equivalent linearization

VERES performs an equivalent linearization to incorporate the effect of the maximum working angle when computing the RAOs. In "method 1" the equivalent linearization option was not used. In "method 2" the equivalent linearization moderates the trim tab and foil flap deflections to obtain the desired values in a specified wave spectrum. The equivalent linearization requires the user to input a maximum flap deflection angle and a wave amplitude, so it may be “tuned” to a specific sea state. The process is applied during the calculation of the vessel response in regular waves, and essentially adjusts the gains automatically to limit the amplitude of the sinusoidal flap deflection to the specified maximum value for a regular wave with the specified wave amplitude. This adjustment is done separately at each wave frequency. For "method 1" the gain settings are constant for all wave frequencies, and adjusted to obtain the desired RMS deflection for the specified distribution of wave energy over all frequencies (the wave spectrum), while for method 2, the gains are essentially adjusted independently at each wave frequency, to obtain the desired RMS deflection for a regular wave with the specified wave amplitude at each wave frequency. It is not obvious what wave amplitude should be specified to obtain the correct tab and foil flap deflections for a given wave spectrum. In the current study, the significant wave amplitude was specified as the input for the wave amplitude used for the equivalent linearization. The wave amplitude has a significant influence on the RAOs as demonstrated in Figure 3, which shows VERES predictions for the pitch RAO for a wave piercing catamaran in head seas at 20 knots, with the ride control input specified according to "method 2", with same specified maximum deflection angle, but different wave amplitudes. The user specifies a maximum deflection angle, which assuming sinusoidal motion for the flap, can be related to the RMS deflection by:

max

2

δ = δ

From a user's perspective method 2 is much quicker and easier than method 1, as an iterative process with manual adjustments of the gains is not required for each speed and sea state. Method 1 should result in a more accurate representation of the flap deflections corresponding to a specific wave spectrum. Figure 4 compares the predicted pitch and roll RAOs for a wave piercing catamaran with active trim tabs obtained using method 1 and method 2 for the same input wave spectrum (the spectrum shown in Figure 6a). These are also compared with the RAO predicted

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for the same vessel without trim tabs. Both methods achieve roughly the same reduction in the peak pitch response and method 1 shows a slightly larger reduction in the peak roll response. For large wave periods method 2 shows a much larger reduction in both the pitch and roll response, which is probably not realistic as the vessel will likely contour the waves when travelling in very

below 10 seconds, one would anticipate the two methods to predict similar motions, while if there is significant energy at longer wave periods, some differences are expected.

CORRELATION WITH FULL-SCALE TRIALS

Comparisons are made between the VERES predictions and data from the full

catamaran. The ride control system on the vessel consisted of a pair of trim tabs mounted to the transom of each side hull, and a large T-foil mounted to the wetdeck of the catamaran on the vessel centerline. The T

retractable, so it could be pulled out of the water and stowed beneath the wetdeck. The T covering about 35% of the chord, and the T

current analysis, only the flap motion of the T data prevent the details of the hull geometry

scales on the y-axis of the plots have been removed; however, these restrictions still allow for comparisons between the trials and calculations. The heading convention is such that 0

180˚ to following seas.

Figure 3: Influence Roll RAO in bow quartering seas for a wave piercing catamaran at 20 knots, examining two methods for specifying controller gain coefficients.

Correlation with data from full-scale trials is challenging because the description of the incident wave field encountered during the trials is not sufficient to define the incident waves for input in the computer simulation. In the current set of trials a measurement of the wa

TSK wave height system installed at the bow of the ship

the distribution of wave energy across wave frequencies, but does not indicate the direction of the waves or amount of wave spreading or if the seas are

bi-octagon maneuver is performed as shown in Figure 5 to obtain data at various headings. In choosing runs to use for the correlation, the pitch and roll response as a function of heading was examined to rule out octagons wh

was clearly a strong swell component to the seas in a direction other than the primary wave direction. For providing input into VERES a spectrum is formed by averaging the measured spectrum recorded at the beginning and end of

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for the same vessel without trim tabs. Both methods achieve roughly the same reduction in the peak pitch response a slightly larger reduction in the peak roll response. For large wave periods method 2 shows a much larger reduction in both the pitch and roll response, which is probably not realistic as the vessel will likely contour the waves when travelling in very long waves. If most of the wave energy is concentrated at wave periods below 10 seconds, one would anticipate the two methods to predict similar motions, while if there is significant energy at longer wave periods, some differences are expected.

RIALS

Comparisons are made between the VERES predictions and data from the full-scale trials for a wave piercing catamaran. The ride control system on the vessel consisted of a pair of trim tabs mounted to the transom of each

foil mounted to the wetdeck of the catamaran on the vessel centerline. The T

retractable, so it could be pulled out of the water and stowed beneath the wetdeck. The T-foil had controllable flaps and the T-foil strut could also be pivoted to adjust the angle of incidence. In the current analysis, only the flap motion of the T-foil is modeled. Restrictions on the distribution of the full

data prevent the details of the hull geometry of the wave piercing catamaran from being published here, and the axis of the plots have been removed; however, these restrictions still allow for comparisons between the trials and calculations. The heading convention is such that 0˚ corresponds to head seas, 90

Influence Roll RAO in bow quartering seas for a wave piercing catamaran at 20 knots, examining two methods for specifying controller gain coefficients.

scale trials is challenging because the description of the incident wave field encountered during the trials is not sufficient to define the incident waves for input in the computer simulation. In the current set of trials a measurement of the wave spectrum before and after each octagon was performed using a at the bow of the ship. The TSK wave probe provides a point spectrum showing the distribution of wave energy across wave frequencies, but does not indicate the direction of the waves or amount -directional. The primary wave direction is observed by the operators and an octagon maneuver is performed as shown in Figure 5 to obtain data at various headings. In choosing runs to use for the correlation, the pitch and roll response as a function of heading was examined to rule out octagons wh

was clearly a strong swell component to the seas in a direction other than the primary wave direction. For providing input into VERES a spectrum is formed by averaging the measured spectrum recorded at the beginning and end of for the same vessel without trim tabs. Both methods achieve roughly the same reduction in the peak pitch response a slightly larger reduction in the peak roll response. For large wave periods method 2 shows a much larger reduction in both the pitch and roll response, which is probably not realistic as the vessel will likely long waves. If most of the wave energy is concentrated at wave periods below 10 seconds, one would anticipate the two methods to predict similar motions, while if there is significant

scale trials for a wave piercing catamaran. The ride control system on the vessel consisted of a pair of trim tabs mounted to the transom of each foil mounted to the wetdeck of the catamaran on the vessel centerline. The T-foil was foil had controllable flaps foil strut could also be pivoted to adjust the angle of incidence. In the foil is modeled. Restrictions on the distribution of the full-scale trials of the wave piercing catamaran from being published here, and the axis of the plots have been removed; however, these restrictions still allow for comparisons between esponds to head seas, 90˚ to beam seas and

Influence Roll RAO in bow quartering seas for a wave piercing catamaran at 20 knots, examining

scale trials is challenging because the description of the incident wave field encountered during the trials is not sufficient to define the incident waves for input in the computer simulation. In ve spectrum before and after each octagon was performed using a . The TSK wave probe provides a point spectrum showing the distribution of wave energy across wave frequencies, but does not indicate the direction of the waves or amount observed by the operators and an octagon maneuver is performed as shown in Figure 5 to obtain data at various headings. In choosing runs to use for the correlation, the pitch and roll response as a function of heading was examined to rule out octagons where there was clearly a strong swell component to the seas in a direction other than the primary wave direction. For providing input into VERES a spectrum is formed by averaging the measured spectrum recorded at the beginning and end of

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the octagon maneuver. A 2-peak JONSWAP spectrum was then fitted to the spectrum, as VERES requires a theoretically defined spectrum. The resulting spectra obtained for two of the octagons from the trials are shown in Figure 6. The runs referred to as “Octagon A” corresponded to a case where the ship travelled at 20 knots in a high Sea State 4 (HS=2.3m). The runs referred to as “Octagon B” corresponded to a case where the ship travelled at 35 knots in low Sea State 5 (HS=2.7m). For both Octagon A and Octagon B, the T-foil was retracted out of the water and only the trim tabs were used to reduce the vessel motions. The modal period was longer during the Octagon B runs. Both spectra show a secondary peak at a shorter wave period than the modal period. As no information is available for the amount of wave spreading in the waves during the trials, a cos² spreading function was applied assuming a 90° spreading angle in the VERES calculations. In order to investigate the influence of wave spreading, a set of simulations were performed both with purely long crested waves and with the spreading function applied.

Figure 7 shows the comparison of VERES predictions, with method 1 used to set the input for the control algorithm for both the long and short crested calculations in Octagon A. The biggest influence of short crested waves is seen for the roll response in head seas and the pitch response in beam seas, but the wave spreading clearly influences both the pitch and roll at all headings.

Figure 4: Pitch RAO in head seas and roll RAO in bow quartering seas for a wave piercing catamaran at 20 knots, examining two methods for specifying controller gain coefficients.

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Figure 5: Octagon maneuver pattern

The comparison of the predicted motions with the trials data for Octagon A is shown in Figure 8. Results are shown for the RMS roll and pitch angle and the RMS vertical acceleration measured by an accelerometer placed near the bow of the vessel. Predictions were made for the vessel with no trim tabs (labeled "bare hull" on the plots) as well as with actively controlled trim tabs predicted using the iterative method (method 1) and the equivalent linearization method (method 2). The trials were performed with the trim tabs actively controlled. There is no trials data available for this vessel with the trim tabs locked at a fixed angle for any condition. For this case the vessel is traveling at 20 knots and the modal wave period was about 9 seconds. For the predicted response with the trim tabs active, there are only minor differences in the predicted roll, pitch, and bow acceleration using methods 1 and 2 for all the headings examined. Both methods predict reduced pitch and roll motion and larger bow accelerations with the trim tabs active compared with the bare hull response. The trials data falls between the predicted results for the bare hull and vessel with actively controlled trim tabs, with the trials data closer to predictions with the trim tabs included for most of the values, particularly for the pitch response. The same comparisons for Octagon B are shown in Figure 9. For this case the vessel is travelling at a higher speed, 35 knots, in a wave spectrum with a longer modal period of about 12 seconds. For Octagon B, there are larger differences in the predicted response obtained using method 1 and method 2 to specify the controller input relative to Octagon A. This is likely a result of the longer modal period with more wave energy at longer wave periods, as Figure 4 indicated larger differences in the RAOs predicted using methods 1 and 2 at longer wave periods. Method 1 predicts a larger reduction in the pitch and roll response and a smaller increase in bow acceleration at all headings. The trials data again falls between the bare hull predictions and the predictions with the tabs active for the pitch and roll response at most cases, with the trials data closer to the predictions obtained with the tabs using method 2.

Some additional cases were examined with the T-foil deployed and the T-foil flaps actively controlled. The goal was to examine nearly identical octagon runs with both the trim tabs and T-foil deployed and with only the trim tabs active and the T-foil retracted out of the water. This would allow for a direct comparison of the ability of VERES to predict the influence of the T-foil. There were only a few cases during the trials for which the vessel was operated at the same speed in a similar wave spectrum with the T-foil deployed and retracted. As the sea conditions vary during the trials, no two octagons will see exactly the same wave spectrum. Two octagons were examined that were performed in succession at the same speed (35 knots) first with the T-foil deployed and then with the T-foil retracted. The wave spectra corresponding to these two octagons are shown in Figure 10.

Octagon C shows the spectrum measured while the T-foil was deployed and Octagon D shows the spectrum measured while the T-foil was retracted. While the spectra are nearly the same near the peak period of around 11 seconds, there is some loss of wave energy at the secondary peak around 7 seconds. The same two-peak JONSWAP spectrum is used in the VERES calculations for the runs with and without the T-foil. The comparison between trials results and the VERES predictions are shown in Figure 11 for the pitch motion and bow acceleration. The VERES predictions used method 2 to specify the ride control settings for trim tabs and T-foils. Since the T-foil is mounted on the centerline of the vessel, the controller input for VERES is set to reduce only the pitch motions, while the trim tabs were set to reduce both pitch and roll motions. The trials data from Octagon C shows the peculiar result that the measured RMS pitch angle was higher in bow and beam seas than in head seas. This indicates perhaps that the seas

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were bi-directional or an error in the observed primary wave direction during the trials. The VERES predictions show the expected result that both the bow accelerations and pitch motion increase as the heading approaches head seas. The VERES predictions show the greatest benefit from the T-foil in head and bow seas. The trials indicate the T-foil has the most influence in bow and beam seas. VERES predicts a similar magnitude for the reduction in pitch motion and bow acceleration due to the T-foil being deployed.

Figure 6: Measured and approximated wave spectra for two octagons examined during trials

Figure 7: Comparison of predictions assuming short-crested and long-crested seas at 20 knots in Octagon A wave

spectrum

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Figure 8: Comparison of predictions and trials for wave piercing catamaran with trim tabs active travelling at 20 knots in Octagon A wave spectrum with two methods for specifying controller gains.

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Figure 9: Comparison of predictions and trials for wave piercing catamaran with trim tabs active travelling at 35 knots in Octagon B wave spectrum with two methods for specifying controller gains.

CONCLUSIONS AND DISCUSSION

Two methods have been demonstrated for modelling the RCS for a high-speed catamaran in VERES. The two methods predict similar motions for a wave piercing catamaran in seas with a short modal period, while some differences in the predicted motions are observed in seas with a longer modal period. The VERES predictions using both methods have been compared to data from the full-scale trials for a wave piercing catamaran. While it is not possible to make any quantitative statement regarding how accurately VERES models the RCS due to limited information describing the encountered seas during the trials and a lack of trials data with the trim tabs locked in a fixed position, some qualitative conclusions can be made. Generally the VERES predictions show a significant benefit from actively controlled trim tabs and T-foils for reducing both pitch and roll motions. For the cases examined with only the trim tabs active, VERES shows reasonable correlation with the trials data for the predicted pitch response, but may over-predict the benefit of the trim tabs to control roll motion. VERES predicts roughly the correct magnitude for the reduction in pitch motion and bow acceleration from the T-foil. There are a variety of sources for discrepancies between the VERES predictions and the trials data.

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Figure 10: Comparison of wave spectra from trials for wave piercing catamaran with only trim tabs (Spectrum C) and with both trim tabs and T-foil deployed (Spectrum D).

Figure 11: Comparison of predictions and trials for wave piercing catamaran with only trim tabs and with trim tabs and T-foil deployed.

Among these are:

• Differences in the incident wave field between the trials and VERES predictions.

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• Assumptions made concerning the control algorithm in the VERES calculations. Perhaps the control algorithm on the actual vessel was designed to limit accelerations at specific locations instead of only reducing roll and pitch motions.

• Error in computing the lift force on the trim tabs and T-foils. VERES treats both the trim tabs and T-foil as

• Error in computing the lift force on the trim tabs and T-foils. VERES treats both the trim tabs and T-foil as