Short history of this project

The physical principles of functioning of gravifugal flying
craft was discovered 1986. Followed mathematical and
technological elaboration and it was patented in Belgrade, ex
Yugoslavia 22.11. 1989. After it, I tried to publish an
articles like this, in all scientifically magazines in the
world. After more than 300 unsuccessful attempts, at 1996. I
published a part of book at internet, at the site
http://agram.phy.hr/~bertovic/antigravity html ,and
www.deneb.org/petrus , and this too. The first serious
interest was shown at the end of 2000. by ing. of aerospace
technology, Kevin Golsh, Clearwater, Florida ,USA, and his
brother Kyle. They asked me all drawings, because they wanted
to build one gravifugal flying craft, and test my ideas. I
hope they will be constant, and their work will be successful.
But I also hope that other people will help to this project.

One of the many reasons:

with gravifugal flying craft it could be easy to get

x - prize - 10. 000. 000 US $

Unfortunately, regard it I can do nothing more. My problem,
now is sheer survival.

Author. P. Bosnic Petrus

Part II

Definition of the Gravifugal Force

When speaking about the gravifugal force we in fact refer to a
certain sort of centrifugal force created by rotation in which
gravity acts as centripetal (i.e.gravipetal) force. Direction
of the gravifugal force is always opposite to that of the
gravipetal (gravity).This concept of gravifugal force is based
on Newton's understanding of gravity as an attracting force,
on the law of action and reaction, and the law of inertia, and
has been deduced from them by means of the mathematical tools
provided by the Huygens's theory of the centrifugal force.

Centripetal and Centrifugal Forces

Designations "centripetal" and "centrifugal" do not denominate
any special forces, but rather directions in which a
particular force acts during a rotational process -- towards
the centre or away from it, or rather, towards the axis of
rotation or away from it. Any of the known forces may be
centripetal in direction, that is to say, perform the function
of the centripetal force.

The following table lists all centripetal and centrifugal
forces

  Designation of
  special forces
                         Centripetal forces
                                                    Centrifugal forces
  Gravity

  Electricity

  Magnetism

  Nuclear force

  Cohesion
                         Gravipetal force

                         Electropetal force

                         Magnetopetal force

                         Nucleopetal force

                         Cohesipetal force
                                                    Gravifugal force

                                                    Electrofugal force

                                                    Magnetofugal force

                                                    Nucleofugal force

                                                    Cohesifugal force
  Fundamental forces
                         Function
                                                    Pseudo-forces


      The above table clearly shows that the function of the
centripetal force is performed by fundamental forces, with the
exception of the cohesive force; hence its slight separation
from the others.

 

Centripetal, Axipetal, and Axilongal Forces

In regard to the direction of action it is also important to
differentiate between axipetal and centripetal forces.
Axipetal force is directed toward the axis of rotation, and
the centripetal toward the gravity centre of the rotating
celestial body.

Particularly, I want to draw attention to the axilongal force
- the one acting along the axis of rotation. This force can be
caused exclusively by the rotation of a celestial body, or by
the rotation of a disc or ring within a gravitational field.

 

Specific Features of the Rotating Mass of Celestial Bodies

First and foremost, it must be pointed out that the
cohesipetal force which enables a solid body to rotate without
being dispersed is not a fundamental force but an inertial,
pseudo-force. Differences in the after-effects of rotation of
solid body(with regard to the rotation of a celestial body)
result from the fact that rotation of celestial bodies is made
possible by the fundamental, gravipetal force. It is of utmost
importance.

Let us observe Figures 1a and 1b which show forces that result
from the rotation of a steel sphere (1a) and the forces
created by the rotation of a spherical celestial body (1b).
Lines of the cohesipetal force resulted from the rotation of a
steel sphere are perpendicular to the rotation axis and at the
same time are parallel to one another, and since they are
directed toward the rotation axis they are designated as lines
of the axipetal force. Lines of the gravipetal force are
directed to a single point in the centre of a celestial body,
while the gravifugal force Fgf spreads radially from that
point -- the point of application of force.



         Figure 1 a and 1 b

In the case of the steel sphere, force Faxl (axilongal force),
active in the direction that is parallel to the rotation axis,
will equal zero for two independent reasons:

1.In accordance with the laws of symmetry, the force directed
upward from the plane of rotation equals the force directed
downward so consequently, the two cancel each other out.

2. We can arrive at the value of the force parallel to the
rotation axis by multiplying either the cohesifugal or the
cohesipetal force by cos90o, which equals zero. Bearing in
mind that , (cos 900 = 0) the force parallel to
the rotation axis, i.e. the force active in the direction,
Faxl, will equal zero regardless of the velocity at which a
ring or some other mass may rotate.

However, the very fact that gravipetal and gravifugal forces
(Fig. 1b) spread in a different manner from cohesipetal and
cohesifugal forces (Fig.1a) indicates that where the rotation
of a celestial body is concerned, the axilongal force, Faxl
could exceed zero value. This in turn means that the concept
of the gravifugal flying craft is not a pointless one, since
the rotation of a ring rotating in the vicinity of some
celestial body would create the axilongal force, Faxl the
value of which would be proportional to the rotation velocity,
v of the ring.

 

Vectorial Analysis of a Rotating Mass at the Geographical
Latitude j = 45O

a) First Group of Facts -- Values of the Gravifugal and
Gravipetal Forces

Rotation of the mass of a celestial body at its equator is
determined by only one force: gravipetal force, Fgp, while
rotation at latitudes greater than zero requires an additional
force: cohesipetal force Fcp (Fig. 2). This force is always
perpendicular to the direction of both the gravipetal and
gravifugal forces. Its function is to maintain the observed
mass on a parallel the radius of which is smaller than the
radius of its equator. Cohesipetal force, Fcp is in fact a
mechanical tension (tension of the solid body material)
directed toward a designated point on the rotation axis of
celestial body which is, in fact, the point of application of
the cohesipetal force.



Figure 2

If there were no cohesipetal force, an observer standing on
Earth (and rotating with it) would notice that the observed
mass is accelerating toward the equator, i.e. in the direction
of the cohesifugal force Fcf. This potential trajectory is
marked by the curved dotted line culminating in an arrowhead.
The component known as the "horizontal component of
geocentrifugal, (i. e. of geoaxifugal) force" is in fact
nothing more than the cohesifugal force Fcf. To a stationary
observer in space recording the trajectory of the observed
mass this trajectory would appear to be circular -- designated
as an ellipse (dotted line) in Fig. 2.

(The cohesipetal force appearing in connection with rotating
celestial bodies is ultimately a derivative of the
gravitational force. This can be observed directly in rotating
gaseous bodies, i.e. those without solid crust. However, this
is neither the place nor the time to go into a detailed
explanation of this phenomenon.)

The expression for the value of the gravifugal force is ; 
             , and for

the value of cohesifugal force it is 

 

b) Second Group of Facts -- Relative Value of the Gravipetal
Force

Figure 3 is a representation of rotation of the observed mass
at . Let us first assume that an observed celestial
body is not rotating, in which case the only force existing
there would be gravity. If that were the case, the observed
mass would exert pressure on the surface of the celestial body
of . There is no rotation and no symmetry in
relation to the rotational plane P.

Now let us assume that the linear velocity of the mass equals
the velocity of satelisation: c. 7900 m/s. At that velocity
and at the given geographical latitude j = 45O all four forces
determining the rotation of the observed mass -- the forces of
the inner circle -- would be equal: c. 9.81 N. It is clearly
visible that they are symmetrical in relation to the
rotational plane, but the weight of the observed mass, or
rather the pressure it exerts upon the surface of the
celestial body, has fallen to zero.

Let us further assume that the rotational velocity of a
celestial body could be considerably increased, and together
with it the velocity of the observed mass, and let us observe
the behaviour of the forces (after such increase in velocity).
The outer circle represents the area of increased speed and
the limit to which the observed forces have increased.



Figure 3

Our observation will tell us that the only forces to have
increased would be pseudo-forces: cohesipetal, cohesifugal,
and gravifugal. This is logical and, indeed, essential, since
the value of these forces depends on the factor , i.e.
it is proportional to velocity v and inversely proportional to
the value of radius R.

The fourth force, gravipetal force Fgp, has not increased.
This is a fundamental force and its absolute value is
determined by the

expression , and it existed prior to rotation, which
was not the

case with the other three pseudo-forces. The relative value of
the gravipetal force is inversely proportional to the
rotational velocity of the celestial body, i.e. to the
velocity of the observed mass. This relative value of the
gravipetal force, Fgp is defined by the expression

              . The greater is the value of pseudo-forces or
rather,the higher is the rotational velocity of a celestial
body, the lower is the relative value of the gravipetal force.

At this juncture I should point out that the value of the
gravifugal force cannot exceed the absolute value of the
gravipetal force since that would contradict Newton's Law of
action and reaction. When the velocity of the observed mass
exceeds the velocity of satelisation vs it is not the value of
the gravifugal force which increases, bur rather the observed
mass must increase the radius R of its trajectory, i.e. the
distance from the centre of the celestial body -- that is to
say, from the point of application, or source of the
gravipetal force. In fact, the observed mass must lift off the
surface -- in other words, it starts to levitate.

The most important observation at this point is that there is
no longer any symmetry in relation to the rotational plane P.
The vector sum of the forces at the "upper" side of the plane
is greater than the sum of the forces at its "lower" side.
This means that the observed mass will accelerate in the
direction of the gravifugal force Fgf.

The ring of the gravifugal flying craft, to be discussed later
in this text, behaves in exactly the same manner.

 

c) Third Group of Facts -- the Value of the Axilongal Force
Faxl

However, vital to the requirements of the gravifugal flying
craft is the value of acceleration in the direction of the
axilongal force Faxl . Figure 4 will assist us in determining
the value of that acceleration.



Figure 4

Velocity of the observed mass is considerably greater than the
velocity of satelisation.

The value of the axilongal force Faxl is arrived at by
multiplying the cohesipetal force Fcp by cosj and the
gravifugal force Fgf by sinj , and then by adding the two
results. From the obtained total we deduct the value of the
cohesifugal force Fcf, multiplied by cosj .









The value of the axilongal force is therefore proportional to
the rotational velocity v, to the sinus of the angle F , and
inversely proportional to the motion radius of the observed
mass R, i.e. to the distance from the centre of the celestial
body.

         only in three cases: a) , b), and c) 
          ( is only at the Equator). only
at the equator.

If we want to know a velocity maintaining in equilibrium
    and derivative of gravitational force , we can
get it by equation:. Values achieved by this
equation are in quite accordance with establish knowledge and
experience

 

Very important note - potential serious objection

Somebody could claim that, for axilongal force, F axl, in
every case (at every geo. lat.) radius R (i.e. radius-vector
of gravipetal force, or acceleration g sinj which is parallel
with axis of rotation of celestial body) will be infinite,¡ ,
and consequently, value of axilongal force, F axl will be
zero,0. This is very serious objection, and I can contravene
it only by my opinion that follows:

This objection is absolute correct in a case of rotating of a
solid body,(e.g. steel sphere) where the direction of
centripetal (cohesipetal) force and its value depends on
rotation of that body.

However, in a case of rotation of celestial body, direction of
spreading of radius-vector of centripetal (gravipetal) force,
R not depends on rotation of celestial body. Direction of
action of gravipetal force is unchangeable because it is not
apparent, than rather fundamental force, which always is
directed to the gravity center of celestial body. Because of
it is impossible that the radius-vector of gravipetal force, R
has an infinite value, ¡ . Acceleration g sinj ( parallel with
axis of rotation) is not radius-vector of gravipetal force, R
but just a quantitative derivative of gravipetal force or
gravipetal acceleration. It has zero value only at the
equator, as I stated above.

List and equations of forces

Given below is the list of all forces as well as the list of
eqations giving their values..

Table 2. List of Forces.

Gravitational, ------------------------------

Gravipetal, or 


Gravifugal,  or 

Cohesipetal, or 

Cohesifugal, or 

Axipetal, or 

Axifugal, or 

Axilongal or 



Figure 5 depicts all those forces graphically



Figure 5

Double-Curved Trajectory of the Ring Mass (The first key part
of the theory)

In an effort to make things as simple and clear as possible,
thereby making the problem easier to understand, I ask the
reader to imagine a rotating ring (as shown in Figure 6) at
some moderately high geo. latitude.

If we wanted to present the motion of the ring mass through
Euclidean geometry we should take into consideration, above
all, the fact that every particle of the ring mass on the way
from point A to point F is always at equal distance from the
centre of the celestial body. It is assumed, of course, that
the axis of rotation of the ring is identical, or co-axial to
the direction of action of gravity. If the trajectory of the
ring mass from point A to point F is projected onto a plane we
shall obtain a symmetrically curved line (part of a circle)
since all points are at equal distance from the centre only
within a circle. From the projected trajectory it is easier to
understand why the rotation of the ring must necessarily cause
the gravifugal force Fgf.

By the way of clarification, during rotation of the ring its
mass is continually "falling" or veering toward the centre of
the celestial body (point of application of the gravipetal
force). The trajectory of the ring mass is simultaneously
curved toward the centre of the ring and the centre of the
celestial body. The curvature toward the ring centre is
visible to the naked eye, whereas the curvature toward the
centre of the celestial body can be understood only on the
basis of a knowledge of spherical geometry and the correct
method of arriving at conclusions

                       

Figure 6, Figure 7

In order to make it quite clear, I would now like to give an
elementary explanation of the above claims whereby the
trajectory of any particle in the ring mass is not straight
but curved, in other words, it veers constantly toward the
centre of the celestial body. I would ask the patient reader
to make a paper cone and then to draw lines on its outer
surface that would extend from the base to the point (Figure
7). Now place the cone base down on a table or any flat
horizontal surface. We shall see that the edge of the base
touches the flat surface at all points, thus giving the
impression of being as flat as the surface upon which it
rests. However, when we open the mantle of the cone and spread
it out we shall see that it is not flat at all, but spherical,
circular (i.e. curved) and that each point on its edge is
removed from the former top of the cone by the same distance.

Just as this edge veers constantly toward the former top of
the cone, so do the particles of the mass of the rotating ring
constantly veer toward the centre of the celestial body
forming a curved, circular trajectory. It is difficult to
perceive that the edge of the base is curved toward the top of
the cone unless the cone mantle is opened and spread out.
Similar difficulty is encountered in observing the real form
of the trajectory followed by the particles of the ring mass.
At first glance no one would venture to say they veer
constantly toward the centre of the celestial body (say,
Earth). The mass of the ring resists this veering toward the
centre of the celestial body, i.e. it resists the change in
direction of its motion. The consequence of this resistance,
i.e. of inertia, is the gravifugal force, Fgf. The direction
of its effect is marked by arrows on Figure 7.

 

Experimental proofs (The second key part of the theory)

Experimental proof of the existence of the gravifugal force
can be found in gravimetrical tables in every text-book of
geophysics. Measured values of the gravifugal force or
acceleration are in absolute accordance with the values
calculated on the basis of the expression .





Gravimeter is measuring slight declinations in values of
gravity caused by gravifugal force, flatnes of Earth and some
other very small factors. Every point on every parallel on
Earth (every geo. lat.) we can regard as point of mass of
rotating ring presented at fig. 6 and 8.

Experimental proof of the existence of the axilongal force can
be found in tables of navigation by gyrocompass. Every
gyrocompass is provided with tables of "error of geograpfical
latitude" (slight declination toward East). This "error"
remains unexplained till today. I have explained it by the
influence of the axilongal force. Now it is possible to
calculate the "error of geographical latitude" by the
following equation:



Angle is the value of "error"; is the force caused by
the gyroscopical inertia (of the gyrocompass rotor).

 

Application of the Presented Principles on the rotation of
ring of the Gravifugal Flying Craft Ring

The gravifugal flying craft is a device in which a
large-diameter ring rotates at high velocity. The rotation
axis would always be co-axial with the direction of action of
the gravitational force. See Fig. 8The craft would lift off
and levitate by means of the force resulting from the rotation
of the ring, and would be active along the rotation axis. I
have designated this force as the "axilongal force". Axilongal
force is, as already explained above, a derivative of the
gravifugal force,





Figure 8

                                              

The ring of the gravifugal flying craft would have a radius
from 1 to, for instance, 20 metres. It would be the same as if
a certain mass were revolving round the polar axis at a
distance of a mere 10 metres, which corresponds to the
geographical latitude of j = 89.9999102. The sinus of that
angle is practically 1, and on that basis the equation for the
value of the axilongal force could be as follows: 
               and for the value of the resulting force or
acceleration it could be: . At the velocity of 7900
m/s the ring of the gravifugal flying craft should levitate,
and at velocities above that value it could lift a casing
enclosing it. A ring of sufficient strength should be able to
carry a flying craft bearing a useful load.

Behaviour of gravifugal Flying Craft and Its Accordance with
Energy Conservation Law

Astronautical experience has confirmed the theory that the
higher an artificial satellite flies, or rather, the greater
is its distance R from the centre of the Earth, The lower must
be its velocity. This is an inevitable consequence of the Law
of conservation of energy: . The greater is the
height h of an artificial satellite, i.e. the longer is the
radius R of its orbit round the centre of the Earth, the
greater is its potential energy , and consequently,
the lower is its kinetic energy which is in turn
lessened by the reduction in the velocity v of the satellite.
Energy conservation law is also valid in case of the
gravifugal flying craft.

Kinetic energy of its ring is calculated by equation 
             and its potential energy by equation. 


 

              , . Factor , than we
can write

 

                     . Since the factor h is in fact radius R,
they cancel each other

 

out, and we write , , 


 



w is the angular velocity of the ring, I is the momentum of
inertia of the ring, mfc is the total mass of the gravifugal
flying craft, including also the ring mass, h, height is
radius R i.e. distance from the centre of Earth.

The last equation clearly shows that behaviour of the
gravifugal flying craft is in accordance with the energy
conservation law. The larger the radius R and its potential
energy, the lower is its kinetic energy i.e.angular velocity,
?w of its the ring.

 

Part III

Small, Experimental Gravifugal Flying Craft

Fig. 9 1: Ring; 1a: section comprising iron core; 1b:
aluminium or copper mass; 1c: carbon fibre; 2: casing area; 3:
iron lamellas making up the iron core; 4: carbon-fibre
construction; 5:stabilising gyroscope ; 6. coils

 



Figure 9

Diameter of the ring is 1.06 m. Maximal, theoretically
possible gravifugal force is 760 N.

The ring has no firm axis. It is floating in the magnetic
field of the casing. Because of the magnetic field of the
casing, the ring cannot touch the walls of the casing.The
magnetic field serves as a frictionless magnetic bearing -
maglev system.

Coils are powered by 3-phase electric current. They are
mounted in such a way as to allow creation of a revolving
magnetic field. By linking the coils into the electric circuit
an opposing magnetic field is also induced in the ring mass.
Due to the effect of the magnetic field the ring detaches
itself from the casing wall on which it has rested and begins
to turn in the same direction as the magnetic field of the
casing. The velocity of the ring is dependent on the velocity
of rotation of the casing magnetic field, while the rotation
velocity of the magnetic field is dependent on the frequency
of the electric power (alternating). Please provide frequency
between 50 Hz - 530 kHz .Casing should be provided by 156
lamelas, i. e. 156 electromagnetic poles.

If a flying craft with an aluminium ring were to be fitted
with a battery of 50 Ah capacity that could feed electric
energy reliably to the device for at least 2.5 hours (i.e.
9000 seconds) and if electricity from a domestic power supply
were used to accelerate the ring up to the moment it is able
to ensure vertical acceleration of the flying craft of only
o.1 m/sec2 (in order to avoid air resistance in the lower
strata of the atmosphere), and if the craft begins to use
power from its own battery only after it peels away from the
launching lawn, then an average acceleration of the craft at
least 2.3 m/sec2, after 9000 seconds, can be relied upon.
According to the formula

        = 

the flying craft will reach the distance, l of 93,150 km,
which is one-quarter of the distance to the Moon. According to
the formula for calculation of the ultimate speed: v = at =
2.3 x 9000 it will move away from Earth at the speed of 20,700
m/sec. If the craft is launched 60 minutes before sunrise it
will travel into the endless Universe at the speed of 50,700
m/sec (including the speed of Earth -- 30,000 m/sec).

Alternative device

If you are using only minimal number of poles (lamelas) (9
electromagnetic poles casing), and want only to make a ring to
levitate, you should to provide frequency of 22,2 kHz. This
frequency could able ring to rotate at cca 8000m/sec and
levitate. If you want just to decrease weight of ring, eg. in
a value of 10%, you should provide frequency of 7,9 kHz. In
this case the gyroscope need not be provided, than rather one
balance.

Attention

The ring becomes to decrease its weight only when its velocity
exceed the linear velocity of Earth at your experimenting
place, i.e. at your geographical latitude. E. g. velocity of
Earth at geo. lat. 300 is cca 400m/sec. and at geo. lat. .450
is 338m/sec.

Gravifugal Flying Craft Fitted with Rings that are Permanent
Magnets

In order to demonstrate just how economical gravifugal
propulsion can be, on the following pages I shall give a
presentation of the construction and utilisation of a
gravifugal flying craft using permanent magnet bearings. These
are, in fact, two steel magnetic rings positioned so that
facing poles repel each other. The bottom, rotating, ring
creates the gravifugal force while the top, stationary, ring
acts as the bearing for the rotating ring. See Fig. 10

 



Figure 10

Fig. 10 1 - the entire rotating ring (rotor); 1a - permanent
magnets used to decelerate the ring; 1b - layer of carbon
fibre; 1c - electromagnets which accelerate the ring. These
magnets comprise no coils, merely a diamagnetic casing round a
ferromagnetic mass; 1d - permanent magnet (ring) which propels
the flying craft; 2 - casing wall; 3 - evacuated casing area;
4 - stationary magnetic ring; 5 - electromagnets which
decelerate the ring; 6 - coils of electromagnets; 7 -
structure of the flying craft with carbon fibre or aluminium;
8 - electric batteries; 9 - useful area.

The advantage of such a flying craft in comparison with the
one described previously lies in the fact that it consumes no
energy when constantly hovering at any given altitude, the
hovering being ensured by the remanent magnetism of the
rotating and static rings, i.e. their repellent force. Should
altitude be reduced, the kinetic energy of the ring rotation
would be transformed back into electric energy by means of
permanent magnets (1a) and coils (6) and stored in batteries.
The electric energy would, of course, also be used for the
horizontal acceleration and deceleration. But for horizontal
movement can be used and some other kind of energy, or fuel.

Bearing in mind that when hovering at any given altitude,
these craft would consume no energy, they would be suitable
for use as floating family homes, hotels, hospitals,
industrial plants, observatories, etc. Floating platforms of
this type could be positioned at any altitude above the
equator, and also above the poles. Main part of future Mankind
will probably live in floating cities and on floating islands.