mam mafia-WE. m3 cs-aamcmsgxrgcs Thesis for fire Deg?” o§ M. S. MICHWAN STATE UNIVERSE” Eritng Gwald Nybca‘g 1967 LIBRARY THESIS ' . M. l . SD” ABSTRACT GRAIN COMBINE LOSS CHARACTERISTICS by Erling Orvald Nyborg A digital computer program was written to analyze grain combine loss data. The program compared the goodness-of-fit of three simple correlation models (expressing loss as a function of feedrate) and of two multiple correlation models (expressing loss as a function of feedrate and grain/straw ratio). The use of feedrate (weight per minute of straw and chaff) and of throughput (weight per minute of grain, straw and chaff) as independent variables was examined by comparing fits of the correlation models. The effect of yearly climatic variation on crop variables was examined in order to determine the validity of comparing loss data from machines tested in different years and crop conditions. Analysis of loss data from nine combines, each tested in five crop conditions, and from one combine tested in twenty crop conditions, over a four year period, indicated the following: (1) A multiplicative model, percent loss = a (feedrate)b (grain/straw)c, described rack, shoe and cylinder performance in fields of varying grain and straw yield. In uniform fields, more simplified models best described performance. (2) The use of "feedrate" as an independent variable accounted for more of the variation in grain loss than did the ERLING ORVALD NYBORG use of ”throughput", when grain/ straw variation was neglected. When grain/ straw variation was considered, both variables described the process equally well. (3) Unless some measure is made of crop physical properties (perhaps straw break-up and ease-of threshing) comparison of loss tests, conducted in different crop conditions and growing seasons, is not valid. A standard combine can, however, be used to make valid comparisons. Approved 7%?. M‘% Major Prdfessor Approved W M QQL Department Chairman GRAIN COMBINE LOSS CHARACTERISTICS BY Erling Orvald Nyborg A 'i H ESlS Subrnittvd to Michigan State University in partial fulfillment of the requirenu-nts for the. degree Of MASTER OF SCIENCE E Department of Agricultural Engineering 1967 ACKNOWLEDGMENT The author wishes to thank the following: The employees of the former Saskatchewan Agricultural Machinery Administration. (All data was collected by A. M. A. during the 1961 to 1964 test seasons.) Major professor H. F. McColly (Agricultural Engineering), minor professor R. T. Hinkle (Mechanical Engineering) and Dr. S. P. E. Persson (Agricultural Engineering). ii TABLE OF CONTENTS Page ACKNOWLEDGEMENT ii LIST OF TABLES vi LIST or FIGURES vii TERMINOLOGY ix LIST OF SYMBOLS x INTRODUCTION 1 Basis For a Problem 1 Literature Review 1 Objectives 2 DATA COLLECTION 4 Field and Crop Conditions 4 Collection Technique 4 Comparison to a Standard Machine 5 Time of Collection 7 Sample Processing 7 PARAMETERS AFFECTING COMBINE PERFORMANCE 9 Purpose of Loss Tests 9 Interdependence of Parameters 9 Elimination of Variables 11 Moisture content 11 Tailings 11 Cylinder loss and grain damage 12 Total Loss 12 Crop Variables 13 Methods of Expressing Variables 14 MATHEMATICAL MODEL FOR REGRESSION ANALYSIS 16 Need for a Model 16 Simple Model, Constant Grain/Straw Ratio 16 Rack loss model 16 Shoe loss model 17 Cylinder loss model 21 Including Variation in Grain/Straw Ratio 22 Multiple Model 23 DATA ANAL YSIS Technique of Analysis Simple Correlation Transformation of data Method of least squares Checking the Goodness of Fit, Simple Model Simple linear correlation coefficient Coefficient of determination Standard error of the estimate Limits of prediction ANOVA for significance of regression Plot of residuals Expanding the Simple Case into Multiple Correlation Checking the Goodness of Fit, Multiple Model Simple correlation coefficients Partial correlation coefficients Multiple correlation coefficient Multiple coefficient of determination ANOVA for significance of additional regression due to Grain/Straw Standard error of the estimate Plot of residuals Interpretation of results DIGITAL COMPUTER PROGRAM Description of Analysis Performed by the Program Interpretation of Sample Output RESULTS AND DISCUSSION Best-Fit Models Rack loss Shoe loss Cylinder loss Dependence of Loss on Grain/Straw Variation Feedrate or Throughput as an Independent Variable Comparing Tests Conducted in Different Years Loss surfaces Comparison to characteristics of the standard combine CONCLUSIONS REFERENCES iv 24 ') L. Z4 Z4 25 26 26 Z7 Z7 27 28 28 3O 31 31 32 32 33 34 34 34 34 36 36 37 43 43 43 45 45 48 49 54 54 59 b4 66 APPENDIX I Fortran Digital Computer Program for Combine Loss Analysis Program LOSSCALC Subroutine CALCULAT Subroutine GRAPH Subroutine FIT Sample data cards Instructions for Using the Program Data preparation Interpretation of confidence intervals Graphs and residual plots Zero loss 68 68 68 69 7O 74 92 93 93 94 94 95 Table Number U‘IstUONH LIST OF TABLES De sc ription ANOVA, Ho:B1 : 0 ANOVA, Ho: B2 : O Best-Fit Models for Rack Loss Data Best-Fit Models for Shoe Loss Data Best-Fit Models for Cylinder Loss Data V i Page 28 35 44 46 47 Figure Number 1 2 10 11 12 13 14 16 17 LIST OF FIGURES Description Batch Collector Batch Collector Drive Grain Tank Solenoid Distance Counter Weighing a Sample Processing in Batch Separator Final Cleaning Schematic Cross-Section View of a Combine Rack Loss versus Feedrate, Linear Model Best-Fit Rack Loss versus Feedrate, Exponential Model Best Fit Rack Loss versus Feedrate, Simple Exponential Model Best Fit Residual Plots Raw Data, Intermediate Calculations and Scatter Diagrams Simple Correlation, Linear and Exponential Models Simple Correlation, Simple Exponential Model and Calculations for Conversion to 1V'Iultipl e Correlation Multiple Correlation, Linear and Multiplicative Models Raw Data, Intermediate Calculations and Scatter Diagrams (Throughout Basis) Vii Page 19 20 29 39 4O 41 42 50 18 19 20 21 22 23 24 25 Simple Correlation, Linear and Expcmential Models (lihi‘OUgiiput Basis) Simple Correlation, Simple Exponential Model and Calculations for Conversion to Multiple Correlation (Throughput Basis) Multiple Correlation, Linear and Multiplicative Models (Throughput Basis) Rack Loss Surface for Standard Combine in Wheat Shoe Loss Surface for Standard Combine in Wheat Cylinder Loss Surface for Standard Combine in Wheat Comparison to Standard Combine at a Constant. Grain/Straw Ratio Comparison to Standard Combine at a Constant Grain/Straw Ratio 51 52 58 61 .u. n . »'-. Name Cylinder loss Exponential model Feedrate Grain/Straw ratio Multiple linear model Multiplicative model Percent loss Rack loss Residual Shoe loss Simple exponential model Simple linear model Tailings Thr oughput Whitecap T ER IVlINOLOG Y Meaning unthreshed grain in the rack effluent and shoe effluent percent loss 2 a (feedrate) the rate (pounds per minute) of straw and chaff passing through a combine the weight ratio of grain yield to straw yield percent loss I a + b (feedrate) + c (grain/ straw) percent loss : a (feedrate) (grain/straw)C weight loss weight total grain X 100 free (threshed) grain in the straw rack effluent A the difference, (Y—Y), between an experimentally determined value for Y and a predicted value for Y free (threshed) grain in the shoe effluent a (b)feedrate percentloss percent loss 2 a + b (feedrate) material which falls through the chaffer but passes over the sieve and is returned to the cylinder for re—threshing the rate (pounds per minute) of straw, chaff and grain passing through a c ombine an unthreshed spikelet of wheat in the combine grain tank ix Symbol :hA CL E( Y) calc. tab. FR G/S Ho RL LIST OF S YIVIB OLS Meaning y-intercept of fitted regression line confidence interval for prediction of Y, given an X slope of fitted regression line coefficient of determination 100(r2) % cylinder loss, percent of yield expected value of Y "F-distribution" statistic, calculated value "F—distribution" statistic, from F-table feedrate, pounds per minute grain to straw ratio null hypothesis rack loss, percent of yield simple correlation coefficient, loss on feedrate simple correlation coefficient, loss on grain) s raw simple correlation coefficient, feedrate on grain/ straw partial correlation coefficient, loss on feedrate with grain/ straw held constant partial correlation coefficient, loss on grain/straw with feedrate held constant "l H 11*. ~<> +<| ><| p "(D m X M M M N (\J M XY Illlllllplt‘ tiOl‘l‘fg‘lal‘ltHl i ()1"lil(ltfl“lf standard error of the estimate of Y shOe loss, percent of yield standard deviation of X standard (lt‘V’lé'il'lOll of Y covariance (X, Y) variance of Y "t-distribution" statistic: throughput, pounds per minute the mean of. the X~measures the mean of the Ymmeasures the predit ted value of Y y-intvrcepti of true regression line slope of true regres81online error tt-ri‘n in titted regression equation 8 um m a ti on -“ ) L. _ ram-x)“ .—. 2x - (11x) //n INTI R ()1 )U("‘ 1 Ii'(;)’I‘\'r Baiis tor the 'l)r1;)bl1=i'11 Evaluating the performance of a grain combine in a specific crop condition is complicated both by machine and crop variables. This makes comparison of perforinz-ince of one machine in two crop conditions difficult. It also makes performance comparison of two different machines in differing crop conditions impossible unless the effect of crop variables is understcmd. At present, there is much different e of opinion in how to evaluate combine performance. A logical approach to this problem would be of value both to manufacturer test (‘11--pai‘1:ineiits and public test agencies. Literature Review Examination of combine test reports from seven different .7, r‘\ public test agencies (1), and from tit'V'f‘l’al pl'lVéiiE}: test departments, indicates that there is rnuzith difference of Opinion in how to rate combine performance. Grain loss is c-,x}‘.1r¢css«-(i in several different ways (percent of yield, bushels pvl‘ at re, pounds per minute) and work rate is also expressed in several different xxays (pounds per minute of straw and chaff, pounds prr‘ ininute of straw, grain and chaff, pounds per n'iinute of grain, miles per hour, acres per hour). Numbers in parenthesis I‘t‘fvl‘ to piibiirn’iions 11: ted in ' References” R.) In most instances, no attempt has been made to compare performance of combines tested in different test seasons. A ”standard" comparison machine has been used at at least two of the public agencies (7), but reports on comparison to a standard are available from only one agency. Considerable work has been done regarding the effect of crop and machine variables on threshing performance (2,12) and separation performance (5, 6, 8, 9,11) but results of such studies have not been fully incorporated into combine test programs. In most instance, the approach has been to assume constant crop conditions in a test field and to simply express loss as a function of combine rate of work. Experiences from test work in Saskatchewan (13) indicate that selecting a uniform field for loss tests is nearly impossible. It further indicates that accounting for variation in crop variables, in a test field, is necessary both for determination of combine loss characteristics and for performance comparison of machines. Objectives The objectives of this research are: (1) To determine the important parameters affecting combine loss characteristics. (2) To determine mathematical models which describe combine performance as a function of machine and crop variables. (3) To test the goodness of fit of these models by comparing them for several combines in several loss conditions. (Comparison "1, V»... \ cu will be on loss data from nine combines, each tested in five crop conditions and on loss data from one combine tested in twenty different crop conditions over a four year period. This represents a total of 576 individual loss collections.) (4) To arrive at a method for comparing performance of two different machines on the basis of loss tests conducted in dissimilar crop conditions. (5) To write a digital computer program to analyze combine loss data, determining the best-fit regression equation. 1"- ~ DATA C OLLEC TION Field and Cr0p Conditions The data was collected in Saskatchewan during the 1961 to 1964 harvests, by the former Saskatchewan Agricultural Machinery Administration. The selected crOps represent typical field conditions occurring in the province. Test sites were selected on a basis of uniformity (level terrain, relatively weed free, uniform straw length, uniform maturity). All loss tests were conducted in windrowed fields. This served two purposes: It eliminated extreme variation in grain and straw moisture content and it enabled full loading of the test machines in light crops. Loss tests were conducted at dry grain moisture contents (spring wheat - below 14.6%, durum - below 14. 9%, barley - below 14. 9%, oats - below 14.1%). Collection Technique As outlined in (l3),abatcli collector (Figure 1), constructed so that it could be quickly coupled to any test combine, was used for collection of the rack effluent, shoe effluent and grain. Operation of the batch collector is as follows: A small engine (Figure 2) drives two adjustable conveyors, one positioned beneath the straw walkers and one beneath the shoe. When the combine reaches a stable operating condition, the bag mechanism is tripped, activating the grain tank solenoid (Figure 3), starting the distance counter (Figure 4) and activating a warning signal (light or buzzer) for the combine operator. Upon receipt of the signal, the combine operator starts a stop-watch. When the bags are full, the procedure is reversed. Collected samples were immediately weighed (Figure 5). Ten such collections, at ten different ground speeds, were made in each test field for each test combine and a "standard” combine. This was a test series. The Use of a Standard Machine As noted above, in each test series, loss data was collected for both the test combine and the ”standard" combine. The value of a standard is explained as follows: In each test series, loss characteristics of the standard combineale compared to those of the test machines. This allows indirect comparison of combines tested in different years and crop conditions. For example, in a 1961 wheat field, the capacity of machine A was 2 times the capacity of the standard combine at a certain loss level, while in a 1963 wheat field, the capacity of machine B was 1. 5 times that of the standard combine. This allows us to say that the capacity of machine A in wheat is roughly 1. 3 times that of machine B, at a certain loss level. Without the use of a standard, or without a method of assessing the importance of crop variables, this sort of comparison would be meaningless. Combine loss characteristics are very dependent upon crop growing conditions in a specific year. Batch Collector Batch Collector Drive Figure 1 Figure 2 Grain Tank Solenoid Distance Counter Figure 3 Figure 4 Time of C olle cti on Since crop conditions may change quickly during the day, loss collections were usually conducted in mid-afternoon when conditions were relatively stable. Loss collections for the group of test machines were collected in as short a period of time as possible, to reduce the effect of change in moisture content (collection of ten samples for one machine took approximately twenty minutes). Sample Proces sinJg Rough scalping of the samples was done with a batch separator (Figure 6), a modified small pull-type combine. The batch separator operates as follows: The rack effluent and shoe effluent are first passed through the separator, by-passing the threshing cylinder. This removes free grain (rack loss and shoe loss) from the effluent. The straw and chaff is collected as it passes through the separator. This material is passed through the cylinder of the batch separator, removing unthreshed grain (cylinder loss). Final cleaning of the samples was done on a fanning mill (Figure 7). Weighing a Sample Processing in Batch Separator Figure 5 Figure 6 Final Cleaning Figure 7 PARAMETERS AFFECTING COMBINE PERFORMANCE Purpose of Loss Tests Loss tests are a method of determining the performance characteristics of a complete machine. They are not an attempt at determining the performance of all the individual components of a combine, such as could be conducted during the intermediate design stages of a machine. Figure 8 is a schematic cross-sectional view of a grain combine, illustrating the points of importance in combine performance determination. Most of the components shown in Figure 8 are interrelated. The adjustment and performance of one component may affect the performance of several other components. For purposes of a loss test, it is necessary that the combine be adjusted to an optimum condition. Grain damage, straw break-up, cylinder loss, rack loss, shoe loss and free grain in the tailings should all be at a minimum. Under-cylinder separation should be maximized and the grain must be acceptable (reasonably free of chaff and whitecaps). Interdependenc e of Parameters In order to maximize performance, the interdependence of the parameters (Figure 8) must be understood: - under—cylinder separation : fl (cylinder speed, concave clearance, feedrate, moisture content, crop) 10 m mchHb mszzoo ZHSUE ¢ .mo 3H2, AdZOHBommammomo OHBSmeom £95.: 9.030: E 0.5 35:2 91%. \ ./ )chucou. 1005 cop: _ _>u .303 xuoc ll - cylinder loss : f cylinder speed, concave clearance, 2( feedrate, moisture content, crOp) - grain damage 2 f3 (cylinder speed, concave clearance, feedrate, amount of grain in tailings, moisture content, crop) - straw damage : f (cylinder speed, concave clearance, 4 moisture content, crop) - rack loss 2 f straw breakup, amount of tailings, feedrate, 5( crop) - shoe loss 2 f6 (straw breakup, feedrate, crop) Elimination of Variable s The effect of some of the above variables can be minimized as follows: Moisture content By windrowing the crop prior to loss collection, the moisture content of the straw and grain stabilizes at a uniform level. This reduces errors due to large variations in moisture content. Conducting all tests on crops that are relatively similar in moisture content (on "dry" grain) improves the validity of comparison between machines tested in different years. Collection of loss data in a short period of time reduces errors due to change in moisture content during c ollection. Tailings Before the test, chaffer, sieve and fan settings must be adjusted to minimize (if possible, eliminate) free grain in the 12 tailings and minimize shoe loss, while maintaining an acceptable sample in the grain tank. These adjustments eliminate further concern about the amount of tailings since the optimum shoe setting, for minimum shoe loss, minimum tailings and an accept- able sample of grain, has been obtained. Cylinder loss and gain damage Before testing, an optimum cylinder setting must be obtained. This is the combination of cylinder speed and concave -to-cylinder clearance which minimizes cylinder loss, crackage and straw break- up for a specific crop and crop condition. This adjustment eliminates further concern about the effect of straw break-up on rack and shoe performance and eliminates concern about the amount of under- cylinder separation, since this is the necessary setting to obtain maximum threshing efficiency. Total L05 3 With the simplifications introduced above, it is now apparent that: - total loss 2 f7 (feedrate, crop variables). The components of total loss are: total loss 2 (rack loss + shoe loss + cylinder loss + pickup loss + body loss). To simplify analysis, body loss and pickup loss can be excluded in analysis of the combine. Body loss is leakage of grain through the body of the machine. It is an indication of quality '-w’ 5-"- AA. 1'“ . .‘.A. u ,rn ~ ‘ 13 control during manufacture rather than of combine performance. Although of concern in small seed crops (rapeseed, clover, alfalfa, etc.) it is of little concern in grain and hence need not be considered in loss tests. On the other hand, pickup loss (3,16) is a function of the type of windrower, stubble height, time of windrowing, pickup adjustment, ground speed, crop yield, straw length, moisture content, weathering, etc. In light crops pickup loss may be the largest component of total loss, whereas in heavy crops it is negligible. Since the pickup mechanism is a machine in itself, it can be evaluated independently from the combine, and need not be considered in loss tests on a combine. After these simplifications, it is apparent that only rack loss, shoe loss and cylinder loss (dependent variables) and feedrate and crop conditions (independent variables) need be determined in combine 105 s te sting. CroLVariables Which crop variables should be measured? Using the simplifications introduced above, for a certain type and variety of crOp, of constant grain moisture cmtent and constant straw moisture content, only two crop variables, grain yield and straw yield, remain undescribed. The final result is: - total loss 2 f rate of work, grain yield, straw yield). 10( 14 Methods of Expressing Variables Loss can be expressed in two meaningful ways: ,- unit weight of grain loss per unit field area (i. e. bus/acre, kg/ha) - loss as percent of total grain (i. e. percent of yield). The second method (percent of yield) is most useful since it allows easy comparison of performance in different crop conditions. Rate of work can also be expressed in several ways: - ground speed (i. e. miles/hour, km/hour) - field rate (i.e. acres/hour, ha/hour) - feedrate (i. e. lbs/minute of straw and chaff passing through the combine) - throughput (i. e. lbs/minute of straw, chaff and grain passing through the combine) The first two (ground speed and field rate) are not good parameters for use in comparison since they do not take into account the actual amount of material passing through the combine. One of the purposes of the following analysis is to decide whether feedrate or throughput is the best parameter describing work rate. Grain yield and straw yield can also be expressed in several ways: - grain yield (i. e. lb/min. , bus/acre, kg/ha) - straw yield (i. e. lb/min, tons/acre, kg/hr) - grain to straw ratio (i. 6. weight grain/weight straw) DIOCE 15 The last method (grain/ straw ratio) is the most sensible since it avoids confusion with units of measurement and allows direct comparison between different field conditions. Using the above terminology, the final model for the process is: - loss (% of yield) = £11 (feedrate, grain/straw), or, - loss (% of yield) = £12 (throughput, grain/straw). MATHEMATICAL MODEL FOR REGRESSION ANALYSIS Need for a Model Before regression analysis can be conducted on the collected data, a mathematical model must be determined so that the data can be examined for closeness of fit to the model. The model should explain both what is expected from theory and what is obtained experimentally. Simple Mpdel, ConflanLGrainLSLraw Ratio Consider a loss test conducted in an ideal uniform field (a field of constant grain yield and constant straw yield). Since the grain/ straw ratio is constant, it will not enter into the analysis. The models for rack loss, shoe loss and cylinder loss may now be constructed as a function of only feedrate (or throughput). Rack loss model At low feedrates, separation through the concave is maximum and the mat of material on the straw rack is of minimum thickness, resulting in efficient separation and negligible loss. As feedrate increases, separation at the concave decreases (non- linearly) resulting in more free grain on the rack. As the amount of material on the rack increases, the oscillation of the straw on the upper portion of the rack virtually ceases. (This can be verified by observing straw rack action at various feedrates, in actual operating conditions.) Once a certain feedrate is reached, 16 17 separation on the rack virtually ceases and a small further increase in feedrate results in an exponential increase in rack loss. Indeed, the loss-versus -feedrate curve probably is asymptotic to some vertical line. It then appears, that if a loss test is conducted to a sufficiently high feedrate, an exponential model (rack loss 2 a (feedrate)b) is a reasonable choice. However, if the runs are all at low feedrates, a linear model (rack loss 2 a + b (feedrate)) or some intermediate model, may be the best fit. To illustrate this point, Figures 9 to 11 show plots of three different sets of loss data. The 90% confidence belts are shown as the shaded area. In Figure 9, in wheat, a linear 1 3 model, RL = - 6.086x10- + 5. 532x10“ (FR), is the best fit. In Figure 10, in barley, an exponential model, RL 2 9. 201x10-6(FR)2' 654 is the best fit. In Figure 11, in wheat, a simple exponential model, RL = 2.587x10“1 (l. 014)FR, is the best fit. Since the best fit model is a function of crop conditions and the range of feedrates achieved, in a series of loss measurements, a regression analysis program should compare all three of the above rack loss models and thus select the best fit. It is also apparent, that for a field of constant grain/ straw ratio, both feedrate and throughput will serve equally well as an independent variable in the loss model. Shoe loss model It is expected that, at high feed rates, the layer of grain and chaff on the shoe will become deep enough to cause matting and nearly complete loss of separation ability (this can be verified Sm 5mm o mane ammo: $3.51 3 . mm. ms mmoq 84m 2:52:34 $253... 08 Can ................ . . . .. ...... ............................................ .................. .............. 11... .1...... .2 ....................... .................................. ..................................... .....1... ... ...“..a. ............................ ......... .......................................................................... ......................................................... ......................................... ................ ooooooooooooo .............. nnnnnnnnnn . u a ........................................ ................... 18 .LNElOHad "" $301 MGVH OH 55ch EH5“ 9mg ammo: Qfigmzomwmgma mmoq Modm .Z_<<\.mm._ I Bison—mm“— 08 8. o.— 8— ON— 8— o. on on o. on 19 n— .lNBDlle -SSO‘I )IDVU \O‘ a 20 can S @555 a: 3.3 ammo: qfiszmzomxm Bamdaénmmm .m> mmoa moss .Z :2ng lwh ' - , ' ' o. Fcalc. Ftab. , reject Ho, otherWlse do not reject H This analysis of variance is explained in Table 1. Table 1. ANOVA, Ho:B = O 1 Source of Degrees of Variation Freedom Sum of Squares Mean Square F Total (n - 1) Z Z Y Regression l r'2 E 2 r2 E 2. 2A F — yx1 y yx1 y calc. Deviation from 2 2 >3 2 Regression (n - 2) (l—r x )E Z (l-r x FIT-L2): B (residual y‘1 Y Y 1 ~ variation) Residual plot As indicated in (4), the above tests niilst be used with caution and can give misleading results when comparing models. The. plot of residuals, (Y - Y), against feedrate gives a Visual indication of the goodness of fit, when conlparing the three models. Figure 12 illustrates some of the information which may be obtained from such a plot. 29 good fit calculation error I N r Variance not constant need for extra terms RESIDUAL PLOTS FIGURE 12 3O Expanding the Simple Case into 1\/iult:iple Correlation Multiple regression of two independent variables as a sequence of straight line regressions is used in transforming the simple models into multiple models (introducing G/S variation).— Let the desired solution be: Y=a+bX1+cX‘Z ,‘ This gives, Y = a + b X the result obtained Regress Y on X 1 1 1, 1. in the previous simple correlation. A Calculate the residuals, (Y - Y). This was also done in the previous simple correlation. Regress X2 on X1. This gives, X2 = a2 + ble° A Calculate the residuals, (XZ - X2). A A This gives, (Y - Y) = b X -X A A Regress (Y - Y) on (X - X 3( 2 Z). Z 2.)' Note that since the sum of the residuals must be zero, this line passes through the origin. C ombine the equations: (Y -(a1+ b1X1)) : b3(XZ - (a2 + bZXl)) A Y = (a1 - b3a2) + (b1 _ b3bZ)X1 + b3XZ A Y=a +bX +bX 4 4 1 3 Z The last equation is the desired multiple regression of Y on (X1 and X2). The above analysis is carried out for the two multiple cases: (1) the linear model: RL = a + b(FR) + c ((3/5) 31 (2) the multiplicative model: RL = a(FR)b ((3/5)C which must be transformed to the linear case, with logarithms, before the above analysis can be carried out: ln RL =1n a + b 1n (FR) + C 1n (G/S) Two more complicated Inultiple models could be constructed from the simple correlation models by combining the linear model for Y on X with the exponential model for X on X and by combining 1 Z l’ the exponential model for Y on X1 with the linear model for X2 on X The latter two models were not used in the analysis. Results 1. from the first two models (linear and multiplicative) indicated that the more complicated models were unnecessary. CheckinLthe Goodness of Fit, Multiple lVlodels The following methods are used to test the goodness of fit of the multiple correlation models: Simple correlation coefficients (1)1‘2 =(Z ,lZ/ZZZ Z yxl yxl y xl r : rdX , -1: r7, :1 YXl y1 ”1 This was calculated previously in the simple model analysis. 2. Z (2)1‘ -‘~ (73 l/2 2 Z Z yxZ yxZ y x2 r = r2 , -l < r < 1 The simple correlation coefficients represent the linear correlation between any pair of variables, disregarding the remaining variable. Note that the sign of the simple correlation coefficients is determined by the sign of the sum within the brackets in the numerator. Partial c orrelation c oefficients (1)rzx,x=(rX-r rxx>2/(1-r2)(1-r:X) V1 2 y1 sz 1 2 “‘2 12 = (r2 , - l _<_ r . :1 YXl X2 y"‘1 X2 YXl X2 (2) r2 = (r - r r )2/(1 - r2 )(l - r2 ) sz Xl sz YXl Xlxz 1 X1x2. r : ’rz , -l _<_ r :1 sz Xl YXl'xz YXZ'XI The partial correlation coefficients represent the relation between two variables, when one or more of the remaining variables is held constant. Multiple correlation coefficients R=\(RZ,O:R:1 The above formula shows the relationship between the multiple 33 correlation coefficient and the partial and simple correlation coefficients. Serious truncation errors, resulting in values of R > 1, may occur if this formula is used in a computer for computation of R. The following basic definition of R yields correct results when used in a computer: n A -—-Z >31 alc. Ftab. ’ This analysis of variance is explained in Table II. Note that the first part of this table is similar to Table I. This analysis tests the value of the additional term (grain/ straw variation). Standard error of the estimate (S. E. )2 = mean square, deviation from multiple regression _ Z S.E.y-\/(1-R )Zyz/(n-3) R esidual plot As explained previously, the most important method of determining the necessity of the additional term (grain/straw) in the equation is by examining the improvement in the residual plot, as compared to the residual plot of the simple model. Integpretation of results In order to determine the validity of the multiple model as compared to the simple model the following criteria are used: 1. An improvement in the residual plot. 2. The additional regression due to X should be significant. 2 3. A decrease in the standard error of the estimate. 35 Table 2. ANOVA, Ho: B2 = O Source of Degrees of Variation Freedom Sum of Squares Mean Squares F Total (n-l) Z Z Y Regression 2 due to X 1 r (2 Z) 1 Yxl Y Deviation 2 from simple (n-Z) (l-r )2 2 regression yX1 Y Additional regression l r‘2 . (l-r2 )2 z r2 (l-r2 )- F :1- due to X2 yx2 xl yx1 y yxZ-xl yxl calc K '2 ‘ = J y2. Deviation from Z 2 Z 2 multiple (n—3) (1-R )2 2 (l-R ) 3) = K regression y n- 36 4. A noticeable increase in the correlation coefficient (i.e. , R > r ). yx1 5. At least a 1% increase in the coefficient of determination. DIGITAL COMPUTER PROGRAM Degcrimon ovanalysis Performed bLthe Program The FORTRAN loss analysis program, written for the M. S. U. CDC 3600 computer is shown in Appendix I. The Program performs the following functions: 1. Print out of raw data. 2. Calculation and printout of performance parameters and crop variables. 3. Printout of scatter diagrams (rack loss (%) vs. feedrate (lb/min), shoe loss (%) vs. feedrate (lb/min), cylinder loss (%) vs. feedrate (lb/min)). 4. Fitting the loss data to the mathematical models and comparing goodness of fit: The simple linear, exponential and simple exponential models are fitted by the method of least squares. Confidence limits (90% level) are calculated for the three equations. The F statistic (for the significance of regression due to feedrate) is calculated and tested for significance at the 95% level and 97 1/2 % level. The simple correlation coefficients, ryx , coefficients of determination l and standard errors of the estimate are calculated. Finally, the graphs of residuals vs. feedrate are printed. This data allows comparison 37 of the three simple models for rack loss, shoe loss and cylinder loss. The regression of grain straw on feedrate is now conducted for the linear and exponential models. The simple correlation coefficients, rxlxz, are determined. The regressions of loss residuals on grain/ straw residuals are calculated, using both a linear model and exponential model. The multiple correlation equations are calculated for both the linear and multiplicative models. The coefficients of simple correlation, rYXZ' and the multiple correlation coefficients, R, are calculated. The standard errors of the estimate are determined and the F statistic (for additional significance of regression due to grain/ straw variation) is calculated and tested for significance at the 95% level and 97 1/2% level. The graphs of residuals versus feedrate are printed. This data allows comparison of the two multiple models for rack loss, shoe loss and cylinder loss. Interpretation of Sample Output Figures 13 to 16 show output of the computer loss analysis program for a loss test on the standard combine in a non-uniform field of Selkirk wheat. Raw data, crop conditions, intermediate calculations and scatter diagrams are shown in Figure 13; Figures 14 to 16 illustrate the fitting process. Comparison of the three simple correlation models shows that either the exponential models or simple exponential models are the best fit for rack loss and cylinder loss, while the linear model is the best fit for shoe loss. Examination of Figures 15 and 16 38 shows a high negative correlation between loss and grain/straw ratio. Comparison of the two multiple models and comparison of the multiple models to the simple models shows that the addition of grain/straw variation significantly improves the fit in all cases. The multiplicative model is the best for rack loss and cylinder loss whereas the linear multiple model is the best fit for shoe loss. Hence, in this example, the best fit equations are: 1.350 -3. 177 RL = 1.125x10-3 (FR) (G/S) SL = 2.085 - 6.853x10'4(FR) - 1.471 (G/S) 3 1. 278 (FR) (G/S)-1'529 CL = 2.9olxlo' The above example represents data from one combine in one crop condition. These results are not necessarily indicative of what may be expected, as is illustrated in the following discussion of results. '1 HZMHDM‘ “U50!- not fivubfi’ujog.‘ QOODOOOOOIIQQIOIOIOIUOOOI.IOU-o-OIOOOOOIOIOIOOCIIC “ICUIN5 Hf 02'" unosg_ ,, N1 39 Inn A DATE "lice-o4 900- slain 01510105_-Iln£--- .57503.1n,0~0£F ._.£Bal§ RACK SHOE CYLt~DER IN" LO500 0.25 01.00 2.00 3.0.0LLLL3L c. 0.17 t 0.39 I 72.0'. 4?.‘0 0.2‘ 30.70 1.0" 18.00 1.50 .‘.24 0.05 12.00 01-:0 0.2: 20.00 2.00 25.00 0.27 0.21 0.: Run S'H04 A‘D TO'AL PEEERITE BACK 1 SAGE - tCYL1~DE8 SPEED 009K 0072 GRAIN RAIN/SYRAI CHA‘F tfiAl- Loss Loss LOSS YIELD RATIO ¢L=S.1 tLES.) tLBS./“l“.) fPERCEHT), (9&50£011_a1££&£E077-.(NILE/noun: (acne/noun) (LBS./Acnsl 1 34.40 27.02 .. .“21.&J --h_..n.:1 , 0.07 0.70 _1.71.7 2.51 1372.44 0.00 9 37.41 ‘e.5° 69.02 0.44 0.06 0.49 1.28 1.00 2142.29 0.90 3 01.40 34.54 05.94 . 0.35 . - 0441......_..LIL_T 1.23 1.79 2450.44 1.10 4 31.‘6 I4.44 00.72 0.20 0.05 0.7! 1.92 2.00 1094.20 1.09 5 29.00 29.92 99.90 , 1.44 --0101__s - i. 2.20 3.20 1160.20 0.09 A 39.‘2 '4.6' 9-.05 0.59 0.49 0.09 1.47 2.14 2001.10 1.07 7 32.21 .90.79s..- 125.54 -i, -1.01, - 0.0: 1.01 2.50 3.04 1760.14 0.03 I 34.41 771.50 14°.“ 7.29 i 1.17 4.13 2.00 3.02 1779.56 0.40 9 29.00 ’6.04 119.94 . 1.09 0.01... _2413 3.05 4.93 1910.02 0.87 at 52 Ans-10 2 when! satnlflt ulnoanu 3 APCOLA 17-0-04 «00- ItS@u«3$3cc m\o mchmS 65:53 5:93me 33 d 25¢: @3338 mUEE SHOES: @952 95.258 @923 m 5539598 @355 333w SHOES: .@mcmu @5353 @mumfi N 53d@comx@ 5655 c5855 .@u.mnv@@w 85?:me 32 an .392; @3E5 NA 33m m 0 mad Hm> .@m:m.n @5353 @mnmd o @>S@3333E m\o wctflnmxr .@wamu @umhw@@m Bod N Haas: @3338 o 55G@comx@ @385 m©5d Spots: .@m§mp @5HU@@H @wn.m~ m. 53d@comx@ 0 figs: @385 MM 550 m\0 wcw>um> w @>S.m33338 o 58:: 23:58 0 53:92:58 @385 332% EH83: N 53G@Coax@ o H@@GS @385 CH >@3@m m 0 m5 Hm». .@wcmu 36.353 @933 m 93.533335 m\0 mcfnumx/ .m@umnv@@m 33 c 23:: @3338 o 55:9893 @385 mwfigm SHONE: 6mg?“ 95.353 @wnmfi N 53:9333 £53m 8983.9 .m@umnv@@w 33 N 58:: @385 m; 5@£>> fih 5@m meBdGEEOU UZBEEOU new 5602 5vo§ monougfiflomz QOHU mo >oa@nw@nh mo H@£EDZ damn” mmod Momm How 3352 arm-59m .m 283 45 Shoe loss Table 4 illustrates the results of comparing shoe loss data, using the five correlations models. Although grain/straw variation influenced shoe loss, its influence was not as great as in the case of rack loss. Exponential models produced better fits than linear models only in those cases having high shoe loads (much chaff and straw break—up). The fact that linear models produced the best fit in oats, in twelve out of thirteen cases, is explained by the low shoe load. (The chaff consists mainly of glumes which offer little hindrance to separation.) Cylinder 105 s The results of comparison of cylinder loss data, using the five correlation models, is shown in Table 5. The exponential model gave a better fit than the simple linear model only in hard- to-thresh crops, when the range of feedrates obtained in the test was large. When loss tests were conducted in easy-to-thresh crops and all runs were at relatively low feedrates, the simple linear model produced the best fit. The inclusion of grain/ straw variation significantly improved the fits in non-uniform fields. The ease of removal of kernels from the heads and "slugging" of the cylinder at low feedrates, explain why linear models usually produced the best fit for cylinder loss data in oats and rye. 46 3080 @3353 >83 .@m8.mu @5353 mmumfi m @>3533338 535.353 m0 @w8dn 303 a 8.5083 @3338 538@8093 @385 538@803X@ 535.358 m0 @m8mn 303 w .5583 @385 NH 93m 8 33825338 m\0 9838.55. .3503 5085 33 p 8.5983 @3338 o 538@8oaxo 5385 0 53858095 5353 88038: .3503 5085 30H 5 8.5583 @385 m3 550 m\_U 883 803.5558, @wan .3503 @085 833 N nut/3.5033338 o 8.5@83 @3338 o 538@80nwx@ @385 5353 880385 .353 5085 833 m 53858095 5353 880.38: .3503 @085 303 m 8.558: 5385 OH >535m m\U 98385.? .3503 @085 833 .3585 @3350, m 993583338 m\U w8w>nm> .3503 @085 303 o ud@83 @3338 0 53808095 @385 o 538@8omx@ 5353 8.8038: .3503 @085 303 o .5583 @385 03 52:5 firm 5@m 5803585800 3858800 80m 5302 5602 mono-@83052 3080 m0 >08odv@8.m m0 850,832 3mm 5504 8:5 .85 53502 38.395 .5 2an 47 N 338853858 m\U w8385> 855837031555 N 8558: @3338 0 538580385 5385 0 538580385 3558370785555 3 8.5583 @385 w 5%3 H 58535033338 m\0 m8>85> 85583-078555 m 8.5583 53338 0 538580385 5385 0 538580385 £5583uouu>555 m 8.5583 5385 m 5350 m\0 w8385> 855837073853 m 5>35033338 m\U M83855. .355883u03u>55@ v 8558: 53338 0 538580385 5385 0 538580385 35583-03u>55@ m 8.5583 5385 OH 35353 m\U m83n85> 855837073853 3 5853583338 m\U m8385> 355883-03..%555 c 85583 53338 55583553 0 538580985 5385 30 5m858 5w85~ 35583-03485: 5 538580985 £558fluuouu>555 m 8583 @385 03 3.5533 3h 553 5803585800 3858800 803 5302 5302 3080-583052 3080 30 >0853U58h 30 850,882 55D 5503 8538330 803 55302 ”Fm-355m .m 53.55 48 Dependence of Loss on Grain/ Straw Variation In all crops and all crop conditions (fifty-four machine—CrOp combinations) the sign of the simple correlation coefficient, r , (loss regressed on grain/straw, disregarding variation in feedrazte) was negative, whenever“ there was any appreciable variation in grain/ straw ratio in the test field. Considering all combinations, the sign was negative in 85% of the cases for rack loss, in 76% of the cases for shoe loss and in 85% of the cases for cylinder loss. In those cases in which ryx2 was positive, the variation in grain/ straw ratio was small and additional regression due to grain/straw variation was insignificant. A decrease in grain/ straw ratio should, therefore, result in an increase in percent loss, at a constant feedrate, if other crop variables are held constant. Results of the multiple regression indicated that a decrease in grain/ straw ratio resulted in an increase in percent loss in all cases in wheat and rye and in most cases in oats and barley. In three non-uniform fields of oats and in six non-uniform fields of barley, however, increases in grain/straw ratio, resulted in increases in loss. This may be explained as follows: In non- uniform fields of oats and barley, high grain/ straw ratio may be associated with short brittle straw, whereas low grain straw ratio may be associated with tall rank straw. Hence, in such fields, grain/ straw ratio may be a direct indication of straw break-up and resultant separation load. Inclusion of grain/ straw variation significantly improved rack loss fits in thirty-four cases (63%), significantly improved shoe 49 loss fits in twenty-two cases (40%) and significantly improved cylinder loss fits in twenty-five cases (46%). This indicates that grain/ straw variation should be considered in analyzing loss data. Its affect can be neglected only in uniform fields (fields of constant grain yield and constant straw yield). Feedrate or Throughput as an Independent Variable In fifty four machine -crop combinations data was analyzed using both feedrate and throughput as the first independent variable. (i. e. , The first analysis considered loss = fl (feedrate, grain/ straw) while the second analysis considered loss 2 f2 (throughput, grain/ straw). ) Comparison between the two methods of analysis revealed the following: 1. For ideal fields (constant grain/ straw ratio) both methods resulted in equally good fits. 2. In fields d varying grain/straw ratio, the simple correlation of loss on feedrate usually resulted in much better fits than the simple correlation of loss on throughput. This was true for rack loss, shoe loss and cylinder loss in all four crop types. In other words, the regression of loss on feedrate accounted for a greater percentage of the variation in loss than did the regression of loss on throughput. 3. When variation due to grain/ straw was introduced, the multiple correlations, loss 2 f1 (feedrate, grain/straw) and loss = f2 (throughput, grain/ straw), both resulted in equally good fits. 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' o o u ‘L _A_ L ‘l 4 U ‘l _ ___—_J 7-- I- -.. ___- ___— T O A 7 o I ' o o A L A L I _ __ _- ' ._ __- ___ ___—— I o n i o u I . o 1“ A A .1 L 1.! ’ . . I a U C . . I g A Q l J ..__! - _ O . O O I ' I JL l .1 I .I _______ _ A..- IULTIPLI LIIIAR ’1? AID IUUIIPLICATIVB 'I! (THROUUI?UT It!!!) 54 Figures 17 to 20 represent output from the computer program, using the same data as was used in Figures 13 to 16, but with ”throughput" as an independent variable, rather than I "feedrate.I Comparison of Figures 13 - 16 to Figures 17 - 20 illustrate the points listed above. Comparing Tests Conducted in Different Years and Conditions Loss surfaces In an attempt to determine if important crop variables were not accounted for in the above analysis, all of the loss data for the standard combine was analyzed on the basis of crop type only. For example, the loss data from seven different fields of hard red spring wheat, collected over a four year period (fifty-nine individual loss collections) was checked for goodness of fit using the previous models. This analysis neglected any differences in moisture content, straw conditions and variety. It also neglected effects of climatic conditions on crop conditions. The results of this analysis is as follows: 1. In wheat (seven crops, f1fty nine collections) a reasonably good fit was obtained using the multiplicative model. The residual plots showed more scatter than in the case of analysis of individual fields, and the multiple correlation coefficients were much lower. The final regression equations for the standard combine, in wheat, were: 1.502 -1.688 Rack loss = 4. 757x10-4 (feedrate) (grain/straw) r (loss on feedrate) = . 7683 YXI 55 r (loss on grain/straw) : - .7576 Z r (grain/straw on feedrate) = - . 5809 X2X1 R = . 8582 C = 73.65% Standard Error of Estimate 2 . 737 .. . . -l. 4 Shoe loss 2 1. 019x10 1(feedrate)O 320(gra1n/straw) 73 r = .5600 yX1 r = - . 7893 sz r x = - .5809 X2 1 R = .7991 C = 63.86% Standard Error of Estimate 2 . 595 Cylinder 1055 = 1.1591(10-1 (feedrate)0'370(grain/straw)-1'345 r = .5278 in ryx2==- .5826 r X = - .5809 X2 1 R = .7092 C = 50. 30% Standard Error of Estimate 2 .651 The loss surfaces, resulting from these three equations, are shown in Figures 21 to 23. The reasonably good fit of the data for rack loss and shoe loss may be explained as follows: The three varieties of wheat (Thatcher, Canthatch and Selkirk) are quite similar in straw characteristics. The grain moisture content was nearly equal, ranging from 12% to 15%. Hence, it may be concluded that yearly climatic variation had little effect on those 56 LOSS(%) =4.757x10"(FR)‘°5°2(G/S)"°°° .44< G/S< 2.06 ‘° 46< FR<328 , . ........ 10¢,- ._.. -150 . ,. 560 25.0... . FEEDRATE- LBS./ MIN. RACK LOSS SURFACE FOR STANDARD COMBINE IN WHEAT FIGURE 21 RAC K LOSS - PE RCE NT 57 LOSS(%) = 1.019x10-‘(FR)0-320(G/s) 4.734 - .44< G/s < 2.06 46< F R < 323 FEEDRATE- LBS/M l N. SHOE Loss SURFACE FOR STANDARD COMBINE IN WHEAT FIGURE 22 SHOE [OSS-% 50 58 lOSS(%) = 1.159 x 10-1 ””0370 (G/S)"'3‘5 .44< G/S < 2.06 46< FR< 328 .~-_ ...... a ....-.-.-.-¢--¢.--.0 .................................................... .‘v ......................................................................... .............................................................................................. ......................................................................................................... ..................................................... too 150 200 250 300 350 FEEDRATE- [BS/MIN. CYLINDER LOSS SURFACE FOR STANDARD COMBINE IN WHEAT FIGURE 23 CYLINDER LOSS—% 59 characteristics of wheat straw influencing straw break-up. The poorer fit for cylinder loss may be explained by the effect of climatic conditions on ease of threshing. The 1963 crops were extremely difficult-to-thresh due to a combination of rust and hot, dry weather at the time of filling, whereas the other wheat crops were relatively easy-to-thresh. (2) In barley, oats and rye, fitting the loss data as above, yielded poor results. This may be explained by a much greater dependence of straw characteristics on variety, moisture content and growing conditions than in the case of wheat. In order for the above analysis to produce good fits more crop variables would have to be considered. Probably the inclusion of some variable describing straw strength (straw break-up) would improve the rack loss and shoe loss fits, whereas some variable describing ease of threshing (perhaps straw moisture content) would improve the cylinder loss fits. Comparison to characteristics of the standard combine From the above results it is apparent that the use of a standard combine is necessary in comparing the performance of combines tested in different years and conditions, unless additional crop variables are measured. The following example illustrates how loss data from the standard combine is used in making performance comparisons. Figure 24 gives a comparison between the standard combine and combine "A", in barley, based on loss data collected in 1963. 60 The best-fit regressions for rack loss are: standard combine: RL = 1.478x10-3(FR)1° 714 (G/S)1°176, .87< c/s< 1.10 combine "A": RL 2 7.136x10-11 (FR)4° 562(G/S)-° 953, .78 < c/s< 1.28 Basing both equations on a constant grain/straw ratio of l. 00, the equations become: standard combine: RL = 1.478xlO-3(FR)1’ 714 combine “A”: RL 2 7.1361410.11 (FR)4' 562 These equations, with 95% confidence belts (:t 2 x S. E. y) are Shown on Figure 24. At a loss of 3%, the capacity of combine “A" is Z. 8 times the capacity of the standard combine. Figure 25 compares rack loss for the standard combine and machine "B", in barley, based on loss data collected in 1961. The best fit regressions are: standard combine: RL 2 7.712x10-6 (FR)3'229 (G/S)-3°161, 1.25 < c/s< 2.48 combine "B": RL 2 2. O6Ox10-15 (FR)6'473 (G/S)4° 902, 1.00 < 0/5 < 2.29 Basing the above equations on a constant grain/ straw ratio of Z. 00, the equations become: standard combine: RL : 8.60x10_6 (FR)3° 229 combine HBH: RL : 6.18X10-16 (FR)6.473 These equations, With 95% confidence limits, are shown on Figure 25. At a loss of 3%, the capacity of combine "B" is 2. 0 times the capacity of the standard combine. G/S— 1.0 . o A o a c . a I n o a o o o o....ou.-.- - o - a o b u o n no coo-Ioo’ou..-nn O on 0.50 V n h v u- o " " 9.907. '2 I- '- 1N3383d -SSO1 )IDVU .2 400 300 1.0 200 160 140 FEEDRATE - LBS/MIN. COMPARISON To STANDARD 0014st AT A CONSTANT GRAIN/3mm RATIO FIGURE 211 100 I20 70 CO 60 50 1N3383d - 400 3 2 160 120' 100 .090 FEEDRATE — LBS/MIN. COMPARISON TO STANDARD comm: AT A CONSTANT ORAm/STRAw RATIO 70 FIGURE 25 65 Since Figures 24 and 25 are based on different, grain/straw ratios and since other unmeasured crop variables may have influenced the results, direct comparison cannot. be made between machines "A” and ”B". The capacity ratios can, however, be compared to give an estimate. Using the 3% loss comparison ratios from above, the capacity of "A” compared to "B" may be estimated as 2.8/2.0 = 1.4. ’1‘ Note: Significant digits in previous regression equations (pages 54, 55 and 60) are retained for purposes of calculation. They are not intended to denote the accuracy of measurements in the experiments. C ONC LU SIONS l. The multiplicative model, percent loss 2 a (feedrate) (grain/straw)c, provides a good fit for rack loss, shoe loss and cylinder loss data collected in non-uniform fields of varying grain yield and varying straw yield. 2. The exponential model, percent loss 2 a (feedrate)b, provides a good fit for rack loss, shoe loss and cylinder loss data collected in uniform fields of constant grain/straw ratio. 3. If loss tests are conducted over only a small range of feedrates, a multiple linear model, percent loss '2 a + b (feedrate) + c (grain/ straw), may provide the best fit in non-uniform fields and a simple linear model, percent loss = a + b (feedrate), may provide the best fit in uniform fields. 4. The correlation between percent loss and grain/straw ratio is negative for rack loss, shoe loss and cylinder loss in wheat, oats, barley and rye. 5. The computer program was successful in fitting loss data and comparing models. A computer program for fitting loss data must compare the four models listed above, to obtain the best fit for the conditions involved. 6. The use of feedrate as an independent variable usually gives a better simple fit (neglecting grain/ straw variation) than the use of throughput as an independent variable. When grain/straw variation is considered, both parameters give equally good fits. 7. A standard machine is necessary in comparing loss data collected in different years and crop conditions, unless some 64 65 measurement is made of straw "break-up" and ”eases-01" threshing”. Best-fit. regression equations can be used to allow comparison, between the standard combine and test machines, at a fixed grain/straw ratio and at a selected loss level. 8) In most instances, rack loss was the major component of total machine loss. This suggests that further study should be conducted on the factors affecting rack loss. A theoretical analysis of grain separation on an oscillating rack would be of great value. REFER ENC ES Combine Test Reports (1959 to 1964) from the following Testing Institutions: - Agricultural Machinery Administration, Regina, Saskatchewan, Canada Institut Voor Landbouwtechniek en Rationalisatie, Dr. S. L. Mansholtaan 12, Wageningen, Netherlands National Institute of Agricultural Engineering, Wrest Park, Silsoe, Bedfordshire, United Kingdom Profungsabteilung fur Landmaschinen, Der Deutschen Landwirtschafts - Gesellschaft, Zimmerweg 16, Frankfurt a. M. , Geromany Schwiezerisches Institut fur Landmaschinenwesen and Landarbeits Technik, Brugg/AG, Switzerland Statens Maskinprovningar, Uppsala 7, Sweden Statens Redskabsprfiver, Bygholm, Horsens, Denmark Csakis, L. (1964). Examination of the flow of the crop with combine harvesters with special respect to the possible increase of performance. Translation No. 169, Scientific Information Department, N. LA. E. , Wrest Park, Silsoe, Bedford. Dodds, M. E. (1966). Grain losses in the field when windrowing and combining wheat. Canadian Agricultural Engineering, \ Vol. 8, No. 1: 31-32. Draper, N. R., and H. Smith. (1966). Applied Regiession Analysis. John Wiley and Sons, Inc., New York. 407 pp. Feiffer, R. , et a1. (1964). Continuous control of forward speed - a possibility for a radical reduction in drum and shaker losses. Translation No. 200, Scientific Information Department, N.I.A. E. , Wrest Park, Silsoe, Bedford. (3053, J. R., R. A. Keppner, and L. G. Jones. (1958). Performance characteristics of the grain combine in barley. Agricultural Engineering, Nov. 1958: 697-702. Hebblethwaite, P. , and R. Q. Hepherd. (1960). A detailed test procedure for combine harvesters. Supplement Annual Report, 1960-61, N.I.A. E.: 365-371. , . (1964). Investigation into the regulation of shaker frequency - a possibility for reducing heavy losses during harvesting. Translation No. 199, Scientific Information Department, N. LA. E. , Wrest Park, Silsoe, Bedford. 66 10. 11. 12. l3. 14. 15. 16. 67 Johnson, W. H. (1959). Efficiency in combining wheat. Agricultural Engineering, Jan. 1959: 16—20. Little, T. M. (1966). Correlation and Regression. University of California Agricultural Extension Service, Riverside, Calif. 62 pp. Mark, Godlewski, and Coleman. (1962). A global approach to the testing and evaluation of combine performance. A. S.A. E. paper No. 62-126. Mitchell, F. S. (1955). The effect of drum setting and crop moisture content on the germination of combine harvested wheat. Report No. 51, N. I.A. E. Nyborg, E. O. (1964). A test procedure for determining combine capacity. Canadian Agricultural Engineering, Vol. 6, No. 1: 8-10. Ostle, B. (1964). Statistics in Research. The Iowa State University Press, Ames. 585 pp. Steel, R. G. D., and J. H. Torrie. (1960). Principles and Procedures of Statistics. McGraw -Hill Book Company, Inc., New York: 481 pp. Test Reports No. 1460, 1560, 1660. (1961). Agricultural Machinery Administration, Regina, Sask. 00000000000 APPENDIX I Fortran Digital Computer Program for Combine Loss Analysis (M. S.U. , CDC 3600 Computer) PROGRAM LOSSCALC DIMENSION NRUN(10)9WIDTH(IO)9DISTANCE(IO)ITIME(10)9STRAWAL(10)9 l CHAFFAL(10)1GRAINH(10)9RACKL(IO)9SHOEL(10)ODRUML(IO)OSPEC(IO) DIMENSION SAC(IO)OGRAIN(IO)OFEEDR(IO)9PLR(10)9PLS(IO)9 I PLC(IO)OSPELD(IO)IAPH(IO)OGS(IO)9PGPA(IO) OGR(54O4SQ3) DIMENSION PLRC(IO)QPLSC(IO)9PLCC(10)9RER(IO)9RES(10)IREC(IO)9 lRLN(10)9SLN(IO)9CLN(IO)CFLN(10)OAPR(IO)0APS(10)9APC(IO) COMMON NRUNOWIDTHODISTANCCOTIMEOSTRAWALOCHAFFALOORAINH.RACRL. ISHOELQDRUMLOSPECOSACQGRAINOFEEDRQPLROPLSOPLCOSPEEUOAPHOOSOPGPAO EGRQJM COMMON PLRCOPLSCOPLCCORERORESORECORLNOSLNOCLNOFLNOAPROAPSOAPC INPUT DATA WIDTH ‘ WIDTH OF CUT (FEET) DISTANCE - LENGTH OF RUN (FEET) TIME — LENGTH OF RUN (MINUTES) STRAWAL - RACK EFFLUENTOSTRAW PLUS LOSS (POUNDS) CHAFFAL - SHOE EFFLUENTOCHAFF PLUS LOSS (POUNDS) GRAINH - GRAIN COLLECTED IN HOPPER (POUNDS) RACKL - RACK LOSS (POUNDS) SHOEL - SHOE LOSS (POUNDS) DRUML - CYLINDER LOSS (POUNDS) SPEC - MACHINE AND CROP SPECIFICATIONS 11 DO 10 J=IOIO READ 20 ONRUN(J)9WIDTH(J)9DISTANCE(J)QTIME(J)oSTRAWAL(J)O I CHAFFAL(J)QGRAINH(J)ORACKL(J)OSHUEL(J)QDHUML(J) 20 FORMAT (1299F602) 10 CONTINUE READ 400(SPEC(I)OI:IOIO) 40 FORMAT (4A690A8) PRINT 50 50 FORMAT (*1*5X99H MACHINE 99H MODEL 99H TEST 99H SERIES 9 1 9H CROP 99H VARIETY 99H WINDRUW 99H STRAW 99HLUCATION 0 2 9H DATE /24X99H NUMBER 9&7XO9HOR STAND /) PRINT 529(SPEC(N)9N=1910) 52 FORMAT (6X910A9////) PRINT 54 54 FORMAT (6X99H RUN 99H WIDTH 09H DISTANCETQH TIME 9 9H STRAW 99H CHAFF 99H GRAIN 99H RACK 99H SHOE 9 9HCYLINDER T/42X99HAND LOSS 99HAND LOSS s9HCOLLECTED9 9H LOSS 99H LOSS 99H LOSS O/IbXOgH (FEET) 99H (FEET) 9H(MINUTES)99H(POUNDS) 99H(POUNDS) 99H(POUNDS) 99H(POUNDS) 9 9H(POUNDS) 99H(POUNDS) 9/) PRINT 56$(NRUN(J)9WIDTH(J)9DISTANCE(J)OTIME(J)OSTRAWAL(J)9 l CHAFFAL(J)OGRAINH(J)9RACKL(J)OSHUEL(J)ODRUML(J)9J=1910) 56 FORMAT (9X9ICOIX99(3X9Fbod)) CALL CALCULAT CALL GRAPH U1b(dh)~ CALL FIT GO TO 11 END 68 (30(W()0(WF)0(70 69 SUBROUTINE CALCULAT I DIMENSION NRUN(IO)9WIDTH(IO)9DISTANCE(IO)9TIME(IO)9STRANAL(IO)9 1 CHAFFAL(IO)OGRAINH(10)9RACKL(IO)QSHOEL(IO)9DRUML(IO)TSPEC(1O) DIMENSION SAC(IO)QGRAIN(IO)9FEEDR(IO)1PLR(lO)9PLS(10)0 l PLC(IO)OSPEED(IO)QAPH(IO)QGS(IO)9PGPA(IO) oGR‘5494503) DIMENSION PLRC(IO)OPLSC(IO)9PLCC(IO)9RER(10)9RES(IO)9REC(10)9 IRLN(IO)QSLN(IO)9CLN(IO)9FLN(lO)9APR(IO)9APS(IO)9APC(10) COMMON NRUNOWIDTHODISTANCEOTIMEOSTRAWALOCHAFFALOGRAINHoRACKLO ISHOELQDRUMLQSPECOSACQGRAINOFEEDROPLROPLSOPLCOSPEEOOAPHOGSOPGPAO EGROJM COMMON PLRCOPLSCOPLCCORERORESORECORLNOSLNOCLNQFLNOAPRoAPSOAPC JM=O DO 149J=IOIO IF(NRUN(J)OGToO) JM=JM+I 14 CONTINUE DO 15 9J=IOJM SAC(J)=STRAWAL(J)-RACKL(J)+CHAFFAL(J)'SHOEL(J)-DRUML(J) GRAIN(J)=GRAINH(J)+RACKL(J)+SHOEL(J)+DRUML(J) FEEDR(J)=SAC(J)/TIME(J) PLR(J)=(RACKL(J)/GRAIN(J))*IOOoOO PLS(J)=(SHOEL(J)/GRAIN(J))*IOOoOO PLC(J)=(DRUML(J)/GRAIN(J))*IOOoOO SPEED(J):(DISTANCE(J)*OOOOO)/(52SOoOO*TIME(J)) APHIJ)=(DISTANCE(J)*WIDTH(J)*60.OO)/(43560000*TIME(J)) GS(J) = GRAIN(J)/SAC(J) PGPA(J)=(GRAIN(J)*43560000)/(DISTANCE(J)*WIDTH(J)) 15 CONTINUE SAC * STRAW PLUS CHAFF ~ POUNDS GRAIN - TOTAL GRAIN - POUNDS FEEDR - FEEDRATE ' POUNDS PER MINUTE OF STRAW AND CHAFF PLR - RACK LOSS - PERCENT PLS — SHOE LOSS - PERCENT PLC - CYLINDER LOSS - PERCENT SPEED - GROUND SPEED - MILES PER HOUR APH - WORK RATE - ACRES PER HOUR GS - GRAIN TO STRAW RATIO PGPA - GRAIN YIELD - POUNDS PER ACRE PRINT 25 25 FORMAT(*2*96X95H RUNOIEH STRAW ANDAQH TOTALolaH FEEDRATE. 19H RACKollH SHOEQIJH CYLINDERollH SPEED. 213H WORK RATE99H GRAIN915H GRAIN/STRAW9/17X95HCHAFF9 311H GRAIN.17X94HLOSSO7X94HLOSSo7X94HLOSSo3OX95HYIEL096X9 45HRATIO./16X.5H(Las.).6X.6H(Les.).isH (Lds./MIN.).1OH (PERCENT)9 511H (PERCENT)ollH (PERCENT)913H (MILE/HOUR)912H (ACRE/HOUR). 612H (LBS./ACRE)o/) PRINT 359(NRUN(J)98AC(J)oGRAIN(J)oFEEDR(J)oPLH(J)oPLb(J)cPLC(J)c 1 SPEED(J).APH(J).PGPA(J).65(J).J=1.JM) 35 FORMAT<9X.12.7(3x.F8.2).ax.Fs.2.sx.Fs.2.1x.F8.2) RETURN END 70 SUDROUTINE GRAPH C - GRAPHING PERCENT LOSSES VS FEEDRATE DIMENSION NRUN(IO)OWIDTfiilOJ9DISTANCE(10)9TIME(10)0STRAWAL(IO). 1 CHAFFALIlO)oGRAINH(10)oRACKLI1O)OQHOEL(IO)9DRUML(IO)QSPEC(10) DIMENSION SAC(IO)9GRAIN(1O)9FEEDR(IO)9PLR(IO)9PLS(IO)9 1 PLC(IO)OSPEED(IO)OAPH(IO)9GS(IO)9PGPA(IO) 9GR(54045C3) DIMENSION PLRC(1O)0PLSC(IO)9PLCC(IO)ORER(IO)9RES(IO)0REC(IO)9 IRLNIIO)QSLN(IO)OCLN(IO)9FLN(IO)9APR(IO)9APS(IDIOAPC(IO) COMMON NRUNoWIDTHODISTANCEOTIMEOSTRHWALoCHAFFALOGRAINHoRACKLo ISHOELODRUMLOSPECOSACoGRAINoFEEDROPLROPLSOPLCoSPEEDOAPHoGSOPGPAO ZGRQJM COMMON PLRCOPLSCOPLCCORLRORESORECORLNOSLNOCLNQFLNOAPROHPSQAPC REAL GRONOLQMQIONIONUL INTEGER YOX DATA (BLANK=IH )9(DOT=IH0)9(PLOT=IH*)0(PLUS=IH+) DATA (P=1HP)9(E=1HE)9(R=1HR)9(C=1HC)9(N=1HN)9(T=1HT)9(L=1HL)9 1(O=IHO)9(S=1HS)O(F31HF)Q(DleD)O(A=IHA)9(DleU)Q(M=1HM) O(I=1HI)9 2(SLASH=IH/)o (PARENR=1H) ) 9(PARENL=IH() DATA (EN=1HI)9(TO=1H2)9(TRE=1H3)9(F1R21H4)9(FEM=1H5)9(SEX=1H6)0 1(SIV=1H7)9(OT=1H8)9(NI=1H9)o(NUL=1HO) PRINT 209(SPEC(NK)ONK=IQIO) 20 FORMAT(*I*6XOIOA9///) PRINT 25 25 FORMAT(19X99HRACK LOSSo3bX99HSHOE LUS5935X913HCYLINUER LOSS/) C - FILL GR WITH dLANK DO 30 K=Io3 DO 30 J=1945 DO 30 I2=Io54 3O GR(I29J9K)=BLANK C - PLACING HEADINGS AND AXES IN GR DO 35 K=Io3 GR(27OIOK)=p GR(2891OK)=E GR(29919K)=R GR(3OOIOK)=C GR(31919K)=E GR(32919K)=N GR(33OIOK)=T GR(35OIOK)=L GR(36919K)=O GR(37019K)=S GR(389I1K)=S 35 CONTINUE DO 37 K=IO3 DO 36 IZ=COIOod 36 GR(I2039K)=TO 37 CONTINUE DO 38 K=Io3 DO 33 IZ=IEOJOOE 33 GR(I2939K)=EN 36 CONTINUE DO 39 K=193 GR(2949K)=FIH GR(4O4OK)=TRE GRI6O49K)=TO GRI8949K)=EN 39 4O 41 42 43 71 GR(10949K):NUL GR(12949K)=NI GR(I404OK)=OT GR(15949K)=SIV GR(18949K)=SEX GR(20949K)=FEM GR(22949K)=FIR GRI24049K)=TRE GR(2694OK)=TO GR(28049K)=EN GR(3O¢49K)=NUL GR(32049K)=NI GR(34949K)=OT GR(36949K)=SIV GR(38049K)=SEX GR(4004OK)=FEM GR(4294OK)=FIR GR(44949K)=TRE GR(46949K)=TO GR(48949K)=EN GR(50949K)=NUL CONTINUE DO 41 K=Io3 DO 40 I2=195O GR(I2960K)=DUT CONTINUE DO 43 K=IO3 DO 42 J=7o45 GR(5OOJ9K)=DOT CONTINUE DO 45 K=Io3 GR(52969K)=NUL GR(52915OK)=EN GR(529169K)=NUL GR(529179K):NUL GR(529259K)=TO GR(529269K)=NUL GR(52127OK)=NUL GR(52035OK)=TRE GR(529369K)=NUL GR(529379K)=NUL GR(549149K)=F GR(54OI59K)=E GR(549169K)=E GR(549179K)=U GR(549189K)=R GR(549199K)=A GR(549209K)=T GR(540219K)=E GR(549239K)=PARENL GR(549249K)=L GR(549259K)=D GR(549269K)=S GR(549279K)=UOT GR(549289K)=SLASH GR(54«?99K)=M 45 72 GR(5493OQK):I GR(549319K)=N GR(5493EOK)=UOT GR(549339K)=PARENR CONTINUE C - ENTERING PLOT IN RACK GR 7O 71 72 73 74 7b 50 DO 50 J=19JM KP=O KF=O Y=PLR(J)/Oo5 IF (PLR(J)/Oo5-O.5.GT.Y) Y:Y+1 II=50~Y IF(IIoLTo1) GO TO 70 GO TO 71 II=1 KP = I X=FEEDR(J)/10.0 IF (FEEDR(J)¢GT.X*10+b) x:x+1 MN=X+6 IF(MN.GT.45) GO TO 72 GO TO 73 MN=45 KF = 1 IF(KP.EO.1.0R.KF.EO.1) GO TO 74 GO TO 75 GR(II¢MN.1)=PLUS GO TO 50 GR(II¢MN¢1)=PLOT CONTINUE C - ENTERING PLOT IN SHOE GR 80 .81 82 83 84 85 51 DO 51 JZIQJM KP=O KF=O Y=PLS(J)/Oo5 IF(PLS(J)/OOD*OODQGTOY) V2Y+1 11:50-Y IF(IIoLToI) GO TO dO GO TO SI II=I KP=1 X=FEEDR(J)/10oO IF(FEEDR(J)¢OT.X*IO+5) XTX+1 MN=X+6 IF(MN0GTo45) GO TO BE GO TO 83 MN=45 KF=1 IFIKPOEQOIOOROKFOEOOI) GO TO 54 GO TO 85 GR(IIoMNoE) = PLUS GO TO 51 GR(IIoMqu) = PLOT CONTINUE C * ENTERING PLOT IN CYLINUEK GR DO 52 J=19JM szo 73 KF=O Y=PLC(J)/Oob IF(PLC(J)/Oob*0.boGToY) Y=Y+I II=SO“Y IF(II¢LT.I) GO TO 90 GO TO 91 90 11:1 KP=I 91 X=FEEDR(J)/I0.0 IFIFEEDR(J)0GT.X*IO+5) X=X+1 MN=X+6 IF(MN.GT.45) GO TO 92 GO TO 93 92 MN=45 KF=1 93 IF(KP¢EO.1.0R.KF¢EO.I) GO TO 94 GO TO 95 94 GR(IICMN93) GO TO 52 95 GR(IIOMN93) b2 CONTINUE DO 65 IN=1954 PRINT 609(6R(IN9J91)9J=Io4b)9(GR(INQJ¢2)9J=194b)9 (GRIINOJ93)9J=IQ45) 60 FORMAT (1H 945A1945A194bA1) 65 CONTINUE RETURN END PLUS PLOT .... 0(W()0(3F)0 74 SUBROUTINE FIT DIMENSION NRUN(IO)QWIDTH(IO)9OISTANCE(IO)9TIML(IO)9STRAWAL(IO). I CHAFFAL(IO)QGRAINH(IO).RACRL(IO)QSHJELIIOIIDRUMLIIO)QSPEC(IO) DIMENSION SAC(IO)0GRAIN(IO)9FEEDR(IO)9PLR(IO)!PLS(IO)0 1 PLC(IO)1SPEED(IO)QAPH(IO)9GS(IO)9PGPA(IO) QGR(5494593) DIMENSION FTAU(1092)9TTAB(IO)9KSIG(4)9PLRC(IO)9PLSC(IO)oPLCC‘IO)‘ 1RER(IO)1RES(IO)0REC(IO)oRLN=0.0I IF(PLS(J)oEQoO) PLS(J)=0.0I 9 75 IF(PLC(J)¢EG¢O) PLC(J)=0.0I CONTINUE C REGRESSING LOSSES ON FEEDRATE 150 10 151 161 152 162 160 IF(LR'2) 15091519152 DO IO¢J=19JM YR=YR+PLR(J) YRL=YR YR2=YR2+PLR(J)**2 YS=YS+PLS(J) YSL=YS YSZ=Y52+PLS(J)**2 YC=YC+PLC(J) YCL=YC YC2=YC2+PLC(J)**2 XIYR=XIYR+PLR(J)*FEEDR(J) XIYS=XIYS+PLS(J)*FEEDR(J) XIYC=XIYC+PLC(J)*FEEDR(J) XI=XI+FEEDR(J) XIZ=XI2+FEEDR(J)**2 GO TO 160 DOléloJ=loJM RLN(J)=LOGF(PLR(J)) SLN(J)=LOGF(PLS(J)) CLN(J)=LOGF(PLC(J)) FLN(J)=LOGF(FEEDR(J)) YR=YR+RLN(J) YRE=YR YR2=YR2+RLN(J)**2 YS=YS+SLN(J) YSE=YS YSZ=YS2+SLN(J)**2 YC=YC+CLN(J) YCE=YC YC2=YC2+CLN(J)**2 XIYR=XIYR+RLN(J)*FLN(J) XIYS=XIYS+SLN(J)*FLN(J) XIYC=XIYC+CLN(J)*FLN(J) XI=XI+FLN(J) XI2=XI2+FLN(J)**2 GO TO 160 DO 1629J=1.JM YR=YR+RLN(J) YR2=YR2+RLN(J)**2 YS=YS+SLN(J) YSZ=YS2+SLN(J)**2 YC=YC+CLN(J) YC2=YC2+CLN(J)**2 XIYR=XIYR+RLN(J)*FEEDR(J) XIYS=XIYS+SLN(J)*FEEDR(J) XIYC=XIYC+CLN(J)*FEEDR(J) XI=XI+FEEDR(J) X12=X12+FEEDR(J)**2 SX2=XI2-(XI**2)/EE SYR2=YR2—(YR**2)/EE SYS2=Y52-(YS**2)/EE SYC2=YC2-(YC**2)/EE (7 950 951 76 SXYR=XIYR-(XI*YR)/LE SXYS=XIYS~(X1*YS)/EE SXYC=XIYC-(XI*YC)/Et IF(LR~2)9509951o952 SYR2L=SYR2 SYS2L=SY52 SYC2L=SYC2 GO TO 952 SYR2E=SYR2 5Y52E=SY52 SYC2E=SYC2 COMPUTING THE CORRELATION COEFFICIENToR 952 900 901 902 903 904 905 1361 1362 906 907 RR2=(SXYR **C)/(SX2*SYR2) CR=RR2*100.0 IF(SXYR.LT.0)9009901 RR=-1.0*SORT(RRK) GO TO 902 RR=SORT