SYSTEM FOR GENERATING ELECTRICITY WITH TANDEM TOWERS

Abstract

A system for generating electricity using the earth's gravitational field for its motive force includes twin electricity generators. Each electricity generator includes a water tower that is vertically juxtaposed with a linear generator. A shuttle, when dropped from the top of a water tower accelerates for engagement with a linear generator at a constant engagement velocity. An electro-magnetic engagement between the shuttle and the linear generator provides the system's output. Its input is provided by a mechanical drive unit that reciprocatingly manipulates water levels in both of the water towers to drive the system.

Claims

1. A system for generating electricity which comprises: a circular cam drive having an excentric axis of rotation; a piston having opposed fore-and-aft surfaces submerged in a water channel for reciprocating movement therein through a predetermined distance s, wherein the piston is connected with the cam drive for reciprocating movements of the piston responsive to cyclical rotations of the cam drive; a recoil spring interconnected with the piston and with the cam drive, wherein a compression and a decompression of the recoil spring are response to cyclical rotations of the cam drive; and a pair of tandem, hydrodynamic, electricity generators separately connected in fluid communication with opposed surfaces of the piston, wherein during a first-half of each 360 cycle rotation of the cam drive, the piston is moved in a forward direction through the distance s by the cam drive to generate a unit of input work U.sub.i for operating one electricity generator and to also compress the recoil spring, and further wherein during a second-half of the 360 cycle the cam drive allows the recoil spring to decompress and thereby move the piston in a backward direction to generate a subsequent unit of input work U.sub.i for operating the other electricity generator.

2. The system of claim 1 wherein each electricity generator is designed to operate at a preselected output power P.sub.o during successive work cycles of X seconds duration to do a unit of output work U.sub.o every second of a machine work cycle.

3. The system of claim 2 wherein during a first-half work cycle one electricity generator will generate an output work of U.sub.o=(X/2)U.sub.o and, likewise, during a second-half work cycle the other electricity generator will generate an output work total of U.sub.o=(X/2)U.sub.o for a machine generated output U.sub.o(total)=2(X/2)U.sub.o=XU.sub.o during a complete work cycle.

4. The system of claim 3 wherein a unit of input work U.sub.i is the work required to manipulate water levels in a water tower to accommodate the transit of a shuttle through the water tower, and wherein U.sub.i=m.sub.wgH where m.sub.w is the water mass being manipulated, g is gravity and H is the head height of the water tower.

5. The system of claim 4 further comprising at least one shuttle which is positioned by the electricity generator with one input work unit U.sub.i to fall from the top of the water tower and engage with the linear generator to do a unit of output work U.sub.o during every second of its engagement, wherein U.sub.o is based on P.sub.o, and further wherein U.sub.o equals the kinetic energy of the shuttle expressed as m.sub.sv.sub.e.sup.2 where m.sub.s is the shuttle mass and v.sub.e is the constant velocity of the shuttle during shuttle engagement with the linear generator.

6. The system of claim 5 wherein the U.sub.i for a piston movement through the reciprocating distance s and equals m.sub.wgH, and the U.sub.i for recoil spring compression equals sk, where m.sub.wgH=sk, where s is the compression distance of the recoil spring and k is the spring constant.

7. The system of claim 6 wherein one input work unit U.sub.i from the piston drives one electricity generator during a first-half work cycle and the other input work unit U.sub.i from the recoil spring drives the other electricity generator during a second-half work cycle, wherein the input work units U.sub.i are finite, time independent, and additive, for a total input work requirement during an X second machine work cycle of U.sub.i(total)=2U.sub.i.

8. The system of claim 7 wherein the system is self-sustaining with closed loop feedback wherein U.sub.o(net)=U.sub.o(total)U.sub.i(total), for a U.sub.(net)=XU.sub.o2U.sub.i.

9. A method for manufacturing and using a machine to generate electricity which comprises the steps of: providing a pair of identical electricity generators, wherein each electricity generator includes a water tower vertically oriented in a juxtaposed combination with a linear generator; separately connecting opposite ends of a water channel in fluid communication with the water tower of a respective electricity generator; joining the periphery of a piston with a water-tight connection to the water channel at a location inside the water channel between the opposite ends thereof, for a reciprocating movement of the piston back and forth inside the water channel through a predetermined distance s; affixing the piston and a recoil spring to a drive bar; and engaging a cam drive with the drive bar to simultaneously reciprocate the piston in the water channel while exercising the recoil spring to alternatingly compress and decompress outside the water channel.

10. The method of claim 9 wherein each electricity generator is designed to operate at a preselected output power P.sub.o during successive work cycles of X seconds duration to do a unit of output work U.sub.o every second of a machine work cycle.

11. The method of claim 10 further comprising the step of off-setting an axis of rotation for the drive cam from the center of the drive cam by a distance of s/2.

12. The method of claim 11 wherein the electricity generators are sequentially operated with one electricity generator generating an output work of U.sub.o=(X/2)U.sub.o during a first-half work cycle and with the other electricity generator generating an output work of U.sub.o=(X/2)U.sub.o during a second-half work cycle, for a machine generated output U.sub.o(total)=2(X/2)U.sub.o=XU.sub.o during a complete work cycle.

13. The method of claim 12 wherein one input work unit U.sub.i from the piston drives one electricity generator during a first-half work cycle and the other input work unit U.sub.i from the recoil spring drives the other electricity generator during a second-half work cycle, wherein the input work units U.sub.i are finite, time independent, and additive, for a total input work requirement during an X second machine work cycle of U.sub.i(total)=2U.sub.i.

14. The method of claim 13 wherein the total input work U.sub.i(total) required during the first-half cycle includes work based on the potential energy of the water volume to be manipulated and equals U.sub.i=m.sub.wgH where m.sub.w is the water mass being manipulated, g is gravity and H is the head height of the water tower, and wherein U.sub.i(total) also includes the work required to compress the recoil spring which equal sk, where m.sub.wgH=sk, where s is the compression distance of the recoil spring and k is the spring constant, and further wherein U.sub.o(total) is based on the cumulative value of U.sub.o for P.sub.o during an X second work cycle where U.sub.o is valued as the kinetic energy of the shuttle expressed as m.sub.sv.sub.e.sup.2 where m.sub.s is the shuttle mass and v.sub.e is the constant velocity of the shuttle during shuttle engagement with the linear generator.

15. The method of claim 14 wherein the system is self-sustaining with closed loop feedback wherein U.sub.o(net)=U.sub.o(total)U.sub.i(total), for a U.sub.o(total)=XU.sub.o2U.sub.i.

16. A system for generating electricity which comprises: a pair of identical electricity generators, wherein each electricity generator includes a water tower vertically oriented in a juxtaposed combination with a linear generator; a means for reciprocating a piston back and forth inside the water channel through a predetermined distance s to manipulate water levels in the water towers of respective electricity generators to accommodate the transit of a shuttle through the water tower; a means for exercising a recoil spring to alternatingly compress and decompress the recoil spring outside the water channel; a means for simultaneously driving the reciprocating means and the exercising means to do one input work unit U.sub.i from the piston for one electricity generator during a first-half work cycle and to do another input work unit U.sub.i from the compressed recoil spring for the other electricity generator during a second-half work cycle, for a total input work requirement for the pair of electricity generators during an X second machine work cycle of U.sub.i(total)=2U.sub.i; and a means for sequentially operating one electricity generator to generate an output work of U.sub.o=(X/2)U.sub.o during the first-half work cycle and then operating the other electricity generator to generate an output work of U.sub.o=(X/2)U.sub.o during the second-half work cycle, for a machine generated output U.sub.o(total)=2(X/2)U.sub.o=XU.sub.o during a complete work cycle.

17. The system of claim 16 wherein the U.sub.i required to manipulate water levels with the piston equals U.sub.i=m.sub.wgH where m.sub.w is the water mass being manipulated, g is gravity and H is the head height of the water tower, and wherein the U.sub.i required to compress the recoil spring equals sk, where m.sub.wgH=sk, where s is the compression distance of the recoil spring and k is the spring constant.

18. The system of claim 17 wherein U.sub.o(total) is based on the cumulative value of U.sub.o having a preselected power value P.sub.o, and is accrued during the X second work cycle where U.sub.o is valued as the kinetic energy of the shuttle expressed as m.sub.sv.sub.e.sup.2, where m.sub.s is the shuttle mass and v.sub.e is the constant velocity of the shuttle during shuttle engagement with the linear generator.

19. The system of claim 18 wherein the exercising means is a circular drive cam having an axis of rotation off-set from the center of the cam by a distance s/2.

20. The system of claim 19 wherein the system is self-sustaining with closed loop feedback wherein U.sub.o(net)=U.sub.o(total)U.sub.i(total), for a U.sub.o(net)=XU.sub.o2U.sub.i.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The novel features of this invention, as well as the invention itself, both as to its structure and its operation, it will be best understood from the accompanying drawings, taken in conjunction with the accompanying description in which similar reference characters refer to similar parts, and in which:

[0034] FIG. 1 is a perspective view of a machine constructed in accordance with the present invention showing a pair of back-to-back output electricity generators mounted on a hydro-mechanical drive unit;

[0035] FIG. 2 is a schematic diagram of interactive components in the hydro-mechanical drive unit of the present invention;

[0036] FIG. 3 is a cross-sectional view of interactive components of the machine as would be seen along the line 3-3 in FIG. 1;

[0037] FIG. 4 is a top plan view of a cam for actuating the hydro-mechanical drive unit;

[0038] FIG. 5 is a graph of output work units resulting during each complete machine work cycle in a sequence of 360 rotations of the cam;

[0039] FIG. 6A is a free-body diagram of the machine's piston in a steady state condition of dynamic equilibrium;

[0040] FIG. 6B is a presentation of steady state, free-body diagrams for work accomplished by the piston to run both electricity generators of the machine during a 360 rotation of the cam;

[0041] FIG. 7A is a diagram showing the output work of a buoyant shuttle while engaged with a linear generator during a machine work cycle;

[0042] FIG. 7B is a graph showing the output work during a complete work cycle;

[0043] FIG. 8 is a schematic diagram of the control system for coordinating the operation of the machine's functional components;

[0044] FIG. 9 is a schematic diagram showing the temporal influence on shuttle locations, piston movements, and spring deformations during a 360 rotation of an drive cam; and

[0045] FIG. 10 is a schematic diagram showing radial distance changes on the cam during a 360 rotation of the cam during a complete machine work cycle.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0046] Referring initially to FIG. 1, a machine in accordance with the present invention is shown and is generally designated 10. As shown, machine 10 includes both an electricity generator 12 and an electricity generator 14 which are each mounted vertically on top of a hydro-mechanical drive unit 16, where they are arranged in a back-to-back configuration. In this configuration, FIG. 1 shows that the electricity generator 12 and the electricity generator 14 will separately produce a respective output work U.sub.o.

[0047] FIG. 2 shows hydro-mechanical drive unit 16 is driven by a mechanical cam drive 18 which is connected to a controller 20 inside the hydro-mechanical drive unit 16. Further, controller 20 is shown electronically connected to a force drive 22, and to both a valving system 24 in the electricity generator 12 and a valving system 26 in the electricity generator 14. Specifically, the valving system 24 provides an hydraulic interface between the force drive 22 and the electricity generator 12 for operating the electricity generator 12. Similarly, the valving system 26 provides an hydraulic interface between the force drive 22 and the electricity generator 14 for operating the electricity generator 14.

[0048] FIG. 3 shows that the electricity generator 12 includes a water tower 28 that is vertically aligned parallel to a linear generator 30. Electricity generator 12 also has a pivot mechanism 32 which is located between the top of water tower 28 and the top of the linear generator 30. The specific purpose of the pivot mechanism 32 is to direct a buoyant shuttle 34 as it breaches from the water tower 28 onto a path between the water tower 36 and the linear generator 30, for travel downwardly toward the hydro-mechanical drive unit 16. During this downward travel the buoyant shuttle 34 engages with the linear generator 30 to generate the output U.sub.o.

[0049] Similarly, FIG. 3 also shows that the electricity generator 14 likewise includes a water tower 36 that is vertically aligned parallel to a linear generator 38 and, like the electricity generator 12, it also has a pivot mechanism 40. The purpose here of the pivot mechanism 40 is to direct a buoyant shuttle 42 as it breaches from the water tower 36 onto a path between the water tower 36 and the linear generator 38, for travel downwardly toward the hydro-mechanical drive unit 16. During this downward travel the buoyant shuttle 42 engages with the linear generator 38 to generate another output U.sub.o.

[0050] Still referring to FIG. 3, it will be appreciated that the electricity generator 12 includes a transfer tank 44 which is part of the hydro-mechanical unit 16. More specifically, the transfer tank 44 extends between a partition 46 and a piston 48. Likewise, the electricity generator 14 includes a transfer tank 50 which is also part of the hydro-mechanical unit 16. This transfer tank 50 also extends between the partition 46 and the piston 48. In this combination, the electricity generator 12 and the electricity generator 14 are hydraulically separated from each other. Nevertheless, they are hydraulically interactive with each other via an operation of the piston 48.

[0051] As shown in FIG. 4, a preferred embodiment of the cam drive 18 is a circular shaped disk with an eccentric axis of rotation 52. In detail, the axis of rotation 52 is offset from the center 53 of the cam drive 18 by a distance s/2. Accordingly, the radial distance r from the axis of rotation 52 to the periphery 54 of cam drive 18 increases as a rotation angle increases from 0 to 180. Specifically, the radial distance increases from r to r+s through the arc from 0 to 180, and it decreases from r+s back to r through the arc from 180 to 360.

[0052] It is noted here that the increment s which increases the radial distance r, is the same as the reciprocating distance s that is traveled by the piston 48 (i.e. to-and-fro) during a machine work cycle. Specifically, this movement of piston 48 is required to produce an input work unit U.sub.i during a first-half work cycle which maintains operational water levels in the water tower 28 and the transfer tank 44 of electricity generator 12. Further, the increase of s to the radial distance r, is same as the spring compression distance (i.e. spring deformation) distance s of the recoil spring 56 which is required to store an input work unit U.sub.i during the first-half work cycle. This stored input work unit U.sub.i is then subsequently used during the second-half work cycle to maintain operational water levels in the water tower 36 and the transfer tank 50 of electricity generator 14.

[0053] FIG. 5 shows a comparison of input work units U.sub.i generated during comparable work cycles for electricity generator 12 and electricity generator 14. In FIG. 5, changes in U.sub.i for electricity generator 12 are shown as a solid line, and changes in U.sub.i for electricity generator 14 are shown as a dashed line. Further, these changes in U.sub.i are shown horizontally relative to a 360 rotation of the cam drive 18 and vertically relative to a movement of the piston 48 through a distance s. A comparison of the work units U.sub.i for a 360 work cycle is thus illustrative of the operational compatibility of the electricity machines 12/14.

[0054] For comparison of input work units U.sub.i for the electricity machines 12/14, specifically consider a complete work cycle caused by a rotation of the cam drive 18 from =0 to 360. In the first-half work cycle, from =0 to 180, the electricity generator 12 is in a power mode wherein two input work units 2U.sub.i are required from the cam drive 18. Specifically, one U.sub.i is required to move the piston 48 and the other U.sub.i is required to compress the recoil spring 56, to thereby store a work unit U.sub.i. Simultaneously, during this first-half cycle, electricity generator 14 is in its reset mode.

[0055] In the second-half work cycle, as cam drive 18 rotates from =180 to 360, the electricity generator 12 is in its reset mode. While electricity generator 12 is resetting, the input work unit U.sub.i which has been stored in the compressed recoil spring 56 is provided to drive the piston 48 in the opposite direction. Specifically, the recoil spring 56 extends through the distance s and releases the stored input work unit U.sub.i to thereby operate the electricity generator 14.

[0056] In detail, a similar analysis for an operation of the electricity generator 14 of machine 18 during a complete 360 work cycle has the same result as for the electricity machine 12, but with different force applications. Specifically, during a rotation of the cam drive 18 through =180-360, as the electricity generator 12 is resetting, the electricity generator 14 will use the stored input work U.sub.i=sk from the compressed recoil spring 56 as a recoil force to move the piston 48 in the opposite direction back to its start point. Note: the recoil force also maintains a mechanical contact between the piston 48 and the rotating cam drive 18 which can be engineered into the recoil force by selecting an appropriate spring constant k.

[0057] FIGS. 6A and 6B together provide a montage of free-body diagrams depicting forces on the piston 48 that are caused either by the cam drive 18 or by the recoil spring 56. First, in FIG. 6A a steady state depiction of the piston 48 indicates that throughout a 360 machine work cycle, the piston 48 is always subject to the opposing effect of hydraulic forces m.sub.wgH from water in the electricity generator 12 and from water in the electricity generator 14. In FIG. 6B, it is shown that during a first-half work cycle, when is in the arc 0-180, the drive force required from the cam drive 18 to lift water in the electricity generator 12, which equals m.sub.wgH, is joined with a recoil force sk from the recoil spring 56. Thus, the force exerted against the piston 48 in its first-half work cycle is two-fold, i.e. m.sub.wgH+sk.

[0058] During the second-half work cycle of the electricity generator 12, when is in the arc 180-360, the electricity generator 12 resets. Meanwhile, during this second-half work cycle of the electricity generator 12, the electricity generator 14 is in its comparable first-half work cycle. Thus, as shown in FIG. 6B, the force sk, which is stored in the recoil spring 56 is both stored and released by the recoil spring 56 during each complete work cycle as the angle transits a 360 arc around the periphery of the drive cam 18.

[0059] During a complete 360 cycle, when is in the arc 180-360, the piston 48 changes its direction of travel. The force of magnitude sk from recoil spring 56 then acts to move the piston 48 as the recoil spring 56 decompresses to thereby use the stored unit of input work U.sub.i. This time, however, the work U.sub.i operates the electricity generator 14.

[0060] In review, when considering the joint operation of the electricity generators 12/14, the total output work generated by a machine 10, i.e. U.sub.o(total), during each work cycle is best described by the physics involved, namely, the kinetic energy of a shuttle 34 and the power values of each work cycle. In this context, the work/energy relationship shows an operation of the present invention relies on the fact that the work performed by a dynamic object (U=Fsds) has the capacity to do this work expressed by the object's kinetic energy (KE=m.sub.sv.sub.e.sup.2+C). Moreover, the output power, P.sub.o, of a machine 10 (P.sub.o=U.sub.o/sec) is commercially pre-selected. Thus, in a steady state analysis P.sub.o will have a given value. Accordingly, U.sub.o can be equated with the pre-selected value of P.sub.o. Moreover, from the work energy relationship it is known that U.sub.o=mv.sup.2. Thereafter, based on P.sub.o e.g. U.sub.o, the only remaining variables that need to be arbitrarily established for a design of the machine 10 are s, the distance of travel for piston 48 and the engagement velocity v.sub.e of the shuttle 34. With one expression and two variables, one variable needs to be guesstimated.

[0061] In accordance with the present invention, designing a machine 10 begins with the selection of a desired output power P.sub.o. Based on P.sub.o, consideration is given to the variables s for piston travel (i.e. spring deformation distance) and v.sub.e for the shuttle engagement velocity. Although both s and v.sub.e are variables, it is the velocity v.sub.e that is directly related to the length L.sub.e of the linear generator 30. Consequently, because v.sub.e=L.sub.e/t.sub.e, where the is the time duration of engagement between the shuttle 34 and the linear generator 30, the velocity v.sub.e is an important factor for joint consideration with the length L.sub.e of the linear generator 30.

[0062] As envisioned for the present invention, a free fall distance L.sub.f from a start point above the linear generator 30 must be added to L.sub.e. Specifically, L.sub.f is needed for shuttle 34 to accelerate to its engagement velocity v.sub.e for engagement with a linear generator 30/38. Further, the combined length L.sub.e+L.sub.f, must necessarily be less than the water tower head height H that is needed to raise the shuttle 34 to the start point.

[0063] Insofar as the design of a shuttle 34 is concerned, consider the kinetic energy required for the shuttle 34 to provide an output work, U.sub.o=m.sub.sv.sub.e.sup.2. Also consider, that the shuttle mass m.sub.s establishes the shuttle weight W.sub.s, i.e. m.sub.s=W.sub.s/g. It has also been shown above that U.sub.o/sec=P.sub.o. Therefore, by pre-selecting a desired engagement velocity v.sub.e the values for U.sub.o can be used to solve for W.sub.s.

[0064] FIG. 7A shows that on a per-second basis, a shuttle weighing W.sub.s travelling at the velocity v.sub.e will travel a length h along the linear generator 30 every second, and will generate one unit of output work U.sub.o which equals W.sub.sh. Also, as disclosed above, during an X second work cycle, the total work output generated is U.sub.o(total)=XU.sub.o. Furthermore, FIG. 7B illustrates this result during a complete machine work cycle of =0-360, where it is shown that the combined total output work generated U.sub.o(total) by both the electricity generator 12 and the electricity generator 14 is XU.sub.o.

[0065] FIG. 8 illustrates how the controller 20 provides for a combined operation of the electricity generators 12 and 14 during a complete machine work cycle =0-360. For disclosure purposes only, the description of this combined operation is limited here to considerations of the work that is accomplished by the reciprocal back-and-forth movements of the piston 48. This requires specific considerations of the valving system 24 of electricity generator 12, and the valving system 26 of electricity generator 14.

[0066] In FIG. 8, the valving system 24 is shown as a combination of the valves 58 and 60, Similarly, the valving system 26 is shown as a combination of the valves 62 and 64. Operationally, the respective valves are shown as darkened circles when closed, and open circles when opened.

[0067] To appreciate an operation of the machine 10, first consider the electricity generator 12 separately. In the first-half work cycle for the electricity generator 12, where =0-180, valve 58 is closed and valve 60 is opened. With this configuration two different operations occur. For one, valve 58 has closed behind shuttle 34 as the shuttle 34 transits through the transfer tank 44 while the valve 60 is opened to provide an exit for the shuttle 34 from the transfer tank 44. For another, with valves 58/60 in this configuration the piston 48 is moved through a distance s in the direction indicated by arrow 66 to displace a predetermined volume of water from the transfer tank 44 into the water tower 28 of electricity generator 12 via the open valve 60.

[0068] In the second-half work cycle for the electricity generator 12, where =180-360, the valve 58 has been opened and valve 60 is has been closed. With this valve configuration, the piston 48 is returned through the distance s in the direction of arrow 68 to the work cycle start point where s=0. This piston movement draws the previously displaced volume of water back from water tower 28 and returns it into the transfer tank 44 of electricity generator 12. This piston movement also resets the electricity generator 12 for the next machine work cycle.

[0069] Regarding electricity generator 14, FIG. 8, also shows that successive operations of the electricity generator 12/14 follow each other in their respective =180 half work cycles. Stated differently, the electricity generators 12/14 alternately mimic each other during the complete =0-360 machine work cycle.

[0070] FIG. 9 presents the temporal relationships between respective locations of representative shuttles 34/42 of the electricity generators 12/14, which result from movements of the piston 48, and deformations of the recoil spring 56. For this purpose, the times t.sub.1 and t.sub.2 have been selected for identifying specific locations of the shuttles 34/42 during the machine work cycle =0-360. Note: the times t.sub.1 and t.sub.2 for shuttle 42 reference the same times t.sub.1 and t.sub.2 for shuttle 34, but at different locations in their respective work cycles. Also note: the times t.sub.1 and t.sub.2 also occur within work cycles having a same time duration.

[0071] As disclosed above, during each =0-360 work cycle, the piston 48 is moved cyclically back-and-forth through the distance s. For this operation, the periphery of piston 48 is internally affixed to a bellows 70 which allow the piston 48 to be reciprocated. Simultaneously, as the piston 48 is being cycled, the recoil spring 56 is compressed through a distance s during a half-cycle, and it is decompressed through a same distance s during the subsequent half-cycle. Mechanically, the cyclical operations of the piston 48 and of the recoil spring 56 result from their structural connections with the cam drive 18.

[0072] Structurally, a drive rod 72 and an extension 74 from the drive rod 72 together establish a connecting structure for driving the piston 48 and the recoil spring 56. In detail, during a first half-cycle, while the drive rod 72 is being drive by the cam drive 18 to compress the recoil spring 56 the extension 74 which connects with drive rod 72 moves the piston 48 in one direction in the transfer tank 50. During the second half-cycle, the recoil spring 56 moves the piston 48 in the opposite direction in the transfer tank 50, as the recoil spring 56 decompresses.

[0073] FIG. 10 shows a configuration for an alternate embodiment of the cam drive 18 in which the periphery of the cam drive 18 is slightly modified as the angle progresses through a 360 machine work cycle. For reference purposes, the times t.sub.1 and t.sub.2 which were used above in FIG. 9 to identify specific locations of the shuttles 34/42 are associated here with the angle during a 360 machine work cycle to provide an operational perspective of the machine 10, relative to a rotation of the cam drive 18.

[0074] In FIG. 10, the point on the periphery of cam drive 18, where =0, is selected as a peripheral reference point 76. Beginning at reference point 76, consider a rotation of the cam drive 18 as it is rotated about a center of rotation 78 in a counterclockwise direction at an angular velocity . For this alternate embodiment, at =0, the radial distance from the center of rotation 78 to the reference point 76 has a value equal to r. As cam drive 18 begins its rotation through an initial arc length (t.sub.1)=0-5, which corresponds with time t.sub.1, r can remain constant while needed operational time adjustments for components of the machine 10 can be made. Thereafter, as continues to increase from 5 to 180 the radial distance from the center of rotation 78 to the periphery of the cam drive 18 is increased to r+s. As considered here, s is the spring compression distance for the recoil spring 56 as well as the distance moved by the piston 48.

[0075] When =180 the radial distance from the center of rotation 78 to the reference point 76 has a value equal to r+s. As cam drive 18 continues its rotation e.g. (t.sub.2)=180-185, r+s can remain constant while the needed operational time adjustments noted above are made. Thereafter, as continues to increase from 185 to 360/0, the radial distance from the center of rotation 78 to the periphery of the cam drive 18 decreases from r+s back to r as the recoil spring 56 decompresses.

[0076] In summary, during each complete work cycle of a machine 10, two units of input work, 2U.sub.i, are simultaneously required from the piston 48. Both, however, are required during the first half-cycle of the machine's operation. One work unit U.sub.i has a value m.sub.wgH, which is the work required to manipulate respective water levels in the electricity generator 12. The other U.sub.i is required to compress the recoil spring 34 as the piston 48 moves through a distance s. The value of this input work is U.sub.i=sk. Meanwhile, during the first half cycle of the machine's operation, electricity generator 14 is being reset. In the second half-work cycle these respective operations are reversed. The result is that during a complete, 360 rotation of the cam drive 18, in an X second work cycle, the machine will generate a total output equal to XU.sub.o. Ergo:

U.sub.o(net)=XU.sub.o2U.sub.i

[0077] A detailed step-by-step disclosure for an operation of the machine 10 is presented below.

Notations

[0078] B is the shuttle buoyancy factor; [0079] g is gravity; [0080] H is the head height for water in the water tower of the machine; [0081] k is a spring constant; [0082] L.sub.e is the linear generator length that engages with a shuttle; [0083] L.sub.f is the shuttle free fall distance required to achieve an engagement velocity v.sub.e with the linear generator; [0084] m.sub.s is the shuttle mass; [0085] m.sub.w is the water mass having a same volume as the shuttle; [0086] P.sub.o is a commercial output power rating for a machine; [0087] r is a radial distance on the cam drive; [0088] s is the one-way distance of piston reciprocation and spring deformation; [0089] t.sub.e is the number of seconds of shuttle engagement with a linear generator in a U.sub.o time interval; [0090] U.sub.i is the input work required to raise a volume of water of mass m.sub.w during a piston reciprocation; [0091] U.sub.i(total) is equal to U.sub.i; [0092] U.sub.o is the output work accomplished during a predetermined time interval (e.g. one second based on P.sub.o); [0093] U.sub.o(total) is the total output work accomplished during one piston reciprocation; [0094] v.sub.e is the constant velocity for shuttle engagement with the linear generator; [0095] W.sub.s is the shuttle weight; [0096] W.sub.w is the weight of water in a volume equal to the shuttle volume; [0097] X is the number per second time intervals needed to accomplish U.sub.o(total); [0098] is the rotation angle of the cam drive; and [0099] is angular velocity.

Step-by-Step Process

[0100] Step 1: Pre-select a power value P.sub.o for the output work U.sub.o/sec that is to be generated separately by each electricity generator of the machine. [0101] Step 2: Pre-select values for the dimensions and operational characteristics for specific components of the machine. Be reasonable. These include B, L.sub.e, v.sub.e, and X; where X=L.sub.e/v.sub.e. [0102] Step 3: Calculate a shuttle weight W.sub.s using the equation P.sub.o=m.sub.sv.sub.e.sup.2/sec where m.sub.s=W.sub.s/g. [0103] Step 4: Determine W.sub.w=W.sub.s/B. [0104] Step 5: Calculate L.sub.f where L.sub.f=v.sub.e.sup.2/2g. [0105] Step 6: Build a water tank consisting of a transfer tank and a water tower mounted vertically on the transfer tank. [0106] Step 7: Create a mechanical drive unit including a piston plate, a recoil spring, and a cam drive. [0107] Step 8: Manufacture a circular cam drive with an axis of rotation which is offset from the cam center by a distance s/2. [0108] Step 9: Select a spring constant k for the recoil spring. [0109] Step 10 Connect the cam drive with the recoil spring, and with the piston plate, for a simultaneous reciprocal motion of the recoil spring and the piston plate through a distance s in response to a rotation of the cam drive. [0110] Step 11: Calculate the same U.sub.i for each electricity generator, where U.sub.i=W.sub.wH=sk, and where H=L.sub.e+L.sub.f. [0111] Step 12: Transform U.sub.i into a per-second value (i.e. U.sub.i/(X/2)) for compatible comparisons with P.sub.o and U.sub.o/sec. [0112] Step 13: Determine a finite value for U.sub.i(total)=U.sub.i+sk where U.sub.i=sk and U.sub.i(total)=2U.sub.i. [0113] Step 14: Establish a work ratio U.sub.i/U.sub.o=W.sub.wH/W.sub.sL.sub.e=Z where U.sub.i=ZU.sub.o. [0114] Step 15: Evaluate U.sub.(net) for an X second work cycle where U.sub.(net)=U.sub.o(total)U.sub.i(total). [0115] Step 16: Solve: U.sub.(net)=XU.sub.o2U.sub.i or, =XU.sub.o2(ZU.sub.o).

[0116] Mathematical calculations for a 100 kW machine which is constructed in accordance with the present invention are provided below to indicate the machine's potential commercial value. These calculations are only exemplary, and are provided primarily to emphasize the design capabilities of a machine, based on an initial commercial objective.

Mathematical Calculations

[0117] In the calculations presented below, the total input work U.sub.i(total) is based on the potential energy of a water volume being raised. It equals m.sub.wgH. The total output work U.sub.o(total) is valued on the preselected output power P.sub.o for the machine and is based on the kinetic energy of a shuttle during a machine work cycle of X seconds duration. It equals X(m.sub.sv.sub.e.sup.2). As shown below, the net result is:

U.sub.(net)=U.sub.o(total)U.sub.i(total)

[0118] For a 100 kW machine, calculations for operational components of the machine are provided below.

P.sub.o=U.sub.o/sec=100 kW=73,756 ft-lbs/sec [0119] Note: P.sub.o is pre-selected and is the basis of all design calculations.

B=0.7 shuttle buoyancy factor (pre-selected)

L.sub.e=300 ft (pre-selected)

v.sub.e=50 ft/sec (pre-selected)

L.sub.f=v.sub.e.sup.2/2g=(50)2/(2[32.2])=38.82 ft

X=L.sub.e/v.sub.e=seconds per cycle=(300 ft)/(50 ft/sec)=6 seconds

W.sub.s=U.sub.o(2g)/v.sub.e.sup.2=(73,756 ft-lb [64.4 ft/sec2])/(33.3 ft/sec)2=1,900 lbs:

W.sub.w=W.sub.s/B=1,900/0.7=2,715 lbs

U.sub.o=73,756 ft-lbs

U.sub.o(total)=2XU.sub.o/cycle=(12)(73,756 ft-lbs)=885,072 ft-lbs [0120] Note: Tandem generator outputs are cumulative for each X seconds cycle.

U.sub.i=W.sub.w(L.sub.e+L.sub.f)/X=(2,715 lbs)(300+38.82 ft)/6=153,036 ft-lbs [0121] Note: U.sub.i/sec (153,036 ft-lbs) and U.sub.o/sec (73,756 ft-lb/sec), are pertinent for each individual electricity generator. They are considered here in a steady state analysis (i.e. per second) to be compatible with P.sub.o=100 kW. Also note: U.sub.i/sec=U.sub.i(total)/cycle because, unlike U.sub.o, U.sub.i is not cumulative and assumes L.sub.e+L.sub.f=H.

U.sub.i(total)=U.sub.i+sk=2U.sub.i=306,072 ft-lbs per cycle [0122] Note: sk equals the spring compression which generates U.sub.i for the second electricity generator. As a piston reset force, sk is considered negligible.

U.sub.o(net)=U.sub.o(total)U.sub.i(total)=885,072/cycle306,072/cycle=579,000 ft-lb/cycle

[0123] While the system and method for generating electricity with tandem towers as herein shown and disclosed in detail is fully capable of obtaining the object and providing the advantages herein before state, it is to be understood that it is merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended to the details of construction or design herein shown other than as described in the appended claims.