I think, that someone of readers was shocked by my
statement" about a doctoral degree without defending a thesis... However, if the conscientious reader will take
a deep look into the content of my entire engineering and architectural activities, he will be very surprised to
find that the engineer Makarov created in the architecture not one, but several new architectural trends. These
new directions, of course, have not received until the decent
real development in our lives. However, note: I am
talking namely about the "theory of architecture", but not about the series of some already built objects.
But let's consider everything in order.
1. Space architecture.
If seriously analyze the history of use of the phrase "space architecture", then we will be forced to state that the
phrase existed, but it had no any real content. As the most valuable book in this direction, I mean the book "the
Architecture of weightlessness" (Yaroslav Golovanov. The Architecture of Weightlessness. Moscow. , Machinery,
1985.). At the same time I want to notice, that the "architecture", which was declared by the author in the title of
the book, inside the book was reduced to a series of engineering structures.
Mankind already had long been launched into space different devices. These were machines to solve some
specific tasks, but they often were not very aesthetic... Let's remember: "Architecture is frozen music..." You will be
able to bring at least one example of such a "frozen music" in space? I think, what is not. The beauty, the harmony,
the aesthetic balance - this is the first of the characteristics of the interesting architectural object. The designers
have such notion as "design line", "design style". Now, I venture to inform you, that before the engineer Makarov
nobody had attempted to offer any specific design line in space architecture, there were only individual space
vehicles. In this direction I am an absolute pioneer. Who doubt this, go, please, to page
"Space Architecture" of British encyclopedia "Wikimedia Commons".
There you will find several architectural directions for the space construction, which are represented with 37 my
structures. By the way: it is I, who created the page "Space architecture" in this encyclopedia. Apparently, before
me, nobody needed such a page.
Earlier there were only "Tensegrity-designs" (which before me were presented, as I conventionally describe them,
with the "the pencils on the threads"), but "Tensegrity-architecture" did not exist earlier at all.
Some people doubt, that my designs are namely "Tensegrity-structures" (see, for example, section
«Tensegrity» of British
encyclopedia "Wikimedia Commons". To this I must tell you that for the first time my structures were called
"Tensegrity-structures" by the American Professor of architecture Mason Peck (Mason A. Peck,
Associate Professor Mechanical and Aerospace Engineering 212 Upson Hall Cornell University Ithaca, NY). I think,
that we can trust him: now he works as a chief technologist in the head office of NASA in New York...
The "tensegrity-architecture" as architectural direction was first time declared by me in my article
Tensegrity - a new direction in architecture, which first time was published in Russian by the architectural
portal "Form" in March 9, 2011. I had to note that in this article I declared the "tensegrity-direction"as a new direction
and for the earth architecture, and for the space architecture.
Interestingly, that the idea of using cable-stayed structures in space
belongs to the "space pioneer" - Konstantin
Tsiolkovsky. It was he pointed the prospects of their application in outer space construction, although, as I know,
he had no any concrete such structures. Apparently, he as an engineer-constructor purely intuitively felt the economic
efficiency of cable-stayed structures application in the direction of "capture" of large space fields and space volumes.
Unfortunately, to date about this has already been almost forget everything...
3. Space nanoarchitecture.
Space nanoarchitecture was proclaimed by me in the article with the same name, this article was
published in Russian by the information Agency "PICTURE of the WORLD" in the middle of may 2012. Previously
were nanotechnology, there was even a "nanoarchitecture" for the Earth (John Johansen, "Nanoarchitecture:
A New Species of Architecture"), but "space nanoarchitecture" never existed before. The idea to apply for the
construction of space objects the structural frameworks schemes, which are known to mankind from the
nanoworld, belongs to me personally.
Space globe-architecture appeared in my article
What is the “space globe-architecture”? This article was published in the information Agency "Earth Space
Agency" in July 2012. I created it for space, although I admit that the application of its main idea may find its
embodiment in the architecture of the Earth too.
"Makarov's Enneper-architecture" was declared by me in the article "Makarov's Enneper-architecture
Earth and for the Space", which was published in the scientific portal "SCIENCEEDGE.NET" in March 2013.
Basis for such an architecture are the three-dimensional graphs of the functions, which were offered in 1864 by
the French mathematician Alfred Enneper. Up to this time such functions were only "pure mathematics" without
any possibility of their practical application. I created the idea about the possible application of such graphs for
building a real architectural objects as in the Earth's architecture as well as in architecture of outer Space. Such
objects, of course, can be built, for example, of reinforced concrete. However, I see a more real perspective.
I propose to build objects of enneper-architecture on the basis of my cable vant networks.
I wrote earlier that my cable-stayed structures are static
rope meshes. These structures clearly belong to mechanics, namely to "statics". However, in none of
books in physics, in none of "mechanics" section and in none of the subsection "static" you will not
find them. The reason for this, I think, lies in the fact that many "pundits" have great inertia of thinking,
they do not like anything new in physics books and handbooks issued by them are very reluctant to give
him a place, especially when the authors of the new are not they. However, I have infinite patience:
why should I hurry if I have an eternity as my future... I have no doubt that my structures in the end
will appear in all sections, "statics" all sections of "mechanics" of all produced manuals on physics.
But until that happens, I'm like 25 years ago have to take care of itself. So I decided to create on my
personal website this section.
For those who do not know, I note that the grid, which is
shown on above, directly under the table - this is the real "Makarov's Five." Looking at it, I recall the
words of Pushkin's poem "Poltava", "One can not harness to one cart horse and quivering doe. "You
can see that in the shown structure were perfectly joined together "incompatible" earlier numbers as
4 and 5. It turned out that the "squared" in his structure network (ie a network which is formed by
two mutually orthogonal families of cables) can be easy created at the support contour, which
contains exactly five periods a sine wave. Before me, it was considered impossible. The reality of
the shown "miracle", as well as an endless series of other such "miracles" is guaranteed by my
"law of compatibility of cable nets".
I want to note that although the "troika" formally not belongs to
the scope of objects of my "law of consistency...", it is certainly also a representative of "Makarov's
structures" and it is suitable for using in many space and architectural projects, because for her, I
a separate scheme of weaving the cables.
For those who do not yet know, I tell: all of my
nets came into being contrary to the opinion of leading experts
in the field of cable-stayed structures.
They are as "illegitimate children" had no right to appear into being because the experts believed their
existence impossible. Among the cable-stayed nets from two families of the cables on the undulating
support contours before me, gipar was considered as "the limit of possibilities". If the waves on the
contour required more than two, the coating was composed of separate gipars which were connected
with each other through a system of hard elements, which significantly reduced the aesthetic and
structural properties of the coating as a whole. I had withdraw this long-term ban of professionals.
Moreover, once removing the ban, I discovered for the world an infinite number of "illegitimate"
structures. In addition, even their infinity is really infinite in several dimensions. When we have made
our selection in one place, we open only one infinity (leaving the other one without our attention),
as we move along this path, we make the choice again, leaving countless number of structures
"overboard". And so on... Generalizing the described process, I named my first method of forming, as
well as attempt to classify my structures as "garden of divergent trails."
The main property, the main feature of my structures is the "power
balance". All my structures are harmonious Union of compressed and stretch elements. In all of my
structures "the game of forces" is closed within the structure. It is this fact allows Me to consider my
structures as very promising for using them in architecture of outer space. My structures are very suitable
for construction in outer space, and on the surfaces of other planets. The structures are easily blocked
both horizontally and vertically. Namely this their ability is very valuable for the construction of a continuous
settlements in outer space.
I don't know much about space architecture worldwide. It is
possible that I am the founder of this direction in all the humanity scale. Yes, there were real spaceships,
there were fiction writers's space settlements. But, as far as I know, NO ONE BEFORE ME has not yet
declared publicly namely about ARCHITECTURE in outer space construction as a focused art of engineering
and design. No one, as far as I know, not offered some "style", some specific "design line" in this regard. There
were only the INDIVIDUAL DEVICES to solve only some SPECIFIC scientific and engineering tasks.
You can, of course, don't believe me - it's your right.
However, at present time, in the section
"Space Architecture" of English encyclopedia "Wikimedia Commons" all space
architecture is shown only as my thirty-seven design solutions. Except my constructive suggestions you can
find here nothing else.
I hope that my suggestions and will form a
solid foundation for the design and construction of future human settlements in outer space.
(The first method of forming Makarov's structures, created on wavy and broken
Different types cable-stayed roofs for Earth, as well as
cable-stayed space platforms for various purposes to accommodate them in outer space and on
the surface of other planets can be created on the basis of multi-variant wavy and broken form
support contours. Their middle zone is made up of separate cables that are joined into a network
without any nodes and tight elements.
Formation of a network of all Makarov's structures is
made in strict accordance with my "law of compatibility of
kvazi-orthogonal cable-stayed networks".
This law guarantees to the constructor obtaining the joint
network with any number of contour waves (four or more), quite apart from the vertical magnitude
of this network and regardless of the horizontally size of the platform.
Starting the building a structure, we need to define some
initial parameters, then during the building process these options become more and more accurate,
complemented and eventually it leads to a quite complete constructive solution.
It turned out that build the concrete structure is much
easier than to describe the general theory creation of such constructions.
I have thought about this theory, many, many months, so believe me: chosen by me the path of
this description is quite justified, although someone may be little shocked by it. If you will find a
little patience and you will read my description to the end, then I assure you: all in your mind
"will take it's place of". And now for the cause.
1.  Choice the shape of the figure of placement of zero-points
Figure of placement of zero-points I mean some everywhere
convex flat curve (parole: plan of coverage). This everywhere convex closed curve is characterised
by that it will always lie entirely on one side of the tangent, which was held at any of the curve points.
This figure we need for placing at its plane all contour zero-points and all zero-lines of cable-stayed
network (i.e. the lines along which all the points of the surface have zeroed vertical values). In points
of crossing of zero-lines with the contour curve will be placed also the points of inflection of the spatial
contour curve (the curve along which are fixed all the ends of the network cables), as well as (possibly)
will be placed vertical supports, if the covering is placed on a rigid surface.
There are the following variants of selecting the figure of
placement of zero-points:
•  Circle - the most balanced shape with maximum symmetry, circle has
endlessly number of symmetry axes.
•  Oval (ellipse) - very balanced shape, which has two axes of symmetry.
•  Ovojt ("chicken egg") - a well balanced shape that has one axis of symmetry.
•  Random convex shape - not balanced everywhere convex shape,
which has no any axis of symmetry.
I would like to note: the shape for zero points placement is always
flat figure, it must necessarily be everywhere convex shaped, because a support contour, that will be placed
later along this curve, has to be able to completely take over the all forces of network and to remain tough.
2.  The central point selection
"The central point" I call such point, selected on the plane of zero
points placement figure (inside this figure), around which later will be formed the whole cable-stayed network.
This point does not necessarily have to coincide with the Centre of gravity of the initial figure, but while the
closer it will be to the point to the center of gravity, the more balanced will be in the future as cable-stayed
network and the whole structure.
3.  Choice of zero-lines number
All zero-lines placed in the plane of the zero-points placement
figure. All zero-lines always pass through the center point.
Architecture of the future coverage always depends on the choice of the zero-lines number. It is known
that the number of zero-lines always match the number of waves on the support contour.
If support contour has four humps, this is "quartet", if it has five humps - this is "five", and so on.
4.  Selection of the zero-lines orientation
Zero-lines should always pass through the center point, however,
they may be generally be oriented rather arbitrarily.
Of course, the best is such their orientation when they are placed under the same angles to each other
(it is such their orientation is envisaged in the "law of compatibility...").
For example, the symmetric "Quartet" has all zero-lines such that between each of their neighboring pairs
of angle 45 degrees; the "Five" -36 degrees; "Six" – 30 degrees, and so on. If the the figure of zero-points
placement has the lines of symmetry, it is desirable that the same axis of symmetry were also the symmetry
axes for the selected zero-lines group.
5.  Choice of convex and concave zones
Each pair of adjacent zero-lines defines two sectors which are
formed with the help of the pairs of lines and relevant pieces of the figure of zero-points placement.
Choosing the sectors which will be directed up or down, we set all the architectonic expressiveness of a
future structure. Usually the most expressive can be such structure, which has the sector of the maximum
area directed up (this makes the structure look like a flying up the airplane). After we choosed the first
sector to bump up, we when crawling around a central point, for example, clockwise, pointing orientation
of all other sectors: concave, convex, concave, convex... (still we will come back to the primary sector)
6.  Choosing angles of inclination of the plane of figure of zero points placement with
respect to the horizontal plane
It is obvious that the zero-points placement figure can be placed
horizontally, then all the vertical supports of coverage (if any and if the bearing surface is horizontal) will
have the same height. In the general case, however, we need to specify two angles to determine the
mentioned plane inclination in relation to the horizontal surface. For the architectural expressiveness of
structure it is preferably to maintain symmetry on appointment of these angles and the maximum pitch
angle to horizont should not be more than 45 degrees.
Look at the following picture below.
This figure shows one of possible variants of implementations of
the above six steps while forming Makarov's structure. It is obvious that the original shape is an oval (ellipse),
the center point is situated on the axis of symmetry of an ellipse, but it does not match with the geometrical
centre of the shape, nor with any of the focuses of the ellipse. Were drawn 4 zero-lines (see black lines), so
will be built the "Quartet". Zero-lines in plane were directed under angles of 45 degrees in relation to each
other, the symmetry of zero-lines and symmetry of the original shape are followed. The biggest sector was
made convex up. The main axis of symmetry of the ellipse (A-A) from the largest sector side rises over the
horizon. In a cross-section direction (axis B-B) the slope is not provided.
7.  Selection the surface, which covers the figure of
of zero-points placement
We made six steps mentioned above. Each of these steps was as a
branching of the roads (similar of Ilya Muromets's road), where we had to make a choice. The following choise
is not too obvious: we must choose one conditionally vertical surface, into which will be included
the figure of zero points placement, which we selected at our first step. Why I named this surface as
"conventional vertical"? Because this may be really lateral surface of the vertical Cylinder, inclined Cylinder,
Cone (direct and non-direct), vertical or inclined Prism, straight or inclined Pyramid. Of course, there are other
variants too, but I do not want much to scare my reader, so about other variants I just shall keep silence.
I think that you have enough imagination, so I won't show a series
of pictures for detailed illustration of this item, and shall proceed immediately to the next item.
8.  Selecting a closed curve of contour
To select a curve of contour I have prepared a lovely picture
This template shows the four options to select a closed curve of
contour. I hope that it is clear to everyone: I showed only one "period" of contour curve. Real contour
consists from several such "periods". Each of these "periods" should be rendered on the surface, which
was chosen in the seventh paragraph, (more precisely: "according to the selected surface"). Then they all
are blocked with each other to form a closed contour.
Is there the full set of all possible contours? Of course not. I've
shown only the most simple variants. If talking futher, then, in principle, the lower part of the contour
curve does not need to be an exact copy of her top part.
You can, for example, all upper parts of a contour to make
double in comparison to it's lower parts. You can make also all upper parts, for example, by using a sine
wave (blue curve on my figure is a sinusoid with double vertical scale), and the lower parts – as the arc
of a circle, and so on. You can, for example, one "period" create from one set of curves, and the other
one - from another. The main thing in this case: make mutual joining of top and bottom parts of contour
in according to a mutual tangent, provide one-directed bend for each upper and each lower parts of
contour, and ensure that you have the same number of mount points for cables at each lower and each
upper zones of the support contour. I, for example, for every upper and every lower part of the support
contour am making usually 8 points for cables mounting.
Thus, in spite of such "hard rules", which is represented by the
above eight paragraphs, you still have relatively greater freedom of action. I wish you inspiration!
(The second method of forming Makarov's structures, created on wavy and broken
I. Wavy support contours
At the very beginning of the creation of "Makarov's
structures" I began my research with a study of the process of building quasi-orthogonal
cable-stayed network on a specially made by me device. It was a square wooden box on the
side walls of which there were vertically placed a series of long spokes (about 30 pieces on
each side of the wooden square box ). These spokes were able to move in the vertical direction.
Each of cables was attached to its own spoke and had the ability to change its height of binding
practically independent of each other.
In the inner area (inside the square) cables were
joined according to the scheme of the "Quartet" (the scheme of which I invented literally "on
my fingers") and they interacted with each other in the process of changing the height of their
suspension on the support contour.
The first figure below schematically shows forming
the contour curve as a sine wave with the cables, being firmly attached to the ends of the
spokes of the contour. Such a scheme was implemented by me on each of the contouring
square sides. Then in the middle of the square box by crossing the cables appeared some
white handkerchief, hovering in the air, because the cables at model were made from the
white fishing line. The edges of the handkerchief repeated the sinusoidal profile, which edges
of the cabled got at support contour.
In those early years, the graphic capabilities of
ordinary people were very limited: in addition to fixing my results on a black-white photos
I couldn't use anything. Now I can show you such flying in air color "handkerchief", which
I created in modern computer program MATHEMATICA. I hope you will like it.
I experimentally determined that the sinusoid
is a good curve to generate the support contour, then I noticed that near the corners of
the square box the sine wave as would be rotated 90° about the vertical axis and has
been going along the other side of the box. Its movement after the turn in the
vertical direction continues quite naturally (the continuous increasing of ordinate)
and the second wave of sine is placed in good connection with the first one (before
Then I decided that the entire contour will be
better to organize on the lateral surface of a right circular cylinder. I did so.
All sine waves became connected into each other on the vertical cylindrical surface into
laconic closed curve of four periods of the sine wave. The following illustration shows
such a curve, however, for greater expressiveness all the ordinates of sine waves were
Next, I began to analize the variants of creation
such a contour of five, six and more periods of sine wave. After I created the
quasi-orthogonal network for nine periods of sine wave I made an opening and
then I have already been able to record my "law of compatibility for cable-stayed networks",
which allowed me to create good quasi-orthogonal network for contour, compiled from
any concrete number of sine waves. This direction of my creativity had come to
the logical conclusion. The law of my networks forming was created.
I now turn to the new direction my creative
process, namely, the theory of forming support contours for my cable-stayed
networks. I have tested many different contours yet, among whom were those drawn on
the lateral surface of a right circular cylinder, were those which consisted of flat arches or
flat sine half-waves. Were the contours composed of straight linear elements. Apparently,
it is time to create the general theory of contours forming. In my head it is already created.
So I decided to describe it and for other people.
First I note: in theory of construction and in the
architectural theory nobody in the world had deal with such a "theory of support contours".
Every building, every vant roof has always been "a masterpiece of author's fantasy" solely
as "unique product". This is the history. If you look at the created in the world coverages
(pictures of them is not difficult to find in published albums), you will notice that the
support contours in plan are always either round or oval, or they are non-existent at all.
In principle, it is clear to me: in the world there were not such thing as "an endless series
of new vant coatings". I am a pioneer in this area, therefore, namely, I have to lay in this
direction my "first ski path".
The second picture shows a right circular cylinder,
on its lateral surface is shown the contour, created with several periods of sine wave.
However, if we will accurately produce these arcs, then each arch, in addition to vertically
bending should get additional bending in horizontal direction, what cause manufacturing of
the arch to be more difficult. In addition to it, bend in the second direction would
significantly weaken each arch.
The bend in the single plane is the "natural bend", but to bend the same rod along the
second plane too, I consider "not natural". We will try to avoid this double curvature.
Look at the third picture. Every half-wave of the
pseudo sine wave is already fully flat, because the initial right circular cylinder has been
replaced by straight prism, side surfaces of which are fully flat. Rear part of the prism
conventionally isn't shown. However, for a good pairing of half-waves I had to draw them
between vertical ribs of the prism, for these half-waves will have a common tangent line
at the point of their contact.
You can go the other way. Look at Figure 4. Blue
curve, which was drawn almost on the lateral surface of the straight prism, is very similar
to a sinusoid. However, I would venture to say that every halfwave of this "sine wave" is a
flat curve. Take a look at the red triangle at the fourth picture. The fact is that the top
point of the triangle is located on the edge of the prism, and the remaining two points
are placed in the centers of the side faces of the prism. It is known that any three points
determine a concrete plane in space. So it turns out that halfwave sine wave, shown in the
center of the picture, is placed in a plane of the red triangle. By similar way I've been
placing each my other halfwave. Thus, each halfwave is placed now not on the side faces
of the prism, but at the planes of shown triangles (see, for example, the triangle ABC).
However, the connection between each pair of halfwaves takes place, namely, in the centres
of the prism faces. Common tangents for each pair of halfwaves (in dots A,C) lie in planes
of prism faces. Thus, each halfwave can be perfectly accurate flat halfwave of sine wave
(possibly with a vertical growth factor), but all these halfwaves with smooth docking with
each other will form a closed support contour for vant network. This is the methodology
with the help of which from the pieces of copper pipe was formed the support contour for
my structure which is shown at the photos in my article «Tensegrity - a new direction in architecture».
And what's next? Of Course... pyramid! To begin
with, let's get back to the third figure. We see a range of vertical side faces of straight prism.
The edges of the prism are parallel straight lines. Imagine that these direct lines are not
parallel lines now, let the top points of lines be converged into one point, the prism was
converted into some pyramid with polygonal base – see Figure 5.
Thus based on a similar pyramid I will construct
later my support contours. Remark: we live in a world where are many different flowers. It
is known that all flowers, appearing from buds, all their buds open up towards the solar rays.
That is why I decided: let all my support contours "reveal all their petals" toward the Sun
(Note: this is just my preference, revealing them down is not forbidden too). From it follows
that all my support contours better to start not on the pyramid which is shown in Figure 5,
namely on the basis of the inverted pyramid. I don't need the top point of the pyramid, so
I will begin my construction on the base of the inverted truncated pyramid - see Figure
In this picture I showed support contour for the
"troika", whose back side is shown by a dotted line. For illustration purposes, I conducted
on the face sides of the pyramid vertical lines which divide these sides into two equal parts.
At the figure are clearly visible three contour petals which are opened "towards the Sun".
Common tangents, which joined "halfs of waves" are, namely, edges of the truncated
pyramid. However, in this variant we have no right to talk about "half-periods of sine wave".
This particular form of "half-periods" of the curve drawn on the side faces of the pyramid
can vary widely. The main thing is to ensure that the pieces of curve were smooth connected
to each other at the edges of the pyramid.
The seventh figure illustrates situation similar to
that shown earlier in Figure 4. Closed contour curve (remote part of which conditionally is
not shown) was collected from flat clear convex parts, which planes are the same planes as
of red triangles. The pairing parts of curves with one another are made in the centers of the
side faces of the pyramid. Portions of the curve in the field of joining have common tangents,
which are shown by a green dashed line.
If the planes of the upper red triangles to continue
down to their intersection with the ribs of the pyramid on the right and on the left, it is not
difficult to imagine how we can form a contour of a series of flat arches (see Figure 8).
In doing so, I wish to draw the attention of the
reader to the part of the A-B of flat contour arch. If this part will have a deflection up (as in
the main-top part of the arch), it will lead to a slight separation of the network near this
area because for all my contours, by definition, all their lower zones must have deflection
down (this is a mandatory condition of compatibility for all my cable-stayed
networks). This little problem can be solved by different ways:
- ignore separation of the network: finished vant network, most likely at each intersection of
the cables would have "special ties", which will joing together the pairs of cables in all their
places of intersections; separation of the network will cause low forces in those ties, however,
because of its small value, they can be neglected; If the full vant network will be covered with
concrete, this separation of the network even physically just couldn't take place;
- the lower parts of flat arches (A-B) you can do just as straight line – will be no separations
- the lower parts of flat arches you can bend down to make them similar to their upper
parts - see. Figure. 9.
In this case, when you look from the side of the
anchor parts of the neighbouring arches will be smooth and aesthetically linked to one another,
but when you look at the same place from the top, the docking of arches will be seen with one
another under certain angle. It makes the structure of docking a little harder, since all arches
must be joined together to create a united and hard support contour of the
II.  Support contours from rectilinear elements
After shown in Figure 9 contour from flat arches, it's
already easy to consider the broken contours, which are compiled from separate rectilinear
elements. I want to note: the elements of my broken contours only conventionally can be
considered as rectilinear. When we manufacture them, prepare to installation, they really are
rectilinear. However, during installation, they are subject to flexural deformation and cease to
be rectilinear. This bending deformation helps to ready support contour in perception of forces
from cable network. Look at Figure 10.
This illustration shows us the familiar lateral surface
of direct prism. On each lateral plane of prism the cruciform elements are drawn. A series of
direct lines give us a zigzag line (blue), and the second one (green) on the horizontal plane
is symmetric zigzag line to the first one. As a result, these two zigzag lines created us a support
contour in the form of "a circle dance of crosses", which are hinge joined to each other in A, B,
C, D and similar dots. The main efforts of the network are perceived in the contour by special
tensioning devices which are placed vertically between the upper and lower joints (see dots B
Of course the situation, which is shown in Figure 10,
give us some idealisation. Real structure is constructed from flat rectilinear elements
which are fastened to one another in all places of their intersection. while the installation each
element gets the bend in the horizontal plane. Distribution of the bending between all elements
lead to the situation that when you look at the contour from the top, it looks as if all elements
of the contour form a right circular cylinder.
Now take a look at Figure 11.
Here is shown a broken contour from "dance of the
crosses", which are placed on the lateral surface of inverted truncated pyramid. The hinges of
these X-shaped contour elements are placed not in the middle of their height now, this shift
gives us the effect of "an opened contour", which is similar to opened flower of Lily. So, the
more down will be moved the hinge of each X-shaped element, the more will be seen the
effect of opening. Tensioning devices for perception efforts of the network as well as in the
previous case, are set between the hinges B and D.
It is for this scheme was assembled the structure
"Star", conceived by me as the basis for a space reflector, which is needed to reflect sunlight
for certain areas of the Earth's surface in the dark time:
The technology of forming a support contour with
the "method of pyramids" I described enough full and enough detailed. Whether the above
technology exhausted all possible variants? Of course not. I'll try to add some details now and
a bit to summarize the described above technology.
III.  Forming the support contour step-by-step
Let's imagine a designer, who began the formation
of some Makarov's structures by method of pyramids. Where to start?
1.  Let's choose a point in space (I conditionally marked it with star of four
ends) located above a horizontal plane (see fig. 12):
2.  In the horizontal plane we draw fully convex polygon and draw the beams
from the initial point to the corners of the polygon. The number of rays and number of angles
of the polygon we select in accordance with the planned number of up-zones of support
contour: number of rays should be twice more than the number of planned up-zones in a
contour (see Figure 13). At a certain height from the first horizontal plane we place the second
one, for example, with some inclination to the horizontal. Then we draw a polygon with which
our pyramid intersects with the second plane - this polygon will become the second base of
our truncated pyramid:
3.  To further purposes we remove from the picture all superfluous details - leave
only truncated pyramid (see fig. 14):
4.  Turn our truncated pyramid "upside down". At each face in the pyramid
we draw the pairs of diagonals. The six dots of their intersection (in the picture they are indicated
by little red rings) set us some meddle plane, which would be for us "zero lines plane".
From the bases of pyramid ribs we build a series of flat arches (blue curves), the lower part of
which (from the bottom up to zero point) are straight lines. The tops of arches are built on rules
of sine wave with some grow factor in the vertical direction (see Figure 15):
5.  Then we delete all the additional lines. We leave only the blue outline of flat
arches and zero points of the contour, which are marked with red little rings
(see Figure 16):
6.  For reasons of aesthetics let's a bit rotate the obtained support contour for
more natural perception of its base points. Now it is standing on its three legs on a horizontal
plane (see Figure 17):
7.  Through zero points of support contour we draw three zero lines. These
zero lines should be intersected at a single common point (see fig. 18):
At this step, our goal - the formation of support
contour with the method of pyramids - is considered to be complete.
The next logical step - electronic creation on this
support contour the cable-stayed Makarov's network. To this issue is devoted section
METHOD OF ELECTRONIC CREATION OF CABLE-STAYED NETS
of this chapter. Thank you for your attention. I wish you successes!
«There is nothing more practical as a good theory.»
When I begin to design the next space platform, I
should imagine the approximate parameters of a real object. The main such options are, of
course, its geometric characteristics. It is with the geometrical characteristics of the structure
we have to understand in details.
Folding space platform is one of the Makarov's
networks, which is stretched on one of the broken form support contours made up of a series
of x-shaped contour elements. One of variants to implement a self-opening space platform you
can see at the photo below.
Simplified (all cables are made up of pieces of direct lines)
mathematical model of such a platform, constructed by me in the MATHEMATICA program, look, for
example, like this:
And there is drawn by me in
the program MATHEMATICA
detailed model of a space platform, its cables look for more than
realistic and correspond to the cables
of the real model:
And now, finally, I can show you quite a perfect
model. In this model all of the details appear as if it is a photograph of a real object. I hope,
you noticed, that even the support contour became now a realistic and impressive.
On the two last figures all mechanisms, with the
of which the space platform was disclosed in space, conditionally not shown. I mean,
that after the opening of the space platform all its joints were frozen from their further moving,
so whole support contour has acquired the necessary rigidity.
For ease and standardise my structures, I adopted
for myself some "start rules" which allow me do not solve the same problems while creating
regular design. These rules are:
1)  I choose the thickness and width
of each straight contour element, of course, intuitively. However, the selected size and
properties of this element must be in the "specific frames", namely :
a)  element must be sufficiently flexible for it can be much flexing like a bow
b)  element must be tough enough to "keep the force", but when removing the
external load it must return itself to its original straight state (i.e. residual deformation and
phenomenon of flow of material must be very small);
c)  for creating x-shaped elements of rectilinear details they need to be drilled
in the middle of their length; the diameter of drilled holes must be as small as possible, so
that the flexibility of rectangular element in place of drilling does not be increased too
d)  elements should not be too fragile, or while pulling x-shaped elements by
the network they just will be breaked at the points of joining rectilinear elements together;
e)  drilling holes for attaching cables should be made with small diameter to
retain strength properties of contour elements; this diameter directly depends on the diameter
of the cord that is selected for the plaiting network; diameter of drilling should be able to
stretch through one hole at least two cords together;
2)  Distribution of holes within the length
of the straight element I try to do always with one manner, namely:
a)  at the ends of the element, and in the middle of its length drilled holes for its
attaching to other contour elements (two holes at the ends and one hole on the middle of the
length of element);
b)  at each of the halves of the linear element are made 4 holes for cables, on
one linear element are made 8 such openings;
c)  for drilling openings under cables the full estimated element length (L) will be
divided into 16 parts (estimated length is the distance between the extreme holes, these
holes are made for fastening the element to adjacent elements);
d)  from the top mounting hole we measure a distance 1/16 part of estimated
element length and drill the first hole for the cables; from first hole for cables we measure
2/16 part of the estimated length and drill second hole for the cables, from it we measure 2/16
of the estimated length and drill third hole for the cables etc; In short: between each pair of
adjacent holes for cables the distance is 1/8 the estimated length and so along the whole
length of the element;
e)  If you've done everything correctly, the extreme holes for cables are at a
distance of 1/16 element length from holes for fastening the element to other adjacent
the hole to connect two direct element into x-shaped element is located at the middle of the
direct element length (between 4-th and 5-th hole for the cables), it is removed from the 4-th
and 5-th hole for the cables at 1/16 of the estimated length of the direct element;
3)  gathering direct elements into
x-shaped elements may be bolted or connected using, for example, tubular rivets (if they
in future not need to be disconnected);
4)  Joining of x-shaped elements among
themselves can also be bolted or on tubular rivets; If in future you need to transform the
platform into high-rise construction, then you should choose the bolts, otherwise – tubular
5)  the tension of the network at folding
contour cannot be taken with the flexural stiffness of the contour (as it is a broken contour
and it contains the hinges), so you need in advance to provide of special elements for
perception of these efforts on the contour; this can be some vertical clamping devices between
each pair of nodes of joining x-shaped elements with each other; in the models I use rubber
rings for this purposes; in a real large-scale structure you can use for these purposes some
special clamp devices such as those used for fastening of vertical masts or conventional
sports horizontal bar; the real space apparatus will have for these purposes some automatic
tension devices (see photo below).
And now let's consider the correlation between the size
and the number of elements of contour and the whole size of the opened space platform.
If n is the number of applied in the contour x-shaped
elements (then the number of initial straight elements will be equal to 2n). Let L will be estimated
length (height) of each direct element of contour, from the pairs of wich all the X-shaped
elements of contour are created.
Naturally: the n >= 3. If n is less than three, we simply
will not be able to create from x-shaped elements structure, which is convex in shape.
Created by us from x-shaped elements the polyline
support contour in his opening will have the two limit states.
The first state: contour is not already open, the height of the whole structure is equal to the
full length of contour element (a), the diameter of whole structure theoretically is equal to zero
(in the evaluating calculations we neglect thicknesses of elements of contour). The second
state: the support contour is fully deployed, the lenght of whole circumference, which became
our contour, is equal to n x L, the height of fully disclosed contour conditionally is equal to zero
(actually this height will be equal to the width of one element of contour, i.e. "b").
I think it is clear to everyone: in reality structure would
not have these two limit States. Note: real space platform will be good only if it has not zero
vertical span. The real platform must have a good stiffness of network.
I believe that for a good space platform creation
x-shaped elements of contour should not be fully disclosed, the best state will be: the angle
between the straight s of contour is equal to 90 degrees, which corresponds the incline of
each element to 45 degrees towards the horizon. In this case all the properties of space
platform is quite good and even further adding another platform in vertical direction will not
cause any additional problems.
In light of all the above conditions, I have compiled
a good table, which will enable us to provide the real relation between geometry of the initial
elements of contour, their quantity and real sizes of space platforms of these contour elements.
For the convenience of automated calculations I decided to make them into an EXCEL
All that has been said above about geometry of
one element of contour, you can see in this picture below:
When initial elements of contour are combined into
cross-shaped workpiece of pairs elements of contour, the picture will look something
All the parameters of individual elements, simple blanks
and the whole platform are presented in the following list. Here shown as initial data and the
But in this table are shown all the necessary data for
your personal experiments: the original data are shown at the yellow field, basic calculated
parameters are red, additional computed parameters are shown in black.
Please forgive me: I have not been able to present to
you "live" EXCEL spreadsheet, which is able "to instantly respond to all your questions" because
the formulas, that were laid in my cell computed values, on your screen automatically will not
work. However, I took care of that every man who likes EXCEL, was able to successfully take
advantage of my table.
Look at the bottom left corner of my table: there in plain
text are placed all formulas to calculate the required values. If you will make your "hard work" a
few minutes with an EXCEL spreadsheet, all your formulas want to appear in the cells of your
spreadsheet. And then your worksheet will answer you on all the questions that you ask him
on the geometry of the space platform, which you are building.
To me, for example, the column with number 6 from the
table indicated that if I shall make 64 simple elements, each of which has 10 centimetres wide
and a length of 20 metres, so the entire package of these elements will look as a cylinder with
a diameter of about two metres and with a length of approximately 20 meters (that's perfectly
fits into modern space ship).
However, after the workpiece is transported in open
space, in unfolded state it allows me to create a platform with a diameter of about 353 metres,
if I choose vertical incline angle of each contour element at 30 degrees to horizon. The full height
of the support contour of my platform will be approximately 10 meters.
"Oh, really big array of people houses I can build on that
platform, if I'll deploy it in the open space!" i thought...
In July 7, 1982, from me into the Patent Institute (VNIIGPE)
was directed an application for an invention of manner of suspension cable roof creation called
«"SEGRIM" METHOD». Expert reaction to this application was very original. First, they sent me the
official certificate of admission my application for consideration.
Secondly, after this certificate absolutely nothing was followed. On my request was not taken any
positive decision, but it was never officially rejected. As I now understand, my application was so
ahead of his time, that to him not only "there was nothing to compare," but the experts, apparently,
were thinking: "It is not clear why this is needed".
Such a situation has already occurred in human history, for
example, after the invention (opening) of the electromagnetic waves, in their application nobody saw
any practical sense...
As I mentioned above, never in the history of construction
and architecture, no one invented the suspension roofs by some "series". But I appealed to register
at one time my "trojka", "quartet", "five", "six", "seven" and «"SEGRIM" method». After recovering
from the shock (which lasted three and a half years), experts registered only one "Suspension Roof"
and into the description placed all that were concerned only the "Makarov's Quqrtet". Everything else
was just "buryed in the cellars" of Patent Institute. Now let's go straight to the essence of the case.
If you have any "starter set" of models of good suspension
roof nets (e.g. at least that is shown on my group portrait "trojka", "quartet", "five" and "six"),
you may well be able to apply these models to create new original structures using my «"SEGRIM"
method». This can be done quite easily.
All people, I think, imagine how echo sounder works: this device,
which allows you to get graphics of heights for some natural surface. You drive, for example, on a boat
on the Lake. You interested in profile lake bottom. You turn on your echo sounder and move in a straight
line. As a result, echo sounder will draw for you graphics of heights of lake bottom exactly along the
direction of your moving (now it can make even simple fishermen as echo sounders for amateur
fishermen already are sold in stores).
Now I suggest you remember how housewives make cookies.
They roll out a dough and with special form or ordinary glass are cutting from this dough the desired
piece of dough for the subsequent roasting. That's all you need to know for applying my "SEGRIM
method". The fact is that this method is very simple: from inside of any good cable-stayed network you
can cut any areal of network, which you need, and then use it for a new assignment. This feature is
garanted by very simple axiom. For example, you mentally crossed the cable-stayed network by any
vertical surface (e.g., plane surface). Then you will fixate each network cable at the same point (with
the same coordinates in space) that it was previously. Then you must ensure for every cable the same
tensile force, as in the original model. After the "truncating" the rest of network will no longer have any
role for the taken part of the network. Taken piece of network will have the same shape and the same
size as it had before the removing truncated zone from it.
"Easy to say but hard to do," you say. And it is absolutely not
right: I made it many times and all was perfect. For the sake of clarity, I will describe to you several
steps of this simulation, then, I think, you will have no more problems with this procedure.
1) Let's choose a comfortable model of
cable-stayed network. This can be, for example, four:
2) Choose the correct form of the new support
contour, as well as its size, that do not exceed the size of your model. For the above four, I decided
to make a contour, which is square in the plan, and its diagonal size is the same as the diameter of
a right circular cylinder, which has this four. I had two options. In the first option I cut out from my
"four" cable-stayed network one square region by directing through the highest points of the contour
four straight lines and then directing four vertical planes straight through these lines.
In the second option, I did the same thing, but took as the
basis the lowest points of the support contour.
3) Then we fixate vertical profile of the
cable-stayed network for the selected vertical planes directions.
Here I have to give additional explanations. The fact is
that "fixate profile" you can by different ways. I, for example, for this work invented a simple tool
called "frontal depth gauge". It consists of a small wood block of square cross section, on the one
side of which is placed series of bicycle spokes. To fixate spokes on a wooden block I used ordinary
small nails. The spokes were fixed so that they can be moved outside the block at the desired depth,
that they can be fixated in new state and that they do not interfere with each other. The external
view of my frontal depth gauge is shown in the following figure:
Using this simple device for profile survey I got a profile
of the surface of my model of network. When I received a curve with such modeling, I transferred
it to paper by simply appending my frontal depth gauge to the paper and fixate on a paper the ends
of spokes with the pencil.
4) We place marks for points of suspension cables on
the obtained curve line of surface profile.
5) From suitable material we are doing a series of workpieces
(or only one workpiece) for the new walls of model of cable network.
6) In accordance with the obtained profiles and information on
crossed cables placing we do a markup on these workpieces. Then we drill new holes for cables.
7) Then we collect the new support contour for cable network
and create the new network on it in exact accordance with the scheme of network, that was created
on the original model.
At this moment the production of new model of the
cable-stayed network by way of "SEGRIM method" can be considered complete.
In the first option (vertical cross sections were made through
highs of support contour) we get the following model of cable-stayed network:
In the second variant (vertical cross sections were made through the
minimums of support contour) the model of cable-stayed network will look similar to the following picture:
If we apply the "SEGRIM method" for the "Makarov's Five", which
is shown under the table at the beginning of this chapter, and the vertical cross-sections will be made
through the minimums on the support contour, so we will have the following architecture decision:
I don't know how you, but me this variant seemed very
aesthetic and worthy of implementation.
For your successful modeling I want to tell you: flat
side walls for models received by way "SEGRIM method" I made from coloured getinaks plates.
It's pretty hard stuff and he not much warp himself from the efforts of tensioning cables of
network. For the getinaks never had the opportunity to warp under tension of cables, the base
of model of cable network I made of furniture thick panel and workpieces from getinaks I
strengthened at the base by the screws. As a result, all was perfect.
I want to give you one advice: when you choose the
form of the new support contour for the any cutting by you area of network, don't forget about
the tension force of cable network. Your new support contour must be able to counter against
it, therefore your new support contour should be everywhere convex.
It is possible that someone wants to, for example,
from my "Trojka" cut a piece of cable network by direct cylinder, which will be an oval cross
section. Architectural expressiveness here already will be provided by "bizarre delta of heights",
what is interesting.
Our possibles of architectural modeling will be even
more if we consider that the original model (cable network) before to "cut" from it some piece
can be located not horizontal, but with some inclination. Our "moulds", with which we will "cut
out" the piece of network can also have various forms of cross-section...
Suppose that we from the inclined "Quartet" decided
to cut a piece by some tube with oval cross section. Then the task will look something like
And the result of its implementation will give us the
following architecture decision:
Some later, when I shall can to do the 3D modeling
of my structures (for example, in 3DS Max, Maple or Mathematica), all the above operations
can be produced fast and easy in electronic form directly on the computer screen. However,
by rotating the obtained result on the screen, you will be able to immediately give him
architectural and aesthetic evaluation without any full-scale tests.
While making described manipulations with my "Five",
I suddenly remembered about real "Pentagon" - United States military Department, which is
located in the State of Virginia:
The architecture of the building is such that inside
it is quite a large courtyard. Why not make him cover roof with a good cable-stayed network?
It would be very practicaly: schema and procedure to do this, I had develope already. If you
are ready to cover the cable-stayed network not by monolithic concrete, but by a transparent
plastic, it would be simply "Super-coating": frost and precipitation remain outside, but the sun
is always shining inside the yard.
Of course, there's a pretty big yard, so the effort of
tension from cables will be very great. However, no one will interfere us to make along the
perimeter of the suspension roof a good metal contour from powerful metal beams. If the main
efforts from the cables will work in the horizontal plane, then the contour beams need to have
apropriate form for this horizontal load. Vertical load of all such coverage will be forwarded to
the vertical wall, but the walls there are VERY POWERFUL...
In the following figure you can see the network of
my "Five", which I made "electronically" in "Mathematica" program.
This network was built on a square plan and by using the described above "SEGRIM method"
from this network you with the help of cylinder can cut a good stretch of cable network for
The second picture directly shows us the corresponding
electronic technology, which allows us to make the necessary "electronic cutting"...
After the removal of superfluous elements and after adding
some cosmetic detail our cable net will look like this:
At this step my "master class" on the practical application of
the "SEGRIM method" let me consider as completed!
In the section "PYRAMID METHOD" above in this chapter I
finished my presentation with forming an interesting support contour, which is shown in Figure 18.
Why this contour is so interesting? The contour is interesting in that it formed by flat arches,
each of which has its own dimensions. Each arch is easy to manufacture. The arches don't have
any axis of symmetry and planes of symmetry. In architectural terms, the contour is interesting
because he personifies the "free flying of architectural thoughts", i.e. contour has maximum generality
of shape, which can be very valuable for its further implementation.
Below I present this contour, he will be my "starting point"
to describe the technology of shaping networks Makarova by means of electronic method creation
of cable nets in EXCEL 2003:
On an EXCEL 2003 worksheet I formed a cellular surface,
placed on it numbered columns and rows, added on this field the shown above contour. The highest
points of contour I marked by blue serifs. In accordance with the stipulated above method, I placed
on a contour the series of points for the future mounting of cables, noting these places with red bars.
I would like to note: usually I put 4 cable mounting marks between each pair of maximum (minimum)
points of contour and point of crossing of support contour with the zero lines. However, in this case,
the arches of different sizes, so the distance between the point of cable mounting will be different.
The main thing in this case is to place the attachment points for the cables by such a way that the
distances between them on the course of movement along the contour does not change too
As a result of the work done, I received the following
EXCEL 2003 has a very nice set of tools for painting and
technical drawing. I so accustomed to this program that when I need to do my technical drawings
for architectural project at the international contest, I made them in
this program. Of course, I know another programs such as Autocad, Arhikad and others but I decided
that if EXCEL 2003 well copes with the task, I have not need to attract the other programs.
The main tool in the electronic method creation of cable
nets is the "Curve" tool, which requires only to specify the attachment points for the cables.Once
you have done this, the curve well puts itself along the route, because it, namely, is intended for
putting itself through the route by the "most natural" manner. To be more precise, this curve will give
you a "Bezier curve" through all the anchor points, which you specified, and it will smoothly encircle
all the points.
We know that all my cable-stayed networks at the given
support contour will move themselfs into state of the minimal surface area (for the given contour).
By the way, this their feature allows to perform their initial architectural modeling using a soapy film.
If you are interested in it - try it. The soap film surface is certainly not durable for a long time. But
what prevents you from the immediately make a photo of this soap surface to have the "collection
of good surfaces" for your further work, similar as it shown in my section
"Space Architecture".To get really big soap surfaces you,
of course, will need some additional chemicals and some of the technology. On this topic I know
the great video in the Internet (in English):
"Soap Films and Minimal Surfaces".
In this video you will find all you need for your successful modeling.
So, the cables of network, as a result of their interaction,
always create for us surface with a minimum area for a given support contour. However, as we
know, these surfaces have also some "zero lines", which take place on each of such surfaces.
I propose "turn this obstacle inside out". Using Bezier curves and directing them through a known for
us points of support contour and points at zero lines, I shall construct whole the surface with
the help of them (!)
For me "in my way not to get lost," I placed a small photo
of the real "troika" directly into an EXCEL worksheet. I don't know about you, but I don't keep in my
mind all creation schemas of my networks... As a result, the beginning of my work on electronic
method of creation of cable nets has become look like this picture:
When I eventually posted on my drawing all cables and
corrected all its routes, my picture became look as follows:
Then I removed the photo, numbers and got such a
Then I deleted all other extra marks: high peaks marks,
the cables mounting points at the contour, zero points, zero lines, then I "repaid" gridlines of a
worksheet (Tools - Options...). Now my structure has become look much more interesting:
I think that you can appreciate now the result of my hard
work. I want to give you a few advices in your way. You should draw your network always with
thin lines - it's easier and more precise. While you working, remember to change the viewed
size of your picture. The maximum increase is 400%. You can manually write this number in the
window "Zoom", then press "Enter". After that, you will be easier to draw small details. When you
insert your curve into the picture, be sure to switch the node types of this curve. To work on
changing the curve and its nodes, select the curve by the left mouse button, and then on the
drawing toolbar click the "edit points" command. Then on the desired node you should call the
shortcut menu and select the desired type of node. End nodes should always be "angled"
("Corner point"), but intermediate nodes should all be "smooth". These types of nodes when
you click on them always will show you their tangents: the corner point - one tangent and
intermediate point - two tangents. After a short training at work with these tangents (they can
be and pulled, and rotated) you will soon be able to manage the form of your curves "as the
The location of a node you can change with a simple
"drag and drop" it with the help of the mouse. By "snuggles" curve with the mouse cursor in any
place and pulling it to the side, you get there the appearance of a new node.
New node in any place of the curve can also be obtained by using the shortcut menu. If a node
is redundant, you can delete it via the context menu.
I do not recommend you to add extra nodes - use only
minimum number of them ("Occam's Razor principle"). If you think that curves shaping is finished,
only then you should begin to select "the real thickness" of curves and pick the real color
combinations. For solving all these isues use the same panel "drawing".
And now you can see the final appearance of my
suspension roof model, which she purchased after "Pyramid Method" and "technique of
electronic method creation of cable nets":
I immediately introduced myself as this suspension
roof was effectively used somewhere for the construction of a modern Catholic Church...
Now take a look at my unusual "Five". There were used
stretching horizontally and offset vertically. Although initially it was created not as an architectural
object, the result is interesting. I hope that this "Five" also will take its rightful place in the history
of architecture and the Visual Arts.
I will say honestly: this model I created in EXCEL
specifically for participation in the contest of the logos for the new model of car of the Japanese
firm NISSAN, which was seeking to move to the Russian market. To my surprise, the administrator
who has been designated to receive via email all design works for participation in the contest, just
don't let my work participate in this contest on her own initiative. It turned out to be a "real Russian
man" and instead of the entire Commission staff gave me a estimate by himself alone...
Good or bad is my logo - not me task to judge. However,
I decided to put the pictures below for your analysis. The logo is represented by two images
because one promotional logo intended to place on the right side of the car, and the second -
on the left.
I think that a good result is worth it to spend on it your
nerves and your time. I wish you success in all your endeavours.
At this point my "master class" on electronic method
of creation of cable nets in EXCEL 2003 will be consider completed. The more time you spend
at work in it, the more satisfaction you get from your work. From my personal experience I can
say: from electronic drawing you'll most likely get no less fun, than get regular artists from the
communication with their canvas and paints. You can believe me!
«I am thankful to all those who said NO to me, Its because of them I
did it myself...»
Designing my structures, I always intuitively felt that
such aesthetic forms, what are my cable-stayed nets on wavy support contours, are "too natural"
to never being meet in the history of mankind. In many math forums I asked people help me: tell
me, where you met such 3D surfaces. As response I got only "full silence". Like Einstein, I now
want to tell you: "Thank you, people! Through your silence I had done it myself!"
Shoveled the Internet, I still found two my predecessors.
It turned out that my «beautiful wavy forms» really already met twice in the history of mankind.
However, in both cases they can't be for me competitors: in one case the wavy surface appeared
as a mathematical model of the wave front in optics, in the other case - as a thin-walled reinforced
concrete shell. In the case of a shell such the surface did not even have a hard support contour and
was reinforced without any cables, only with the usual iron rod fittings.
Frits Zernike (1888 – 1966)
Frits Zernike was a Dutch scientist, Nobel Prize in Physics in 1953.
Take a look at the following pictures. Even an inexperienced
reader can easily see: there is something very similar to my cable-stayed networks, namely: "two", "three"
and "four". Coincidentally this is not accidental.
The question arises: are it really my cable networks on
wavy support contours have already been developed by someone before me? It turned out, that
the minimum surface, which is formed with the help of the contour in the form of a piece of sinusoids,
ïðî÷åð÷åíîé on a lateral surface of a direct circular cylinder, was known earlier. However,
such surfaces had no relation to the cable nets. Analysis of such minimal surfaces and engaged in Fritz
Zernike. He has dealt with such surfaces very conscientiously. Zernike received mathematical expressions
(equations) of such surfaces in our three-dimensional space. He created the great series of such equations for
the number of waves on the contour of from two up to a hundred and even more. Zernike created his equations in
cylindrical, and in the Cartesian coordinate systems. So now we can not "sway our heads" and just use for our
purposes all those equations, which created to us Fritz Zernike.
Interestingly, Zernike not had any relation to the construction, or to
the cable networks. By means of the surfaces shown above he described the various optical defects that may
occur in the lenses, including in the lens of the human eye.
He was the winner of the Nobel prize for physics for his invention of the phase contrast microscope.
Felix Candela (1910 – 1997)
Felix Candela - Mexican architect and engineer.
He was born in Spain (Madrid), however, in 1939 he emigrated to Mexico and lived there all
his further life.
During his active creative activity he built a large number of buildings
of various purposes. He paid great attention to calculation and construction of thin reinforced concrete shells.
Not satisfied with the available earlier the theory of their calculation, he independently created for this his new theory.
Thanks to his perfect theory of shells, the shells become much more subtle and more light, than it was possible
Interesting direction of its activity was design and construction of a
specific series of new architectural shells. Take a look at the following picture.
On this picture shows the building of the Oceanarium in the «City of
Science» (Spain, Valencia). The building is covered by a thin six-petaled reinforced concrete shell. I want to
note: such buildings Candela built and with other number of petals.
However, from the point of view of forming, all these structures were represented as a series
interlocked with each other hyperbolic paraboloids. Candela developed and the technology of construction of
formwork for such buildings. In spite of such expressive forms, all formwork for such
buildings were collected only from direct wooden boards. All such shells were reinforced with the usual iron rods.
If you analyze, for example, structure of my shells with
flat arches, you will notice their certain architectural similarities with Felix Candela's shells. What is the difference
between the «Felix Candela's shells» and comparable to them «Sergey Makarov's shells»? This difference
consists in the following:
1/ Makarov's shells have the contour arches, the Candela's shells have none of them.
2/ In the Makarov's shells all contour arches are connected into one reinforsed support contour, Candela's shells have
no such a contour.
3/ In Makarov's roofs the entire load is perceived by the flexible cables of network, which transmit this load to the
closed support contour.
4/ Candela's roofs - «it is namely reinforced concrete», they cannot be made from another material,
as the efforts of roof perceived by means of this «monolithic reinforced concrete».
Makarov's roofs can be made from light materials too (all efforts are perceived only by cables), in some versions
it is possible building even fully transparent roofs, that is impossible in Candela's roofs.
5/ Candela's roofs have the contour edges in the form of semi-detached with each other parabolas, Makarov's roofs
can be implemented and with a series of parabolas, and with a wave-shaped contour curve (sine wave
on the cylinder surface).
6/ Candela's roofs have a Central symmetry, Makarov's roofs can have it, and can have not. They may be
implemented with the contours, which were collected from the arches of various height.
Thus, the Candela's roofs is fully separate architectural branch,
which has only a superficial resemblance to some of Makarov's roofs variants.
If the reader wants to learn more about Candela's roof shaping,
I recommend him to view the following video:
Southern Federal University (Russia,
Rostov-on-Don) invited me to participate in a festival of science south of Russia, who
was appointed to the end of September - beginning of October 2012. At the festival I had
to do a report on my structures, and to create and to present one of my
I gratefully accepted the invitation. In published
by University program of the festival I was presented as "the leading scientist abroad":
Especially for this festival, I made small model,
which, in according to my plan, must be the prototype for the creation of next large-size
model in the future. Since I try never to produce twice the same model, I decided to make
"Makarov's Five" on an oval in plan undulating circuit that was formed with ten flat arcuate
elements. I did not create nothing like it earlier. How interesting was my engineering and
architectural structure, you can be judged on the following three photos. These photos
show the model, which I called "Yellow Bird", due to the fact that for the network was used
yellow cable, but the word "bird" is caused simply as my association with the flight, which
arise at me almost every time I look at my models...
Further in Rostov at my sample was made a model
with dimensions of approximately 3.5 x 5.0 meters. To create a visual contrast to the existing
location for the demonstration, it was decided to braid this model with the red cord. The result
which was received, it seems, is now called "Red Bird", if you will follow my logic described
above. Good is my "Red Bird" or not - do not judge me.
However, I want to note the following: such
structure on the five-wave support contour of ten flat arcuate elements with oval in terms
contour using three-dimensional convex-concave cable net was made in the global
construction practice for the first time. Therefore, this architectural-engineering solution,
of course, has a complete world novelty.
The following series of pictures shows as the
individual stages of the construction process, and the result, which was received
at the end.
You probably already have noted that my "Red Bird"
is just hanging in the air, and this leads to the conclusion: all forces from the cabling network are
completely covered up with the help of the support contour. This shows that such a structure is
also applicable at space-based architecture. It remains to add that given above, "Red Bird" from
September 29 will be showed in the "Creative center" at Rostov, Suvorov street., 52a. Hurry to see:
the exposition will last only until October 5.
In the first presentation in Rostov was made also
the booth that is dedicated to my developments in the field of space architecture. This booth
you can see at the picture below.
At the festival of science of South Russia I read the report
of the "Makarov's cable-stayed networks for terrestrial and space-based architecture."
My report of 7 October 2012 was read in the exhibition hall "VertolExpo" of Rostov (Russia,
Rostov-on-Don, M. Nagibina street, 30). For this report only one hour was given to me, but in
fact it lasted one hour and 25 minutes. This has been possible due to the fact that my report was
the last. Namely the abundance of questions from the audience caused elongation of my report
over the established regulations. I was asked a lot of questions about my report. This suggests
that the information, I told, was important to the audience and caused their concernment.
In the report I showed the audience my model the "Yellow Bird"
- "Makarov's Five", which was collected by me from ten flat arcuate elements. Model sparked keen
interest among the audience: everyone wanted to touch it with their hands. One moment of my report
and my "yellow bird" you can see in the photograph below.
In the course of the report I have told to my listeners about many of my
misadventures related to the fact that I'm lone inventor, which has no any company and no any funding. The fact is
that in our time, science is considered as the range of namely "research teams", which is provided with good
funding (usually from government sources). In this regard, my presence before the audience as lone scientist
who is a member of only the "self," added, I think, special piquancy to my report. The rest reports presented at
the Festival had mainly type of "essay on a given topic." I presented in my report absolutely new information,
which is the result of my personal development. And all of my structures have the signs of the world novelty.
In this regard, I looked like some "dinosaur" because due to my separation from all the research teams, my
personal requirements for the scientific results proved to be much too high compared to the accepted in the
scientific community level.
It did not go unnoticed. After the end of my report the series of
questions was poured to me as a continuous stream. Of course, with all the questions I have coped, since all this
was "my personal topic," in which I have been involved for over 25 years. At the end of the stream of questions I
was asked to finish my presentation at some "positive note", that I did.
I remembered my correspondence with the American Professor Mason
Peck, who in the spring of 2011 asked me a lot of questions on the properties of my structures and about their
advantages, compared with other space developments intended for solving such problems. When I said that since
mid-2011, this professor (Mason A. Peck, Associate Professor Mechanical and Aerospace Engineering 212 Upson
Hall Cornell University Ithaca, NY) was appointed as NASA chief technologist and now he works at NASA
headquarters in New York City, it caused at the audience some cheerful positive waves. However, I said that in
view of the Professor's heavy workload, I now try not to distract his attention from his main work with my "small
worries". However, I think this my "unusual acquaintance" yet somehow will be usefull for me in the future.
After the end of my report pretty solid lady came to me and introduced:
"I am Rector of the Southern Federal University..." Of course, it was a complete surprise for me. I absolutely did
not count on such attention to my person from the side of such very busy person. Then this lady - doctor of
economic sciences Marina Aleksandrovna Borovskaja - thanked me for an interesting report, handed me her
business card and said that from now I can to contact her personally at any time and for any questions...
After the end of the festival of science seven of its organizers
expressed a desire as guests to visit my habitation with the aim "in good company" to note the success of my
presentation. Of course, that's what we did. The party was very warm. I concluded that this my second
presentation in Rostov was good!
P.S. Video of my report (in Russian) on the Science Festival of the South of Russia in Rostov can be found
with the link below:
Since 2008, the American Institute of
arranges annual international project competition. These projects may involve a variety of areas of
human activity. The most important requirements that apply to projects are their universal significance,
prospects (on a scale of mankind) and the possibility of their implementation.
Since I have long been engaged in development of various
designs for space, I decided in 2013 to suggest my project to participate in this competition. It is known
that currently in many countries are being developed various designs of space hotels, where people
will be able to settle in space for a long time. However, no country in the world has not yet begun the
actual construction the hotel in space . I wonder who will be first? I think that the first "space hotel"
and will determine all further space-based architecture.
The project, which I put forward for consideration by
the Competition "Challenge-2013" is called "Multi-storey space hotel". The basic ideas of this project
you can see, if you look at the following picture.
In terms of competition, I could not present for the consideration of more than six pictures. all these
pictures are shown at the photo shown above. If you are interested in my project, all the details about it,
you can read and view in my presentation: "Multi-storey space hotel".
The picture, shown by me, you can see directly on the competition website, if you will use the following
"Makarov's Multi-storey Space Hotel".
My project is very strictly complies with all the competition
requirements. Of course, I hope to win. However, experience has shown that in many competitions
winners are already known before the competition will be announced to the public. How fair is this contest,
we, I hope, very soon find out. Results of the competition "Challenge-2013" to be announced
October 1, 2013.
P.S. Even before considering projects by the jury I was informed that "in view of the large number of
submitted projects" my project is not submitted to the jury (?!)
No correspondence, none of my criticisms did not help. I asked to give me back my $ 100, which I paid
for the review of my project, but this was never done. Such crooks are operate in Buckminster Fuller
Institute... Sad but true!