MAKAROV'S STRUCTURES


In the theory of architecture so rarely happens something new, that to the man, who created in it an entirely new direction, it would be very natural to assign a doctorate without protection thesis...



«After a certain high level of technical skill is achieved,
science and art tend to coalesce in esthetics, plasticity, and form.
The greatest scientists are always artists as well.»
Albert Einstein.

TABLE OF CONTENTS
Consec. numbers Subsection Summary Links Last update
1 FOREWORD But it turns out, that there were few directions... Link 01 04/03/2013
2 INTRODUCTION The introduction into this new and limitless topic Link 02 01/23/2012
3 PROPERTIES OF MAKAROV'S NETS On what networks of Makarov and designs, created on their basis, are different from what was before them Link 03 01/06/2013
4 GARDEN OF DIVERGENT TRAILS Description of the first method of creation an infinite series of designs that are created on the basis of cable-stayed nets of Makarov Link 04 02/13/2012
5 METHOD OF PYRAMIDS Description of the second method of creation an infinite series of designs that are created on the basis of cable-stayed nets of Makarov Link 05 03/09/2012
6 ABOUT SELF-OPENING SPACE PLATFORMS This is description of self-opening Makarov's space platforms method of creation Link 06 02/20/2013
7 CABLE STRUCTURES CREATION WITH THE "SEGRIM" METHOD The "Segrim" method is fully new manner of cable-stayed nets creation Link 07 12/27/2012
8 METHOD OF ELECTRONIC CREATION OF CABLE-STAYED NETS Description of process of Makarov's nets creation on a computer screen in the program EXCEL 2003 Link 08 03/24/2013
9 EXCURSION INTO HISTORY I found that my surfaces with wavy support contours have already met in the history of mankind... Link 09 01/29/2013
10 FIRST PRESENTATION IN ROSTOV-ON-DON Creating a large-size model of "Makarov's Five" and its first presentation at the Festival of Science of South Russia Link 10 05/11/2015
11 SECOND PRESENTATION IN ROSTOV-ON-DON Lecture about Makarov's structures for Earth and for Space at the Festival of Science of South Russia Link 11 05/11/2015
12 CHALLENGE-2013 About engineer Makarov's participation in the competition in Buckminster Fuller's Institute "Challenge-2013" Link 12 05/11/2015




FOREWORD

      I think, that someone of readers was shocked by my "bold 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.

2. Tensegrity-architecture.

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 as "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.

4. Globe-architecture.

 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.

5. Enneper-architecture.

"Makarov's Enneper-architecture" was declared by me in the article "Makarov's Enneper-architecture for the 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.

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INTRODUCTION

      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 personally developed a separate scheme of weaving the cables.

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PROPERTIES OF MAKAROV'S NETS

      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.

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GARDEN OF DIVERGENT TRAILS

(The first method of forming Makarov's structures, created on wavy and broken support contours)

      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 for you.



      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!

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METHOD OF PYRAMIDS

(The second method of forming Makarov's structures, created on wavy and broken support contours)

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 turn).
      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 doubled.



      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 6.



      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 of network;

- 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 network.

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 and D).
      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!

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ABOUT SELF-OPENING SPACE PLATFORMS

«There is nothing more practical as a good theory.»
Robert Kirchhoff.

      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 help 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 crossbar;
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 much;
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 contour elements; 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 rivets.

      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 table.

      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 like this:



      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 evaluated values.



      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...


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CABLE STRUCTURES CREATION WITH THE "SEGRIM" METHOD

      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 this:



      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 further use.



      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!

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METHOD OF ELECTRONIC CREATION OF CABLE-STAYED NETS

      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 drastically.
      As a result of the work done, I received the following picture:



      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 picture :



      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 soul desires".
      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!

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EXCURSION INTO HISTORY

«I am thankful to all those who said NO to me, Its because of them I did it myself...»
Albert Einstein.

      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 previously.
      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:

"Felix Candela in Revit"


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FIRST PRESENTATION IN ROSTOV-ON-DON

      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 large-scale models.
      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.

Thank you for your attention!



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SECOND PRESENTATION IN ROSTOV-ON-DON



      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:

"Sergey Makarov. Cable-stayed networks for terrestrial and space-based architecture"




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CHALLENGE-2013

      Since 2008, the American Institute of Buckminster Fuller 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 hyperlink: "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!

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