Vibristor-R Vibrational Wave Energy Converter FAQ List
Categories of questions:
<![if !supportLists]>1. <![endif]>Physics of ocean waves
<![if !supportLists]>2. <![endif]>LEG’s and WEG’s
<![if !supportLists]>3. <![endif]>Structure of the Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]>
<![if !supportLists]>4. <![endif]>Structure and purpose of the PMA and CRMFT
<![if !supportLists]>5. <![endif]>Structure and purpose of the FCA
<![if !supportLists]>6. <![endif]>Operation of the Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]>
<![if !supportLists]>7. <![endif]>Mechanical simplicity of the Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]>
<![if !supportLists]>8. <![endif]>Environmental considerations of the Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]>
Q1: What is a Wave Energy Converter (WEC)?
<![if !supportLists]>1. <![endif]>A device that intersects an incoming propagating ocean wave that absorbs the wave’s kinetic energy and through some electromechanical mechanism converts the captured energy into electrical energy that is then harvested from the device. It may be employed in any body of water capable of sustaining wind induced water waves of sufficient size so as to efficiently activate the device.
Q2: What is a vertically oriented Faraday Linear Electric Generator (LEG)?
<![if !supportLists]>1. <![endif]>A Faraday generator is a device that produces a movement of a magnetic field relative to coils of conductors. It consists of a fixed component called the stator which may be either magnets or coils of wire and a moving component called the rotor which may be either coils or magnets depending on which component forms the stator. If the movement is a rotary motion, it is called a rotary generator where the stator windings or magnets form a fixed cage around a rotating inner rotor consisting of magnets or windings respectively. If the motion consists of a linear array of magnets or coil windings (rotor) sliding past a linear array of coil windings or magnets respectively in a vibrating linear motion, the device is known as a linear generator. Whether the Faraday Generator is rotary or linear, the induced electric field and current (power) is always induced in the coils which are known as the armature. The armature can be fixed comprising a stator or mobile comprising a rotor that is paired with a corresponding mobile magnet rotor or fixed magnet stator respectively. If one desires a minimum of moving parts in a water environment, and given that the wave oscillation is a vertical semi-sinusoidal one, the optimal generator to use is a linear one oriented in a vertical direction parallel to the direction of vertical oscillation of the water wave surface.
Q3: How much energy is available in ocean water waves?
<![if !supportLists]>1. <![endif]>A considerable amount of energy is available and it is expressed as the wave energy flux or wave power available per meter of oncoming propagating wave. The kinetic power (kinetic energy per second delivered by the wave per meter of wavefront) is proportional to the product of the square of the significant wave height and the period of the wave. The approximate formula is: P = 0.5HteT where P is Kw / meter of wavefront, Hte is the significant wave height, and T is the period of the wave.
<![if !supportLists]>2. <![endif]>The significant wave height, Hte, is defined as the average height of the one third largest waves that are observed during a defined time period that are crossing a particular point.
<![if !supportLists]>3. <![endif]>The total amount of potentially harvestable energy that can be converted into electrical power from the world’s oceans has been estimated by the World Energy Council to be approximately 2 Terawatts. This represents twice the current world electricity energy production.
<![if !supportLists]>4. <![endif]>Extractable ocean wave energy with its high power density is thought to be the most concentrated, most consistent, and potentially cheapest renewable energy source.
Q4: What is an omnidirectional energy point absorber?
<![if !supportLists]>1. <![endif]>It is a type of wave energy converter (WEC) that can absorb wave energy from waves approaching the device from any direction. It does not need any steering mechanism or permanent orientation toward the waves, and can absorb energy from multiple simultaneous wave trains intersecting the device from multiple different directions. The ideal point absorber will absorb energy equally from all directions (omnidirectional) as opposed to a unidirectional absorber that absorbs from only one direction, or absorbs varying amounts from different directions. Examples would be a circular WEC, a line shaped WEC, and a square shaped WEC respectively.
Q5: What is a surface energy attenuator?
<![if !supportLists]>1. <![endif]>Virtually all the kinetic energy of propagating water waves is found at the surface and near the surface of the ocean. As the depth of the water decreases, the water particle velocity and hence the energy in the moving water particles set into motion by the wave decreases with the square of the depth. To capture the greatest percentage of energy lying on and at near the surface, one needs a device that can harvest the kinetic energy from this surface and sub-surface zone of a region, body, or area of water of arbitrary shape and size and capable of sustaining propagating water waves. Do this, a surface energy attenuator is used which generally consists of a multi-device WEC that is laid out in an array configuration occupying the targeted area of water so that water wave kinetic energy is harvested from that entire water area as waves propagate through that bounded region. The individual devices can either be unidirectional point absorbers that have to have a steering mechanism or must be permanently moored in such a fashion that the devices always points at least most of the time in the direction of propagation toward the oncoming wave fronts or they can be omnidirectional point absorbers such as the LEG Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]>that are not subject to these restrictions. Furthermore, the devices themselves can be surface energy attenuators rather than energy point absorbers depending upon the technology employed. Note that harvesting is maximal when the direction of propagation of the wave is perpendicular to the surface of the WEC facing the incoming wave.
Q6: What kind of WEC is the Vibristor® device?
<![if !supportLists]>1. <![endif]>This device is an omnidirectional energy point absorber capable of harvesting the energy of wave trains approaching and intersecting the device from any direction or from multiple directions.
<![if !supportLists]>2. <![endif]>It does not need a steering mechanism nor does it have to be pointed in a fixed direction though if it is moored to a fixed structure it might be.
<![if !supportLists]>3. <![endif]>When used in large arrays, the collection of devices becomes an ocean surface energy attenuator.
<![if !supportLists]>4. <![endif]>Thus the Vibristor® has characteristics of both classifications of wave energy converters.
Q7: Why is the Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]> WEC (Wave Energy Converter) not run in resonance with the waves?
<![if !supportLists]>1. <![endif]>The rotor of the generator consisting of the Permanent Magnet Array (PMA) is attached to the buoy floatation collar via a spring and cable at least the upper end of the buoy and possibly by a spring at both ends of the PMA.
<![if !supportLists]>2. <![endif]>In small versions of the WEC, the metal spring is replaced by a magnetic levitation device which serves as a “magnetic” spring.
<![if !supportLists]>3. <![endif]>In any of these configurations, the system will have its own spring constant (the spring constant of the upper spring only, or the parallel spring constant if both a perturbing force (upper) and restoring force (lower) spring are used). Note in the case of the magnetic repulsive “spring”, the “spring constant” varies with the distance of the end of the PMA from the end braking magnet and hence, unlike natural elastic non-deformed springs, the spring expansion and contraction is not linear with the applied force making for very complicated analysis.
<![if !supportLists]>4. <![endif]>In either of the above cases, the above system will have its natural resonant oscillation frequency; when the incoming wave frequency (the driving frequency) matches that of the system’s natural resonance frequency, the heaving motion of the rotor will be greater than one (much greater than one if the damping factor of this resonant system is low) wave amplitude, the velocity of the PMA will be greater at resonant mode, and thus more power will be generated.
<![if !supportLists]>5. <![endif]>Problem #1: Unless the device is located in certain ocean areas of the world (i.e. – 15 to + 15 degrees latitude, the Pacific off the Oregon coast, etc., where the wave motion is uniform in height and frequency, this won’t work. In most ocean areas of the world, the waves are far from sinusoidal; consist of multiple frequencies and amplitudes that vary with a wave and height spectrum that vary with place and time. Furthermore, multiple wave trains emanating from distant discrete widely separated sources i.e. weather systems propagate at different velocities from multiple different directions leading to complex wave form patterns that chaotically vary with time and place and producing varying areas of constructive and destructive wave patterns in the wave harvesting area.
<![if !supportLists]>6. <![endif]>Problem #2: Each WEC would have to be built very specifically for one particular location so that the wave frequency and the resonant frequency of the WEC match and hence the WEC would not be a standard mass produced part.
<![if !supportLists]>7. <![endif]>Problem #3: If such a device is operated at resonance, its sliding tube and vertical height for a given sized maximum operational wave would have to be much larger to handle the resonant heaving motion or else the device would destroy itself with repeated severe impacts to the ends of the stator. The braking magnet system could not handle the impact unless the device was made much larger (a larger height) to accommodate the increased stroke distance of the rotor.
<![if !supportLists]>8. <![endif]>Problem #4: If the driving wave frequency deviated even by a small amount from the natural frequency of the large WEC needed to accommodate the wave amplitude magnification, the efficiency of the device in terms of generated watts per cubic unit of device volume would fall off drastically.
<![if !supportLists]>9. <![endif]>Problem #5: For a small WEC with a small rotor mass, if the damping factor is purposefully not made high enough, the buoy floatation collar might try to lift itself completely out of the water overwhelming the upper end braking unit and slamming hard into the lower braking unit with significant potential damage to the WEC.
<![if !supportLists]>10. <![endif]> Problem #6: For large amplitude, low frequency ocean waves, i.e. storm generated swells, in order to bring down the natural frequency of the WEC to match that of the waves, the rotor would have to be huge in mass relative to the surface area of the buoy floatation collar to be operated in resonance mode, and the device would be horribly inefficient by being both out of resonance and by having most of its potential rotor movement not occurring whenever these large waves for which it was designed were not present.
<![if !supportLists]>11. <![endif]> Problem #7: Given the situation created by problem #7, a very large massive rotor will require a huge and massive WEC as the stator has to be fixed to a fixed subunit of the WEC that has to be at least 30 times more massive than the rotor in order for the stator fixed subunit to be relatively immobile relative to the rotor with the passage of the wave and generate electrical power at a reasonable efficiency. This is a problem only for floating tethered WEC devices and not a problem if the stator fixed subunit of the device is rigidly mounted to either the seabed or a fixed coastline structure nearby.
<![if !supportLists]>12. <![endif]> Problem #8: While it is possible for single large WEC to have sophisticated computer controlled outboard sensors which determines the period of the wave in advance of the arrival of the wave at the WEC to change the resonant frequency of the WEC in response to the particular incoming wave period, this greatly adds to expense, complexity, and its reliability especially since several different waves can impinge on the sensor at once from different directions. This active adaptive system does not lend itself to low cost small WEC’s arrayed in a large array consisting of many devices.
<![if !supportLists]>13. <![endif]> The loss of efficiency in running a large single WEC at off-resonance frequency relative to the incoming wave frequency is offset by a multi-layer array of many small WEC Vibristor® devices. No matter what the frequency (period) of the incoming wave train is, if it encounters a WEC array of multiple Vibristor® layers, each layer will harvest a portion of the incoming wave energy, albeit at less than optimal device vibration frequency relative to the incoming wave frequency, the incoming wave amplitude and energy will be cumulatively attenuated by the multiplicity of layers, and by the time the wave train exits the array, most of its energy will have been harvested with a great degree of efficiency. Thus while the single WEC, Vibristor® included may be a device whose efficiency may be greatly dependent upon the matchup between the device’s internal vibratory frequency and the incoming ocean wave frequency, a multi-layer array is relatively frequency independent and would exhibit high energy absorbing efficiencies at all incoming wave frequencies (subject to certain limitations described at other locations in this document – the wave period cannot be either too short or too long) independent of the internal vibration frequency of the individual Vibristor® WEC devices.
Q8: What are the advantages of single or several large WEC’s versus many small WEC’s used in a densely packed carpet-like array to harness energy in ocean areas with wide ocean wave spectrum?
<![if !supportLists]>1. <![endif]>Advantages of large WEC’s include: 1.) Ability to handle extremely large waves; 2) Ability to produce large amounts of power from extremely large waves; 3) More likely to be used in possible grid scale applications.
<![if !supportLists]>2. <![endif]>Disadvantages of large WEC’s include: 1) Huge initial capital costs; 2) Are difficult to deploy and install; 3) Must be used either singly or in a “wave farm” group where the units are widely spaced allowing much of the propagating wave front to go past the devices without any energy harvesting occurring; 4) Difficult presence on the environment; 5) are terribly inefficient if the large sized waves for which they were designed are not present at all times; 6) Are very difficult to replace upon device failure. 7) Not suitable for mass production of standard designs since they are designed for specific sized waves in specific locations.
<![if !supportLists]>3. <![endif]>Advantages of using many small WEC’s in a dense carpet-like array include: 1) May be used singly or in closely packed arrays of many hundreds of units; 2) Devices are small in size; 3) Low initial cost per WEC and total cost is dependent on the number of WEC’s in the array that is determined by the size and shape of the array; 4) Shape and size of the array can be designed to fit the specific size and shape of the body of water; 5) Can be used in any body of water with a minimum size sufficient to support propagating waves; 6) Can harvest useable electric power from extremely small waves; 7) A large wave encountering a series of such WEC’s can have its energy extracted over the series of units allowing for a wide range of wave frequencies, wavelengths, and amplitudes to be used; 8) Easy to install, transport, service and replace; 9) Very low environmental presence; 9) Effective energy extraction even with waves that vary in time with respect to amplitude, wavelength, height, frequency and direction of propagation; 10) Ability to harvest energy from multiple simultaneous intersecting wave trains traveling from different directions; 11) Tethering to the seabed or surrounding structures are easier; 12) Can tolerate adverse weather conditions better as a carpet-like array of smaller WEC’s can float and ripple with large waves propagating through the array; 13) The WEC would be a standard component and only the size and shape of the arrangement of deployed arrays would change; 14) An entire wavefront of a propagating wave can intersect a large array without any areas of the wavefront being wasted because of the failure of a portion of the wave to intersect a WEC; 15) The array can be constructed on site rather than requiring transport of a large and unwieldy structure to the point of deployment, an expensive process; 16) The magnet-coil structure of the array can be scaled up in dimensions so that the power producing capability of each WEC, if the array is located in an area of sufficiently frequent and powerful waves, so that grid applications become realistic; 17) Small WEC’s can easily be used in “wave riding” mode and hence operate with a wide bandwidth of available wave spectrums; 18) Small WEC’s in arrays can act as a sort of frequency multiplier. Normally when one wavefront intersects one WEC, only one electrical power pulse is produced. If the array has 8 rows of WEC’s facing the wavefront, 8 electrical power pulses are produced as the wave propagates through one WEC after another; 19) Small WEC’s in arrays can act as a bandwidth extender; if waves of different frequencies and wavelength intersect one WEC, only the wave with the frequency closest to the natural resonant frequency of the WEC will respond maximally to the wave; however, a series of WEC’s can efficiently absorb the energy of waves of a wide spectrum of frequencies and wavelengths as the individual WEC’s do not have to be operating on waves of their resonant frequency – even if they are not and individually are less efficient, the summation of all of the energy absorption of the combined effect of all the WEC’s will act as if energy was extracted at the same efficiency as if any incoming wave was at the “resonant frequency” of an individual large WEC. The Vibristor® array of WEC devices operates at a high level of energy extraction independent of the frequency of the incoming ocean waves (subject to certain restrictions described elsewhere in this document).
<![if !supportLists]>4. <![endif]>Disadvantages of using many small WEC’s in an array: 1) The array would cover a larger area of ocean surface to produce a greater harvesting of electrical energy; 2) Multiple successive layers of WEC’s in an array could allow such a high fraction of the available wave kinetic energy to be harvested that the water behind the array would be so depleted of kinetic energy that ocean turbulence and mixing of plankton and other small organisms in the ocean food chain could be impaired (solvable – just don’t use an excessively large number of WEC’s to do too high an energy extraction efficiency).
Q9: What is wave riding mode?
<![if !supportLists]>1. <![endif]>The WEC, being a spring mass system whose spring constant depends of the individual spring constants of either the upper perturbing force spring or the lower restoring force spring, or both (with a K1*K2 / (K1 + K2 parallel spring constant). This spring constant is further modified by the braking magnet “magnetic spring constant” and motion dampening end coils that influences the motion of the rotor only when it is being braked at the end of the stroke at the wave crest and trough. The “magnetic spring constant”, a complex non-linear parameter, can be ignored for the sake of simplicity unless it is the only “spring” component in the absence of conventional springs. The WEC spring mass system has its own natural frequency Ѡz as compared to the impinging wave Ѡ. (Ѡz = (ρgA/m)1/2, p=density of sea water (1030 kg/m3,) g=gravity constant (9.8 m/s2), A= area of floatation collar, m= mass of the rotor or mobile subunit of WEC (= mass of PMA + mass of buoy floatation collar + mass of springs etc.). The mass of the stator attached to the fixed subunit of the WEC is relatively stationary and is not part of the mass spring system of the WEC.
<![if !supportLists]>2. <![endif]>When Ѡ / Ѡz = 1, the system will be at resonance with the oncoming wave and for the wave height (twice wave amplitude) at that frequency, the heaving motion of the rotor will be at a maximum and a multiple of that wave height (that multiple, the motion magnification factor, Q, will vary with the damping factor characteristic of all resonant electromagnetic and mechanical resonance systems).
<![if !supportLists]>3. <![endif]>Unless the LEG and WEC was built for precisely that location, that is, unless the mechanical resonant frequency of the WEC was precisely equal to that of the incoming waves, the heaving motion of the rotor will drop off considerably and theoretically, therefore, the amplitude of the rotor’s heaving motion will drop off and its velocity during all points of the wave cycle (except at the minimum and maximum) will also drop off, with both factors decreasing power output.
<![if !supportLists]>4. <![endif]>One can graph the heaving motion as a function of the frequency ratio of the incoming wave relative to the natural frequency of the WEC (Ѡ/Ѡz) and one will see a peak at the resonant point where the ratio = 1 and whose height will depend on the mechanical and electrical damping factors of the system (due to factors such as kinetic energy conversion to electrical energy, friction, air damping, elastic losses within the springs etc.)
<![if !supportLists]>5. <![endif]>If one proceeds much to the right of the peak resonant point (the wave frequency that matches the natural mechanical resonant frequency of the WEC), where Ѡ/Ѡz progressively increases, there is a sharp drop in the heaving motion of the rotor (PMA plus the springs plus the buoy floatation collar) and the electrical power output drops off to zero. This occurs as a result of the natural frequency of resonance of the WEC becoming so low relative to the high frequency of the incoming waves which has three consequences: 1. The higher the frequency of the waves, the more difficulty the WEC has keeping up with the vertical wave motions impinging on it (unless A was made much larger and m was made much smaller); 2. The WEC vibrations will fall behind in phase with the incoming waves; 3. The higher frequency waves are associated with lower amplitude as they are produced by less forceful driving forces. For instance, wind capillary waves (capillary waves – waves that initially propagate because of the friction between the wind and the water surface associated with its surface tension) are high frequency low amplitude as compared to storm swells (gravity waves – water waves that propagate because of the restoring force of gravity) that are high amplitude but low frequency). All three factors that operate to the right of the resonance peak cause a much smaller amplitude of vibration of the rotor and a progressively severe decrease in electrical power output with the amplitude of the rotor, the velocity of the rotor, and the power generated by the rotor eventually approaching zero as the Ѡ/Ѡz ratio becomes quite large.
<![if !supportLists]>6. <![endif]>If one proceeds much to the left of the peak mechanical resonant point where Ѡ/Ѡz becomes steadily less than one, there is a gradual decrease of the heaving amplitude of the rotor (one half of the rotor’s total excursion) and it gradually approaches and equals the amplitude of the incoming wave for a wide range of frequencies greater than the resonance frequency. The WEC can follow the wave motion at all wave frequencies greater than the resonant frequency of the WEC and will thus produce power over a broad bandwidth of wave frequencies. In this mode, the WEC appears to float on the wave at all points along the waveform including its crest and trough in a smooth manner, and hence the device is “wave riding” the incoming wave.
Q10: What is the range of frequencies that are optimal for the wave riding mode of operation for the WEC?
<![if !supportLists]>1. <![endif]>Empirically it is believed that it is optimal that wave frequencies fall into the range where the Ѡ/Ѡz ratio is at most 1.2 on the upper end and at least 0.1 on the lower end. At ratios higher than that, the heaving range of motion of the rotor will be less than the wave height and thus the WEC efficiency will be unacceptably diminished at higher wave.
<![if !supportLists]>2. <![endif]>Empirically it is also believed that any wave frequency sufficiently below the point where Ѡ/Ѡz ≤ 1.2 will produce acceptable amounts of heaving motion of the rotor as the buoy floatation collar “rides” the wave and hence significant electrical power will be produced, subject to one limitation described in the next segment. This upper limit maybe subject to being raised subject to further quantitative testing of the WEC.
<![if !supportLists]>3. <![endif]>The wave riding mode however has a low frequency limitation from another cause. We know that Energy = Force x Distance, and that the time derivative of Energy, Power = Force x Velocity. The power produced by the rotor is a function of the rotor’s PMA velocity, and the time derivative of the PMA’s deviation from the mean rest water level for a driving wave disturbance with a displacement of Z = Zo cos(Ѡt) (assuming the wave train is starting from a crest at t=0) is the velocity of the rotor VPMA=-ѠZ osin(Ѡt). Hence, the power developed in the kinetic energy of the rotor is proportional to the frequency. As a result the electrical energy developed in the Field Coil Array (FCA) will also be proportional to the frequency (as is expected from Faraday’s Law which predicts that the power produced is proportional to the speed of the conductor through the magnetic field). Thus, if the waves become too infrequent, even though wave height(and amplitude) increase as wave frequency decreases making more kinetic energy and power available per meter of wavefront, the velocity of the rotor will decrease so much that the net effect is a drop off in the efficiency of the WEC and in the amount of power converted. The rotor might move a very large distance but the rate of movement will be so slow that very little power will be generated. For an extreme example, the frequency of a tsunami is so low that that it will pass through a wave riding WEC with scarcely a movement of the rotor producing virtually no electricity. Empirically, it is believed that this velocity effect requires that the wave frequencies should be sufficiently high so that Ѡ/Ѡz ≥ 0.1. This lower limit may be subject to further decrease depending upon results of further quantitative testing.
<![if !supportLists]>4. <![endif]>We define the wave frequency interval where Ѡ/Ѡz is < 1.2 but > 0.1 to be the operating bandwidth of the Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]> where the heaving motion amplitude of its rotor and PMA is at least equal to or greater than the amplitude of the driving wave. That is the interval on the plot of rotor heaving amplitude versus Ѡ/Ѡz where the magnification factor, Q, is ≥ 1. Note that if Hz is the heaving amplitude of the rotor and the PMA, Z=Zocos(Ѡt), and Zo is the amplitude of the oncoming wave that is a function of the force that produced the wave, then Hz = QZocos(Ѡt). Q itself is a function of Ѡ/Ѡz, the damping factor Δ, and the force of the wave exerted against the underside of the circular floatation collar Fc . Fc is a function of Hte and hence, Fc is also a function of the wave amplitude. Thus, Q = f(Ѡ/Ѡz, Δ, Hte).
Q11: Why is the WEC run in wave riding mode?
<![if !supportLists]>1. <![endif]>Two or more small low cost standardized WEC’s intersecting an oncoming wave train in succession can be made to absorb as much energy as a single large expensive custom made WEC.
<![if !supportLists]>2. <![endif]>A small wave riding WEC can oscillate in sync with virtually any wave train, even jagged non-sinusoidal wave trains caused by rough weather or waves coming from multiple directions.
<![if !supportLists]>3. <![endif]>If one defines useable incoming wave bandwidth as the bandwidth of waves that can be used to harvest useable electric power by the WEC, an array of WEC’s of just a few rows can harvest the energy over a huge range of incoming wave frequencies.
<![if !supportLists]>4. <![endif]>One can accommodate oncoming waves of large amplitude by using rows or arrays of WEC’s sufficient in number to absorb and harvest efficiently a reasonable percentage of the energy contained within these waves with the capability of markedly attenuating even large waves propagating through the array.
<![if !supportLists]>5. <![endif]>The one problem in using multiple WEC arrays in absorbing the energy of waves of virtually any frequency and amplitude (other than from severe storms) is that it might absorb too much energy causing very still water in back of the array which might produce environmental concerns if too many small WEC’s were used within a given area of the ocean. These concerns involve lack of sufficient water turbulence created by wave action caused by overly efficient wave energy attenuation and extraction which has the consequence of interference in the movement of plankton which could negatively impact on the ocean food cycle. One avoids this scenario by keeping the level of energy extraction to below a certain point to insure that some wave action persists behind the array. This is done by limiting the size and depth (number of rows) of the array.
<![if !supportLists]>6. <![endif]>In intense storms with extremely large waves, if a series of waves of very large height happen to come and intersect the device at the resonance frequency of the device, especially if it is a single large WEC and not an array, you might get a situation like the Tacoma Narrows Bridge in the state of Washington which destroyed itself in 1941 when it went into a resonance vibration mode initiated with wind currents.
Q12: How can too much energy be prevented from being extracted from propagating wave fronts intersecting the array and thus prevent too much energy from being removed from the ocean surface and sub-surface area?
<![if !supportLists]>1. <![endif]>Making sure the size of the array is small compared to the body of water in which it is placed.
<![if !supportLists]>2. <![endif]>Making sure the size of the array is small enough to not be overly efficient extracting energy from the waves of size most likely to be encountered in that location.
<![if !supportLists]>3. <![endif]>Designing the array so that the maximum number of rows of small WEC’s that face the propagating wave fronts is such that the product of the number of rows and the maximum stroke distance of the rotors of the individual WEC’s is no more than 75% of the significant wave height of waves most likely to be encountered in that area.
<![if !supportLists]>4. <![endif]>If waves propagate in a given location predominantly from one direction only, the depth of the array can be made much deeper than the width of the array so that at the far end of the array, diffraction of the surrounding wavefront that did not intersect the array will bend around the rear end of the array preventing calm water behind the array.
<![if !supportLists]>5. <![endif]>If the waves are propagating from one general direction, a strip shaped array can be used where the long axis of the array is much greater than the width of the array and it is oriented approximately perpendicular to the direction of wave propagation. Wave diffraction effects as described above will prevent the problem of a calm water region from forming.
<![if !supportLists]>6. <![endif]>If the array is attached to a fixed coastline structure such as a seawall, the calm water turbulence problem will not occur and in fact will be a significant advantage in protecting the attached coastal structure against large waves from impacting it.
Q13: How can an array of WEC’s prevent coastal structures from being damaged?
<![if !supportLists]>1. <![endif]>A strip array can be tethered rigidly or by flexible means to a sea wall to protect it and increase its life expectancy.
<![if !supportLists]>2. <![endif]>Such an array can also be floated off shore close to a beach to decrease beach erosion from ocean waves.
<![if !supportLists]>3. <![endif]>A circular ring shaped array surrounding a central structure like a marine wind generator will protect it.
<![if !supportLists]>4. <![endif]>The mechanism behind all such applications would be that attenuating the kinetic energy of ocean waves impacting upon marine exposed structures would lead to lessening the damaging impact of such waves leading to longer lifetimes and decrease maintenance issues.
<![if !supportLists]>5. <![endif]>The effect would be to have an “electrokinetic sea wall” (patent issued) that would create electrical power from the attenuated harvested energy as a useful byproduct.
Q14: In a large array of WEC’s, how can one prevent some of the WEC’s further into the interior of the array from becoming progressively inefficient in wave energy extraction the further back into the array that they are located?
<![if !supportLists]>1. <![endif]>Method 1: employing only a maximum number of rows of WEC’s in the array so that the attenuation and subsequent harvesting of wave energy would be significant even for the last row of WEC’s encountering a wave still having enough energy as it passes through it. As an example, instead of having a circular array of WEC’s where the WEC’s in the interior of the delay would see the most attenuation of the wave and therefore would be the least efficient in energy extraction, one could have a ring array and leave out the WEC’s in the central area of the array.
<![if !supportLists]>2. <![endif]>Method 2: With each successive row, decrease the size of the array as each row would encounter a wave of progressively smaller amplitude and energy flux as the row before it would remove a certain amount of energy from the wave. Thus efficiency of the device in terms of power generated per unit volume or weight of WEC would remain fairly constant. The problem with this approach would be that the WEC would have to be manufactured in many different sizes and this is less optimal for the mass production of a low cost standardized device with great flexibility of use as is desired.
Q15: How does an array of Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]> WEC’s act like a frequency multiplier?
<![if !supportLists]>1. <![endif]>Small WEC’s in arrays can act as a sort of frequency multiplier. Normally when one wavefront intersects one WEC, only one electrical power pulse is produced. If the array has 8 rows of WEC’s facing the wavefront, 8 electrical power pulses are produced as the wave propagates through one WEC after another. In fact, if a wavefront intersects n rows of WEC’s or n WEC’s one behind the other in a strip, n power pulses will be generated from that single wave front. These multiple power pulses are than filtered and combined into one master power output source by the Power Collection Circuitry (PCC) of the array.
<![if !supportLists]>2. <![endif]>If the WEC array is shaped so that it is omnidirectional, that is like a circle or a ring, then no matter from what direction the wavefront approaches, the number of WEC’s it intersects will produce the same number of power pulses per wave front.
<![if !supportLists]>3. <![endif]>If the WEC is shaped so that it is more efficient in one direction, the number of power pulses produced will depend on the angle of incidence of the wavefront with the array. For instance, a strip of WEC’s of depth n of width one WEC will emit n power pulses per waveform if the waveform is traveling parallel to the long axis of the strip but only one simultaneous pulse from each of the WEC’s (summed of course into one much larger pulse) if the wavefront intersects the strip array traveling perpendicular to its long axis. A square n x n matrix array of WEC’s will produce n power pulses if any wave comes from one of 4 directions that are each perpendicular to the intersected face of the array and will produce a varying number of pulses of different sizes if it comes from any other direction.
<![if !supportLists]>4. <![endif]>Often in oceans, there are usually multiple simultaneous wavefront propagating in numerous different directions especially if there are several active intense weather systems active in some part of the ocean. The energy streams propagating as the group velocity of the various wave fronts entering the array from different directions set up an interference of constructive and destructive wave patterns within the array causing electrical power pulses to be generated in a somewhat chaotic fashion with respect to both magnitude and frequency which are of course filtered and summated into one master output.
<![if !supportLists]>5. <![endif]>Thus the array of small WEC’s is best suited to handle the chaotic pseudo-sinusoidal wave patterns that comprise the ocean surface and sub-surface wave energy layer. These pseudo-sinusoidal and often completely chaotic wave patterns might be very difficult for a single larger sized WEC to handle efficiently in a device in the wave riding mode and virtually impossible for a device trying to operate in the resonance mode. However, an array of small wave riding WEC’s with its broad response bandwidth and with each individual WEC producing its own power pulse train output will convert the majority of water surface fluctuations into useable output power pulses. The array should accomplish this even if these surface fluctuations are standing waves with their constructive and destructive interfering waveform patterns or if the waveforms are totally non-sinusoidal and chaotic. The result would be a fairly high variable frequency output that can be filtered and summed together as one power output by the PCC. Useable significant power would be produced no matter what the surface conditions of the sea were.
Q16: How does an array of Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]>WEC’s act like a bandwidth extender?
<![if !supportLists]>1. <![endif]>Small WEC’s in arrays can act as a bandwidth extender; if waves of different frequencies and wavelength intersect one WEC, only the wave with the frequency closest to the natural resonant frequency of the WEC will respond maximally to the wave; however, a series of WEC’s operating in the wave riding mode can efficiently absorb the energy of waves of a wide spectrum of frequencies and wavelengths as the individual WEC’s do not have to be operating on waves of their resonant frequency. Even if they are not in the resonant mode and individually are less efficient, the summation of all of the energy absorption of the combined effect of all the WEC’s will act as if energy was extracted at the same efficiency as if any incoming wave was at the “resonant frequency” of the individual WEC’s.
Q17: How is the WEC protected against large incoming waves?
<![if !supportLists]>1. <![endif]>At either end of the LEG there is a mechanical electromagnetic braking system that damps down and extinguishes the excessive vertical motion of the PMA and prevents it from slamming into the ends of the LEG as a result of a very large wave intersecting the device.
Q18: How is the braking accomplished?
<![if !supportLists]>1. <![endif]>The braking unit consists of three components, a braking coil, an end-braking magnet, and in large unit LEG’s, a stiff spring. As a result of an excessively large wave whose amplitude is higher than for what the unit was designed for, the PMA will have considerable motion as it approaches either the upper or lower end of the magnet sliding tube and will slam into the ends of the sliding chamber causing a possibly violent inelastic collision that can damage the structure, shorten its lifespan, and in the least, waste kinetic energy turning it into heat rather than electricity.
<![if !supportLists]>2. <![endif]>As the PMA reaches the end of the sliding tube, it encounters first, it reaches the large wire gauge end coil which can be either shorted out or connected to the Power Collection Circuitry (PCC) so as not to waste this kinetic energy in the moving PMA. If the coil is shorted out, the braking action is greater but the energy is dissipated as unwanted heat wasting the energy. The coil can also be replaced by a long ring of conductor – copper or brass would do. No matter what the arrangement, the large current flows induced in the braking coil, through Lenz’s Law, induces a back EMF force that opposes the motion of the PMA and brakes the moving rotor.
<![if !supportLists]>3. <![endif]>If the PMA is not stopped by the end braking coil, the end-deflecting magnet of the PMA will approach the end-braking magnet of like magnetic polarity causing a repelling magnetic field to build up as the field is compressed between the two magnets which will stop the remainder of the motion of the PMA. A braking spring can be used as a third component to the braking action.
<![if !supportLists]>4. <![endif]>Two benefits of the end braking are: First, the remaining kinetic motion of the PMA ends up being temporarily stored in the end repulsive magnetic field and then as the PMA slows, stops, and is repelled in the opposite direction, the stored energy is restored as kinetic energy of the PMA moving in the opposite direction where it can be converted into electrical energy by the FCA (Field Coil Array). Second, as the PMA approaches the end-braking magnet, any magnetic flux lines that have escaped the PMA and the surrounding FCA from getting past the end deflecting magnets will get deflected back into the PMA by the repulsive field of the end-braking magnet instead of being lost into space thereby increasing the efficiency of the device. Thus as the PMA approaches the end-braking magnet, flux leakage from the PMA gets reduced considerably.
<![if !supportLists]>5. <![endif]>In large WEC Vibristor units that handle very large waves, to stop the occasional rogue wave, any PMA kinetic energy that is left after the first two mechanisms will be stopped by a stiff spring that lies in front of the end-braking magnet that will finally bring the PMA to a stop before it crashes into the end-braking magnet. Like the repulsive magnetic field, the spring also will store kinetic energy of the PMA and restore it later to the system for energy conversion while helping to keep the encounter of the PMA with the end-braking magnet a completely elastic collision with all of the advantages outlined above.
<![if !supportLists]>6. <![endif]>The spring component of the end-braking unit is not required in small devices with small displacement stroke distances as the end-braking magnets itself interacting with the approaching end-deflecting magnet on the PMA acts as a “magnetic spring” that in association with the damping effect of the end coil windings, all act as a damped mass spring system.
Q19: Are there weather conditions where the array should be shut down?
<![if !supportLists]>1. <![endif]>Extremely intense weather conditions will call large waves that will surpass the ability of the array to safely generate electric power. It should be shut down under such weather conditions.
<![if !supportLists]>2. <![endif]>While the WEC’s in the array are small, if they are tethered together in a flexible array, the array can ripple in shape as the waves propagate through it providing stability for the array even if waves larger than what it was designed to operate with intersect the array. In this respect they would have more tolerance to wave size than a single fixed array. However, past a certain point, the array should be shut down.
<![if !supportLists]>3. <![endif]>If the WEC’s are rigidly fixed to a coastal structure such as a linear array fixed to a seawall, in rough weather, the WEC’s are designed to be water tight and resist submergence by large waves.
<![if !supportLists]>4. <![endif]>Storm surges for fixed rigidly tethered waves along the coast could be problematical as they might require the WEC’s to be under water for hours at a time which will require engineering considerations that will have to be dealt with.
<![if !supportLists]>5. <![endif]>Quite important with regards to device shutdown is that electrically, the array as a device has to be turned off in the event of an impending major storm and this is done by using a remote internet controlled switch from a distance. A single large WEC also would have to have this same feature.
<![if !supportLists]>6. <![endif]>However, a large WEC has to be mechanically stabilized against large waves to prevent a large magnet from repeatedly impacting against the braking unit which in spite of the braking unit, might lead to damage in a prolonged intense storm. This is especially true if there was any possibility of the device operating in a severe storm with the chance that it can encounter a train of very large waves coming in at the resonant frequency of the device.
<![if !supportLists]>7. <![endif]>A small WEC with a rotor and PMA of small size, even with extremely large waves, would have a relatively small kinetic energy because of the rotor’s small mass, and thus would be much less likely to sustain damage and the PMA’s energy can be damped safely on a repeated basis by the end braking unit operating on the PMA by the repulsive end braking magnet, the power absorbing Lenz EMF barking effects of the end braking coils, and a braking mechanical spring. Hence, it is anticipated that an array of small WEC’s can ride out an intense storm successfully if the tethering device connecting the WEC’s have sufficient tensile strength against breaking.
<![if !supportLists]>8. <![endif]>The fact that the individual WEC’s will be in wave riding mode with the buoy floatation collar floating in synch with the wave surface rather than in resonance mode will also make the chance of damage to the individual WEC’s less likely.
Q20: How can a large PMA be stabilized against excessive and dangerous motion during an intense storm or when the device is needed to be shut down for maintenance repair work?
<![if !supportLists]>1. <![endif]>The individual coils can each have a control circuit that can short out the coils by remote control or by direct wire control so that the PMA will encounter huge back Lenz EMF forces when it moves against every Field Coil Array (FC A) coil.
<![if !supportLists]>2. <![endif]>In effect, the entire FCA upon command of a shorting electrical signal, becomes a braking coil to stabilize the PMA against excessive movement.
Q21: How is an array shut off in the event of impending violent storms?
<![if !supportLists]>1. <![endif]>There would be a remotely controlled switch that via the internet can be turned on and off to activate the output of the PCC circuitry output for each WEC in the array.
<![if !supportLists]>2. <![endif]>If the WEC device was large with large magnets capable of producing large power pulses, a switching circuit could be used to short out all the coils of the WEC which would stabilize the magnets from moving significantly during an extreme weather event. It too would be remote controlled. Haphazard movement of large magnets in the device which in itself could damage the device would thereby be prevented.
<![if !supportLists]>3. <![endif]>In either case, a switch to shut off the PCC final output would also be needed to prevent any errant power pulses from being on the WEC or WEC array power output that would cause safety issues.
Q22: How is an individual WEC replaced in the event of electrical or mechanical failure?
<![if !supportLists]>1. <![endif]>A large WEC used in a single or few device wind farm would require an attempt to fix a mechanical or electrical malfunction while the device is deployed in place as the cost of removing the device and transporting it to a repair point on shore, or even on a ship, would be prohibitive. There would also be safety considerations in immobilizing large magnets in relationship to large coils to prevent unwanted power pulses that could jeopardize personnel trying to repair such a unit and thus utmost care would have to be taken to shut off the unit completely and stabilize the magnets to prevent an errant power pulse.
<![if !supportLists]>2. <![endif]>The preferred option to use a densely packed array of small WEC’s would allow a WEC to be simply unplugged, removed, and replace with a new functional device. The malfunctioning device could be subsequently repaired and returned to service. It would be very easy to switch off the device either by remote control or manually.
Q23: How is the power collected from the numerous WEC’s in an array?
<![if !supportLists]>1. <![endif]>This is done through a hierarchal Power Collection Circuitry (PCC) that uses modular component circuits of 4 different varieties that combines multiple AC inputs to form one DC output.
<![if !supportLists]>2. <![endif]>Each of the 4 different circuits can combine anywhere from 2 two many hundreds of different low level AC inputs (from sources such as WEC coils) as well as and DC inputs (such as piezoelectric transducers, solar cells, etc.) and thus a practically unlimited number of outputs from WEC coils on the same or different devices can be summated into one output DC current.
<![if !supportLists]>3. <![endif]>All circuits use low powered Schottky diodes to lessen power loss across multiple levels of diode rectifying junctions.
<![if !supportLists]>4. <![endif]>Circuit #1 is an n phase bridge rectifying and filtering circuit that produces a monopolar positive output from n number of low level AC or DC inputs.
<![if !supportLists]>5. <![endif]>Circuit #2 is an n phase bridge rectifying and filtering circuit that produces a bipolar positive, negative, and ground outputs from n number of low level AC or DC inputs.
<![if !supportLists]>6. <![endif]>Circuit #3 is a current summation circuit that sums the current outputs from n number of low level AC or DC low level sources together to form one summation output current.
<![if !supportLists]>7. <![endif]>Circuit #4 is a voltage summation circuit that sums the voltage outputs from n number of low level AC or DC low level sources together to form one summation output voltage.
<![if !supportLists]>8. <![endif]>What is new and unique about these modules aside from using n number of AC or DC inputs, producing a bipolar voltage output, and low power Schottky diodes is that each circuit itself can be used as a component in a hierarchal network of power collection circuits that can combine an unlimited number of AC or DC inputs into one master power output making them perfect for collecting the power out of an array of WEC’s each with a number of coils.
<![if !supportLists]>9. <![endif]>Each circuit can rectify and filter a large number of input power sources, and its single output can serve as an input to the next circuit, and thus, many such circuits with all 4 varieties being present at the same time can have their outputs summed together by any of the 4 circuits to produce one master output and so forth.
<![if !supportLists]>10. <![endif]> An example of how this might work is as follows: We have an array of 15 WEC’s that are in three rows of five each and each WEC has 8 coils servicing a PMA of 4 magnets (2 Structural Magnetic Units, SMU’s). Thus we have a total of 120 coils producing power that need to be summed up into one master output. We will use a 3 level hierarchal PCC. Each WEC FCA is wired as two groups of four. Each group of 4 goes through an n = 4 phase rectifier filtering circuit (circuit #1). Each row of 5 WEC’s has a total of 10 groups of 4 coils producing 10 outputs (first level of the PCC). These 10 output power sources now have their currents added together to produce one output current by using an n = 10 source current summation circuit (circuit #3). This is done for each row (second level of the PCC). Now we have 3 output sources for the entire array. We can combine these three inputs in 4 different manners (level 3 of the PCC): a) put these 3 inputs through circuit #1 (3 phase rectifier and filter) to produce an output of approximately the same voltage as the average voltage of the 3 voltage inputs; b) put these 3 inputs into circuit #2 (bipolar n = 3 phase rectifier filter circuit) to produce bipolar positive, negative, and ground outputs for the entire array; c) sum the currents of these 3 inputs to produce a relatively low voltage high current output for the array with circuit #3 (n = 3 input current summation circuit) or d) sum the voltages of these 3 inputs with circuit #4 (n = 3 input voltage summation circuit) to produce a relatively high voltage low current output for the array. Thus using a 3 tier PCC circuit we were able to combine a multitude of WEC coil outputs into one master power output from the array whose characteristics good be changed to suit the application for the harvested electrical energy.
<![if !supportLists]>11. <![endif]> The coils in the WEC’s can be substituted with piezoelectric energy vibrational energy harvesters producing very low frequency AC or DC power, very low voltage batteries (DC inputs), atmospheric diode power collectors (so called “free energy” devices, DC or AC inputs), solar cells (DC inputs), thermoelectric modules (DC inputs), etc.
Q24: How can the impact inelastic collision energy from a large wave be captured as useful electrical energy?
<![if !supportLists]>1. <![endif]>By three mechanisms: a) storing the kinetic energy transferred to the rotor and PMA (containing most of the rotor’s mass) temporarily in the compressed repulsive magnetic field of the end-braking magnet interacting with the end deflecting magnet magnetic field; b) storing the kinetic energy temporarily in the spring in front of the end-braking magnet; c) by braking the magnet through Lenz’s Law with the end-braking coils.
<![if !supportLists]>2. <![endif]>In the case of a) and b), the temporarily stored energy in the compressed magnetic fields is returned to the PMA as it is reconverted to kinetic energy which can then be converted to electrical energy on the next pass of the PMA through the FCA.
<![if !supportLists]>3. <![endif]>In the case of c), the remaining kinetic energy of the PMA, originally derived from the wave kinetic energy, is converted into electrical energy by the end-braking coil which can be collected, a process identical to the conversion of wave kinetic energy into electrical energy as the PMA interacts with the FCA. However, the amount of energy in the electrical pulse so collected would be significantly less than the electrical pulses from the FCA overlying the power producing magnets.
<![if !supportLists]>4. <![endif]>Furthermore, the magnetic field around the ends of the PMA collapses around the PMA instead of leaking away into space as the PMA approaches the end-braking magnet which causes an increased electromagnetic interaction and linkage with the end-braking coil increasing the braking effect of the coil and the current pulse generated by the coil.
Q25: What are the advantages of a fixed end-magnet braking system versus the disadvantages?
<![if !supportLists]>1. <![endif]>Advantage: When the PMA approaches the end magnet braking system coil, the motion of the magnet is considerably slowed down by the braking coil which converts much of the kinetic energy remaining in the PMA after encountering a large wave either to heat or if desired into electrical energy which may be collected and added to the output of the power magnets interacting with the FCA.
<![if !supportLists]>2. <![endif]>Advantage: Whatever remaining kinetic energy is left over in the PMA causes is stored in the increasingly compressed repulsive magnetic field between the end braking magnet and the end deflecting magnet (or end power magnet) that occurs as the PMA continues to approach the end braking magnet. At the point the forward velocity of the PMA has completely been halted, all of the kinetic energy remaining in the PMA has been converted to potential energy stored in the compressed magnetic field and will be ready to be released in the wave’s next half cycle for conversion into electrical power by the FCA.
<![if !supportLists]>3. <![endif]>Advantage: the presence of a mechanical spring in larger systems assists the function of the end braking magnet because as the spring is progressively compressed by the approach of the PMA to the end of the sliding tube, the energy of the PMA is sequentially stored and then released during the next half cycle as is the case with the end braking magnet.
<![if !supportLists]>4. <![endif]>Advantage: The “collision” with the end braking electromagnetic unit is completely elastic (unless the end braking coils are shorted out to produce heat) and the energy of the PMA as it travels to the end of the LEG slide tube is conserved completely for conversion to electric power.
<![if !supportLists]>5. <![endif]>Advantage: Since the end braking magnet and the entire braking unit is fixed to the much more massive fixed subunit which holds the stator, the recoil velocity of the stator upon impact of the PMA with the braking unit is near zero, a desirable situation for more efficient power conversion.
<![if !supportLists]>6. <![endif]>In case the WEC goes into resonance with a series of waves whose amplitude is not only large but whose frequency remains so close to the natural frequency of the mass spring system of the LEG causing the possibility of very violent motions of the rotor and damage to the device, the fixed end braking magnet, coil, and if present, spring, provides sufficient damping so as the device will not destroy itself. (Note #1: The damping from the spring is thermo-elastic and is therefore part of the mechanical damping characteristics of the device, and the damping from end braking coils contribute to the electrical damping characteristics of the device (whether PMA kinetic energy is dissipated as heat with a direct short of the end braking coils or as electrical power if the generated pulse is sent over to the PCC); the end braking magnet essentially contributes virtually nothing to either damping component.) (Note #2: these components of the LEG damping are not present constantly – they are active only when the PMA is in the vicinity of the end electromagnetic braking unit.)
<![if !supportLists]>7. <![endif]>Disadvantages: None.
Q26: What would be the advantages of mobile end braking magnets?
<![if !supportLists]>1. <![endif]>The kinetic energy left in the PMA when a large wave hit and all of the power could not be attenuated by the field coil array (FCA) could be changed into electrical power over a somewhat larger bandwidth of wave frequencies as compared to a fixed end braking magnet.
Q27: What would be the disadvantages of mobile end braking magnets?
<![if !supportLists]>1. <![endif]>Increased mechanical complexity with a longer string that would have to be run through the end-braking magnet and attached to the PMA at one end and then attached to the end of the stator fixed unit. A cable would still have to be attached to the buoy collar. This would have to be done at each end. The mobile end magnet would then have to move with that spring meaning that it too would have to be attached to the spring in some manner.
<![if !supportLists]>2. <![endif]>Energy is generated only with a large wave, and most waves except in storm conditions when the device should be shut down, will not cause sufficient electric power to be generated because the end magnet would not move enough.
<![if !supportLists]>3. <![endif]>The incremental increase in energy extraction by making the end-braking magnet vibrate if it were mobile would not be much more than the electric energy pulse produced by the PMA slowing being slowed down by the large fixed coils at each end of the rotor slide tube.
<![if !supportLists]>4. <![endif]>The incremental increase in energy extraction would be less both in terms of amount and cost then if simply another PMA magnet and more coils were added to the PMA; the PMA would be lengthened by one more structural magnetic unit of 2 power producing magnets and its pole pieces with additional coils to keep the polarity of the PMA end poles the same.
<![if !supportLists]>5. <![endif]>You would attenuate somewhat the focusing effects of the end-braking magnet pushing back the magnetic flux of the ends of the PMA back into the interior of the PMA for more power production.
<![if !supportLists]>6. <![endif]>You would decrease the braking effect against the PMA for large waves if the end-braking magnet was mobile and not a fixed component of the stator fixed subunit.
<![if !supportLists]>7. <![endif]>While a mobile braking magnet would allow the WEC to be responsive to a range of frequencies of waves (increase bandwidth), the combined power of the damped wave train generated as the PMA forced the end-braking magnet to oscillate would be approximately the same order of magnitude as the one large pulse generated by the PMA being braked by the large gauged end coils. Furthermore, no matter which method is chosen, the amount of extra power generated by an occasional wave is just a tiny fraction of the power being generated with each wave by the PMA. However, nevertheless it is power that can be captured.
<![if !supportLists]>8. <![endif]>Only one movable braking magnet would be potentially useful notwithstanding the above disadvantages a moving braking magnet to produce extra power. However, if both were mobile, non-linear instabilities such as bucking of the cable etc. would totally neutralize any power increase and this could potentially develop if both end braking magnets were vibrating at the same time.
<![if !supportLists]>9. <![endif]>A mobile braking magnet would produce a damped series of electrical pulses in the end braking coil that would partially coincide with the electrical impulse produced in the end braking coil just previously by the decelerating PMA and there could be undesirable interference.
<![if !supportLists]>10. <![endif]>A vibrating end braking magnet would transmit vibrations to the PMA via their interacting repelling magnetic fields, which could cause the PMA (though much more massive than the end braking magnet) to vibrate as it slowed to a stop which is less satisfactory than a smooth deceleration.
Q28: Are there differences in operation of an LEG where the rotor is the PMA and the stator is the FCA as is been analyzed with these FAQ issues versus the LEG where the PMA is the stator and the FCA is the rotor?
<![if !supportLists]>1. <![endif]>The physics, magnetic field distribution, and the electrical power output generated are the same between these two variants of the Vibristor-<![if !msEquation]><![if !vml]><![endif]><![endif]>
<![if !supportLists]>2. <![endif]>The structural mechanical operation is somewhat different between the two varieties of WEC but the functional operation is similar.
Q29: What is the advantage of an array of WEC’s if one WEC becomes operationally impaired?
<![if !supportLists]>1. <![endif]>If one WEC develops an open coil, the PCC simply ignores the high impedance of that coil and the device operates as before with some loss of power output because of that defective coil.
<![if !supportLists]>2. <![endif]>If one WEC develops a shorted coil, the PCC will protect the WEC via its blocking diodes to prevent other coil outputs from shorting out through the shorted coil thereby destroying the FCA for that device. As the PMA passes over the shorted coil, there would be a momentary braking action “bump” but it would be of minor degree as even though the coil is shorted significantly increasing Lenz back EMF force over that coil, the large number of coil turns of small gauge wire keeps the shorted current low (as opposed to the braking coils of large gauge diameter wire and few turns).
<![if !supportLists]>3. <![endif]>If more than one coil of one WEC shorts out or opens, the same effects as above would occur, but the effects would be more pronounced, the WEC output and therefore its conversion efficiency would drop but the device would still be functional.
<![if !supportLists]>4. <![endif]>If the entire WEC, that is its output, developed an open circuit, nothing would happen because as a result of the PCC, each WEC is in parallel with all the other WEC’s of the array and hence the only consequence would be a slight decrease output and efficiency of the energy conversion of the array but the array would remain fully functional.
<![if !supportLists]>5. <![endif]>If the entire WEC, that is its output, shorted out, again nothing would happen because as a result of the PCC, each WEC is in parallel and isolated from all the other WEC’s in the array no matter what the number of WEC’s were, and no damage or significant loss of power conversion of the array would occur. In fact, the shorted output would keep the PMA of the WEC relatively immobile because of the large load current would stall the PMA from Lenz’s back EMF and largely keep it stationary.
Q30: Are versions of the Vibristor-R, usually small ones with short stroke distance, where there are no perturbing and restoring force springs and where these functions are taken over by the “magnetic spring” repulsion and levitation between the end braking magnet and the end of the PMA covered under the patents granted?
<![if !supportLists]>1. <![endif]>Yes, one of the patent claims covers the function of the upper end braking magnet performing the function of the perturbing force spring and the lower braking magnet performing the function of the restoring force spring. If the Vibristor-R is in a horizontal vibrating mode, upper and lower springs lose their “upper” and “lower” significance.
Q31: Are there any serious impacts to the environment using arrays of small Vibristor <![if !msEquation]><![if !vml]><![endif]><![endif]> WEC’s?
<![if !supportLists]>1) <![endif]>If an array is too large in area through which the wave train propagates, too high a percentage of the impacting wave will be harvested potentially reducing turbulence in the water below what is necessary for mixing of food plankton thereby possibly interrupting the food chain for fish and other organisms.
<![if !supportLists]>2) <![endif]>The problem can be ameliorated by harvesting no more than 75% to 90% of the energy in a given area of ocean surface and by having restrictions on the dimensional size of the array. Thus the geometric dimensions of the array as well as the number of layers of Vibristor-R WEC’s impacting the incoming waves would be limited.
<![if !supportLists]>3) <![endif]>Because the Vibristor-R has only one moving part with no hydraulic fluids or significant amounts of liquid lubricant, there would be no chemical impact on the environment in the event of device failure.
<![if !supportLists]>4) <![endif]>If a single Vibristor-R failed, it would not sink to the ocean floor as debris to decompose as it would be held in place by the other WEC’s in the array.
<![if !supportLists]>5) <![endif]>Even if a single Vibristor-R got loose and sunk to the floor, it is such a small volume of debris that there would be no environmental impact.
<![if !supportLists]>6) <![endif]>Properly designed electrical circuitry would prevent stray electrical currents from impacting ocean life.
<![if !supportLists]>7) <![endif]>If a large storm destroyed the entire array and caused it to sink to the ocean bottom, the only chemicals released would be decomposition products of the copper and the rare earth magnets. Given the relatively total cumulative amounts of these two substances present, the environmental hazard would be minimal.
Q32: Are there any serious impacts to the environment using single or several large widely spaced Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]> arrays, that is, in a “wave farm”?
<![if !supportLists]>1) <![endif]>For the reasons explained in Q32, there would be none except for the fact that the destruction of a large Vibristor® WEC would produce a large debris field on the ocean floor but no more than a ship that sunk in deep water with minimal environmental impact.
Q33: What are the environmental advantages of using a single large Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]>WEC?
<![if !supportLists]>1) <![endif]>No effects on ocean life and the food chain, plankton, and ocean turbulence.
<![if !supportLists]>2) <![endif]>No lubricants, hydraulic fluids.
<![if !supportLists]>3) <![endif]>No major obstruction to fishing, shipping.
<![if !supportLists]>4) <![endif]>Its low presence above the surface of the water will make it relatively invisible at small distances thus not affecting the seascape appearance and generally not visible from shore.
Q34: What are the environmental advantages of using a large WEC array with small multiple Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]> WEC’s?
<![if !supportLists]>1) <![endif]>No hydraulic or liquid lubricants to escape.
<![if !supportLists]>2) <![endif]>Low profile above the surface of the water makes it invisible to viewers from the shoreline.
<![if !supportLists]>3) <![endif]>Less likely to break up from large waves in a storm.
<![if !supportLists]>4) <![endif]>Will not sink to ocean floor in even of device failure.
<![if !supportLists]>5) <![endif]>Amount of energy extractable from a given area of ocean surface is adjustable by varying the geometric size and number of layers of the array.
<![if !supportLists]>6) <![endif]>Excessive extraction of energy can be avoided thereby preventing harm to marine life by interference with plankton and the food chain.
<![if !supportLists]>7) <![endif]>Easily co-existent with fisherman and other users of the ocean.
Q35: What are the advantages of other types of types of non-Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]> WEC’s both used singly and in arrays?
<![if !supportLists]>1) <![endif]>Some can be used in resonant mode with the predominant wave frequency in the area of deployment.
<![if !supportLists]>2) <![endif]>Single unit can produce an enormous amount of power, up to a MW.
<![if !supportLists]>3) <![endif]>Structurally can be very strong.
<![if !supportLists]>4) <![endif]>The highest conversion efficiencies, such as the Salter Duck, are linear to rotary motion devices.
<![if !supportLists]>5) <![endif]>They can handle the largest waves.
<![if !supportLists]>6) <![endif]>They can be fitted to out rigger wave period sensing devices that can change their natural resonant frequency if they are dependent upon that parameter.
Q36: What are the disadvantages of other types of types of non-Vibristor<![if !msEquation]><![if !vml]><![endif]><![endif]> WEC’s both used singly and in arrays?
<![if !supportLists]>1) <![endif]>Huge capital costs.
<![if !supportLists]>2) <![endif]>Environmentally unfriendly – problems with navigation, fishing, lubricant spills, high visibility.
<![if !supportLists]>3) <![endif]>Large non-Vibristor® units must be spaced far apart allowing large amounts of the wavefront and its energy to pass through without any energy capture.
<![if !supportLists]>4) <![endif]>Difficult to attach securely to the sea bottom especially with severe storms.
<![if !supportLists]>5) <![endif]>Often not omnidirectional in response and needs a steering mechanism.
<![if !supportLists]>6) <![endif]>Mechanically complicated, requiring numerous parts, linear to rotary mechanical power trains, with bearings, gears, hydraulics, or other mechanical structures.
<![if !supportLists]>7) <![endif]>Many moving parts.
<![if !supportLists]>8) <![endif]>Difficult to service and replacement is almost impossible; one defective part will render a large unit inoperative.
<![if !supportLists]>9) <![endif]>Expensive to transport for deployment.
10) Increased difficulty handling simultaneous wave trains propagating in different directions.
11) Have to be custom made and does not lend itself to mass production.
12) Terribly inefficient at wave lengths other than for which it was designed.
13) More likely to become unstable in a storm with very large waves.
Q37: How is the potential electrical power (energy delivered per unit of time) dependent on the height, period of the wave and the force exerted by the wave on the WEC and how does that translate into the force exerted on the rotor and the resultant velocity of the rotor and thus the amount of kinetic energy of the wave harvested into the rotor?
<![if !supportLists]>1) <![endif]>The potential electric power, the wave energy flux per unit of wavefront length, is proportional to the square of the wave height (or significant wave height for a random sea spectrum) and the period of the wave.
<![if !supportLists]>2) <![endif]>The motion amplitude of the rotor and the kinetic energy developed into the rotor is dependent on the mechanical damping factor of the mass spring system of the Vibristor® and the frequency of the ocean wave relative to the natural resonant frequency of the WEC.
<![if !supportLists]>3) <![endif]>The motion of amplitude of the rotor and the kinetic energy harvested by the buoy rotor component is dependent on the amplitude (height) of the wave which is determined by the magnitude of the original stimulus that produced the wave, and the force of that given wave amplitude (height) upon the Vibristor® which is in turn dependent upon the cross sectional area of the buoy collar, the depth of submersion of the collar, and the wavelength of the impinging wave.
<![if !supportLists]>4) <![endif]>In a random sea wave spectrum, it is the significant height and wave amplitude that is used defined as the average height (or amplitude = one half the height) of the highest one third waves transversing the point of observation within a given time period of observation.
Q38: What is the response of vertical linear electric generator (LEG) in a wave energy converter (WEC) that operates with linear heaving motions to a sine wave of resonant frequency? Non-resonant frequency? Semi-sinusoidal frequency? Impulse or square wave input, Standing Wave Input? Multiple simultaneously arriving wave trains from different directions?
<![if !supportLists]>1) <![endif]>Resonant frequency: Maximal vertical response of the rotor to the oncoming ocean wave.
<![if !supportLists]>2) <![endif]>Non-resonant frequency: A decreasing of the maximal vertical response amplitude of the rotor as the wave frequency increases past the Vibristor® natural frequency dropping down toward zero (the right of the rotor amplitude vs. frequency curve) and a decreasing of the maximal vertical response of the rotor dropping down toward the amplitude of the ocean wave (the left of the rotor amplitude vs. frequency curve) as the wave frequency decreases from the resonant frequency of the WEC.
<![if !supportLists]>3) <![endif]>The explanation in the next question, Q39, gives a more detailed explanation of the above.
<![if !supportLists]>4) <![endif]>Semi- Sinusoidal frequency: The WEC will respond predominantly to the frequency as in # 1 and #2 above that forms the predominant harmonic of the non-sinusoidal wave.
<![if !supportLists]>5) <![endif]>Impulse or Square Wave frequency: Similar to that of a Semi-Sinusoidal response, only the higher frequencies will be quickly damped out by the WEC with no response to these higher harmonics.
<![if !supportLists]>6) <![endif]>Standing Wave: There will be no vertical response to the standing wave as for any given point in space, the vertical displacement of the water level remains constant and hence the rotor will not move. However, there will be harmful drastic pitch motions if the wave length of the wave approximates the diameter of the collar unless the WEC is sitting relatively motionless at an anti-node trough in the standing wave pattern.
<![if !supportLists]>7) <![endif]>Simultaneous wave trains coming from different directions: The resulting wave form hitting an omnidirectional WEC like the Vibristor® will exhibit chaotic vertical movement that will virtually never be in resonance with the natural vibrational frequency of the WEC (and if it is, would the resonance effect would only be transitory). Any summation or difference frequency formed by the superimposition of multiple wave fronts will be damped out if greater than the natural frequency of the Vibristor® and the WEC will act as a wave rider in chaotic fashion if these frequencies are less than the WEC’s natural frequency of resonance.
Q39: What happens with the vertical oscillation distance versus natural resonant frequency / wave frequency ratio graph and why does a wave wider allow operation both at the resonant peak and either side of the graph; Why does power output of the WEC will drop to very low levels if it operates at extremely low wave frequencies (i.e. a tidal wave) – the extreme left of the curve and extremely high wave frequencies – the extreme right of the curve.
<![if !supportLists]>1.) <![endif]>At the wave frequency that matches the natural resonant frequency of the Vibristor®, the magnitude of the motion of the buoy collar attached to the rotor will exceed the magnitude of the height of the wave by a fraction depending on the damping factor of the system. Power output is therefore a maximum at the resonant frequency of the WEC, equal to the frequency of the predominant wave impinging on the WEC. At that point the vertical movement of the collar of the WEC is in phase with the vertical movement of the ocean wave maximizing the captured harvested energy of the vertically moving rotor.
<![if !supportLists]>2.) <![endif]>At high wave frequencies, the resonant frequency of the Vibristor® will be much less than the wave frequency and the WEC could not keep up with the rapid vertical oscillation of the water from the waves propagating past, and thus the collar will tend not to move nearly as much as the wave amplitude or not at all. The movement of the buoy collar will become more and more out of phase with the vertical displacement of the wave as the wave frequency goes up. Furthermore, the diameter of the collar may be several times the wavelength of the small wave and the large number of troughs and large number of wave crests will tend to cancel each other out producing no net vertical motion. This effect becomes more pronounced as the wave frequency goes up and eventually the rotor stays stationary and no power is produced. This limits to some extent the effect of increasing the cross-sectional area of the buoy floatation collar in order for the natural frequency of the WEC to try to approach resonance with higher frequency ocean waves.
<![if !supportLists]>3.) <![endif]>3) At ocean wave frequencies lower than the natural resonant frequency of the Vibristor® the buoy collar and rotor will follow exactly the vertical water displacement of the wave because of its very low mass. (If the mass was very high, not only would the stator also move in compensation as per Newton’s third law, but also, the movement of the rotor might even lag the motion of the wave unless the wavelength of the wave was very low.) Thus as the frequency continues to drop, the rotor buoy collar will continue to follow the wavefront water displacement in phase with it. However, at very low frequencies, while the rotor will displace at the same amount as the vertical displacement of the impinging wave front, power will go down because the vertical motion velocity of both the rotor and the wave will go down leading to less magnetic lines of force being cut by the stator coils per unit of time causing the amount of power produced to go down. In fact with really large waves of low amplitude and huge wave length, i.e. a tsunami, there is no power produced at all because the rotor hardly moves much like a ship does not feel a tsunami when it is out in the middle of the ocean. Again, the developed kinetic energy of the rotor which represents kinetic energy harvested from the wave is proportional to the square of the ocean wave frequency (the velocity of the rotor is the time derivative of the displacement of the rotor with the ocean wave vertical distance displacement, and thus proportional to the frequency of the ocean wave, and hence, since the kinetic energy developed in the rotor is proportional to its velocity squared (as well as its mass), the amount of energy harvested in the rotor is proportional to the wave frequency squared). Note that with a tsunami the ocean wave frequency is very close to zero, hence, there is virtually no power developed in the rotor. (See also Question 9).
<![if !supportLists]>4.) <![endif]>Also, with wavelengths longer than the diameter of the buoy collar, the loss of vertical displacement linear energy due to pitch effects is less because of the lower slope of the water level for a wave of given amplitude.
Q40: How does a PMA using compressive repulsive magnetic field technology (CRMFT) work?
<![if !supportLists]>1. <![endif]>PMA’s using CRMFT take magnetic fields from adjacent like repulsive magnetic fields and under great pressure cause them to be compressed together such that when a stack of alternating pairs of repulsive magnetic poles are placed one upon another to produce the magnet stack, a very intense magnetic field radiates out the sides of the stack perpendicular to the long axis of the stack. If the stack is cylindrical in cross sectional area, the flux lines radiate outward in a uniform density around the cylinder. Along the axis of the stack of magnets, areas of N pole regions alternating with S pole regions with these pole regions extending around the entire perimeter of the stack.
<![if !supportLists]>2. <![endif]>If one goes from one end of the PMA to the other along the curved outer cylindrical surface, one will encounter repulsive alternating N and P magnetic regions with the fields radiating outward perpendicularly along the entire long axis of the PMA. This arrangement of magnetic fields is what allows the FCA coil windings to be placed along the entire length of the PMA.
<![if !supportLists]>3. <![endif]>The compression of the magnetic fields into a confined area formed by the space occupied by the low carbon steel pole pieces between the magnets is what allows for the intensification of the magnetic fields seen in this configuration.
Q41: How is the structure of the CRMFT PMA comprised?
<![if !supportLists]>1. <![endif]>The basic structure of the CRMFT PMA is the structural magnetic unit (SMU). It consists of two magnets, usually rare earth magnets because of their strong magnetization and field formation, oriented together in such a manner that two of their poles are in repulsive mode that is NSSN or SNNS. In between each magnet is a pole piece of low carbon 1018 steel (or similar steel) that contains the repulsive magnetic field that is compressed and confined to them. Also at one of the ends of this SMU structure is another pole piece making 2 pole pieces per SMU. If the SMU is the end SMU, it will have pole pieces at both ends of the structure as well as in the middle or 3 in total.
<![if !supportLists]>2. <![endif]>The magnets have to be forced together under great force and this is done by attaching a magnet when it is being installed at the growing end of the PMA to a pole piece that is threaded in its central hole and then the complex of the magnet and pole piece is threaded slowly onto the growing end of the PMA. Once about to be placed in its proper position, a special type of magnetic epoxy that is extremely strong is placed between the magnet and the pole piece below it and the structure is bonded together. Hex nuts at the ends of the PMA can be attached to the threaded rod to make the connection even sturdier. As result there is a tremendous amount of magnetic energy stored in a PMA and it would fly apart explosively if it were not held together in this type of packaging.
<![if !supportLists]>3. <![endif]>The PMA consists of an even number of SMU’s to insure that the polarity of both ends of the PMA is the same. This is done to make sure that no lines of force emanating from one end of the PMA would loop around in air to get to the other end thereby avoiding the coil windings. The number of SMU’s that can be attached together is theoretically unlimited as is the length of the PMA subject only by the structural stability of a very long PMA structure.
<![if !supportLists]>4. <![endif]>The strong large magnets of the PMA are known as the power producing magnets.
<![if !supportLists]>5. <![endif]>At each end of the PMA, to cut magnetic flux leakage being wasted by radiation into space without intersection with coil windings, lie the smaller end-deflecting magnets that are facing both the outer pole of the end power producing magnet and the pole of the end-braking magnet that lies at the end of the rotor slide tube. The N pole of the end-braking magnet would be facing the N pole piece of the last power producing magnet and the S pole of the end-braking magnet would be facing the S pole of the end braking magnet and likewise, the same would be occurring for the lower other end of the PMA structure. Note here an N pole can be exchanged for a S pole and an S pole can be exchanged with an N pole.
<![if !supportLists]>6. <![endif]>Note that the PMA can be used without the end-deflecting magnets if a need to do this actually arose.
Q42: How does a CRMFT PMA differ from a conventional stack of magnets placed N pole to S pole to N pole etc.
<![if !supportLists]>1. <![endif]>In conventional magnet stacks of north poles of one magnet being stacked above the attracting opposite pole of the magnet below it, the field lines do travel out the N pole of one end of the stack, circle around in space, and re-enter the stack through the S pole end, and then travel through the stack’s interior to complete the magnetic loop when it enters the N pole end from the interior of the stack.
<![if !supportLists]>2. <![endif]>In the CRMFT PMA the field lines form localized loops within the magnet stack such that a magnetic field flux line leaves a N pole and arcs to the two nearest S poles completing the magnetic line loop within either of the two adjacent magnets. No flux lines go through all the magnets from one end to the other.
<![if !supportLists]>3. <![endif]>In the conventional magnet stack, one end is a N pole; the other end is a S pole. In the CRMFT PMA both ends of the stack are of the same polarity, either both N poles or both S poles.
<![if !supportLists]>4. <![endif]>In the conventional magnet stack, many of the flux lines emanating out of and into the stack go into and come out of the surrounding space parallel to the long axis of the stack. These flux lines parallel to the long axis never would intersect coil windings, while in the CRMFT PMA, there are hardly any magnetic lines parallel to the long axis, whatever lines to exit out of an end must curve back and intercept a pole of opposite polarity within the stack, and thus virtually all the lines of force intersect coil windings to produce current.
<![if !supportLists]>5. <![endif]>Since in a conventional magnet stack, the lines radiate out and into only the ends of the stack, that is where the coils must be located and the coils have to be large, bulky, and long on the stacks long dimension to capture as many coil flux linkages as possible including many almost parallel to the long axis flux lines. Even so, many flux lines that are completely parallel to the long axis escape into space.
<![if !supportLists]>6. <![endif]>In the CRMFT PMA, since the flux lines emanate to and from the stack along the circular side of the stack, coils that are smaller in dimension and cost can line the entire length of the stack and produce electricity with very little leakage into space of the magnetic field.
<![if !supportLists]>7. <![endif]>In the conventional magnet stack, there is no magnetic field compression that increases flux density interacting with the coils whereas in the CRMFT PMA, there is repulsive magnetic fields that are compressed together to greatly increase the intensity of the magnetic field in the vicinity of the coil windings.
<![if !supportLists]>8. <![endif]>Conventional magnet stacks cannot be made arbitrarily long by adding an unlimited number of magnets. While initially, two conventionally stacked NSNS magnets together will have twice the magnetic field strength and holding power as each of the individual magnets, and three magnets will have three times as much, there is a point of diminishing returns where adding on additional magnets will not increase the strength of the magnet stack end pole magnetic fields any further. The reason: magnetic flux lines travel in closed loops. The longer the stack, the longer the closed loop. The resistance of a material to the flow of lines of flux is known as the reluctance and the lower the permeability of the material to a magnetic field, the higher the reluctance or resistance to magnetic flux flow (analogous to resistance in an electrical circuit). While the portion of the loop in the magnet stack is relatively not affected by the length of the magnet stack because of the magnet’s internal low reluctance, the half of the loop path outside the magnet stack is in air that has a very high reluctance and resistance to the flow of magnetic field lines. This limits the buildup of the magnetic field emanating out of the end poles to a maximum and adding additional magnets creates a point of diminishing returns.
<![if !supportLists]>9. <![endif]>CRMFT PMA structures possess totally different magnetic flux flow patterns. Such a PMA consists of an pairs of magnets oriented so that their like polarities are adjacent to each other and their end poles have magnetic fields that are reach repulsive with respect to the adjacent magnet poles in those locations. The result is that the flux flow loops always flow out of one N pole repulsive region between the two magnets into the S pole of each of these two magnets and in no case is the magnetic flux required to follow a path longer than somewhat greater than twice the thickness of each magnet and this holds true no matter how many magnets are in the stack and how long the PMA is. Thus, PMA’s can be constructed that are many meters long subject only to the structural strength and stability of the PMA itself.
Q43: Why is the preferred cross-sectional geometry of the PMA is circular?
<![if !supportLists]>1. <![endif]>For a given sized amount of magnetic material in a circular disk magnet, a disk of thickness t and radius r with a cross sectional area of πr2 and curved side area of πr2h: the curved side area of the disk produces the highest flux density along its sides compared for instance a magnet with a square cross section but equal amount of magnetic material.
<![if !supportLists]>2. <![endif]>Circular windings surrounding a cylindrical magnet stack provides for the shortest coil windings thus conserving copper and is thus cheaper.
<![if !supportLists]>3. <![endif]>The magnets themselves are cheaper because they are easier to fabricate.
<![if !supportLists]>4. <![endif]>The inner coil windings can be closer to the magnet if circular windings are wound around circular magnets.
<![if !supportLists]>5. <![endif]>The produced magnetic fields are more uniform with no discontinuities or hot spots or cold spots (isolated spots) of severely decreased or increased magnetic fields.
Q44: How is the CRMFT PMA stabilized?
<![if !supportLists]>1) <![endif]> A patented method of attaching and stabilizing a configuration of magnets with repulsive magnetic fields is used.
Q45: What functions does the pole pieces serve in the PMA?
<![if !supportLists]>1. <![endif]>Allows a space for the repelling magnetic field of high intensity to reside instead of the field lines being pushed back into the interior of the two repelling magnets which could eventually demagnetize the magnets.
<![if !supportLists]>2. <![endif]>Low carbon steel has a very high saturation point of 20,000 Gauss (2 Tesla) which is 4 times the saturation of air and higher than iron pole pieces (1.2 T). Thus the magnetic fields can be compressed to a higher level resulting in greater field intensities.
<![if !supportLists]>3. <![endif]>With low carbon pole pieces whose thickness is as thin as one eighth the thickness of the magnet, maximum field intensities coming out of the magnet pole surfaces can be increased from 0.5 T to 1.0T achieved in the lab so far, and can easily be increased to 2.0T, the limit of magnetic field saturation in the pole pieces.
<![if !supportLists]>4. <![endif]>The pole pieces act as magnetic flux lenses that focus the magnetic flux onto the coils surrounding the PMA (The coils of the FCA) without the need for heavy ferromagnetic focusing structures.
Q46: What are the end-deflecting magnets and what is their function?
<![if !supportLists]>1. <![endif]>They are magnets that are smaller in size as compared to the power producing magnets of the PMA and are located at each end of the PMA and attached to the PMA power magnet stack with a pole piece.
<![if !supportLists]>2. <![endif]>Their primary purpose is to decrease magnetic flux leakage out into space and instead reflect these lines of force back into the interior of the PMA.
<![if !supportLists]>3. <![endif]>The amount of flux leakage into space which wastes magnetic field lines that can be used to produce electricity is much less with the CRMFT PMA then with a conventional magnet stack of alternating magnetic poles. However, even so there still is a sizeable amount of leakage.
<![if !supportLists]>4. <![endif]>If the N pole end of the PMA has added onto it an additional pole piece and a smaller magnet in a repulsive pole configuration such that the N pole of this end-deflecting magnet faces the N pole end of the PMA, almost all of the flux lines leaving the end N pole of the PMA will be deflected back onto the interior of the PMA.
<![if !supportLists]>5. <![endif]>Since magnetic flux must travel in closed loops, and since these loops can only flow in two adjacent magnets forming a pair that we call one structural magnetic unit, the vast majority of the flux lines deflected from the N pole of the end-deflecting magnet will be bent back and go into the S pole closest to it that is on the other side of the end power magnet of the PMA.
<![if !supportLists]>6. <![endif]>In doing this deflection, almost all of the flux lines will curve back onto the PMA and cut across the coil windings creating additional electrical power that would have otherwise been wasted from magnetic leakage into space.
<![if !supportLists]>7. <![endif]>In small Vibristor® units without springs in the end-braking unit, the S pole of the end-deflecting magnet would also be repulsed by the S pole of the end-braking magnet, and thus the end-deflecting magnet would serve the dual purpose of decreasing flux leakage and helping to brake the PMA in the event of a large wave.
<![if !supportLists]>8. <![endif]>The end deflecting magnets may be omitted if the magnets in the PMA are large and strong enough and the PMA stroke distance is relatively short so that a repulsive force of the ends of the PMA can be produced against the end braking magnets as the PMA approaches the latter with a large wave while it is still a considerable distance away; this repulsive force would exert the equivalent of the focusing effect of the end deflection magnets as the PMA approached the end braking magnet. However, for smaller magnet PMA’s that are travelling over long stroke distances, the end deflecting magnets are essential.
Q47: What is the structure of the Field Coil Array (FCA), the power producing armature of the LEG?
<![if !supportLists]>1. <![endif]>The FCA ideally should consist of coils that surround the entire length of the rotor slide tube though in smaller less powerful versions, a smaller number of coils can be used.
<![if !supportLists]>2. <![endif]>There is a defined multiple of the number of coils used for each Structural Magnetic Unit (SMU) of the PMA (consisting of two magnets and their associated pole pieces).
<![if !supportLists]>3. <![endif]>A minimum of 4 coils per SMU.
<![if !supportLists]>4. <![endif]>A larger number of coils may be used for very thick magnets.
<![if !supportLists]>5. <![endif]>The number of coils per SMU is intimately related to the most optimal power production for a given number of coils and magnets, the efficiency of the power conversion process improves because a smaller percentage of the windings will be contained in coils that are over regions of net zero magnetic flux, or regions in which adjacent N and S poles are contributing to equal opposing amounts of flux intersecting the coil with no resultant power generation.
Q48: Why is the width of the air gap between the inner coil windings and the outer surface of the PMA much less critical than in other generator configurations?
<![if !supportLists]>1. <![endif]>The only component of the magnetic field that produces power in the coils are those flux lines that are oriented perpendicular to the direction of movement of the PMA (or the long axis of the PMA cylinder).
<![if !supportLists]>2. <![endif]>Eventually, these perpendicular field lines (also called radial, or orthogonal) begin to curve around to approach adjacent magnetic poles, and field lines traveling in this direction are parallel to the direction of motion of the PMA (and its long axis). They produce no power in the coils because of their direction of orientation.
<![if !supportLists]>3. <![endif]>In order for a field line to produce a voltage in a conductor, 3 quantities known as vectors because direction is important are required to point in directions perpendicular to each other. These 3 quantities are the direction of orientation of the magnetic field line (which for power production must radiate perpendicularly out of the side cylindrical surface of the PMA), the direction of movement of the PMA (which is always parallel to the long axis of the PMA), and the orientation of the coil winding (the cross section of the coil winding is perpendicular to the direction of motion of the PMA).
<![if !supportLists]>4. <![endif]>Normally, in the conventional configuration of NSNS magnet stacking, lines that exit out from a magnet perpendicular to the magnet’s surface curve immediately around to the adjacent pole to complete the magnetic loop circuit so that a surrounding coil must be extremely close to the moving magnet’s surface to produce what is known as a coil magnet air gap or simply air gap to be as small as possible to allow for reasonably efficient power conversion. This requires expensive precise machine tolerances in assembly.
<![if !supportLists]>5. <![endif]>The CRMFT avoids the need for critically small air gaps because of the compression of the magnetic fields between repelling poles. This compression accomplished with great force causes the magnetic field lines to exit from the PMA perpendicular to its surface it remains in that radial direction perpendicular to the direction of motion of the PMA for some distance out. Thus, the air gap can be considerably wider than with conventional magnet configurations with no loss of power generating efficiency.
<![if !supportLists]>6. <![endif]>This tolerance to air gap width occurs because it can be shown that the number of perpendicular radial field lines that intersect a coil winding remains constant at any given cross-section of the PMA and surrounding coil winding provided that the field lines have not yet appreciably began curving around in a direction tangential to the long axis of the coil and coil movement direction as they flow toward an adjacent magnetic coil. If the number of radial magnetic flux lines intersecting a winding remains constant, the induced voltage will remain constant for a constant velocity of the PMA rotor independent of the width of the air gap as long as the width is a very small percentage of the radius of the PMA magnets.
<![if !supportLists]>7. <![endif]>Of course, even with the compression of the magnetic fields and the further focusing of the magnetic field lines into the radial direction by the pole pieces in between the magnets, the magnetic field lines have to eventually start curving around to adjacent magnetic poles so that the coil windings cannot be too far away from the PMA or else power conversion will fall off sharply as the number of field lines remaining in the radial power producing direction will drop off sharply at significant distance from the PMA.
<![if !supportLists]>8. <![endif]>The larger the diameter of the magnets in the PMA, the larger the air gap can be with no loss of power conversion efficiency. A finite element computer simulation is being worked out to analytically define the air gap’s optimal parameters.
Q50: Are there any limitations on the length of the PMA?
<![if !supportLists]>1. <![endif]>For reasons to be explained below, there is no limit other than the structural stability of the means to support a very long PMA in a WEC device.
<![if !supportLists]>2. <![endif]>A PMA can be theoretically hundreds of meters long, especially if the largest commercial magnets are used, maximizing the diameter of the magnets for structural support for a very long PMA and maximizing the diameter of the central threaded rod of the PMA without producing a loss in power producing efficiency.
<![if !supportLists]>3. <![endif]>In conventional NSNS magnet stack configuration, once one gets beyond 10 magnets stacked, there is no useable increase in the total amount of magnetic flux lines generated by the stack and thus long magnet stacks of this type are not feasible. With the Compressive Repulsive Magnetic Field Technology (CRMFT) this problem is entirely eliminated and the total amount of magnet flux lines available for power conversion is linearly proportional to the number of magnets used for magnets of a given shape, size, and magnetization, and this total magnetic flux is distributed along the sides of the PMA.
Q51: What are the advantages of compressive repulsive magnetic fields in the LEG?
<![if !supportLists]>1. <![endif]>Eliminates huge long coils at the end of the Permanent Magnet Array Cylinder (PMA) thereby using less expensive amounts of copper.
<![if !supportLists]>2. <![endif]>Even without the end blocking focusing magnets, there is significant reduction in end leakage of magnetic flux lines out the ends of the PMA from flux lines whose direction are parallel or nearly parallel to the long axis of the PMA cylinder simply because there are vastly less flux lines in a magnetic circuit comprising a magnetic circuit through the entire length of the PMA.
<![if !supportLists]>3. <![endif]>The use of powerful magnets may cause dangerous magnetic fields at the ends of the PMA which might be a problem for handling the Linear Electric Generator (LEG) when not in use or installed in a device. This is helped by the end blocking magnets whose fields are much smaller.
<![if !supportLists]>4. <![endif]>The use of two much smaller end focusing blocking magnets at each end of the PMA acts an excellent magnetic shielding because these two magnets are also used in the Compressive Repulsive Magnetic Field Technology (CRMFT) configuration and thus virtually all lines of force are bent backward back onto the PMA to an interior opposing pole virtually reducing magnetic flux leakage to almost nothing. Note that the flux leakage of the end focusing blocking magnets which are much smaller and are not used for power production is of no consequence and is very small in amount.
<![if !supportLists]>5. <![endif]>Further decreasing the amount of magnetic leakage into space is the fact that the end polarities of the CRMFT PMA are the same. Hence, any leakage of a flux line out one end can never return to the other end of the PMA and thus to complete the magnetic circuit which is a must, it must return to an interior pole of opposite polarity, and it would be more probable to a nearer interior pole, and thus it must cut across a coil winding. Note that the effects of #4 and #5 does make for some variation in the maximum field strength in the various compressive repulsive field regions along the axis of the PMA cylinder.
<![if !supportLists]>6. <![endif]>A high intensity and relatively uniform magnetic field is produced in a direction perpendicular to the long axis of the PMA cylinder other than for small node regions located at the direct center of an individual magnet’s side.
<![if !supportLists]>7. <![endif]>The compression of the magnetic fields in regions of like adjacent poles produces a significant increase in the flux density that cuts across the coil windings in a favorable perpendicular or near perpendicular direction to the axis of the coils.
<![if !supportLists]>8. <![endif]>Although the sum total of the flux produced by the standard (NSNS) configuration is equal the sum total of the flux of an equal number of equally sized magnets in the CRMFT configuration, nearly 100% of all the flux lines in the latter come out of the circular surface of the PMA cylinder in a direction perpendicular or nearly perpendicular to the long axis of the surrounding coils, a condition necessary for optimal maximum power output whereas in the former standard configuration, a significant number of lines of flux come out in a direction parallel or nearly parallel to the long axis of both the field coil array and the PMA cylinder which is not suitable for coil winding flux linkages and electrical power production.
<![if !supportLists]>9. <![endif]>There are no long regions relatively void of magnetic flux along the side of the PMA cylinder with the CRMFT whereas there are with the standard configuration, and whatever the small amount of flux is present, their direction is parallel to the long axis of the coil array and PMA cylinder, and only lie adjacent to the cylinder surface – thus they are useless for electrical power generation.
<![if !supportLists]>10. <![endif]>There is no significant eddy or hysteresis energy losses anywhere in the magnetic assembly as there are no large ferromagnetic flux focusing structures present that move relatively to the linear motion of the magnets.
<![if !supportLists]>11. <![endif]>The magnetic field focusing is done by the magnets and the pole pieces themselves with no heavy ferromagnetic structures to do this.
<![if !supportLists]>12. <![endif]>There are no Lenz Law back EMF forces produced in the pole pieces because they do not move relative to the motion of the magnetic field.
<![if !supportLists]>13. <![endif]>There are no back EMF forces generated from the magnet motion other than in the coils themselves as there are no bulky ferromagnetic structures surrounding the coils in an attempt to focus and concentrate the flux around the coils as in conventional generators.
<![if !supportLists]>14. <![endif]>In the conventional configuration, as you stack the number of magnets to a larger and larger number, the incremental field strength at the ends of the magnets becomes smaller and smaller until after about configuring a PMA of about 10 magnets, there is virtually no further gain to increase the PMA length with more magnets. In the CRMFT configuration, the number of lines of force leaving the side of the PMA cylinder is more or less constant except for small node areas at the midpoint of an individual magnet’s thickness, and the average amount of flux per unit length along the entire cylindrical surface remains fairly constant no matter how many magnets are added making for PMA lengths that can be meters long. This is very advantageous to wave energy converters (WEC) employing LEG’s where large wave energies can be absorbed and converted with long PMA cylinders. The technical reason for this is that in the standard configuration, as the length of the PMA long axis increases, magnetic circuit consisting of the path of the flux through the interior of the PMA and the return path through air (which is of low magnetic flux permeability or permanence) becomes longer and longer between the two end poles increasing the reluctance of a good portion of the magnetic circuit there thereby reducing the flux density and total flux going from the end N pole to the end S pole. Contrast that with the CRMFT array in which repulsive pole regions of the PMA cylinder prevent any flux lines from traveling through the interior of the PMA. Instead, the magnetic circuits are all local coming out of one N pole repulsive region and quickly back into the adjacent S pole repulsive region and so forth. Thus no matter how many extra magnets are added and how long the LEG is, the return air path of the flux will always be both shorter, relatively the same or almost the same length and the length of the PMA or number of magnets used will have no significant effect on the flux output average per magnet and will have no decreasing effect on the benefit of adding additional magnets to the PMA length. Another way of putting it, the Permanence Coefficient goes down as the standard PMA grows in length and number of magnets, and stays constant in the CRMFT PMA no matter how long it is and how many magnets are added.
<![if !supportLists]>15. <![endif]>The CRMFT array is very scalable both in terms of going from using very small rare earth magnets to extremely large magnets and the number of magnets may be at a minimum one pair to a maximum of many hundreds of magnets with no theoretical maximum, only limits subject to safe handling, assembly, wave size, and structural stability of the LEG itself (not the PMA itself which can be made quite stable even with huge diameter and length scaling). Thus the CRMFT array can be used from miniature structures for tiny environmental vibrational energy harvester generators to moderate structures such as buoys to grid scale power generating WEC’s.
<![if !supportLists]>16. <![endif]>If the PMA is in a neutral position relative to the coils (i.e. a wave node), a small wave that moves the PMA a short distance in the conventional configuration will produce no power as the vertical oscillation of the magnets will be completely within the “dead zone” interior region of low magnetic flux density that occurs along most of its length at all points except at the ends. In contrast, with the CRMFT array, the smallest ocean wave vibrational disturbance will produce electrical power.
<![if !supportLists]>17. <![endif]>The use of pole pieces and the compression of magnetic fields together from repelling adjacent magnetic poles significantly increases the measured magnetic field intensity (B) that occurs If the along the long axis of the PMA as the lines of force exit perpendicularly from the cylindrical surface. In the lab this was measured to be on the order of 80 to 90% (5500 Gauss (G) or 0.55 Tesla (T) to 9700 G or 0.97 T) with magnets and pole pieces of thickness 2 to 1 respectively. If this effect is maximized using optimally predicted effective ratios of magnet thickness to pole piece thickness depending upon the application, the B magnetic field intensities can be increased for the magnets we used in the research PMA’s (2” in diameter 1” thick NdBrFe rare magnets and 2” in diameter 0.5” thick 1018 steel pole pieces) from about 5500 G (0.55 T) to about 18000 to 20,000 Gauss (1.8 to 2.0 T), an up to 400% gain, with the limit being set only by the magnetic saturation permeability of the steel pole pieces.
<![if !supportLists]>18. <![endif]>The pole pieces at as magnetic lenses that direct the flux back onto the coil windings working in concert with the other design factors that do this.
<![if !supportLists]>19. <![endif]>Normally, the severe repulsion of the repelling like polarity magnetic fields (which are stabilized by a patent pending structural assembly array and assembly process) would repel the magnetic flux back into the interior of the magnets located at the repulsive magnetic field regions. This effect is extremely delirious and should not be allowed to happen as it would happen if there were no pole pieces used at all. If this situation in fact does occur, the magnets will be slowly but progressively demagnetized with time as the repulsive magnetic force will act as a coercive magnetic force operating in a direction opposite to the original force of magnetization of the magnets. This effect is neutralized by using pole pieces which because of their much greater permeability pulls the flux lines into them and away from the magnet interior pole regions. Until the pole pieces are saturated, they can prevent this effect from happening. Thus again, the optimal design of the CRMFT PMA is such that the ratio of the magnet thickness to the pole piece thickness results in the pole pieces being saturated. If one goes beyond that, even with the pole pieces, the magnetic repulsive field between adjacent magnets will not be able to be confined to the pole pieces and the magnets could be eventually demagnetized. One can either limit the size of the magnet thickness or increase the thickness of the steel pole pieces to keep the pole pieces in magnetic saturation. Note that low carbon steel rather than iron or other types of steel are used because of its superior high permeability and saturation characteristics.
<![if !supportLists]>20. <![endif]>Because the magnets travel through the surrounding coils rather than adjacent to them as in some other WEC’s powered by LEG’s we have another factor that causes virtually all of the flux lines generated by the PMA to intersect the coil windings and produce power.
<![if !supportLists]>21. <![endif]>The PMA’s themselves are scalable in arrays to produce 3 dimensional “crystalline like” matrices because of the unique geometrical and pole configuration. This structure has been patented.
<![if !supportLists]>22. <![endif]>So far, we have been discussing the CRMFT in terms of wave energy converting LEG’s. All generators can be used as linear motors and the characteristics of this magnetic array need yet to be explored for use in rail guns, linear servo mechanisms and actuators etc.
<![if !supportLists]>23. <![endif]>The CRMFT PMA has so far been discussed as being used as the rotor in an LEG with the Field Coil Array (FCA) being used as the stator. The PMA and the FCA can be interchanged to the stator and the rotor respectively with no change in function.
<![if !supportLists]>24. <![endif]>Because one can use long CRMFT PMA’s in wave energy conversion as well as any other vibrational energy harvestable source of energy, as the size of the PMA increases relative to the height of the wave, the efficiency of the energy conversion will increase toward a theoretical 100% subject to all of the other physical constraints that would put a limit on the conversion efficiency but it is clear that very high efficiencies can result.
<![if !supportLists]>25. <![endif]>The shape of the CRMFT PMA is conducive to its use in long strips or geometrical arrays to disperse wave energy for the protection of coastal beaches and structures with electrical energy as a useful byproduct. A patent has been granted for these structures.
<![if !supportLists]>26. <![endif]>When compared to the Halbach magnetic array in which the total flux of magnetic field as on the top of the array is twice the flux that would be on either side of a NSNS standard conventional permanent magnet array with very little flux on the bottom side of the array (assuming rectangular magnets), the CRMFT is superior because all of the flux is compressed into a perpendicular or near perpendicular direction of the motion of the magnets and the long axis of the coils, and this compression causes flux densities in the region of the coils to be much higher than would be seen in the Halbach array (estimated at least to be 400% with magnets capable of being used in the lab, twice that of the Halbach array). Note that many of the flux lines in the Halbach array flow parallel to the long axis of the PMA and the coils and thus many of the flux linkages are in effective for producing power. For that reason, the Halbach array is not used for electrical power production.
<![if !supportLists]>27. <![endif]>In the conventional magnet stacking of alternate poles, the air gap between the innermost coils and the outer surface of the PMA is critical – the larger the gap, the greater the diminution of the magnetic field intensity crossing the inner coil windings and the less the power output. Furthermore, the further the radial distance from the PMA outer curved surface, the greater the component of the magnetic field parallel to the long axis of the PMA (which produces less power as there are less flux winding linkages created) and this problem because more critical very quickly with the coil thickness (outside diameter minus the inside diameter) as it is the radial component of the magnetic field perpendicular to the long axis of the PMA that cuts across the full thickness of the coil that creates the maximum number of coil flux linkages that produces the maximum power output. Because the magnetic fields are compressed and then focused by the magnetic pole pieces to such an extent that virtually all of the magnetic field lines emanating from the curved cylindrical surface of the PMA are in the radial direction perpendicular to the PMA long axis, and because the very great proportion of the field stays radial and perpendicular to that axis, the size of the air gap is no longer that critical as the number of flux linkages for a surrounding coil remains the same no matter what the size of the air gap (that is a reasonably sized air gap from a fraction of a mm. to several mm, depending upon the diameter of the magnet and the degree of magnetization of the magnet). Hence the PMA rotor stator sliding mechanism and interaction can be built more economically to a less critical precision and dimensional tolerance.
<![if !supportLists]>28. <![endif]>Because in the CRMFT configuration, the compression of the magnetic fields cause virtually the entire magnetic field as it leaves the cylindrical surface of the PMA to be perpendicular to the long axis of the PMA, and it to stay perpendicular to the long axis for quite some radial distance out. As a result, the field lines begin to diverge toward the direction parallel to the long axis quite a distance away and they immediately begin to point again back to the perpendicular direction as the field lines travel the short magnetic loop quickly to the adjacent magnetic poles instead of pursuing wide air spaced magnetic loops as per the conventional configuration. As a further result, even if the coil thickness is considerable, the direction of the magnetic field lines throughout the coil thickness is perpendicular to the long axis of the FCA (which is parallel to the long axis of the PMA) which produces the maximum flux winding linkages and power production. The thickness of the coils used with the conventional configuration has to be sharply limited, a limitation that does not occur with the CRMFT configuration.
<![if !supportLists]>29. <![endif]>The cylindrical cross-section, though not required, in most cases is used as the optimal configuration of the CRMFT PMA as it results in totally uniform and symmetric radial feels emanating out of the entire cylindrical surface of the cylinder.
<![if !supportLists]>30. <![endif]>If two identical magnets are placed in the conventional NS attachment configuration, the total space occupied by the flux lines will be significantly greater than the same two magnets forced together in the CRMFT mode. The total amount of magnetic flux will be equal in either case, but in the CRMFT configuration, that flux will occupy a smaller volume, and hence, the average magnetic field intensity in the region near the magnets where power producing coils would be located will be greater.
<![if !supportLists]>31. <![endif]>Using materials with a higher magnetic saturation than 1018 low carbon steel will lead to even higher magnetic field compression and intensity.
<![if !supportLists]>32. <![endif]>Measurements with and without the end deflecting magnets using a gauss meter has shown that with the size PMA being used ( 3 magnet pairs, 2" diameter and 1" thickness magnets), measurements indicated a 20% increase in the intensity of the peak magnetic fields when the end deflecting magnets were used. This is over and above the estimated 200% increase in efficiency of magnetic flux cutting across a given amount of coil windings as compared to the standard NSNSNS configuration.
<![if !supportLists]>33. <![endif]>If we use just the PMA without the end deflecting magnets, it is estimated (and this will be shown hopefully analytically by the computer simulation) that there is a significant loss of magnetic flush for small PMA's and therefore, the end deflecting magnet is much more significant for small PMA structures. The explanation is as follows: If each magnet produces N total magnetic lines of flux, the PMA as a whole produces nN total flux where n = the number of magnets in the PMA. However, flux only escapes into space and does from the N pole end of the PMA, goes into space with most of this flux not intersecting the coils because their direction is parallel to the long axis of the PMA and when they do curve around to return to a S pole in the interior of the PMA, it is way beyond the location of the coils. Thus this represents magnetic flux leakage which impairs the efficiency of the generator. The amount of leakage remains the same no matter how long the PMA is and how many magnets are used, because unlike the conventional configuration of NSNS where all the flux comes out the end of the PMA, in the CRMFT configuration only the flux from the end magnet comes out as flux loops in this configuration is only to the adjacent poles and not out into space except for the end magnet. The use of end deflecting magnets is critical for short small PMA's such as wrist watches, personal energy harvesters, buoys, etc but less critical for larger PMA's such as Wave Energy Converters. Reason: (A semi-analytical explanation) If the minimum sized PMA using 2 magnets produces a total amount of flux of 2N, and let's assume that 50% of the flux emanating out of the end magnet that is lost is N/2, the % loss of flux of the system is (N/2)/2N or 25% which is significant. However, if the PMA has 10 magnets, n=10, the total flux is 10N, the amount lost to space at the ends is still only N/2 (as opposed to 50% of 10N or 5N in the conventional configuration), the percentage leakage is (N/2)/10N or only 5% and an end deflecting magnet is not really necessary to prevent flux leakage and its effect on the power generation is nil (though an end deflecting magnet is still useful to help in braking the PMA with the end braking magnet). It is this arrangement of magnetic fields that is responsible for an estimated 200% improvement in the magnetic flux coil winding linkage for magnets and coils of a given size of the NSSNNSSN CRMFT versus the standard older NSNSNSN technology.
<![if !supportLists]>34. <![endif]>While the CRMFT causes virtually all of the magnetic flux lines to curve around to the interior of the PMA cutting across the coil windings producing power, some of the lines further away from the PMA may curve around in such a manner that the radial component of the magnetic field perpendicular to the axis of movement and long axis of the PMA (the only component of the field that produces power in the coil windings) may less than and even small relative to the tangential field component(parallel to the direction of motion and long axis of the PMA) in the vicinity of the winding which produces no power and wastes magnetic flux reducing the efficiency of conversion. The ratio of the perpendicular component to the tangential component can be enhanced at points further out from the PMA in the outer windings of the coil by surrounding the coils with a thin circular sheet of very high permeable magnetic shielding sheeting.
Q52: How can you show what number of successively intersected small WEC’s operated at the wave riding mode be equal in the ability of a single large unit operating in the resonant mode?
<![if !supportLists]>1. <![endif]>A very large wave will contain a huge amount of power per meter of wavefront. A LEG WEC would have to have a rotor moving through at least 3 times the distance optimally of the amplitude of the wave it most likely was to encounter and perhaps considerably more to take into consideration resonance matching between the WEC and the incoming wave. The device can only capture energy of that section of the wavefront that intersects the diameter of the WEC, so if a large unit has to harvest a large amount of energy from a large wave for a reasonable efficiency, it has to be of a very large circumference. If several units are to be used in close proximity to each other, they still have to be spaced a reasonably distance apart from each other because of their large size to prevent collisions thus allowing much of the wavefront to pass between them without intersecting a WEC. Generally, such a device should be run at a resonance mode with respect to the oncoming waves expected at that location. Such units are hard to transport, install, and in the event of mechanical failure, to replace and are extremely expensive. Because they would be designed for a specific location to be matched with the prevailing sized waves in that location, they would be custom made. If waves other than the ones they were specifically designed for did not occur at a particular time, the device’s efficiency would drop dramatically. Three smaller WEC’s whose combined stroke distance is equal to a WEC three times larger, and by placing these WEC’s one behind the other in close proximity to each other, one can achieve the same power extraction as with the large unit. Each Vibristor® removes its share of power from the passing wave and the sum total of the energy removed by all 3 devices would approximate the energy harvested from the optimized larger device.
Q53: How can small wave riding WEC’s decrease loss of efficiency due to pitch motion as compared to large WEC units?
<![if !supportLists]>1) <![endif]>If the wavelength of the ocean wave is much larger than the diameter of the buoy collar, the slope of the wave (change in height of the wave with distance) will be low which would cause the tipping angle of the buoy collar to be very low and near zero causing the rotational motion of the collar to be minimal. This effect is more pronounced with smaller waves as compared with waves of larger height. With less of the wave’s energy being converted into rotational kinetic energy, more of the harvested energy is converted into linear kinetic energy. Note that only the vertically directed kinetic energy harvested in the rotor produces electric power and there is no contribution from any rotational component as the LEG does not respond to that type of kinetic energy and indeed its operation may be hampered if there is too much pitch rotation to the movement of the buoy floatation collar.
<![if !supportLists]>2) <![endif]>Ideally, for a given wave height and wavelength, the diameter of the collar should be long enough so that there are usually two wave crests under the collar at all times minimizing pivoting rotational energy and maximizing vertical linear displacements.
<![if !supportLists]>3) <![endif]>Note that for one peak to be under the collar at any one time you have the maximum amount of linear vertical displacement kinetic energy but you also have the maximum amount of pitch rotational energy as well. However, if you have two wave peaks and one trough under the collar, one peak is cancelled out by one trough but you still have a net gain of one peak of vertical motion while the two peaks together cancels out the rotational component.
<![if !supportLists]>4) <![endif]>However, if the buoy diameter exceeds many wavelengths of the wave, there is little linear vertical motion as all of the wave peaks are cancelled out by the wave troughs, which is the situation of a very large tanker or cruise ship being relatively motionless even with sizeable waves of considerable amplitude.
Q54: What applications exist for the Vibristor® LEG?
<![if !supportLists]>1) <![endif]>Any application that involves a linear vibrational source of kinetic energy.
<![if !supportLists]>2) <![endif]>Sample applications: mountain bike charger, personal electronics charger, animal migration GPS power source, emergency boating power source, ocean powered navigational and instrumented buoys, electrokinetic coastal protection arrays, electromagnetic shock absorbers, vibrational energy harvester circuit component for powering low power electronic circuits, sensor power sources, harvesting energy from vibrating buildings, car braking surfaces in front of toll booths, ocean powered mines, and most importantly, grid scale electrical energy harvesting from the world’s oceans.
<![if !supportLists]>3) <![endif]>The device can be used in reverse – an electric signal is provided to the coils causing a magnet to move or if the magnet is stationary, the coil to move – audio loudspeakers, linear motors, rail guns, linear actuators and stamping devices, crowd control sound weapon.
<![if !supportLists]>4) <![endif]>The Vibristor® because of its scalability both upward and downward in size as well as the numerous applications in which it can be used can be described as a platform technology.
Q55: How can the Vibristor® be scaled upward in size?
<![if !supportLists]>1. <![endif]>By increasing the thickness, diameter of the magnet, and hence the volume of each magnet: Power increases with the dimensions raised to the 3.5th power.
<![if !supportLists]>2. <![endif]>The N magnetization factor (energy product in Mega gauss-oresteds can be increased from the N42 level (in the prototype) to N55, the magnets with the highest possible commercially available rare-earth magnet magnetization (scale runs from N1 to N70).
<![if !supportLists]>3. <![endif]>The number of magnets in the PMA (SMU’s) can be unlimited making for stacks that are up to many, many meters in length.
<![if !supportLists]>4. <![endif]>Using the largest magnets with the highest magnetization levels and very long PMA’s can produce very large WEC’s which in itself may be used in multiple device closely packed arrays making grid scale applications realistic.
Q56: How can the Vibristor® be scaled downward in size?
<![if !supportLists]>1. <![endif]>By scaling down the geometric dimensions of the magnets and associated coils to produce Vibristors<![if !msEquation]><![if !vml]><![endif]><![endif]> small enough to allow for small scale energy harvesting devices such as human motion energy harvesting devices.
<![if !supportLists]>2. <![endif]>Even smaller downscaling will allow the Vibristor® to be used as a circuit component that can power sensors and low power electronics in areas of the environment where vibrational energy sources are present.
<![if !supportLists]>3. <![endif]>Theoretically, the technology could be scaled down to MEMS (micro-electromechanical systems) dimensions.
Q57: How is the magnetic field of the PMA radiating across the FCA made more intense?
<![if !supportLists]>1. <![endif]>By using larger diameter magnets and pole pieces.
<![if !supportLists]>2. <![endif]>By using the thinnest possible pole pieces with the optimal ratio of the magnet thickness to pole piece thickness. Note the pole pieces will be such so as to prevent the compressed repulsive magnetic fields from supersaturating the low carbon steel ferromagnetic pole pieces forcing the repulsive magnetic fields back into the interior of the adjacent magnets which will cause the magnets to slowly demagnetize.
<![if !supportLists]>3. <![endif]>By using end-deflecting magnets at the end of the PMA to deflect any magnetic lines of force escaping into space back around onto the PMA magnetic poles thereby intersecting the coil windings in the process.
<![if !supportLists]>4. <![endif]>By using a cylindrical cross section for the PMA, the distance across which a given amount of flux lines radiate outward from the PMA from one repulsive magnetic field region is minimized and kept most uniform as opposed to other geometric shapes. Total flux / area through which the flux radiates = flux density (field intensity). Also, flux density varies with the radius of curvature of the region through which the flux radiates and the cylindrical surface of the PMA has a constant radius of curvature at all points on its surface.
Q58: How can the windings comprising the FCA surrounding the PMA be made more efficient?
<![if !supportLists]>1) <![endif]>The inner windings of the coil are of thinner gauge and therefore there are more turns in the region of the highest intensity of the magnetic field thereby increasing the voltage produced in the inner windings.
<![if !supportLists]>2) <![endif]>One uses an increasing number of coils for each structurally magnetic unit as the thickness of the magnets increases.
<![if !supportLists]>3) <![endif]>The relationship between the length of the SMA and the number of coils per SMA occurs because as n goes up, that is the number of coils per SMA goes up, the fraction of the coils that are over equal but opposite amounts of magnetic flux decreases (only two coils are ever over an equal amount of N and S directed flux) goes down, thereby causing the sine wave output to gradually shift to a square wave resulting in a higher duty cycle train of half cycles which when rectified increases output efficiency, output, and decrease ripple voltage.
Q59: How is the produced electrical energy collected from the WEC’s? (PCC)
<![if !supportLists]>1) <![endif]>The power output from each coil of the FCA is collected along with other coils through an n-phase bridge rectifier circuit, a current summation circuit, a bipolar n-phase bridge rectifier circuit, or a voltage summation circuit to form one power output from one WEC.
<![if !supportLists]>2) <![endif]>The power output from all of the WEC’s of each row of the array is combined together at the next level using the above 4 collection circuits.
<![if !supportLists]>3) <![endif]>The power output from each of row of the array is combined together at the third level of collection using the above 4 collection circuits.
Q60: How is the produced electrical energy transmitted from the WEC’s
<![if !supportLists]>1) <![endif]>Undersea cables running to shore that can be as long as 80 km. for AC and 125 km. for DC.
<![if !supportLists]>2) <![endif]>If the array is adjacent to a seawall, the cable running out of the array can run along the sea wall.
Q61: How can the produced electrical energy be stored after it is produced?
<![if !supportLists]>1) <![endif]>Batteries (Lithium Ion)
<![if !supportLists]>2) <![endif]>Hydrogen (Compressed)
Q62: How is an array of WEC’s structured?
<![if !supportLists]>1) <![endif]>Single configuration, dual units.
<![if !supportLists]>2) <![endif]>Strips of single or dual layers of units.
<![if !supportLists]>3) <![endif]>Geometric shaped arrays – square, circular (most optimal), rectangular, polygonal.
<![if !supportLists]>4) <![endif]>Attached to a large fixed floating heavy structure (“boat mass”)
Q63: How is a single WEC or array of WEC’s tethered?
<![if !supportLists]>1.) <![endif]>Freely floating.
<![if !supportLists]>2.) <![endif]>To the ocean floor.
<![if !supportLists]>3.) <![endif]>To piers, bulwarks, and sea walls.
<![if !supportLists]>4.) <![endif]>To off shore wind farm turbines.
<![if !supportLists]>5.) <![endif]>To each other in arrays.
<![if !supportLists]>6.) <![endif]>By flexible or rigid connectors.
Q64: How is the efficiency of the WEC determined?
<![if !supportLists]>1) <![endif]>There are several different types of efficiency that are of relevance.
<![if !supportLists]>2) <![endif]>First: Device Energy Harvesting Efficiency: Kinetic energy developed in the rotor divided by the energy of the area of ocean surface beneath the floatation collar.
<![if !supportLists]>3) <![endif]>Second: Electrical Energy Conversion Efficiency: Electrical Energy Output divided by the kinetic energy developed in the rotor.
<![if !supportLists]>4) <![endif]>Third: Total Device Energy Harvesting and Conversion Efficiency: Electrical Energy Output of the device divided by the energy of the area of ocean surface beneath the floatation collar.
<![if !supportLists]>5) <![endif]>Fourth: Total Array Energy Harvesting and Conversion Efficiency: Total Electrical Energy Output (= to n times the Device Electrical Energy Output, assuming an array of n devices, each with the same output) divided by the total ocean surface area covered by the array.
<![if !supportLists]>6) <![endif]>Fifth: Device Power Harvesting Efficiency: Mechanical power developed by the rotor divided by the power present in the wavefront distance intersecting the device.
<![if !supportLists]>7) <![endif]>Sixth: Electrical Power Conversion Efficiency: Electrical power output of the WEC divided by the mechanical power developed in the rotor.
<![if !supportLists]>8) <![endif]>Seventh: Total Device Power Harvesting and Conversion Efficiency: The electrical power output of the device divided by the power of the wavefront intersecting the device.
<![if !supportLists]>9) <![endif]>Eighth: Total Array Power Harvesting and Conversion Efficiency: Total Electrical power output of n devices of an n device array divided by the Total Wavefront power entering the array.
10) From a practical standpoint, the Total Device Power Harvesting Conversion Efficiency and the Total Array Power Harvesting and Conversion Efficiency are the two most used.
Q65: How is the mechanical complexity of the Vibristor® compared to other devices?
<![if !supportLists]>1) <![endif]>Very simple mechanically with only one moving part, the buoy collar rotor structure.
<![if !supportLists]>2) <![endif]>No gear trains, hydraulic drives, slide bearings, rotary generator components.
<![if !supportLists]>3) <![endif]>May be mass produced with low cost off the shelf components.
<![if !supportLists]>4) <![endif]>The energy harvesting component (the floatation collar), the prime mover (the rotor) all moves linear, usually but not necessarily in a vertical direction as one single part.
<![if !supportLists]>5) <![endif]>The floatation collar and rotor directly covert kinetic mechanical energy into electrical energy.
Q66: In summary, what are the most important characteristics of the Vibristor® Linear Electric Generator?
<![if !supportLists]>1) <![endif]>Single moving part, the buoy collar-rotor structure.
<![if !supportLists]>2) <![endif]>Mechanical energy harvesting and direct conversion of harvested mechanical energy into electricity all with a single action.
<![if !supportLists]>3) <![endif]>Inelastic interactions between the rotor and the stator of the LEG.
<![if !supportLists]>4) <![endif]>Ability to be deployed by the hundreds or even thousands in arrays.
<![if !supportLists]>5) <![endif]>No deleterious environmental impact.
<![if !supportLists]>6) <![endif]>A new type of power generating magnetic field configuration (compressed repulsive magnetic field technology) that can be up to 200% more efficient in producing power.
<![if !supportLists]>7) <![endif]>Magnetic bearing levitation technology.
<![if !supportLists]>8) <![endif]>Focusing magnetic fields without heavy ferromagnetic armatures.
<![if !supportLists]>9) <![endif]>Electromagnetic, magnetic, and mechanical elastic braking technology.
<![if !supportLists]>10) <![endif]>Off the shelf parts.
<![if !supportLists]>11) <![endif]>Easy replacement and serviceability for maintenance.
<![if !supportLists]>12) <![endif]>Does not have to operate at resonance with ocean waves.
<![if !supportLists]>13) <![endif]>Can be used in wave riding mode.
<![if !supportLists]>14) <![endif]>Arrays capable of extremely high efficiencies of energy extraction.
<![if !supportLists]>15) <![endif]>Scalable dimensionally from huge devices down to tiny devices.
<![if !supportLists]>16) <![endif]>Scalable from rotors with just two magnets and four coils to devices that are many meters long with hundreds of magnets and coils.
<![if !supportLists]>17) <![endif]>No liquid lubricants or hydraulic fluids.
<![if !supportLists]>18) <![endif]>Can be tethered to anything – bulwarks, seawalls, each other in arrays, freely floating, seabed, structures attached to the seabed, massive floating boat-like structures.
<![if !supportLists]>19) <![endif]>Arrays can be of any size or of any geometric shape suitable to fit the particular area of ocean where deployed.
<![if !supportLists]>20) <![endif]>Ability to continue operation even if part of the WEC is non-functional (open or shorted coils, non-functioning electronic circuits etc.)
<![if !supportLists]>21) <![endif]>Easy ability to be shut off in anticipation of maintenance or storms.
<![if !supportLists]>22) <![endif]>Vibristor® LEG’s can be of any arbitrary length up to including very long devices containing hundreds of coils and magnets.