SPRINKLER SYSTEM ACCOUNTING FOR WIND EFFECT

Abstract

A novel sprinkler system designed to take into account the effect of wind on water droplets. There is also disclosed a wind shifting algorithm which, when used, corrects the sprinkler water spray to counteract the effect of wind, such that good water coverage and precipitation uniformity can be achieved.

Claims

1. An irrigation system for irrigating a user-defined target area, the irrigation system comprising: a sprinkler having a spray angle controllable according to one or more instructions received from a controller; a flow control valve between a water supply and the sprinkler for controlling a flow velocity of water sprayed by the sprinkler according to the one or more instructions received from the controller; a wind detector located proximate the user defined target area for measuring a wind speed and a wind direction and sending the wind speed and the wind direction to the controller; and the controller coupled to the sprinkler, the flow control valve and the wind detector; wherein, by executing a plurality of computer coded instructions of a windshifting algorithm, a processor of the controller is operable to generate the one or more instructions to thereby spray water from the sprinkler to a target position within the user-defined area at least as follows: the processor first determines the spray angle and the flow velocity according to a known position of the sprinkler relative to the target position assuming no wind is present; the processor then calculates an error representing a difference between the target position and a position where water would be sprayed if utilizing the spray angle and the flow velocity and taking into account the wind speed and the wind direction received from the wind detector; when the error is greater than a threshold representing a desired precision, the processor repeatedly optimizes the spray angle and the flow velocity, and, each time adjusting one of the spray angle and the flow velocity, recalculating the error utilizing the spray angle and the flow velocity as adjusted until the error is less than the threshold representing the desired precision; and when the error is less than the threshold representing the desired precision, the processor generates the one or more instructions to thereby control the sprinkler to spray water to toward the target position utilizing the spray angle and the flow velocity as determined by the processor to result in the error less than the threshold.

2. The irrigation system according to claim 1, wherein the wind detector is an anemometer.

3. The irrigation system according to claim 2, wherein the anemometer is a vane anemometer.

4. The irrigation system according to claim 1, wherein the wind detector is adapted to wirelessly relay information to the processor.

5. The irrigation system according to claim 1, wherein the sprinkler is of a single head rotary type.

6. The irrigation system according to claim 1, further comprising a manifold fluidly connected to the water supply via the flow control valve, wherein said manifold is operated by the one or more instructions from the controller.

7. The irrigation system according to claim 1, wherein the controller is a computer.

8. The irrigation system of claim 1, wherein the processor further determines the spray angle and the flow velocity according to stored lawn contour information.

9. The irrigation system of claim 1, wherein the processor further determines the spray angle and the flow velocity from geospatial lawn contour information.

10. The irrigation system of claim 1, wherein, when the error is greater than the threshold representing the desired precision, the processor repeatedly optimizes the spray angle and the flow velocity by searching for an optimal flow velocity and optimal spraying angle utilizing a method of traversal.

11. The irrigation system of claim 1, wherein, when the error is greater than the threshold representing the desired precision, the processor repeatedly optimizes the spray angle and the flow velocity in real time.

12. The irrigation system of claim 1, wherein: the controller stores a database pre-determined spray angle and flow velocity values; and when the error is greater than the threshold representing the desired precision, the processor repeatedly optimizes the spray angle and the flow velocity by looking up pre-determined spray angle and flow velocity values in the database.

13. The irrigation system of claim 1, wherein, when the error is greater than the threshold representing the desired precision, the processor repeatedly optimizes the spray angle and the flow velocity independently from one another by solely adjusting the spray angle and by solely adjusting the flow velocity.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0035] The invention may be more completely understood in consideration of the following description of various embodiments of the invention in connection with the accompanying figure, in which:

[0036] FIG. 1 is a graphical depiction of droplet trajectory with fixed diameter and different flow velocities;

[0037] FIG. 2 is a graphical depiction of droplet trajectory with fixed velocity and different diameters;

[0038] FIGS. 3A, 3B and 3C are graphical depictions of the spraying trajectory of the conventional sprinkler system;

[0039] FIG. 4 is a graphical depiction of the spraying trajectory of the conventional sprinkler system with three sweeps;

[0040] FIG. 5 shows a rectangular lawn with the dimension of 80 m×40 m with the positioning of a sprinkler;

[0041] FIG. 6 is a graphical depiction of a characteristic curve of the droplet with the droplet diameter=0.01 m;

[0042] FIGS. 7A, 7B and 7C are graphical depictions of a simulation for a rectangular lawn;

[0043] FIGS. 8A, 8B, 8C and 8D are graphical depictions of simulations for polygonal lawns;

[0044] FIGS. 9A through 9F are graphical depictions of the spraying effect in a three round spraying program;

[0045] FIG. 10 is a graphical depiction of droplet diameter distribution;

[0046] FIG. 11 is a graphical depiction of a 1D water distribution with normally distributed droplet diameter assumption;

[0047] FIGS. 12A through 12F are graphical depictions of a simulation spraying under windy conditions;

[0048] FIGS. 13A through 13F are graphical depictions of a simulation spraying under windy conditions under the mean diameter d=0.007 m;

[0049] FIGS. 14A through 14C are graphical depictions of cases 1, 2, and 3 which are simulation spraying under windy conditions where the droplet size is under the mean diameter d=0.007 m;

[0050] FIG. 15 shows of a lawn with dimension 30 m×30 m with a sprinkler positioned in its center;

[0051] FIG. 16 is a graphical depiction of the wind shifting results for the 5 cases listed in Table 3;

[0052] FIG. 17 is a 3D depiction of figure of se(v, y) under conditions: To=(0 m, 25 m), w=1 m/s, =30°;

[0053] FIG. 18 is a schematic depiction of an adaptive step length algorithm to find a solution that meets the error requirements or reaches the hardware limitations of precisions;

[0054] FIG. 19 is a 3D depiction of the optimizing path of the algorithm with similar conditions being the same with FIG. 17;

[0055] FIG. 20 is a graphical depiction of the figure of the algorithm performance shown in Table 5;

[0056] FIG. 21A through 21F are graphical depictions of the wind effect with different wind velocities for wind from south to north with 30 degrees;

[0057] FIG. 22A through 22F are graphical depictions of the wind effect with different wind velocities for wind from east to west;

[0058] FIG. 23A through 23F are graphical depictions of a sensitivity test conducted;

[0059] FIG. 24 provide graphical depictions of an example using target distances set up at 0.9, 0.7, 0.4 (proportion) to cover a lawn;

[0060] FIG. 25 provide graphical depictions of an example of arithmetic progression method.

[0061] FIG. 26 is a graphical depiction of an example of n-divide method. Light lines denoting target distances, while darker lines denoting divider lines;

[0062] FIG. 27 is a graphical depiction of an example of the divider lines method;

[0063] FIG. 28 is a depiction of a generated database in the format of 3D matrix

[0064] FIG. 29 is an example of a graphical user interface to generate the required database

DESCRIPTION OF A PREFERRED EMBODIMENT

[0065] The platform developed can be used to facilitate the sprinkler system design, test system performance under windy condition, and generate the wind effect shifting database. Starting with mathematical modelling of droplet dynamic, the droplet movement from a nozzle was simulated. The basic principle of the platform is illustrated in details accompanied by some simulation results. Particularly, the wind effect is studied by using the example of square lawn, and provide the shifting solution for different cases. A wind shifting algorithm is presented in details. Given the irrigation range, droplet distribution and wind condition, the proposed algorithm is capable to achieve optimal water coverage and uniform precipitation distribution by counteracting the wind effect.

[0066] Single Droplet Dynamic

[0067] The modelling of droplet dynamic has been studied by several authors. Lima (J. De Lima, P. Torfs, V. Singh, A mathematical model for evaluating the effect of wind on downward-spraying rainfall simulators, Catena 46 (4) (2002) 221-241) investigated the mathematical model for a single droplet for a downward-spraying rainfall simulator.

[0068] Lorenzini (G. Lorenzini, Simplified modelling of sprinkler droplet dynamics, Biosystems Engineering 87 (1) (2004) 1-11) proposed a simplified modelling for droplet dynamics without considering the wind effect.

[0069] Salvador (R. Salvador, C. Bautista-Capetillo, J. Burguete, N. Zapata, A. Serreta, E. Playa 'n, A photographic method for drop characterization in agricultural sprinklers, Irrigation science 27 (4) (2009) 307-317) proposed a photographic method to determine the droplet diameter.

[0070] Moita (R. D. Moita, H. A. Matos, C. Fernandes, C. P. Nunes, M. J. Pinho, Dynamic modelling and simulation of a heated brine spray system, Computers & Chemical Engineering 33 (8) (2009) 1323-1335) investigated the dynamic modelling for a heated brine spraying system.

[0071] Conti (A. Conti, D. DeWrachien, G. Lorenzini, Computational fluid dynamics (cfd) picture of water droplet evaporation in air, Irrigation and Drainage Systems Engineering 2012) studied the water droplet evaporation in the air based on computational fluid dynamics.

[0072] To arrive at the platform designed, the following hypotheses were adopted: the forces applied to the system were weight and frication; the buoyancy was ignored; the evaporation was not considered; and the droplet keeps a spherical shape during the flight, thus its volume does not change.

[0073] In practice, the buoyancy has negligible effect to the droplet movement, thus was also neglected. The variables and parameters used in this study are listed in the following Table 1.

TABLE-US-00001 TABLE 1 Symbols Definition v.sub.x The velocity component in theX direction v.sub.y The velocity component in the Y direction v.sub.z The velocity component in the Z drection v.sub.0 The initial Bow velocity of droplets from nozzle α The vertical spraying angle of nozzle γ The horizontal spraying angle k The drag coefficient m The mass of a single droplet h The initial height of nozzle d The water droplet diameler p.sub.w The density of water p.sub.a The density of air ψ The Reynolds number of water droplets w wind speed w = [w.sub.x, w.sub.y, w.sub.z] w.sub.x wind speed at x direction w.sub.y wind speed at y direction w.sub.z wind speed at z direction β the angle between wind and x-axis

[0074] With the assumptions above, and according to Newton's second law of motions, the mathematical model can be described as the following:

[00001]$\begin{array}{cc}m\frac{{\mathrm{dv}}_x}{\mathrm{dt}}=-k\left(v_x-w_x\right)\sqrt{{v_x-w_x)}^2+{\left(v_y-w_y\right)}^2+v_z^2}& \left(1\right)\end{array}$$\begin{array}{cc}m\frac{{\mathrm{dv}}_y}{\mathrm{dt}}=-k\left(v_y-w_y\right)\sqrt{{v_x-w_x)}^2+{\left(v_y-w_y\right)}^2+v_z^2}& \left(2\right)\end{array}$$\begin{array}{cc}m\frac{{\mathrm{dv}}_z}{\mathrm{dt}}=-{\mathrm{kv}}_z\sqrt{{\left(v_x-w_x\right)}^2+{\left(v_y-w_y\right)}^2+v_z^2}-\mathrm{mg}.& \left(3\right)\end{array}$

[0075] where the droplet mass m is defined as

m= 4/3πr.sup.3=⅙πd.sup.3,

[0076] and the drag friction coefficient is denoted by k which is given by k=ψρad2.

[0077] A fast numerical solver using Runge-Kutta methods is implemented in the platform to compute the solution for the system of nonlinear ordinary differential equations (ODE). In a sprinkler system, one of the most important characteristic is the size of droplet that the nozzle can generate. For a constant spraying velocity, the different droplet diameter can result on different spraying distance. Similarly, given a constant droplet diameter, the variant spraying velocity will generate variant spraying distance. Thus we begin with analyzing the relationship between the droplet diameter, spraying velocity and spraying distance by testing a 2D single droplet spraying case. Under the windless condition, in FIG. 1, the trajectory of a water droplet with fixed diameter d=0.01 m is illustrated for the range of flow speeds ν.sub.o=[25, 50, 100, 200, 500, 1000] m/s.

[0078] Based on the various calculations the droplet distance would only be increased by about 2 times, from 55 m to 105 m as the flow speed vo is increased from 100 m/s to 1000 m/s. The trajectory of a single droplet with fixed initial speed=120 m/s for droplet with diameter d=[0.002 0.004 0.008 0.016] m in FIG. 2 was plotted.

[0079] From FIG. 2, it was noted that the droplet distance can be significantly increased by enlarging the droplet diameter. The droplet with d=0.01 m and ν.sub.o=1000 m/s has a similar performance with the droplet with d=0.016 m and vo=120 m/s. Therefore, a sprinkler system with the nozzle that can generate large droplet more robust under the wind condition and easier to control in terms of wind shifting.

[0080] Through the platform developed, it was possible to simulate a conventional sprinkler system with circular coverage. In FIG. 3, the spraying profile for the case with droplet d=0.01 m, ν.sub.o=120 m/s is displayed. In FIG. 4, the spraying process of semi-circle lawn with three round of sweeps is simulated.

[0081] Actually, besides the conventional sprinkler pattern, the proposed platform was determined to properly simulate the sprinkler system with more complicated design discussed in the next section.

[0082] Modelling of Intelligent Sprinkler System

[0083] The platform developed was shown to be capable of simulating a sprinkler system with the following features: [0084] the nozzle can continuously adjust its flow velocity at any angle; [0085] the system is able to detect the real time wind condition; [0086] the system has sufficient computing power to implement the wind shifting algorithm

[0087] With these features, it is clear that the intelligent sprinkler system according to an embodiment of the present invention is superior to a conventional sprinkler system in terms of the following aspects: [0088] the water spray of intelligent sprinkler can perfectly cover lawn with any shape, since the flow velocity can adjust with the angle; [0089] the intelligent sprinkler system can automatically calculate the pull back amount according to the user custom setting, such that a good water distribution uniformity can be achieved; [0090] the sprinkler system is capable to counteract the wind effect to achieve good coverage and uniformity under various wind conditions

[0091] As an illustration, assuming a rectangular lawn with the dimension of 80 m×40 m, where the nozzle is placed on the boundary of the lawn as shown in FIG. 5, the elevation angle of the nozzle is set as 30 degree.

[0092] The basic idea to achieve optimum water coverage is that first the rectangular area is divided into n pies, where n is a user-defined value, then for each pie, the required velocity is computed such that the spray precisely reach the target distance. To just cover the shape of the lawn, the target distances are just the boundary of the lawn. As would be clear to the person skilled in the art, the target distances are determined by the contour of the lawn. To find the accurate required flow velocity to reach certain target distance, the characteristic curve is used. The characteristic curve is a function that provides the information regarding the spraying distance vs initial flow velocity for droplet at certain diameter. Once the droplet diameter is selected and the elevation angle, the characteristic curve is determined. The characteristic curve for the droplet with d=0.01 m is shown in FIG. 6.

[0093] The x and y axis in FIG. 6 denote the droplet velocity and corresponding spraying distance, it indicates that for the droplet with d=0.01 m, given the initial flow velocity, what is the corresponding spraying distance. Note that the dots in FIG. 6 are resulted from the numerical solution, and a 4th order polynomial interpolation is employed to find the continuous characteristic curve. By using the generated characteristic curve, the required flow velocity can be computed for the given the lawn in FIG. 5. For example, according to the characteristic curve in FIG. 6, to reach the target distance 40 m, the required initial flow velocity should be around 50 m/s. Using the solver to find the roots for the polynomial, the exact required flow velocity can be found.

[0094] In fact, for a typical sprinkler system, the spray generated by the nozzle contains droplets with various diameters.

[0095] Besides the conventional rectangle lawn, the platform is capable of simulating sophisticated spraying process for lawn with more complex contours. In any case, the location of the sprinkler can be selected to be either inside the lawn perimeter or on the boundary of the lawn.

[0096] FIG. 8 reports a spraying process for triangular and pentagonal lawns, where the nozzle is placed inside the lawn.

[0097] By assigning multiple target distances to the sprinkler system, and let each target distance keep same proportion at each angle, the multiple round spraying process can be simulated. As shown in FIG. 9, the proportion selected is [1.0, 0.75, 0.5], such that the resulting target distances are [40, 30, 20] m respectively.

[0098] Conventionally, the spraying process, is from outer round to inner round, and the distance between each round is called pull back amount. For the simulation process conducted and reported in FIG. 9 was carried out from inner round to outer round in order to achieve a better visualization effect. The speed at which the sprinkler head rotates can be adjusted by the control system. The wind shift algorithm can calculate the sprinkler head rotational speed and optimize it to produce the correct distribution density. Rotational speed can be adjusted by each degree in the control system. Adjustable speed allows the sprinkler head to rotate slower and increase the precipitation rate in selected areas or allow the sprinkler head to rotate faster and decrease the precipitation rate in other selected areas.

[0099] The platform provides a high degree of freedom to the users, and most variables in the simulation process can be set by users via a Graphical User Interface.

[0100] Estimate of the Precipitation Distribution

[0101] The spraying process simulation described previously is based on droplet with a constant diameter. In reality, the spray jetted from nozzle consists of hundreds of thousands of droplets, and the diameters of these droplets are different. Therefore, to estimate the overall precipitation distribution, the estimate of droplet diameter distribution is needed. Given a certain droplet diameter distribution, the spraying pattern of droplets with various diameters can be computed, such that the corresponding water volume can be estimated. Obviously, the droplet diameter distribution is an important characteristic of the nozzle, and for given nozzle, its diameter distribution can be obtained from field test or experiments. As a general assumption of the droplet diameter distribution, the normal distribution is used in the following work. According to the definition, the percentage of droplet with certain diameter in terms of total water volume is given by

[00002]$f\left(d.Math.\mu ,\sigma \right)=\frac{1}{\sigma \sqrt{2\pi }}\text{?}.$$\text{?}\text{indicates text missing or illegible when filed}$

[0102] where μ is the mean value of the droplet, σ is the variance of the droplet. Let x axis be the droplet diameter, and y axis denotes the water volume percentage, then the droplet diameter distribution with mean diameter μ=0.01 m and standard deviation σ=0.002 m is given in FIG. 10.

[0103] Assuming the water volume used in each sweep is C, then the total water volume of droplet with the diameter d is given by

N(d)=C*f(d|μ,σ).

[0104] If the mean droplet diameter is p=0.01 m, σ=0.002 m, and the range of the droplet diameter is [0.001, 0.002, . . . , 0.019, 0.020] m, then the droplet trajectory of the droplet with each diameter is denoted by the light narrow lines in FIG. 11, and with the assumption of normal distributed droplet diameter, the precipitation distribution of one spray at a fixed direction is denoted by the bold dark line in FIG. 11.

[0105] Considering now the precipitation distribution result can be effectively estimated. In FIG. 9, a multi-round spraying process was simulated, where the pull back amounts between each round were the same. In practice, the pull back amount is not fixed the determination of the pull back amount, experimental results or empirical methods can be applied.

[0106] Considering the wide range of the droplet diameter distribution, the selection to find the required flow velocities and corresponding angles was based on the mean droplet diameter, thus the choice of target distance was very important for achieving a uniform precipitation distribution.

[0107] Preferably, the system provides an algorithm called divider lines method to automatically compute the optimal pull back amount for given number of pull back. All the boundary lines in the following simulations were computed by the divider lines method.

[0108] Wind Effect Simulation Results

[0109] Considering the wind effect is now incorporated into the simulation. Consider the lawn of FIG. 5, the characteristic curve described above can be used to find the required flow velocity to reach the target distance under the windless condition. If these computed flow velocity under a windy condition are used, then the wind effect can be simulated.

[0110] In the first wind effect simulation the wind is from west to east having an angle of 30 degree between wind direction x-axis. FIG. 12 reports the simulation of overall spraying with the droplet range from 0.001 m to 0.015 m with mean diameter 0.010 m; FIG. 13 reports a simulation of overall spraying with the same droplet range 0.001 m to 0.015 m with mean diameter 0.007 m. Six passes are applied as indicated by the boundary lines. The pull back amount between each red line is determined by the algorithm.

[0111] For the simulation results in FIGS. 12 and 13, the upper parts depict the droplet trajectory and the lower parts are the precipitation distribution. To quantify the uniformity of water distribution, one must define MeanSquareError (MSE) and Entropy. First, the original lawn is divided into several 5 m×5 m blocks and the water volume is measured in each block. Then the MSE is defined as following:

[00003]$\begin{array}{cc}\mathrm{mse}=\frac{1}{n}\underset{i=1}{\overset{n}{.Math.}}{\left(p_i-{\mathrm{target}}_i\right)}^2,& \left(4\right)\end{array}$

[0112] where i denotes all the blocks within and outside the lawn, and target, is defined as 5,

[00004]$\begin{array}{cc}{\mathrm{target}}_i=\{\begin{array}{c}0\mathrm{block}i\mathrm{is}\mathrm{outside}\mathrm{the}\mathrm{lawn}\\ \frac{1}{n}\mathrm{block}i\mathrm{is}\mathrm{within}\mathrm{the}\mathrm{lawn}\end{array}& \left(5\right)\end{array}$

[0113] Obviously, the MSE measures not only the uniformity inside the lawn, but also the water wasted outside the lawn. It is well known that the entropy can be used to measure the amount of order or disorder of a system, the higher the entropy of a system, the more ordered the system is. A person skilled in the art will understand that for the precipitation case, the higher the entropy after he spraying, the more uniform the lawn is. The Entropy is defined as 6:

[00005]$\begin{array}{cc}\mathrm{entropy}=\underset{i=1}{\overset{n}{.Math.}}-p_i\ln \left(p_i\right).& \left(6\right)\end{array}$

[0114] where i denotes all the blocks within the lawn, pi is the water proportion in block i. By using MSE and entropy, the wind effect shown in FIGS. 12 and 13 can be quantified as was done in Table 2 below.

TABLE-US-00002 TABLE 2 Droplet mean diameter d.sub.mean = 0.01 m Wind speed (m/s) 0 1 2 3 4 5 MSE (×10.sup.−3) 5.07 5.31 6.99 8.05 9.20 9.41 Entropy 4.57 4.53 4.44 4.39 4.34 4.32 Droplet mean diameter d.sub.mean = 0.007 m Wind speed (m/s) 0 1 2 3 4 5 MSE (×10.sup.−3) 2.98 5.03 4.58 5.31 5.52 6.65 Entropy 4.67 4.57 4.58 4.55 4.53 4.45

[0115] From Table 2, it can be seen that as the wind speed increase, the MSE increases and Entropy decreases, showing the wind effect severity from MSE and Entropy aspects. As mentioned before, the proposed platform provides a big degree of freedom for the simulation. In FIGS. 14A through 14C, the wind effect is investigated and the simulation results of the three cases are reported. The three cases simulated are the following: [0116] Case 1: The wind is from west to east with linearly increasing wind speed from 0 to 5 m/s [0117] Case 2: The wind is from south to north at first 180 degree with w=5 m/s, and then become from east to west at another 180 degree with w=3 m/s [0118] Case 3: The wind is from west to east, and wind speed has the form of sin(13), where the beta is the spraying angle

[0119] FIG. 14 confirms that the platform is sufficiently flexible and accurate to simulate various wind effect cases. The wind effect can be effectively quantified by MSE and Entropy, and it is concluded that the wind effect significantly deteriorates the precipitation uniformity as well as water coverage, causing the increase of MSE and decrease of Entropy. The wind effect cause significant water wastage in the lawn irrigation.

[0120] Wind Shifting Algorithm and Simulation

[0121] To introduce the idea of wind shifting technology, one considers the lawn in the shape of square as in FIG. 15, where the nozzle is placed at the center of the lawn:

[0122] Assuming a fixed flow velocity=55 m/s, the spray can accurately reach the lower right corner from the center under the windless condition. Assuming there are five different wind conditions, where the wind speed w=4.92 m/s, and the wind directions are indicated by arrows in FIG. 16, then the wind effect is listed in the second column of Table 3, and to counteract the wind effect, the corresponding solution is listed in the last column of Table 3. The results after the shifting are reported in FIG. 16.

TABLE-US-00003 TABLE 3 Case No. Wind direction wind effect concentration solution 1 southeast to northwest Decelorate the droplet velocity in both directions Increase flow velocity from 55 m/s to 115.25 m/s 2 northeast to southeast Accelerate the droplet velocity in both directions Reduce flow velocity from 55 m/s to 8.5 m/s 3 west to east Reduce the flow velocity in x-direction Increase flow velocity from 55 m/s to 92.4 m/s Change the spraying angle from  to 4 aast to west Accelerate the flow velocity in x-direction Increase flow velocity from 55 m/s to 41.25 m/s Increase the spraying angle from  to 5 northeast to southwest accelerate the flow velocity in y-direction Increase flow velocity from 55 m/s to 59.4 m/s decelerate the flow velocity is x-direction Increase the spraying angle from  to indicates data missing or illegible when filed

[0123] By using the counteraction solutions in Table 3, the wind effect can be quite effectively counteracted as shown in FIG. 16.

[0124] In the next section we will illustrate how to find the required flow velocity as well as corresponding angles under the wind conditions.

[0125] Algorithms

[0126] Denoting the target spraying distance as T.sub.o. According to the algorithm in the previous section, the required velocity ν.sub.o and spraying angle ν.sub.o without wind can be computed from the lawn contour information. To counteract the wind effect, the optimal flow velocity and angle are studied as the following:

ν.sup.i=ν.sup.i-1+Δν.sup.i-1,  (7)

γ.sup.i=γ.sup.i-1+Δγ.sup.i-1, i+1,2,  (8)

[0127] where Δγ.sup.i-1 and Δν.sup.i-1 are the i.sup.th searching step size of flow speed and angle, v.sup.i and y.sup.i are the updated speed and angle after i.sup.th correction. To find the appropriate ν and y such that the wind effect can be efficiently counteracted, define the actual dropping point of droplet after i.sup.th correction as T(ν.sup.i, y.sup.i), then the spraying error SE after n.sup.th correction can be defined as the distance between T(ν.sup.n, y.sup.n) and T.sub.0:

SE(ν.sup.i,γ.sup.i)=√{square root over ((T.sub.γ(ν.sup.i,γ.sup.i)−T.sub.0γ).sup.2÷(T.sub.γ(ν.sup.i,γ.sup.i)−T.sub.0γ).sup.2)}.  (9)

[0128] Under wind speed w and wind direction β, the appropriate velocity and angle can be found by minimizing the target function (9) until the error se is less than user custom threshold value.

[0129] FIG. 17 shows an error distribution for the lawn in FIG. 15, where the x, y and z coordinates correspond to spraying velocity, spraying angle, and error respectively. According to FIG. 17, it is clear that the error function has a global minimum, such that the method of traversal can be used to find out the optimal solution. Table 4 displays the minimum spray errors under the different precisions (searching step size). [0130] FIG. 17. The 3D figure of se(ν, γ) under conditions: T.sub.0=(0 m, 25 m), w=1 m/s, β=30°

TABLE-US-00004 TABLE 4 v precision (m/x) γ precision (°) optimal solution (m/s, °) spray error (cm) prs.sub.v = 5,00000000 pra.sub.γ = 10.00000000 v = 25.00000000, γ = 90.00000000 se = 172.209 prs.sub.v = 2.50000000 prs.sub.γ = 5.00000000 v = 27.50000000, γ = 90.00000000 se = 113.986 prs.sub.v = 1.25000000 prs.sub.γ = 2.50000000 v = 26.25000000, γ = 92.50000000 se = 48.912 prs.sub.v = 0.62500000 prs.sub.γ = 1.25000000 v = 26.87500000, γ = 92.50000000 se = 30.527 prs.sub.v = 0.31250000 prs.sub.γ = 9.62500000 v = 26.56250000, γ = 91.87500000 se = 11.954 prs.sub.v = 0.15625000 prs.sub.γ = 0.31250000 v = 26.71875000, γ = 91.87500000 se = 3.381 prs.sub.v = 0.07812500 prs.sub.γ = 0 15625000 v = 26.71875000, γ = 91.37500000 se = 3.381 prs.sub.v = 0.03906250 prs.sub.γ = 0,907812500 v = 26.67968750, γ = 91 87500000 se = 0.767 prs.sub.v = 0.01953125 prs.sub.γ = 0.03906250 v = 26.67968750, γ = 91.87500000 se = 0.767 prs.sub.v = 0.00976563 prs.sub.γ = 0.01953125 v = 26.67968750, γ = 91.89453125 se = 0.347

[0131] Although an optimal solution can be reached by a method of traversal under a specified precision, it's time-consuming and impossible to provide a real-time result on an embedded sprinkler system.

[0132] Preferably, one uses a more efficient algorithm as shown in FIG. 18. In every round of the function, one first uses 2 steps to reach the approximate solution under current precision, i.e. first optimize by solely adjusting v, then optimize by solely adjusting y. The reason why these 2 steps work is that the shape of se(v, y) is a cone. The precision can be improved by reducing the searching step by half round by round until the error requirement is met. FIG. 19 shows an example of the optimizing path. In this example, first the velocity and angle is initialized to be P.sub.i: ν=27.4 m/s, y=90°, se=107.8 cm, which is the solution obtained by the windless model. With precision prs.sub.ν=1.25, prs.sub.y, =2.5, the algorithm adjust ν and then y, reaching a approximate solution P.sub.2: ν=26.15 m/s, y=92.5°, se=57.0 cm. Then it improves the precision to prs.sub.ν,=0.625, prs.sub.y=1.25 and reaches P.sub.3: ν=26.755 m/s, y=92.5°, se=26.9 cm in the next round. Finally, it meets the error required at P.sub.4: ν=26.7750 m/s, y=91.8750°, se=8.5 cm at precision prs, =0.3125, prs.sub.y, =0.625 and stops.

[0133] Using the adaptive searching step, the global minimum can always be reached, such that the spraying error se=0. However, in practice the instruments can never be exactly accurate, and one does not always require a completely accurate shifting as water can move on the ground within a certain range. On the other hand, the higher precision wind shifting compensation consumes more time, which limits the real-time implementation of the algorithm, thus the appropriate threshold can be set according to the computing power as well as the precision of the equipment.

[0134] In light of this, the wind shifting algorithm is applied with different threshold value, and the corresponding time is reported in Table 5 and FIG. 20.

TABLE-US-00005 TABLE 5 acceptable maximal se average running time.sup.1 average se  200 cm 0.057981 s 25.9066 cm  100 cm 0.057785 s 25.9066 cm   50 cm 0.057619 s 24.8865 cm   20 cm 0.077819 s 11.3012 cm   10 cm 0.121891 s  5.6259 cm    5 cm 0.177913 s  2.7142 cm    2 cm 0.254274 s  1.0006 cm    1 cm 0.302861 s  0.4923 cm  0.5 cm 0.357425 s  0.2433 cm .sup.1Measured by 1000 test cases using Matlab code on laptop with Intel i7-5500U processor.

[0135] Wind Shifting Simulation

[0136] Based on the wind shifting algorithm set out above, the algorithm was applied to a 30 m×30 m lawn as in the FIG. 15. Six cases were tested as per the below: [0137] Wind from south to north with 30 degree angle with the speed of 1, 3 and 5 m/s respectively; and [0138] Wind from east to west with the speed of 1, 3 and 5 m/s respectively.

[0139] The results before and after shifting are reported in FIGS. 21A through 21F and FIGS. 22A through 22F, the corresponding MSE and Entropy are reported in Table 6 and 7.

TABLE-US-00006 TABLE 6 wind speed (m/s) 0 1 2 3 4 5 Before shifting MSE (×10.sup.−5) 1.11 1.22 1.27 1.51 1.77 2.13 Entropy 4.82 4.81 4.80 4.77 4.73 4.68 After shifting MSE (×10.sup.−5) 1.11 1.06 1.08 1.08 1.08 1.07 Entropy 4.82 4.82 4.82 4.82 4.82 4.82

TABLE-US-00007 TABLE 7 /CATENA 00 (2016) 1-29 wind speed (m/s) 0 1 2 3 4 5 Before shifting error(×10.sup.−3) 1.11 1.15 1.30 1.53 1.84 2.19 entropy 4.82 4.82 4.80 4.76 4.72 4.67 After shifting error(×10.sup.−3) 1.11 1.08 1.09 1.10 1.09 1.09 entropy 4.82 4.82 4.82 4.82 4.82 4.82

[0140] From Table 6 and 7, it can be seen that the wind shifting algorithm provides very good shifting results in terms of MSE and Entropy. Particularly, in some cases the precipitation after shifting is even more uniform than the case without wind: when the wind speed w=5 m/s, the MSE without shifting is 2.13 and that with shifting is 1.07, which is a significant improvement. It should also be noted that the shifting results are very stable, for instance, the Entropy after shifting is always 4.82 in both cases.

[0141] Sensitivity Analysis

[0142] To achieve the best wind shifting effect, the wind condition should ideally be updated in real time. However, it is quite normal that the wind measuring apparatus are not accurate and contain certain delays. Therefore, sensitivity analysis is essential to test the performance of the shifting algorithm when certain errors are included in the measured wind. To do this, a constant measured wind is used such that the wind shifting parameter unchanged, and let the actual wind change, then test if the performance of wind shifting still be good, or it will deteriorate quickly.

[0143] Assuming that the measured wind is 5 m/s, and the actual wind is from 2 m/s to 8 m/s, which denotes about 60% measured error in terms of wind speed. The shifting results are reported in FIGS. 23A through 23F.

[0144] Similar to the previous cases, the precipitation uniformity is quantified when the measure error exists in terms of MSE as well as Entropy as listed in following Table 8

TABLE-US-00008 TABLE 8 actual wind (m/s) 0 1 2 3 4 5 6 7 8 9 10 measured error 5 4 3 2 1 0 1 2 3 4 5 (W.sub.m − W.sub.d) error (×10.sup.−5 ) 1.98 1.79 1.60 1.32 1.17 1.07 1.21 1.33 1.71 2.14 2.73 entropy 4.71 4.75 4.77 4.80 4.81 4.82 4.81 4.79 4.74 4.67 4.60

[0145] The shifting error νs. the wind measuring error was reported in terms of wind speed and wind angle for the measure wind w=6 MPH and w=11 MPH.

[0146] Computation of Target Distances

[0147] The wind shifting algorithm can be used to calculate the required flow velocity and spray angle to reach any target point on a predetermined lawn. To cover the whole lawn, different target distances td are set up for each round of spraying.

[0148] FIG. 24 provides an illustration of an example in which 3 target distances were set as 0.9, 0.7, 0.4 (proportion) respectively to cover the lawn.

[0149] One must consider how to set up the target distances for each round in order to reach a good distribution uniformity and compare three kinds of different methods.

[0150] The most straightforward way to set up target distances is to use an arithmetic progression. An example is shown in FIG. 25, where 4 rounds of spray were used to cover the lawn and target distances are 0.2, 0.4, 0.6, 0.8 respectively. The second method is n-divide method. To reach a better water distribution in n rounds, the lawn can be split into n parts as shown in FIG. 26. It is then easier to distribute the same volume of water in each part. For each round of spraying, the droplet is controlled to fall on the middle of a ring, intuitively then most of the water should fall into the target part. As in FIG. 26, the rectangle is divided into four area equal parts, and let the mean droplet to reach the middle of each part.

[0151] The third method is divider lines method. The lawn is divided into n+1 area equal parts, and use the n divider lines as the target distances. In FIG. 27, there is an example in which the lawn is divided into 5 area of equal parts and use the 4 divider lines as target distances.

[0152] To determine the value of n, one divides the desired total irrigation amounts by the water volume per round. Given the value of n, one can use the above-mentioned method to reach a good water distribution. The MSE and Entropy for the three methods mentioned above are reported in the following Table 9. It can be seen that the divider lines method provides the smallest MSE and the largest Entropy, thus it is the best method of the three to automatically select the target distance.

[0153] Implementation of the Database and Graphical User Interface

[0154] According to a preferable embodiment of the present invention, one can apply the simulation platform into a real application by computing the shifting parameters in real time.

[0155] According to another preferable embodiment of the present invention, one can apply the simulation platform into a real application by computing the shifting parameters in advance and storing those in a database. Upon use, the corresponding required flow speed as well as required angles are extracted from the database to counteract a measured wind.

[0156] The implementation of the first method is quite straightforward. However, the implementation of the database to achieve the wind shifting is more a more efficient way when the computing power is limited. Assume the need to generate a database for a lawn, where the wind speed can be [1, 2, 3, 4] MPH, the wind direction can be [10, 20, 30, 40] degree with x-axis, and the lawn is divided in the n pies, then the database which includes the required flow speed and spraying angle can be stored as a 3D matrix as in FIG. 29.

[0157] Each bar in FIG. 29 represents a set of required flow velocity and spraying angle. Assume initially the measured wind has speed 3 and direction 40 degree as indicated by light colored bar, therefore the parameters in the light colored bar are used to conduct the spraying. Later on at the time point indicated by the black point, the wind speed reduce from 3 MPH to 1 MPH but keeps the same direction, then use is made of the data in the blue bar from the pie at the black point.

TABLE-US-00009 TABLE 9 arithmetic progression n-divide method divider lines method entropy mse entropy mse entropy mse n (10   ) (10   ) (10   ) 3 5.558696094 4.42160258 8.07620625 4.374741098 2.9303625 4.569562261 4 8.259328906 4.378891534 2.83796875 4.629912844 3.072691406 4.579520176 5 6.527041406 4.468568559 5.40473125 4.501883035 2.039260156 4.662217445 6 5.3655125 4.523570614 3.516091406 4.602540766 1.515209375 4.704216864 7 6.00218125 4.55079514 2.777072656 4.634861083 1.677571875 4.689678252 8 7.196332813 4.502444524 2.336932031 4.668657601 1.456821875 4.707640548 9 5.962136719 4.535717316 1.96940625 4.703067124 1.278915625 4.723180948 10 5.378573438 4.547683044 1.58806875 4.731825277 1.415141406 4.715942761 11 5.199463281 4.554497897 1.215084375 4.762482496 1.338676563 4.725311081 12 5.327989063 4.545030052 1.087489063 4.770234491 1.16085625 4.739435545 13 5.115610156 4.552588626 0.926891406 4.777530711 1.091857031 4.752680653 14 5.432188281 4.5436487 0.774389844 4.787503575 0.969915625 4.766071533 15 6.872671875 4.519616769 0.923022656 4.781199631 0.834810938 4.77725098 16 7.271442969 4.058731115 1.379680469 4.752244574 0.795260156 4.779267223 17 6.797624219 4.518178005 1.662914063 4.729969358 0.8054375 4.77978694 18 6.3583875 4.525970252 1.606871875 4.73047667 0.788395313 4.780496854 19 6.164800781 4.52945914 1.572677344 4.729296313 0.804582031 4.779366649 20 6.06593125 4.529817106 1.356619531 4.750071517 0.798092969 4.779872878 indicates data missing or illegible when filed

[0158] For a multiple pull back spraying process, the proportion of the pull back amount can also be included in the database in the format of a 4D matrix. The platform includes a Graphic User Interface (GUI) to generate the required database.

[0159] According to an embodiment of the present invention, the sprinkler apparatus used in conjunction with a system compensating for wind effect comprises: (a) a base housing configured to confiningly receive a pressurized water flow; (b) a nozzle housing coupled to the base housing, the nozzle housing sized to slidingly couple with the base housing to pop-up into an operating position or retract into a nested position; (c) an upper nozzle assembly positioned at a top end of the nozzle housing, the upper nozzle assembly comprising a rigid outer frame and a resilient inner nozzle positioned therein, the diameter of the inner nozzle being smaller than the rigid outer frame to provide space for the inner nozzle to distend to a maximum orifice size determined by the circumference of the outer frame, the resilient inner nozzle responsive to the rate of pressurized water flow to distend up to the maximum orifice size to vary the wetted radius of discharged water from the upper nozzle assembly; (d) a lower nozzle assembly positioned below the upper nozzle assembly at the top end of the nozzle housing, the lower nozzle assembly comprising a vertical slit-shaped aperture through which water is discharged in a curtain effect; and (e) a flow control valve assembly fluidly coupled to the base housing to controllably supply the pressurized water flow; wherein the upper and lower nozzle assemblies together achieve a substantially uniform elliptical spray pattern.

[0160] Programmable Spray Pattern—Uniformity Distribution Optimization

[0161] As a person skilled in the art would know, the spray pattern of a sprinkler apparatus is known to have inconsistencies in uniformity. Inconsistencies in spray pattern uniformity can result in over-watering and/or under-watering of the water receiving area leading to inefficient irrigation. To minimize such inconsistencies, uniformity of water distribution by a sprinkler apparatus used in the purposes of the present disclosure can be programmably controlled, according to some embodiments, using computer instrumentation programmed to create and implement a spray partem that is designed to compensate for inconsistencies in spray pattern uniformity based on nozzle profile and target precipitation density for the water receiving area. In such embodiments, the rate of flow of the pressurized water supply into and out of the flow control valve assembly and into and out of the pop-up type sprinkler head is modulated to vary the wetted radius of the water projected outward from the sprinkler head with each sweep of the sprinkler, so that the water receiving area is uniformly watered over the geometry of its entire area.

[0162] According to a preferred embodiment of the present invention, a sprinkler apparatus used in conjunction with the system according to the present disclosure can comprise computer instrumentation programmed to select a desired target level of precipitation density for the water receiving area; determine the number of sprinkler sweeps needed to achieve the selected precipitation density; pair the number of determined sprinkler sweeps with the selected precipitation density to determine the amount to pull back (i.e., reduce the wetted radius) on each sweep; determine a new flow rate based on the amount of pull back determined; and generate a spray pattern that applies the pulled back flow rates at the calculated rates on each sprinkler sweep to correct the inconsistencies in the uniformity of the spray pattern. In this way, a sprinkler spray pattern can be created that is adjusted with each spray sweep to correct inconsistencies in the uniformity of the spray pattern so that the water receiving area is ideally as optimally uniformly watered as possible (within the limitations of the instrumentation) over the geometry of its entire area.

[0163] Another exemplary embodiment of the present disclosure pertains to a method for irrigating an irregularly shaped and/or an asymmetrically shaped water receiving area while enduring winds which affect the optimal water distribution. The method generally comprises: (a) providing a sprinkler system as described above; (b) determining the geometry and irrigation needs of the water receiving area; (c) selectively diverting the water supply to the one or more sprinkler apparatus suitable to the geometry and irrigation needs determined for the water receiving area; (d) positioning the orientation of each of the one or more sprinkler apparatus according to the geometry and irrigation needs determined for the water receiving area; and (e) adjusting the pressurized water flow to each of the one or more sprinkler apparatus according to the geometry and irrigation needs determined for the water receiving area and, optionally, (f) altering the sprinkler head speed through out each sprinkler sweep to correct inconsistencies in the uniformity of the spray pattern. According to further embodiments, the step of adjusting in step (e) comprises optimizing each of the one or more sprinkler apparatus to create a sprinkler spray pattern that is adjusted with sprinkler sweep to correct inconsistencies in the uniformity of the spray pattern, said optimizing comprising: (a) selecting a desired target level of precipitation density for the water receiving area; (b) determining the number of sprinkler sweeps needed to achieve the selected precipitation density; (c) pairing the number of determined sprinkler sweeps with the selected precipitation density to determine the amount to pull back on each sweep; (d) determining a new flow rate based on the amount of pull back determined; and (e) generating a spray pattern that applies the pulled back flow rates at the calculated rates on each sprinkler sweep to correct inconsistencies in the uniformity of the spray pattern.

[0164] According to a preferred embodiment of the present invention, the sprinkler system can further include a system controller or other computer instrumentation to synchronize the operation of each sprinkler apparatus in the system. In other preferred embodiments, the controller or other computer instrumentation is programmable for example, following a logic and steps specific to the lawn to be watered. Exemplary components for the controller include a microprocessor, a programmable logic circuit (or “PLC”), an analog control circuit, and electronic components (e.g., transistors, resistors, diodes, etc.) on a circuit board.

[0165] According to further embodiments, the system can be programmed to establish a watering program that is activated in response to the environmental conditions of the water receiving area. In such embodiments, for example, the system can comprise sensors for continual monitoring of the conditions of the water receiving area in order to determine whether watering is required, and further to establish the parameters for achieving sufficient watering for the particular water receiving area. According to certain embodiments, the sensors are moisture sensors for continually monitoring the soil to determine when watering is required, how it is watered, and for how long it is watered. For example, the system can be configured to monitor one or more environmental conditions to make this determination, including without limitation, moisture level of the soil, temperature of the soil, solar load on the soil, salinity of the soil, wind measurements, and/or precipitation measurements. Once the system determines that watering is required, the system is activated to water the water receiving area for a predetermined time. Moisture values can continue to be monitored and compared to original values in order to determine water absorption by the soil, and/or achievement of target moisture rates.

[0166] According to a preferred embodiment of the present invention, the sprinkler system can comprise computer instrumentation programmed to select a desired target level of precipitation density for the water receiving area; determine the number of sprinkler sweeps needed to achieve the selected precipitation density; pair the number of determined sprinkler sweeps with the selected precipitation density to determine the amount to pull back (i.e., reduce the wetted radius) on each sweep; determine a new flow rate based on the amount of pull back determined; and generate a spray pattern that applies the pulled back flow rates at the calculated rates on each sprinkler sweep to correct the inconsistencies in the uniformity of the spray pattern. In this way, a sprinkler spray pattern can be created that is adjusted with each spray sweep to correct inconsistencies in the uniformity of the spray pattern and thereby further optimize the uniformity of watering the specific water receiving area.

[0167] Although the invention has been described with reference to certain specific embodiments, various modifications thereof will be apparent to those skilled in the art without departing from the scope of the invention. All such modifications as would be apparent to one skilled in the art are intended to be included within the scope of the following claims.