BACKGROUND OF THE INVENTION Technical Field [0002] The present invention relates to a buoy for measuring the height and frequency of waves and to a method for self-calibrating data measured by the buoy.

Description of the Related Art [0003] Many oceanographic studies and marine operations require accurate data concerning wave heights and frequencies. Numerous types of devices and methods have been developed to acquire such data. For example, there are a variety of wave height measuring sensors that are suitable for use on piers or other stationary platforms. These include resistive or capacitive wave wires, and submerged pressure sensors. U. S. Pat. No. 3,587, 308 to Tucker discloses a thin wire probe that measures wave height by determining the conductance between a thin wire and a body of water which is proportional to the length of wire immersed. Such devices however cannot be effectively deployed in open water on small buoys, because the buoys heave up and down with wave action and distort the data. The devices have been deployed on massive spar buoys, which remain relatively stationary in the water, but such buoys are necessarily large and heavy, often longer than 10m with a mass of hundreds of kilograms.

[0004] There is a need therefore for wave height measuring buoys that can be deployed in the open sea and that are small, reliable and inexpensive. Efforts to develop such buoys began in the 1950's with the introduction of floating buoys with accelerometers to measure the heaving of the buoy. The first such buoys utilized a single accelerometer mounted so as to nominally measure the vertical motions of the buoy. A problem with that design is that the buoys are subject not only to vertical accelerations, but also to horizontal accelerations and tilts. The single-axis accelerometer is also sensitive to these latter motions, which enter in a nonlinear fashion. The resulting acceleration time series is therefore often badly corrupted at low frequencies. U. S. Pat. No. 4,135, 394 to Middleton et al. discloses a wave height buoy that compensates for the above horizontal motion by suspending a single-axis accelerometer inside a water-proof housing located at the center of rotation of the buoy assembly so that the accelerometer is substantially insensitive to roll and pitch motions of the buoy. Such a design however adds considerable complexity and cost to the buoy assembly. Many modem wave height buoys contain multiple accelerometers and angle or angular rate sensors that are integrated into a motion-sensing package capable of distinguishing true vertical heave from roll, pitch, and horizontal accelerations. Such buoys are widely available but cost thousands of dollars, in large part because of the expense of the motion measuring sensors. They are also relatively heavy, weighing hundreds of pounds, and require a crane to deploy and recover.

[0005] Other early designs of wave height buoys incorporated vanes that rotated as a buoy went up and down in the water. An example of this design is disclosed in U. S. Pat. No.

3,225, 593 to Richard. The movements of the vanes are recorded and correspond to the wave induced vertical travel of the buoy. Such buoys are complex however and their moving parts make them unreliable.

[0006] Still another wave height buoy design comprises a force transducer mounted to a floating buoy and a long, vertical elastic cord connected to the transducer on one end and to a high-drag reference plate at the other. Such a design is disclosed in U. S.

Pat. No. 3,610, 038 to Joy et al. As the buoy rides upward with a wave, the cord is stretched between the buoy and the relatively motionless reference plate and the cord exerts a downward force on the transducer. Assuming the spring constant of the cord is known, the vertical stretch of the cord and the wave height may then be calculated according to Hooke's Law. The'038 patent discloses an umbrella-like structure for use as the high drag reference plate. The umbrella traps large amounts of water, making the effective mass (also called the "virtual mass") of the umbrella quite large, and therefore lowers the resonant frequency of the system. When subjected to waves with frequencies above the resonant frequency, the umbrella will remain relatively motionless, while motions can occur for frequencies lower than the resonant frequency. Thus a low resonant frequency of the system is desirable because it enables the system to measure low frequency waves.

[0007] There are several limitations however to the invention disclosed in the '038 patent. First, horizontal subsurface currents may pull the high-drag umbrella sideways and lead to distortions of the frequency content of the wave data. The currents induce a Doppler shift in the wave height time series by advection of the buoy. Such currents are ubiquitous in the ocean and the resulting errors introduced into the wave data could be significant. Second, both turbulent and internal wave motions at the depth of the umbrella may advect that structure up and down, leading to forces on the surface float that cannot be distinguished from wave motions and therefore distort the vertical wave measurements.

[0008] A third limitation of the invention disclosed in the'038 patent involves calibration of the buoy. Calibration of such a buoy requires knowing the spring constant of the elastic cord. The'03 8 patent suggests the use of a rubber cord. This has the advantage of being inexpensive, foldable and compact. However a limitation is that the spring constant for both natural and man-made elastic cords, including rubber, exhibit great variability in manufacturing. Furthermore the spring constant of such cords changes with both age and temperature. Even if one could determine the spring constant of the elastic cord on the deck of a ship just prior to buoy deployment, the spring constant would change when the buoy was deployed into the ocean. Thus there is no simple and practical way to accurately calibrate the buoy disclosed in the'038 patent.

[0009] There is therefore a need for an improved wave measuring buoy that has the advantages of low manufacturing, storage, deployment, and operating costs, comprising a compact design with a minimum number of moving parts, but without the above described limitations.

SUMMARY OF THE INVENTION [0010] The present invention is therefore an improved wave measuring buoy including a surface float, a force transducer attached to the surface float, supporting electronics, and an elastic cord attached to both the force transducer at one end and to a low- drag mass at the other end. The design of the low-drag mass enables data measured by the force transducer to be self-calibrating, meaning that the natural resonant frequency of the system including the surface float, cord and low-drag mass may be calculated from a force time series measured by the force transducer. Once the natural resonant frequency of the system is known, the force time series measured by the transducer can be converted to a wave height time series in either real time or in a post processing step.

BRIEF DESCRIPTION OF THE DRAWINGS [0011] For a more complete understanding of the present invention and the advantages thereof, reference is now made to the following detailed description taken in conjunction with the accompanying drawings in which: [0012] Fig. 1 is a schematic diagram of a preferred embodiment of a wave measuring buoy according to the present invention; [0013] Fig. 2 is a diagram of a simple physical model of the present invention including a mass on a spring with forced motions applied to the top of the spring; [0014] Fig. 3 shows two plots illustrating the amplitude of motion of a low-drag mass according to the present invention and a high-drag mass according to the prior art; [0015] Fig. 4 shows a plot of a predicted power spectral density of an ocean wave height time series; [0016] Fig. 5 shows plots of the predicted power spectral density of three different force time series obtained by modeling three different load-cell based buoys, including a prior art design and a design according to the present invention, deployed in the oceanic environment illustrated by Fig. 4.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT [0017] As shown in Fig. 1, a preferred embodiment of a wave measuring buoy according to the present invention comprises the following components: a surface float 10 with sufficient buoyancy to support the entire mass of the buoy and to which is attached a force sensing transducer 15 and supporting electronics 20, the surface float 10 floating near a water surface 75; a low-drag mass 25; and an elastic cord 30 connected at one end to the force sensing transducer 15 on the float 10 and at the other end to the low-drag mass 25.

[0018] The force sensing transducer 15 is shown as a load cell. (A load cell consists of a strain gauge attached to a flexible bar. The bar flexes when force is applied and the strain gauge measures the amount of flexure. ) However numerous other types of force transducers could work in the present invention.

[0019] A simple physical model of the invention is a mass on a spring with forced motions applied to the top of the spring as shown in Fig. 2. Waves on the water surface will cause the float 10 to move up and down, which in turn will produce forces on the cord 30 (shown as a spring), which in turn will cause the mass 25 to move up and down.

Mathematically, this simple physical system is known as a forced and damped harmonic oscillator. Both the motions of the mass 25 and the force exerted on the float 10 can be easily calculated.

[0020] The force exerted on the float 10 by the cord 30 is proportional to the extension of the cord 30, which equals the distance between the float 10 and the mass 25. (This relationship is known as Hooke's Law. A constant of proportionality in this relationship is <BR> <BR> known as the spring constant. ) If the mass 25 remains stationary in a body of water, then the force exerted on the float 10 will be proportional to the displacement of the float 10, and also to the height of a wave that is lifting the float 10. However because the mass 25 according to the present invention is a low drag mass, the mass 25 will also move in response to a force on the cord 30 and its motion must be considered when calculating the actual height of waves.

[0021] The forces measured by the transducer 15 depend on the amplitude and frequency of the surface waves, the spring constant, the actual mass of the low-drag mass 25, and the drag induced by the motion of the mass 25 through the water. The spring/mass system has a natural resonant frequency in hertz given by where m is the mass, k is the spring constant, and y is the damping factor. The damping factor makes only a small correction to the resonant frequency when the damping is small due to the use of a low-drag mass 25.

[0022] To illustrate differences between the present invention and the prior art, Fig. 3 shows two plots of the amplitude of the motion of a mass induced by a one meter high surface wave on a 1.8 kg (4 lb) mass connected to a surface float 10 by a 1/8"diameter bungee cord 30 having a length of 17 m. The amplitudes are plotted as a function of the surface wave frequency.

The plot that shows a spike in amplitude (the resonant frequency) near 0.05 Hz (solid curve) represents the case where a mass is shaped according to the present invention as a low-drag mass 25 to exhibit moderate to low drag in water; the other plot that shows no apparent resonant frequency (dotted curve) represents the prior art where a mass is shaped to exhibit high drag in water. For example, a small, compact mass will have low-to-moderate drag, while a mass shaped as a flat plate will have high drag.

[0023] In Fig. 3 the resonant peak is pronounced in the moderate-drag case (solid curve) but effectively eliminated in the high-drag case (dotted curve). Also, the mass motion is minimal as long as the surface wave forcing frequencies are significantly higher than the natural resonant frequency of the mass/spring combination. This is true independent of drag on the mass 25. Thus if the natural resonant frequency of the buoy can be kept low enough, then the low-drag mass 25 will remain relatively stationary even though its drag coefficient is low. The extension of the cord 30 will be proportional to the height of the float 10, and the force on the float 10 will be proportional to wave height 35.

[0024] If the characteristics of the buoy are well known (mass, spring constant, and drag coefficient of the mass 25) then the motion of the mass 25 can be predicted for any surface wave, and removed from a recorded force time series in post-processing. The effectiveness of such an approach may be limited at low frequencies close to the system's natural resonant frequency due to measurement error and second-order effects, but the approach can be used to extend the range of useful wave measurements to lower frequencies than would otherwise be the case.

[0025] The present invention overcomes several of the limitations of prior art wave measuring buoys, including calibration errors due to changes in the spring constant and wave height measurement errors due to subsurface currents. These limitations are overcome by providing a means for in-situ self-calibration of the spring constant of the elastic cord 30 and by providing a low-drag mass 25. The present invention comprises a design opposite to that disclosed in the'038 patent cited above-instead of employing a high-drag, high-virtual mass to anchor the vertical cord 30, the present invention utilizes a low-drag mass 25. The mass and spring constant are then adjusted to achieve a low resonant frequency response to keep the mass 25 relatively still in the water as the float 10 moves up and down.

[0026] Fig. 4 shows a predicted power spectral density of an ocean wave height time series. This is the forcing function that a wave-measuring buoy is designed to record.

The power spectral density was computed from a commonly used wind-wave spectral model, with the addition of a low-frequency noise floor. Such noise floors are always present in nature because of the presence of low-frequency swell waves, waves induced by atmospheric pressure variations, and internal oceanic turbulence, although the absolute level and spectral shape will vary from case to case.

[0027] Fig. 5 shows plots of the predicted power spectral density of three different force time series obtained by modeling three different load-cell based buoys, including a prior art design and a design according to the present invention, deployed in the oceanic environment illustrated by Fig. 4. The high drag time series 40 models a buoy according to the design disclosed in the prior art'03 8 patent including an umbrella-like, high-drag virtual mass. The low drag time series 45 models a buoy made according to the present invention including a low drag mass 25. The medium drag time series 45 models a buoy including a mass that has a drag coefficient between that of the other two cases. Fig. 5 is obtained by multiplying the forcing spectrum of Fig. 4 by the predicted modulation transfer function of each wave-measuring buoy. The predicted power spectral density plots consist of a high- frequency component that is due to the wave height spectrum, and a low-frequency component due to the resonant response of each particular buoy system.

[0028] A key aspect of the present invention is that the resonant frequency of a buoy made according to the present invention may be derived directly from a force time series measured by the buoy. As shown in Fig. 5, the resonant frequency cannot practically be derived from a force time series measured by prior art buoys that include a high-drag mass. The high-drag mass creates a highly damped system and therefore a resonant peak 55 on the power spectral density plot for the high-drag time series 40 is very difficult too detect.

For operation of the present invention in real world sea states, surface gravity waves will generally not be perfectly flat so the resonant peak 55 should be reasonably pronounced to obtain a calibration measurement. The ability to identify the resonant peak 55 requires an adequate signal-to-noise ratio of the transducer and related electronics and relatively low damping of the low-drag mass 25.

[0029] The frequency of the resonant peak 55 is dependent on only the mass of the low-drag mass 25, which is known, and the spring constant, which must be determined to calibrate the system. So a measurement of the frequency of the natural resonant peak 55 of the low-drag mass 25 can be used to determine the in situ spring constant, which can in turn be used to calibrate the rest of the time series measurements. The in situ spring constant is the actual, real-time spring constant and therefore eliminates spring constant estimation errors associated with the prior art. As discussed above these errors associated with the prior art are introduced when the spring constant of the cord 30 changes due to manufacturing variability, age and temperature. The data measured by a buoy according to the present invention can therefore be described as self-calibrating. That is, the information necessary to convert the raw force data from the transducer 15 into wave height data is already contained in the raw force data. Using the low-drag mass 25 enables the natural resonant frequency to be determined from the raw force data. Once the natural resonant frequency is known, the force data can be converted to wave height data in real time by electronics on the buoy or in a post- processing step after the data has been transmitted from the buoy [0030] As noted above, all that is required for self-calibration of the data is the detection and measurement of the buoy's natural resonant frequency. The resonant peak of the low-and moderate-drag cases shown in Fig. 5 arises due to the buoy's linear response to low-frequency motions that are modeled as a noise floor. An additional source of low- frequency response may arise if there are small nonlinearities in the buoy's response. These nonlinearities will interact with high-frequency motions to create low-frequency energy, which will still peak at the natural resonant frequency of the buoy. The degree of nonlinearity in the elastic cord 30 can be adjusted by selection of the mean stretch in the system. Thus nonlinearities could be introduced into the design if the natural noise floor of low-frequency motions is too low.

[0031] Accurate self-calibration of the force data requires accurate estimation of the natural resonant frequency, assuming that the mass of the low-drag mass 25 is known.

The accuracy of the natural resonant frequency estimate is controlled by the width of the resonant peak 55 and the length of the time series used in the estimation. Therefore, in general using a low-drag design and analyzing a relatively long-time series will result in the most accurate data.

[0032] There are a variety of algorithms that can be utilized to estimate the resonant frequency of the buoy system for the purposes of calibration. Examples include the periodogram method, the Pisameko Harmonic Decomposition method, the general class of autoregessive spectral techniques including Maximal Entropy and Maximum Likelihood, as well as a broad class of Bayesian techniques. All of these techniques have well documented advantages and disadvantages. Some of these modem spectral estimation techniques, such as Maximal Entropy, could be used to estimate the resonant peak 55 even if only a very short time series is available. The above techniques are well understood by those reasonably skilled in the art.

[0033] Examples of specific embodiments of the present invention may be based on the specifications given in Table 1 of commercially available"bungee cord". Note that the spring constant of a continuous elastic cord is dependent on the length of the cord. A given force will always stretch a cord a fixed percentage of its unstretched length. Thus a longer cord will have a smaller spring constant than a shorter cord.

[0034] To allow for an easy comparison, Table 1 lists the spring constant for 10 m lengths of cord of varying diameters and the mass required to achieve a natural resonant frequency of 0.05 Hz. The mass was computed from the low-drag formula: - 4 0 A resonant frequency of 0.05 Hz was selected as a design goal because it is lower than all but the longest swell waves, as illustrated in Fig. 4. This would allow a buoy made according to the present invention to sense most low-frequency swell. CORD STRETCH Mean Spring Spring Total mass DIAMETER Mass Constant Constant @ required to to Formula 10 m obtain a Stretch (N/m) Unstretched 0.05 Hz (kg) (N/m) resonance 1/8"50% 1. 4 15. 7 N/xu 1. 6 N/m 15. 8 kg 75% 1. 8 3/16"50% 3. 0 23. 5 N/xu 2.4 N/m 23. 8 kg 75% 3.6 1/4"50% 4. 5 74. 5 NI x,, 7.5 Nhn 75. 2 kg 75% 6.4 Table 1 [0035] Table 1 shows that the total mass required to obtain a 0.05 Hz resonance is much greater than the mass required to obtain a 50% stretch of the elastic cord 30. Therefore some design tradeoffs are appropriate. One option to reduce the required mass so that the buoy is easier to store and deploy is to further lengthen the elastic cord 30. A 20 m long cord 30 would require only 70% of the mass of a 10 m cord 30 to achieve the same resonant frequency. In addition to lowering the total mass of the buoy, a longer cord 30 reduces the effect of horizontal motions of the low-drag mass 25. A longer cord also helps insure the linearity of the spring constant. On the other hand, longer cords 30 may be more difficult to store and deploy and may limit use of the buoy in shallow waters. Also, using a 20 m long cord 30 the variation in force on the transducer 15 due to the presence of a 1 m high wave is just 12%. That means that the transducer 15 and electronics 20 would have to resolve variations of 0.12% about the mean force to achieve a height resolution of 1 cm.

[0036] Another way to reduce the total mass of the buoy for ease of storage and deployment, is to use trapped water as a virtual mass. For example, the 15.8 kg mass described in Table 1 could be replaced by a 31-cm diameter metal sphere with a number of small holes drilled in the sphere to allow the sphere to flood when it is placed in water. In order to account for the buoyancy of the sphere, assume the sphere is made of a metal with a density of 3 g/cc and a mass of 2 kg. When such a sphere is deployed in water, it will fill with water and sink. The sphere itself will weigh about 13.7 Newtons in water (equivalent to a 1.4 kg mass in air), but the water trapped within the sphere has a mass of just over 16 kg.

Thus the 2 kg sphere will stretch the cord like a 1.4 kg mass when placed in water, but have a resonant frequency associated with a 16 kg mass. While this illustrates the concept of virtual mass, in a commercial design the virtual mass body itself would likely be more streamlined than a sphere to reduce drag. It could also be made from a porous material like cloth if it included stays to holds its shape. A major advantage of using a flexible material like cloth is that the structure could be collapsible for easy storage.

[0037] The electronics 20 in the buoy will generally require amplification and signal conditioning for the transducer 15. For an expendable buoy the package should also include an inexpensive, short-range telemetry system to transmit the force data back to a nearby shore, ship or aircraft receiving station. These could include commercially available telemetry systems that are often used in radiosondes launched for meteorological purposes. Such systems are inexpensive and receiving systems are widely available. A recoverable version of the buoy could include a more expensive satellite-telemetry system or be self-recording, with the data played back for analysis after recovery of the buoy.

[0038] The time series consisting of the transducer force data can be digitized on the buoy. (Such digitization is already built into modern radiosonde packages. ) The degree to which the data are processed on the buoy will depend on the application. On-buoy processing will drive up on-board computer costs, but can significantly reduce the amount of data that needs to be transmitted or stored. On-buoy processing can also be used to improve low-frequency response by accounting for motions induced in the low-drag mass 25, as described above.

[0039] In most embodiments of the present invention the surface float 10 should be waterproof, simple, rugged and low-cost. Numerous shapes will work including a simple tube with end caps. The force transducer 15 can be inside or outside of the float 10. In one embodiment including a tube with end caps for the float 10, the transducer 15 may be built into one of the end caps.

[0040] The elastic cord 30 may also be made of numerous different materials.

Examples include bungee cord, surgical tubing, and very long rubber band. As described above, the level of the natural frequency of the cord 30 can be adjusted by changing the mean stretch of the cord 30, although in most embodiments this should not be necessary.

[0041] The low-drag mass 25 may also be made of numerous different materials and in a variety of hydrodynamic shapes. Fig. 1 illustrates one exemplary embodiment of the mass 25 comprising a small lead weight 60 attached to the bottom of a cloth tube 65 with closed ends.

The shape of the cloth tube 65 may be maintained by a series of wire hoops 70 attached to the cloth tube 65. The cloth tube 65 is collapsible for storage, and expandable to trap a required volume of water during deployment. As described above, the trapped volume of water creates a virtual mass and is used to set the resonant frequency of the buoy. The elongated shape of the cloth tube 65 is still low-drag. Other embodiments of the low-drag mass 25 include metal or plastic rigid cylindrical containers with small holes to allow water to enter and create low-drag virtual mass.

[0042] Buoys made according to the present invention may be very light with some embodiments having a real mass (not including the virtual mass of entrained water) of less than seven kilograms. The buoys can also be inexpensively manufactured, stored, deployed and recovered. Rugged designs could be deployed from aircraft or from the deck of ships and allowed to free-fall to the water. Depending on the economics of particular applications, some embodiments could also be designed to self scuttle after a period of time due to built in weaknesses in the design of the surface float 10.

[0043] The above therefore discloses a buoy for measuring the height and frequency of waves and a method for self calibrating data measured by the buoy. Alterations, modifications, and improvements of the detailed disclosure above will readily occur to those skilled in the art. Such alterations, modifications, and improvements as are made obvious by this disclosure are intended to be included in this disclosure though not expressly stated herein, and are intended to be within the spirit and scope of the present invention.

Accordingly, the foregoing description is by way of example only, and not limiting. The invention is limited only as defined in the following claims and equivalents thereto.