system was activated.
I
1
Figure 9: Time-traces of the translated water elevation, speed carriage and vertical peak accelerations at the bow in
a regular wave of 5.0 rad/s
For a wave frequency o f 5.0 the required speed reduction was little; approximately 0.25 m/s. The first and last peaks o f the run were underestimated. The speed was therefore reduced somewhat late. The control system could not react on the last predicted peaks, because the end o f the t o w i n g tank was reached. Generally speaking, the vertical accelerations could be kept w i t h i n the bandwidth o f - 1 7 . 5 to -12.5 m / s l
For a wave frequency o f 5.5 rad/s the vertical peak accelerations were overestimated by 2 to 5 m / s ' . The
measured peaks, however, were kept w i t h i n the bandwidth o f - 1 7 . 5 to -12.5 m / s l The speed varied due to the slowly varying wave amplitude. For waves having a high frequency a constant wave amplitude could not be generated. The final forward speed was therefore not constant.
Figure 10: Time-traces of the translated water elevation, speed carriage and vertical peak accelerations at the bow in
a regular wave of 5.5 rad/s
Figure 11: Time-traces of the translated water elevation, speed carriage and vertical peak accelerations at the bow in
a regular wave of 6.0 rad/s
For the shortest waves (6.0 rad/s), however, the variation o f the wave amplitude was large. A t the start o f the run the control system did not decrease the speed in time. The wave amplitude and thus the vertical accelerations varied quickly. The acceleration capacity o f the carriage was insufficient to f o l l o w these changes. The vertical peak accelerations were overestimated by 2 to 5 m/s', causing that sometimes the actual peaks were greater than -12.5 m/s'.
The presented time-traces show that proactive o f the forward speed based on predicted vertical peak accelerations is possible. It is, however, essential that the peaks are predicted w i t h a certain degree o f accuracy. The relation between the forward speed and the vertical peak accelerations should be captured accurately i n the computational model.
4.2 M O D E L TESTS I N B I C H R O M A T I C W A V E S Figure 12 and Figure 13 display the time-traces o f the measured water elevation (translated to the CG o f the model), the speed o f the carriage and the vertical
accelerations at the bow for a bichromatic wave w i t h a mean frequency o f 5.5 rad/s and an envelope duration o f 62.8 s. The predicted peaks are also displayed. The wave amplitude was increased from 2 to 4 cm and 3 to 5 cm respectively. The shape o f the bichromatic wave is clearly visible. The first unacceptable vertical peak acceleration was detected early. For an increase o f wave amplitude from 2 to 4 cm the increase o f the magnitude o f the vertical acceleration could still be counteracted by reducing the speed. The speed reduction, chosen based on the predicted response, was sufficient. I f the wave amplitude was increased to 5 cm, the speed reduction was not in time. The increase o f the vertical peak acceleration due to the increase o f wave amplitude was too quick in relation to the deceleration o f the towing carriage. Besides, not all peaks were predicted at the beginning o f the run, causing a late reaction o f the control system.
Figure 12: Time-traces of the translated water elevation, speed carriage and vertical peak accelerations at the bow in
a bichromatic wave of r„,v=63 s, wave height 2 to 4 cm
iiiiii
liBi
— — 1 ' i 4^^^^ ^ .
Figure 13: Time-traces of the translated water elevation, speed carriage and vertical peak accelerations at the bow in
a bichromatic wave of 7'„,v=63 s, wave height 3 to 5 cm Figure 14 and Figure 15 display the time-traces o f the measured water elevation (translated to the C G o f the model), the speed o f the carriage and the vertical accelerations at the bow f o r a bichromatic wave w i t h a mean frequency o f 5.5 rad/s and an envelope duration o f 125.7 s. The wave amplitude was increased from 2 to 4 cm and 3 to 5 cm respectively. For both increases o f wave amplitude was detected i n time and the corresponding speed reduction was sufficient. The predictions o f the vertical peak accelerations were more
consistent tlian for the shorter bichromatic waves. They were, however, slightly overestimated. Overall, the vertical accelerations were kept within the predefined bandwidth.
Figure 14: Time-traces of the translated water elevation, speed carriage and vertical peak accelerations at the bow in
a bichromatic wave of r„„.=126 s, wave height 2 to 4 cm
Figure 15: Time-traces of the translated water elevation, speed carriage and vertical peak accelerations at the bow in
a bichromatic wave of T„„=126 s, wave height 3 to 5 cm Figure 12 to Figure 15 have shown the relation between the increase o f wave amplitude over time and thus the increase o f vertical peak accelerations, the corresponding speed reduction and the actual measured vertical accelerations. For the longer bichromatic waves (envelope o f 125.7 s) the increase o f the vertical accelerations was more gradual. The forward speed could be adjusted in time and the measured vertical peak accelerations were kept within the bandwidth.
5. C O N C L U S I O N S
A proof o f concept o f proactive control o f the forward speed has been presented in this paper. A solution for increasing the operability o f planing monohulls sailing in head seas may be found in proactive control o f the thrust. The proof o f concept presented in this paper shows that proactive control for the forward speed, where the control is based on the predicted vertical peak accelerations (for a severely nonlinear system as the response o f a planing boat in head seas), is possible. I f the vertical peak accelerations were predicted accurately the vertical accelerations were kept within the predefined bandwidth. For gradual increases o f the wave amplitude
in case o f bichromatic waves the speed was adjusted in time as w e l l .
R E F E R E N C E S
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