Accuracy of Determining Ecologically Safe Territories in the Zones of Electromagnetic Fields Caused by Radio-Television Antennas and Cellular Communications

This article addresses issues of ecological safety in conditions of intensive development of radio-television systems and cellular communications. The main purpose of the article is to develop an algorithm for determining the accuracy of the boundaries of safe and comfortable living of the population in the area of electromagnetic fields. The mathematical dependences are deduced allowing to define the exact parameters of the boundaries of safe zones on the basis of maximum permissible standards of power flux density, which are generated by radiation sources. Theoretical work is supported by practical examples that confirm the feasibility of using the obtained mathematical dependencies.


Introduction
Improving environmental security is an important component of sustainable economic development of the areas in which geodetic science plays an important role.The growing needs of comfortable living standard have led to the development of a large number of new technologies and technical means that need to be studied in detail in terms of its impacts on the environment and, in particular, on human health.Electromagnetic pollution affects the membrane structure of living organisms.In particular, the properties of water diffusion or osmosis change; the regeneration of plant and animal tissues slows down; the shape and size of plants alter; the central nervous and cardiovascular systems of animals and humans are disturbed apart from the disturbances in metabolism.
In this regard, research related to the impact of electromagnetic radiation of radio-television antennas and cellular communications on human health is particularly important.Over the last decades, a new environmental factor has emanated-and it is "electromagnetic smog" of anthropogenic origin.In this context, the environmental hazards have increased from the radio transmission, radio and television, radar, radio relay and cellular base stations, which together significantly affect the balance of the ecosystem.
Critical aspects like protecting human health from the effects of electromagnetic radiation are of great socioeconomic importance and are based on a number of medical, biological, technical and other studies that generally solve the problem of safe living in a given area.One important characteristic of safe living is the allocation of zones of electromagnetic radiation distribution where its extent does not exceed the maximum permissible limit, as defined by regulations.Regulations of many countries determine the numerical values of protection, sanitary-protection and other regime zones for individual objects in order to establish safe areas for the population to live.However, in most cases, the parameters of accuracy of boundary determination of these zones are not investigated.The same applies to the establishment of the accuracy of the boundaries of sanitary-protection zones needed because of the harmful effects of electromagnetic fields on human health (Alfonso, 2021;Lennart and Cindy, 2008).
As a result of unresolved legal and technical issues of determination of boundaries' accuracy, it is necessary to investigate the accuracy of the boundaries of sanitary-protection zones and, in particular, zones of negative impact on human health caused by electromagnetic fields of radio-television antennas and mobile cellular communications.

Review of Literature
Electromagnetic radiation belongs to the class of non-ionizing radiation that does not destroy biological cells.The effect of electromagnetic fields on the human body is assessed in terms of the following parameters: Power Density (PD) or power flux density; Specific Absorption Rate (SAR) or power absorption coefficient; Maximum Permissible Exposure (MPE) or maximum permissible power level; and exposure time (t).The International Commission on Non-Ionizing Radiation Protection (ICNIRP) has developed a standard on the permissible values of non-ionizing radiation levels.This standard also defines the maximum permissible levels of alternating electromagnetic fields, which can adversely affect human health.Of particular importance in the standard is that the power flux density is defined as the only physical quantity to assess the effects of electromagnetic radiation on human health that can be easily measured from outside of the human body (International Electrotechnical Commission, 2017).
In terms of values of power flux density, there are three zones around the radiation source: -compliance zone, in which the power flux density does not exceed the applicable limits; -occupational zone (safe zone for service personnel), in which the stay within the limits of observance of certain precautionary measures is allowed; -exceedance zone (danger zone), in which the level of power flux density exceeds the applicable limits for service personnel.
The European Parliament and the Council of the European Union have adopted a Directive on the requirements for the prevention of risks to human health from possible exposure to electromagnetic fields.The Directive consists of four chapters covering all known direct and indirect effects caused by electrical, magnetic and electromagnetic fields (European Parliament and the Council of the European Union, 2013).The power flux density limits in the EU for a typical 3G and 4G cellular communications are set at 1,000 μW/cm 2 .However, some countries may set their own national tolerance limits.For example, in Italy, Poland and Ukraine, the maximum permissible level of power density is set at 10 μW/cm 2 , but in Slovenia it is 100 μW/cm 2 (Stam, 2017).
Protection of the population from the negative effects of electromagnetic fields is possible in two ways: the first is by the development of appropriate technologies, tools and techniques; the second is by the placement of technological devices in areas that ensure safe living of the population.The second way of safety involves establishing the boundaries of sanitary-protection zones in the area where there may be negative effects on human health.The values of these zones, depending on the technical characteristics of sources of electromagnetic radiation are widely reported in the modern scientific and practical literature (Council of the European Union, 1999;Mileusnic, 2006).
It should be noted that current research works related to the accuracy of the determination of various kinds of "buffer zones", including zones caused by electromagnetic fields, are not widely used.Currently, the problem, which unfortunately has not yet been solved, is to determine the accuracy of the display of "buffer zones" i.e., sanitary zones along transport corridors, distribution of concentrations of harmful substances, the negative impact on human health of electromagnetic fields and active noises, special zones of protection of the objects and ecological safety.Partially, such studies on determining the maximum size of sanitaryprotection zones and the accuracy of their determination on the terrain, taking into account the maximum permissible standards for the impact of electromagnetic fields of power transmission lines on human health, are reflected in the publication by Perovych, Kazanivska and Kereush (2015).

Methodology
The authors performed a theoretical substantiation of the accuracy of determining the safe zones from the influence of radio-television antennas and cellular antennas, which are located in large numbers on the territories of settlements and outside them.Using the well-known Pythagorean Equation, the value of the width of sanitary-protection zone is presented as: where d -width of the sanitary-protection zone, m; h -height of the antenna, m; r -radius of the boundary isoline, m.
Or, on the other hand, in the coordinate system, the value d can be determined by the Equation: Using the mean square error of the radius of propagation of electromagnetic waves, from Equation (5) it is obtained: where mp, mG, mS -mean square errors of the power of transmitter, coefficient of antenna gain and power flux density of electromagnetic waves, respectively.
Considering the values of the power of transmitter and the coefficient of antenna gain as infallible, a simplified Equation for determining the error of propagation of electromagnetic waves is obtained depending on the magnitude of the power flux density of electromagnetic waves and the error of its determination: Substituting the obtained value from Equation (7) into Equation ( 4), after minor transformations the expression for determining the mean square error of the distance d is obtained: According to Equation (3), the mean square errors of the coordinates of the sanitary-protection zone boundaries due to the influence of electromagnetic waves of radio-television antennas and cellular antennas can be calculated by the Equation: It should be noted that limit levels of exposure to electromagnetic fields of 0.1 W/m 2 are set by regulations of Italy, Poland and Ukraine.In other European countries, the maximum permissible standards of power flux density are higher.

Results
In order to implement the theoretical calculations, the mean square errors of the boundary isoline coordinates of the boundary markers in sanitary-protection zones of electromagnetic fields was determined.In the calculations, the maximum permissible standard of the power flux density equal to 0.1 W/m 2 was taken, and the mean square error of its determination is 0.01 W/m 2 .The mean square error of determining the antenna height is assumed to be 0.1 meters.Calculations are given for power P = 60W, coefficient of antenna gain G = 50, and antenna heights h = 3 m, 20 m and 30 m.
Technological scheme of calculations is the following: o by Equation ( 5), the maximum permissible value of the radius of propagation of the power flux density was determined; o using the obtained value of r and the known height of the antenna h, by Equation (1) the horizontal position d was determined; o under the established assumptions, according to Equation ( 8) or ( 9), the required accuracy of determination of sanitary-protection zones in the field was calculated.The analysis of the calculations given in the table 1 shows that the safe or comfortable for living zone (compliance zone), in which the level of power flux density does not exceed the limits.To some extent it depends on the height of the antenna.In this example, when the height of the antenna is increased by 10 times, the width of the danger zone decreases by 1.2 times.The mean square error of determining the width of the zone, in which the limit value of the power flux density does not exceed 0.1 W/m 2 , is in the range of 2.45 meters to 3.08 meters, and the mean square error of determining the coordinates X, Y in the established coordinate system is in the range of 1.74 meters to 2.31 meters.The mean square error of the influence of the antenna height can be neglected by using modern methods of its determination.

Conclusions
The dominant factor in the development of solutions for the development of territories is the establishment of geometric parameters of "buffer zones", which characterize the qualitative and quantitative indicators of the impact on the environment.This article presents mathematical dependencies which, at a scientifically based level, establish the accuracy of determining the size of sanitary-protection zones of the influence of electromagnetic fields caused by radio-television antennas and cellular communications, in which the limit values of power flux density do not exceed the allowable standards.Thus, the results of the research can be effectively used in the design and construction of radio-television and cellular antennas to establish the size of sanitary-protection zones and the accuracy of determination of sanitary-protection zones in the field.The literature quoted in the article does not take into account the influence of natural and artificial factors on the propagation of electromagnetic waves, and hence the maximum sizes of sanitary-protection zones may be a separate special area of research.Practical approbation of theoretical research showed the expediency of their application to determine the sanitary-protection zones to protect the population from exposure to electromagnetic fields of radio-television antennas and cellular communication.

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ISSN 2581-6853 | CODEN GJNRA9 Doi: https://doi.org/10.33002/nr2581.6853.050103 ) where с х , с у -coordinates of the running point C; 0 х , 0 у -coordinates of the antenna center (point O).Grassroots Journal of Natural Resources, Vol.5, No.1 (March 2022), p.40-46 | ISSN 2581-6853 | CODEN GJNRA9 Doi: https://doi.org/10.33002/nr2581.6853.050103Taking the coordinates of the point O as the error-free coordinates and the mean square error of the coordinates of the point C equal to for determining the mean square error md of the width of the sanitary-protection zone are obtained (Perovych, Kazanivska and Kereush, 2015): mean square error of the marginal isoline radius of electromagnetic radiation propagation;  ℎ 2 -the mean square error of determination of antenna`s height.By Equation (3) it becomes possible to determine the mean square errors of the coordinates of the boundary zone of constraints.It is assumed that the propagation of electromagnetic waves is a function of the physical parameters of transmitting antennas.From the theory of propagation of electromagnetic waves, formula of relation was used between technical parameters of the transmitting device and value of radius of propagation of the power flux density (Ukrainian State Center of Frequencies, 2020of the transmitter; G -coefficient of antenna gain; S -power flux density of electromagnetic waves. ) Grassroots Journal of Natural Resources, Vol.5, No.1 (March 2022), p.40-46 | ISSN 2581-6853 | CODEN GJNRA9 Doi: https://doi.org/10.33002/nr2581.6853.050103

Table 1 :
Calculation of the accuracy of determining the boundaries of sanitary-protection zones