METHODOLOGY FOR DESIGNING A TANDEM TOWER MACHINE FOR GENERATING ELECTRICITY

Abstract

A methodology for designing a machine to generate electricity using the forces of gravity and buoyancy is provided which generates an output sufficient to sustain the machine's operation and provide a remainder amount of electricity for commercial purposes. The machine has two independent electricity generating units. Output work, U.sub.o, for each generating unit is based on the kinetic energy of a buoyant shuttle falling under the influence of gravity, and each unit's input requirement, U.sub.i is based on the work required to manipulate a volume of water during shuttle transit through water tanks of the machine. The methodology is based on a pre-selected output power P.sub.o which is used to establish machine component configurations. The shuttle's kinetic energy is then compared to U.sub.i to evaluate the machine's operational efficiency.

Claims

1. A method for designing a machine to generate electricity using motive forces from the earth's gravitational field, wherein the machine includes tandem electricity generating units, wherein the electricity generating unit has a water tower mounted vertically above a transfer tank for fluid communication therewith, and wherein the water tower is juxtaposed with a vertically aligned linear generator above the transfer tank to create the electricity generating unit, and further the machine has a mechanism positioned in the transfer tank for manipulating water levels in the water tower to return a buoyant shuttle to an elevated start point where it is dropped into engagement with the linear generator to operate the electricity generating unit, wherein the method comprises the steps of: specifying values for a plurality of individual design factors needed to construct the machine; calculating values for the design factors values to establish structural characteristics and operational attributes of components for the machine; evaluating an interaction of the machine's operational components for optimizing values of the selected design factors to achieve a desired machine performance; and preparing a protocol for designing a machine, wherein the protocol incorporates the optimized design factors.

2. The method of claim 1 wherein the design factors for an electricity generating unit are selected from the group consisting of: an output power P.sub.o for each electricity generating unit of the machine; a constant velocity v.sub.e for the engagement of each shuttle with its respective linear generator; a length L.sub.e for the linear generator; and a buoyancy factor B for the shuttle, where B is the ratio of the shuttle weight to the weight of an equivalent water volume displaced when the shuttle is submerged.

3. The method of claim 2 further comprising the steps of: mathematically determining a shuttle weight W.sub.s based on the equivalence of a selected output power P.sub.o, and the steady state kinetic energy KE of the shuttle at the velocity v.sub.e during shuttle engagement with the linear generator; selecting a head height H for the water tower; establishing a shuttle free-fall distance L.sub.f needed for the shuttle to accelerate to its constant engagement velocity v.sub.e; calculating a weight W.sub.w for a water volume equal to the shuttle volume where W.sub.w=W.sub.s/B; calculating an input work requirement U.sub.i for operating each electricity generator of the machine, where U.sub.i=W.sub.wH; and calculating an output work U.sub.o generated by a single water tower, where U.sub.o is based on kinetic energy of the shuttle and the output power P.sub.o expressed as U.sub.o/sec=(W.sub.s/g)v.sub.e.sup.2/sec.

4. The method of claim 3 wherein H is greater than L.sub.f+L.sub.e.

5. The method of claim 4 wherein each electricity generating unit has a work cycle which comprises; a work output-time component of X seconds duration where the shuttle is engaged with the linear generator; a transit-time component of Y seconds duration which begins when the shuttle disengages from the linear generator to transit through the transfer tank, and ends when the shuttle enters the water tower from the transfer tank; and a shuttle reset-time component of Z seconds duration where the shuttle rises in the water tower to a start point for the next machine work cycle.

6. The method of claim 5 wherein machine performance for two electricity generating units is measured by comparing U.sub.o(total) with U.sub.i(total), where U.sub.o(total) equals 2X(U.sub.o/sec), and U.sub.i(total) equals 2Z(U.sub.i(sec)/Z)=2U.sub.i.

7. The method of claim 6 wherein Y is greater than X, and Z is greater than Y.

8. The method of claim 3 wherein the machine comprises a first electricity generating unit and a second electricity generating unit with a water channel having a first end connected in fluid communication with the water tower of the first electricity generating unit and a second end connected in fluid communication with the water tower of the second electricity generating unit and a piston positioned for reciprocal movements in the water channel to operate the first electricity generating unit during the first-half of a machine cycle, and to operate the second electricity generating unit during a second-half of the machine cycle, wherein the method further comprises the steps of: applying a force against the piston at the beginning of the machine cycle to move the piston to the left through a distance s to do an amount of input work equal to 2U.sub.i during the first-half machine cycle, wherein a first U.sub.i(mgH)=W.sub.wH is used to operate the first electricity generating unit and a second U.sub.i(sk) is stored by simultaneously compressing a recoil spring connected to the piston, wherein k is a spring constant and the second U.sub.i(sk)=sk; and allowing the piston to move to the right during the second-half work cycle to decompress the spring and use the stored U.sub.i(sk) to operate the second electricity generating unit.

9. The method of claim 8 further comprising the steps of: establishing a time duration for the machine cycle equal to X seconds; and sustaining the operation of the machine by taking feedback from the machine output for a net output U.sub.(net)=2X(U.sub.o/sec)2U.sub.i.

10. A machine for generating electricity using motive forces from the earth's gravitational field, wherein the machine sequentially drives two electricity generating units, and wherein each electricity driving unit comprises: a transfer tank; a water tower mounted vertically above and on the transfer tank for fluid communication therewith; a linear generator mounted on the transfer tank, wherein the linear generator is juxtaposed in vertical alignment with the water tower; a buoyant shuttle; and a conduit connecting the electricity generating unit with a pumping mechanism to reciprocally manipulate water levels in the water tower to return a buoyant shuttle to an elevated start point after the shuttle has been dropped for engagement with the linear generator at a constant engagement velocity under the influence of gravity to operate the electricity generating unit.

11. A machine as recited in claim 10 wherein the pumping mechanism comprises: a cam drive; a means for rotating the cam drive about an eccentric axis of rotation at a predetermined angular velocity , wherein each 360 rotation of the cam drive defines a machine work/energy cycle; a drive rod engaged with the cam drive, wherein the drive rod is moved in response to a rotation of the cam drive in a back and forth movement through a predetermined distance s in X seconds each way, during a 2X seconds work/energy machine cycle; and a piston plate having a first side and a second side, wherein the piston plate is attached to the drive rod for reciprocating movement to alternatingly operate a first electricity generating unit in X seconds, and a second electricity generating unit in X seconds, during a 2X seconds machine cycle.

12. A machine as recited in claim 11 wherein the first electricity generating unit is mounted on the transfer tank and the second electricity generating unit is juxtaposed and vertically aligned with the first electricity generating unit, and wherein the water tower of each electricity generating unit is individually connected in fluid communication with a respective side of the piston plate, and further wherein the machine further comprises: a recoil spring engaged with the drive rod, wherein the recoil spring has a spring constant k and is compressed by the drive rod to store work/energy, U.sub.i(sk)=sk, while simultaneously the piston plate is being moved during the first-half work cycle to expend an active work/energy U.sub.i(mgH) to operate the first electricity generating unit, and further wherein subsequently, U.sub.i(sk) in the recoil spring is expended during a second-half work cycle to operate the second electricity generating unit.

13. A machine as recited in claim 12 wherein U.sub.i(mgH) and U.sub.i(sk) are equal and U.sub.i(total)=U.sub.i(mgH)+U.sub.i(sk)=2U.

14. A machine as recited in claim 13 wherein U.sub.o equals the per second value of the kinetic energy of a shuttle, U.sub.o/sec=(W.sub.s/g)v.sub.e.sup.2/sec where W.sub.s is the shuttle weight and v.sub.e is the engagement velocity of the shuttle with the linear generator.

15. A machine as recited in claim 14 wherein an input work U.sub.i is required to operate each electricity generator and equals the weight of water W.sub.w to be lifted during half the 2X second machine cycle times the head height H of water in the respective water tower, where U.sub.i=U.sub.(sk)=U.sub.i(mgH).

16. A machine as recited in claim 15 further comprising a feedback loop which removes a work value equal to 2U.sub.i from U.sub.o(total) for use in operating the machine, to provide a net output work of value U.sub.(net)=2XU.sub.o2U.sub.i wherein X>U.sub.i/U.sub.o.

17. A protocol for designing a machine to generate electricity using motive forces from the earth's gravitational field, where the machine operates by dropping a buoyant shuttle from an elevated start point under the influence of gravity into engagement with a linear generator for converting the kinetic energy of the falling shuttle into electricity, and for returning the shuttle to the start point via a water tower under the influence of the buoyancy force on the shuttle, wherein the protocol comprises the steps of: picking an output power P.sub.o for the machine; selecting design factor values, based on P.sub.o, for mass and velocity elements of the kinetic energy expression in the work-energy relationship needed to construct the machine; calculating structural characteristics and operational attributes for the machine using design factor values; evaluating calculations of the design factors to determine machine performance; and revising selected design factor values to optimize machine performance.

18. The protocol of claim 17 wherein the selected design factor values comprise: B, a shuttle buoyancy factor; L.sub.e, a length for the linear generator; v.sub.e, a steady state engagement velocity of the shuttle with the linear generator; and U.sub.o, an output work value where U.sub.o/sec=P.sub.o.

19. The protocol of claim 18 wherein calculations for physical characteristics and operational attributes of the machine involve determining values for machine variables which comprise: W.sub.s a shuttle weight wherein W.sub.s=2gU.sub.o/v.sub.e.sup.2; W.sub.w=a water volume weight where W.sub.w=W.sub.s/B; X=time duration shuttle is engagement with the linear generator, where X=L.sub.e/v.sub.e; Y=time duration from shuttle/linear generator separation to water tower entry; L.sub.f=a free-fall distance for shuttle to attain v.sub.e, where L.sub.f=v.sub.e.sup.2/2g; H=a water tower head height, where H=L.sub.e+L.sub.f; U.sub.o=W.sub.sL.sub.e; U.sub.i=W.sub.wH; U.sub.(net) is the net output work (twin towers) where, U.sub.net)=U.sub.o(total)U.sub.i(total)=2XU.sub.o2U.sub.i; and sk=U.sub.i.

20. The protocol of claim 19 wherein calculation results from claim 19 are evaluated within constraints which comprise: X is greater than U.sub.o/U.sub.i; and Y is greater than X.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The novel features of this invention, as well as the invention itself, both as to its structure and its operation, 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:

[0021] FIG. 1 is a perspective view of an electricity generating machine in accordance with the present invention;

[0022] FIG. 2 is a cross section view of the machine as seen along the line 2-2 in FIG. 1;

[0023] FIG. 3 is a plan view of the drive cam of the present invention;

[0024] FIG. 4 is a presentation of mechanical parts in the hydro-mechanical electricity generating unit of the machine which provide the input work needed to run the machine;

[0025] FIG. 5 includes free body diagrams showing the change in forces acting on the piston and the recoil spring that provide the input power during a machine work cycle;

[0026] FIG. 6 is a diagram showing time zone components of a machine work cycle;

[0027] FIG. 7 is a presentation of output power segments along a linear generator relating to the distances traveled by a shuttle while engaged with the linear generator during a machine work cycle; and

[0028] FIG. 8 is a protocol presentation of steps in a methodology for empirically designing a machine in accordance with the present invention.

THEORETICAL OVERVIEW OF THE INVENTION

[0029] An appreciation of the definitions and mathematical expressions upon which the design of a machine are based is essential for an understanding its structure and its operation. Specifically, basic definitions for the terms WORK, POWER, and ENERGY are indispensable for this purpose. The definitions presented below are excerpted from the Dictionary of Science and Technology, Academic Press, 1992.

[0030] WORK, U, is defined as a force, F, times a distance, s. Work is mathematically expressed in units of ft-lbs; where U=.sub.sFds.

[0031] POWER, P, is defined as the time rate of doing work. It is mathematically expressed in units of work per unit time, ft-lbs/sec; P=U/sec.

[0032] ENERGY, E, is defined as the capacity to do work. E is simply expressed in units of ft-lbs.

[0033] Potential Energy, PE is the energy of position.

[0034] Kinetic Energy KE is the energy of motion.

[0035] It is noteworthy that in the above definitions, only Power P directly requires the consideration of time. Work U and Energy E, however, are influenced by time. In the work-energy relationship which is based on Newton's Second Law of motion, F=ma, the notion of time is introduced with the consideration of an object's acceleration a. Thus, In the context of the present invention, the shuttle mass, m.sub.s does work, U, with a force F=m.sub.sg as it falls under the influence of gravity g while engaged with a linear generator.

[0036] As indicated above, work is mathematically expressed as U=.sub.sFds. Thus, because the shuttle mass m.sub.s is related to the shuttle weight by the expression m.sub.s=w.sub.s/g, the force F can be expressed as F=(w.sub.s/g)a. Furthermore, acceleration a is mathematically expressed as a change in velocity per unit time, a=dv/dt. And, velocity v is expressed as a change in distance per unit time, v=ds/dt. In the context of the present invention, the engagement velocity, v.sub.e, of the shuttle with the linear is held constant. Nevertheless, the force of gravity continues acting to accelerate the shuttle. The linear generator, however, restrains acceleration of an engaged shuttle, and the work to do this is harvested from the linear generator as the machine's output. Mathematically, for the work-energy relationship:

[00002]$\begin{array}{c}U={}_s\mathrm{Fds}={}_s\left(m_{s}a\right)\mathrm{ds}={}_s\left(m_s\right)\left(\mathrm{dv}.Math.\mathrm{dt}\right)\mathrm{ds}={}_s\left(m_s\right)\left(\mathrm{ds}/\mathrm{dt}\right)\mathrm{dv}={}_s{m}_s\mathrm{vdv}=1/2m_s{v}^2\\ U={}_s\mathrm{Fds}=1/2m_s{v}_e^2\end{array}$

[0037] For the design of a machine, values for physical components and operational factors of the machine must be selected to achieve an optimal performance efficiency. The selection of these values, and their resultant operational consequences are crucial considerations in the design of a machine.

DESCRIPTION OF PREFERRED EMBODIMENTS

Pre-Selected Variables

[0038] P.sub.o: machine output power, U.sub.o/sec, expressed in ft-lbs/sec. [0039] B: shuttle buoyancy factor. [0040] L.sub.e: length of the linear generator. [0041] v.sub.e: constant velocity for shuttle engagement with the linear generator.

Calculated Variables

[0042] U.sub.o/sec=output work value based on KE, where U.sub.o=mv.sup.2=(W.sub.s/g)v.sub.e.sup.2 [use to solve for W.sub.s]. [0043] W.sub.s: shuttle weight, W.sub.s=2gU.sub.o/v.sub.e.sup.2. [0044] L.sub.f: shuttle acceleration free fall distance to attain v.sub.e, L.sub.f=v.sub.e.sup.2/2g. [0045] H: head height of water tower, H=L.sub.e+L.sub.f. [0046] h: distance of shuttle travel on linear generator per second. [0047] W.sub.w: water weight (shuttle volume equivalent), W.sub.w=W.sub.s/B. [0048] sk: recoil spring input work, where s is compression distance and k is a spring constant. [0049] U.sub.i: input work value based on PE, where U.sub.i=W.sub.wH/Z; and also U.sub.i=sk. [0050] U.sub.o: Output work value based on P.sub.o. [0051] X: engagement time between shuttle and linear generator; X=L.sub.e/v.sub.e. [0052] Y:=time duration for shuttle transit from linear generator separation to water tower entry (TBD). [0053] Z:=reset time component (TBD) [Time in seconds for shuttle to rise in the water tower].

[0054] Referring initially to FIG. 1 a machine for generating electricity is shown and is generally designated 10. As shown, the machine 10 includes a pair of tandem electricity generating units 12a and 12b. Each electricity generating unit 12a,b is shown to include a respective water tower 14a or 14b which is vertically aligned with a respective linear generator 16a or 16b. Further, the electricity generating units 12a and 12b are mounted on a transfer tank 18. In combination with each other, the electricity generating units 12a and 12b define a hydro-electric component for the machine 10.

[0055] FIG. 2 shows that the electricity generating unit 12a includes an access port 20a which provides access into the transfer tank 18. Similarly, the electricity generating unit 12b includes an access port 20b which also provides access into the transfer tank 18. In the transfer tank 18, however, a barrier 22 hydraulically separates the electricity generating unit 12a from the electricity generating unit 12b. Consequently, the electricity generating units 12a and 12b operate separately to provide separate units of output work Uo. On the other hand, this cooperation of structure allows the electricity generating units 12a and 12b to be driven by a same hydro-mechanical component.

[0056] Still referring to FIG. 2 it is shown that the hydro-mechanical component of the machine 10 includes a piston 24 which is engaged with a bellows 26. Specifically, the bellows 26 allows reciprocal movements of the piston 24 back and forth in a water conduit 28 of the transfer tank 18. Consequently, these movements will individually manipulate water levels in both of the water towers 14a and 14b. Also, like the barrier 22, the piston 24 hydraulically separates the electricity generating unit 12a from the electricity generating unit 12b.

[0057] In addition to the piston 24, the hydro-mechanical component of the machine 10 includes a recoil spring 30 and a drive cam 32. As shown in FIG. 2, a drive bar 34 interconnects the drive cam 32 with the piston 24, and with the recoil spring 30. Thus, a rotation of the drive cam 32 at an angular velocity will exercise both the piston 24 and the recoil spring 30.

[0058] In detail, FIG. 3 shows the structural configuration of the drive cam 32 is essentially defined by changes in the distance of its periphery from an eccentric axis of rotation 36 at a rotation angle . With reference to FIG. 3, it is to be appreciated that the direction of rotation for is arbitrary. For purposes of this disclosure, is shown to be in a counter-clockwise direction with the distance between the eccentric axis of ration 36 and the periphery of drive cam 32 increasingly from r to r+s as increases from 0 to 180. Note: this increase need not be uniform, and most likely will not be.

[0059] An important consideration when cross referencing FIG. 3 with FIG. 2 is that as the angle increases between =0 and 180, the piston 24 moves to the left through the distance s. On the other hand, as the angle decreases between =180 and 360, the piston 24 moves back to the right and the distance between the eccentric axis of rotation 36 and the periphery of drive cam 32 decreases back to the distance r. As further indicated in FIG. 3, a reset capability can be engineered for the machine 10 by maintaining r constant during a predetermined rotation arc 38, while simultaneously maintaining r+s constant during the diametrically opposed rotation arc 40.

[0060] With reference to FIG. 4 the hydro-mechanical component of the machine 10 is shown separate from the hydro-electric component. Functionally, as the drive cam 32 rotates it pushes against a roller 42 mounted on the drive bar 34 to facilitate reciprocation of the drive bar 34. This moves the piston 24 to the left. It will also compress the recoil spring 30. Thus, this action requires two units of input work 2U.sub.i.

[0061] In detail, one of the input work units exerted on drive bar 34 during a machine cycle is referred to here as U.sub.i(mgH) to indicate its purpose is raise water in one of the respective water towers 14a and 14b of the machine 10. Specifically, in the expression for the work unit U.sub.i(mgH)=m.sub.wgH, m.sub.w is the water mass being raised, g is gravity, and H is the head height of the water tower 14a or 14b where water is being raised. The other input work unit is designated U.sub.sk to identify the work that is stored in the recoil spring 30 as water is being raised in one tower 14, and then subsequently released during the machine work cycle to raise the water mass in the other water tower 14. Specifically, the value of U.sub.sk=sk, where k is the spring constant and s is the spring compression distance. Note: U.sub.(mgH)=U.sub.sk where s equals both the compression distance of recoil spring 30 and the travel distance of the piston 24 during a machine work cycle.

[0062] FIG. 5 correlates the forces acting on the piston 24, for each water tower 14a and 14b, during a rotation of the drive cam 32 through rotation arcs =0-180 and =180-360. Note: U.sub.sk is stored during the rotation arc =0-180, and subsequently used during the rotation arc =180-360. Specifically, FIG. 5 shows that during an operation of the machine 10 the tower 14b is reset during rotation arc =0-180, and tower 14b is reset during rotation arc =180-360.

[0063] In FIG. 6, a schematic is shown of the pathway 44 that is followed by a shuttle 46 during an operation of the machine 10 in the electricity generating unit 12b. Specifically, the pathway 44 is shown as a succession of sequentially connected time sectors. For example, an A-B sector of the shuttle pathway 44 extends from an elevated start point A where the shuttle 46 begins its free fall distance 48 into engagement with the linear generator 16b. The A-B section then continues through an engagement distance 50 to a point B where the shuttle 46 disengages from the linear generator 16b. Sequentially, a B-C sector of the shuttle pathway 44 is shown to include valving components of the machine 10 associated with the access port 20b at the point B and with a transfer port 52 at the point C. Specifically, the B-C sector must require sufficient time to allow for the transit of the shuttle 44 from its disengagement with the linear generator 16b to its entry into the water tower 14b. Further, a C-D time sector identifies the portion of the pathway 44 where the shuttle 46 rises by it buoyancy to the top of water tower 14b where in breaches. The importance of the C-D time sector is that it has the potential to accommodate at least one additional shuttle 46 in the machine 10 during a machine work cycle. Finally, a D-A sector of the shuttle pathway 44 extends from where shuttle 46 breaches from the water tower 14b to the elevated start point A for a subsequent machine cycle.

[0064] As a practical matter it is necessary for time sector B-C to have a longer duration than the time required for sector A-B. In part this requirement is based on the simple fact that both the access port 22b and the transfer port 52 cannot be open at the same time. Stated differently, one shuttle 46 must exit the transfer tank 18 before another shuttle 46 can enter the transfer tank 18.

[0065] The output work U.sub.o generated by the linear generator 16b during the time section A-B will be best appreciated by cross referencing FIG. 6 with FIG. 7. Specifically, for this evaluation, the length L.sub.e of the linear generator 16b (FIG. 7) will depend on both a desired output power P.sub.o for the machine 10 and the engagement velocity, v.sub.e. of the shuttle 46 with the linear generator 16b. Moreover, because U.sub.i is greater than U.sub.o, based on the ratio (U.sub.i/sec)/(U.sub.o/sec)=U.sub.i/sec/P.sub.o=m.sub.wgH/msL.sub.e=1.55 [approximately], each electricity generating unit 12 of the machine 10 must operate for more than 1.55 seconds during every machine work cycle.

[0066] With specific reference to FIG. 7, the cumulative effect of a total output work U.sub.o(total) for an electricity generating unit 12 of the machine 10, is based on the fact that U.sub.o/sec=P.sub.o is preselected. Accordingly, as shown in FIG. 7, U.sub.o/sec=m.sub.sh/sec, where m.sub.s is the shuttle mass, and h is the distance traveled by the shuttle 46 along the linear generator 16b every second. Thus, in a configuration for the machine 10 wherein the shuttle 46 is engaged with the linear generator 16b for X seconds duration, the U.sub.o(total)=XU.sub.o for the electricity generating unit 12b, and U.sub.o(total)=2XU.sub.o for the machine 10.

[0067] An operational methodology 54 is provided in FIG. 8 which essentially outlines a procedure 56 for designing a machine 10 in accordance with the present invention. As shown in FIG. 8 the procedure 56 involves the activities of i) specifying preselected design factors needed to construct the machine 10; ii) calculating values for the design factors values to establish structural characteristics and operational attributes of components for the machine; and iii) evaluating an interaction of the machine's operational components for optimizing values of the selected design factors to achieve a desired machine performance.

[0068] In detail, the methodology 54 will include a specification function 58 wherein values for design factors for the machine 10 are established. The specification function 58 can begin simply with the selection of a desired output power P.sub.o for each electricity generating unit 12. Also, a constant velocity v.sub.e for shuttle/generator engagement, and a length L.sub.e for the linear generator can be reasonably chosen.

[0069] Also included in the methodology 54 is a calculation function 60 which will include the step of mathematically determining a shuttle weight Ws. Then, using the relationship U.sub.o=L.sub.eW.sub.s, a value for Ws can be determined. Another step in the calculation function 60 involves establishing a shuttle free-fall distance L.sub.f needed for the shuttle to accelerate to its constant engagement velocity v.sub.e, where L.sub.f=v.sub.e.sup.2/2g.

[0070] As noted above, when starting with a desired shuttle weight W.sub.s, rather than having a value for the output power, P.sub.o must still be calculated. Note: v.sub.e and a length L.sub.e can still be reasonable chosen. The calculation of an output power P.sub.o=U.sub.o/sec can then be made using W.sub.s/g=m.sub.s in the work-energy relationship U.sub.o=m.sub.sv.sub.e.sup.2. The calculation for W.sub.s here is then based on the steady state kinetic energy KE of the shuttle 46 at the velocity v.sub.e. The shuttle weight W.sub.s can be determined by equation W.sub.s=2gU.sub.o/v.sub.e.sup.2. Another design factor that can be determined in the calculation function 60 is the buoyancy factor B for the shuttle 45, where B is the ratio of the shuttle weight W.sub.s to the weight W.sub.w of an equivalent water volume which is displaced when the shuttle 46 is submerged in the transfer tank 18. The weight W.sub.w for a water volume equal to the shuttle volume can then be calculated where W.sub.w=W.sub.s/B.

[0071] Additional steps in the calculation function 60 include calculating an input work requirement U.sub.i for operating each electricity generator of the machine, where U.sub.i=W.sub.wH, and calculating an output work U.sub.o generated by a single water tower, where U.sub.o is based on the kinetic energy of the shuttle, and the output power P.sub.o is expressed as U.sub.o/sec=(W.sub.s/g)v.sub.e.sup.2/sec.

[0072] The evaluation function 62 for the procedure 56 involves comparing the total input work U.sub.i and the total output work U.sub.o machine performance of the two electricity generating units 12a and 12b. More specifically, this involves comparing U.sub.o(total) with U.sub.i(total), where U.sub.o(total) equals 2X(U.sub.o/sec), and U.sub.i(total) equals 2Z(U.sub.i(sec)/Z)=2U.sub.i. sustaining the operation of the machine by taking feedback from the machine output for a net output U.sub.(net)=2X(U.sub.o/sec)2U.sub.i.

Work Evaluations

[0073] U.sub.i(total)=U.sub.i+sk=2U.sub.i with a finite value, regardless of X. This evaluation is reached because the machine 10 has tandem water towers 14a and 14b. Accordingly, U.sub.i=m.sub.wgH powers one tower of the machine during the first half of the machine's work cycle, and U.sub.i=sk powers the other water tower of the machine 10 during the second half of the work cycle. Thus, U.sub.i(total)=2U.sub.i for the machine 10 during each machine work cycle.

[0074] As disclosed above, U.sub.o(total)=2XU.sub.o with a cumulative value during the machine work cycle.

[00003]$A\mathrm{Numerical}\mathrm{Example}$$\begin{array}{c}\mathrm{Let}:B=0.7;L_e=20\mathrm{ft};v_e=10\mathrm{ft}/\sec ;W_s=200\mathrm{lbs}.;\mathrm{and}X=L_e/v_e=2.\\ \mathrm{Calculated}{L}_f=v_e^2/2g={\left(10\right)}^2/64.4=1.55\mathrm{ft}.\\ \mathrm{Calculated}:U_o=W_s\left(L_e\right)=4000\mathrm{ft}-\mathrm{lbs}.\\ \mathrm{Calculated}:H=L_e+L_f=20+1.55.\\ \mathrm{Calculated}:W_w=W_s/B=200/0.7=285\text{.7}.\\ \mathrm{Calculated}:U_i=W_{w}H=\left(200/0.7\right)\left(20+1.55\right)=6157\mathrm{ft}-\mathrm{lbs}.\\ U_{i\left(\mathrm{total}\right)}=U_i+\mathrm{sk}=2\left(6157\right)=12,314\mathrm{ft}-\mathrm{lbs}.\\ U_{o\left(\mathrm{total}\right)}=2{\mathrm{XU}}_o\sec =2\left(2\right)\left(4000\right)=16,000\mathrm{ft}-\mathrm{lbs}.\\ U_{\mathrm{net}}=2{\mathrm{XU}}_o-2U_i.\\ U_i/U_o=6157/4000=1.55.\end{array}$

[0075] In this example, U.sub.net=2XU.sub.o2U.sub.i=(2)(2)(4000)(2)(6,157)=160012,314=3,686 ft-lbs.

[0076] 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.