Precision Agriculture

, Volume 12, Issue 4, pp 534–545

Estimating off-rate pesticide application errors resulting from agricultural sprayer turning movements


    • Department of Biosystems and Agricultural EngineeringUniversity of Kentucky
  • Santosh K. Pitla
    • Department of Biosystems and Agricultural EngineeringUniversity of Kentucky
  • Rodrigo S. Zandonadi
    • Department of Biosystems and Agricultural EngineeringUniversity of Kentucky
  • Michael P. Sama
    • Department of Biosystems and Agricultural EngineeringUniversity of Kentucky
  • Scott A. Shearer
    • Department of Biosystems and Agricultural EngineeringUniversity of Kentucky

DOI: 10.1007/s11119-010-9199-9

Cite this article as:
Luck, J.D., Pitla, S.K., Zandonadi, R.S. et al. Precision Agric (2011) 12: 534. doi:10.1007/s11119-010-9199-9


Pesticide application is an essential practice on many U.S. crop farms. Off-rate pesticide application errors may result from velocity differential across the spray boom while turning, pressure fluctuations across the spray boom, or changes in boom-to-canopy height due to undulating terrain. The sprayer path co-ordinates and the status (on or off) of each boom control section were recorded using the sprayer control console which provided map-based automatic boom section control. These data were collected for ten fields of varying shapes and sizes located in central Kentucky. In order to estimate potential errors resulting from sprayer turning movements, a method was developed to compare the differences in application areas between spray boom control sections. The area covered by the center boom control section was considered the “target rate area” and the difference in these areas and the areas covered by remaining control sections were compared to estimate application rate errors. The results of this analysis conducted with sprayer application files collected from ten fields, many containing impassable grassed waterways, indicated that a substantial portion of the fields (6.5–23.8%) could have received application in error by more than ±10% of the target rate. Off-rate application errors exceeding ±10% of the target rate for the study fields tended to increase as the average turning angles increased. The implication of this is that producers may be unintentionally applying at off-label rates in fields of varying shapes and sizes where turning movements are required.


Precision sprayingNo-till farmingVariable-rate applicationChemical applicationSpray boom


To counteract the potential for negative environmental impacts and rising input costs associated with crop production, many U.S. grain producers have adopted no-till farming practices. Without the availability of pre- and post-emergence herbicides to control weed competition, no-till farming would be impractical. Another major factor affecting increased no-till crop production has been the development of genetically modified (GMO) corn (Zea mays) and soybeans (Glycine max). Glyphosate resistant (GR) corn and soybeans are common GMO crops utilized on U.S. farms. The use of GR soybeans has increased significantly over the past several years in the U.S., a trend that is expected to continue into the near future (Bonny 2008). Producers in Kentucky typically apply a burn-down herbicide (such as glyphosate) prior to planting. When weed competition begins to reach an undesirable level, producers then follow up with a second glyphosate application. This magnifies pesticide application errors as GR crops planted using no-till practices are typically sprayed two or more times, doubling or tripling the impacts of application errors.

Many farmers are utilizing larger equipment to reduce labor costs and improve the timeliness of their operations. Producers have turned to faster sprayers with boom widths in excess of 30 m. Pesticide application errors, especially those associated with larger equipment; result in a costly and time-consuming problem for agricultural producers. Off-target pesticide application errors as defined by Luck et al. (2010a) include: skipped-application, multiple-application, or unintentional-application to environmentally sensitive areas. Previous research indicated that off-target errors may contribute an additional 15–17% of the field area resulting from multiple-application in irregular shaped fields (Luck et al. 2010a). In another study, an automatic boom section control system with a control resolution of approximately 6.0 m reduced coverage areas by an average of 6.2% compared to manual boom control for 21 study fields of various shapes and sizes (Luck et al. 2010b).

Off-rate application errors could be described as errors resulting from incorrect pesticide rates applied across portions of a field. These errors could result from velocity differential across the spray boom induced by sprayer turning maneuvers, pressure changes across the width of the spray boom, or undulating terrain which affects boom to canopy distance, causing irregularities in nozzle pattern overlap. Problems associated with off-rate application errors are exacerbated with larger equipment as increased boom widths result in greater velocity, pressure, and height variations across the spray boom. Aside from problems relating to pesticide efficacy resulting from off-rate application, researchers have shown that over application of glyphosate to GR soybeans can result in reduced plant growth (Reddy et al. 2000; Reddy and Zablotowicz 2003). Controlling these application errors deserves more attention as pesticides are one of the more significant production costs, exceeding seed costs for the production of soybeans in Kentucky from 1999 to 2003 (Gibson 2004).

Although research concerning site-specific application of herbicides and pesticides has been conducted (Faechner et al. 2002; Wilkerson et al. 2004), the effects of sprayer turning movements on pesticide application have not yet received much attention. Analyzing spatial data could provide a method for evaluating the quantity and the location of pesticide application based on machine geometry and geographic position. Geographic Information Systems (GIS) are excellent tools for analyzing spatial data in agricultural environments. Modeling the distribution of dry fertilizer from spreading vehicles using GIS has received significant attention as demonstrated by Fulton et al. (2003). Giles and Downey (2003) used GIS techniques with GPS field-based data collection in an attempt to create quality control maps of spray applications. More recently, Lawrence and Yule (2007) created a GIS model for evaluating field application variation of dry fertilizer distribution. Results of these investigations suggest GIS could be a useful tool for analyzing field data to determine the effects of the sprayer path on off-rate application errors.

The main goal of this study was to estimate off-rate application errors that could result from sprayer turning movements during field application. The specific objectives of this study were: (i) to calculate the coverage areas for individual sprayer boom control sections based on the sprayer geometry, geographic co-ordinates, and the recorded status (“on” or “off”) of each control section, (ii) to estimate the errors in coverage areas for control section positions across the spray boom resulting from sprayer turning movements, and (iii) to determine if any relationship existed between the average turning angle and off-rate application errors for the fields studied.

Materials and methods

This study was conducted with data collected from a co-operating producer located in Shelby County, Kentucky. This central Kentucky farm consists of numerous irregularly shaped fields, many of which contain grassed waterways that cannot be traversed while spraying. Fields were considered irregular in shape when they contained non-navigable grassed waterways within the field boundaries. This type of field shape typically creates situations where a substantial portion of end rows around the field border must be sprayed while turning which can contribute to off-rate application errors. According to the operator, typical spraying operations on this farm consist of making two passes around the field boundary to allow for adequate space for turning in end rows. The remaining portions of fields are then typically sprayed using parallel passes when possible (M. McClure, personal communication, June, 2009). Ten fields were selected for this analysis representing a variety of field shapes and sizes and totaling 185 ha (Fig. 1). Each field selected received a pre-emergence treatment of glyphosate prior to soybean planting during the 2006 cropping season.
Fig. 1

Boundaries for the ten fields used in this study (boundaries are to scale; fields were moved from actual locations for placement within this figure)

Map-based automatic boom section control was added to a self-propelled sprayer (RoGator 664, Ag Chem/AGCO, Duluth, Georgia, USA) with a 24.8 m boom consisting of 48 nozzles spaced at 510 mm. The boom section control consisted of a console (ZYNX X15, KEE Technologies, Sioux Falls, South Dakota, USA) and a 30 channel electronic control unit (ECU) (Spray ECU 30S, KEE Technologies, Sioux Falls, South Dakota, USA). The control console and ECU provided 30 separate control channels which actuated solenoid valves (TeeJet Nozzle Valves, Capstan Ag Systems, Inc., Topeka, Kansas, USA) connected to each spray nozzle body. In addition, the control console provided light bar guidance for the operator. As each control section passed over a previously sprayed area, individual channels were switched off eliminating excess spray overlap. Spray nozzles were mapped to individual channels as follows: six nozzles at the left and right boom ends were controlled via channels 1–6 and 25–30, respectively; with the remaining 36 interior boom nozzles paired and mapped to channels 7 through 24. Effective control section widths were 510 mm for individual nozzles and 1.02 m for paired nozzles which provided relatively high boom control resolution.

The control console not only provided map-based automatic boom section control but also served as the data logging system. Utilizing proprietary software within the control console, sprayer path co-ordinates were automatically recorded along with each control section status when any channel was set to the “on” state and continued recording this data until all channels were set to the “off” state. As the sprayer traversed each field, the control console recorded the geographic co-ordinates (x and y co-ordinates (m) in NAD 1983 Universal Transverse Mercator (UTM) format) at 1 s intervals (1 Hz typical) up to 5 Hz when boom control sections were actuated, which was provided by the DGPS receiver (Ag132, Trimble Navigation, Ltd., Sunnyvale, California, USA). The DGPS receiver used a nearby U.S. Coast Guard radio beacon for differential correction which provided sub-meter accuracy. At each co-ordinate pair, the control console also recorded the control section state (on = 1 or off = 0) of the 30 ECU control channels which created a 30 bit binary number.

The General Algebraic Modeling System Data Exchange (GDX) files created for each field by the control console were imported in ASCII format into ArcMap (ArcGIS v9.3, ESRI, Redlands, California, USA). Having the co-ordinate pairs in UTM format allowed the subsequent analyses to be conducted on Cartesian co-ordinates using MS Excel®. The UTM co-ordinate pairs were imported into MS Excel® and matched with the corresponding control section status recorded for all 30 ECU channels.

The first step in the analysis was to mathematically model boom position relative to the DGPS receiver location on the sprayer which is demonstrated in Fig. 2 (with the sprayer turning right). Using Cartesian co-ordinates, the sprayer headings were represented as the line slope from x1, y1 to x2, y2 and x2, y2 to x3, y3 as m1,2 and m2,3, respectively. The intersection of the inverse slope lines (m1,2−1 and m2,3−1) from the midpoint of the sprayer heading lines provided the center point of a circle, the radius of which was considered the turning radius of the sprayer (Rturning). The sprayer’s turning angle (θ, shown in Fig. 2) was calculated between m1,2−1 and m2,3−1, and is proportional to the change in sprayer heading between the three consecutive GPS co-ordinates. The corrected turning radius (Rannular) was calculated by adding or subtracting (depending on the direction of turn) the distance along the spray boom of each control section along the line m1,2−1. For paired nozzle control sections, the center point between the two nozzles was used for determining Rannular. This procedure also provided the co-ordinate for each control section at every GPS co-ordinate recorded by the control console. The coverage area for each control section was calculated by multiplying Rannular by θ (from point x2, y2 to x3, y3 shown in Fig. 2), the control section width (510 mm for a single nozzle and 1.02 m for paired nozzles), and the status (on = 1 or off = 0) of each control section. For all control sections with an “on” status, the result was an estimate of the coverage area for each control section between consecutive GPS co-ordinates.
Fig. 2

Geometry used to determine the coverage area for each control section corresponding to the “on” state of the ECU control section channel

To calculate off-rate errors across the spray boom while turning, the assumption was made that the two center control sections on the spray boom were applying the target rate. This assumption was made for two reasons. First, since the sprayer was calibrated by the producer, it was assumed that the center control section velocity relative to the ground would be essentially the same as that of the receiver location on the sprayer traveling at the calibrated speed. Second, the purpose of this study was to develop a simple method to quantify off-rate errors across the spray boom resulting from turning maneuvers. The coverage areas calculated for the center control sections were therefore treated as target rate coverage areas between consecutive GPS co-ordinates. At each GPS co-ordinate recorded by the control console, the target rate coverage area was divided by the coverage area for the remaining control sections along the spray boom. The resulting value was considered the application error for each respective control section. Boom control sections covering less than the target coverage area over-applied (>100%) while sections covering more than the target coverage area under-applied (<100%).

Maps were created by plotting the co-ordinates of each control section in ArcMap along with its respective calculated percentage of the target application rate for Fields 38 and 512. Specifically, areas receiving application rates that may have exceeded ±10% of the target rate were illustrated using different colors compared to the target rate. All 30 control section positions appear as lines perpendicular to the direction of travel and represent the errors in area applied between two consecutive GPS co-ordinates. The sprayer path co-ordinates were converted to a line using ArcMap with arrows to better represent the sprayer path and direction traveled through each field. This range of off-rate errors (±10%) was selected as Bode and Butler (1983) recommended an allowable coefficient of variation (CV) of 10% for nozzle-to-nozzle discharge variation across a spray boom.

Coverage areas of the field applied above or below the target rate (from 10 to 200%) were summed. This information was plotted to show the trend in application errors as a function of percent deviation from the target rate for each field. The average value of θ was calculated for the study fields to determine the average sprayer turning angle (θavg) for each field. It is important to note that θavg did not include turning movements in the end rows. Typically, all boom control sections were off as these areas had been previously sprayed by the two initial passes around the field boundary (as previously described). Therefore, at these locations, the control console did not record GPS co-ordinates as all control sections were turned off and the turning angle was only calculated for situations when one or more nozzles were on. The percent of field areas where off-rate errors exceeded ±10% of the target rate were plotted versus θavg in an attempt to identify if any relationship existed between the two.

Results and discussion

Line segments perpendicular to the direction of travel in Fig. 3 represent the spray boom at every GPS co-ordinate pair recorded for Field 38. Figure 3 shows areas of Field 38 that were over-applied (in red) and under-applied (in blue) when compared to the target rate ±10%. The operator appeared to make two passes around the field border before attempting to cover the remainder of the field using parallel (although not often straight) passes. Off-rate errors are observable as control section coverage areas increased along the outside of the turns and decreased along the inside of the turns. Figure 3 shows that off-rate errors appeared to be most concentrated in areas around grassed waterways; however, because of the boundary shape of Field 38, it was also necessary to spray a significant portion of the field while turning. Based on the sprayer path generated from the data file, it appeared the operator was only able to spray a small portion of the field with straight, parallel passes. Although the shape of Field 38 was irregular because of the grassed waterways, these errors seemed to be reduced in locations where the sprayer was able to travel in straight lines with parallel passes.
Fig. 3

Areas of Field 38 deviating by more than 10% (above or below) of the target application rate

Figure 4 shows areas of Field 512 that were over-applied (in red) and under-applied (in blue) when compared to the target rate ±10%. Because the shape of Field 512 was somewhat rectangular, the majority of it was sprayed with straight, parallel passes. The operator chose to make two full passes around the interior of the field border, and then proceeded to cover the interior of the field using parallel passes. Off-rate errors occurred at locations where the operator was forced to make turns while covering the field. However, comparing the errors from Field 512 (Fig. 4) to those found in Field 38 (Fig. 3) show that parallel passes can help minimize off-rate errors from turning movements.
Fig. 4

Areas of Field 512 deviating by more than 10% (above or below) of the target application rate

Figure 5 displays a summary of the areas of Fields 38 and 512 receiving application above or below the target rate. The percentage of field coverage is based on the total area covered by the control sections operating in the “on” position. The trend of the data in Fig. 5 is somewhat intuitive in that as the percentage of the target rate increased, the percent of the field coverage area applied below that decreased. Conversely, as the percentage of target rate increased, the percent of field coverage areas applied above that increased. Figure 5 indicates that 13.9% of Field 38 and 3.41% of Field 512 were sprayed at a rate below 90% of the target rate, while 9.9% of Field 38 and 3.1% of Field 512 were sprayed at a rate above 110% of the target rate. The end result is that approximately 23.8 and 6.4% of Fields 38 and 512, respectively, may have been applied outside the target rate ±10% with this off-rate error attributed to sprayer turning movements.
Fig. 5

Distribution indicating percentage of field areas covered above or below the target application rate

Table 1 summarizes the θavg, area sprayed (ha), and the area and percentage of each field where errors exceeded ±10% of the target rate. The analysis indicated that Fields 38 and 197 exhibited the most significant accumulation of off-rate areas (23.8% of the field area) for both fields, while Field 512 had the lowest areas where off-rate application exceeded the target rate ±10%. Interestingly, θavg for Field 512 (2.86°) was the lowest among the fields, while θavg for Fields 38 and 197 (5.9° and 6.46°, respectively) were the highest values calculated for all study fields. The data contained in Table 1 indicate that substantial portions of the study fields received application rates that exceeded ±10% above and below the target rate. Figure 6 shows the off-rate application errors exceeding ±10% versus θavg for the study fields. A regression line was fitted to these data to illustrate the relationship that existed between the two. As θavg increased, the percentage of field areas exceeding ±10% of the target rate increased and had an R2 value of 0.89 over the range of data collected from the study fields. The implication here is that as θavg increases during field application, areas of the field-applied off-rate may also increase.
Table 1

Summary of θavg and off-rate application errors exceeding ±10% of the target rate

Field number

θavg (°)

Total field area sprayed (ha)

Portion of field applied at specified percentage of target rate

<90% of target rate (ha)

>110% of target rate (ha)

<90% of target rate (%)

>110% of target rate (%)

Target rate ±10% (%)
















































































Fig. 6

Percentage of field with off-rate application errors exceeding ±10% of the target rate versus average turning angle for all study fields

Although the effects of off-rate application are relatively unknown in terms of crop yield, over-application of herbicides such as glyphosate has been shown to reduce plant growth in soybeans (Reddy et al. 2000; Reddy and Zablotowicz 2003). Additionally, materials wasted from over-application of pesticides can be estimated assuming they are proportional to the areas covered during application. Similarly, pesticides applied below the target rate usually may not result in crop damage; however, yield loss may occur due to weed competition when application rates fall below prescribed levels, which has been shown in corn (Cox et al. 2006) and soybeans (Shafagh-Kolvanagh et al. 2008).

This study was performed on fields of varying shapes and sizes located in central Kentucky. Some of the study fields were irregular in shape as they contained multiple non-navigable grassed waterways. When spraying these fields, a substantial number of turns were required to navigate around grassed waterways and field boundaries. Off-rate errors may have been reduced, as seen with Field 512, if the producer could have utilized more parallel passes and less turning while spraying some of the fields. While this may have led to higher off-rate errors, small, irregular-shaped fields are very common to central Kentucky. Also not considered in this study would have been additional errors resulting from spray boom overlap, pressure variations across the boom, or boom-to-canopy height changes during application. The sprayer was equipped with map-based automatic boom section control; however, the control console setup ensured total coverage of the field, which would have resulted in additional overlapped areas for each control section, specifically, areas where point rows may have been encountered or overlaps occurred during parallel field passes. This study focused solely on potential off-rate application errors resulting from turning movements. Had errors resulting from spraying previously treated areas been considered, total application errors in the study fields may very well have been higher. Pressure variations and height changes across the boom during field application would have likely affected off-rate errors as well.


Turning movements affected estimated off-rate application errors based on the maps generated from the sprayer paths for ten fields in central Kentucky. Areas where off-rate errors seemed to be most significant included spraying around grassed waterways and field boundaries while turning. In cases where the sprayer operator could cover the field with straight, parallel passes, errors seemed to be well within 10% of the target rate. By observing the cumulative areas where application errors were occurring, it was possible to identify how much of the field was being sprayed within a specified percentage of the target rate. This analysis estimated that areas of the study fields applied outside the target rate ±10% ranged from 6.5 to 23.8% of the total field area. Areas of the study fields with off-rate application errors exceeding ±10% of the target rate followed a direct relationship with θavg. As θavg increased for the study fields, off-rate errors also increased. This information indicates that producers may be over-applying chemicals to fields where excessive amounts of turning are required at application. Off-rate errors will continue to be a problem until variable-rate application techniques are developed and successfully implemented for precision spraying.

Although beyond the scope of this introductory study into the subject of potential off-rate errors, collecting more field data for an analysis of this type may reveal more about how field shape and size can affect these types of errors. Additionally, incorporating off-target errors (from sprayer overlap) would provide more information regarding its effects on pesticide application errors. An analysis of changes in equipment width may provide indicators on the magnitude of application errors due to larger or smaller spray booms. Based on this type of information, producers could potentially utilize tools such as path planning to reduce or eliminate these errors.


The authors would like to express their appreciation to Mike Ellis, Bob Ellis, Jim Ellis, and Matt McClure of Worth and Dee Ellis Farm for their cooperation on this research project. This material is based upon work supported by the Cooperative State Research, Education and Extension Service, U.S. Department of Agriculture, under Agreement no. 2008-34628-19532. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the U.S. Department of Agriculture. The information reported in this paper (no. 10-05-045) is part of a project of the Kentucky Agricultural Experiment Station and is published with the approval of the Director. Mention of trade names is for informational purposes only and does not necessarily imply endorsement by the Kentucky Agricultural Experiment Station.

Copyright information

© Springer Science+Business Media, LLC 2010