IE52975B1 - A wave powered prime mover - Google Patents

Abstract

Essentially the prime mover comprises a pair of rafts 1 and 2 pivoting about a pivot shaft 3 supported on a semi-submersible bridle structure 5 which retains the pivot shaft 3 in position substantially fixed relative to the mean wave water level. The bridle structure comprises a mast 10 projecting from a damping plate 8 which damps out vertical movement. The pivotal movement of the rafts 1 and 2 about the shaft 3 is converted to usable energy by means of pumps 20 and 21 which pump sea water to a header tank on shore through a conduit 27. Connecting rods 22 and 23 of the pumps 20 and 21 are connected to the mast 5 of the semi-submersible bridle structure. In another embodiment, Fig. 3 (not shown), both pumps are mounted on the raft 1.

Description

The present invention relates to a wave powered prime mover.

According to the invention there is provided a wave powered prime mover comprising at least one wave eng5 aging float pivotally connected to a semi-submersible bridle structure so as to be free to pivot relative thereto and means to convert the pivotal movement of the float into usable energy, the semi-submersible bridle structure comprising a mast supporting the pivot and projecting upwardly from a base member^in the form of a damping plate which damps out vertical movements of the bridle structure to retain the pivot axis substantially fixed relative to the mean wave water level. in one embodiment of the invention a flexible mooring member is provided to moor the retaining means to the sea bed.

Preferably, a pair of floats are provided on opposing sides of the retaining means.

ZO - 3 Advantageously* the floats pivot on a common pivot axis.

In one embodiment of the Invention In use* the free end of the leading float 1s moored to a mooring buoy by a flexible mooring member.

In a further embodiment of the invention the means to convert the pivotal movement of each float is provided by a water pump mounted on a float and operable by a linkage assembly.

Advantageously, the water pump delivers sea water to a header tank.

The invention will be more clearly understood from the following description of some preferred embodiments thereof given by way of example only with reference to the accompanying drawings in which: Fig. 1 is a partly diagrammatic elevational view of a wave powered prime mover according to the invention, Fig. Z is a sectional side view on the line II - II of the prime mover of Fig. 1, Fig. 3 is a partly diagrammatic elevational view of a wave powered prime mover according to another embodiment of the invention, - 4 Fig. 4 is a diagrammatic representation of the prime mover of Fig. 1 illustrating the notation used in the experiment, Fig. 5 is a graph illustrating a plot of the magnification S factor as a function of the frequency ratio and wavelengthto - raft length ratio, Fig. 6 is a diagram illustrating the energy efficiency as a function of the frequency ratio, and Fig. 7 is a graph showing a plot of power efficiency as a function of frequency ratio.

Referring to the drawings and initially to Figs. 1 and 2 thereof there is illustrated a wave powered prime mover according to the invention. The wave powered prime mover comprises a pair of wave engaging floats, in this case steel rafts 1 and 2 which are pivotly mounted on a pivot shaft 3 which defines a pivot axis 4. The pivot shaft 3 is supported on a semi-submersible bridle structure 5. The rafts T and 2 are free to pivot about the shaft 3 under the action of passing waves 7. The semi-submersible bridle structure 5 comprises a base member formed by a damping plate 8 of reinforced steel plate and a mast 10 extending from the plate 8. The mast 10 is formed - 5 by a pair of hollow steel tubular uprights 11 joined by a cross member 12 also of steel. The pivot shaft 3 extends between the uprights 11. The bridle structure 5 under the action of the damping plate 8 which damps out vertical movement substantially retains the pivot shaft 3 in a fixed position rela-tive to the mean wave water level illustrated by the broken line 14 in Fig. 1. The uprights 11 being tubular act as ballast tanks and sea water may be pumped in and out of the uprights as desired to alter the trim and the level of the bridle. The means for doing this is not shown but such means should be well known to those skilled in the art.

As can be seen in Fig. 1, the waves move in the direction of the arrow A and the prime mover is moored by a mooring buoy 15 which is connected by a mooring rope 16 to the bow of the leading raft 1. An anchor 17 anchors the buoy 15.

Means to convert the relative pivotal movement of the rafts 1 and 2 into useful energy is provided by a pair of piston type water pumps 20 and 21 mounted on the rafts 1 and 2 respectively. The pumps 20 and 21 are connected to the upright 11 by means of their connecting rods 22 and 23 and accordingly are actuated by the pivotal movement of the rafts 1 and 2. The pumps 20 and 21 pump the sea water to a header tank (not shown, on shore. The sea water is delivered to the pumps through inlet pipes 25 and 26 projecting through the bottom of each raft 1 and 2. A flexible delivery conduit connected to the outlets of each pump 20 and 21 delivers sea - 6 water from the numps to the header tank. The conduit 27 extends down the mast TO and along the sea bed. The fact that the conduit 27 is flexible accommodates the rising and falling of the prime mover due to tidal variations.

In use» the wave powered prime mover is towed to the desired site and moored in position by the buoy 15. The passing waves cause the rafts T and 2 to pivot about the shaft 3, thereby actuating the pumps 20 and 21. Sea water is delivered by the pumps 20 and 21 to the header storage tank (not shown).

The water in the storage header tank may then be used to power any suitable apparatus, for example, water turbines to drive an electrical generator and the like. In fact, it is envisaged that the prime mover would be ideally suited to store water in the header tank for the generation of peak electricity.

Referring now to Fig. 3, there is illustrated a wave powered prime mover according to another embodiment of the invention. This prime mover is substantially similar to that just described with the exception that the linkage assembly for the pump is different. In this embodiment of the invention two pumps 40 and 41 are mounted in the raft 1, and the linkage assembly 42 is connected between the pumps 40 and 41 and a mast 45 rigidly mounted on the deck of the raft 2. Accordingly, the pumps 40 and 41 in this embodiment of the invention are actuated by the relative pivotal movement between the rafts 1 and 2. The linkage mechanism comprises a main link 46 pivotally connecting the mast 45 with an upstanding link 48. - 7 The link <8 is pivotal on the deck of the raft 1 and is pivotally connected by means of links *9 and 50 to actuate levers 51 and 52 of the pumps 40 and 41. Accordingly, as the rafts 1 and 2 pivot relative to each other the linkage assembly 42 acutates the pumps 40 and 41. It can clearly be seen from Fig. 3 that while one pump is on a suction stroke, the other will be pumping to a header tank (not shown). Pipes 56 and 57 in the base of the raft 1 connect the pumps 40 and 41 to the sea while the flexible delivery conduit 27 delivers sea water from the pumps to the storage header tank (not shown) on the shore.

The mast 10 of the semi-submersible bridle in this embodiment of the invention is also formed by hollow vertical steel tubes which support the pivot shaft 3, and act as ballast tanks. The leading raft 1 is moored by a mooring rope 60 to a buoy (not shown).

Having described the wave powered prime mover in detail, results of experiments carried out on a scale model and the theoretical analysis behind the results will now be described.

Exgerimental_ResuIts Experiments were carried out on the prime mover illustrated in Figs. 1 and 2. The rafts 1 and 2 were of equal length each being 2.4 metres. The experiments were carried out in a tank - 8 4.88 metres deep end 7.92 metres wide. Regular waves generated by a wave generator were used in the experiment.

Theoretical analysis Referring to Fig. 4 for notation, the component rafts of the 5 wave powered prime mover obey the following equations: «aft Ho. 1: (ly1 + Α,ΐθ^ + 8^6., + Β&1(θη - βρ + , M]0 cosfrnt + ip (1) Raft Ho. 2: (ly2 + Α2)θ2 + Ba2S2 + Bb2(62 - ep + cp2 = K2Q cos (at + «ρ (2) where £y = mass moment of inertia about the pivot shaft £ = added-mass moment of inertia about the pivot shaft Ba = radiation plus linear viscous damping coefficient 15 of the raft Bb = equivalent linear damping coefficient due to the energy conversion £ = hydrostatic restoring moment Μθ ” wave-induced pitching moment amplitude S' pitching displacement ω = circular wave frequency (2irf = 2ir/T), where f is the wave frequency in Hz and T is the wave period 5297s In seconds * phase difference between the wave and the waveinduced moment.

In equation (1) and (2) the coupling is due to the energy 5 extraction mechanism which, for the wave powered prime mover is a hydraulic pump.

For this prime mover having two identical rafts equations (1) and (2) can be combined into a single equation of motion.

That is (Iy + A)(6, - 02) + β^θ, - e2) + 2 Bb(e, - e2) + C(01 - θ2) · Mlo cos(ut + dp - M20 cos (int + «2) « Μθ COS(u>t +6) (3) where the exciting linear wave is described by n = y cos(ut) (4) where H is the wave height.

Before solving equation (3) an explanation of the damping coefficient B^ should be suppliecl. This is an equivalent linear coefficient used to represent a nonlinear damping.

Me can assume that the damping due to the energy extraction (caused by the pumps and waterlines) is quadratic so that the actual damping moment can be represented by the S2975 expression Mfa · Bfe·, - ΘΖ)Ζ « βφ2 (5) where The average energy removed by the prime mover is ψ) Vdt Jn (6) Since the motion of the prime mover is nearly sinusoidal, we can approximately equate the energy obtained by combining equations (5) and (6) to that obtained by combining equation (6) with the linear damping moment, b “ M (7> The resulting equivalent linear damping coefficient is found to be Bb “ Ζ “φθ ' bb“*0 I®) J ιΓ where is the amplitude of Φ.. The average power converted by the prime mover is, then, (9) where the quadratic damping coefficient, β, is determined experimentally.

Returning to the equation of motion, eq. (3), the coefficients can be approximated by using the strip theory as described in Principles of Naval Architecture edited by Comstock (1967) published by Society of Naval Architects and Marine Engineers, New York and illustrated in Ocean Engineering and Wave Mechanics by McCormick (1973) published by Miley Interscience, New York. The strip theory is found to have best applicability to marine vehicles in motion. The Application here. then, must be considered to be a rough approximation used for the purpose of illustration since the raft system is not under way. Each raft is assumed to have a box shape with no bow or stern flare, although the rafts of the prime mover of the invention, the subject of the experiment do have bow and stern flare. The coefficients for the theoretical model are the following: (10) where Z is the raft height. The raft mass is m - p L H d (11) 53975 where £ is the mass-density of sea water, M 1s the raft width and d is the draft.

A * 0.04nm(L3/d) (12) *a(«Bb> ' C°3 (13) C = eg L3 H/3 (14) «0 = p g H W(e-Itd + 1) [kL cos(kL) - sin(kLjj (15) where the wave number is k = 2π/λ and, finally, ί = 90° (16) With the approximation in equation (13) the solution of equation (3) is, then. φ = $0 cos(ut + 5 - γ) , (Hq/C) cos((ot + δ - γ) (17) tRT: (2 Β, ω .,2 Lan ω cr n where the phase angle between the sioment and the motion is Βκ ω Kb 3 cr n ,2 tan - (m/un)‘ (18) the natural frequency Is (19) and the critical damping coefficient is cr A) (20) Note: The equivalent linear damping coefficient, B^, defined by equation (8) is a function of both frequency and displacement amplitude. Thus, the magnification factor « *0 C/H0 (21) is not obtained directly from equation (17). Instead, we must first combine the amplitude expression of equation (17) with equation (8) and solve for φθ. The result is For low values of (ω/ωη) the approximation of equation (13) does not hold since the quadratic damping is also of zero order. A plot of the magnification factor of equation (21) 53975 - 14 is discussed later, using the results of the amplitude equation, eq. (22).

If the radiation damping, viscous damping and quadratic damping are all of the same order of magnitude, then the equation from which Ψο is obtained is biquadratic. Altough closed solutions of this equation can be obtained, the level of complexity of the solution discourages the use of this approach.

The analytical expression for the power conversion efficiency in deep water (where X>h/2) is Ep = pb/p x 1024 3 where, again, the value of £ is and the deep water wave power e 15 P = P9ZH2 T tl (24) 32” Results obtained from applying equation (23) to the experimental model are discussed below. (23) experimentally determined, xoression is - 15 Experiment and Results The experimental model of the wave powered prime mover is illustrated in Figs. 1 and 2 and 4. For that model the following values apply: L, « 4 · L « 2.40 m W * 1.20 m d « 7.87 x 10*3m m « 22.7 kg Z » 0.102 m Using these values, the parameters described by equations (10), (11), (13) and (14) are, respectively, I « 43.6 N-m-sZ/rad A · 5,010 N-m-sZ/rad C « 54,200 N-m/rad and 53975 - 16 The prime mover had two Identical pumps, each excited by one raft only. This allows for the separate analyses of the results of each component raft.

The damping for each pump 1s found to vary with frequency and 5 angular displacement of the specific raft. This fact 1s seen In the results of Fig. 5 where the theoretical and experimental values of the magnification factor, Ζθ, are shown as functions of the frequency ratio, f/fn· In F1g. 5 results are for the following conditions. 1. undamped linear vibrations, equation (17). 2. critically damped linear vibrations, equation (17). 3. quadratically damped vibrations where 8b “ 2Bcr at f/fn*°·8 (β-10.3 x 107N-m-s2/rad2) in equation (9), 4. experimental values of rafts 1 and 2.

The experimental results of equation (4) show that the leading raft (1) has a maximum energy loss at a frequency ratio of 0.8. This, then should correspond to a maximum energy or power production, according to equation (9). The values for raft (2), however, continuously decrease with f/fn. with the exception of the value at f/f - 1,92. It appears that above f/fn * 0.80 the power absorbed by raft 1 is significantly greater than that of raft 2 since 6Z is significantly less than θρ Hence, the use of a one float embodiment is equally valuable 53975 - 17 The average energy absorbed by each raft, as evidenced by the raft motions, is calculated by using the expression Eb * | [ly + *)“Z + C]e0 <25> where is the amplitude of the raft in question, as shown 5 in Ocean Have Energy Convertion* by McCormick (1981) published by Wiley Interscience, New York. Values obtained from this expression using the experimental frequencies and displacements result in efficiency values obtained from eE ’ Eb/E « 2 Γ(Ι + Α)ω2 + cl ω2 β2 —k—ί----ο· pgZHZn U (26) where the deep water wave energy expression is E « pg2 Η2 T2 W (27) 16ir These energy efficiency values are presented in Fig. 6. Ue note that the efficiency values of rafts 1 and 2 are approximately equal for f/fn * 0.8; however, for f/fn > 0.8 the efficiency of raft 2 decreases with f/f„. except when f/ffl = 1.92. For this frequency ratio value the total system effic20 iency (EE1 + E£2) is 118J.

Also shown in Fig. 6 are the energy efficiency values as determined from pumping and maintaining a head of water in a - 18 1-inch diameter (0.0254 meter) tube. The head can be increased or decreased by adjusting the length of the level arm. The maximum head obtained is 3.26 m, and is obtained using the level arm configuration sketched in Fig. 7. This maximum head corresponds to an efficiency of 28.OS and a frequency ratio value of 0.77.

The experimental power efficiency values are determined from the expression of equation (9), where the maximum quadratic 5 2 2 damping value is 6 1 5.17 x 10 N - m - s /radt These power 10 efficiency values are presented in Fig. 8 for rafts 1 and 2, the total system efficiency and the efficiency obtained from pump 1 with a constant head of 0.532 meter. The maximum power efficiency obtained by the pump is 8.70S at a frequency ratio of 0.960. Needless to say, by using a more efficient pump, for example a pump with an efficiency of 65S to 70S considerably improved results would be achieved.

Discu55Ϊ9Π_5SS_£SO£ΐϊ5ions Results of the experimental study of the prime mover are presented in Figs. 5, 6 and 7.

The curves in Figure 5 are from the (a) undamped linear theory, equation (17),- - -, (b) critically damped theory, equation (17), ---------- , and (c) quadratically damped analysis, equations (8), (9) and (22), where 8 = 10.3 x 107 N-m-s2/ 2 rad---' The experimental data are for raft no. 1 (G) and raft No. 2 (G0· -18aIn Figure 6 the data points correspond to raft No. 1 (©), raft No. 2 (GJ), total mechanical energy efficiency (A) and the overall energy delivered by the pump (+). The two pump values at f/fn = 0.77 correspond to that sketched in Figure 6, where the lower value is for configuration 6a and the upper value is for configuration 6b.

In Figure 7 the data points correspond to raft no. 1 (□), raft no. 2 (0). total mechanical power (A) and the overall power delivered by the pump (+). The maximum pump efficiency is 8.750 while the mechanical efficiency for the corresponding raft is 29.9%. Thus, the pump design is critical in the system performance.

In Fig. 5 the magnification factor is presented as a function of the frequency ratio. The data show that the system damping due to the energy extraction is greater than the critical damping at f/fn = 0.8, where Bb/Bcr = 1.13 for each raft. Since each raft-pump system in the study is operating independently, we can see that for f/fn> °·8 the ener9ies absorbed by the two rafts are significantly different, while for f/fn< 0.8 the energies are approximately equal. For this nonlinear system - 19 therefore, we must assume that the damped natural frequency for each raft is fd = 0.8 (28) This frequency, of course, depends on the magnitude of the 5 damping which, according to equation (9), is indicative of the wave power converted. Also presented in Fig. S is the equivalent deep water wavelength-to-raft length ratio. He see that the value of this ratio corresponding to f/f · 0.8 is λ « 3.75 L (29) a value which has no particular significance. We must conclude, therefore, that the frequency ratio is the significant independent dimensionless parameter. The wave steepness is actually implicit in magnification factor; thus, the results in .Fig. do include the H/λ effects.

The energy efficiency, e^, is shown as a function of f/f„ in Fig. 6. The values for rafts 1 and 2 and, therefore, the total efficiency are shown to have inflection points at f/f = 0.8.

For f/f > 0.8 the energy efficiencies of raft 1 and the total mechanical increase, while those for no. 2 decrease (with the exception of f/f = 1.92). The exception noted n corresponds to λ/L 0.176, a value which has no significance.

The exception, therefore, is attributed to a standing wave resulting from the radiated wave from the raft systems.

One can conclude from the data of Fig. 6 that the two-raft systems are equally efficient in energy production for f/f < 0.8, while raft 1 absorbs most of the energy for n * f/f > 0.8. The pump efficiency values shown in Fig. depend on the lever arm configuration. For a given wave condition εΕ can be increased by adjusting the lever arm to the optimum configuration shown in Fig. 7. An overall peak energy efficiency of 28X is seen at f/f = 0.77. Although no amplitudes were measured during the lever arm adjustment, it was noted that the amplitude of the raft did increase as the overall efficiency increased. This indicates impedancematching is accomplished.

The power efficiency data of Fig. 7 are the most significant.

We see that combined efficiency value of 65X is obtained at f/f = 0.88, where the efficiency of raft 1 is 591 and that of raft 2 is 6%. The next highest combined efficiency value is approximately 46X where the efficiencies of both rafts are 23X at f/f = 0.77. The measured values of the overall power efficiency of each pump never exceed8.7X, as shown in Fig. 7. Thus, we can conclude that the pump inefficiency is significant. It must also be noted that the pumps used in the study are commercially available bilge pumps which are not designed for energy production. The pump design for the prototype system is critical to the system performance. For f/fn < 0.8 two pumps are required in the system since the efficiencies of each raft system are equal. For f/f > 0.8, t · - 21 however, only the leading raft is required since the power produced by the trailing raft is relatively small.

These results may be used to determine the performance of a full scale prototype. By way of example the results are applied to a prototype sixty times larger than the model tested.

The scaling equations as presented in “Ocean Wave Engineering Conversion* by McCormick {1981} are used. These are the following: Length: Time: Energy: Power:Lm/Lp VTP Em/Ep Pm7Pp = n = 1/16 « 0.0625 = n1/2 - 0.25 ® n = 0.0625 - n7/Z = 6.10 x IO'5 where the subscript “m“ refers to model values and refers to prototype values.. Applying these equations to the 15 prototype, we obtain L = 38.4 m (87.8 m overall) U * 19.2 m Z - 1.63 m d = 0.126 m T_ = 7.68 sec. n Using the maximum head developed at f/f = 0.77 (ε£ » 282) in Fig. 6, the maximum prototype head developed from equation (32) is - 22 3.26/n » S2.2 meters while the maximum power produced by the raft motions at f/f = 0.88 (e = 65X) indicate a maximum prototype raft η ' p power of 16.9/n7/2 « 277 kW.

These prototype values show that the wave powered prime mover according to the invention is particularly suitable for a wave energy excited pump-storage system. With an improved pump design the peak raft motion power can nearly be achieved as the overall power. For f/fn £ 0.8 a two-raft system is most feasible, while for f/fn > 0.8 only the lead raft is needed. The sea condition of f/f„ < 0.8 can be considered to be that corresponding to a swell, whereas f/ffl > 0.8 can be considered the range of the wind-generated sea.

It has been found that fixing the pivot shaft relative to the mean wave water level of the waves produce a relatively efficient prime mover. It will be appreciated that a considerable advantage of this is that the prime mover according to the invention may operate with a substantially constant efficiency.

It will also be appreciated that while a particular construction of means to retain the pivot shaft in a fixed vertical position I · - 23 has been described, any other suitable means could be used.

For example, 1t is envisaged that a structure mounted on the seabed may be used. Indeed, it is envisaged that instead of mooring the prime mover to the mooring buoy, the semi5 submersible structure could itself have been moored to the seabed, for example, a mooring cable connected to the semisubmersible structure could be anchored to the seabed. Furthermore, it will be appreciated that although the rafts have been described as being pivotal about a pivot shaft, they could be pivotal about any other suitable member. Additionally, although the invention has been described as comprising two rafts, an efficient prime mover could be provided with only one raft without departing from the scope of the invention. Similarly, many more than two rafts could be provided.

Additionally, floats other than rafts could be used.

It will also be appreciated that although a particular construction of means for converting the relative pivotal movement of the rafts into useable energy has been described, any other suitable means could have been used. For example, instead of using a piston pump in each raft, many piston pumps could have been provided in each raft. Additionally, diaphragm pumps could have been used, or indeed a combination of diaphragm and piston pumps. Needless to say, it will be apparent to those skilled in the art that other suitable means could be used. 53975 Furthermore, it is envisaged that instead of the pumps being connected directly to the semi-submersible bridle Structure, by means of their piston rods, they could be connected through a linkage arrangement to the structure, or adjacent raft.

One such linkage assembly is illustrated in Fig. 3, and it will be appreciated by those skilled in the art that other arrangements could be used.

It is also envisaged that in certain cases, the delivery conduit instead of being routed to the seabed through the semi-submersible bridle structure could have been routed to the seabed through the mooring buoy. Indeed, it will be appreciated by those skilled in the art that any suitable routecould be used for the delivery conduit.

While the damping plate of the bridle structure has been described as a steel plate, any suitable plate could be used, for example, it is envisaged that a damping plate of stainless steel or fibreglass could be used. Indeed, in certain cases the damping plate could contain ballast tanks.

Claims (5)

CLAIMS;

1. A wave powered prime mover comprising at least one wave engaging float pivotally connected to a semisubmersible bridle structure so as to be free to pivot relative thereto and means to convert the pivotal 5 movement of the float into usable energy, the semisubmersible bridle structure comprising a mast supporting the pivot and projecting upwardly from a base member in the form of a damping plate which damps out vertical movements of the bridle structure 10 to retain the pivot axis substantially fixed relative to the mean wave water level.

2. A wave powered prime mover as claimed in Claim 1 in which the pivot axis is defined by a pivot shaft.

3. A wave powered prime mover as claimed in claims 15 1 or 2 in which a flexible mooring member is provided to moor the semi-submersible bridle structure to the sea bed

4. A wave powered prime mover as claimed in claim 1, 2 or 3 and in which there is a pair of the floats, these being provided at opposite sides of the semi-submersible 20 bridle structure. 5. A wave powered prime mover as claimed in Claim .4 in which the floats pivot on a common pivot axis. 6. A wave powered prime mover as claimed in Claims 5 or 6 in which In use the free end of the leading float is moored 5 to a mooring buoy by a flexible mooring member. 7. A wave powered prime mover as claimed in any preceding claim in which the means to convert the pivotal movement of each float is provided by a water pump mounted on a float and operable by a linkage assembly. 10 8. A wave powered prime mover as claimed in Claim 7 in which the water pump delivers sea water to a header tank. 9· A wave powered prime mover as claimed In Claims 7 or 8 in which the linkage assembly is connected between e water pump and the semi-submersible bridle structure. 15 10. A wave powered prime mover as claimed in Claims 7 or 8 in which the linkage assembly is connected between a water pump in one float and the other float. 11. A wave powered prime mover as claimed in any of Claims 7 to 10 in which a water pump is provided in each float. 20 12. A wave powered prime mover as claimed in any of Claims 7 to 11 in which a mast is provided in each float and the 52S75 - 27 linkage assembly Is connected between · water pump in one float and the mast in the other float. 13. A wave powered prime mover as claimed in any preceding claim in which each float is provided by a raft.

5. 14. Wave powered prime movers substantially as described herein with reference to and illustrated in the accompanying drawings.