Predicted vs measured vertical-plane dynamics of a planning boat

Predicted vs. Measured Vertical-Plane Dynamics of a

Planing Boat

Richard

H.

(AM), Stephen A. Hoeckley2, Ronald S. Peterson2 (M), Armin W.

Troesch3 (M)

The design of high speed planing craft presents special challenges for the practicing naval architect. Operational difficulties associated with the powering and dynamics of these types of hulls have been extensively documented. Unlike in displacement vessels, planing craft dynumics and hydrodynamics generally do not lend themselves to a linear analysis. High speeds, small trim angles, and shallow drafts produce signtjicant nonlinearities. The analytical study of planing hydrodynamics began as early as 1930, when von Karman (1929) and Wagner (1931) examined the landing of seaplanes. Since that time, much effort has been expended on studying the steady, calm water behavior of planing hulls. In contrast, planing dynamics have received less attention. This paper describes an effort to validate one such predictive tool, a time domain planing hull simulator named PO WERSEA. The program is based upon theory developed by Martin (1978(a) and (b)) andZarnick (1978). Full-scale tests were conducted with a 25-foot, 6,400-pound boat at the Navy’s Coastal Systems Station in Panama City, Fiorkla. The boat was instrumented with two three-axis accelerometers and a Watson inertial measurement unit. The testing was pe~ormed both in calm water and in the wake generated by a passing boat. Measured parameters included speed, surge and heave accelerations, pitch rate, and wave elevation time histo~. The boat’s geometry and speed and the wave elevation were input into POWERSEA. The test data were then compared with the resulting dynamics predictions.

INTRODUCTION

Naval architects have been designing high-speed planing craft for most of this century, but the problem of predicting the motion of these craft has proven to be extremely difficult. Particularly difficult is the problem of predicting the motion of a planing craft in transient conditions. Savitsky (1964) and Savitsky and Brown {1976) developed methods for predicting the quasi-static behavior of planing hulls in calm water and in irregular seas, but these methods cannot be used to predict the transient motion expected in single wave or short episode wave encounters.

A major problem in the development of algorithms for the prediction of transient behavior of planing craft is that it is difficult to collect physical data describing planing craft behavior. This data is essential for the calibration and validation of planing craft motion prediction tools. Transient wave elevations such as Kelvin diverging waves are a function of time and

location. Although some wave patterns such as diverging wakes can be described mathematically, they are not periodic in either time or location. As a result, the motion of a planing boat must be correlated with the individual wave elevation that caused the motion. In other words, the wave elevation and boat response must all be captured simultaneously; it is very difficult to recreate the wave elevations after the fact without knowing the time and location relationships as well.

A 25-foot utility boat was used as a test boat to collect transient motion data. A Kelvin diverging wake pattern was created by a 42.5-foot, 28-ton dive boat, and the test boat was sent through the diverging wake at a range of speeds. The time-history of the diverging wake pattern was collected by videotaping a wave buoy. As the diverging wake traveled out from the dive boat’s path, the test boat accelerated toward the wake and, after reaching a steady speed and trim, crossed the initial wave crest at right angles and proceeded through the wake in a straight line. Motion data was recorded

]ShipMotionAssociates,Inc., 10DanfortbStreet,Portland,Maine04101-4567.

‘2CoastalSystemsStationDahtgrenDivision,Naval SurfaceWarfareCenter,PanatnaCity, FL 32407-7001. 3 Departmentof Naval Architectureand MarineEngineering,Universityof Michigan,Ann Arbor,Michigan48109.

Nomenclature

B = Beam (assumed constant) CBF= Buoyancy force coefficient CBM= Buoyancy moment coefficient C~,C= Crossflow (transverse) drag coefficient

C~ = Overall friction coefficient CG = Center of gravity

(location)

F~ = Total drag force in -~ direction

F~ = Force normal to boat hull, positive down

Fx = Force in X direction (global coordinates), positive forward

Fz = Force in Z direction (global coordinates), positive down Fe= Moment in pitch direction,

positive bow-up I = Pitch moment of inertia L = Vessel length

M = Mass of vessel M,= Total added mass Q,= Total added mass moment

of inertia

T = Thrust force (magnitude) Tx = Thrust force component in

X direction

Tz = Thrust force component in Z direction U, U = Velocity, acceleration in ~ direction V, V = Velocity, acceleration in ~ direction V~ = Velocity in knots W = Weight of vessel b = Sectional half-beam

f~ = Sectional friction drag g = Acceleration of gravity m,= Sectional added mass ma = Time-derivative of

sectional added mass . . .

‘! ‘b,’~ = Normal vector, normal to body, normal to fite surface

x,X, x = Longitudinal position, velocity and acceleration in surge (longitudinal)

direction, global coordinate;

by two longitudinally spaced three-axis accelerometers and by a three-axis, solid-state gyroscopic inertial measurement unit.

In this paper, a two-dimensional low-asp@ ratio strip theory proposed by Zarnick (1978) will be reviewed. The method was implemented in a computer program called POWERSEA. This program can create regular and irregular waves, and includes a simple wake model that can approximate the Kelvin diverging wake waves. A POWERSEA model was created of the test boat, and simulations were performed under conditions that matched the physical test conditions, The results of the simulation are included in this paper, and comparisons are made between the physical data and the simulated data. The paper concludes with recommendations for collecting accurate physical data and with comments on the validity and usefulness of the simulation results.

Portions of the simulation work were funded by the National Coastal Resources Research & Development Institute (NCRI) under NOAA Grant NA76RG0163 and the Department of Naval Architecture and Marine Engineering, University of Michigan. The at-sea tests

xc= Distance from CG to center of normal force

x~ = Distance from CG to center of action for drag force XP= Distance from CG to thrust

vector

z, z, z = Vertical position, velocity and acceleration in heave direction, global coordinates, positive downwards

A, ALT= Displacement, displacement in long tons j3= Deadrise of prismatic hull A = Water wavelength

a, &, $ = Pitch position, velocity, acceleration, positive bow-up p = Density of water ~ = Trim angle, radians ~= Longitudinal boat

coordinate, measured positive forward from CG ~= Vertical boat coordinate,

measured positive down ftom CG

were funded by the Ocean Engineering and Marine Systems program of the OffIce of Naval Research.

PHYSICAL MEASUREMENTS

Description of Test Boat

The test boat was a 25-foot, 6,400-pound, commercially available, utility boat with twin outboard engines. Since the lines for this boat were not made available from the manufacturer, the lines were taken off to be used as input for the POWERSEA simulations. The waterline of the loaded boat was marked on the hull. The boat was then loaded onto a trailer, and the waterline marks were used to level the boat. Heights and half-widths to the strakes, the chine, and the sheer were measured from a reference line below the keel. The points were laid out in a CAD program and faired to generate the hull lines, The resulting lines are shown in Figure 1. The CAD file was used as input in the POWERSEA simulation.

The longitudinal and vertical locations of the center of gravity of the test boat were determined by

suspending the boat at three different angles and calculating the intersection of the three plumb lines from the suspension point. The location of the center of gravity is shown in Figure 1. The weight of the boat, which was measured while suspending it for the center of gravity test, was measured at 6,010 pounds. With crew and equipment, the boat was at 6,430 pounds during testing.

Test Conditions

A series of runs were made in which the test boat encountered a Kelvin diverging wake pattern (refer to Figure 2). A 42.5-foot LOA, 28-ton dive boat was used to create the wake wave pattern. The dive boat speed was 19 knots in all runs and traveled through the test area on a marked path. The dive boat speed corresponded to a Froude number based on the vessel wetted length of about 1.0. This speed is close to the critical Froude number, and Kelvin transverse waves were not observed. Furthermore, assuming that transverse wake waves were created, their wavelength would be approximately 803 feet. Encountering these waves at an oblique angle would result in a very low encounter frequency that was not observed in the physical measurements.

Test speeds were 22,27, and 30 knots. The speeds were determined by using a GPS before and after the test. Three different engine speed settings were selected and the boat speeds were measured at each one. The engine speed settings were selected so that they could be easily repeated for each mn. The test boat was mounted with twin outboard engines without contra-rotating propellers. The engine trim angles were set to level the boat in roll and were measured during the speed measurement runs. An average engine trim angle was used in the POWERSEA simulations.

Test personnel in a support boat recorded the waves of the diverging wake with a video-camera as it passed the wave buoy, After a short delay, so that the test boat wake would not interfere with the wake to be

measured, the test boat accelerated from its starting point toward the wake. As the test boat approached the wake, engine speed and heading were steadied to bring the boat through the wake perpendicular to the wave crests of the diverging wake at as steady a condition as possible. Just before impact with the wake, the two accelerometers were triggered and the test boat

Figure 2. Kelvin Ship Wave Pattern

proceeded through the wake. A minimum of seven runs were recorded at each speed.

Since the POWERSEA validation was for a transient wave event, a calm test area was required to minimize accelerometer signal-to-noise ratio problems associated with small, wind-driven waves. An area within the St. Andrew Bay system near Panama City, FL, was selected so that the wind was offshore with a minimum of fetch. Water depth was about 30 feet throughout the test area.

Measurement Techniques

Measuring the motions of a small boat and the wave input in an uncontrolled, marine environment is a challenging task, Wind, waves, and other boats can contaminate both data and electronics. For this reason,

CL _ _{— — — — .} ~ - / 63&nter of Gravity / 8 Accelemnw@ / _i–– 0-/ — LWL ■ . ~ ‘/ ~ \ k -I. I-/ Ref Transom 10 9 8 7 6 5 4 32 1 Bow I

the data measurement techniques were as simple, robust, waterproof, and redundant as possible.

Wake Measurement

The wake from the wave producing boat was recorded on video. The video recorded the waves as the wake passed a 10-foot closed pipe anchored at one end so that it floated vertically with about 24 inches above the water surface. A scale on the buoy allowed the wave height to be measured to within 0.1 foot. There were no currents on the test area, so the buoy floated vertically. Also, there was sufficient reserve buoyancy so that the buoy remained stationary as the wave troughs passed.

This arrangement allowed for the measurement of the time history of the wave height past a fixed point. No attempt was made during testing to synchronize the wake recordings with the recorded motion data.

After testing, the video from three of the test runs was digitized at 10 Hz. The remaining runs were analyzed to confirm the peak wave amplitudes and the wave frequency. In general, the measured wakes consisted of nine waves with a peak amplitude of 11 inches. The leading edge of the wake was very subtle. As a result, the test personnel recording the wake did not consistently catch the first half to full wave of the approaching wake. This indicates that some type of continuous recording, either video or digital, is necessary.

A characteristic wake was built from the digitized wakes for input into POWERSEA. There were difficulties in developing an accurate wake model from the single-point, wave height time history that was recorded, due to the lack of a spatial description of the wake near the boat. This problem (described in greater detail in the wake model section) will be addressed in future testing.

Motion Instrumentation

The test boat was equipped with two sets of instrumentation. The first set was a pair of Instrumented Sensor Technology (1ST) EDR-3 accelerometers. The 1ST units are piezoresistive accelerometers with built-in data recorders, They have a full-scale range of MO g with a resolution of 0.1 g. The units were programmed to record at 200 Hz for 30 seconds after triggering. The units were triggered several seconds before impact with the initial wave of the wake. One accelerometer was mounted on the centerline on a bulkhead in the deckhouse. The second was mounted on a crossbeam 10.4 feet aft and 0.88 foot above the forward unit. The accelerometer locations

are shown in Figure 1. The purpose of this separation was to calculate the pitch angular acceleration from the vertical and longitudinal accelerations. The pitch acceleration could then be integrated to determine the pitch rate and pitch. Since the 1ST units are sealed devices, an external triggering mechanism was devised. A hammer blow to a board mounted between the two accelerometers triggered the 1ST units, which resulted in a sharp trigger event that was used for time synchronization between the two 1ST units and the Watson IMU.

The second set of instrumentation was a Watson Industries IMU-BA604 inertial measurement unit. This unit was included as a redundant method for motion measurement. The Watson IMU is a solid-state gyroscopic system with built-in three-axis rate gyros and accelerometers, pitch and roll pendulums, and a heading sensor. The output used from the IMU was digital at 24 Hz and was continuously recorded by a laptop computer. The output range for the accelerometer, *2 g’s, was not ideal for this testing. Preliminary tests had shown accelerations of nearly 2 g’s in the forward accelerometer location. For this reason, the Watson IMU was located next to the aft 1ST accelerometer where the accelerations would be lower. The mounting plate for the IMU was attached to the deck of the test boat. The trigger event for the 1ST units was sensed by the Watson accelerometer and was used to synchronize the Watson and 1ST units.

Motion Data Analysis

After testing, the data from both instrumentation setups was synchronized and analyzed for noise and suitability for comparison with the POWERSEA simulation runs (Figure 3 and Figure 4). A spectral analysis of the 1ST accelerometer data indicated energy peaks at 7, 35, and 50 Hz in both X and Z directions, and in both locations. The 1ST data was filtered with a hi-directional, Sti-order, Butterworth, low-pass filter with an 8 Hz cutoff. Referring to Figure 3, the filtered 1ST accelerometer data compares favorably with the Watson accelerometer data with no phase shift from the raw signal.

However, the synchronization of the 1ST and Watson data indicated that the 1ST accelerometers were not triggered early enough. This was likely due to the subtle nature of the leading edge of the wake and the inability of the test personnel to definitively detect it, As with the wake recording, this indicates that a continuous data recording system is beneficial for accurate data.

1.0 0.5 0 -0.5 -1.0 -1.5

I

EE!x!M

Figure 3. Filtered and Unfiltered Aft 1ST Z Accelerations with Watson Z Acceleration (RUN03, 22 knots)

20 0 -20 -40 -60 -80 t I o 1 2 3 4 5 6 7

~ 1STPitch Rate (deg/see)

B—+ Watson Pitch rate (deg/see) Time (seconds)

Figure 4. Comparison of the Watson Pitch Rate With the Pitch Rate Derived from the 1ST Accelerometers (RUN03, 22 knots)

Additionally, the attempt to calculate the pitch rate from the separated 1ST accelerometers was only marginally successful. The 1ST accelerometers did record different accelerations in the fore and aft locations. However, comparing the processed pitch rate from the 1ST accelerometers with the Watson pitch rate, as in Figure 4, indicates that a slight bias or drift in one or both of the accelerometers would prevent a correct integration of the 1ST data. The error could likely have been removed. However, given that the accelerometer trigger was late, the Watson data was clean horn the wake approach through the wake impact event, and the

pitch rate data was available directly from the Watson IMU, the Watson motion data was chosen for comparison with the POWERSEA simulations.

COMPUTER SIMULATION OF TRANSIENT BEHAVIOR

Low Aspect Ratio Strip Theory

Planing hulls create lift by dynamically displacing water. At high speeds, the perturbation water velocity in the surge direction of the vessel is negligible. As a

result, the perturbation flow can be approximated by the sum of a series of two-dimensional sections. Individual sections resemble impacting wedges.

E. E. Zarnick (1978) formulated a mathematical model of forces acting on a planing craft. Zarnicks method assumes that wavelengths will be large with respect to the craft’s length and that wave slopes will be small.

Zarnick (1978), following the work of Martin (1976), developed a mathematical formulation for the instantaneous forces on a planing craft. In Zarnick’s method, a planing craft is modeled as a series of strips or impacting wedges (refer to Figure 5 and Figure 6).

Zarnick derived the normal hydrodynamic force per unit length as:

{ f = - ~(rn,V)+C~CfibV2 Dt

1

D

Figure 5. Substantive Surface (Equivalent to Impacting Wedges)

A characteristic outward normal vector fi is defined for each strip and submergence. The normal vector is arbitrarily defined at the longitudinal midpoint of the strip and at a height of 2/3 of the submergence above the keel line. The instantaneous deadrise angle is defined as the angle of the normal with respect to the baseplane as seen in the body plan view.

Sectional added mass is modeled as if it were an impacting wedge:

=k dfib2andm _k ~fibb

m,

a? a-a

where k~is an added mass coefficient.

In the preceding equations, the time-dependency of the added mass coefficient k. is neglected. Zarnick used the value k. = 1.0, which is taken from the derivation of Wagner (1931). Most modern sources agree that the added mass coefficient is deadrise-dependent, so the following formula is used in this analysis:

k, -“_— (

1-9).4+KAR)

4 ₎

where KAR is an added mass correction factor.

Using KAR=l.0 is equivalent to using the added mass coefficient of Wagner (1932), while using KAR=O.O roughly matches the added mass coefficient curve of Vorus (1996).

Since the horizontal component Wx of the wave orbital velocity is considered small with respect to ~c~, only the vertical component Wzis included. The boat relative velocities with the vertical wave component included are:

U= Xc_ *cos(~)-(~ -wz)*sin(~) V = xc~ *sin(~) +(2- wz)*cos(&)-i$l

Hydrostatic forces and moments must be included in the analysis, but are difficult to predict. Water rise at the bow of a planing vessel increases hydrostatic lift, flow separation at the stern decreases hydrostatic lift, and both cause an increase in pitching moment. These effects are speed dependent, and there is no single factor that can be used to correct the hydrostatics calculations for flow separation. In the following equations, coefficients CBFand CBMcorrect the vertical force and pitching moment. These coefficients can be set to 0.5 based upon the recommendation of Shuford (1958) and Zarnick (1978), or they can be set empirically so that simulation results match tank test results.

Figure 6. 2-D Impacting Wedges (Derived from Substantive Surface)

Combining these redefinitions with the general A summary of the forces acting on the planing craft

is:

Fz=- F~ * COS(~)+ ~iigC~~Adi Fx = –F~ * sin(i?)

+ C~+CfibV2+ iigCR~A * COS@)}i di

Making the substitutions described in Akers (1999) and Zarnick (1978), and simplifying the vertical force yields:

Fz = {-M,cos{~~c~ –M~sin(~)xc~ +Q,~ + Ma&(zcGsin(&)- Xcoms(a))

J

- UVm, l,k~ - Vrnadi

-ii~CD,cbV2df } *COS(&)+ ~iigC~~Adf

Similar analyses are performed to derive the horizontal force and the pitch moment.

The sectional fiction force fD is calculated using the Prandtl-Schlichting line. For highly curved sections the water velocity will be significantly greater than the nominal water velocity past the hull, so the local velocity is used to calculate sectional friction drag. Numerical Solution to Equations of Motion

The governing equations that determine the motion of a planing craft are:

Mx ~~ = Tx - F~sin(k)– F~cos(~)

MZCG =Tz –F~cos(5)+ F~sin(k)– F, + W I~=F~*xc -FD*xD+T*x P- F~*x~

The sectional force and moment equations derived above are redefined to exclude the acceleration terms:

F; = Fx - (acceleration terms) F; = Fz - (acceleration terms) F: = F* - (acceleration terms)

equations of motion yields:

M+ M~sin2~ M~sin(b~os(?) - Q~sin? Masin(?~os(&) M + M~cos2k - Q,cosi? - Q,sin& - Qacos5 1+1=

..

x CG Tx + F; - F~cos& x ZCG = Tz +F~ +FDsin& -FB + W

i F;– FD*xD+T*xP-FB*xB

A set of state variables x ~~, zc~, ~ ~~, xcc, zc~, andkc~ are chosen. The matrix equation above can be written as IAI ~ = ~ where IAIis the mass matrix, ~ is the derivative of the state variable vector (x c~, zc~, “~~ , and f is the right-hand side forcing ~)-function, which is itself a function of the state variables. At each time step, the matrix equation is solved for ~ = IAI-I ~. The resulting equations are integrated to find the new value of the state variables x c~, zc~ and ~ cc, and the previous value of the state variables x cc, i cG ~d ~ cG me integrated to find the new value of the state variables x cG, zcG, and~cG

-Wake Model

To predict the time-domain response of a planing craft when it encounters a ship’s wake, a model of Kelvin diverging waves is required. Newman (1977) describes the method of stationary phase, which can be used to calculate wake elevations exactly. Unfortunately, this algorithm is not suitable for inclusion in a high-speed simulator.

A simple model for the diverging waves is required that allows the frequency and wavelength to change linearly as a function of time and distance. The following model was incorporated into POWERSEA:

g(x,t)=Acos((ti +iil *t’+i12 *x’)* t’+k*x’+g) k_(h+U, *t’+ti2 *x’)2

, t’=t-to, X’=x–xo g

The first wave crest of the diverging wake is defined at t=b and x=h. A blending function is used to go from calm water to the first crest of the wake pattern, and again from the last crest of the pattern back to calm water. The blending functions were designed so that q, dq/dx, dq/dt, d$l/dt2 and d~/dxdt are all continuous at the beginning and ending of the blending period, and also at the first and last crests of the wake

pattern. This minimizes the impact of the start and end of the wake pattern on the boat’s response to the wake itself.

Ideally, the wave elevation would be measured at a point on the test boat as it passes through the wake, In this case, there was no easy or economical way to make such measurements, so the coefficients had to be estimated indirectly.

The coefficients A, o) and q can be calculated by observing the diverging wake as it passes a stationary object. A time-series of wake wave elevations were collected and the zero-crossings were used to create a table of instantaneous wave periods and frequencies versus time. The frequency coefficients o.)and w were calculated by applying a linear regression to the zero-crossing data. Figure 7 illustrates the measured wave elevation at the wave buoy for a portion of one run. The coefficients A, co and @ were extracted from this data, and an idealized waveform created from these coefficients. The idealized waveform is also displayed in Figure 7. From this figure it appears that the wake model does an excellent job of reproducing the diverging wave elevations at a single point.

All of the runs had similar wave buoy time histories, so a single set of values were used for A, co and o+. Coefficient Value w A 7 inches 0.5833 feet co 1.07756 rad/sec * 0.039306 rad/sec2

It is more difficult to calculate the x-dependent frequency coefficient COl. One method might be to study a photograph of the wake pattern as it passes multiple wave buoys. The elevation data at multiple probes could be used to accurately calculate co and W. Hopefully, the co value calculated using this method would match that of the time-series method in the previous paragraph.

POWERSEA Model of Test Boat

A boat model was created with POWERSEA based on the measured hull lines described earlier (refer to Figure 8). The measured data was supplied in the form of an AutoCAD DXF file, which was used as a guide for creating the POWERSEA model. Each section or station in POWERSEA is modeled as a straight line between the keel and chine space curves. The POWERSEA keel and chine lines are specified so that they create an effective hull surface that will approximate the physical surface.

15 10 5 0 -5 -10 -15 0 2 4 6 8 10 12 14 16 18 20 Time (seconds)

— Measured Waw Ele@ion (in) — Synthesized Wave Elevation (in) I

FQure 7.Elevations at Wave Buoy Versus Synthesized Elevations

\

LWL _{Ik \ \}

~

Sef

10 9 8 7 6 5 4 32 1

38 37 ‘“ T \ 36 _r 35

A

_EE!EET7

34

&

Figure 9. Drop in Velocity as Test Boat Passes Through Diverging Wake (RUN03, 22 knots)

Surface details such as small spray rails are usually ignored. Larger details such as lifting strakes are modeled based on whether or not the designer expects them to be wet during normal operation. Typically, a POWERSEA chine line is set to the outer edge of a lifting strake at the transom because the entire strake will be wet at the transom during normal operation. Conversely, a chine line is set to the inner edge of a lifting strake at the bow because the strake is rarely wet during normal operation. This results in an effective deadrise that closely matches that of the physical vessel. The chine sweeps in from the outer edge of the strake to the inner edge at about 1/3 LWL abaft the forward perpendicular.

Hydrostatic Lift and Moment

As described above, POWERSEA includes two correction factors for the hydrostatic lift and moment. The quasi-static trim angles of the test boat at different speeds can be used to set these coefficients. At 22 knots, the measured trim angle ranged from 2.2 degrees to 4.0 degrees in different runs, and at 30 knots the trim angle was approximately 2.0 to 2.6 degrees. Using the default values of 0.5 for CBF and CBM resulted in a pitch of about 6 degrees at 22 knots and 4 degrees at 30 knots. Increasing CBF to 0.8 and CBM to 1.0 resulted in a simulated trim angle of 3.98 degrees at 22 knots and 3.54 degrees at 30 knots.

These running trim angles are still significantly higher than the observed trim angles, but in Akers (1999) it was demonstrated that in many cases underestimating the hydrostatic forces gave better dynamic results than by using the exact hydrostatic forces. This may occur because most transient behavior of a high-speed vessel is the result of hydrodynamic forces, not hydrostatic forces, so more accurate results are obtained if the hydrostatic forces are understated.

Simulating the Instantaneous Velocity

In all cases, as the test boat passed through the wake, the boat’s forward velocity dropped slightly. This could be modeled several ways in POWERSEA. The program has the ability to predict the forward speed of a vessel with constant thrust force or power. The algorithm has been found to be accurate for calm water performance, but to under predict the speed loss in waves. Akers (1999) found that for relatively large waves, the added resistance predicted by POWERSEA may be off by as much as 50 percent.

Letting POWERSEA predict the drop in speed as the test boat passes through the waves based upon a constant thrust analysis may significantly under predict the speed loss. A more direct method is to instruct POWERSEA to ramp the speed from an initial value to a final value based on the measured data. The speed loss observed in the runs was not large, and the second method was felt to be more accurate than the first.

Figure 9 shows the simulated velocity for a 22 knot run versus the velocity integrated from the accelerometer data. From this figure, the largest velocity error is less than 3 percent, and probably does not significantly affect the dynamic results. This procedure was repeated for the runs at 27 knots and 30 knots.

Wake Parameters

As described earlier, the diverging wake amplitude A, starting frequency o) and time-dependent frequency co] parameters were set by observing wave elevation histories at a wave buoy. The remaining xdependent frequency parameter w had to be set indirectly as there was no way to calculate the spatial wave distribution from measurements. The only data available was the measurements of the test boat dynamic motions.

The most accurate measured data were the pitch rates, so these were used to predict the wake spatial distribution in the following manner:

1. Simulate the boat traveling through regular waves whose encounter frequency would be the same as that observed in the measurements.

2. Find the time difference between the zero-crossing of the incident wave (maximum wave slope) and the peak of the pitch rate at the forward perpendicular.

3. Synthesize a diverging wake pattern starting at the first peak from step 2, and adjust w until the wave encounter history aligned well with the measured pitch rate history.

Assuming infinite depth water and steady boat speed, the initial encounter frequency is:

/

iio2

iie=iio-t

g

Using co = 1.07756 rad/see, the initial encounter frequencies and equivalent wavelengths are:

Ufk?K!m

-22 2.417629 174.10 27 2.722189 174.10 30 2.904925 174.10 POWERSEA was used to simulate the test boat in regular waves at the three speeds listed above. The time delay from the maximum wave-slope to the peak pitch rate at these encounter frequencies were predicted to be:

Pitch Rate U41WM) Period [see) Phase Lag (see)

22 2.60 0.30 27 2.31 0.25 30 2.16 0.27

Using both the pitch rate phase lag at the initial frequency of encounter and the pitch rate time history, the final wave parameter w can be estimated. Using this method, the value of e+ for the 22 knot runs is 0.003142. Figure 10 shows both the synthesized wake wave, the measured pitch rate, and the simulated pitch rate for the 22 knot run labeled “RUN03 .“ Notice that more effort was put into matching initial wake waves than in matching the later waves.

SIMULATION RESULTS AND COMPARISON WITH PHYSICAL MEASUREMENTS

Reliable measured data was available for the following variables:

. Pitch Angle

. Pitch Rate

● X, Z Acceleration at Center of Gravity ● X, Z Acceleration at Watson Sensor

Test conditions were extracted from the best runs at 22 knots (RUN03), 27 knots (RUN17) and 30 knots (RUN22). POWERSEA was used to simulate the test boat under each of these conditions. Figure 10 shows the measured and simulated pitch angular velocity for RUN03 displayed on a single chart.

The peak measured and simulated pitch rates are remarkably close (refer to Table 1 for a summary of the minimum and maximum motion variables). The peak measured pitch rate occurs at a different wave in the wake episode than it does in the simulated episode. There are a number of possible reasons for this. First, the simplified POWERSEA model may be missing some of the important transient forces during the wake episode. Second, the simulated wake waves may not be accurate. The diverging waves may not be linear in frequency or they may not be constant amplitude. The boat exhibits a strong response to waves of a particular wavelength. If the simulated wake model is not accurate, POWERSEA could predict a different peak response than that of the actual test boat. In general, though, the measured and simulated pitch response corresponds quite well.

Figure 11 shows the simulated and measured test boat pitch angle during the RUN03 22 knot wake event. The simulation predicts a larger pitch swing during the early wake waves than was actually measured. For waves in the middle of the episode, the pitch response was comparable between the measured and simulated data. Finally, both the simulated and measured data showed a net drop in trim angle as the test boat passed through the wake. The drop in pitch angle was certainly caused in part by the drop in forward velocity during the episode.

Figure 12 shows both the simulated and measured vertical acceleration at the Watson sensor. As observed earlier, the peak accelerations do not occur at the same wave in the measured response data as in the simulated response data. The maxima and minima, however, are comparable between the two data sets.

Figure 13, Figure 14, and Figure 15 are comparisons between measured and simulated motion response data for RUN17 at 27 knots. Figure 16, Figure 17, and Figure 18 are comparisons between measured and simulated motion response data for RUN22 at 30 knots. As can be seen in these figures, at higher speeds it became more difficult to reconstruct the diverging wake wave pattern from the measured response data.

One conclusion that can be drawn from the later sections of each figure is that the POWERSEA wake model has difficulty predicting the frequency/wavelength distribution of an entire diverging wake episode. This is not as much of a

drawback as it might seem because the motion of degree. For the higher speed runs, the peak-to-peak interest usually occurs at the earlier, lower encounter swing in measured pitch rates was somewhat higher frequency portion of the data. than those of the simulated pitch rates. The measured A summary of the maxima and minima of each and simulated swings in vertical acceleration at the measured variable for all three runs appears in Table 1. Watson sensor were ~emarkably close.

For all three sets of data, the average measured pitch angle was above the simulated pitch angle by about 1

Minimum Maximum Measured Simulated Measured Simulated RUN03, 22kllOtS

Pitch (degr)

Pitch Rate (degr/see)

Vertical Acceleration at Watson Sensor (Gs)

RUN17, 27kIIOtS

Pitch (degr)

Pitch Rate (degr/see)

Vertical Acceleration at Watson Sensor (Gs)

RUN22, 30 knots Pitch (degr)

Pitch Rate (degr/see)

Vertical Acceleration at Watson Sensor (Gs)

0.2 -15.9 -0.46 0.9 -18.3 -0.58 1.0 -21.1 -0.70 0.03 -15.5 -0.52 -0.28 -15.3 -0.57 -0.89 -17.5 -0.65 4.7 17.2 0.45 5.2 20.6 0.53 6.1 21 0.62 Table 1. Summary of Measured versus Simulated Response Data

20 10 0 -lo -20 2 3 4 5 6 7 8 9 10 Time (seoonds) 5.84 12.6 0.53 6.11 12.7 0.62 5.69 13.1 0.66

z

(degr/see)

—Waw ElewXio

at FP (in)

—Meas Pitch

Rate

7 6 5 4 3 2 1 0 I I I I I I

/31-I

r

L

Figure 11. Simulated and Measured Pitch Angle (RUN03, 22 Knots)

0.6 , 1 0.4 u — Sim Z-Accel 0.2 (G’s) o -0.2 _—Meas Z--0.4 Accel (G’s) -0.6 2 3 4 5 6 7 8 9 10 Tme (seconds)

Figure 12. Simulated and Measured Vertical Acceleration at Watson Sensor (RUN03, 22 Knots)

30 20 10 0 -lo -20 -30 2 3 4 5 6 7 8 9 10 Tme (seconds)

— Sim Pitch Rat

(degr/see) 1

—Waw+ Elewdio

at FP (in)

1

Figure 13. Simulated and Measured Pitch Rate (RUN17, 27 Knots)

8 6 4 2 0 -2 —Meas Pitch (degrees) 01234567 89 10 11 12 Tme (seconds)

Figure 14. Simulated and Measured Pitch Angle (RUN17, 27 Knots)

1

0.5

0

-0.5

4

5

6

9

Figure 15. Simulated and Measured Vefiical Acceleration at Watson Sensor (R~l7,27~o@)

30 20 10 0 -10 -20 -30 2 3 4 5 6 Time (seconds) 7 8 9

— Sim Pitch Rat(

(degr/see)

—Wavs Elemtiol

at FP (in)

—Meas Pitch

Rate

8 6 L —Sire Pitch 4 (degrees) 2 —Meas Pitch o (degrees) -2 01234567 89 10 11 12 Time (seconds)

Figure 17. Simulated and Measured Pitch Angle (RUN22, 30 Knots)

1 0.5 0 -0.5 -1 2 3 4 5 6 7 8 9 — Sim Z-Accel (G’s) —Meas Z-Accel (G’s) Time (seconds)

Figure 18. Simulated and Measured Vertical Acceleration at Watson Sensor (RUN22, 30 Knots)

CONCLUSIONS AND AREAS FOR FURTHER INVESTIGATION

A large number of test runs were performed at three different speeds on a planing utility vessel as it crossed the diverging wave portion of a Kelvin wake pattern. Data on the actual wave elevations and on the vessel motions were collected.

A low-aspect ratio strip theory developed by Zarnick (1978, 1979) was extended and implemented in the form of a computer program called POWERSEA. A simple model of a Kelvin diverging wake wave train is included in POWERSEA. This model is based on a linear frequency variation in both time and space.

The test boat was modeled and simulated with the POWERSEA program. R was found that the POWERSEA simulator did an excellent job of predicting minimum and maximum accelerations at the sensor location in the hull, a relatively good job of predicting the pitch rate range and waveform shape, and a fair-to-good job of predicting the actual pitch position of the test boat.

Many of the inconsistencies between the measured and simulated response data could be attributed to the

following deficiencies in the low-aspect ratio strip theory:

. The hydrostatic force and moment are not modeled with enough accuracy.

. The requirement for straight-line geometry sections causes inaccuracies in the vertical accelerations at the bow due to bow flare.

● POWERSEA’s wake model could probably be

more robust.

Further research is required in all of these areas.

The instrumentation used performed well, with some exceptions. The Watson IMU is a superior instrument for the purpose of this work. Its ability to continuously record self-consistent, three-degree-of-freedom data for comparison with the POWERSEA simulation will lead to its use in future planing boat motion testing. However, an accelerometer with slightly higher amplitude (so that it could be placed at the boat’s center of gravity) would lead to more convenient and accurate comparisons.

A method for accurately recording the spatial distribution of the wake and the location of the boat in time is needed and will be required for fiture testing. Two possible methods would be to use multiple,

synchronized, continuously recording wave height buoys, or to use a stop-action camera to record the progress of the wake past a set of buoys. The latter could offer the added benefit ofsynchronizing the boat location with the wake location.

Overall, after real-world validation, the strip theory algorithm as implemented in the POWERSEA program shows a great deal of promise in the simulation of the transient behavior of planing vessels

REFERENCES

Akers, Richard H., Dynamic Analysis of Planing Hulls in the Vertical Plane. Presented to Society of Naval Architects and Marine Engineers, New England Section, April 29,1999.

Martin, M., Theoretical Predictions of Motions of High-Speed Planing Boats in Waves. David W. Taylor Naval Ship Research and Development Center, DTNSRDC-76AN69, 1976.

Newman, J. N.,Marine Hydrodynamics, The MIT Press, Cambridge, Massachusetts, pp. 275-278, 1977. Savitsky, D., Hydrodynamic Design of Planing Hulls.

Marine Technology, Vol. 1, No. 1, pp. 71-95, Society of Naval Architects and Marine Engineers, Jersey City, New Jersey, October, 1964.

Savitsky, Daniel, and Brown, P. Ward, Procedures for Hydrodynamic Evaluation of Planing Hulls in Smooth and Rough Water. Marine Technology, Vol.

13, No. 4, pp. 381-400, Society of Naval Architects and Marine Engineers, Jersey City, New Jersey, October, 1976.

PO WERSEA Reference Manual, Ship Motion

Associates, Portland, Maine, Version 2.0, February, 1999.

Shuford, Charles L., Jr., A Theoretical and

Experimental Study of Planing Surfaces Including Effects of Cross Section and Plan Form. NACA Report 1355, 1958.

Vorus, William S., A Flat Cylinder Theory for Vessel Impact and Steady Planing Resistance. Journal of

Ship Research, Vol. 40., p. 100, Society of Naval

Architects and Marine Engineers, Jersey City, New Jersey, June, 1996.

Von Karman’, T., The Impact of Seaplane Floats During Landing. NACA Technical Note TN 321, Washington, D.C, 1929.

Wagner, H., Landing of Seaplanes. leitschrififir Flegtechnik und Motorlujlsshifl- fahrt, (14 Jan 1931) National Advisory Committee for Aeronautics TM 672, May 1931.

Wagner, H., Uber stoss-und gleitvorgange an der oberflache von flussigkeiten. leitschrififir

Angewandte Mathemutik und Mechanik, Volume 12, page 193 August, 1932,

Zarnick, Ernest E., A Nonlinear Mathematical Model of Motions of a Planing Boat in Regular Waves. David W. Taylor Naval Ship Research and Development Center, DTNSRDC-78/032, 1978.

Zarnick, Ernest E., A Nonlinear Mathematical Model of Motions of a Planing Boat in Irregular Waves. David W. Taylor Naval Ship Research and Development Center, DTNSRDC/SPD-0867-Ol, 1979.