Wave direction measurement by a single wave follower buoy

i

CHIEF

WAVE DIRECTION MEASUREMENT BY A SINGLE VE FOLLOWER BUOY

w. I. Sternberger, L. R. LeBlanc, F. H. Middleton Department of Ocean Engineering

University of Rhode Island

Narragansett Bay Campus

Narragansett, Rhode Island 02882

Abs tract

This paper describes a system for measuring

the direction of ocean 'cave propagation, as well as wave height and period. The system employs a con-ventional wave follower buoy, modified so as to

provide compass, pitch and roll signals in addition to the vertical component of buoy acceleration.

The modifications are indicated in the paper, and

the buoy was tested in two sea state conditions in

Narragansett Bay. The pitch, roll, compass, and

heave acceleration signals were all processed on the computer in the laboratory to provide a variety

of results. One test condition was ideal in that the wind and wave conditions were changing steadily throughout the data recording process. The second

test was exactly opposite, with small waves and a consistent wind direction. The results presented

in the paper include the wave height power spectral

dens itv a molar tilt histogram for the buoy motiox

and a family of polar plots of the average tilt

angle in each 50 sector of azimuth of the buoy pitch/roll.

1. Introduction

This paper is one of a series of papers on

the subject of the develooment of wave follower

buoys. The series commenced in 1975 with OTO paper

2424 on the mathematical analysis of wave data mak-ing optimum use of fast computer techniques. Next,

was OTC paper 2597 in 1976 devoted to the problem

of spectral compensation of acceleration data in order to produce e true wave height power spectral

density (PSD). Finally, a preliminary set of

re-sults, of wave direction measurements, was

pre-sentad in 1978 in OTO paper 3180.

It is the

pur-pose of the present paper to elaborate upon the ceasurement of the diretion of propagation of wave mode(s) present in an open-sea field.

In many important ocean operations, either ori

the open sea or near shore, the direction of prop-agation is often of more importance than the

significant wave height, or the power spectrum. This is clearly the case, for instance, for storm

waves striking a beach, a harbor channel, a break-water or any sort of offshore structure. Up to

the present time, anyone needing wave incidence direction data has been forced to deploy complex,

Illustrations at end of paper

37

Lab. y. Scheepsbouwkun.

Technische Hogeschool

Deift

complicated, and expensive spatially distributed

arrays of wave measurement devices. Using wave

staffs on a structure requires spatial separation on the order of the wave length of interest in order to obtain reliable results.

The buoy used in this study was a Model

WE-100 Wave Follower Buoy manufactured by Coastal

Data Service, Inc., (licensed to Hydro Products,

San Diego), on loan to the University of Rhode

Island for purposes of the present develooment.

It was necessary for Coastal Data Service to

mod-ify their standard buoy, by the addition

of tilt

and compass sensors, to make it possible to

mea-sure propagation direction. Some internal modifi-cations were required to provide space for the necessary additional sensors.

This paper will describe these modifications, explain the operation, and rhow at-sea test re-sults from a particular wave field. The rere-sults will include the usual power spectral density plots and the directional pattern of the dominant

wave frequency bands that were present at the time and place of the experiment.

2. Theory

The wave follower buoy which was used in this

study is designed so that it acts as an inverted

pendulum. It is the small pitching and rolling of

the buoy which makes it possible to sense the

pro'-pagation direction of the various dominant wave

frequency bands. The primary hydrodynamic f

ea-tures of the WF-l00 buoy assembly were given in detail in the 1976 OTO paper mentionedearlier.

The most important feature for the present discu-ssion is the "inverted pendulum' configuration wherein the center of horizontal drag is located near the bottom of the assembly.

With this arrangement, when a wave passes by-the free-floating buoy, by-the wave surface slope pre-sents a pitch/roll driving moment to the buoy

assembly. Since the buoy is axisymmetric, pitch

and roll really apply to orthogonal

tilt angles

relative to an arbitrary fore-and-aft direction of

the buoy. The only sensors required in addition

to the high sensitivity accelerometer are two good incliriometers and a magnetic compass fixed to the buoy hull. The tilt angle magnitude and its

wave and its direction of propagation.

There is rarely interest in individual wave slope characteristics. The data user is much more interested in wave direction statistics, because

this is more relative to wave forces on structures,

or slamming effects on beaches and breakwaters.

Since there is no apparent standard method for

displaying directional spectra, the tilt data from

the experiment are displayed in different ways. In an ideal model instance, with sinusoidal

waves passing a buoy, the magnitude of the wave

slope on the front (before a crest) of a wave would

be the same as on the back (after a crest) of a wave. In the real world, with non-symmetric waves,

the magnitude of the slope is higher and the

dura-tion of the slope shorter on the front of an in-dividual wave. Another source of roll asymmetry

is the relatively steady roll force applied to the

exposed portion of the buoy in an actual wind driven wave field. For these reasons it is not

simple to predict the roll behavior of a given buoy on an open water wave situation. In fact,,

the one safe prediction is that tilting in the

direction of propagation on the front of a wave,

as well as the reverse tilt on the back side of

the wave will occur with most small surface buoys. This sort of rocking behavior, enhanced

some-what by the roll resonance of the buoy would at first appear to present a 1600 ambiguity problem.

In most wave measurement operations, the local geography, wind data, and other conditions make it

quite simple to eliminate the ambiguity if the wave direction display fails to do so

itself.

3. Equipment and Processes

As indicated earlier, the buoy used in this study is a Coastal Data Service Model wF-lOO

mod-ified to incorporate two inclinc'meters and a

mag-netic compass. The WF-l00 is thoroughly described and shown in photos in the 1976 OTC paper. The hull shape has changed to more of an ellipsoid of

revolution than the spherical shape shown in the

paper.

The incilnometers first used were commercial

units that proved to be unsuitable for two

rea-sons. They displayed resonant behavior and were

Sensitive to inclination at right angles to their normal response axes. For this reason, the two orthogonal inclinometers were unavoidably

cross-coupled, so that another solution had to be found.

The solution came from a special inclinometer de-sign which provided two analog output de-signals

(DC voltage) almost linearly proportional to the pitch and roll angles. (Fìgure 1). Pitch is

de-fined as a tilt in the direction of the arbitrarily

established lubber line on the buoy.

Calibration of the tilt sensor is performed

in the lab with the aid of a tilt jig.

Static tilts of known magnitude, along each of the orth-ogonal p1ane, are correlated to the D.C. output

of the unit under test.

38

The commercial magnetic compass performed

satisfactorily and it provided an analog output

voltage produced by a low-torque pot connected to the compass card. Finally, the output signals from the complete buoy system included four analog voltages -- buoy vertical acceleration, pitch,

roll, and magnetic heading of the lubber line. To make use of these four analog signals for this experiment they were delivered by a tether wire to the small surface vessel which carried

the tape recorders and other support equipment.

The four signals were each applied to an

individ-ual FM magnetic tape channel on the same recorder so the signals were synchronized.

Since the end result of this study was to be

wave propagation direction, there was no specific need to generate an accurate wave height PSD. In-stead, the acceleration PSD was transformed by dividing through by w4 which was an easy way to

produce a crude PSD for wave height which was

valid for most of the energetic wave frequency

band.

This wave height PSD was then used as a guide for processing the tilt data. The data will be shown later, but for the present discussion, there

are many processes that might be of some use with

the tilt date.

For example, to a first

approxima-tion, the two tilt signals constitute a Cartesian form of displacement from the vertical. One can

readily convert this to a polar form, with the

magnitude corresponding to the tilt angle and the

polar angle giving the direction of the tilt rela-tive to magnetic North.

4. Results and Data

There were several ideas for ways to handle the tilt and bearing data to get the most out of

it.

One was to generate a polar histogram (10 intervals) of events which corresponded to the magnitude of the tilt exceeding some arbitrary

threshold angle. The purpose of the threshold is

to simply remove a great deal of the purely

ran-dom tilting motion that any surface buoy

encoun-ters in surface waves. A sample polar histogram produced on the computer for the total 15-minute

data set is shown in Figure 2 simply because it

ir intererting. In this case, an event was

de-fined as a tilt exceeding an atbitrary threshold

value, within a 10 ezimuth bin and the radial scale is arbitrary corresponding to the number of

events.

For comparisons sake, a polar histogram for the data corresponding to the calm sea conditions is presented as Figure 3. Both figures are plotted versus the sama scales with thresholds of

l

. Because of the apparent lack of activity

in the calm sea case, it was decided that further analysis be limited to the rough sea condition

data.

What is interesting to note about the his to-grams is the fact that more occurances of large

tilt happen into the wind rather than with the

result of the extended duration of the back of the

wave. Then data smzìpling occurs at a fixed rote,

an extended tilt duration results in a

proportion-ally larger incidence count.

This discussion will be limited to one field operation in Narragansett Bay, under rough storm

conditions (see Figure 4). The locations marked

1, 2, and 3 correspond to the beginning of each of three continuous five-minute data recording inter-vals. The test site was selected because it was obvious that the support vessel would drift roughly

North by Northwest in the wind, and drift would be

out of the lee of Prudence Island. This seemed

ideal because the combination of the steady waves plus those refracted by Prudence Island would be changing as time progressed. In addition, the wind was not steady from one direction and the

rasult was a highly confused sea, as far as

observers were concerned.

All of the data was brought back to the com-puter lab for processing, first for the PSD of wave height which is plotted in Figure 5. This is the

PSD for the entire 15-minute data run and was

pro-duced by the mY transfer function mentioned

earlier. This rough PSD plot is sufficient to show

the maximum wave height power point at about 0.43

Hz. The corresponding period is about 2.32 seconds

which appeared consistent with visual observations at the time. The lower local peak in the PSD at

about 0.725 Hz. is known to be related to the l-1/3 second natural heave frequency of the buoy.

Compensation for this non-wave feature is

thoroughly discussed in the 1976 paper, and it is of minor importance in the present study.

Figures 6 - 9 are polar plots of the average

magnitude of the tilt angle within each 50 azimuth

interval after removing the purely random

compon-ent of tilt.

This random component is the tilt of the particular 50 interval which has the

small-est average tilt.

The question naturally arises as to which dom-inant wave bands are influencing this polar plot

the most. The processing was set up to perform a

numerical filtering process on the wave data at

the dominant frequency 0.425 Hz + 0.05 Hz at the 3 db down points. The objective was to isolate

this dominant mode to determine its own propagation

direction. Figures 6, 7, and 8 are respectively

the Ist, 2nd, and 3rd five-minute segments, while

Figure 9 is the entire 15-minute data interval. 5. Interpretation of Data

Figure 4 shows the sites marked 1, 2, and 3 corresponding to the three sequential five-minute

data intervals. They are situated some 1500 and

2000 feet apart, indicating a wind (and tidal

current) drift on the order of five to seven feet

per second (3 knots) roughly in the direction of

the wind. Each time interval finds the vessel and buoy further out of the lee of Prudence Island and

in a different position relative to the waves be-ing refracted by the island. Observers on the

vessel agreed that refracted waves could be seen

by the eye, the wind was mainly out of the heading 165° and shifting back and forth to a considerable

extent. The sea was cuite mixed also, and

occas-ional large troughs came at the vessel from unex-pected directions. The reason for picking this

position near Prudence was that we would have an

opportunity to expose the buoy to quite different sea conditions.

It is interesting tocornparethe "event'

pat-tern of Figure 2 with the tilt angle magnitude pattern of Figure 9. Both were produced from the sane collection of data -- the total 15-minute run. In the former case, there is no averaging

across adjacent bins, which process would have produced a smoother pattern. In such a case,

re-latively small rocking components of tilt produce the large number of counts in the 10 bins and th corresponding large spikes in the polar pattern.

Now referring to Figure 9, the number of tilt events in a given polar interval (hare 5° of

azi-muth) is given no weight at all. A single large

buoy roll in a particular 50 sector will cause a large average value of tilt angle or a large ra-dius in this figure. The asymmetric character of

surface waves is important here. Because the slope is greater on the front of the wave than it

is on the back, the pattern of Figure 9 indicates a large average tilt tendency of the buoy in the

direction of propagation.

These differences discussed relative to the

tilt count and the tilt magnitude do not cons ti-tute any sort of problem with the data, but rather

they display a useful range of information that can be extracted fron the same data. Since the

accelerometer output signal is always available,

it is a trivial matter to detect whether a

parti-cular tilt of the buoy is associated with the

front or the back of an individual wave crest by the polarity of the accelerometer signal.

6. Conclusions and Suggestions

The application of a single wave follower

buoy to determine both the PSD of a wave field and the direction of propagation of dominant wave modes was successfully demonstrated. No attempt

was made to exhaustively treat the data gathered in the experiment, but rather to show in simple ways that the data is good. The proposition that a single buoy having the proper pitch-roll-heave properties can be so effective in observing essential wave characteristics has been proven

The buoy can actually be handled by two men

-without the aid of lifting gear ort the vessel.

It

can just as well be launched from a small dinghy

because of its light weight. The data in this

ex-periment was transferred from the buoy to the re-corder on the support vessel by means of an

elec-trical cable containing a wire for each of the

four analog signals. There is some extra power

required to energize the compass and the two tilt

sensors, but there is no reason to prohthit

tele-metering the data to shore to avoid the need for a support vessel.

An mentioned in the introduction, this paper is the third in a series dated back to the 1975 OIC meeting. The developmental process is continu-ing, and present efforts are maintaining the focus on buoy deployment during extreme sea events

(storms). A control clock has been used which can

detect the onset of a storm and adjust the data sample length and period to suit the us er An

on-Fig. 1 Buoy Instrmment Package

't:

â

(

L

Fig. 2 Polar Histogram Test 1, 1° bins.

40

board microprocessor is being designed which can easily pick out such wave parameters as a signi-ficant wave height, wave period, etc., to be up-dated and delivered over the telemeter link. Such

features as these can be selected, changed, im-proved, etc., by simple program changes in the microprocessor. Remote command of an unattended

buoy, well off shore, is well within the realm of possibility in the near future.

EOPE IsLmm Wind NAPRACA$E TT BA.! N

--Fig. 3 Polar Histogram Test 2,10 bins

e3 Ø2 01 Test Site SUtCa nd

o

Fig. G

Average Tilt in 5

bins

ist 5-minute filtered

3000 1000 300 loo 4i 30 ni _H O.) 10 3 N Frequency (He) Fig. 5 Wave Height PSD Fig. 7 AVerage tilt in 50 bins 2nd 5-minute filtered N o Fig. 9 Average tilt in 5 bins

Total 15-minutes tutored

o \ Fig. 8 Average tilt in 5 bins Wind\ 3rd 5-minute filtered I i i ud N N Wind 0.0 0.8 0.4