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Differences between historical documentation and actual structure of the Shukhov tower in Moscow: 3D model-based analysis 1 An d r ey V. Leon ov D e p t . fo r t h e H i s t o r y o f Te ch n i cs a n d Te ch n i ca l Sci e n ce s S. I . Va vi lo v I n s t i t u t e fo r t h e H i s t o r y o f Sci e n ce a n d Te ch n o lo gy o f t h e R u s s i a n Aca d e m y o f Sci e n ce s M o s co w , R u s s i a a n d r e y. v. le o n o v@ya n d e x. r u

Shukhov tower on Shabolovka (Moscow) 2 Point 3D model Interactive 3D cloud (solid, visualization meshed) Stages of creating a virtual 3D m odel

Laser scanning of the Shukhov tower 3 Mikhail Anikushkin at the level of 10 0 m . Photo by Andrey Leonov, Dec. 1, 20 11.

Creating a virtual 3D model 4 a) Positioning of cross-sections (channels, angles) in the point cloud; b) Precise 3D modeling based on pre- positioned cross-sections. Point cloud (65 mln. points) and precise 3D modeling 4

Outline of the tower 5 ————— project #1, linear dependence of R on H. ‒ ‒ ‒ ‒ ‒ project #2, quadratic dependence of R on H (parabola). • • • • • • • • • actual outline of the tower. “Outline of the tower. Basic dimension. Cone with variable r that accumulates constant increment; in our case r, 2r, 3r, 4r ... or generally r, r + f, r + 2f, r + 3f, etc.; and variable increment with a continuous increase of slope from the vertical line α. The slope increment is expressed by the formula α × n × (n-1) / 2, where n is the number of the tower section starting from the top. Thus, the following series is obtained: 1) f, 2) 2f + α, 3) 3f + 3α, 4) 4f + 6α, 5) 5f + 10α, 6) 6f + 15α, 7) 7f + 21α, 8) 8f + 28 α etc. where the sizes r, f and α are set. In this case, r = 2.75 m, f = 2.75 m = r, α = 0.25 m and thus the radii get 2.75, 5.75, 9, 12.5, 16.25, 20, 25 (slopes 3 → 3.25 → 3.5 → 3.75 → 4)” (V.G. Shukhov, Feb. 28, 1919)

Structure of sections 6 Structure № of the section Workbook Drawing Actual Element (1919) (1919) (1922) 24 angles 9/8 cm legs 12 double channels No.10 double lines 6 (I from the top) (lower/upper part) rings a not specified 8 rings 9 rings legs 16 double channels No.12 double lines 24 angles 9 cm 5 (II from the top) rings a not specified 8 rings 9 rings legs 24 double channels No.12 double lines 48 angles 9 cm 4 (III from the top) rings a not specified 6 rings 9 rings 48 angles 12/10 cm legs 24 double channels No.14 double lines 3 (IV from the top) (lower/upper part) rings a not specified 8 rings 7 rings 30 double channels No.14 or 36 48 double channels legs double lines 2 (V from the top) double channels No.12 No. 14 rings a not specified 4 rings 4 rings 48 double channels legs 36 double channels No.14 double lines 1 (VI from the top) No. 14 rings a not specified 4 rings 4 rings a) Intermediate rigidity rings

“Connection of the legs of two sections” 7 Drawing of 1919, fragment The same drawing in the book of G.M. Kovel’man, 1961 (page 157).

“Upper ring of the II section” Drawing of 1919, fragment Drawing of 1947, fragment

Actual joint of 1 and 2 sections Draving of 1947, fragment

Actual joint of 2 and 3 sections Чертёж 1947 г., фрагмент.

« Шуховская башня на Шаболовке» Actual joint of 2 and 3 sections (upper ring of the 2 nd section)

The height of the tower 12 The current height of the six hyperboloid sections is 144.61 m according to our 2011 laser scanning. In 1991, the upper section was reduced at 0.3 ... 0.36 m. Thus, the true height of the six hyperboloid sections of the tower in 1922-1991 was 144.91 ... 144.97 m. This figure is close to the "round" value of 145 m. Shukhov’s idea: 145 = 25+25+25+25+25+20 “Sixth section: 16 legs, channel No.10, height 20 m, number of rings 5” (V.G. Shukhov, May 13, 1921). According to the 1947 survey documentation, the level of the upper ring of the 6th section: 144.16 m, and the level of the lower supporting ring of the 1st section: 0.5 m. Thus, the total height of the six hyperboloid sections according to the 1947 docs is 143.66 m. It is a mistake.

Fastening of intermediate rings 13 Fastening of the 1st Unused holes in intermediate ring of the the 2nd Unused holes in the 3rd intermediate ring of the 1st section to a leg intermediate ring of 1st section through a U-shaped the 1st section. bracket.

Conclusions 14 The 3D-model based analysis helped us to identify a number of differences between the design, working and survey documentation and the actual structure of the tower. In particular, it was found that: A.The actual structure of the Shukhov Tower on Shabolovka (outline, construction of legs and joints) has significant differences from the existing design and working drawings of 1919-1921, as well as the calculations in the workbook of V.G. Shukhov. B.The information on the height of the tower given in the archival documents is more than a meter different from the true value. According to our data, the original height of the six hyperboloid sections without superstructure was approximately 145 m. C.The method of mounting of the intermediate rings was simplified directly during the installation process. The laser scanning and 3D-modeling of the tower allowed us to efficiently detect and analyze the discrepancy between the historical documentation and the actual structure, identify mistakes in the description of the technical monument and raise new questions for further research.

Acknowledgment 15 The author thanks Elena Shukhova, the great-granddaughter of V. G. Shukhov, for providing information from the personal archive (diary of V. G. Shukhov), as well as Andrey Marsavin, deputy chief engineer of the Moscow Regional Center (a branch of RTRS), for providing survey documentation from the 2011 project of the reconstruction of the Shukhov radio tower on Shabolovka. The author also thanks archives (Archive of the RAS, RGANTD, Archive of TzNIIPSK im. Mel’nikova, and Archive of GSPI RTV) for providing the following archival documents:  V. G. Shukhov, workbook (notes from March 22, 1918 to October 10, 1922), Archive of the RAS, F. 1508, Op. 1, D. 61.  “Shabolovskaya radio-tower of the engineer Shukhov's system. Height 150 m. Project of 1919”, Archive of the RAS, F. 1508, Op. 1, D. 85, L. 1.  “Project of the tower of the height of 350 m constructed of 9 sections. 1919”, Archive of the RAS, F. 1508, Op. 1, D. 84, L. 2.  “Lattice tower of the engineer V.G. Shukhov's system. Height of the tower is 150 m for wireless telegraphy. Basement. 1921”, RGANTD, F. 166, Op. 1, D. 36, L. 1.  “The upper ring of the second section of the radio tower. 1921”, RGANTD, F. 166, Оp . 1, D. 36, L. 2.  “The Inspection of Metal Structures of the Tower of the Shukhov’s System of the Moscow TV Center. 1947”, Archive of TzNIIPSK im. Mel’nikova, Shifr 281.  “Order № 4138. Reconstruction of the terminal equipment of the radio relay link. Moscow TV Center ( Shabolovka). GSPI Minsvyazi SSSR. Moscow. 1969”, Archive of GSPI RTV.  “Evaluation of bearing capacity of metal structures of TV tower of Shukhov’s system and drawing conclusions about the possibility of its further exploitation. 1971”, Archive of TzNIIPSK im. Mel’nikova, Shifr ORIS-569.  “Metal structures of the superstructure of the Shukhov’s tower for fastening FM antennas. 1991”, Archive of TzNIIPSK im. Mel’nikova, Shifr 20-F 5720-1-KM.