Note: Descriptions are shown in the official language in which they were submitted.
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MACHINE FUNCTIONING ON THE PRINCIPLE OF EXPLOITATION
OF CENTRIFUGAL FORCES
FIELD OF THE INVENTION
The present invention is concerned with a functioning principle for machines
generating mechanical energy from centrifugal forces of masses in a closed
mechanical circuit, and that is optionally maintained in a permanent state of
dynamic unbalance using the falling of masses under the effect of earth's
gravitational field.
BACKGROUND OF THE INVENTION
As is well known, a mass (M) that is situated at a given height (h) has a
stored
potential energy (PE) of PE = M*g*h. When mass (M) is in free fall, potential
energy (PE) is transformed into kinetic energy, and the energy conservation
law
permits the formulation of the following:
M*g*h = (1/2)*M*V"2
where (V) is the velocity attained by the mass (M) after falling from height
(h)
and (g) is the acceleration of mass (M) due to the earth's gravitational
field,
namely 9.81 m/s"2 (or 32.2 ft/s"2).
However, to perpetuate the falling motion of mass (M), it is necessary to
raise
the mass (M), after it (M) has fallen, once again to the starting point for
the
falling motion of the mass (M), namely the height (h). This raising requires
furnishing of energy to mass (M), namely [M*g*h], without taking resistance
into
account, and thus there is no gain of energy as i.e. M*g*h = M*g*h when M, g,
and h all have the same value.
It is to be noted that the fall of any mass in the earth's gravitational field
is
considered to be a state of dynamic unbalance (the sum of the external forces
acting on the mass (M) during the fall is not null, i.e. not zero), which is
different
form any today existing machine.
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To date, no machine can continuously generate more mechanical energy
(positive gain, energetic efficiency ratio larger than one (1)) than the
amount of
energy input therein from outside, such as from Man.
Accordingly, there is a need for a machine functioning on the principle of
exploitation of centrifugal forces, and typically on the principle of
potential
energy gain for generating mechanical energy.
SUMMARY OF THE INVENTION
It is therefore a general object of the present invention to provide a machine
functioning on the principle of exploitation of centrifugal forces, and
typically on
the principle of potential energy gain for generating mechanical energy.
An advantage of the present invention is that the machine functioning on the
principle of exploitation of centrifugal forces can be implemented in
different
ways, with different sizes for different output gains, while exploiting the
centrifugal forces over at least one curved section.
Another advantage of the present invention is that the machine, also
functioning
on the principle of potential energy gain, to have an energetic efficiency
ratio
defined by a ratio of the mechanical energy generated by the machine over the
sum of all external energy inputs (including from Man) provided into the
machine larger than one, is permanently maintained in a state of dynamic
unbalance, while having a system for exploiting centrifugal forces.
Another advantage of the present invention is that the machine functioning on
the principle of potential energy gain can be realized in a multitude of
different
ways, and sizes for different output gains.
In accordance with an aspect of the present invention, there is provided a
machine for generating mechanical energy, said machine comprising: a closed
circuit rotationally driven around at least one rotationally free wheel at
least
temporarily by an input of external energy, a plurality of masses selectively
connecting to the closed circuit to move therealong; a system for guiding the
masses along the circuit to allow the masses to travel therealong; and a
system
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for exploiting centrifugal forces of the masses located on at least one curved
section of the closed circuit to add to the circuit an energy from the
centrifugal
forces of the masses and different than said input of external energy.
In one embodiment, the system for exploiting centrifugal forces of the masses
allows the masses to move, typically generally freely, in a substantially
radial
direction when on said at least one curved section.
In one embodiment, the masses selectively connect to the closed circuit
between a relatively upper point thereof and a relatively lower point thereof,
and
provide kinetic energy to the closed circuit due to transformation of
potential
energy of the masses while falling within the earth's gravitational field from
the
upper point to the lower point, and wherein the guiding system inciudes a mass
track adapted to allow the masses to travel from the lower point to the upper
point while being disconnected from the closed circuit and using at least
their
own kinetic energy at the lower point, said machine comprising: a system for
disconnecting the masses from the closed circuit at a location adjacent the
lower point so as to selectively maintain the closed circuit into a state of
permanent dynamic unbalance; a system for connecting the masses to the
closed circuit at a location adjacent the upper point so as to selectively
maintain
the closed circuit into the state of permanent dynamic unbalance; and said at
least one curved section of the closed circuit being at least partly located
between the upper point and the lower point.
Conveniently, the mass track includes a substantially circular arc portion
thereof
extending between the lower point and the upper point.
Typically, the mass track inciudes a generally semi-circular portion thereof
extending between the lower point and the upper point.
Conveniently, the closed circuit includes a lower portion ending at the lower
point, the mass track includes a lower track portion selectively and movably
supporting the masses therealong before reaching the lower point.
In one embodiment, the mass track immediately follows the system for
exploiting centrifugal forces of the masses and is substantially tangentially
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oriented relative to a trajectory of the masses exiting the system for
exploiting
centrifugal forces.
In one embodiment, the guiding system includes a subsystem for selectively
retaining the masses along the closed circuit at least between the upper point
and the lower point.
Conveniently, the guiding system includes a plurality of mass trucks
displaceable around the at least one wheel for selectively receiving the
masses
therein along the closed circuit between the upper point and the lower point,
the
retaining subsystem maintaining the masses into respective said trucks
between the upper point and the lower point.
Conveniently, each of said trucks includes a fixed part movable along said at
least one wheel along the circuit between the upper point and the lower point,
and a mobile part radially movable relative to the fixed part between a closed
configuration in which the fixed and mobile parts are in proximity to one
another
and a deployed configuration in which the mobile part is spaced away from the
fixed part.
Typically, mobile part of the truck is selectively and freely radially movable
from
the closed configuration into the deployed configuration when the truck is on
said at least one curved section.
Conveniently, the disconnecting system includes a release mechanism to
selectively disconnect the masses from the respective of said trucks adjacent
the lower point.
Conveniently, the closed circuit includes an upper portion starting at the
upper
point and ending at an upper portion endpoint, and the connecting system
connects the masses to the closed circuit at a location between the upper
point
and the upper portion endpoint.
Typically, the connecting system includes a mass magazine for receiving the
disconnected masses from the lower point adjacent the upper point, the mass
magazine temporarily containing at least one said disconnected masses therein
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and connecting one said at least one said disconnected masses to an empty
one of said trucks between the upper point and the upper portion endpoint for
each one of the disconnected masses reaching the upper point.
Conveniently, the system for connecting masses recuperates at least part of
the
5 kinetic energy of the masses disconnected from the lower point once arrived
into said magazine.
Alternatively, the system for connecting masses allows each said mass to have
at least the velocity of said circuit at the time of connection therewith
using an
input of work extemal to the circuit.
Alternatively, the connecting system includes a mass delivery mechanism
receiving the disconnected masses from the lower point adjacent the upper
point and connecting a received one of said disconnected masses to an empty
one of said trucks between the upper point and the upper portion endpoint for
each one of the disconnected masses reaching the upper point.
Conveniently, the release mechanism selectively operates when velocity of the
masses at the lower point is equal to or larger than a predetermined value,
thereby ensuring the masses have sufficient kinetic energy to reach the upper
point.
In one embodiment, the masses are equally spaced apart from one another
along the closed circuit.
Conveniently, the kinetic energy provided to the closed circuit is greater
that a
resistant work including work consumed by friction forces of the plurality of
masses in the relative respective displacement therealong and by the mass
connecting system for connection of the respective said masses adjacent the
upper point.
Conveniently, the system for connecting masses accelerates the masses when
arrived at the upper point up to a velocity generally equal to the velocity of
said
circuit using an input of external energy.
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Typically, the systems for disconnecting masses, for connecting masses and for
exploiting centrifugal forces of masses are only activated once the circuit
has
reached a predetermined velocity.
In accordance with another aspect of the present invention, there is provided
a
machine for generating mechanical energy, the machine comprising: a closed
circuit located around one or a plurality of rotationally free wheels with a
plurality
of masses being displaced therealong, said closed circuit being movably driven
to reached a predetermined velocity equal to or larger than a minimum velocity
using an at least temporarily maintained input of external initial energy; a
system allowing the masses to be guided along their displacement along the
closed circuit; and a system allowing exploitation of centrifugal forces of
the
masses located on at least one curved section of the closed circuit to add to
the
circuit an energy from the centrifugal forces of the masses and different than
said input of external initial energy.
In one embodiment, the masses provide the closed circuit with kinetic energy
due to the transformation of potential energy of the masses while falling
within
the earth's gravitational field, said machine including: a system allowing the
masses to disconnect from the closed circuit at a lower point thereof in order
to
maintain the closed circuit into a state of permanent dynamic unbalance; a
system allowing the masses to connect to the closed circuit at an upper point
thereof; and a system allowing the masses, once disconnected from the closed
circuit at the lower point, to join the closed circuit at the upper point
using kinetic
energy from the mass' own velocity at a time of disconnect from said closed
circuit.
Conveniently, the system allowing the masses to connect to the closed circuit
allows the masses to reach the velocity of the circuit at the time of
connection
thereto with an input of external energy.
Typically, the system allowing the masses to connect to the closed circuit
includes a system allowing recuperation by the circuit of kinetic energy of
the
masses once arrived at the upper point.
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In one embodiment, the shape of the circuit generates tangential reactions due
to centrifugal forces so as to add positive work to its components in motion.
Alternatively, the shape of the circuit allows the masses to have a quantity
of
energy due to centrifugal forces when disconnecting form said circuit at the
lower point, in addition to the kinetic energy generated by the velocity of
said
circuit.
Other objects and advantages of the present invention will become apparent
from a careful reading of the detailed description provided herein, with
appropriate reference to the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
Further aspects and advantages of the present invention will become better
understood with reference to the description in association with the following
Figures, wherein:
Figure 1 is a schematic elevation view of a machine functioning on the
principle
of potential energy gain, without any system for exploiting centrifugal
forces, in
accordance with an embodiment of the present invention showing a basic
closed circuit defined by four wheels and having empty trucks;
Figure 2 is a schematic elevation view showing the circuit of Figure 1 with
masses shown in situ within the trucks;
Figure 3 is a schematic elevation view of Figure 2 with some masses removed
from the trucks moving upward (from point G to point A);
Figure 4 is a schematic elevation view of Figure 3 with an off-circuit by-pass
track for the masses moving upward disconnected and away from the trucks;
Figures 5a to 5d are schematic elevation views of other embodiments of the
basic circuit configuration;
Figure 6 is a schematic elevation view of Figure 4 provided with a magazine
feed for feeding the upper empty trucks with masses and receiving the masses
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exiting the mass track, as well as the two systems of external input work WO
(at
the circuit level) and, in this version, Wmag (at the level of the system for
connecting masses to the circuit at its upper point A);
Figure 7 is a schematic elevation view of Figure 4 provided with an alternate
embodiment of mass delivery mechanism;
Figures 8a and 8b are schematic elevation views for explanation of the way
centrifugal forces acting on masses are exploited by a system for exploiting
centrifugal forces in accordance with an embodiment of the present invention;
Figures 9a and 9b are enlarged schematic elevation views showing an
example of the different parts of a truck in a closed configuration and a
deployed configuration, respectively;
Figure 10 is a schematic elevation view of Figure 6 with a system for
exploiting
centrifugal forces of masses located just after the upper portion endpoint of
the
circuit;
Figure 11 is a schematic elevation view of Figure 6 with a system for
exploiting
centrifugal forces of masses located just before the lower point of the
circuit;
and
Figure 12 is a schematic elevation view of Figure 6 with a combination the
systems for exploiting centrifugal forces of masses of Figures 10 and 11.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
In the following sections, in order to explain the functioning principle,
object of
the present invention, the following example of a corresponding machine will
be
looked at.
It is noted that the following description shows that the machine of the
present
invention can have a vertically oriented component to take advantage of the
potential energy of masses, although the machine can also operate in a
generally horizontal plane where only the friction forces will be considered.
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The functioning principle consists in maintaining a closed mechanical circuit
under motion generated by falling masses (M) due to the earth's gravitational
field in a permanent state of dynamic unbalance with the exploitation of
centrifugal forces and a selective input of external energy, without
contradicting
the energy conservation law.
The present invention is gradually described in the following paragraphs in
order
to ease comprehension thereof.
A- Basic Systems (without exploitation of centrifunal forces)
With reference to Figures 1 to 4 there is shown a machine 10 functioning on
the principle of energy gain caused by masses M falling under the influence of
gravity in a closed mechanical circuit 12 that is permanently maintained in a
state of dynamic unbalance.
The closed mechanical circuit 12 is driven by an initial external energy WO
and
potential energy of masses M around at least one, four shown in Figures 1 to
4,
rotationally free wheels R1, R2, R3 and R4 disposed in corners of a
substantially rectangular format. Any one of the wheels R1, R2, R3, R4 could
be used to recuperate the gained mechanical energy and to transfer the same
to other machines (not shown) in order to transform this mechanical energy
into
electrical energy for example. Typically, the circuit 12 includes a mass
guiding
system that includes a truck guiding subsystem including an inner rail Ri or
track
on which a plurality of trucks 14 is mobile in an anti-clockwise direction as
viewed in the figures.
Preferably, each truck, having a mass (m), rolls on internal rails Ri,
typically with
bearings 16, although any other friction reducing mechanism could be
considered. The trucks 14 are preferably equidistant and connected to one
another by a flexible mechanical link 18, such as chains, as shown in Figure
1.
The circuit 12 shown in Figure 1 is in dynamic balance, and a mass M is added
to each truck 14. Conveniently, the masses M slide, on their bearings 20 or
the
like friction reducing mechanism, along external rails Re or tracks that form
part
of another subsystem of the mass guiding system for selectively retaining the
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masses M along the closed circuit 12, at least between the upper point A and
the lower point F.
With the masses M, the circuit 12 remains in dynamic balance (the sum of the
external forces being zero), as shown in Figure 2.
5 The circuit 12 typically defines a substantially horizontal upper portion 22
extending between a relatively upper point A of the circuit and an upper
portion
endpoint B, and a similar substantially horizontal lower portion 24 extending
between a lower portion start point E and a relatively lower point F of the
circuit.
The circuit 12 also defines a lowering portion 26 between points B and E and a
10 raising portion 28 between points F and A. Although all the portions 22,
24, 26,
28 are shown as being substantially straight, one skilled in the art would
understand that any other shape could be considered without deviating from the
scope of the present invention.
A dynamic unbalance is introduced into the circuit 12 according to the
following
conditions:
1- The circuit 12 is turned (operated) around wheels R1, R2, R3, R4 at an
initial velocity VO, using an externally provided input energy WO.
2- Mass M is disconnected, detached or released from its corresponding
truck 14 (and therefore the circuit 12) adjacent lower point F via a release
mechanism (such as the shape of the mass receptacles of the trucks 14 or any
other mechanism) of a mass disconnecting system.
3- An additional mass M is connected or attached to the circuit 12 (or an
empty truck 14) at upper point A via a mass connecting system each time an
empty truck 14 is located adjacent the upper point A. Typically, the mass M is
accelerated at the mass connecting system level up to a speed equals to the
velocity, or speed, of the circuit Vcir using external energy Wmag (the
influence
of the additional mass M as well as the provenance of the additional mass M is
explained below).
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The guiding system, connecting system and disconnecting system are typically
mechanical systems although they could easily be at least partially
electrical,
electronic, etc.
The periodic distance P which separates two adjacent trucks 14 refers to the
period (i), namely the distance traveled by a truck 14 for it to arrive at the
position of the truck immediately preceding it.
The balance of energy for each period (i) is then as follows:
1- Potential work:
Wpot = M*g*(h+2*RM)
where RM is the radius of displacement of the center of mass of the mass M, h
is the vertical distance traveled by the masses (and trucks) in which friction
does not occur between wheels (R2, R3, and R4, R1; i.e. between points C and
D (circuit lowering portion 26) and between points G and H (circuit raising
portion 28)) and g is the acceleration constant of the earth's gravitational
field.
2- Resistant Work (friction between points; from point H to point C
and from point D to point G, assuming that the trucks 14 are free from the
inner
rails Ri from point C to point D and from point G to point H; which could not
be
the case and then added into the following equation):
Wres = P*g*Cf*f(M+m)1z
where E(M+m)72 is the sum of all the masses being along the circuit 12, and Cf
is the coefficient of friction of the bearings (different coefficients of
friction could
be considered for different locations, but assumed to be all the same in this
example).
This simplified formula (not taking into account integral calculus due to the
centrifugal forces, which should be considered for accurate prediction) is
provided as an example to show the different parameters (M, m, Cf, P, etc.)
that
could intervene within the calculation of the resistant work. In fact, the
calculation formula for the resistant work varies from a circuit configuration
to
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another, for example if the ciosed circuit is supported by inner rails Ri
between
all points A, B, C, D, E, F, G, H, or only along the portion from point H to
point C
for example, or if the weight of masses (M+m) is supported by external rails
Re
between points C, D, E, F, or according to the shape of the closed circuit
which
depends on the actual values of h and L (see Figure 5). The goal of the above-
noted resistant work Wres formula is to show that the parameters used therein
(M, m, Cf, P, etc.) can be selected to minimize the resistant work.
We state:
W(+) = Wpot - Wres
This work W(+) may be positive depending on the choice of sizes of M, m, Cf,
h,
L, r, and RM.
L is the horizontal distance traveled by the masses (and trucks) between
wheels
(R1, R2, and R3, R4; i.e. between points A and B (circuit upper portion 22)
and
between points E and F (circuit lower portion 24)), and r is the radius of
wheels (R1, R2, R3, R4).
3- At the beginning of each period (i), the circuit 12 looses a quantity of
energy equals to [(1/2)*M*Vcir(i-1)~2] due to the disconnecting of the mass M
around lower point F, and with the connecting of mass M to the circuit 12
around upper point A, the circuit provides to the mass, during period (i), a
quantity of energy equals to [(1/2)*M*Vcir(i)"2]. Mass M gets to the upper
point
A with its own kinetic energy (WMA(i): energy of mass M at point A for period
(i)) to connect to an empty truck 14. The mass' energy WMA(i) will subtracted
from the energy to be provided by the circuit 12.
Mass M disconnects from truck 14 at lower point F, shown in Figure 3, while
maintaining the same velocity Vcir as that of the circuit 12. By having a mass
track 30, for off-circuit 12 upward displacement, of the mass guiding system
forcing mass M to typically follow a substantially circular arc, preferably
semi-
circular curve, of radius R which returns mass M to upper point A, as shown in
Figure 4.
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Mass M can gain height up to the upper point A of the circuit 12 in function
of
the velocity of mass M at the departure from lower point F, i.e. in function
of the
velocity of the circuit Vcir when mass M is disconnected from the truck 14, by
taking the mass track 30. It is therefore needed, at the time of disconnect of
mass M, that the velocity of the circuit Vcir exceeds the required
predetermined
value that enables mass M to reach the upper point A with a velocity VMA
larger
than [SQUARE ROOT(g*R)].
In fact, for mass M to reach the upper point A, the velocity of mass M at
lower
point F must permit the mass M to have, at upper point A, a centrifugal force
at
least equal to the gravitational weight (earth gravitational force) of mass M:
M*g = M*VMAA2/R
This means that mass M must arrive at upper point A with a kinetic energy at
least equal to [(1/2)*M*g*R] by adding sufficient energy to raise mass M by a
height equals to (2*R), namely [2*M*g*R] as an increase in its potential
energy,
and to include WfM, the amount of energy required to counter the friction
along
the curve R of the mass track 30 (friction due to the mass' weight and to
centrifugal forces); thus obtaining a departure kinetic energy for mass M of
WMF = [(112)*M*g*5*R] + WfM = (1/2)*M*Vcir"2
Accordingly, the velocity of departure of mass M from lower point F, i.e. the
velocity VMF of mass M when mass M disconnects from the circuit 12 at lower
point F, must be at least equal to:
Vcir = VMF = SQUARE ROOT [(5*g*R)+(2*WfM/M)] = Vcir(min)
From which, in a general way:
WMA(i) = [(1/2)*M*Vcir(i-Nh-2)~2] - [M*g*2*R] - WfM
where Nh is the number of periodic distances P between points C and D, and
also between points G and H, and Vcir(i-Nh-2) is the speed of mass M at the
time of disconnection from the circuit at lower point F (VMF).
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During the return of mass M towards upper point A, mass M has no influence on
the behavior of the circuit 12. In fact, once the mass M is disconnected from
the
circuit 12 at lower point F, the mass M and the circuit become totally
independent of each other.
4- Input of external energy into the circuit:
wo
5- (Another embodiment) With input of extemal energy Wmag(i), at
the level of magazine 40 (see details hereinbelow), to the mass M at the time
of
connection to the circuit at the upper point A during period (i):
Wmag(i) = [(112)*M*Vcir(i)"2] - WMA(i)
The formula for energy balance of the circuit writes:
Wcir(i) = Wcir(i-1) + WO + W(+)
Remark: this formula is true when, for each period (i), there is a quantity of
energy equals to Wmag(i) provided to mass M at the time of its connection to
the
truck 14 at the upper point A.
The formula for energy balance of the circuit (by period) can also write:
Wcir(i) = Wtcir(i-1) + W(+)
where Wcir(i) is the total quantity of energy of the circuit at the end of
period (i).
In fact, once the circuit 12 reaches, via WO, a velocity VO exceeding the
minimum
velocity Vcir(min) required for masses M disconnecting form the circuit at the
lower point F to reach the circuit back at the upper point A and for these
masses
M to start following the mass track 30 (see Figure 6), work WO is no longer
provided to the circuit, as long as W(+) is positive (larger than zero).
It has to be reminded that W(+) = Wpot - Wres and that Wpot, at the
disconnecting of the first mass M, is equal to [M*g*RM], and to [M*g*(RM+P)]
at
the disconnecting of the second mass M, and to [M*g*(RM+(2*P))] at the
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disconnecting of the third mas M, up until Wpot reaches its maximum value,
being
Wpot = M*g*(h+(2*RM)) with [h=Nh*P].
In the functioning principle (subject of the invention) of the machine 10,
W(+) must
be positive, and it is possible to keep or change the value of WO for
increased
5 gain of energy.
For the following, let's take:
Wcir(i) = Wcir(i-1) + W(+)
Hence, at each period (i), a quantity of energy equals to W(+) gets added to
the
circuit 12, but one should not forget that for this condition to apply one had
to
10 provide to the mass M, at the time of connection at the upper point A, at
the
beginning of period (i), a quantity of energy equals to:
Wmag(i) = [(1/2)*M*Vcir(i-1)"2] - WMA(i)
Wmag(i) is then equal to the energy lost by circuit 12 with the disconnecting
of
mass M at the lower point F and which is equal to [(1/2)*M"'1/cir(i-1)~2] less
the
15 kinetic energy WMA(i) that is gained back by the system for connecting
masses
at the upper point A of the circuit 12, from the mass M reaching the magazine
40
after its disconnection from said circuit at period (i-Nh-2).
Hence, in order to allow the circuit 12 to gain for each period (i) due to
potential
energy from masses M, one must input to the circuit, at each period (i), a
quantity
of energy equals to Wmag. But, after a certain number of periods, the total
amount of provided energy Wmag exceeds the amount of energy stored into the
circuit 12. This is explained by the fact that the quantity of energy W(+)
added to
the circuit 12 for each period (i) (which increases the circuit's velocity
Vcir) is a
constant, while the quantity of energy Wmag, provided to the circuit 12 for
each
period (i), increases with its velocity. Furthermore, Wmag reaches the value
of
Wpot once the velocity of the circuit 12 reaches the minimum value required
for
the mass M to run all the way along the mass track 30 because of its own
kinetic
energy, from which it is required to have the existing centr'rfugal forces,
the value
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of which depends on the velocity of the circuit, intervene in such a way that
provide to said circuit an addition of energy, which leads to the following.
B- System for exploiting centrifuaai forces
Referring to Figure 8a, it is well known that a mass M following a circular
trajectory has a natural tendency to follow a rectilinear trajectory that is
tangential
to the circle it draws, the mass M is then forced to follow the circular
trajectory
because of a centripetal force due to the physical link between the mass M and
the center of rotation (o).
When this link is broken, the centripetal force is absent and the mass M is
not
forced to follow the circular trajectory anymore, which is explained by the
fact that
the mass, once freed, follows a rectilinear trajectory tangent to the circle,
because
of its own stored energy.
Now referring to Figure 8b in which frame o-x-y is linked to rod (a-b), there
is
shown the case in which mass M is free to slide along rod (o-b) (shown in a
first
position in dotted line and in a second position in solid line) that is in
rotation,
illustrated by angle 4), vrith a constant angular velocity [Vy(M(a))/r].
Hence, there
is, between points (a) and (b), a mass M without any physical link to the
center of
rotation (o) for it to be retained radially relative to the center of rotation
in such a
way to eliminate the centripetal force. In the opposite, mass M, because of
its
sliding connection to rod (o-b), will have to follow the rotation thereof,
which will
make this mass M to undergo a centrifugal force pulling it along the rod (o-
b),
from point (a) towards point (b). This centrifugal force is variable since it
depends
on the position of the mass M therealong, where axis (o-x) (x=o-M is the
distance
separating mass M from the center (o)), and on its the linear (tangential)
velocity
Vy(M(x)), two parameters varying between points (a) and (b).
For a better explanation, in a more specific case, the following calculation
is
obtained from schematic of Figure 8b.
For tV=0, the linear Iineaire (tangential) velocity of mass M is equal to
Vy(M(a)).
Therefore, mass M has a tangential kinetic energy of
[Ecy(M(a))=(M*Vy(M(a))A2)/2]. Because of its only one degree of freedom,
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being a translation along rod (o-b), mass M also undergoes, at point (a), a
centrifugal force equals to [Fcx(M(a))=(M*Vy(M(a))A2)/r], where (r) is the
distance (o-a) along axis (o-x).
For an incremental rotation of delta(4P), mass M, under the effect of
centrifugal
force Fcx(M(a)), will move towards point (b) of (delta(x)), and its radius of
rotation will then be:
x = r + delta(x)
and its linear velocity will be:
Vy(M(x)) = (r + delta(x))*Vy(M(a))/r
because the angular velocity Vy(M(a))/r remains constant. During this
incremental displacement, kinetic energy is added to mass M. Then at this
point, the kinetic energy of the mass M must be of
Ecy(M(x)) = (M*Vy(M(x))"2)l2 = [((r+delta(x))/r)~2]*Ecy(M(a))
Which implies that mass M undergoes then a centrifugal force at point
x=(r+delta(x)) of
Fcx(M(x)) = (M*Vy(M(x))"2)/(r+delta(x)) = [(r+delta(x))/r]*Fcx(M(a))
It is then possible to write down
Fcx(M(x)) = M*G(x)
where G(x) is the acceleration of mass M due to the centrifugal force along
rod
(o-b), or the axis (o-x) within frame (o-x-y) (see Figure 8b). Hence:
G(x) = (Vy(M(x))"2)/(r+delta(x)) = (r+delta(x))*(Vy(M(a))/r)A2
Since the tangential velocity Vy(M(a)) is constant, it is possible to get the
time
duration needed to induce a rotational increment of delta(4j).
In general [V=Ut], hence [t=UV], which gives
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delta(t) = (r"delta(4i))Ny(M(a))
And the position of mass M, x(M(x)) and its velocity Vx(M(x)) along axis (o-x)
are obtained as a function of deltaff):
x(M(x)) = [(G(x)*delta(t)"2)/2] + Vx(M(a))*delta(t) + r
Vx(M(x)) = G(x)*delta(t) + Vx(M(a))
As the radial velocity of mass M at point (a) (at angle 4P=0) Vx(M(a)) is null
[Vx(M(a))=0], for the first angular increment of deltaff):
x(M(x(1))) = [(G(x)*delta(t)~2)/2] + r
Vx(M(x(1))) = G(x)*delta(t)
And for subsequent ones,
x(M(x(1))) = [(G(xQ-1))*delta(t)~2)/2] + Vx(M(x(j-1)))*delta(t) + x(M(x(j-1))
Vx(M(xQ))) = G(x{j-1))*delta(t) + Vx(M(x(j-1)))
Using these above two equations, it is possible to calculate, point by point,
the
trajectory of mass M for a determined rotational angle, as well as its
velocity at
the longitudinal extremity of rod (o-b), and the direction that will follow
the mass M
once detached from said rod. The velocity of the mass will therefore be the
vector sum of its tangential velocity Vy(M(b)) and its normal, or radial
velocity Vx(M(b)):
V(M(b)) = Vy(M(b)) + Vx(M(b))
And the mass kinetic energy will be:
Ec(M(b)) = (M*V(M(b))~2)/2
In order to maintain the angular velocity constant, a quantity of tangential
eneregy
had to be provided to the mass M as an amount of kinetic energy of:
M*[Vy(M(b))"2 - Vy(M(a))A2]/2
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This amount of energy will be part of the mass' energy at point (b), and will
be the
kinetic energy of mass M along axis (y) Ecy(M) [Energy conservation law] and,
in
addition, there is some kinetic energy Ecx(M) due to the centrifugal forces.
This surplus of kinetic energy Ecx(M) due to the centrifugal forces will be
exploited within circuit 12 of the present invention in two different ways
described
hereinbelow, and, accordingly, trucks 14 as schematically illustrated in
Figures 9a and 9b will be considered.
Figures 9a and 9b are an embodiment (amongst many others possible) of a
truck 14 made of two main parts, a fixed part 14f and a mobile part 14m, in
closed
and deployed configurations, respectively. The fixed part 14f is typically
provided
with bearings 16 allowing it to follow the trajectory of the internal rails
Ri, and the
mobile part 14m is typically telescopically, or the like, linked to the
respective
fixed part 14f with a translation generally perpendicular the axis 16a
extending
through the center of rotation of the bearings 16f of the fixed part 14f of
the truck
and generally perpendicular to the local trajectory of the internal rails Ri
as its only
one degree of freedom. The mobile part 14m is the part that selectively
receives
the mass M that connects thereto via a mechanical system or the like (not
shown). A mechanical connecting system or the like, such as the extemal rails
Re (shown as illustrative purposes only in Figures 9a and 9b), on which roll
the
bearings 16m of the mobile part 14m of the truck and/or the bearings 20 of the
mass M (depending on the position of the truck or the mobile unit, truck+mass
M,
along circuit 12), maintain the two parts 14f, 14m of the truck in proximity
relative
to each other in the closed configuration and further allow the free radial
deployment, along a trajectory predetermined by calculation, of the mass M
and/or the mobile part 14m relative to the fixed part 14f in predetermined
curved
section(s) of the circuit 12.
Example of an embodiment of the system for exaloitina centrifunal forces
In the following paragraphs, each of the different points A, B, C, D, E, F, G
and H
of the circuit are denoted with 'i' and 'e' indicia in order to differentiate
the
corresponding levels of the internal Ri and external Re rails at these
respective
points (point A includind points Ai and Ae, etc.).
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Figure 10 shows an example of an embodiment of a system for exploiting
centrifugal forces in accordance with the present invention mounted on the
circuit
of Figure 6. In a superior zone Zs, just after the upper portion 22 of the
circuit 12,
at the endpoint B, the system for exploiting centrifugal forces is located
into a
5 circular portion that exploits centrifugal forces of the masses M over a
curved
section of the circuit 12 of a typical angle of 180 degrees (Tr radians) (any
other
angle could also be possible) that is part of the system. Accordingly, the
extemal
rails Re are modified to have a shape Be-Ce (the trajectory of which can be
calculated point by point) such that the component Rt of the reaction R on the
10 masses M due to the centrifugal force Fc that is tangential to the
trajectory is the
largest possible. The centrifugal force Fc is due to the radially mobile mass
unit
(Mcm+M) (the mass of the mobile part 14m of the truck 14 plus mass M), to the
distance separating that mass from the center of rotation, and to the velocity
of
the circuit Vcir. It is only required that this trajectory be within the
trajectory that
15 could be followed by the mass unit (mobile part 14m plus mass M) while
remaining free of any radial (normal) obstruction. This condition ensures the
permanent contact with the extemal rails Re, which generates a reaction R
thereform acting on the mass unit. This reaction R can be broken down into a
normal (radial) force Rn opposing to the deployment of the mobile part 14m of
the
20 truck relative to the corresponding fixed part 14f, and another tangential
force Rt
in a same direction than that of the movement of circuit 12 that will generate
work
in addition to the work from the weight forces of the masses M along the
lowering
portion 26 of the circuit 12.
Remarks:
- The centrifugal force is always perpendicular to the trajectory of the
intemal rail Ri of circuit 12 along portion Bi-Ci (of internal rail Ri) as
well as
the work it generates, work due to the displacement of the mass unit
(mobile part 14m plus mass M) relative to the fixed part 14f of the same
truck 14, thus making this work totally independent from the work of the
circuit 12.
- The moving away of the mass unit from the centre of rotation of wheel R2
increases the mass unit tangential velocity, hence its kinetic energy. This
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21
energy is taken from the circuit energy but will be given back to the circuit
from the beginning of the lowering section 26 at points Ci to Ce from the
energy conservation law.
- The weight force of the mass unit has not been taken into account
between points B and C since the work generated there between is null.
- Along the lowering portion 26, the external rails Re bring the mass unit
back into contact with the fixed part 14f of the truck while absorbing a
quantity of energy, due to friction, equals to the mass of the mobile part
14m of the truck plus the mass M times the earth gravitational
acceleration constant (g) times the coefficient of friction Cf times the
horizontal distance between points Ce and De.
Other example of an embodiment of the system for exploiting centrifunal
forces
Figure 11 shows another example of an embodiment of a system for exploiting
centrifugal forces in accordance with the present invention mounted on the
circuit
of Figure 6. In an inferior zone Zi, just after the lower portion 24 of the
circuit 12,
at the lower point F, the system for exploiting centrifugal forces is located
into a
circular portion that exploits centrifugal forces of the masses M over a
curved
section of the circuit 12 of a typical angle of 180 degrees (rr radians) (any
other
angle could also be possible) that is part of the system, in a way of
extending the
lower point F up to point G. Accordingly, the extemal rails Re end at point Fe
(point F at the level of the external rail Re), in order to release the mass
unit that
undergoes an acceleration, due to centrifugal forces, moving it away from the
center of rotation of wheel R4. This displacement remains generally
perpendicular to the trajectory of the inner rail Ri between points Fi and Gi,
hence
the work generated by this displacement does not depend from the work of the
circuit 12, and in these conditions, the mass unit moves along the trajectory
betwnne points Fe and Ge under the action of two velocities, a tangential
velocity
V'cir with [V'cir=Vcir"r(Mmc+M)/r] and a normal or radial velocity Vc due to
centrifugal forces. At point Ge', beginning of the mass track 30 and in
proximity of
point Ge, the mass unit runs through the mass disconnecting system which
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22
disconnects the mass M from the mobile part 14m of the truck with no
constraint
to the displacement of the mass (the mass disconnecting system could be
mechanical based or any other).
Once mass M is disconnected, it is at the beginning of the mass track 30 that
has
its entrance portion always maintained tangential to the direction of motion
of
mass M, typically automatically. The direction of motion of mass M, once
disconnected from the mobile part 14m, is function to the direction of its
velocity
VMGe' at point Ge', that is the vector sum of the two velocities V'cir and Vc
which
are always perpendicular to each other.
~ --4 -.>
VMGe' = V'cir + Vc
Mass M then enters the mass track 30 with a kinetic energy equals to:
Ec(MGe') = M*(VMGe'~2)/2
Once mass M is disconnected from the mobile part 14m of the truck, the mobile
part 14m is in contact with the external rails Re at point Ge via its bearing
16m
(this contact must occur after the disconnection mass M therefrom). In moving
up along the raising portion 28 of the circuit 12, between points Ge and He,
the
extemal rails Re bring the mobile part 14m back into contact with the
corresponding fixed part 14f, and this absorbs, per period (i), an energy due
to
the friction equals to the mass of the mobile part 14m times the earth
gravitational acceleration constant (g) times the coefficient of friction Cf
times the
horizontal distance between points Ge and He.
Both embodiments of the system for exploiting centrifugal forces described
hereinabove could also be used on a same circuit as schematically shown in
Figure 12, and then the balance of work of the machine 10 would be:
Wcir(i) = Wcir(i-1) + WO + W(+) + WMA(i)
with
W(+) = Wpot + W[Fc(Be-Ce)] - Wres
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where Wres is the energy dissipated by the friction forces along circuit 12;
W[Fc(Be-Ce)] is the energy generated by the centrifugal forces between points
Be and Ce; and
WMA(i) = [(1/2)*M*(V'cir(i-Nh-2)"2 + Vc(i-Nh-2)"2)] - [M*g*2*R] - WfM
where WfM is the energy dissipated by the friction forces along the mass
track 30.
In all cases presented in Figures 10, 11 and 12, it is possible to temporarily
stop the input of external energy WO as soon as [Wcir(i)-Wcir(i-1)] becomes
and remains positive.
OPERATION OF THE MACHINE OF THE PRESENT INVENTION
Step a: Using an input of external energy WO, the velocity of circuit 12 is
brought up to a predetermined velocity Vpre (in function of the different
physical
parameters of the machine 10 and of the closed circuit 12) larger than the
required minimum velocity Vcir(min) allowing for the value [Wcir(i)-Wcir(i-1)]
to
become positive.
Stepb:
For the embodiment shown in Figure 10, once the circuit 12 has reached the
predetermined velocity Vpre, the mass disconnecting system is activated,
typically automatically, and disconnects mass M from its truck 14 at lower
point
F of said circuit 12, and the disconnecting of the mobile part 14m of the
truck
from its fixed part 14f occurs only between points Be and Ce.
For the embodiment shown in Figure 11, and partially Figure 12, once the
circuit 12 has reached the predetermined velocity Vpre, the mass disconnecting
system is activated, typically automatically, and disconnects mass M from the
mobile part 14m of the truck 14 each time a mass unit gets to point Ge' at the
beginning of the mass track 30. Typically, there is no need in these cases of
a
specific system for connecting to and disconnecting from each other of the
fixed
14f and mobile 14m parts of the truck, and which is typically provided by the
external rails Re.
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Step c: As soon as the first empty truck 14 gets to the upper point A of
the circuit 12, the mass connecting system is activated ans connects,
typically
automatically, a mass M to each empty truck arriving at upper point A of
circuit
12. Also, said mass connecting system recuperates the kinetic energy WMA of
each mass M reaching its magazine 40 from the lower point F or Ge' (according
to the system for exploiting centrifugal forces being present (Figure 10 or
Figure 11 or other)), after running along the mass track 30. In the case shown
in Figure 10, the mass connecting system provides to the mass M the same
velocity reached by the circuit Vcir using an input of external energy Wmag,
as
long as required.
Step d: As soon as it is possible, it is preferred to stop or modify the input
of all external energy.
Step e: There is a selective coupling of the machine 10 to a load machine
once the value of work aimed for is reached.
Remarks:
- A plurality of machines 10 can be coupled to a same load machine.
- Referring to Figures 5a to 5d, depending on the values of h and L,
namely whether they are zero or not, the circuit 12 may have different
configurations as shown. Furthermore, when h=0, the mass track 30 is
preferably slightly placed laterally horizontally away from the upper and
lower portions 22, 24 of circuit 12 by a distance I to allow masses M to
fully disconnect from their respective truck 14 before raising toward the
upper point A, as shown in Figures 5c and 5d.
Alternatives
Although the closed circuit 12 disclosed hereinabove and shown throughout the
figures lies in a generally vertical plane, one skilled in the art would
easily
understand that any other closed-circuit having only a portion thereof located
in
a non-horizontal plane could be considered without deviating from the scope of
the present invention.
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Also, it is obvious that many technical solutions can reduce considerably the
coefficient of friction, which will in turn reduce the resistant work (Wres).
For
example, instead of using roller bearings 16, the trucks 14 could be displaced
on oil or pressurized air, or be levitating spaced away from the inner rail(s)
using
5 permanent magnets or the like.
In a different way, as in the case of Figure 10, the masses M could partially
disconnect form their respective truck 14 when reaching the start point E of
the
circuit.lower portion 24 and start rolling on a lower portion 32 (see Figures
4, 6
and 7) of the mass track 30. The masses M would remain partially connected
10 to their truck 14 with roller bearings (not shown) mounted on the trucks to
rollably push the masses M along the track lower portion 32 such that they
could completely disconnect from the trucks at the lower point F.
The mass connecting system for the connection of masses M to the respective
trucks 14 adjacent upper point A could be effected in different ways, as
15 described in the following examples, with no intention of any limitation.
a- By using a magazine 40 of masses M which is driven by, typically
horizontally, or operatively connected to the circuit 12 itself to operate at
a
velocity substantially equal to the circuit velocity Vcir, as schematically
shown in
Figure 6. This permits simple connection (insertion) of a mass M to each empty
20 truck 14 which arrives at upper point A, by providing the mass M (as in the
case
of Figure 10) with an input external work the quantity of energy that will
allow it
to reach the velocity of the circuit 12 with the mass M being disconnected
from
lower point F being placed into the magazine 40, where its kinetic energy will
be
recuperated. The only condition for such a configuration would be that the
25 number of masses M in the magazine 40 (in addition to the masses M
connected to the circuit 12 all along its length), shown in dotted lines in
Figure 6, must be at least equal to the distance d which separates the
location
of empty truck 14, from which a respective mass M is disconnected at lower
point F, from the respective mass M when the respective mass M reaches the
upper point A divided by the periodic distance P of a period (i). In other
words:
Number of masses M in the magazine >_ (d / P)
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This solution could prove particularly adequate if h = L = 0 or if L = 0 (see
Figures 5b and 5d).
b- The connecting system includes a mass delivery mechanism 42
equipped with two equidistant arms 44, separated by the distance d + P,
typically driven in rotation by an external work Wmag (as in the case of
Figure 10) with a velocity ratio Rv = (d+P)/P relative to the circuit velocity
Vcir to
displace the mass M from the upper point A to the empty truck 14 with a system
velocity Vsys = Rv*Vcir. In this case, as schematically shown in Figure 7, the
friction force due to the weight of the mechanism on its own rotation axes 46
adds up to the friction of the resistant work (Wres). The condition required
for
this mechanism to be implemented is:
L >(d+P)
In a different embodiment, as in the case of Figure 11, where applicable, the
trucks 14, with their mass M attached thereto via a mechanical system (not
shown), could turn around the 4 wheels Ri, R2, R3, R4 by being releasably
attached thereto without rolling on the inner rails Ri, which generates
considerable friction and centrifugal forces on the wheels and directed
towards
their axes. In this fashion, the effect of friction caused by the centrifugal
forces
on any outer rail Re gets eliminated and thus reducing everything down to a
question of managing a problem of friction forces acting on the axes on which
the wheels turn. This reduced problem can easily be solved by a film of
pressurized oil. Such a solution allows the closed circuit to reach high
velocities, and therefor high levels of generated power.
Although not illustrated herein, a plurality of similar closed circuits 12 can
drive a
common output shaft, preferably connected to one or a plurality of load
machines, by being positioned in parallel relative to one another, which
multiplies the power available at the output shaft by the number of circuits.
As mentioned at the beginning of the description, it would be obvious to one
skilled on the art that the closed circuit 12 could be located in a generally
horizontal plane, while having a system for exploiting centrifugal forces over
at
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least one curved section of the circuit (without any consideration of
transformation of potential energy of masses into kinetic energy), without
departing from the scope of the present invention.
Although the present invention has been described with a certain degree of
particularity, it is to be understood that the disclosure has been made by way
of
example only and that the present invention is not limited to the features of
the
embodiments described and illustrated herein, but includes all variations and
modifications within the scope and spirit of the machine functioning principle
based on the principle of exploitation of centrifugal forces, and optionally
on the
principle of gain of potential energy, subject of the present invention as
hereinafter claimed.
