World Journal of Mechanics, 2013, 3, 319-322
Published Online November 2013 (
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Discovery in Statics
Sergey Makarov
Independent Researcher, Riga, Latvia
Received September 3, 2013; revised October 1, 2013; accepted October 25, 2013
Copyright © 2013 Sergey Makarov. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This article described the opening of a new law in fundamental physics, namely the law of the formation of an endless
series of suspension (cable-stayed) networks coatings. Opening relates to the mechanics, section of statics.
Keywords: Cables; Cable-Stayed Network; Support Contour; Suspension Roof; Space; Space Hotel
1. Introduction
One of the branches of basic physics is mechanics. Me-
chanics is divided into statics, kinematics and dynamics.
Statics is the section of mechanics that studies the equi-
librium of solid, liquid or gaseous bodies at rest under the
influence of external forces. We know that all construc-
tion projects are static objects, so the construction indus-
try has long been the main consumer of scientific re-
search statics. The needs of the construction, in their turn,
stimulated the development of this science.
How much do we know of discoveries in statics?
Probably not much. Apparently, the latest discovery, re-
gistered in the statics, is the “Law of Archimedes” about
the force, which acts on a body immersed in a fluid.
I am a trained civil engineer. In 1977, after graduation
from the institute instead of a diploma project, I have
“excellent” defended my scientific research work. Around
1983 I began to research the development of suspension
roofs (cable-stayed systems).
2. The Emergence of Cable-Stayed Systems
in Construction
The first building, which was covered with a suspension
roof was built in the Raley city (USA) in 1953. A general
view of the building is shown in Figure 1.
After that, the building began construction of cable-
stayed roofs around the globe. As the carrier elements in
the coating was first applied cable-stayed network,
whereby the entire coating became about four times
lighter than was previously possible. This building has
convincingly shown a clear advantage of cable systems
over all other coating systems. It was later built a lot of
buildings that used cable system. However, each such
building was a unique object. In the matter of creation of
cable structures of roofs any explicit methodical system
were no created.
3. My Researches of Cable-Stayed Systems
In the course of my research, I was able to create a num-
ber of new cable-stayed systems. The first four of these
are shown in Figure 2.
My cable-stayed systems of coatings do not require
any device side braces for the perception of effort from
the cables. All internal efforts in structure are fully
closed to itself and they are completely perceived by
rigid support contour which can be made, for example, as
a thin wavy closed rod. This fact turns out to be promis-
ing for application such structures in space and on the
surfaces of other planets. In Figure 3 is shown one of the
structures whose contour is made of thin copper pipe.
This model is in my closet for over twenty years, but the
tension force of its network virtually unchanged.
Waves of support contour do not necessarily have the
same magnitude in the vertical direction. For the best
possible removal of rainfall from the roof to the entire
surface be better to give the overall slope. An example of
such a cable-stayed system is shown in Figure 4.
Following the development of schemes of creation ca-
ble-stayed nets for the three, four, five, six (according to
the number of waves on the support contour), I decided
to patent them. As a result, I got the one-man’s authors
certificate for “suspension roof”:
Inventor’s Certificate SU 1270256 A1
aics?CC=SU&NR=127 0256A1&KC=A 1&FT=D&date=
Figure 1. Raley arena.
Figure 2. My first four models.
( mid_10.htm#X00)
Figure 3. My “quartet”.
Shown in scheme in the description of invention “sec-
tors of unchanged cables orientation”—a central angles
within which each of the cables is placed either strictly
on the top of surface, or strictly on the bottom of surface.
The more waves are made on the support contour, the
less are these angles.
Next, I continued to develop the schemes of creation
cable-stayed nets to contours with more number of waves.
Figure 4. My “Gorb quartet”.
I have developed the network schemes for seven, eight
and nine.
From the mathematics is known: for the discovering of
the general formula for the sequence you must have at
least three of its first members. If we consider the ca-
ble-stayed structures with an even number of waves on
the contour, it will be four, six and eight. If you will
analyze the coatings with an odd number of waves, it will
be five, seven and nine.
The schemes of creation each of mentioned above ca-
ble-stayed nets I re-invented every time. When I created
a number of networks to nine inclusive, I became able to
detect and record the mathematical law of their formation.
As a result, I got the ability to create the joint (i.e. with-
out separations in all of the intersections of cables) cable-
stayed network with an arbitrary previously fixed num-
ber of contour waves of four to infinity. I wrote the
discovered by me law of formation of such networks and
registered it with the notary.
4. The Law of Compatibility: Law of
Compatibility of Quasi-Ortogonal
Tangentially-Undulated Cable-Stayed
It is established the previously unknown regularity of
existence of joint quasi-orthogonal strained networks,
which are formed by two families of cables, which are
focused along the geodesic lines of approximated with
the help of network the tangential-undulating surface,
which has a rotational symmetry of order “n” (“n”—a
positive integer greater than or equal to four) consisting
in the fact that, starting from the main zero line all the
following each other in the tangential direction central
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angles, corresponding to sectors of unchanged orientation
of cables relative to the approximated surface, within a
complete revolution obey to the following sequences:
nn n
-if “n”—an even integer and , then
4n-if “n”—an odd integer and , then
  
52 5252 52
,,, ,,,,,, ,,,,,,,,,,,, ,,
nn nn
nnn nnnnnnnnnnnnnnn nn
 
    
 
    
(Signature) MAKAROV S.G.
I, PASHALIS O.V., a notary public of the 3-d State
notary office of the city of Leningrad, certify that on Sept
8, 1989 in 12 hours and 45 minutes this document is pre-
sented to me in the aforesaid state notary’s office by
Makarov Sergey Grigorievich citizen residing at the ad-
dress GATCHINA, Leningrad region, Gagarin street,
house number 19, a hostel.
Man’s personality, who gave the document, was iden-
Registered in the register 3122-Д2
(The stamp of the Notary’s Office) Recovered state fee
50 cents
NOTARY PUBLIC: (Signature)
Explanation: zero lines is contingent lines passing
horizontally through the center of the coating. Through-
out the whole length of such lines the heights of all
points of coating are equal to zero (the vertical axe of the
coordinate system is directed up). The main zero line is
such line, from which in going counter-clockwise (when
viewed from the top down) the heights of points of the
support contour increases.
In Figure 5 I present a photocopy of the original
document certified by a notary public (in Russian).
5. Judgment of Specialists
In the book [1] to the page. 32 you can read the following
text: “However, creation a rational orthogonal cable-
stayed network on the support contour of three and more
inclined to the horizont arches, using just two families of
cables through the entire surface is not possible”.
On the page 31 in the same book [1] it is written the
following: “Justified... is seeking for new rational deci-
sions for creation of cable networks, which would have
all the advantages of hyperbolic-parabolic networks and
will not contain hard elements, except the support con-
Thus, in 1974 leading specialists declared all my
shown above structures as “impossible structures”. How
could this happen? As far as I understand, the experts did
not imagine that someone will begin create a cable-
stayed networks FROM CONVEX-CONCAVE cables.
Until me all the suspension roofs were created from the
cables, which had throughout whole their path of the
same sign of curvature. One series of cables was re-
garded as the CARRIER series, another series of cables
was considered to be STRESSER series. If you needed to
create a cable-stayed network with several waves on-
support contour (more than two), then the series of “hy-
pars” (this word is derived from two words “hyperbolic
paraboloid”) were simply blocking with each other with
the help of some rigid details, which significantly wors-
ened the quality of this coating and led to the increasing
of its weight.
6. Prospects of Application
Cable-stayed networks of my structures do not lose con-
sistency network after different affine deformations (com-
pression, tension, shear), which makes them suitable for
the construction of buildings, even on sloping surfaces.
Figure 5. My law certified by a notary public.
Further on the basis of this law, I established a series
of new designs, which are particularly suitable for the
construction in space the “space towns” about which a
hundred years ago wrote Tsiolkovsky. This series of de-
signs you can see at the page “Space Architecture
( title=Categ
ory:Space_architecture) of British encyclopedia “Wiki-
media Commons”. Nowadays, one of the most urgent
tasks in space exploration is the need to build space ho-
tels. My solution to this problem is based on the applica-
tion of the above law (look the presentation “Multi-Sto-
rey Space Hotel
With the method, which is described in this presentation,
can be built also the solar reflector with a diameter of
several kilometers. Such reflector is required to change
the trajectory of asteroid Apophis, which will arrive to
our Earth April 13, 2029.
7. Recent Comments
The above law marked the beginning of an endless series
of new cable-stayed structures. The history of architec-
ture and building was not like this.
Is it possible that the law declared above be really
recognized as DISCOVERY? For professional patent
specialists, the main feature of discovery is the presence
of the SERIES OF INVENTIONS that arise on the basis
of opening. If such a series exists—opening exists. For
comparison as an example, I can give the opening of the
Niels Bohr of the quantum transitions of electrons from
orbit to orbit. When the working body is pumping by the
energy, the electrons are increasing their energy and they
are moving to the upper levels of the electron orbits, fur-
ther if under certain conditions the electrons are “falling”
to lower orbits, they synchronously emit stored energy.
All this was described by Niels Bohr in a small article
about a hundred years ago. However, his discovery be-
came the beginning of the “laser era”. This discovery
was followed by the inventions of a lot of lasers for a
wide range of electromagnetic frequencies.
Previously, information about my discovery has been
published in the press. See, for example, such sources:
All of my cable-stayed networks are static rope con-
structions of mechanics. Until now, the latest discovery
in mechanics, in “static” section, was registered by man-
kind for more than two thousand years ago.
[1] L. G. Dmitriev and A. V. Kasilov, “Cable-Stayed Roof
Systems,” Budyvelnik, Kiev, 1974.
[2] S. Makarov, “Discovery in Mechanics,” Techno-Com-
munity of Russia, 2013.
[3] S. Makarov, “Discovery in Mechanics,” Agency Technical
and Scientific Information, Scientific and Technical Li-
brary, 2013.
[4] S. Makarov, “Discovery in Mechanics,” Techno-Com-
munity of Russia, 2013, in Russian.
[5] S. Makarov, “Discovery in Mechanics,” Science Internet
Portal “SCIENCEEDGE.NET”, 2013, in Russian.
[6] S. Makarov, “Discovery in Mechanics,” Agency Techni-
cal and Scientific Information, Scientific and Technical
Library, 2013, in Russian.
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