Background of the Invention

One of the principle problems facing the country over the next several decades is a potential shortage of energy. Current efforts at solving this problem have been directed to the negative approach of having the country use less energy. While this may delay the problem it in no way pro¬ vides a solution. If a solution is not forthcoming in the immediate future the world faces an industrial slow down which can only have dire socio-economic effects on all peoples of the world. It has been forecasted by reliable sources that the world's need for oil, one of the primary sources of today's energy will outrun the supply by the end of the century and possibly sooner. This makes the develop¬ ment of alternative sources of energy a national imperative. This invention is directed to the development of such an alternative source of energy and provides a unique method and means for extracting energy from bodies of water. The method is pollutionless, does not degrade or taint our natural resources and is for all practical purposes limit¬ less in its capacity for power generation.

The manner in which the foregoing, as well as other objectives and advantages of the invention may best be achieved will be more fully understood from a consideration of the following description, taken in light of the accom¬ panying drawings.

Summary of the Invention This invention relates to a unique method and means for developing power through use of the earth's natural forces. The system in its broadest concept com¬ prises placing suitably proportioned fluid-conduit means within a body of water such that the earth's gravitational and centrifugal force fields acting on the system are moderated in a manner to neutralize the effects of the gravitational force field while concomitantly maximizing the effects of the earth's centrifugal force field. More specifically the inventive concept when applied, for example, to the extraction of power from a body of water, comprises placing a generally "U"-shaped section of relatively large diameter piping within the body of water and then orienting the section with ^' in the ^' earth's ^* centrifugal" a-nd-gra i-tationa-1- force fields to induce flow of water through the pipe of sufficient volume and velocity to produce useful work. The theory underlying the invention is first to neutralize to the fullest practical extent the adverse effect of gravity on the system. This objective can be accomplished by pro¬ portioning the inlet and outlet legs of the "U" to be substantially identical in their position relative to the earth's center of gravity and by disposing the longitudinal section of the "U" at the same gravitational elevation. By this technique the gravitational forces acting on the operational portions of the system are for all practical purposes effectively neutralized. The next step is to orient the system in the centrifugal force field of the earth such that the centrifugal forces acting on the system are maximized in the direction of intended flow. The cen¬ trifugal forces generated by the rotation of the earth act in a direction perpendicular to the axis of rotation of the earth. To maximize the effect of these forces on the body of water contained within the longitudinal section of the pipe the pipe is required to be oriented in a generally

north-south direction when working in the northern hemi¬ sphere and in a generally south-north direction when working in the southern hemisphere. The third objective is to mini¬ mize frictional losses. This is accomplished by using pipe of large diameter having smooth inner surfaces and gradual transitions when changes in direction of flow are required. The practical extension of this inventive concept is de¬ scribed in detail below.

Brief Description of the Drawings

Figure 1 illustrates in schematic form one manner of utilizing the present invention to effect transport of water from one location to another or as a means of supply¬ ing a driving head of water to a turbo-generating system, a d

Figure 2 is a graphic depiction of the preferred method of orienting the system relative to the gravitational and centrifugal force fields of the earth.

Figure 3 is a graph illustrating values of kinematic viscosity for water at various degrees of temperature, and

Figure 4 is a plot of Reynolds numbers versus friction factors for various types of pipe and roughness derived by empirical determinations.

Description of the Preferred Embodiment With specific reference to the drawing there is shown in Figure 1 the basics of a system incorporating the method¬ ology of operation comprising one aspect of the invention. Reduced to its simplest form the system consists of fluid conduit means 10 comprising inlet and outlet sections 12 and 14 respectively separated by a longitudinal section 16. The system is proportioned and arranged to minimize friction losses by eliminating abrupt transitions in flow patterns and by providing a conduit having a smooth inner surface and a substantial cross sectional diameter. In the embodi¬ ment shown the conduit is made of steel pipe of eight foot diameter having an inner polished surface. The longitudinal

section 16 and inlet and outlet sections 12 and 14 are then positioned in the earth's gravitational and centrifugal force fields in a manner to neutralize to the fullest extent possible any adverse effects of gravity on the system while maximizing the effects of the earth's centrifugal force field in order to augment fluid flow through the system. By providing the arrangement shown in figure 1 the inlet leg 12 of the system, as shown in phantom, in figure 1 is effectively provided by the body of water 18 which serves as a forebay for furnishing the systems operating head. This eliminates the need for inlet piping and its associ¬ ated friction losses. The longitudinal section 16 of the system is generally maintained throughout its length at a more or less constant depth from the surface to minimize gravitationally induced losses. In the illustration, section 16 is assumed to be approximately twenty five miles long. It is on this basis that the computations set-out in this disclosure are made.

For purposes of illustration, referring to figure 2, system 10 has been chosen as being in the northern hemis¬ phere at a latitude of sixty degrees. At this location the centrifugal forces acting on the slug of water existing at any instant of time within the longitudinal section 16 of the pipe act through a radius arm 18 having a lenghth of 1,979.5 miles measured from the rotational axis 20 of the earth to the center of gravity 22 of the slug of liquid con¬ tained within the pipe. To maximize the centrifugal force acting on the water, the pipe section 16 is oriented such that the component 24 of the earth's centrifugal force 26, as seen in figure 2, acts in a direction parallel to the selected flow path and in a direction which augments fluid flow. In the Northern Hemisphere the orientation of the system is in a North-South direction and the direction of fluid flow is from North to South. With the system so positioned flow of water into and through the system is initiated by opening a gate valve 28 located at the en¬ trance to the system. The pressure head 30 acts to provide

the initial thrust to initiate fluid flow. For purposes of illustration this starting head has been chosen as thirty feet. The prime mover for the system, however, is the centrifugal force generated by the earth's rotation. Since the system is essentially U-shaped the gravitational forces exerted on the incoming and outgoing legs 12 and 14 measured from the surface of the water (referred to in this application, along with the longitudinal section 16, as the operational portions of the system), are in equilibrium. It is also to be noted that no gravitational forces are required to be overcome during movement of the water through the longitudinal section 16 of the pipe by reason of its uniform depth as measured in respect to the earth's surface. The only forces required to be overcome in order to lift the water back to the earth's surface is that caused by frictional losses. Any head generated in excess of this frictional loss can be used to produce useful work such, for example, as simply moving water from one location to another or for generating a head of water necessary to power a turbo- generating system as is well known in the art.

Before elaborating on the use of the invention refer¬ ence should again be made to figure 2 in order to under¬ stand the procedure for orienting the system 10 in the earth's gravitational and centrifugal force fields. As previously noted the system is assumed to be located at a north latitude of 60 degrees. At this latitude the radius of rotation of an object located on or near the earth's surface is approximately 1,979.5 miles. This is determined by multiplying the earth's radius of 3,959 miles by the Cosine of 60 degrees. Accordingly the centrifugal force represented by the vector 26 acts through a radius arm of 1,979.5 miles in a radial direction. To maintain the system in substantially gravitational equilibrium, as already dis¬ cussed, while at the same time maximizing the effect of the earth's centrifugal force on the system requires the system to be oriented in a north-south direction and the fluid flow to be in a north to south direction. Given this orien-

tation of the system the magnitude of the component of the earth's centrifugal force, 24, acting in a direction parallel to the flow path is equal to the Sine of 30 degrees multi¬ plied by the value of the earth's centrifugal force at a northern latitude of 60 degrees. The formula for determin¬ ing centrifugal force is F = MRW ² , where "M" stands for the mass of the object being acted on, "R ^M the radius arm through which the centrifugal force acts and "W" the angular velocity expressed in radians per second. Given a system in which the diameter of the pipe is 8 feet, the longitudinal length of the pipe is 25 miles, the system is .located at north latitude 60 degrees and is positioned in the manner described above the formula can be rewritten as follows: F = W/G x R x W ² . The weight of fluid on which the centrif¬ ugal force ¥cts is the body ^" of ^" fluid in the illustrated embodiment the fluid is assumed to be water, contained within the 25 mile long 8 foot diameter pipe- and is equiva¬ lent to the area of the pipe multiplied by its length in feet times the density of water. In mathematical terms the weight of water in the above described system is equal to (3.14) x R ² x length of the pipe in feet x density of water or in the system selected for illustration (3.14) x 16 x 25 (5,280) x 64 lbs./ft ³ = (50.24) (132,000) (64) = 424,427,520 pounds. This weight is then divided by the gravitational force of the earth to obtain the mass. Multi¬ plying this by the radius of the centrifugal force arm of 1,979.5 miles . expressed in feet and the velocity of the earth's rotation expressed in radians per second squared gives the following results:

F = 3.14 x 4 ² x 132,000 x 64 (1,979.5 x 5,280) (2 x 3.14 x 1 ) ²

32.174'/sec. ² 86,400

F = 3.14 x 16 x 132,000 x 64 (10,451,760)(.0000726) ²

32.174 F = 50.24 x 132,000 x 64 ( 10,451,760)(.00000000527076)

32.174 F = 6,631,680 x 64 (10,451,760)(.00000000527076)

32.174

F = 424,427,520 (10,451,760) ( .00000000527076) 32.174

F = (13,191,630. ⁵ ) (10,451,760)( .00000000527076)

F = 137,875,755,994,680 (.00000000527076)

F = 726,710 lbs.

The component 24 of the centrifugal force which acts along the axis of the longitudinal section of pipe at a northern latitude of 60 degrees is obtained by multiplying the cen¬ trifugal force by the Cosine of 30 degrees. Hence the com¬ ponent of centrifugal force acting along the axis of the longitudinal section of the pipe is 629,330 pounds of force. This equates to a head of approximately 195 feet. To de¬ termine the useful head one has to subtract from the gross head of 195 feet losses due _ to friction. For a straight pipe of uniform diameter friction losses are given by the formula h>- = f (V /2g) (L/d) . If we assume a velocity suf¬ ficient to produce a discharge of 90 cubic feet per second for powering a large reactor turbine using an 8 foot diame¬ ter pipe the velocity of flow is 3.5828 feet per second. This is based upon the formula Z = AV where Q is the quan¬ tity of flow, A is the cross sectional area of the pipe and V is the velocity of'flow. To determine the friction factor f it is assumed that the system will employ water having a temperature of 50 degrees fahrenheit. Referring to Figure 3 kinematic viscosity (v) is given as .000015 square feet per second. ith the velocity and the kine¬ matic viscosity known the Reynolds number for the system can be determined from the formula R = LV/v. For a unit length of pipe this calculates to be 238,853.33. If the material chosen for the pipe is smooth steel, the graph shown in Figure 4 indicates that the friction factor for the above Reynolds number is .016. For long pipelines of uniform diameter, such as here contemplated, the formula for loss of head due to friction is h _f = f(L/dJV/lg. In addition there are frictional losses due to pipe bends. In the illustrated embodiment there are three such bends, each

bend corresponding to an additional 55 feet of pipe per bend or a total of an additional 165 feet of pipe, this assumes a bending radius of 30 feet per bend. It is also assumed that the inlet section of the pipeline employs a bellmouthed opening so as to eliminate friction losses at the point of entry to the pipeline. The calculations for friction loss to follow are conservative in that they are overstated. The length of pipe used in these friction-loss calculations has been exaggerated and the friction factor for a 6 foot diameter pipe rather than an 8 foot diameter pipe has been used to insure adequate accounting for fric¬ tion losses. These calculations follow: h _f = f(L/d) V ² /2g hf = (.016) (132,565/8) (12.81/64) h _f = (.016)(16,570.62)(.20r ^{" " '} hf = (265.13M.20) hf = 53.026 feet By subtracting these friction losses from the gross head previously calculated a net useful head of approxi¬ mately 141 feet results. This net head can be utilized to perform productive work - be it to raise fluid above the surface to power a generator, transport fluid from one place to another, or for whatever other practical purpose desired.