Copyright is owned by the Author of the thesis.  Permission is given for 
a copy to be downloaded by an individual for the purpose of research and 
private study only.  The thesis may not be reproduced elsewhere without 
the permission of the Author. 
 



Improving Granular Fertiliser Aerial 
Application for Hill Country Farming 

 

 

 

 

 

A thesis presented in partial fulfilment of the requirements for the degree of 

 

Doctor of Philosophy 

In 

Agricultural Engineering 

 

At Massey University, Palmerston North, New Zealand 

 

 

 

 

 

 

Sue Chok 
2017





1 
 

Abstract 
Soil fertility and pasture productivity varies significantly over hill country farms. Therefore 

conventional aerial fertiliser application of a single application rate is inefficient. Automation 

of the aircraft hopper door increases control of fertiliser application. This includes the ability to 

achieve variable rate application, where multiple application rates can be applied over the 

farm. Ravensdown Limited has installed variable rate application technology (VRAT) on their 

Pacific Aerospace Cresco (PAC) 600 aircraft to improve the aerial application of granular 

fertiliser to hill country farms. The objective of this study was to measure and improve the 

performance of the VRAT system. Various aspects of the system’s performance were 

examined; including hopper flow dynamics, control of the hopper door, estimation of a 

fertiliser particle’s landing position from a known release point, collection of field data, and 

prediction of wind effects on the ground fertiliser distribution. 

Performance trials, bench testing and static hopper flow tests were used to improve the VRAT 

system. Three performance trials were carried out. Each had a different sampling 

configuration: grid, nested grid and line. Sampling configuration varied because the objective 

of each trial differed, and there were advantages and disadvantages to each configuration. 

Accuracy, precision, level of off-target application, and capability of the VRAT system to vary 

application rate was measured. The trials observed accurate application rates, and improved 

precision when compared to pilot operated hopper doors. Off-target application occurred 

because the buffer was insufficiently sized, and did not consider the forward motion of 

particles, wind effects, and the mechanical/hydraulic limitations of the VRAT system. Bench 

testing, modelling and field trials can be used to improve the sizing of buffers under varying 

field conditions. Statistical tests showed the VRAT system was capable of applying different 

application rates to application zones. 

While some parts of aerial topdressing can be controlled, there are other factors that cannot 

be controlled and are a source of variation. Several factors are discussed. Particle bounce out 

of the collectors was observed after the second performance trial. This issue under-estimated 

the field application rate in the first two performance trials. Additional trials were completed 

to improve the capture efficiency by 38% for superphosphate, and provided correction factors 

for DAP and urea.   

Wind contributes to variability in aerial applications, and automation of the hopper door is 

unlikely to significantly mitigate its effects. Ravensdown Limited wished to develop a wind 



2 
 

displacement calculator tool. The calculator uses a single particle granular fertiliser ballistics 

model to predict the displacement of the transverse spread pattern and swath width by wind. 

To achieve this, the ballistics model was validated for superphosphate, urea, di-ammonium 

phosphate (DAP), and a 70% superphosphate/30% Flexi-N blend.  

The model was validated from two data sets for each fertiliser type. From the first data set, the 

propeller wash component was excluded because fertiliser particles leave the hopper door in a 

mass flow. Therefore in the initial time steps, the particles are not singular and the propeller 

wash does not significantly influence their motion. There was good agreement between the 

field and modelled transverse spread patterns. Additionally, the Kolmogorov-Smirnov test 

statistically showed that the two distributions were similar. The development of the wind 

displacement calculator tool and production of wind displacement look up tables is described.  

From a limited number of inputs, the calculator predicts the displacement of the peak mass in 

a transverse spread pattern. To decrease modelling time, wind displacement look up tables 

were created from the tool for superphosphate, urea and DAP.  

In conclusion, the VRAT system will improve fertiliser application to hill country. However, 

aerial topdressing is highly variable and some factors cannot be controlled. Ballistics modelling 

can be used to minimise these factors and improve understanding of the variability. The model 

and wind displacement calculator should be used with care, as they are based on assumptions, 

which may not be completely representative of field conditions. 

 

  



3 
 

Acknowledgements 
 

Many people contributed to the success of this project. Firstly, I would like to thank my 

supervisors Professor Ian Yule and Dr. Miles Grafton for their advice and guidance throughout 

this project. I am grateful to them for giving me the opportunity to complete this PhD.   

Next, I would like to thank the incredible team at the New Zealand Centre of Precision 

Agriculture, who helped me with my trials and provided sound advice in troubled times. In 

particular, I would like to acknowledge Kate Saxton for her work in organising staff and the 

logistics of the trials. I have also enjoyed my time with my fellow PhD students. They have not 

only provided entertainment and encouragement, but also voluntarily participated in my trials. 

Additionally, I would like to thank John Edwards for his years of advice and kindness in the lab, 

and Ray Watson (Comtel Limited) for being an amazing problem solver. 

I am thankful for the funding provided by Callaghan Innovation and Ravensdown Limited. This 

project could not have been completed without the support of Ravensdown and their staff. I 

want to thank Michael White and Michael Manning for mentoring me and giving me the 

opportunity to learn more about Ravensdown. I would like to acknowledge Grant Lennox and 

Mark Tocher, who operated their aircraft for my trials and co-operated with my ideas.  

Lastly, I would have not made it without the love and support of my family and friends. My 

parents have continued to support all my endeavours, and I am eternally grateful for their 

encouragement and advice.  

  



4 
 

  



5 
 

Table of Contents 
Abstract ..........................................................................................................................................1 

Acknowledgements ........................................................................................................................3 

Table of Contents ...........................................................................................................................5 

List of Tables ..................................................................................................................................9 

List of Figures .............................................................................................................................. 11 

Chapter 1 – Introduction ............................................................................................................. 17 

1.1. Introduction ..................................................................................................................... 17 

1.2. Specific Objectives ........................................................................................................... 18 

1.3. Aerial Topdressing ............................................................................................................ 19 

1.4. Variability in Aerial Topdressing ...................................................................................... 22 

1.4.1. Fertiliser Characteristics ............................................................................................ 23 

1.4.2. Fertiliser Transportation and Storage ....................................................................... 28 

1.4.3. Wind .......................................................................................................................... 29 

1.4.4. Altitude...................................................................................................................... 30 

1.4.5. Topography ............................................................................................................... 31 

1.4.6. Aircraft Velocity ........................................................................................................ 31 

1.4.7. Spreaders .................................................................................................................. 31 

1.4.8. Swath width .............................................................................................................. 32 

1.5. Variable Rate Application Technology ............................................................................. 33 

1.6. Ballistics Modelling for Aerial Topdressing ...................................................................... 37 

1.6.1. Mass Flow Prediction ................................................................................................ 40 

1.7. Sampling Methods ........................................................................................................... 42 

1.7.1. Geo-statistics ............................................................................................................. 44 

1.8. Main Points ...................................................................................................................... 47 

1.9. Structure of Thesis ........................................................................................................... 48 

Chapter 2 - Ballistics Modelling for Aerial Topdressing of Granular Fertiliser ............................ 49 

2.1. Introduction ..................................................................................................................... 49 

2.2. Method ............................................................................................................................ 51 

2.2.1. Validation Trial 1 ....................................................................................................... 51 

2.2.2. Validation Trial 2 ....................................................................................................... 54 

2.2.3. Validation Trial 3 ....................................................................................................... 56 

2.2.4. Pre – Processing ........................................................................................................ 57 

2.3. Initial Model Program Set Up ........................................................................................... 61 



6 
 

2.3.1. Particle Size Distribution ............................................................................................ 61 

2.3.2. Wind Power Law ........................................................................................................ 64 

2.3.3. Particle Sphericity ...................................................................................................... 65 

2.3.4. Initial Discharge Variables ......................................................................................... 65 

2.4. Validation Results and Discussion .................................................................................... 67 

2.4.1. Trial 1 ......................................................................................................................... 68 

2.4.2. Trial 2 ......................................................................................................................... 74 

2.4.3. Trial 3 ......................................................................................................................... 79 

2.4.4. Model Accuracy ......................................................................................................... 82 

2.5. Wind Displacement Calculator ......................................................................................... 86 

2.5.1. Python script .............................................................................................................. 87 

2.5.2. GIS Tool ...................................................................................................................... 87 

2.5.3. Wind Displacement Look Up Tables .......................................................................... 90 

2.6. Conclusion ........................................................................................................................ 94 

Chapter 3 - Methods and Evaluation of Sampling for Aerial Topdressing Performance Trials ... 97 

3.1. Introduction ...................................................................................................................... 97 

3.2. Trial 4 – Grid Sampling ...................................................................................................... 98 

3.3. Trial 5 – Nested Grid Sampling ....................................................................................... 101 

3.4. Trial 6 – Pickwick Trial ..................................................................................................... 103 

3.4.1. Objective 1 ............................................................................................................... 105 

3.4.2. Objective 2 ............................................................................................................... 116 

3.4.3. Objective 3 ............................................................................................................... 117 

3.4.4. Objective 4 ............................................................................................................... 118 

3.5. Collector Improvement .................................................................................................. 119 

3.5.1. Initial Collector Study .............................................................................................. 119 

3.5.2. Trial 7 – Collector Trial ............................................................................................. 123 

3.6. Trial 8 – Line Sampling .................................................................................................... 126 

3.7. Conclusion ...................................................................................................................... 131 

Chapter 4 - Performance of an Aerial Variable Rate Application System ................................. 133 

4.1. Introduction .................................................................................................................... 133 

4.2. Results and Discussion of Performance Trials ................................................................ 134 

4.2.1. Accuracy................................................................................................................... 134 

4.2.2. Precision .................................................................................................................. 135 

4.2.3. Capability ................................................................................................................. 137 



7 
 

4.3. Bench Testing ................................................................................................................. 142 

4.3.1. Method ................................................................................................................... 143 

4.3.2. Results and Discussion ............................................................................................ 146 

4.4. Static Hopper Flow Calibration ...................................................................................... 155 

4.5. Trial 8 ............................................................................................................................. 163 

4.6. Static Hopper Flow Calibration Re-test .......................................................................... 168 

4.7. Conclusion ...................................................................................................................... 172 

Chapter 5 - Variability in Aerial Topdressing ............................................................................ 175 

5.1. Introduction ................................................................................................................... 175 

5.2. Part 1: Release of Fertiliser Particle from Aircraft ......................................................... 179 

5.2.1. Hopper Flow Characteristics ................................................................................... 179 

5.2.2. Future Work ............................................................................................................ 181 

5.3. Part 2: Fertiliser Particle Motion through Air ................................................................ 183 

5.3.1. Wind and topography ............................................................................................. 183 

5.3.2. Future Work ............................................................................................................ 185 

5.4. Part 3: Fertiliser Placement and Measurement ............................................................. 185 

5.4.1. Data Collection ........................................................................................................ 185 

5.4.2. Collector Efficiency .................................................................................................. 185 

5.4.3. Collector Placement ................................................................................................ 187 

5.4.4. Future Work ............................................................................................................ 190 

5.5. Implications of Research ................................................................................................ 192 

5.6. Improvements to Research Methodology ..................................................................... 194 

5.7. Conclusion ...................................................................................................................... 196 

Chapter 6 - Summary ............................................................................................................. 199 

6.1. Summary ........................................................................................................................ 199 

6.2. Concluding Remarks ....................................................................................................... 202 

6.3. Publications .................................................................................................................... 204 

References ................................................................................................................................ 205 

Appendix ................................................................................................................................... 213 

 

  



8 
 

  



9 
 

List of Tables 
Table 1.1: Standard SGN and UI values set by Spreadmark (NZFQC, 2016b). ............................ 25 
Table 2.1: Target application rate, swath width and hopper door opening for Trial 1. ............. 54 
Table 2.2: Target application rate, swath width and hopper door opening for Trial 2. ............. 56 
Table 2.3: Particle size distribution from the bulk pile for Trial 1. .............................................. 58 
Table 2.4: Particle density, size guide number (SGN) and uniformity index (UI) of particles from 
the bulk pile of Trial 1. ................................................................................................................ 58 
Table 2.5: Particle size distribution from the bulk pile for Trial 2. .............................................. 58 
Table 2.6: Particle density, size guide number (SGN) and uniformity index (UI) of particles from 
the bulk pile of Trial 2. ................................................................................................................ 59 
Table 2.7: Particle size distribution from the bulk pile for Trial 3. .............................................. 59 
Table 2.8: Inputs for the Beverloo equation. .............................................................................. 60 
Table 2.9: Image analysed particle size distribution from Trial 1 for DAP and urea. ................. 63 
Table 2.10: Air velocity in a nine duct spreader at an aircraft velocity of 62 m s-1. .................... 66 
Table 2.11: Pacific Aerospace Cresco 600 aircraft parameters. ................................................. 66 
Table 2.12: Input values for the hopper door when a spreader is not attached for the 
application. ................................................................................................................................. 66 
Table 2.13: Input values for a Transland spreader. .................................................................... 67 
Table 2.14: Input values for a FarmAir spreader. ....................................................................... 67 
Table 2.15: Application rates and swath widths from Trial 1 for each collector row. ................ 70 
Table 2.16: Application rates and swath widths from Trial 2 for each collector row. ................ 76 
Table 2.17: Image analysed particle size distribution from Trial 2 for urea. .............................. 78 
Table 2.18: Application rates and swath widths from Trial 3 for each collector row. ................ 79 
Table 2.19: Comparison of ballistics model and Beverloo flow rates for Trial 1 and 2. ............. 82 
Table 2.20: Comparison of ballistics model and Beverloo flow rates for Trial 3. ....................... 83 
Table 2.21: Comparison of intended, trial and model application rate and swath width for Trial 
1-3. The difference (%) is between the trial and model application rate. .................................. 84 
Table 2.22: P and D values from the Kolmogorov-Smirnov test for Trial 1 and 2. ..................... 84 
Table 2.23: P and D values from the Kolmogorov-Smirnov test for Trial 3 for a 70% 
Superphosphate and 30% Flexi-N fertiliser blend. ..................................................................... 85 
Table 2.24: The wind velocity, wind angle and flow required to produce a transverse spread 
pattern for DAP in Trial 2 that rejected the null hypothesis when tested with the K-S test. ..... 86 
Table 3.1: Level settings for swath width, intended application rate and aircraft groundspeed 
for Trial 6. .................................................................................................................................. 106 
Table 3.2: ANOVA and interaction test results for urea in Trial 6. ........................................... 107 
Table 3.3: Using Figure 3.7, Figure 3.8 and Figure 3.9 equations to predict field application rate 
from Longview validation trials (Trial 1 and 2). ........................................................................ 110 
Table 3.4: Percentage of particles bouncing out of a collector and their average particle 
strength. .................................................................................................................................... 119 
Table 3.5: Height required to reach terminal velocity for three fertiliser types. ..................... 120 
Table 3.6: Average masses collected from the three fertiliser collectors in Trial 7. ................ 126 
Table 3.7: Percentage difference in masses between collector types in Trial 7. ...................... 126 
Table 4.1: Summary of collector data for Trial 4 (Limestone Downs) and Trial 5 (Longview). . 135 
Table 4.2: ANOVA test for collector distance and application rate from Trial 5. ..................... 136 



10 
 

Table 4.3: Percentage of correct hopper door openings for bench tested prescription maps of 
different sizes. ........................................................................................................................... 151 
Table 4.4: Two-way ANOVA test comparing hopper door opening and the aircraft velocity to 
the distance the hopper door closes in relation to the application zone boundary. ................ 152 
Table 4.5: Comparison of parameters determined by linear regression for Beverloo equation 
and original coefficients. ........................................................................................................... 162 
Table 4.6: Comparison of field results with calculated clam shell door openings. Linear and 
Beverloo equation application rates were calculated using an aircraft velocity of 59 m s-1. ... 163 
Table 4.7: Summary of collector data for Trial 8. ...................................................................... 166 
Table 4.8: One way ANOVA test comparing the applications rates in the 250 kg ha-1 and 500 kg 
ha-1 application zones at a 95% confidence interval. ................................................................ 166 
Table 4.9: Comparison of field results with calculated cantilever door openings for 
superphosphate. Linear and Beverloo equation application rates were calculated using an 
aircraft velocity of 59 m s-1. ....................................................................................................... 172 
Table 5.1: Summary of trials undertaken in this study.............................................................. 176 
Table 5.2: Original results from Trial 4 and 5. The samples were not adjusted for bounce out of 
the collectors. ............................................................................................................................ 186 

  



11 
 

List of Figures 
Figure 1.1: Example of Spreadmark calculating the average field mass from the transverse 
spread pattern and set swath width (i.e. 15 m). The blue line represents the distribution 
created from a racecourse (round and round) flight path, and the purple is for a to and fro 
flying pattern. .............................................................................................................................. 21 
Figure 1.2: Factors that affect the transverse spread pattern in aerial granular fertiliser 
application. ................................................................................................................................. 24 
Figure 1.3: Examples of the relationship between UI and SGN sourced from NZFQC (2016b). 
The images represent fertiliser in a sieve box, where the x axis is the mesh size in mm. .......... 26 
Figure 1.4: Chemical compatibility of common New Zealand fertilisers (Fertiliser Association, 
2007). .......................................................................................................................................... 27 
Figure 1.5: Port side image of an 11 duct spreader that is attached to the hopper door on an 
aircraft. ........................................................................................................................................ 32 
Figure 1.6: Predicted field scale application on a 25 ha site where the hopper door is pilot 
operated and there is no GPS guidance (Murray, 2007). The application rates were modelled 
using Jones et al. (2008) and recorded aircraft data. ................................................................. 35 
Figure 1.7: Predicted field scale application using an automated GPS guided hopper door. 
Murray (2007) produced this image from Figure 1.6 by removing all points outside the 
application area except when it was within 45 m of an application area. ................................. 35 
Figure 1.8: Collector developed by Laslett (1994). ..................................................................... 43 
Figure 1.9: Collectors used by the New Zealand Agricultural Aviation Association. .................. 43 
Figure 1.10: Example of a semi-variogram adapted from Bohling (2005). ................................. 45 
Figure 2.1: Pacific Aerospace Cresco 600. .................................................................................. 49 
Figure 2.2: Pre-determined location of collectors for Trial 1 in ArcGIS 10.1. ............................. 52 
Figure 2.3: Trial 1 set up. ............................................................................................................. 52 
Figure 2.4: Wind anemometer that records wind velocity and direction. ................................. 53 
Figure 2.5: The wind velocity and direction over the trial period in Trial 1. True north is denoted 
by 0 degrees. ............................................................................................................................... 53 
Figure 2.6: Pre-determined location of collectors for Trial 2 in ArcGIS 10.1. ............................. 54 
Figure 2.7: Trial 2 set up. ............................................................................................................. 55 
Figure 2.8: The wind velocity and direction over the trial period in Trial 2. True north is denoted 
by 0 degrees. ............................................................................................................................... 55 
Figure 2.9: Trial 3 set up. ............................................................................................................. 56 
Figure 2.10: The wind velocity and direction over the trial period in Trial 3. True north is 
denoted by 0 degrees. ................................................................................................................ 57 
Figure 2.11: A riffler used to equally divide a fertiliser sample. ................................................. 58 
Figure 2.12: Example of Mapstar 8 output for Trial 2. The green outline represents the 
application area. Blue lines are flight lines, where the hopper is closed, and the red rectangles 
are the flight lines where the hopper door is open. The width of each individual rectangle 
represents the set swath width. ................................................................................................. 60 
Figure 2.13: Image analysis of a collected DAP sample using a New Zealand 50 cent coin as a 
size reference. ............................................................................................................................. 62 
Figure 2.14: Cumulative particle size distribution of bulk and collected samples for DAP in Trial 
1. ................................................................................................................................................. 63 



12 
 

Figure 2.15: Cumulative particle size distribution of bulk and collected samples for urea in Trial 
1. .................................................................................................................................................. 63 
Figure 2.16: Trial 1 spread patterns collected from the nine rows for superphosphate. ........... 68 
Figure 2.17: Trial 1 spread patterns collected from the nine rows for DAP. ............................... 69 
Figure 2.18: Trial 1 spread patterns collected from the nine rows for urea. .............................. 69 
Figure 2.19: Comparison of Murray (2007) model and Trial 1 spread patterns for 
superphosphate. For this spread pattern, the aircraft was travelling at a heading of 92°, aircraft 
velocity of 69 m s-1 and an altitude of 34.2 m. The wind direction was 158.62° and wind speed 
was 0.1 m s-1. The modelled flow rate of superphosphate out of the hopper was 1261 kg min-1.
 ..................................................................................................................................................... 71 
Figure 2.20: Comparison of model and Trial 1 spread patterns for superphosphate. For this 
spread pattern, the aircraft was travelling at a heading of 92°, aircraft velocity of 69 m s-1 and 
an altitude of 34.2 m. The wind direction was 158.62° and wind speed was 0.1 m s-1. The 
modelled flow rate of superphosphate out of the hopper was 1261 kg min-1. .......................... 72 
Figure 2.21: Comparison of model and Trial 1 spread patterns for DAP. For this spread pattern, 
the aircraft was travelling at a heading of 92°, aircraft velocity of 62 m s-1 and an altitude of 
32.5 m. The wind direction was 149.15° and wind velocity was 0.214 m s-1. The modelled flow 
of DAP out of the hopper was 1300 kg min-1. ............................................................................. 72 
Figure 2.22: Comparison of model and Trial 1 spread patterns for urea. For this spread pattern, 
the aircraft was travelling at a heading of 92°, aircraft velocity of 65 m s-1 and an altitude of 
34.4 m. The wind direction was 178° and wind speed was 0.58 m s-1. The modelled flow rate of 
urea out of the hopper was 551 kg min-1. ................................................................................... 73 
Figure 2.23: Trial 2 spread patterns collected from six rows for superphosphate. .................... 74 
Figure 2.24: Trial 2 spread patterns collected from six rows for DAP. ........................................ 75 
Figure 2.25: Trial 2 spread patterns collected from six rows for urea. ....................................... 75 
Figure 2.26: Comparison of model and Trial 2 spread patterns for superphosphate. For this 
spread pattern, the aircraft was travelling at a heading of 273°, aircraft velocity of 59 m s-1 and 
altitude of 33.3 m. The wind direction was 77° and wind speed was 1.6 m s-1. The modelled 
flow rate of superphosphate out of the hopper was 982 kg min-1. ............................................ 77 
Figure 2.27: Comparison of model and Trial 2 spread patterns for DAP. For this spread pattern, 
the aircraft was travelling at a heading of 273°, aircraft velocity of 58 m s-1 and altitude of 32.5 
m. The wind direction was 81° and wind velocity was 1.44 m s-1. The modelled flow rate of DAP 
out of the hopper was 1490 kg min-1. ......................................................................................... 77 
Figure 2.28: Cumulative particle size distribution of bulk and collected samples for urea in Trial 
2. .................................................................................................................................................. 78 
Figure 2.29: Comparison of model and Trial 2 spread patterns for urea. For this spread pattern, 
the aircraft was travelling at a heading of 273°, aircraft velocity of 63 m s-1 and altitude of 41.8 
m. The wind direction was 85° and wind velocity was 2.57 m s-1. The modelled flow rate of urea 
out of the hopper was 845 kg min-1. ........................................................................................... 79 
Figure 2.30: Trial 3 spread patterns collected from Flight 1 for the 70% superphosphate/30% 
Flexi-N blend. ............................................................................................................................... 80 
Figure 2.31: Trial 3 spread patterns collected from Flight 2 for the 70% superphosphate/30% 
Flexi-N blend. ............................................................................................................................... 80 
Figure 2.32: Comparison of model and Trial 3 spread pattern for Flight 1. For this spread 
pattern, the aircraft was travelling at a heading of 251°, aircraft velocity of 67 m s-1 and altitude 



13 
 

of 18.6 m. The wind direction was 185° and wind speed was 0.4 m s-1. The flow rate of the 
blend out of the hopper was 684 kg min-1. ................................................................................. 81 
Figure 2.33: Comparison of model and Trial 3 spread pattern for Flight 2. For this spread 
pattern, the aircraft was travelling at a heading of 251°, aircraft velocity of 69 m s-1 and altitude 
of 11.6 m. The wind direction was 184° and wind velocity was 0.215 m s-1. The flow rate of the 
blend out of the hopper was 822 kg min-1. ................................................................................. 82 
Figure 2.34: Comparison of model and Trial 2 row 6 spread pattern for DAP. For this spread 
pattern, the aircraft was travelling at a heading of 273°, aircraft velocity of 58 m s-1 and altitude 
of 32.5 m. The wind direction was 88.2° and wind speed was 1.8 m s-1. The modelled flow rate 
of superphosphate out of the hopper was 1090 kg min-1. ......................................................... 86 
Figure 2.35: Example vector diagram of the wind offset calculated for a wind speed of 0.75 m s-

1 at 300°. ...................................................................................................................................... 89 
Figure 2.36: Example of application area and its offset when the average wind speed is 0.75 m 
s-1, wind direction is 300° and aircraft heading is 10°. This was modelled for superphosphate. 89 
Figure 2.37: Peak lateral mass displacement for wind direction of 180°, 270° and 340°, and 
wind velocity for superphosphate with no spreader. ................................................................. 91 
Figure 2.38: Swath width for wind direction of 180°, 270° and 340°, and wind velocity for 
superphosphate with no spreader. ............................................................................................. 92 
Figure 2.39: Peak lateral mass displacement for wind direction of 180°, 270° and 340°, and 
wind velocity for urea with an 11 duct spreader. ....................................................................... 93 
Figure 2.40: Swath width for wind direction of 180°, 270° and 340°, and wind velocity for urea 
with an 11 duct spreader. ........................................................................................................... 93 
Figure 3.1: Sampling configuration for Trial 4. ........................................................................... 99 
Figure 3.2: Sampling configuration for Trial 5. ......................................................................... 102 
Figure 3.3: Wind velocity and direction over the trial period in Trial 5. True north is denoted by 
0 degrees. .................................................................................................................................. 103 
Figure 3.4: Wind velocity and direction over the trial period in Trial 6. True north is denoted by 
0 degrees. .................................................................................................................................. 105 
Figure 3.5: Sample areas for Trial 6. ......................................................................................... 106 
Figure 3.6: Trial set up in Area 3 in Trial 6. ............................................................................... 107 
Figure 3.7: The relationship between the measured field application rate and hopper door 
opening for urea in Trial 6. The dashed lines are the confidence interval (CI) of the linear 
equation. ................................................................................................................................... 109 
Figure 3.8: The relationship between the measured field application rate and hopper door 
opening for superphosphate in Trial 6. The dashed lines are the confidence interval (CI) of the 
linear equation. ......................................................................................................................... 109 
Figure 3.9: The relationship between the measured field application rate and hopper door 
opening for DAP in Trial 6. The dashed lines are the confidence interval (CI) of the linear 
equation. ................................................................................................................................... 110 
Figure 3.10: Relationship between intended and measured field application rate in Trial 6. 
Lines representing 1:1, 1:1.5 and 1:2 are included to illustrate the magnitude of difference 
between the two application rates. .......................................................................................... 111 
Figure 3.11: The relationship between the measured field application rate and swath width for 
urea in Trial 6. ........................................................................................................................... 112 



14 
 

Figure 3.12: The relationship between the measured field application rate and swath width for 
superphosphate in Trial 6. ......................................................................................................... 113 
Figure 3.13: The relationship between the measured field application rate and swath width for 
DAP in Trial 6. ............................................................................................................................ 113 
Figure 3.14: Relationship between the measured field application rate and the recorded 
aircraft velocity for urea in Trial 6. ............................................................................................ 115 
Figure 3.15: Relationship between the measured field application rate and the recorded 
aircraft velocity for superphosphate in Trial 6. ......................................................................... 115 
Figure 3.16: Relationship between the measured field application rate and the recorded 
aircraft velocity for DAP in Trial 6. ............................................................................................. 116 
Figure 3.17: Comparison of the field application rate and the field Beverloo equation for Trial 6.
 ................................................................................................................................................... 116 
Figure 3.18: Distance fertiliser particles were found from the boundary for different edge time 
settings in Trial 6. A positive distance from the boundary indicates the particle landed within 
the application area and vice versa. .......................................................................................... 118 
Figure 3.19: Image still of a video taken at 500 frames per second recorded at Pickwick farm of 
superphosphate taken at Trial 6. ............................................................................................... 119 
Figure 3.20: Set up for terminal velocity of 9 m height. ............................................................ 120 
Figure 3.21: Comparison of calculated and measured terminal velocities for various 
superphosphate particle sizes. Calculations were made using Haider and Levenspiel (1989). 121 
Figure 3.22: Comparison of calculated and measured terminal velocities for various urea 
particle sizes. Calculations were made using Haider and Levenspiel (1989). ........................... 121 
Figure 3.23: Comparison of calculated and measured terminal velocities for various DAP 
particle sizes. Calculations were made using Haider and Levenspiel (1989). ........................... 122 
Figure 3.24: Sampling configuration for Trial 7. ........................................................................ 124 
Figure 3.25: Collector set up for Trial 7 on trial day. ................................................................. 124 
Figure 3.26: Wind velocity and direction over the trial period in Trial 7. True north is denoted 
by 0 degrees. ............................................................................................................................. 125 
Figure 3.27: Collectors set up with the bubble wrap liner in Trial 8. ........................................ 127 
Figure 3.28: Collectors set up in a line with replicates in Trial 8. The collectors travel over one 
hill and up one hill. .................................................................................................................... 128 
Figure 3.29: Sample configuration and application zones for Trial 8. ....................................... 129 
Figure 3.30: Wind velocity and direction over the trial period in Trial 8. True north is denoted 
by 0 degrees. ............................................................................................................................. 130 
Figure 4.1: Comparison of application rate with the collector’s proximity to the nearest 
treatment boundary line for Trial 4. A positive distance means the collector was in the 250 kg 
ha-1 application zone. ................................................................................................................ 137 
Figure 4.2:  Comparison of application rate to the collector’s proximity to the nearest 
treatment boundary line for Trial 5. A positive distance means the collector was in the 162 kg 
ha-1 application zone. ................................................................................................................ 137 
Figure 4.3: Semi-variogram of aircraft data from Trial 4 (A) and Trial 5 (B). The y-axis is the 
semi-variance and the x-axis is the lag distance (m). ................................................................ 138 
Figure 4.4: Semi-variogram of collector data from Trial 4 (A) and Trial 5 (B). The y-axis is the 
semi-variance and the x-axis is the lag distance (m). ................................................................ 139 
Figure 4.5: Proof of release (A) and placement (B) maps for Trial 4. ........................................ 140 



15 
 

Figure 4.6: Proof of release (A) and placement (B) maps for Trial 5. ....................................... 140 
Figure 4.7: Error between predicted values and recorded aircraft values for Trial 4 (A) and Trial 
5 (B). The y-axis is the predicted application rate (kg ha-1) that was found using kriging, and the 
x-axis is the aircraft application rate (kg ha-1). .......................................................................... 141 
Figure 4.8: Error between predicted values and collector data for Trial 4 (A) and Trial 5 (B). The 
y-axis is the predicted application rate (kg ha-1) that was found using kriging, and the x-axis is 
the field application rate (kg ha-1). ............................................................................................ 141 
Figure 4.9: Prediction standard error maps for collector data for Trial 4 (A) and Trial 5 (B). .. 142 
Figure 4.10: Aircraft hopper door in closed position. ............................................................... 144 
Figure 4.11: Aircraft hopper door in the open position. ........................................................... 144 
Figure 4.12: Mechanical set up of variable rate bench testing unit. ........................................ 145 
Figure 4.13: Satloc user interface with simulated flight example. Blues lines represent a closed 
hopper and bold green lines are an open hopper. The red square is the application area. .... 145 
Figure 4.14: Example of 1000 m by 1000 m application zone displayed in Mapstar 8. ........... 147 
Figure 4.15: Distance to/from boundary against the edge on/off setting for a dual accumulator.
 .................................................................................................................................................. 147 
Figure 4.16: An example of a prescription map and flight lines for Part 3 displayed in Mapstar 8. 
This shows a 50 m gap. The green line represents the application area. Flight lines are 
represented by the blue (fully closed hopper) and red lines (open hopper). .......................... 148 
Figure 4.17: An example of a prescription map and flight lines from Part 4 displayed in Mapstar 
8. This polygon is angled 20 degrees. ....................................................................................... 149 
Figure 4.18: An example of a prescription map and flight lines for Part 5 displayed in Mapstar 8. 
This polygon has 100 vertices. .................................................................................................. 150 
Figure 4.19: An example of a prescription map that consists of adjacent polygons (250 and 500 
kg ha-1), exclusion zones (0 kg ha-1) and different application rates (200, 350, 400 kg ha-1). This 
is displayed in Mapstar 8. ......................................................................................................... 153 
Figure 4.20: Two polygons separated by a gap of 50 m, where no application should occur. 
Application rates in the polygons are 200 and 400 kg ha-1. This is displayed in Mapstar 8. .... 153 
Figure 4.21: Simulated response of Figure 4.20 from the bench VRAT system in Mapstar 8 
based on ‘edge on’ setting of 0.5 s and ‘edge off’ of 1.6 s. Entry into the application zone is 
denoted by the black arrows. The system did not react as intended. ..................................... 154 
Figure 4.22: Large farm prescription map for variable rate application. .................................. 154 
Figure 4.23: Response from creating an exclusion application zone displayed in Mapstar 8. 
Entry into the application area is denoted by black arrows. The red strips represent an open 
hopper door. ............................................................................................................................. 155 
Figure 4.24: Hopper door was manually opened using the lever and, in this case, the flow rate 
of superphosphate was being measured. ................................................................................. 157 
Figure 4.25: Static PAC hopper with clamshell doors operated by a lever (on left). A Mettler 
Toledo display is fixed on the front (centre of picture). ........................................................... 157 
Figure 4.26: Example of funnel flow regime for a powder, courtesy of John Maber (Grafton, 
2010). The angle of the standard PAC hopper allowed the hopper to empty and ratholing did 
not occur. .................................................................................................................................. 158 
Figure 4.27: Flow rate out of the clamshell hopper door against time for three door openings 
(0.025 m, 0.046 m and 0.075 m). .............................................................................................. 159 



16 
 

Figure 4.28: Relationship between flow rate and the clam shell hopper door opening with 
linear regression for superphosphate. ...................................................................................... 159 
Figure 4.29: Relationship between flow rate and the clam shell hopper door opening with 
linear regression for DAP. .......................................................................................................... 160 
Figure 4.30: Relationship between flow rate and the clam shell hopper door opening with 
linear regression for urea. ......................................................................................................... 160 
Figure 4.31: Relationship of flow rate to the 2/3 power and the clam shell hopper door opening 
with linear regression for superphosphate. .............................................................................. 161 
Figure 4.32: Relationship of flow rate to the 2/3 power and the clam shell hopper door opening 
with linear regression for DAP. .................................................................................................. 161 
Figure 4.33: Relationship of flow rate to the 2/3 power and the clam shell hopper door opening 
with linear regression for urea. ................................................................................................. 162 
Figure 4.34: Flight points recorded every 0.2 s on VRAT system. Hopper door opening in 1/16th 
inches are labelled. .................................................................................................................... 164 
Figure 4.35: Field application rate across the line of bubble wrap lined collectors from the west 
to east direction. Replicate lines are included. The location of the replicate line is denoted in 
the legend as north or south of the main center line. AZ stands for application zone. ............ 165 
Figure 4.36: Categorised application rate from collectors at each location. Yellow coloured 
points represent the target application rate range for the 250 kg ha-1 zone and red is the target 
range of application rates for the 500 kg ha-1 zone. ................................................................. 167 
Figure 4.37: Particle size distribution comparison between the bulk and field samples for Trial 
8. ................................................................................................................................................ 168 
Figure 4.38: Comparison of the intended hopper door opening and the measured hopper door 
opening. ..................................................................................................................................... 169 
Figure 4.39: Flow rate out of the cantilever hopper door against time for three door openings 
(0.032 m, 0.047 m and 0.066 m). .............................................................................................. 170 
Figure 4.40: Open cantilever hopper door illustrating the main door opening and the smaller 
opening. ..................................................................................................................................... 170 
Figure 4.41: Relationship between average flow rate and the cantilever hopper door opening 
with linear regression for superphosphate. .............................................................................. 171 
Figure 4.42: Relationship of flow rate to the 2/3 power and the cantilever hopper door opening 
with linear regression for superphosphate. .............................................................................. 172 
Figure 5.1: Factors that affect the transverse spread pattern in aerial granular fertiliser 
application. ................................................................................................................................ 178 
Figure 5.2: Top view of the cantilever hopper door with door hinges annotated. ................... 179 
Figure 5.3: Flow rate out of a 0.0254 m cantilever hopper door opening against time for 
superphosphate. ........................................................................................................................ 180 
Figure 5.4: Aircraft flight lines recorded every 0.2 s by the VRAT system for Trial 4. ............... 188 
 

 

  



17 
 

Chapter 1 – Introduction 

1.1. Introduction 
Aerial topdressing is used in New Zealand to apply over 1.65 million tonnes of granular 

fertiliser to hill country (Statistics New Zealand, 2012). The current practice is to uniformly 

apply one application rate over an area. The extent of the application area is controlled by the 

pilot, where boundaries are visually reconciled and the pilot must take timely actions to 

control the hopper door. This is completed while the aircraft is operating at approximately 200 

km h-1 and 35 m above varied terrain.  

Within New Zealand’s hill country farms, soil fertility and pasture productivity varies 

considerably. Slope, aspect, soil erosion, environmental conditions and fertiliser use have been 

identified as factors that affect pasture production, and therefore the stocking rate (Gillingham 

and During, 1973; Gillingham et al., 1998; Suckling, 1959).  Thus, hill country is far more 

variable than New Zealand’s other farming systems. Clearly the fertiliser requirements within 

farms will be highly variable, and it is beyond the scope of a pilot operating an aircraft 

manually to achieve a variable rate application. A variable rate application technology (VRAT) 

system will be required to recognise boundaries automatically, and reduce or eliminate off-

target application.  

In order to provide a controllable application rate, the hopper door must be able to 

compensate for changes in aircraft velocity as it varies during flight. The system is linked to 

GPS (Global Positioning System) in order to provide information on velocity and location. If 

variable rate technology is to be employed then variable rate application maps must be 

provided. Ballistics modelling can be deployed to account for dynamic issues surrounding the 

release of fertiliser from the aircraft and calculate the approximate landing point, especially in 

the presence of wind. Based on the application map, the VRAT system will select the hopper 

door opening from the recorded aircraft position, and control its closing and opening around 

wind compensated boundaries. 

Ravensdown Limited, through Ravensdown Aerowork Limited, own and operate topdressing 

aircraft, and are developing and installing VRAT systems. While aspects of their performance 

have been partially studied, the overall field operational performance of such systems has not 

been studied. Some of the previous work has also been subject to only partial measurement 

with a number of assumptions made about the consistency of performance (Grafton et al., 

2012; Morton et al., 2016).  



18 
 

The scope of this project includes the validation of a single particle ballistics model formulated 

by Jones et al. (2008), but developed for a different aircraft (Gippsland Aeronautics GA-200C). 

This study validated the model for a Pacific Aerospace Cresco (PAC) 600, with the intention to 

create a wind displacement calculator tool that can be used to recalculate aircraft flying 

pattern according to the average wind conditions. This wind displacement calculator tool gives 

the operators information to avoid off-target application.  

As an introduction, this literature review discusses previous studies, explains key concepts and 

provides relevant background information. Topics include:  

- Aerial topdressing 

- Variability in aerial topdressing 

- Variable rate application technology 

- Ballistics modelling 

- Sampling methods 

The work presented in this thesis is linked to a Primary Growth Partnership (PGP) project called 

‘Pioneering to Precision – Application of Fertiliser in Hill Country’, which seeks to create 

variable rate application fertiliser plans from remotely sensed data (Ministry of Primary 

Industries, 2017). The intention is for a fertiliser application plan to be pre-loaded into an 

aircraft before an application, so that there is automated control of the aircraft hopper door. 

In addition to addressing the requirements for more accurate fertiliser application and to 

improve the ability of delivering the prescribed application rate, the VRAT system has been 

developed to minimise some of the safety and off-target application issues encountered by 

aerial spreaders. The objective is to have a safer, more accurate, and easy to operate system 

that delivers benefits to both the applicator and farmer. 

1.2. Specific Objectives 
1. Validate the particle ballistics model formulated by Jones et al. (2008) for three 

common New Zealand fertiliser types: superphosphate, urea and di-ammonium 

phosphate. 

2. Validate the particle ballistics model for a superphosphate/Flexi-N blend of a particular 

composition. 

3. Create a Geographical Information Systems (GIS) tool that considers average wind 

speed and direction, using the ballistics model when planning on-farm flights. This tool 

is named the ‘wind displacement calculator’. 



19 
 

4. Determine appropriate methods of field fertiliser collection in aerial application trials 

in order to evaluate spreading efficiency. This includes an examination of the efficacy 

of current field collectors. 

5. Measure the performance of a variable rate application system on a fixed wing 

agricultural aircraft. 

1.3. Aerial Topdressing 
The temperate New Zealand climate allows medium to steep hill country to grow pasture and 

support all year grazing. In order to maintain and optimise pasture growth, good farm 

management is required. Fertiliser is one part of that equation. Previous studies have 

illustrated that withholding superphosphate on hill country farms negatively effects pasture 

production, plant species quality, and animal production (Gillingham et al., 1998; Lambert et 

al., 1990; O'Connor et al., 1990). However, due to the significant variations in hill country 

topography, fertiliser cannot be applied by truck. A cost effective solution is to use fixed wing 

aircraft and helicopters to topdress these pastures.   

The first known aerial application was carried out by a hot air balloon applying seed. Aerial 

topdressing was developed in New Zealand in the 1940s as a means to apply granular fertiliser 

on to hill country (Geelen, 1983). This was completed because nutrient levels within hill 

country were becoming depleted, resulting in poor performance. Shortly after, this was 

adopted by other countries, such as Australia, United States and the United Kingdom. Globally, 

aerial topdressing is primarily used in the spraying of liquid fertilisers and 

insecticides/fungicides for crops. It is also used in applying seed, granular fertilisation of 

pasture, in commercial forests, and for pest control. However, the majority of fixed wing 

aircraft hours in New Zealand are spent topdressing hill country farms with granular material.  

Topdressing by aircraft is common for hill country pasture. In New Zealand, the Pacific 

Aerospace Fletcher (PAF) and Cresco (PAC) are popular fixed wing aircraft used for spreading. 

The PAC hoppers have a capacity of 2 m3. Flow out of the hopper is gravity fed with the 

application rate controlled by the hopper door aperture. In a pilot operated system, the pilot 

adjusts a lever in the cockpit to set the hopper door opening. Pilots often carry out an on-farm 

calibration flight for each job to ensure the hopper door is correctly set to apply the required 

application rate. This is completed by recording the time required for the hopper to fully 

empty at a hopper door opening, and is repeated until the correct application rate is reached. 

This method of determining the correct field application rate assumes that the flow out of the 

hopper is constant and therefore the application rate for the flight is consistent. Calibration is 



20 
 

important because aircraft, hopper, hopper door design and environmental conditions vary, 

which will affect the field application rates. Pilots also need to complete calibration as they 

move to different jobs since fertiliser physical characteristics will vary and will affect flow from 

the hopper. 

Approximately 15 million hectares of land is used for agriculture and forestry in New Zealand. 

In 2009, 66% of this land was utilised for sheep and beef farming making it the dominant 

agricultural land user (Ministry for Primary Industries, 2012). A significant quantity of fertiliser 

is required to maintain the productivity of this land. Common granular fertilisers applied by 

aircraft to pasture are single superphosphate, di-ammonium phosphate (DAP), urea, lime and 

micronutrients. To ensure these are applied responsibly, Spreadmark was developed as a 

voluntary quality assurance programme by the New Zealand Fertiliser Quality Council (NZFQC, 

2016b). It provides guidelines on how to apply fertiliser aerially and by ground based vehicles 

for optimal pasture growth, and how to minimise its environmental impact. An operator 

certified under this programme is trained, and their equipment is independently assessed. The 

programme therefore assures a farmer that fertiliser is applied at an appropriate rate and 

distribution pattern.  

Aerial Spreadmark (NZFQC, 2016b) has different test methods to ground based vehicle testing. 

Aerial Spreadmark uses the fertiliser transverse distribution pattern in fly over tests to 

determine the certification swath width for an aircraft. Bout or swath width is the distance 

between two parallel flight lines. An aircraft is certified to a maximum bout width that will 

achieve the minimum standard of performance prescribed. A minimum of three rows of 

collectors are required to calculate the average and standard deviation of the application rate. 

Spreadmark calculates the average field application rate by overlapping the collected 

transverse spread pattern by the set swath width (Figure 1.1). It assumes that the collected 

transverse spread pattern is the same for each parallel swath width completed by the aircraft. 

In areas where the parallel spread patterns overlap, the masses are combined. It calculates the 

average field application rate by converting the average mass using the area of the collector 

(i.e. 0.25 m2) (Equation 1.1).  

      (1.1) 



21 
 

 
Figure 1.1: Example of Spreadmark calculating the average field mass from the transverse 
spread pattern and set swath width (i.e. 15 m). The blue line represents the distribution 

created from a racecourse (round and round) flight path, and the purple is for a to and fro 
flying pattern. 

Each row needs a sufficient number of collectors so that the entire transverse spread pattern is 

obtained, and this is dependent on the wind conditions and the observed swath width. The 

collectors can be a maximum of 3 m apart. The transverse spread pattern from an aerial 

application is normally distributed (Akesson and Yates, 1964). Variations in the transverse 

spread pattern occur for a number of reasons, including local wind conditions and the use of 

‘fishtail’ ram air spreaders. Spreaders are attached to the hopper door opening to increase the 

lateral distance fertiliser particles travel. The resulting distribution is normal with a large 

standard deviation. Some spreaders create an M shape distribution. Wind will skew the 

distribution depending on its direction relative to the aircraft’s heading, and it is important to 

take this in to consideration to minimise off-target application.  

Spreadmark calculates the coefficient of variation (CV), which quantifies the precision of a 

fertiliser application. It is the standard deviation of the application rate divided by the average 

rate. The Spreadmark certification test will establish the bout width required so that the 

overlap in the transverse spread pattern can achieve a CV of 15% for nitrogenous fertiliser and 

25% for all other fertilisers. This is a set guideline based on the International Organization of 

Standardization (1985). Spreadmark also states that accuracy is achieved when the average 

field application rate is within 30% of the intended application rate. These tests are carried out 

when the wind speed is less than 4.2 m s-1 and the wind direction is ± 15° to the plane’s 

heading. Therefore the CVs achieved in the Spreadmark tests are completed in close to ideal 

conditions.  

In the field, fertiliser applications will have a starting CV of 15 – 25%. Failures in the aircraft 

operation and maintaining the bout width will increase variance, and therefore the CV. The CV 

0
1
2
3
4
5
6
7
8
9

10

-30 -20 -10 0 10 20 30

M
as

s (
g)

 

Distance from centre (m) 



22 
 

calculated from field data is referred to as the field CV (Grafton et al., 2012). So far the CV has 

only been estimated by assuming a consistent swath width and repeatable transverse spread 

pattern.  

Calibration and testing of aerial topdressing in North America is done in accordance with ASAE 

S386.2 (ASAE, 1999). ASAE S386.2 was used to develop Spreadmark so they are similar. The 

main differences between ASAE S386.2 and Spreadmark are about how calibration tests 

should be carried out. For example, ASAE dictates that pilots need to complete three replicates 

of the calibration flight. This ensures that the swath width is repeatable. With Spreadmark, the 

pilot is only required to complete one flight and they have unlimited attempts to achieve the 

maximum swath width. ASAE S386.2 also requires that the collection of the transverse spread 

pattern should occur at least 100 m after the hopper door opens and 100 m before the hopper 

closes. This is to ensure an equilibrated flow rate is collected. Spreadmark does not dictate a 

distance. Another difference is the distance collectors are placed from each other with 

Spreadmark dictating 3 m, while the ASAE standard is 1 m. Spreadmark has standards on the 

accuracy of an application, while ASAE does not. Both assess the spread pattern and 

coefficient of variation for precision.  

Additionally, there may be greater benefit if a spread pattern is assessed for robustness, which 

is a value based on the average CV over a range of swath widths. A robust pattern is expected 

to produce a suitable application over a range of swath widths. Grift (2000) proposed this 

assessment criteria, and suggested that spread patterns with a robustness factor under 5% are 

robust. Initial studies determined that a Gaussian/normal distribution were the most robust 

for a ground application. The robustness of aerial spread patterns was investigated in Grift et 

al. (2000). Four hundred spread patterns from 1992 – 1997 were assessed, using the Spatial 

Pattern Analysis Tool (SPAT). The study found approximately 70% of spread patterns had a 

robustness factor of 5 – 15%, which suggests that there is a need to improve how fertiliser is 

aerially applied. The authors discussed the necessity in redesigning spreading equipment and 

procedures to achieve higher quality applications.  

1.4. Variability in Aerial Topdressing 
This section discusses factors that influence the aerial application of granular fertiliser. There 

are three basic mechanisms by which fertiliser are energised during spreading. In spinning disc 

land based applications, fertiliser is accelerated by centrifugal forces and flung off a vane on 

the disc. This is common for urea and compound fertiliser applications. These applicators are 

often characterised as being European styled machines. Fertiliser can also be impacted off the 



23 
 

disc with shorter more aggressive vanes. This is more common in the application of 

superphosphate and lime. In aerial application, particles gain their energy by being dropped 

through the hopper door into a fast flowing stream of air under the aircraft, while it is 

operating at approximately 200 km h-1. Figure 1.2 illustrates the many factors that influence 

the field application rate in aerial topdressing.  

 Since there are significantly more studies on ground based vehicle fertiliser application, some 

pertinent information will be referenced. There are noticeable differences between a truck 

and aerial application, such as the fertiliser’s initial velocity, direction and the effect of wind on 

small particles. However, some conclusions are applicable to both. For example, the effect of 

particle characteristics on the accuracy and precision of a truck fertiliser application is 

applicable to an aerial application, as they are governed by the same fundamental laws of 

motion.  

1.4.1. Fertiliser Characteristics 
Particle size distribution, sphericity, particle strength and density are important fertiliser 

characteristics that influence aerial application. Single superphosphate is the primary source of 

added phosphorus and sulphur to hill country, and is New Zealand’s most commonly applied 

fertiliser. It is manufactured within New Zealand by two fertiliser companies. Single 

superphosphate is not a uniform product, which introduces difficulty during application (Chok 

et al., 2014). Superphosphate is produced in batch processes by combining sulphuric acid and 

phosphate rock, which is sourced from a number of countries. The elemental composition (i.e. 

phosphate, cadmium, aluminium) of the phosphate rock will differ across sources and time. 

Therefore, each batch of superphosphate will have slight variations in particle strength, 

elemental composition and particle size. A drum granulator is used at the end of the 

manufacturing process to produce particles in the ideal size range. However, the particle size 

distribution can be inconsistent. Although manufacturers try their best to ensure uniformity, 

this is not always achievable. Despatch, transportation and storage are also inconsistent, which 

increases the potential for the spreading performance to be affected. Therefore during 

fertiliser application, the fertiliser distribution leaving the aircraft varies.  



24
 

 

 
Fi

gu
re

 1
.2

: F
ac

to
rs

 th
at

 a
ffe

ct
 th

e 
tr

an
sv

er
se

 sp
re

ad
 p

at
te

rn
 in

 a
er

ia
l g

ra
nu

la
r f

er
til

ise
r a

pp
lic

at
io

n.
 

Tr
an

sv
er

se
 

Sp
re

ad
 

Pa
tt

er
n 

En
vi

ro
nm

en
ta

l 

Tu
rb

ul
en

ce
 

W
in

d 
Sp

ee
d 

an
d 

Di
re

ct
io

n 

W
ea

th
er

 
To

po
gr

ap
hy

 

Fi
el

d 
M

ea
su

re
m

en
t 

Sa
m

pl
in

g 
Co

nf
ig

ur
at

io
n 

Ho
w

 a
re

 
Co

lle
ct

or
s 

pl
ac

ed
? 

Co
lle

ct
or

 
Ef

fic
ie

nc
y 

Ho
pp

er
 

Fu
nn

el
 F

lo
w

 
Dy

na
m

ic
s 

Vi
br

at
io

n 
an

d 
G

-
Fo

rc
es

 

N
on

-C
on

st
an

t 
Fl

ow
 R

at
e 

Ai
rf

lo
w

 O
ve

r t
he

 
Ho

pp
er

 D
oo

r 

Ai
rc

ra
ft

 

Al
tit

ud
e 

Gr
ou

nd
sp

ee
d 

•P
ar

tic
le

 V
el

oc
ity

 
Sp

re
ad

er
 

Ai
rc

ra
ft

 
He

ad
in

g 

Fe
rt

ili
se

r 
Ch

ar
ac

te
ris

tic
s 

Sp
he

ric
ity

 

Pa
rt

ic
le

 S
ize

 
Di

st
rib

ut
io

n 

Pa
rt

ic
le

/B
ul

k 
De

ns
ity

 

Sw
at

h 
W

id
th

 

Se
t v

s.
 F

ie
ld

 

O
ve

rla
p 

Be
tw

ee
n 

Sw
at

h 
W

id
th

s 



25 
 

Variations in particle characteristics make it difficult to predict the transverse spread pattern. 

Particle size has an effect on the distance a particle will travel. Larger particles tend to travel 

further in the direction of flight since they have greater initial momentum. The particle size 

distribution, which is found by sieving a representative fertiliser sample, has an effect on the 

shape of the transverse spread pattern. The benefit of having a particle size distribution with 

larger particles is a lower CV. Yule (2011) showed that an increase in the fines fraction (< 1.0 

mm) increases the field CV for truck application. However, this effect is only significant if the 

percentage of fines is greater than 15%. A benefit of having a wide particle size distribution is 

that different particle sizes will have different fall times (i.e. time it takes for a fertiliser particle 

to reach the ground). This helps in achieving a normally distributed transverse spread pattern. 

Spreadmark provides guidelines on particle size and uniformity (NZFQC, 2016b). The size guide 

number (SGN) expresses the average particle size of a fertiliser sample. It is calculated by 

multiplying the average particle diameter in millimetres by 100. The uniformity index (UI) is the 

ratio of small particles to large particles. It quantifies the particle size range, and is calculated 

by determining the percentage of fertiliser in each sieve range (Figure 1.3). A UI of 100 

represents a sample with a uniform particle size, while a UI of 50 represents a well granulated 

particle range. SGN and UI for New Zealand fertilisers can be 95 – 475 and 5 – 68, respectively. 

Bulk density is another fertiliser characteristic that should be considered, since it affects a 

particle’s ballistic properties. Table 1.1 shows typical SGN, UI and bulk density values for 

superphosphate, DAP and urea.  

Table 1.1: Standard SGN and UI values set by Spreadmark (NZFQC, 2016b). 
Product Size Guide Number Uniformity Index Bulk Density 
Superphosphate 245 – 300  11 1030 – 1280 
Di-ammonium phosphate 265 – 335  55 900 – 1000 
Urea 290 – 340  60 700 – 800  
 



26 
 

 
Figure 1.3: Examples of the relationship between UI and SGN sourced from NZFQC (2016b). 

The images represent fertiliser in a sieve box, where the x axis is the mesh size in mm.  

There are three general guidelines used to interpret SGN and UI (NZFQC, 2016b). 

 A SGN lower than 150 and UI less than 20 could result in an inaccurate distribution. 

The product may have a large percentage of fines. 

 A SGN of 250 – 350 and UI of 20 – 60 should result in an even application if the 

applicator is operating correctly. 

  If the SGN and UI are greater than 350 and 50, respectively, the material is likely to be 

coarse and spreading will be difficult.  



27 
 

SGN and UI can also be used to determine if two products can be blended and applied 

together. Spreadmark (NZFQC, 2016b) states that if the difference between the two SGN or UI 

values is less than 10, segregation of the two products is unlikely to occur. Differences of 11 – 

20 show moderate compatibility where some segregation is expected. Blending products with 

differences over 20 should be avoided.  These guidelines were developed around ground 

spreaders, and will differ in aerial topdressing due to different conditions (i.e. particle exit 

velocities). Limited work has been done to determine if these guidelines are suitable for aerial 

spreading, so care should be taken when using them. Chemical compatibility of the two 

fertiliser types should also be considered, since some fertiliser types react to each other. 

Figure 1.4 shows the chemical compatibility of common New Zealand fertilisers that could be 

blended together to create a fertiliser mix. 

 
Figure 1.4: Chemical compatibility of common New Zealand fertilisers (Fertiliser Association, 

2007). 

Research has mainly been completed on spreading blended fertilisers using twin disc 

centrifugal spreaders, where the initial conditions from the spreader are different (Miserque et 

al., 2008; Virk et al., 2013; Yule and Pemberton, 2009). Little research has been completed on 

the aerial topdressing of blended materials. However, the effects of uneven topdressing have 

been observed in the field when blended products were used.  

Sphericity is a measure of how much an object resembles a sphere. Wadell (1932) defined 

sphericity as the surface area of a sphere of the same volume as the particle, divided by the 

actual particle’s surface area. A particle’s sphericity affects its motion through air and is related 

to the drag coefficient (Grift et al., 1997). Spherical particles have a lower drag coefficient, 

which improves their aerodynamics allowing them to travel further. Superphosphate is not a 

perfect sphere. In comparison, urea and DAP are more spherical in shape. 



28 
 

The study by Hoffmeister et al. (1964) found that particle size, and therefore the particle size 

distribution, has the most significant impact on the transverse spread pattern. A triple 

superphosphate potassium chloride blend was applied with a fan type spreader in a truck 

application. The percentage of potassium chloride (KCl) particles was found to decrease with 

distance due to its smaller average particle size. In contrast, Yule and Pemberton (2009) found 

that KCl particles retained in the 2 mm and 2.8 mm sieve range was applied further than larger 

particle sizes. They also completed a truck spreading trial with a 30% potassium chloride and 

70% superphosphate blend, comparing two mixing methods. The two superphosphate samples 

were found to produce different spread patterns. This was because the two samples had 

different SGN values (182 compared with 141). Hedderwick and Will (1982) compared 

superphosphate with a diameter of 5 – 10 mm and 0 – 5 mm in an aerial application and it 

showed that larger particles travelled further. This is because larger, heavier particles have 

higher terminal velocities than smaller, lighter particles. Particle density is therefore another 

significant factor.  

Miserque et al. (2008) found that particle density had a significant effect on the spread pattern 

when applying a 50/50 blend of two materials, using a centrifugal truck spreader. At 16 m from 

the centreline, the proportion of the blend was 70/30 with analysis showing that heavier 

particles travelled further. On the other hand, Walker et al. (1997) found that particle shape 

significantly influenced a particle’s landing position when aerially applied. Due to the 

complexity of aerial application, most studies focus on one factor. However, the factors are 

interconnected and the interaction effects require analysis.  

To complement Spreadmark, the Fertmark code of practice (NZFQC, 2016a) was developed to 

ensure that there is a standard for fertiliser quality in New Zealand. Fertmark sets standards 

for nutrient and heavy metal content. For fertiliser physical characteristics, it monitors granule 

strength, granule degradation and the particle size distribution. The code of practice also sets 

out guidelines for production, transportation and storage. 

1.4.2. Fertiliser Transportation and Storage 
Fertiliser transportation and storage further complicates particle size and distribution 

variations. In New Zealand, fertiliser is transported from manufacturing sites to the 

distribution stores by truck or train. When required on farm, the fertiliser is transported from 

the stores by truck. Therefore, fertiliser can travel hundreds of kilometres before being 

applied. Superphosphate has low granule strength and will experience attrition during 

transportation. This increases the percentage of fine particulates (< 1.0 mm) and could 



29 
 

decrease the precision of an aerial application. Fertiliser age and its exposure to moisture will 

also have an effect on particle hardness and aerodynamic qualities (Adams and Merz, 1929).  

Segregation, environmental exposure, and treatment are issues in fertiliser storage. Fertiliser is 

stored in covered sheds as large piles. Depending on the storage capacity of the shed, these 

piles can be over 8 m in height. Hoffmeister et al. (1964) observed that, on average, large 

particles will migrate down the outside of a fertiliser storage pile. This is an issue because 

fertiliser is first removed from one face of the pile. Therefore over a large fertiliser application 

there will be a change in the fertiliser particle size distribution. Front-end loaders are 

sometimes used to shift the fertiliser piles into trucks. Large stores use conveyor belts and 

hopper systems. Some particles are crushed as they are loaded. Although the crushed fertiliser 

is removed and sold as non-conforming material, some remain and increase the fines fraction 

of the particle size distribution. 

Although these stores and sheds are covered, they are not fully enclosed. Therefore, the 

stored fertiliser is still exposed to humidity and temperature changes. This can negatively 

affect fertilisers depending on their hygroscopy (extent the material absorbs and holds 

moisture from the air) (Adams and Merz, 1929). Fertilisers with high hygroscopicity, such as 

superphosphate, will soften and become sticky, which reduces particle strength. This 

simultaneously leads to the formation of fine particles and large conglomerates. The stickiness 

negatively affects the spreading equipment and increases the chance of clogging. These issues 

are further exacerbated when fertiliser is stored at a distribution centre for a few months. 

Although manufacturers practice ‘Just in Time’ production, application delays occur during the 

winter season when fertiliser that has been ordered is produced, but not applied because 

conditions are too wet. These issues are prevented by maintaining a dry environment and 

reducing the time between manufacture and application when possible, so that there is not a 

significant change in fertiliser properties. 

1.4.3. Wind 
Wind conditions significantly contribute to the variability in the ground fertiliser distribution. 

Hedderwick and Will (1982) found in their study of aerial application to forests that 

superphosphate granules less than 2 mm were more affected by wind. Displacement of these 

small particles can negatively affect the evenness of the application and create off-target 

application.  

Macfarlane et al. (1987) investigated the effects of increasing crosswind on the transverse 

spread pattern of aerially applied superphosphate. They found that an increase in crosswind 



30 
 

will widen the swath width and reduce positive kurtosis. Although the distribution was 

displaced in the direction of wind, continued application at the swath width reduced variation. 

The study used three rows of 25 funnel shaped collectors. With a crosswind of 1.6 km h-1, 

Macfarlane et al. (1987) found that the application rate ranged between 4 kg ha-1 and 270 kg 

ha-1. A crosswind of 2.4 m s-1 and 3.5 m s-1 yielded a fertiliser application rate of 66 – 163 kg ha-

1 and 48 – 181 kg ha-1, respectively. The intended average application rate for the experiments 

was 100 kg ha-1. Gillingham et al. (1985) showed that the greater the crosswind, the greater 

the spread pattern displacement in an unmodified fixed wing aircraft. It was concluded that 

this could be beneficial, since fertiliser would be applied more evenly. However, wind has a 

negative effect near boundaries as there is an increased likelihood of off-target application if 

wind is not considered during the flight. Although this has been identified as an issue, it is not 

well addressed in previous studies, because the flight path is at the discretion of the pilot.  

It is difficult to minimise the effect of wind since there are a limited number of days in a year 

for an aircraft to be able to service all the farms. This is because farmers prefer to apply 

fertiliser in spring and autumn when it can dissolve into the soil. Single superphosphate has 

low levels of fluorine, which can be toxic to stock if consumed during grazing (Chok et al., 

2014). The likelihood of ideal weather, in New Zealand, for the majority of spring and autumn 

is slim. Therefore, some applications will be done under unfavourable wind conditions. This 

has a significant impact on the accuracy and precision of the ground fertiliser distribution.  

1.4.4. Altitude 
Fixed wing aircraft fly 15 – 60 m above ground. Lower altitudes have a negative effect on the 

transverse spread pattern, because fertiliser particles have insufficient time to reach their 

terminal velocity and spread laterally. Trayford and Tremayne (1966) found that the swath 

width increased and the centre peak of a transverse spread pattern decreased with increasing 

altitude. They reasoned that the increased altitude gave the particles more time to travel 

laterally. Scott (1970) showed there was a significant difference in the swath width as the 

aircraft altitude increased for applications rates of 112 kg ha-1 or below. It was also observed 

that aerial superphosphate application experienced an increase in swath width with increasing 

altitude (23 m – 122 m), while there was no effect on homogenous granulated 

superphosphate. However, a disadvantage of operating at higher altitudes is that there is a 

greater chance of off-target application due to wind drift. Pilots have to consider both of these 

issues, as well as their safety, when selecting what altitude they will apply at.   



31 
 

1.4.5. Topography 
Aerial application over challenging topography, such as steep or irregular terrain, adds to the 

on-ground variability in the spread pattern. Variable topography increases the difficulty of 

applying fertiliser, since pilots have to avoid obstacles. Aircraft experience leeward low 

pressure and uplift on the windward side of a hill, which could result in a rapid loss of altitude 

if not accounted for by the pilot. In the worst case scenario, the pilot will lose control of the 

aircraft and crash. Another consideration with hill country’s variable elevation is that the 

aircraft altitude above ground will vary. At points where the aircraft and ground are closer 

together, the transverse spread pattern will have a narrower swath width, because there is 

insufficient time for the material to travel laterally. Akesson and Yates (1964) found that aerial 

application at 9 m did not produce a narrow lateral distribution compared to an altitude of 3 

m. Although an aerial spreader is unlikely to apply at an altitude of 3 m, Akesson and Yates 

(1964)  demonstrated that altitude has an effect on the spread pattern.  

1.4.6. Aircraft Velocity 
Aircraft velocity can be described in two ways. True airspeed is the speed the aircraft is moving 

through the air, while groundspeed is the true airspeed corrected for wind. It was not possible 

to measure groundspeed until the integration of GPS into aircraft navigation systems. Aircraft 

velocity affects the application rate. For a constant flow rate out of the hopper (measured in kg 

s-1), an increase in aircraft velocity would decrease the application rate (kg ha-1), since a larger 

area is covered in the same amount of time. To maintain the target application rate, the flow 

rate would have to increase. A case study by Murray and Yule (2006) showed that large 

variations in groundspeed may have a significant impact on the flow rate out of the hopper. 

Additionally, Murray (2007) found that minor fluctuations in groundspeed (average 56 m s-1 

and standard deviation 2.5 m s-1) have little effect on the fertiliser flow rate.  

1.4.7. Spreaders 
Ram air or venturi type spreaders were developed to achieve wider swath widths and reduce 

positive kurtosis of the transverse spread pattern. This improves CV and decreases the 

application time (NZFQC, 2016b). Spreaders have a multitude of designs but those discussed 

here are fish tail shaped spreaders with 9 or 11 ducts. Ducts are separated by vanes which 

curve out in the transverse direction (Figure 1.5). R. K. Bansal et al. (1998a) found, through 

simulation of an 11 duct spreader, that the air velocity within the ducts is greater than aircraft 

ground speed velocity by 1.04 – 1.14 times. The average air velocity in the centre duct was 

lower than the sides because it has the shortest length.  



32 
 

 
Figure 1.5: Port side image of an 11 duct spreader that is attached to the hopper door on an 

aircraft. 

Ram air spreaders are designed for application rates less than 200 kg ha-1. At higher application 

rates, fertiliser can clog the spreader ducts resulting in the spreader detaching from the 

aircraft (Charlton et al., 1983). Another disadvantage of spreaders is that it limits aircraft speed 

due to increased shear forces (Gillingham et al., 1985). A typical stainless steel spreader can 

weigh approximately 80 kg, and increase the drag forces on the aircraft.  

A few settings can be adjusted on a spreader to optimise performance. These are the 

installation angle of the spreader, its distance from the hopper door and the amount of 

fertiliser that travels through each duct. The fertiliser flow rate through each duct is set by 

widening or narrowing the duct’s entrance. This is a coarse adjustment, which could result in 

large flow rate variations through each duct. Therefore adjustments should be checked in the 

field to ensure an appropriate transverse spread pattern is achieved. 

1.4.8. Swath width 
A pilot will select the swath width based on their experience and their Spreadmark 

certification. The selected swath width is usually set at an optimistic swath width for a fertiliser 

type to maximise aircraft efficiency. Wide swath widths will decrease the amount of time 

required to complete a job, since fewer flights will be required to cover the application area. 

However, a pilot’s first priority is to ensure an appropriate swath width is chosen so that the 

correct application rate is applied (NZFQC, 2016b). Although a pilot can set a swath width, it 

may not be the optimal field swath width because of changes in wind conditions, aircraft 

operation or fertiliser properties. Akesson and Yates (1964) found that increasing the fertiliser 

flow out of the hopper will decrease the swath width when applied with a Stearman aircraft. 

Striping can occur in this instance, where there is a visible difference in pasture/crop growth 

because the majority of fertiliser is applied along the centre of the flight path and insufficient 

fertiliser reached the edge. Therefore, the set swath width results in poor overlap between 



33 
 

flight lines. This could occur in situations where pilots maximise the set swath width in order to 

minimise the application time and therefore costs.  

Before the introduction of GPS for aerial application, applicators relied on landmarks to 

determine the swath width and identify farm boundaries. This led to uneven swath widths, 

which was used to explain variability in aerial topdressing in several studies (Ballard and Will, 

1971; Hedderwick and Will, 1982). Methods to reduce uneven applications included ground 

staff with flags, helium balloons and flares (Barker, 1979). Hedderwick and Will (1982) 

introduced a radar guidance system on to New Zealand helicopters for fertiliser application in 

forestry, which required multiple ground receiving stations. In recent years, operators have 

adopted DGPS (Differential Global Positioning Systems). DGPS is an improvement on 

uncorrected Global Positioning Systems, as it uses ground based reference stations to correct 

between GPS and the known fixed positions. VRAT uses the farm boundaries with their GPS co-

ordinates, and the DPGS position of the aircraft in real time to improve the accuracy at which 

pilots can fly parallel swath widths (Murray, 2007).  

1.5. Variable Rate Application Technology 
Nutrient availability in pasture is spatially variable over a farm (During and Mountier, 1967; 

Gillingham and During, 1973; Morton et al., 2000). Therefore, blanket fertiliser application is 

not an efficient use of fertiliser. Variable rate application allows for different rates to be 

applied over a farm. The technology is established in truck fertiliser applications and irrigation. 

It has also been developed for variable rate aerial spraying of crops. However, only 3% of New 

Zealand agricultural land is cropped, while more than 50% is grazed (Hedley, 2014). Therefore, 

aerial application of granular fertiliser for pasture is the major use of agricultural aircraft in 

New Zealand, and utilising VRAT may increase the efficiency of fertiliser use on hill country. 

A desktop economic study of a variable aerial application by Gillingham et al. (1999) showed 

that the benefit of the technology is dependent on the specific needs of the farm and the stock 

carrying capacity. However, it illustrated that the correct application of variable rate 

technology will achieve greater pasture and animal production. A more recent economic 

analysis by Murray and Yule (2010) found that a full variable rate application can increase a 

farm’s cash surplus by 26% per hectare under optimum pasture growth conditions for a 

specific case study. Introduction of GPS technology alone is thought to increase farm efficiency 

by 5 – 10%, as it reduces overlaps and gaps, and prevents off-target application (Hedley, 2014). 

By reducing the number of overlaps and gaps, uneven application will decrease.  



34 
 

Grafton et al. (2012) showed that conventional applications using a pilot operated hopper door 

could yield a CV as high as 70%. This could be reduced to 43% with a GPS controlled hopper 

door, which is a 27% improvement in CV.  This trial was carried out at application rates of 125 

kg ha-1 and 250 kg ha-1 for pilot operated, and 250 kg ha-1 and 750 kg ha-1 for the automated 

system. The pilot completed each application zone individually. After the area was flown, the 

samples were collected before the collectors were moved to the next trial area. This sampling 

procedure was undertaken because the number of collectors was limited. The trial is not 

considered a variable rate application trial, because two application rates were not measured 

simultaneously and the variability at the boundaries was not captured. The most recent aerial 

variable rate application study was completed by Morton et al. (2016), but measurements of 

accuracy, precision and capability were not specified. They focussed on the initial development 

of a variable rate application system, and the field trials consisted of calibration, and flight 

observations.  

Figure 1.6 and Figure 1.7 are simulated comparisons of an aerial application between a pilot 

operated and automated hopper door, respectively (Murray, 2007). It illustrates that an 

automated door can reduce off-target fertiliser application (Figure 1.7). In the simulation, the 

automated system only applied 6% of the total fertiliser outside of the application area 

compared to 16% in the pilot operated system. This constituted a saving of 10%. To model this, 

it was assumed that the hopper door closed on the boundary. Therefore, the majority of off-

target application in the variable rate simulation was due to the forward motion of particles. 

Murray (2007)  did complete a field trial with a target application rate of 150 kg ha-1 of 

superphosphate using a six duct non-air ram spreader. The pilot had a Satloc M3 navigation 

system for flight track guidance, but the hopper was pilot operated.  



35 
 

 
Figure 1.6: Predicted field scale application on a 25 ha site where the hopper door is pilot 

operated and there is no GPS guidance (Murray, 2007). The application rates were modelled 
using Jones et al. (2008) and recorded aircraft data. 

 
Figure 1.7: Predicted field scale application using an automated GPS guided hopper door. 

Murray (2007) produced this image from Figure 1.6 by removing all points outside the 
application area except when it was within 45 m of an application area. 

A fully automated fertiliser delivery system will improve pilot safety. Between 2003 and 2012 

there were 19 fatalities, 12 serious injuries and 8 minor injuries that were connected with 

aerial topdressing. A Civil Aviation Authority report on fixed wing accidents stated pilot fatigue 



36 
 

and inattention to surroundings as contributing factors to agricultural accidents (Wackrow, 

2005). Grafton et al. (2012) estimated that a topdressing aircraft may land and take off 150 

times a day. In a conventional application, the pilot will operate the hopper door at least four 

times per load. This equates to approximately 600 openings and closings of the hopper door. 

On a fine summer’s day, a modern turbine Cresco could apply 300 tonnes of fertiliser per day 

(Grafton et al., 2009). However, this is usually not achieved because of farm storage 

limitations. The variable rate system will reduce the workload on pilots and allow them to be 

more aware of dangers in the surrounding area (i.e. power lines, hill top, other aircraft). It 

allows them to concentrate on where they are