Author: Sergey Makarov
Address: Esplanades, 6 - 64, Riga, Latvia
In October 2012 at the invitation of the
Federal University of Rostov I did in Rostov-on-
Don (Russia) report, which was called
"Makarov's Cable-stayed Networks for Earth
and Space Architecture." During my speech
one of the enthusiasts made a full video of my
report, and then he put this record into
For several months, this report was pumped
to over 50 video warehouses and they
showed it at the Internet as their own. Almost
everywhere the report was viewed by
hundreds of people and everywhere it was
rated 5 stars out of five. This gave me a
reason to create this presentation. In this
presentation, I showed this report in the full
Report: «Makarov's Cable-stayed Networks
for Earth and Space Architecture».
Author: independent researcher Sergey
Makarov from Latvia.
I represent information, which is the fruit of
many years of my individual work. My report is
chock full of new ideas. In preparing this
report I have tried to placed it into given to me
time, so I am obliged to hold the required rate.
I think that this report for someone will be
difficult to understanding. However, if you will
be interested in the content of the report, by
the end of it you'll be able to ask me some
In the book L.G. Dmitriev, A.V. Kasilov,
«Cable-stayed roof systems», "Budyvelnik",
Kiev, 1974 at 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 horizon arches, using just two families of
cables through the entire surface is not
On the page 31 in the same book it is
written the following: “Justified... is seeking for
new rational decisions for creation of cable
networks, which would have all the
advantages of hyperbolic-parabolic networks
and will not contain hard elements, except the
All my following information shows that the
above-mentioned leading specialists in the
creation of cable-stayed coatings were very
mistaken in their forecasts. The main "raisin"
of my designs is that I was the first in the
world, who used the convex-concave cables
to form the cable-stayed nets. This has
opened up tremendous opportunities for
And what was before that?
Earlier in the architecture were used only
convex and concave cables. Convex cables
were carrying a payload, concave cables were
used to pre-stress and to stabilize the
concave cables. So many buildings in the
world were built under this scheme, in
particular, the famous "Raley arena" (Raley
town, USA, 1949), in which were started the
using of cable-stayed saddle coverings in
The curvature of the coatings was clearly
not sufficient to stabilize them, this required
the using of special stabilizing cables placed
inside the building.
I decided to improve this solution and
create a similar coating not on flat arches, but
on the sinusoidal support contour. As a result,
my expectations were fully confirmed: the
curvature of the coating increased, were not
the need in special cables anymore. The
result of this decision, you can see on the next
The next slide shows the new structure -
"Makarov's Quartet", namely it destroyed the
mislead of the experts, who considered this
structure impossible. At concave zones the
cables work in the usual manner, but at the
convex zones they are redistributing their load to
the concave zones of other cables of the net.
If you are interested in where I got this idea,
take a look at the next slide.
Here you can see "chair of four crossed
arms", which many people know. It is this chair,
which children enjoy when bathing in the sea for
throwing each other to simulate the jumping from
the tower. Note the scheme of the crossing
hands in this "chair": each hand arises up from
under the previous one, moves up and comes to
the top side on the next half. Similarly, behave
and my cables in shown above structure.
After the "quartet" I made models “Three",
“Five", “Six" and “Seven" (accordingly with the
number of waves on the support contour). All
these nets I have described as inventions and
referred them to the Patent Institute.
Correspondence with the Institute lasted three
and a half years. Against my grids they put
forward a variety of arguments that I successfully
refuted. One day as one of the arguments in the
dispute with the institution I made the structure
with different high of humps: I just flexed a piece
of ordinary wire for the support contour and
made my network on such contour. Such model
can be seen in the next slide.
Patent Institute was so pleased by this
model, that namely it was used as the main
image in the issued me an inventor's certificate,
which is shown on the next slide.
When I received a certificate of authorship, I
decided to meet with one of the authors of the
above-mentioned book - Alexander Vasilyevich
Kasilov, which essentially was my main
opponent. I arrived to Kharkov and secured his
audience, waiting for him to tell me what he think
about my designs. To my surprise, he did not
say about my designs virtually nothing.
Apparently, appearance of my designs was so
unexpected for him, that he simply not found for
me any "decent words." Unfortunately, at the
present time Alexander Vasilyevich Kasilov is no
longer alive. And now look, please, at the next
Some experts had doubts that curved in three
ways cables can withstand severe pressure.
Above was shown my “Quartet", which was
braided by me 25 years ago. The fact that the
bearing ability of the network is very high, each
man can see at these two pictures shown:
deformation of the network from the iron anvil is
so small that it simply impossible to note.
At the next slide from the side of one of the
humps of the support contour is shown the
quasiorthogonal network spanned at the support
contour with the three sine waves.
On the next slide you can see a similar network
spanned by the support contour consisting of five
waves of a sine wave.
The next slide shows a quasiorthogonal net
on seven waves of a sine wave. Support contour
was created from thin copper pipe. It is not
difficult to see that this construction has no any
thrust: all the efforts from the cable network are
entirely extinguished by support contour. With
the construction of such a structure on the
ground we do not need any external quickdraws,
which often were used in the construction of
cable-stayed structures based on the hyperbolic
paraboloid with two humps.
I want to note: for each of the shown networks I
re-invented the scheme of weaving. After "Seven" I
created the "Eight" and "Nine", and then I got the
afflatus and discovered a law for the formation of
networks of such type. I opened a law, which
covers a range of cable-stayed networks with the
number of waves on the contour from four to
infinity. This law is very important discovery, I
think. Nothing like this discovery previously not
existed nor in engineering, nor in architectural
design. Previously, every structure was the result
of process of the solely single product creation.
Now let us turn to the cosmos. My structures
have no thrust. This allows you to use them to
create a wide variety of structures in outer
space. Have long was voiced the idea of c reating
in space some confined spaces, such, for
example, as Dyson spheres. While creating the
Dyson sphere around a planet, we can create an
atmosphere inside the sphere and make this
planet habitable for humans. To create the
hermetic shell inside the sphere we can use, for
example, a special self-hardening in space resin
by firm "Hughes".
The next slide shows an embodiment of
blocking together two modules of the "Six". Such
blocking may be needed for the Dyson Sphere
creation and for building in outer space of others
necessary to mankind facilities.
There is an idea: to create a structure at low-
Earth orbit that would act like a conventional
mirror (reflector). Reflecting sunlight to Earth
such a structure would allow to work at the
cornfield, build the objects and make some other
works at night with very good lighting. To solve
this problem may well be applied and my
structures. The next slide shows the initial stage
of the creation a space reflector from my "Six" .
Reflecting surface of the reflector can be
collected from the individual reflective petals,
each of which must be "stitched" to the existing
The next slide idea of p lacing at low-Earth orbit
space reflectors has been further developed. Here,
one reflector is connected to the second one.
Developing this idea, we can go on and lock
together several my "Sixes" to get in the needed
area of t he Earth's surface a very high level of
The next slide shows the option to create the
space laboratory, for example. The outer concave
surface of such laboratory may be, for example, a
space reflector. One such reflector may be in use,
but the opposite reflector may be used, for
example, for repair work or maintenance work.
The next slide shows the idea of u sing, for
example, "Six" for the construction of multi-storey
facilities on the Moon or any other planet. Because
the force of gravity on the Moon is very small,
number of storeys of such structures can be quite
large. The main thing - the initial idea, but further
Intuition tells me that in outer space will be
most in demand my "Trojka", "Quartet", "Five"
and "Six". Corresponding models are shown on
the next slide.
The next slide shows the schemes of cables
for "Trojka", "Quartet", "Five" and "Six". In these
schemes the concave zones of networks are
marked with black dots, the cables going along
the bottom of the network are dashed, but the
cables, which are on top of the network, are
shown by solid lines. On the left halves of
schemes are shown corners occupied by zones,
which are clearly raised up or clearly omitted
down. Angles "phi" (see the right halves of
schemes) show the sectors of the same
orientation of cables.
It is seen that while the number of humps on
the support contour becomes more and more,
number of sectors with the same relative
orientation of cables getting bigger. Not difficult
to notice that due to the using of convex-concave
cables the whole network consists from an
interlocked individual zones of the gipar-type that
previously thought impossible without the using
of harsh elements. In this case one area of net
succinctly goes into the next area. The same
cable in one area of its path have the carrying
function, but in another area it is already strained
I have often thought that the cable-stayed
networks created by me on the sinusoidal wave-like
support contours look very succinctly. It can
not be that such undulating surfaces are not met
before in the history of mankind. I spent a lot of
time on trying to find somewhere in the history of
something like my surfaces. And I did it.
Take a look at the next slide. It shows a picture
that I found on the Internet. My predecessor in a
similar simulation was Dutch scientist Frits
Zernike, winner of the Nobel Prize in Physics in
1953. Zernike was engaged mainly in optics. He
was awarded the Nobel Prize for the development
of phase-contrast microscope.
As about the shown surface, this surface is a
three-dimensional graph of one of the functions,
which all the world now call "Zernike polynomials."
Without going into deep math, I note the following:
although the Zernike and had nothing with the
cable-stayed structures, he created for optics an
interesting family of orthogonal polynomials. It is
possible to apply such polynomials for the
mathematical description of the surfaces of my
cable-stayed networks. Limited time just does not
allow me to delve more into this topic.
One of the space problems is the task of
creation of cosmic multifunctional platforms. This
problem can be solved with the using of cable-stayed
networks. It turned out that my networks
can successfully be formed for support contours
that are composed of straight elements. After
creating a network the structure can be assembled
to the center. As a result, we get a ready platform
with the full operational readiness. One
embodiment of such a platform is shown on the
The next slide is also devoted to space
platform. Unlike from the preceding platform this
platform, for example, has a two-layer network.
Such a network would be certainly tougher. With
the help of such kind of network were formed
additional hangars around all the outer contour.
These hangars can be used, for example, in
military aims to place there some kind of
defensive missile systems.
The next slide shows the further development
of the theme of space platforms. Here you can see
the folding cosmic hangar. On the top zigzag
contour is spanned the first network. At the bottom
zigzag contour is spanned the second network. As
a result, was created some internal space, which
can become hermetically closed volume for
creation in it some kind of research laboratory.
The next slide shows the same hangar
folded. In this form it can be easy delivered from
the plant to the near-Earth orbit, and then we can
make its opening and perform additional
installation works and of encapsulation.
Space platform does not have to be a simple
flat surface. Take a look at the next slide. Here is
shown the structure, which can be, for example, a
cosmic reflector or cosmic radio antenna. The
peculiarity of this construction is that the joint point
for assembling of pair of contour elements was
moved so that ratio of one its shoulder to the other
was 2:1. Due to this, when opening the contour,
arises the effect of the structure opening like a lily.
The next slide shows another space platform,
or more precisely - its mathematical model. This
platform has a support contour of thirty-two
cruciform elements. Due to this, it can be unfolded
to cover a very large area.
The idea of its application in space is as
follows: field formed by its mesh surface, can be
effectively used as the site for the construction
on it of various habitable sealed modules. In
short, we create a space platform and build on it
a "community." To live in such a community
would be much better than, for example, in the
isolated capsule that hangs alone in the cosmos.
At the same time all navigation issues and
mutual assistance in such community could be
resolved much more efficiently.
The next slide shows the design that I would
call "artificial planet". The shown above
structures of the "double layer platform" type
(three copies) are integrated in such a way that
together they form a rigid three dimensional
structure. To imagine her structure, let's think
about the three-dimensional Cartesian
coordinate system. Three above-mentioned two-layer
space platforms are placed into three
mutually intersecting planes of the system.
The next slide shows the possible
development of the theme of creation in the open
space artificial planet. For its creation, applied
two series of inclined rigid elements (in this my
structure is similar to the famous tower of
Shukhov). One group of rigid elements is tilted to
the right. Another series of the similar elements
is tilted to the left. My networks could be created
on such obtained zigzag support contours.
In this case, you can create multiple "floors"
for their using in different needs. The most
interesting thing is that all the forces of cable
networks perceives only one rope, which is at
the center of design and pulls the two poles as
shown on this picture.
As I mentioned earlier, the modules on the
basis of a regular hexagon very conveniently
could be blocked to each other into a structure
like a honeycomb. The next slide shows a
module, which I have modeled in the program
After horizontal blocking of such modules
they may be coupled and vertically too. This give
us high-rise buildings, which can be
implemented on the surfaces of other planets,
and in outer space. Such vertical structure is
shown on the next slide.
To implement the idea of a multi-storey
building you can use not only hexagonal, but
also any other module. The next slide shows the
option to create a cosmic multi-storey building on
the basis of three octagonal space platforms.
Having found that the program «Wolfram
Mathematica» is very convenient for me to
construct the necessary objects, I began to
widely use it in my work. The following series of
pictures - is the result of my exercises with this
program. The following image shows how the
above-described "construction field" could be
used to host the series of residential space
After placing on the specified field several
housing units, we can build at the top of them the
second floor as is shown on the next slide.
But for what we need a second floor? On this
floor you can place another series of inhabited
residential units. And it is possible to use the
upper floor as a landing site for the space
Much has been said and written about the
future creation of a "space hotels". Even several
private companies have such plans. I see a
similar hotel consisting of the above-described
series of airtight units that are, namely,
"residental modules". These modules are
mounted on a space platform of the cables.
Several such platforms are blocked in the
vertical direction. The upper platform serves as
the landing site for the space shuttle that brings
guests and then returns them to the Earth. The
following slide also shows us a possible variant
of the "space hotel" organization.
I want to note: you can build the residential
floors as many as you need. The moving
between them will provide you a space elevator,
or even a simple rope. I think that for many will
be interested in the following: the shown in the
upper and lower slides space shuttle was also
created by me mathematically in the program
«Wolfram Mathematica». At the same time I can
"put" it on any of my structures and show you
from all sides and at any angle.
Graphene - a new material with a thickness
of one carbon atom. Its hexagonal cells formed
by the carbon atoms are blocked to each other
like a honeycomb. Now imagine several layers of
such cells, which are arranged in tiers, having
some vertical communication. Such construction
is shown on the next slide. This slide
demonstrates the spatial structure of the
graphite. Graphite is very known to us, because
it is used in all ordinary pencils. Hope that this
structure reminds you of something else. Namely
such manner we can place our residential cells
in our outer construction.
Suppose that we need to build a Dyson
sphere around some of the space objects. The
scheme of a possible solution of such a problem
is shown on the next slide.
Let's develop this theme further. I recently
opened a new direction of space architecture
and called it "cosmic nanoarchitecture." My idea
is that for the construction of space structures is
reasonable to apply the constructive schemes
that have already been created by nature in
microcosm. Presented at the next slide fullerene
C60 shows my vision in establishing a closed
shell around any space object. The series of
modules such as "Makarov's Five " and
"Makarov's Six" in my Dyson sphere are
consistently combined with each other to create
a completely closed sphere.
The next slide shows the space nanotube. All
that is said above for the fullerene C60 applies to
it too. With the rotating such a tube around its
axis, we will get inside the tube artificial gravity.
Of course, in the open space dimensions of such
a tube may be very large, which allows a person
to comfortably live on inner side of its surface.
For some specific purpose, we may need and
not closed "nanotube". One possible solution of
this problem is shown on the next slide.
I want to draw your attention to the fact that
all three-dimensional objects, which I presented
above, contain a closed shell, inside of which is
already possible to create a sealed volume and
create the atmosphere. However, to meet some
tasks we can need the presence of some
"windows" in our shell. The following slide shows
an embodiment of the organization of these
windows: when installing the elementary
modules, some of them we can just do not
You may ask: what tasks will require such
tricks? My answer: while you mount the
"nanotubes" one to other, you may need to
organize some passes from one tube into the
next one. By making some transitions from the
tube into the tube you can create an "integrated
laboratory" of the individual tubes, which is
shown on the next slide.
I am waiting the question: and what about the
space cold? Not cold will be in our cosmic home
with such a "single-layer glazing”? The answer
is: yes, our "single-layer glazing" will not give us
the necessary protection from the cold of space.
Take a look at the next slide. What prevents us
to create our cosmic home from several
concentric coaxial space "nanotubes"?
If we thus will create a transparent coverage
sealed to the inner surface of each of the
illustrated coaxial "nanotubes", then inside the
innermost tube will be not simply heat. There you
will can even "walk naked" because the sun itself
will deliver to you the necessary energy for
heating your cosmic home.
And now let's turn our attention to the Moon.
As it turned out, on the Moon there are many
natural wells, which are called "lava tubes".
Many organizations are engaged in study of
options of using these lava tubes as the space
inhabited by man. The next slide shows my
option to create a lunar inhabited settlement with
the construction at the top of lava tube some
double dome, mounted into the concrete ring.
The space between the domes must be filled by
the air that will protect people from large
All objects of space nanoarchitecture need
only two types of modules - "Five" and "Six". The
next slide shows not "mathematical model", but
real "Makarov's Five", which really exists (hangs
on the wall of my flat). Network of "Makarov's
Five" was braided exactly by my law.
The next slide shows actually existing
"Makarov's Six". Its network was also braided
according to my law. Thus, the effective
preparation of the "cosmic space capture" with
the objects of my "space nanoarchitecture" I
theoretically already have prepared.
The next slide shows us the real blocking of
actually existing modules. I hope that I showed
the whole theory of the question fully honestly
and transparently in the literal and figurative
sense: for manufacturing of my "Five" and "Six",
I used transparent plexiglass.
Objects of nanoarchitecture - are not only
fullerene C60 (on the scheme of which are
based, by the way, the model of most modern
sports balls). This may be, for example, and
such sphere (see below).
Some number of possible nano-spheres are
shown on the next slide. Keep in mind that the
larger will be the object, around which you create
a Dyson sphere, the greater (in quantity of used
cells) will be the figure, what you need. This is
due to the fact that each person is more
convenient to work with objects of moderate
size. It is unlikely that someone will be interested
in assembling Dyson sphere, if the size of one
elementary module ("Five" or "Six") will be a few
Recently was published my article "Space
Globe Architecture." In this article I stated
another new direction in space architecture.
Take a look to the globe of the Earth. It is divided
by the parallels and meridians on a series of
dissimilar triangular and quadrilateral cells. If on
a convex figure is possible to create such a grid,
then further this object can be collected in space
using a series of modules such as "Three" and
"Four“ (“Trojka” and “Quartet”).
Actually existing "Makarov's Trojka" we have
- let's look it at the next slide. I draw your
attention to the fact that virtually all of the
modules "Three", which we will need for the
particular sphere construction, will have the
same shape and the same size, which allows us
to establish their mass production.
Actually existing "Makarov's Quartet" is also
available - let's look at the next slide. A series of
blocked in vertical direction "Quartets" will be
collected from the modules of different sizes: the
closer to the equator of the globe the larger will
be module. However, each circular tier of our
globe will be constructed with the belts of
“Quartets", which have the same shape and the
Now back to the Earth architecture. In the
article "Tensegrity - a new direction in
architecture" I announced the discovery of a new
trend in architecture that uses in coatings of
buildings and structures tense cable-stayed
designs without any thrust. Such structures are
already available in architectural practice.
However, only with the appearance of an infinite
series of "Makarov's networks" we can speak,
namely, about the new direction in architecture.
"Trojka", which is shown on the next slide, I
have collected from three flat arches. Previously,
such a structure was considered as impossible.
For lack of time, I can not now explain to you
why each plane arch, which is "pulling in one
direction only“, does not fall to the center of the
structure. However, it is so. Those who are
strongly interested in this issue, will be able to
read about it in my article "About hunting bows
and arches of support contour" (in Russian),
which is located at the St. Petersburg
architectural portal «Art to Build».
On the following slide is shown the interesting
"Makarov's Five," in which, among other things,
was used a vertical shift. Such a solution can be
used, for example, in the construction of
buildings on a mountainside.
The next slide shows the proposal of the
architect Alexey Karachinsky to create mobile
theater. This project uses the "Makarov's
Quartet," which has an inflatable support
contour. Inflatable structures are characterized
by the fact that they can be fairly quickly and
easily installed and removed. Such operations
do not require large expenditures.
The next slide shows the same project
proposal of Alexey Karachinsky when you are
looking at the building from the ground. Also
there is shown the option of arranging of internal
space of theater.
Below you can also see the said mobile
theater of Karachinsky when you look at it from
the side. I want to note that this theater has a
good interesting form. When theater is operating
in the summer it does not require any heating. If
desired, such a theater you can do even without
The following four slides are about my
participation in the international architectural
competition for the reconstruction of the cinema
"Pushkinsky" in Moscow. For this project, I have
used four flat arches. The following slide shows
an actual skeleton of these arches and the
network. I draw your attention to the fact that the
arches do not fall to the center. Model stands
just on the sheet of paper. Thrust of the network
is fully repaid by the support contour.
Below slide shows the same support contour
from the front. Contour is installed in the design
position - on headroom of vertical columns.
The next slide shows the same frame after
mounting a waterproof coating on it. To reflect
the sun's rays the coating has a silver surface,
which protects the building from overheating.
I would like to inform you that this
international competition received over 1,000
projects. My project was not ranked among the
winners. However, such my structure have never
been used in the world. The following slide
shows a general view of the cinema
"Pushkinsky" after its possible reconstruction by
the proposed by me project. I think you'll agree
that this building acquired expressive modern
form and well fit into the surrounding historical
I hope that a series of new designs, which
are presented in my report, did not leave you
indifferent. I mentioned earlier about made by
me discovery - "law compatibility of quasi-orthogonal
networks." All shown by me networks were built
on this law. In this regard, I think it is not
acceptable not show the text of the law in this
report. Full text of my law is shown in the next
On the upper slide are shown three
hyperlinks. The first line of this slide shows the
internet address of the personal English-Russian
website of the author. There you can find all
additional information that you may need. The
second line shows the site address "Space
Architecture" of English encyclopedia
"Wikipedia", where you will find my several
works. The third line shows the address of
"Space Architecture" of English encyclopedia
I note that the page "Space Architecture" in
the encyclopedia "Wikimedia Commons" I
personally created about a year ago and
administration agreed with me. At this moment
the presentation of my report can be considered
to be finished. If you have any questions for me,
I will try to answer them.
Thank you for your attention!