GRAVITATIONAL WATER PUMP AND GRAVITATIONAL MOTOR Energy triangle closed cycles employing generators with special attention to: gravitational water pump and gravitational motor The subjects of the invention are the reversible closed energy cycles that employ the energy generator. The generator of energy is a device that enables the process of transformation of the energy of an agent contained in the absolute velocity of the agent, the simple machines utilised in mechanics, which transform path or velocity into force described as mechanical gain. The technology of the discussed energy triangle is the continuation of the energy triangle that employs generators as it appears in the thermodynamics. It enabled the science of mechanics to create the closed cycle of energy triangle with a single source of energy and an energy generator. When analysing the forces of action in the energy triangle cycles the inner energy of an agent in thermodynamics is based upon the pressure and the temperature multiplied by the velocity, while in the mechanics it is based upon the weight and earthpull multiplied by the velocity. At the same time the forces of gravity, conservation of momentum and inertia are the three forms of the same energy. It is an statement assumed in the"Introduction to the theory, space-time as the fourth dimension of energy" which is confirmed by the operation of the gravitational water pump and the gravitational motor.

There are three basic generators of energy that operate differently: 1. The first type of generator in the mechanics is the isoenergetic generator in which the energy contained in the absolute velocity and weight of the agent renders inner work upon the cycle. In the mechanics such type of generator is represented by flywheel. The operation of the flywheel is based upon the moment of inertia of a stiff substance. During the process of energy transformation a force is created whose one of the constituents is the velocity. In the science of mechanics, the most common energy agent is a stiff substance of the weight"m"and a velocity"v." These constituents contribute to the inner energy called kinetic energy Ek.

Ek = 1/#m#v2 2 2. The second type of energy generator in the science of mechanics is the energy amplifier. The typical energy amplifiers in mechanics are the simple machines that are in common use, such as levers, wheel gears, etc. The amplification to which the external force is subjected, is described as mechanical gain Zm = F2-F1.

F, =. F.

R2 3. The third type of energy generator in mechanics is the dynamic source. This kind of energy generator is-in a sense-a combination of the two preceding types of generators, however, while the previously discussed types considerably enhanced the efflclency or me energy cycies, tilts cycle fully substitutes the renewable sources of energy. In thermodynamics, the long convergent channel is a device in which the process of transforming the energy contained in the absolute velocity of the agent into the inner energy and heat takes place. In mechanics, the counterpart of the long convergent channel is the first-class lever and weight is the energy agent. Depending upon composition the dynamic sources are divided into single or double-spot-supported. The single-spot- supported source means that the lever is suspended upon the pivot of the spindle, while the double- spot-supported source, apart from support upon the pivot of the spindle, possesses an additional fixed point; in both cases the cycle of operation equals the half-turn angle of 180°. In the case of the single-spot-supported sources the angular speed depends on to what extent the source is loaded. If there is no load it can lead to escalating angular speed which, in turn, may lead to destruction of the mechanisms. That is why this kind of propulsion requires to be used under constant load, e. g. for the purpose of continuous delivery of water to a higher level. The double-spot-supported mechanical source devices behave differently. Missing load or loads that do not exceed the nominal load level do not influence the angular speed of the spindle. The second type of the device is commonly used for industrial purposes.

3 a). The gravitational water pump Basing upon the diagram of the gravitational water pump's motor I will discuss the operation of the single-spot-supported dynamic source in mechanics. Figure 1 depicts the structure of the gravitational motor utilised by the water pump. The motor consists of an ellipsoidal path 1, a spindle 2 with three pairs of arms 2 and bearings which move along the path. The suspension of the bearing on the spindle arm enables it to move along the axis of the arm. The bearing simultaneously moves along the path owing to a system of rollers. Figure 2 depicts the proportions in the layout of the path, where R2 = R3 and R1 = 3R2, while R3 is the arm of the flywheel. The half-turn of the spindle consists of three stages. For the sake of simplification, the turn was divided into 30 parts each of which equals 12°, Figure 4a. During the first stage (Figure 3a) we shall regard the arms of the spindle as first-class lever suspended in the 0 spot. In accordance with the first-class lever principle the arms shall be marked right Ri and left R2. During the first stage the arm Ri is the propelling arm subjected to the gravitational force of the bearing Fg1 = 10 kg, directed vertically downwards. The counterweight to this arm is the left arm R2 and the gravitational force Fg2 = 10 kg of the other bearing that is attached to that arm. The slope of the path on the left and the right sides slides the bearing along the arm, depending upon the angle of the slope, changing the length of the arm and behaving as inclined plane. The left bearing is subjected to the gravitational force Fgz directed vertically downwards and the force FN of natural impact of the slope and it is directed perpendicularly to the path. The presence of these two forces creates the accelerating force Fa and the resultant force Fw directed in the opposite direction.

Fg2 = m2 g Fa = Fg2 (sin cos, 6) u-friction ratio Fiv = Fa7 (sin, B +, u cos ß) The acceleration caused by the slope of the path can be calculated in the following equation: a2 = g(sin ß - µcosß) In order to overcome the acceleration the force Fw must thrust to create a reverse accelerat on that equals : aw2 = g(sinß + µcosß) Time required to traverse the slopes equals : Opposing the gravitational force Fg is the force imposed upon the arm by the bearing Fd. The angle y contained between Fw and Fd is described by the following equation: Fw Fd-siny The angle y = 90-ß and cos (90 - ß) which effects in the equation describing the force Fdz : <BR> <BR> <BR> <BR> <BR> Fd = Fw = Fg(sinß + µ#cosß)<BR> <BR> <BR> <BR> <BR> <BR> sin,ß sin, The axis of the lever O is subjected to the moment of the force required to move the bearing along the path: FM = Fd2#cos##R2 And the moment of inertia of the bearing: <BR> <BR> <BR> <BR> <BR> <BR> Mk=mk#Rk2<BR> <BR> <BR> <BR> <BR> 2 Totally, the bearing of the weight mi is subjected to force Fr directed in the opposite direction from the gravitational force Fgl : <BR> <BR> <BR> <BR> <BR> <BR> Fr=FM+Mk#g<BR> <BR> <BR> <BR> <BR> <BR> Rl cos a The gravitational force of the bearing on the arm Ri pushes the path as described in the equation: Fg,-- = m1#g-Fr The gravitational force Fg1 with which the bearing presses the slope of the path creates the accelerating force: Fal = Fg, (sin α-µcosα) which allows us to come up with the angular acceleration : Fa zu Ri Time required to traverse the slope can be calculated with the use of this equation: The speed the bearing gains once it has traversed the slopes results from this equation: v=+,-F whence we arrive at the angular velocity: v <BR> <BR> ZU =-<BR> <BR> <BR> <BR> Rl The first stage, when the slope of the path is an inclined plane for the bearing, which accelerates rotation equals 9 parts of which 4.5 parts is the movement of the right bearing along the path and the accompanying increase of speed of the bearing and the length of the arm Ri with simultaneous shortening of the arm R2. In the second stage the process reverses, the length of the arm R, decreases while that of the arm R2 increases. The fluent change in the length of the arm enables the increase of the kinetic energy of the system by the means of changing the velocity of the weight. At first, the kinetic energy contained in the velocity of the right bearing grows in order to-owing to shortening of the arm Ri-transfer this energy to the increase of the velocity of the left bearing with simultaneous lengthening of the arm R2 and the increase of spindle rotation speed. During calculations the complex movement of the right bearing shall be split into two independent moves.

The first is the movement of the bearing at a constant speed with the shortening arm as in Figure 2a: Li =m#1R12+(Mk##1+m2#2R22) L, = angular momentum of the spindle consisting of angujar momentums of bearings and flywheel.

Mk = moment of inertia of flywheel At a constant speed v of the bearing the shortening of the arm R1 causes the acceleration of angular velocity mi versus (tt2. The ratio of acceleration depends upon the amount of kinetic energy transferred while the arm Ri was being shortened.

The acceleration of the right bearing caused by the force of gravity at the slope of the path is added to the acceleration in question.

The second and the third stages feature a drop in angular velocity while the kinetic energy contained in the absolute speed and weight of the spindle, the flywheel and bearings render the work required to bring the bearings up by six segments of the turn. During the second stage there is an additional gravity force of bearing of weight mi which tends to locate the bearing and the arm Ri in the vertical position on the axis of the spindle 0. the amount of energy required to traverse 9 parts of the turn of the spindle can be calculated with the use of inclined plane equations. The amount of energy that is necessary to cover the remaining 6n parts of the turn of the spindle is deducted from the kinetic energy stored in the spindle. Figure 4a depicts the division into stages and parts. The straight'lines marked by numbers represent the middle part i. e. the average par whose boundaries are defined by the neighbouring straight lines a and b. the first stage is divided into two parts: during the first one the length of the arm grows and it shortens during the other.

Figure 4b contains a diagram coordinated by Q and c versus the angular velocity and kinetic energy of the whole spindle. If the angle between the straight lines 2-3 and 3-4 is below 90° it means the rotation of the spindle will continue to grow, if the angle is obtuse, the speed tops. The differences of speeds and kinetic energies between 1-la define the increase of energy on the spindle shaft. At each half-turn the triangle contained between corners la- 2-3-4 moves to the right and up along the straight 1-2. The efficiency of the motor can be calculated on the basis of increase of speed at the first turn at the point where Rcos 5 = R, the arm tilt angle is So and cost = 1. At this point the process of shortening of the arm Ri starts.

Mw-moment of inertia of the spindle The efficiency of the dynamic source depends upon the shape and dimensions of the path the bearings move along versus the weight of the flywheel. The theoretical efficiency of the source should equal QT = Mw (1. 4-, u) 2. the efficiency was calculated on the basis of this example. The weight of the bearings is 10 kilograms each whereas the weight of the flywheel is 20 kilos ; the efficiency is Q = Mw (1. 21 P) 2.

A change of the shape or dimensions of the fiywheel should increase the efficiency of the source, if, for instance, the weight of the flywheel is located at the ends of the arms it may result in better efficiency. The discussed dynamic source take advantage of the phenomenon of losing speed of the weight for the benefit of increased kinetic energy of the spindle. The shortcomings of the device are the limited feasibility of minimising the dimensions of path and constant load. The reason why I called this device a gravitational water pump was because this source of energy can be applied where water is constantly being lifted to considerably high levels under a constant load.

3b. The gravitational motor The principles of operation of the gravitational motor are similar to those of the gravitational water pump. One major difference is the application of two points of support. This enables the circulation path of the active weight to be shortened. Figure 5 is a diagram of the spindle which is constructed of a flywheel 1 mounted on propeller shaft. The bearing 2 moves the weight of the energy agent along the path 3. the path consists of two poles solidly fixed on the flywheel through the clutch A.

The bearing is moved with the use of a set of toothed bars 5 and half-toothed wheels fi which are moved by levers Z. The guide-block 8, marked by intermittent line, which connects the flywheel with the movable weights serving as auxiliary weight 2, is bound to move the weights along the axis of the lever Z during the turn of the toothed-wheel 6. The stop which constitutes the second point of support is composed of housing 1Q, spring 11, basis of the stop 13. and regulation screw a. Figure 6a depicts the distribution of external and potential forces which affect the spindle in its start position. The gravitational motor operates under the influence of an external force being gravity and that is why its autogenous starts depends upon the position of the spindle. At the moment of start the bearing and the active weight are located in the upper position being held by the gravity forces of the auxiliary weight impacting the system of levers. The driving forces to the spindle are the The movement of the bearing along the path is accompanied by lul 9 u, Lrie arm oi tne moment of inertia of bearing's weight which results in the increase of angular velocitq of the spindle and reduction of kinetic energy of the agent. The straight line 3-4 is the third part of the turn of the spindle. Further movement of the bearing along the path extends the arm of the weight of the agent and brings about further reduction of speed and kinetic energy of the system. During the third stage of the turn the force at which the spring impacts the arm of the toothed wheel provides the arms with accelerated motion and causes completion of the bearing upward climb. The efficiency of the motor is similar to the efficiency of the motor used in the gravitational water pump. An advantage of the gravitational motor is its self-regulation of revolutions, it appears when the second part of the path is being traversed by the bearing. The slow-down speed increases together with the increase of bearing speed. In the subsequent cycle the reduced speed of the bearing reduces the slow-down.

The discussed invention shall find a wide array of uses in all kinds of stationary sources of power such as electricity generators, water pumps, etc. The application on vehicles that move wherever there is gravity is not impossible.