A statistical comparison of international fertiliser spreader testmethods — Confidence in bout width calculations
Jim R. Jones b,⁎, Hayden G. Lawrence a, Ian J. Yule a
a Centre for Precision Agriculture, Massey University, Palmerston North, New Zealandb Institute of Technology and Engineering, Massey University, Wellington, New Zealand
Received 30 April 2007; received in revised form 28 August 2007; accepted 11 September 2007Available online 15 September 2007
There are several test methods used worldwide to certifyfertiliser spreaders. Certification determines the allowabledistance between adjacent transects of the spreader as it isdriven across the field. Each international test method has adifferent test protocol, but all measure the amount of fertiliserlanding on trays. They are; (i), the ISO standard [1] which hastwo forms, ISO 5690/1 and ISO 5690/2; (ii), ASAE standard [2]in United States of America; (iii), European Standard [3]
operated in European Union countries; (iv), ACCU Spread [4]in Australia; and (v), Spreadmark [5] in New Zealand. Thesetest methods are simple to set up and conduct, requiring onlycollection trays and a weigh balance.
Alternative technologies can be used to predict spreadpattern but none of these methods are used to test spreaderperformance. These methods include using image processing[6], mathematical calculation [7–11], cylinder measurement[12] and the use of optical sensors combined with ballisticmodelling [13] have also being successfully used to predictspread pattern information, but are not covered in the presentanalysis. A new test device for centrifugal spreaders is describedby Piron and Miclet [14]. The method moves a spreader radially
Table 1Test constraints for various international testing programs used around the world to test the transverse distribution accuracy of fertiliser spreaders
Standard Tray size Tray frequency Transversespacing
No. ofrows
No. of passes Weighfrequency a
(i) ISO 5690/1 (World)
0.5×0.5 m Enough to cover totaldistributing width
Continuous 1 Test requires 3 fertilisers (typically lime, superphosphate, urea), 1pass for each
Each pass
(ii) ISO 5690/2 (World)
0.25×1.0 m Enough to cover totaldistribution width
Continuous 1 Test requires 3 fertilisers (typically lime, superphosphate, urea), 1pass for each
Each pass
ASAE S341.3(USA)
0.5×0.5 m 10 per swath Uniformspacing
1 1 Each pass
ES (Europe) 0.5×0.5 m 112 per 56 m Continuous 2adjacent
Test requires 6 fertilisers, 1 pass each Each pass
ACCU Spread(Aus)
0.5×0.5 m 50 per 25 m Continuous 2, 50 mapart
Test requires a minimum collection of 600 kg ha−1 (e.g. 6 passes at100 kg ha−1, 4 passes at 150 kg ha−1)
After minimumcollection
Spreadmark(NZ)
0.5×0.5 m 60 per 30 m Continuous 1 Test requires 3 fertilisers, 1 pass each Each pass
Typical application rates are 80–150 kg ha−1 for urea, 200–500 kg ha−1 for superphosphate and 500–1000 kg ha−1 for lime.a Weigh frequency defines whether the mass collected is weighed after each pass or after all passes.
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around a single row of collection trays fitted with load cells inorder to define the spatial distribution of the spreader. Themethod can be used to extract a smoothed transverse spreadpattern rather than an instantaneous spread pattern as acquiredfrom the international test methods discussed.
Each of the standard spread tests has trays arranged intransverse rows, some having more than one row, over whichthe spreader makes a given number of passes. The mass offertiliser landing in the trays is either measured after each passor after the passes have been completed depending on the testmethod. A test is made for each designated application rate ofeach fertiliser tested. Table 1 provides the details of individualtest methods.
The mass data collected from spreader testing provides ameasure of the uniformity of the transverse distribution fromwhich the bout width is calculated. The bout width is theallowable distance between adjacent transects of the truckspreader as it is driven across the field. This paper directlycompares the accuracy of these international spreader testsusing a comprehensive field trial from which all tests can bereconstructed. The field trial consisted of 0.5×0.5 m trays
Fig. 1. Test tray layout used to reconstruct international fertiliser spreader test methodmatrix.
arranged as 18 adjacent transverse rows of 80 trays each,leaving spaces for the truck wheels (Fig. 1). Two passes weremade at each application rate and the mass of fertiliser (ingrams) landing in each tray every pass was measured.
2. Methodology
In order to accommodate all international tests, a matrix of1400 collection trays were laid out edge to edge consisting of 18transverse rows. Each row contained 80 trays with four lines oftrays removed for the wheels of the spreader truck. In all testmethods trays that are removed are credited with the average oftrays at either side of them. The collection trays comply with theSpreadmark Standards [5], each measuring 0.5 m wide, 0.5 mlong and 0.15 m high and made of 4 mm thick plastic. A seriesof cardboard dividers (0.1 m high) were placed inside each trayto reduce particle energy on impact and avoid particles fromricocheting out.
Urea (46% N) was chosen as the test fertiliser, which iscommonly applied at rates between 80 kg ha−1and 150 kg ha−1 inNew Zealand. Therefore fixed application rate tests were
s; 1400 trays 0.5×0.5 m in size were used to construct an 80×18 (40×9 m) tray
Fig. 2. Mean and 95% CI (2 s.d.) for mass landing on trays as a function of longitudinal position, at nominal application rates of (A) 80 kg ha−1, (B) 100 kg ha−1, and(C) 150 kg ha−1.
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conducted at a low (80 kg ha−1), medium (100 kg ha−1), and high(150 kg ha−1) rates. Two replicates weremade of each applicationrate meaning that 36 transverse rows of data were obtained.
The spreader used was a Transpread ‘W’ chain twin spinneron a Mercedes truck. The spreader has an electronic flowcontrol system to control the application rate as a function ofdriving speed by altering the hopper belt speed. The machinesettings were the same as used for field spreading of urea, wherethe spreader had previously been certified by Spreadmark (NZ)to spread to a bout width of 15 m. A spinner disc speed of 750RPM was used for all tests. The hopper had a capacity of10 tonnes. For these tests, 200 kg of urea was placed at the rearof the spreader to cover the feed mechanism which was found tobe sufficient to produce normal flow [5]. Tests were conductedon a flat asphalt surface. Wind speed was monitored during allexperiments to ensure that the specified maximum wind speedwas not exceeded (b2 m s−1 to conform to all test methods).
The spread material was collected from each tray intoindividual labelled bags and later weighed using scalesaccurate to ±0.01 g. Particle size distributions were notinvestigated in this study. However, one observation of
statistical importance is that larger particles were thrownfurther from the point of distribution. This means that the masscollected near the outer edge of the swath consisted of a smallnumber of large particles. Because mass is a discrete functionof the number of particles, when the numbers are fewer thevariability is inherently higher.
2.1. Statistical analyses
The total mass collected by the trays is
Mtrays ¼Xpk¼1
Xr
j¼1
Xni¼1
xk;j;i ð1Þ
where n is the number of trays in a transverse row, r is thenumber of rows and p is the number of passes employed in thetest. However, the total mass distributed by the spreader alsoincludes fertiliser landing on the ground left bare for the truckwheels. By convention, the amount landing on these missingtrays is interpolated from the neighbouring trays. The followingcalculations are performed for each longitudinal position.
Fig. 3. (A) Coefficient of variation CVi and (B) expected industry measure of variation MVi, plotted as a function of transverse tray position at nominal applicationrates of 80 kg ha−1, 100 kg ha−1, and 150 kg ha−1.
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The mean amount of material landing at the ith transversetray position, Pxi is
Pxi ¼
Ppk¼1
Prj¼1
xk; j;i
prð2Þ
The sample standard deviation at ith transverse tray position,Si, is calculated from the sample variance
S2i ¼
Ppk¼1
Prj¼1
xk; j;i � Pxi� �2pr � 1
ð3Þ
The uniformity of the spread is measured by the coefficientof variation, CVi, where the subscript i refers to the ithtransverse tray position
CVi;tray ¼ SiPxi
ð4Þ
However, the international spread tests collect and weigh thefertiliser only once from each row which means they cannotcalculate an expected mean or variance at each longitudinal
position. Therefore they use a swath averaged measure ofvariation given by
MVi ¼ xiPx
ð5Þ
where xi is the amount of fertiliser landing on the ith tray and Pxis the mean averaged over all trays in the test
Px ¼ Mtrays
prnð6Þ
Boutwidth certification is an outcomeof these international spreadtests. In practise this means the MVi calculations are repeated anumber of times by overlapping the test results at various boutwidths until an optimum is achieved. Clearly, overlapping willaffectMtrays, xi,
Pxi and Si2, particularly for the outer regions of the
swath. The optimum is defined as themaximum bout width acrosswhich MVi≤0.15 for nitrogen based fertilisers. This study willfirstly compare the international tests based on their test variabilitythen, using the above criteria, the confidence with which thecertifiable bout width can be calculated will be determined.
The application rate, Ai (kg ha−1), at each ith transverseposition is converted from the mass of fertiliser measured in allr rows for all p passes and the summed area of each tray. For a
Fig. 4. Mass collected on trays at selected transverse tray positions over all 18 rows at nominal application rates of (A) 80 kg ha−1, (B) 100 kg ha−1, and (C) 150 kg ha−1.Trays are 0.5 m square: therefore, spacing between rows is 0.5 m.
1 Furrows (or remnants of) are a typical ground topography affecting variability.
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single tray, without overlapping, the application rate is simplyforty times the amount landing on the tray
Ai ¼ 40pr
Xpk¼1
Xr
j¼1
xj ð7Þ
In these calculations of the statistics of spreading at each ithtransverse tray position, it must be noted that we assume indepen-dence between the rows. Independencemeans that themass landing
on one tray is independent of the mass landing on the same tray inan adjacent row. In contrast, we do not expect independence in thetransverse direction because some sort of spread pattern is expected.
A number of things can affect variability such as groundtopography1 or time dependent behaviours within the spread-ing machine. This potential problem of lack of longitudinal
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independence affects tests that have adjacent or closely spacedrows of trays, namely the study reported here and the ESinternational spread test which has two adjacent rows of trays.The data set presented here will be used to ascertain whether a“near neighbour effect” exists and, if so, to determine the rowspacing necessary to ensure independence.
Statistically we can detect this near neighbour effect bycalculating the difference between masses landing on adjacentrows, j and j+1, at the same (ith) transverse tray position(i.e. along the same longitude)
di;j ¼ xj � xjþ1 ð8Þ
The variance of the differences at each ith tray position is then
S2d;i ¼Pr�1
j¼1 d2i;j
r � 2ð9Þ
where di,j is the adjacent tray difference and Sd,i2 is the sample
variance of the differences. If the mass landing on the trays is
Fig. 5. Comparison between 2Si2 and Sd,i
2, where 2Si2 is twice the variance of the ma
adjacent trays. Results are shown for the both passes at each nominal application ra
independent, that is, no periodicity occurs over the 18 rows oftrays, then the difference variance should be approximatelytwice the measured variance, Sd,i
2≈2Si2, for the 17 differences
that are obtained from an 18 tray test. The statistical f-testuses a one tailed test to determine the probability that thevariances of the two populations are the same assuming thatthey are both normally distributed. As a spreadsheet operation,the 18 rows of masses collected were multiplied by √2 andcompared in the FTEST Microsoft Excel worksheet functionto the 17 pairs of difference values. (The multiplier √2 isneeded to obtain twice the original sample variance.) Thef-test assumes the two arrays of values are normally distri-buted so it is important to test this assumption. Although notshown here, the masses are distributed normally about themeans over most of the spread swath, but the assumptionbreaks down at the outer edges where little fertiliser lands andthe variability is high. In later calculations of bout width,overlapping increases the mean and the variability becomesapproximately normal.
sses collected and Sd,i2 is the variance of differences between masses landing on
te (A) 80 kg ha−1, (B) 100 kg ha−1, and (C) 150 kg ha−1.
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3. Results
Comprehensive field test results were obtained for eachnominal application rate (80, 100 and 150 kg ha−1) using themethod described previously. As the dataset was approximatelynormally distributed over much of the swath as described above,the calculated mean and variance can be given by Eqs. (2) and(3) where r= 18 and p= 2. The uniformity is measured by thecoefficient of variation (4) and the industry measure of variation(5). Fig. 2 plots the mean and 95% confidence interval (2standard deviations) as a function of tray position for all threenominal application rates. Fig. 3 plots the coefficient ofvariation for each tray CVi and the industry measure ofvariation MVi. Clearly the uniformity of the distributionbecomes worse near the edges of the distribution patternwhere CVi goes from∼0.3 to 6.0 between 12 and 18 m from the
Fig. 6. F-test comparison between pass pairs of 2Si2 and Sd,i
2 as a function of tray pvariance of differences between masses landing on adjacent trays. Results are s(B) 100 kg ha−1, and (C) 150 kg ha−1.
centreline of the spreading vehicle. Similarly the MVi
approaches zero. These results do not represent an ideal spreadpattern where the mean and its variability are constant across themid section of the swath. The implications of this not discussedhere. Rather, the dataset is used to compare the international testmethods. First, the issue of independence between the amountof fertiliser landing on adjacent rows of trays is addressed, afterwhich the expected variability of international tests and theconfidence in the bout width calculations are determined.
3.1. Near neighbour effect
It is possible that the masses of fertiliser collected on adjacenttrays at a given longitude are not independent. Fig. 4 shows themass collected at selected transverse tray positions over the18 rows of the first pass of each test. It is clear that some
osition, where 2Si2 is twice the variance of the masses collected and Sd,i
2is thehown for the both passes at each nominal application rate (A) 80 kg ha−1,
Fig. 7. F-test comparison of variances Si2 and Sd,i
2 as a function of tray position, where Si2 is twice the variance of the masses collected and Sd,i
2 is the variance ofdifferences between masses landing on every 8th tray. Results are shown for the both passes at a nominal application rate of 150 kg ha−1.
Fig. 8. Test tray layouts for six international testmethods reconstructed froma 1400 traymatrix (Fig. 1) to compare levels of confidence in individual traymassmeasurement.
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interdependency occurs between trays, however, not alllongitudinal positions shows these patterns. Because the numberof rows is small, interrogation by Fourier analysis only revealswhat the eyes see; that is, some periodicity occurs over a 2 to8 tray cycle. It must be noted that because of the small samplesize, both Fourier analysis and visual inspection are susceptibleto recognising experimental artefacts of periodicity. In this work,the dependency between trays is termed a near neighbour effect,where the variance of the differences between adjacent trays(Sd,i
2 ) is significantly less than twice the variance for all 18 rows(2Si
2). Fig. 5 compares these variances for both passes at eachapplication rate. At 80 and 100 kg ha−1 they appear similar andindeed the statistical f-test (Fig. 6) shows that the majority ofthe 2Si
2 and Sd,i2 comparisons have probabilities N0.7 that the
variances are the same.2 Therefore, for later calculations it isassumed that the near neighbour effect is not present for the 80and 100 kg ha−1 application rates. This is not surprising as theflat tarmac over which the test was conducted removes groundtopography as an influencing factor and also removes somemachine parameters associated with vehicle roll. In contrast,the 150 kg ha−1 application rate shows a time dependentbehaviour which can be seen in. Fig. 4 where the fertiliser mass
2 The selection of the significance level is arbitrary. Although each f-testcompares the variance of 18 rows of data to 17 pairs, hence constituting a smallsample, there aremany transverse tray positions for which this comparison ismade.
per tray increases with row number. The cause of this is notknown; the second pass did not have this increasing trendalthough all machine and environmental factors were the same.Also, within the longitudinal profile other periodicities can beseen by visual inspection and Fourier analysis. The result is thatthe f-test plot (Fig. 6C) is a scatter diagram with probabilitiesevenly distributed between 0 and 1.
The presence of a near neighbour effect demonstrates that rowsof trays should not be adjacent in order to obtain an accuratemeasure of the variance.Wider tray spacings can also be tested forthe near neighbour effect, for example, by calculating the varianceof the differences between every 3rd, 4th, 5th, etcetera, tray. Fig. 7shows the f-test result for every 8th tray for the 150 kg ha−1
application rate and shows higher probability values compared toFig. 6c, but they are not as good as the 80 or 100 kg ha−1
application rates due to the net increase in fertiliser across the rowson the negative (tray position) side of pass 1 and an observed dipin the middle rows of the positive side of pass 2 (not shown). Itmust be noted that, because differences are calculated whendetermining the near neighbour effect, this technique cannotaccount for time average trends in the mean. Therefore, for latercalculations at the nominal application rate of 150 kg ha−1, thesample mean and variance will be used although it isacknowledged that time averaged trends did occur in the test data.
The only way to detect the near neighbour effect is in a largefield trial such as conducted here. However, this is not
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commercially practical. A small test like the ES internationalspread test which does use adjacent rows will not pick up a nearneighbour effect if it exists. To avoid this possible problem, therows in an international test method should be spaced as farapart as feasible to ensure independence.
3.2. International test reconstruction
The tray layout for each international spread test is shown inFig. 8. The statistical confidence of each international test canbe reconstructed from the sample mean and variance obtained inthe large field trial (2 passes of 18×80 trays) given in Fig. 2.The ISO (i) (World), ES (Europe), ASAE (USA), and Spread-mark (NZ) spread tests have the same expected mean andstandard deviation, Pxi and σi, as obtained for the longitudinalpositions in the large field trial. While the ASAE has the sameexpected values, these are for the minimum 10 trays across theswath. Because the certified bout width of the spreader used is
Fig. 9. Expected coefficient of variation, CVi (Eq. (4)), for all international tests as a f80 kg ha−1, (B) 100 kg ha−1 and (C) 150 kg ha−1.
nominally 15 m, the trays are positioned at intervals of 3 m forthis analysis. Normally one tray is placed at the centreline oftruck travel, but here it is offset slightly to align with the traypositions in the large field trial.
For tests that have larger tray sizes, multiple passes andmultiple rows, the row mean and standard deviation are givenby
where R (rows) and c (columns) define the size of the largertrays (in terms of the smaller 0.5×0.5 m trays). Clearly, for the
unction of tray position for test data collected at nominal application rates of (A)
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large field trial presented here, all tests except the ISO (ii)(World) have R=c= 1. The variable p is the number of passesbefore the mass of fertiliser is measured, r is the number oftransverse rows each test employs. The test statistics Pxtest;i andσtest,i are the longitudinal mean and standard deviation offertiliser mass at the nominated ith transverse position.
The ISO (ii) (World) uses a tray size of 0.25×1.0 m, alignededge-to-edge in a single transverse row with a single pass.Because the tray area is the same as the 0.5×0.5 m trays, themean and standard deviation for each tray are taken as the sameas those for the corresponding half metre tray in our large fieldtrial. The ACCU Spread (Aus) test uses two transverse rows oftrays of 0.5×0.5 m size, but only measures the mass of fertiliserafter a minimum of 600 kg ha−1 has been applied. For anapplication rate of 80 kg ha−1 this means 8 passes, with 6 passesat 100 kg ha−1 and 4 passes at 150 kg ha−1. Using Eqs. (10) and(11) for the 80 kg ha−1 application rate the expected tray meanis 8Pxi and standard deviation about the mean is
ffiffiffiffiffiffi82ri
q. The
division by root 2 accounts for the two rows which togethernarrow the variability of the averaged mean of the collecteddata.
Fig. 9 shows the coefficient of variation calculated for eachtest method using Eq. (4). It shows that the CVi is lower for theACCU Spread (Aus) and the ES (Europe) than for the other
Fig. 10. a. Industry measure of variation for six international spread tests (a) ISO (i) (W(Aus) and (f) Spreadmark (NZ) as a function of tray position when applying urea at a nsix international spread tests; (a) ISO (i) (World), (b) ISO (ii) (World) (c)ASAE (USA)of tray position when applying urea at a nominal application rate of 100 kg ha−1. c. In(b) ISO (ii) (World) (c)ASAE (USA), (d) ES (Europe), (e) ACCU Spread (Aus) and (fapplication rate of 150 kg ha−1.
spread tests at all three application rates. This is because theycollect more data; both use two rows of trays plus the ACCUSpread (Aus) test has repeated passes before the fertiliser isweighed. Fig. 10 shows the 95% confidence interval for theindustry measure of variation, MVi, calculated using Eq. (5).This means any test will provide MVi results that fall withinthese limits 95% of the time. For the same reasons, the ACCUSpread (Aus) and ES (Europe) have tighter confidence limits.
3.3. Bout width confidence
Spreader tests are used to certify the bout width at which thetruck can drive between transects across the field. Therefore,it is important to determine the confidence in the bout widthcalculations. All tests determine certifiable bout width bylimiting the allowable industry measure of variation across theswath. The choice is somewhat arbitrary, but all tests haveadopted the limit of MVib0.15 for nitrogen based fertilisers.Therefore, the confidence in each test method can be estimatedby using the sample statistics gathered from the large field trial todetermine the probability that MViN0.15 at the outermost edgesof the bout. This involves a series of overlapping calculationsthat simulate the transect driving pattern of the truck. Here,the round-and-round (not the to-and-fro) driving pattern is
orld), (b) ISO (ii) (World) (c)ASAE (USA), (d) ES (Europe), (e) ACCU Spreadominal application rate of 80 kg ha−1. b. Industry measure of variation, MVi, for, (d) ES (Europe), (e) ACCU Spread (Aus) and (f) Spreadmark (NZ) as a functiondustry measure of variation for six international spread tests; (a) ISO (i) (World),) Spreadmark (NZ) as a function of tray position when applying urea at a nominal
Fig. 10 (continued ).
347J.R. Jones et al. / Powder Technology 184 (2008) 337–351
examined. Overlapping increases the application rate to give anoverlapped mean mass per tray across the bout width of x̄bout. Atthe outermost edge of the bout width, the expected fertiliser massis the sum of that landing on the two trays that overlap at thislocation, x̄overlap ¼ x̄i þ x̄j, where the subscripts i and j (here)specify the trays numbers that overlap when two transects at aspecified bout width are driven by a spreading vehicle. Theexpected industry measure of variation is the ratio of these twoamounts, MVbout ¼ x̄overlap
x̄ bout. Each international test will yield an
MVbout that varies about this expected value according to thesample statistics gathered in the large field trial reported here.The standard deviation at the outermost edge of the bout isroverlap ¼
the measure of variation is MVbout ¼ x̄overlapF2roverlapx̄ bout . By using the
z-statistic3, the probability that the experimental MVbout fallsabove the acceptance threshold P(MVboutN0.15) can becalculated. Fig. 11 plots this probability of an unacceptableMVbout for the two round-and-round scenarios: the right side ofthe swath with left overlap and the left side of the swath withright overlap. Both are plotted because the spreader does notspread evenly over both sides of the swath. At low bout widths,there is plenty of overlap and little variation about the meanand hence P(MVboutN0.15)∼0. At high bout widths, thevariability is high compared to the mean and hence P(MVboutN0.15)∼1. Somewhere in-between these limits is
3 The z-statistic can be used when n N 30. Here the sample size equals 36.
the ideal certifiable bout width for the spreader. It must benoted that the concern here is the confidence with which aninternational spread test can certify a bout width, rather thanthe bout width itself. In this respect, the ACCU Spread (Aus)test exhibits the steepest curve which corresponds to thegreatest certainty in determining the bout width, followed bythe ES (Europe) test. All the other tests except the ASAE(USA) provide the same probability curve. The ASAE (USA)test probability curve has not been calculated because the traysare so far apart they do not overlap at the outermost edges ofthe bout where the calculations have been performed for theother tests. Instead, the ASAE (USA) method requires that theMVi profile across all trays must be plotted for each boutwidth where the trays overlap. This means bout widthstatistics can only be calculated at intervals of 3.0 m whichis less accurate than the other international test methods.Interpolation methods may be used to estimate the full ASAE(USA) swath spread pattern from which the required boutwidth can be estimated, however these techniques are notexplored here. The following section discusses the signifi-cance of these probability curves for estimation of bout width.
4. Discussion
All international spread tests are experimentally expedient tolimit the time and expense to conduct them. This means thatthe certified bout width has some level of uncertainty depending
Fig. 10 (continued ).
348 J.R. Jones et al. / Powder Technology 184 (2008) 337–351
on the test. This above analysis demonstrates that the ACCUSpread (Aus) test is the best because it predicts the bout width towithin a single 0.5×0.5 m tray. It performs best because it hastwo enhancing features that reduce the variability, two rows ofcollector trays and multiple spreader passes up to a thresholdapplication rate of 600 kg ha−1. Most other methods use justone row of trays and one pass of the spreader. The ES (Europe)test is the next best performing but is not preferred becauserows of trays are adjacent to one-another and are susceptibleto the near neighbour effect where dependency occurs betweenthe masses landing on nearby trays due to time dependentmachine parameters. However, because the ES (Europe) test isa one pass test, the near neighbour effect will be undetectedand the time dependency may carry through to the bout widthcalculations resulting in an erroneous result outside the con-fidence limits given here. To ensure independence, the rowsin an international test method should be spaced as far apartas feasible.
The ISO (i) and (ii) (World) and the Spreadmark (NZ), allproduce the same curve for the estimated probability, P(MViN0.15), as a function of specified bout width. However,ISO (ii) (World) has higher resolution of these probabilitycalculations because they are performed for bout widthsseparated by 0.25 m instead of 0.5 m. This work calculatesonly a single point probability (i.e., at a specified bout width),
not a weighted probability based on nearby values. If weightingmethods are used, the higher resolution of the ISO (ii) (World)test method will prove more accurate than its sister method.The ASAE (USA) test method is not preferred because thedata collected is sparse; interpolation methods are not onlynecessary but more susceptible to variability than for othertest methods.
Most test methods use a 0.5×0.5 m trays because they areeasy to handle. The ISO (ii) (World) test is different, but its0.25×1.0 m trays have the same area and (it can be assumed)the same variance. The advantage of the ISO (ii) (World) testtrays is that the transverse resolution is improved. However,increasing tray size is desirable because it reduces the varianceabout the mean, but, it must not comprise the transverseresolution of the bout width calculations. Therefore, longertrays are desirable, rather than wider trays. The relationship isgiven be Eq. (12) where variability ratio is related to the squareroot of the area ratio between a tray size for which statistics havebeen collected (1) and a new proposed tray size (2)
r2r1
¼ffiffiffiffiffiffiffiA1
A2:
rð12Þ
For example, if tray size increases from 0.5×0.5 m to0.5×2.0 m the standard deviation reduces to half the original
349J.R. Jones et al. / Powder Technology 184 (2008) 337–351
value. This assumes normally distributed data with theadditional advantage of eliminating b2.0 m periodicities (ofthe type seen at −3.75 m longitudinal position for the 80 kgha−1 data in Fig. 4). The benefit of longer trays would be furtherenhanced by having multiple passes before the fertiliser iscollected, but practically long trays become unwieldy tohandle. Therefore, additional passes are preferred to largertray sizes.
The ACCU Spread (Aus) test method represents the besttest method with the necessary experimental expediency forcost effectiveness. Further improvements in bout widthcalculations are possible by reducing experimental variabilityby increasing the number of rows, defining a higher thresholdapplication rate for multiple passes, and increasing thelongitudinal length of the trays. However, the need to do thisdepends upon the spreading precision required by theworldwide agriculture industry, which is an issue of spreaderdesign to deliver a controllable spread pattern linked togeographic information system (GIS) maps for variable rate
Fig. 11. Probability ofMVboutN0.15 as a function of specified bout width for the internand C. 150 kg ha−1. The international tests are; (a) ISO(i) (World), (b) ISO(ii) (World)shown for the two round-and-round overlap scenarios.
application. Current spreader technologies are well behindour ability to determine the ground fertiliser requirements.The arrival of GIS into agriculture provides a significantdriver for improvement, and inevitably it must be linked tothe quality of the certification testing methods. This paperdemonstrates that the ACCU Spread (Aus) test method is thebest at predicting the certifiable bout width. It therefore re-presents the current cornerstone quality standard upon whichfurther improvements in fertiliser spreading technology canbe assessed.
5. Conclusions
A large fertiliser spreading field trial was performedconsisting of 18 adjacent rows of 80 trays, each 0.5×0.5 min size with trays removed for the wheels of the spreader.The data was analysed for (a), time dependent behaviours inthe longitudinal direction for trays located at commontransverse positions; and (b), the sample mean and variance
ational spread tests for nominal application rates of A. 80 kg ha−1, B. 100 kg ha−1,, (c) ES (Europe), (d) ACCU-Spread (Aus) and (e) Spreadmark (NZ). Results are
Fig. 11 (continued ).
350 J.R. Jones et al. / Powder Technology 184 (2008) 337–351
for all transverse tray positions from the large field trialwere used to reconstruct each of the six internationalspreader tests. Each reconstruction established the 95% CIfor the expected values and the confidence in the bout widthcalculation.
Time dependent behaviours were detected statistically usinga technique termed here, the near neighbour effect. The 80 and100 kg ha−1 application rates showed no near neighbour effect,but an effect was observed at 150 kg ha−1. This findingdemonstrates that test methods should not employ adjacent rowsof trays, which rules out the ES (Europe) test as a preferredmethod. Instead, rows of trays should be placed as far apart asfeasible.
Reconstruction of all international test methods using thelarge field trial data revealed the ACCU Spread (Aus) testmethod was superior to the other test methods. It had thenarrowest 95% CI range for expected values and could predictthe certifiable bout width to within a single 0.5 m tray (forurea over the application rates tested). The ES (Europe) test
method was second best, but is not preferred because ofits susceptibility to the abovementioned near neighboureffect that can bias the bout width calculations. The ISO (i)(World), ISO (ii) (World) and Spreadmark (NZ) tests wereall comparable. The ASAE (USA) method is not preferredbecause the trays are spaced widely apart across the swath,resulting in sparse data which limits the ability to makeaccurate bout width calculations. This paper does not exploreinterpolation or weighting techniques, which can be used forall test methods, but are essential for the ASAE (USA) testmethod. When using such techniques the transverse reso-lution becomes important and therefore the ISO (ii) (World)method has an advantage over the ISO (i) (World) method,to which it is otherwise identical, because its trays are 0.25 m(c.f. 0.5 m).
The ACCU Spread (Aus) test method represents the currentcornerstone quality standard upon which further improvementsin fertiliser spreading technology can be assessed. Furtherimprovements are possible by lowering variability by using
Fig. 11 (continued ).
351J.R. Jones et al. / Powder Technology 184 (2008) 337–351
multiple rows of trays, multiple passes of the spreader andlonger trays.
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