Regulation of pesticide and fertilizer rates with applied by unmanned aerial vehicle

. The technology of application of pesticides, fertilizers and other agrochemicals by unmanned aerial vehicles (UAVs) in the precision farming system provides for differentiated treatment of agricultural fields with variable standards of pesticides and differentiated application of fertilizers. Existing UAVs do not provide differentiated fertilization of plants with fertilizers and differentiated treatment of plants with pesticides due to imperfect flow control systems and working fluid application rates. Substantiation of methods for regulating the flow rate and norms of working fluids of pesticides and fertilizers is based on the flow continuity equations, Bernoulli and the equation that determines the rate and dose of pesticides and fertilizers depending on the operational and technological parameters of the UAV. The paper shows that to differentiate the norms for applying the working fluid of pesticides and fertilizers, it is advisable to use methods for regulating the norms by changing the area of the outlet openings of sprayers and the step of their placement, while differentiating the norms can be carried out both by a combination of these methods and by including one or several standard sizes in the work of sprayers simultaneously.


Introduction
The technology of applying pesticides, fertilizers and other agrochemicals by unmanned aerial vehicles (UAVs) in the precision farming system provides for the differentiated treatment of agricultural fields with variable pesticide rates based on the phytosanitary state of the agrocenosis, taking into account the economic threshold of harmfulness, weed infestation, pest population density, differentiated introduction of variables doses of liquid nitrogen fertilizers in the form of foliar feeding of plants and plant growth regulators based on an agrochemical cartogram of an agricultural field [1][2][3][4].
For each elementary section of the field that requires processing, a predetermined amount of pesticide or fertilizer working fluid is introduced in an uninterrupted stream with deviations not exceeding the permissible values established by agrotechnical requirements. Differentiation of the norms of working fluids of pesticides and fertilizers within the limits established by agrotechnical requirements, according to a given program in the form of an electronic task card, is one of the main conditions for the implementation of the technological process in a precision farming system using BVS, which in turn must be equipped with automatic control systems (ACP) flow rate and automatic dosing systems (MAD).
To implement the technology, an unmanned aerial system BAS-137 VIM was developed on the basis of an unmanned aerial vehicle (UAV) of a coaxial helicopter type BVS-137 VIM (takeoff weight 280 kg, payload 80 kg) and an unmanned aerial vehicle (UAV) based on a gyroplane (takeoff weight 750 kg, payload up to 400 kg) for differentiated application of pesticides, fertilizers and other agrochemicals in the precision farming system [5,6].
There is a variety of ways to regulate the flow rate and systems for automatic dosing of liquids [7,8].
Regulation of the flow rate of the working fluid can be carried out in automatic mode by changing the working chamber of the pump, changing the number of revolutions of the pump motor shaft, bypassing a part of the main flow, throttling the flow through the regulating body.
For the programmed dosing of the working fluid of pesticides and fertilizers when they are introduced with the help of UAVs, a continuous-action SAD with an ACP of flow rate, with electric control of actuators can be used.
Value of the norm (dose) N can be defined as the integral of the flow rate of the working fluid) Q (t) for a certain period of time (t1, t2) dose formation [7,8]: where s (t) -flow section; ω (t) -flow rate; Ci (t) -concentration of the i-th component in the flow of matter. The proposed definition of the dose characterizes the effect on its value of the main parameters -the area and flow rate, the concentration of the substance in the flow, but does not take into account the influence of the technical and operational parameters of the technological process of introducing the working fluid.
The flow rate of the working fluid for differentiated application on the cultivated agricultural field is set based on the calculated doses of the active substance of pesticides and fertilizers for each selected elementary area of the field, which are rectangles with a width equal to the working width of application and a length equal to the length of the selected contour.
The analysis of the developed UAVs for plant protection showed that the pesticide spraying systems, as a rule, are integrated with the UAV flight control system and operate according to the specified GPS coordinates in accordance with the program for the processing of agricultural fields, however, the regulation of the working fluid flow rate is carried out by changing the operating pressure in the system or in the "on / off" mode [9][10][11][12]. This approach to regulating the flow rate of the working fluid is unproductive when differentiating the rates of application of working fluids of pesticides and fertilizers.
Research Objective: substantiate the ways of regulating the norms of working fluids of pesticides and fertilizers when they are applied by an unmanned aircraft.

Material and methods
The substantiation of methods for regulating the norms of working fluids of pesticides and fertilizers was based on the law of conservation of mass, energy and the equation that determines the rate (dose) of the working fluid of pesticides, fertilizers and agrochemicals, depending on the operational and technological parameters of the BVS.
The law of conservation of mass in the form of an equation of continuity (continuity) of the flow is represented by the equation :   , ( where G -mass flow rate; ρ -flow medium density; ω -average flow rate; ƒ -cross-sectional area of flow. The energy conservation law is written in the form of the Bernoulli equation, which expresses the energy balance of the flow: , where Z -geometric height of the center of gravity of a given flow section, specific potential energy of a position in a given section; -specific potential energy of fluid pressure; -specific kinetic energy of the flow in a given section; Ρ -flow medium density; g -acceleration of gravity. The equation that determines the rate of application of the working fluid of the pesticide or fertilizer, depending on the design and technological parameters of the BVS spraying system, has the form: , where fсп -compressed flow area. , where -jet compression ratio, -outlet area. Flow rate can be obtained from the Bernoulli equation: where -pressure drop in front of the atomizer; -total drag coefficient; -flow medium density.
Coefficient predetermines the speed ratio: Taking into account (7), (8), (9) flow equation (6) takes the form: Product of odds and gives the nozzle flow coefficient μ. Coefficients μ, and depend on the Reynolds, Froude and Weber numbers.
In practical cases, when liquid flows through holes, the influence of the Froude and Weber numbers is neglected and the coefficients are calculated , and μ function of number Re. In the range of numbers Re = 104  106 the flow coefficient, therefore, and the velocity coefficient in round holes, vary within insignificant limits, they can be considered constant values [13]. For slotted nozzles, the flow rate depends on the ratio of the length of the nozzle to its width [14,15].
Substituting into equation (4) the value of the flow rate from equation (9), we obtain an expression characterizing the rate of application of the working fluid, depending on the flow characteristics of the nozzles, design and flight technical parameters of the UAV.
Given that the attitude B/n determines the step l the arrangement of sprayers on the boom of the UAV sprayer module, expression (10) takes the form:

Results and discussion
Expressions (10) and (11), determining the rate of application of the working fluid, show that with the differentiated application of BVS pesticides, fertilizers, plant growth regulators and other agrochemicals, the regulation of their rates (doses) can be carried out by changing the number of sprayers on the sprayer module boom, the area and, accordingly, the nominal diameter of the nozzle outlet sprayer, differential working pressure in front of the nozzles, UAV operating speed, working width, the ratio of the working width to the number of nozzles, characterizing the distance between adjacent nozzles -the spacing of the nozzles on the boom. It should be noted that the regulation of the application rates by changing the working width of the working in a practical aspect does not make sense.  Dependency Analysis H = h (V) shows that in the operating range of BVS-137 VIM flight speeds from 30 to 60 km / h, the rate of the working solution of nitrogen fertilizer changes from 120 to 60 l / ha, that is, it is halved. The rate of pesticide working fluid within 30-60 km / h varies from about 25 to 12 l / ha and also halves. The UAV autopilot, in accordance with a given flight program along a given trajectory, can change the operating speed and, as a consequence, the application rate is adequate for each elementary section of the cultivated field. However, the range of regulation of the rates of the working fluid consumption within the operating flight speeds does not provide the prescribed doses of nitrogen fertilization for foliar feeding of plants. Dependence H = h (l) shows that when changing the spacing of the nozzles on the sprayer module boom from 0.6 to 0.1 m, the application rate of the nitrogen fertilizer solution and the pesticide working fluid increases approximately six times from 37.5 to 225 l / ha and from 7.7 to 46.4 l / ha, respectively. Typically, the spacing spacing for pesticides and fertilizers is kept constant. It is possible to change the distance between adjacent nozzles by equipping them with electromagnetic shut-off valves. With an increase in the flow rate of the working fluid, for example, three times, the pressure drop must be increased nine times; therefore, it is irrational to control the flow rate of the working fluid and, accordingly, the application rate by changing the working pressure. Dependence N = h(f), characterizing the change in the rate of application of the working fluid from the area of the outlet of the sprayer shows: with an increase in the area of the outlet of the sprayer with 0,452×10-7 m2 (nominal diameter 0,24×10-3 m) to 25,45×10-7 m2 (nominal diameter 1,8×10-3 m) the application rate increases 51.5 times from 3.88 to 200 l / ha. This method of changing the application rate provides a fairly wide range of regulation of the working fluid rates of both pesticides and nitrogen fertilizers and is the most promising. To implement it, the boom system of the BVS sprayer module must be equipped with selective electronic units, consisting of at least four nozzles of different sizes, equipped with electro-hydraulic control systems.
Ranking the differences from maximum to minimum values of functions N = h (V), N = h (l), N = h(∆P), N = h(f), presented in Figures 1,2,3,4 gives the series: From expression (12) it follows that the widest range of regulation of the rates of the working liquid of pesticides and fertilizers is provided by changing the area of the outlet of the sprayers, a slightly smaller range by adjusting the spacing of the sprayers and least of all, with practically equal ranges of rates, by changing the pressure drop in front of the sprayers and by changing the flight speed of the UAV.

Conclusions
1. Methods of regulating the flow rate and application rate of the working fluid of pesticides and fertilizers -by changing the flight speed of the BVS, the working pressure in the system of the sprayer module, the spacing of the sprayers, and the area of their outlet openings. 2. It is shown that to differentiate the rates of application of the working fluid of pesticides and fertilizers, it is advisable to use the methods of regulating the rates by changing the area of the outlet openings of the nozzles and the step of their arrangement, while the differentiation of the rates can be carried out both by a combination of these methods and by including one or several standard sizes in the operation of the sprayers at the same time. 3. It has been established that the widest range of application rate regulation from 3.88 to 200 l / ha is provided by changing the area of the spray nozzles and the step of their arrangement on the boom of the BVS sprayer module.