PHYSICAL PROPERTIES OF STRAWBERRI‘ES AS RELATED TO PNEUMATIC SORTING Thesis for the Degree of M. S. MICHIGAN STATE UNIVERSITY .IOSSE 6. DE BAERDEMAEKER 1972 utt‘oul‘ /453fi337 RAH IIIIIIIIIIIIIIIIIIII L 6715 LIBRAR Y Michigan State A University r i 1"339‘9' ’ .a j _'_" L'XI‘FU ABSTRACT PHYSICAL PROPERTIES OF STRAWBERRIES AS RELATED TO PNEUMATIC SORTING by Josse G. De Baerdemaeker The need for cleaning and sorting of the harvested crop arises in machine harvesting of strawberries. The possibility of using an airstream for this sorting operation was investigated in this study. The terminal velocity of individual strawberries was determined using the air velocity required for flotation. A linear regression analysis showed that the terminal velocity was primarily a function of the square root of the weight with the shape of the strawberry producing a variation in terminal velocity for any particular weight. Density and stage of maturity did not have significant influence on the terminal velocity. A method for studying the feasibility of pneumatic sorting of strawberries was formulated in terms of a sorting matrix and a field maturity matrix. The sorting matrix which gives the percent of strawberries removed by a specific airstream velocity was cal- culated from the weight-terminal velocity data. A field sample was divided into weight and maturity groups and the composition of the product after using an airstream at certain velocities was calcu- lated. It was concluded that complete pneumatic sorting of green Josse G. De Baerdemaeker strawberries cannot be accomplished without losing some of the ripe product. A sizeable amount of the ripe strawberries would be lost if the field sample contains green strawberries of the same weight as the ripe ones. This results because pneumatic sorting is really another form of sorting by weight. Approved: gi;ék.}¥JJkJn~JVn {91%A73 Ma r rofe sor Department Chairman PHYSICAL PROPERTIES OF STRAWBERRIES AS RELATED TO PNEUMATIC SORTING .by I u ‘ Josse G; De Baerdemaeker A'UEBIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1972 AC KNOWLEDGEMENTS The author would like to express his appreciation to Dr. Larry J. Segerlind for his guidance throughout the research program. Appreciation is also expressed to the University of Leuven, Belgium for allowing the author to pursue his studies here, to the Department of Agricultural Engineering of Michigan State University and to the (kmmfission for Educational Exchange between the United States and Belgium for their financial support. II III IV VI VII TABLE OF CONTENTS Introduction Review of Literature Aerodynamic Theory Relevant to the Problem Experimental Procedure Experimental Results and Discussion Feasibility of Pneumatic Sorting of Strawberries Conclusions Suggestions for Further Work Bibliography 10 15 24 47 48 49 LIST OF TABLES Table Page 1. Specific Gravity of Strawberries . . . . . . . . . . . . . . 17 2. Regression Analysis of Terminal Velocity Vt Versus Weight w Model Vt = a + b W . . . . . . . . . . . . . . . . . . . 18 3. Regression Analysis of Terminal Velocity Vt Versus Weight W Model Vt = a1 + b1 W% . . . . . . . . . . . . . . . . . . 19 4. Ratio's of the Dimensions of Strawberries in Different Directions (For Symbols see Figure 5) . . . . . . . . . . 22 5. Sorting Matrix [B] from Experimental Data:Cumulative Percentages by Number . . . . . . . . . . . . . . . . . . 28 6. Sorting Matrix [B] from Experimental Data:Cumulative Percentages by Weight . . . . . . . . . . . . . . . . . . 30 7. Mean and Standard Deviation of the Weight and the Terminal Velocity of the Different Weight Groups . . . . . . . . . 32 8. The Calculated Sorting Matrix [BJzCumulative Percentages . . 34 9. Weight Distribution Per Color Group of a Field Sample: Matrix [An] (Percentages by Number) . . . . . . . . . . . 38 10. Weight Distribution Per Color Group of a Field Sample: Matrix [Aw] (Percentages by Weight) . . . . . . . . . . . 39 11. Field Sample Divided into Weight and Color Groups by Number: MatrixanJ 40 12. Field Sample Divided into Weight and Color Groups by Weight: Matrix [Cw] . . . . . . . . . . . . . . . . . . . . . 41 13. Strawberries of each Color Group Sorted out at Different Air Velocities (Percentage by Number) . . . . . . . . . . 42 14. Composition of the Final Product after Using an Airstream at Different Velocities (Percentage by Number) . . . . . 43 15. Strawberries of each Color Group Sorted out at Different Air Velocities (Percentage by Weight) . . . . . . . . . 44 16. Composition of the Final Product after Using an Airstream at Different Velocities (Percentage by Weight) . . . . . 45 LIST OF FIGURES Figure Page 1. Forces Acting on a Body in an Airstream . . . . . . . . . . . 6 4 2. Terminal Velocity Versus Falling Time . . . . . . . . . . . . 9 3. Aerodynamic Properties Testing Apparatus . . . . . . . . . . 11 4. Measured Dimensions of Strawberries . . . . . . . . . . . . . 14 5. Terminal Velocity vs Weight: Linear Model Vt = a + b W for each Color Group . . . . . . . . . . . . . . . . . . 20 6. Linear Model Vt = a1 + b1 W% for each Color Group . . . . . . 21 7. Strawberry Orientation before Lifting . . . . . . . . . . . . 23 8. Frequency Distribution and Cumulative Frequency Distribution of Strawberries Lifted at Different Air Velocities (4-5 gram weight group) . . . . . . . . . . . . . . . . . . . . 25 9. Terminal Velocity—-Weight Relationship Obtained from the Mean of the Terminal Velocity for each Weight Group . . . 33 I INTRODUCTION Mechanical Harvesting of Strawberries The introduction of mechanical harvesting in the tradi- tionally labor intensive fruit and vegetable production is often based on the once-over harvesting concept. The human harvester searches the crop, decides which to pick and which not, handles it carefully and often also grades the harvested fruit. Once-over machine harvesting needs devices which will obtain a final product of acceptable quality for processors and consumers. The avail- ability of, or the possibility to develop these devices, their quality of operation and their economic feasibility are some of the factors which determines the success of mechanical harvesters. In the case of strawberries, decreasing availability of harvest labor and competition from imported lower-cost Mexican strawberries dictates a need for mechanical harvesting (Larsen, 1968). Booster £5. 31, (1968) concluded that the state of art has been sufficiently developed to demonstrate that strawberries can be harvested by mechanical means, but unless equipment can be developed to cap, sort and grade the fruit, the advantages offered by mechanical harvesting will be lost. Therefore, current efforts are directed towards further improvement of a mechanical picker as well as to the development of equipment to perform sorting, grading and capping operations. Experimental harvesters are capable of separating the fruit from leaves and other foreign material (Nelson and Rattan, 1967). Another desirable property is the separation of machine harvested strawberries into groups according to maturity, since once-over harvesting of present varieties results in berries with varying degrees of maturity. Nelson and Kattan (1969) reported that maturity seems to be a function of berry size. They constructed a tapered-finger sizing device that permits the fruit to be separated in groups according to maturity. While the machine performed quite well, they concluded that hand-sorting would still be required to obtain complete maturity sorting. A very limited amount of data taken at Michigan State University in 1970 indicates that it may be possible to sort strawberries by passing them through an airstream. The following objectives for this study were established: a) investigate aerodynamic properties of strawberries, more specifically the terminal velocity as related to the maturity; b) determine physical properties of strawberries such as dimensions, weight, volume and density; and c) investigate the feasibility of pneumatic separation of strawberries into maturity classes. II REVIEW OF LITERATURE Moving air in combination with other mechanical devices has long been used for cleaning and sorting of grains and seeds. Although this application is widely adopted in current grain harvesting and handling equipment, continuing investigations of the interaction of air and materials are aimed towards the design of more efficient and economical equipment (Uhl and Lamp, 1968; Kashayap and Pandya, 1966; German and Lee, 1969). There also has been increasing interest in airstream.applications for harvesting and handling of fruits and vegetables, especially for picking, conveying and sorting. Crowther and Gilfillan (1959) and Hallee (1972) investigated physical and aerodynamic properties of potatoes and stones that would be important in the design of an aerodynamic separator. Tiwari (1962) studied physical and aerodynamic properties of dry beans and associated materials in relation to separation. AriStizabal gt, 21- (1969) showed that an airstream can be used for maturity and quality separation of peanuts. In another investigation, Soule (1970) tried to link the aerodynamic behavior of blueberries to the aerodynamic behavior of common geometrically shaped objects. Such documentation would have enabled Iihn to use the published fluid-dynamic data to design more efficient harvesting and processing systems. However, from the results of the data collected and calcu- lated he concluded that the behavior of blueberries in a turbulent airstream differed significantly from that of spheres under the same 3 conditions. Idell £5, El, (1971) experimented with an air suspen- sion-vibration strawberry harvester. They found that the overall average drag coefficient for strawberries is 1.15 to 1.38 depending on air velocity but independent of berry size. Igbeka and Sagi (1971) investigated pneumatic separation of dropped citrus flower particles. They concluded that complete separation cannot be achieved by air alone. III AERODYNAMIC THEORY RELEVANT TO THE PROBLEM DragiForce Consider the fluid flow about an immersed object, then the forces acting on that body can be represented by the resultant force F1 (Figure 1). The component of this force in the direction of the fluid flow is the drag force Ed, the component orthogonal to the fluid flow is the lift F1. The relationship between these forces and the fluid and body characteristics are given by (Lapple, 1956) where Cd and C1 are the drag coefficient and lift coefficient F.1=C1Ap[of\21_2 (1) Fd Cd Ap ff %3 (2) of the object. For particle motions in general applications it is not necessary to separate the force in two components since the body is usually free to assume its own random orientation and no perma- nent lift can act (Lapple, 1956). The net resistance force Fr can be given in terms of an overall drag coefficient C as: F=CA £v2 (3) r pf}... Where: Fr drag force (lbs.) C = overall drag coefficient Ap = projected area normal to direction of motion (Ft.2) 3 (0f mass density of the fluid 1b-sec2/ft-ft V = relative velocity between undisturbed fluid and object (ft/sec) 5 Figure 1 Forces Acting on a Body in an Airstream Fd V air Terminal Velocity Consider a particle moving in a vertical airstream. The forces acting on it are the drag force and the gravity force, and the equation of motion is: MdV=Fr-mg (4) When F; = mg the velocity difference between fluid and particle is constant and called terminal velocity Vt. From (3) and (4) it follows that: Vt=[2W ,(Pp— far (5) fp (aiApc where W is the weight and (Op-is the density of the particle. When an airstream.is used for sorting purposes, the terminal velocity of the particles to be separated will determine the range of air-velocities useful for separation. The difficulty in calculating the theoretical terminal velocity lies in obtaining reasonable values for C. For spherical and other regular shaped particles Lapple (1956) discusses how the drag coefficient is a function of the Reynolds number, and how terminal velocities can be calculated from the drag coefficient- Reynolds number relationship through a trial and error solution. Data on drag coefficients for irregular particles are not very complete or conclusive. In some cases they are calculated by approximating the shape as a sphere using an equivalent diameter derived from.the volume or from averaging the dimensions in different directions. Torobin and Gauvin (1960) give a detailed discussion of the effects of particle shape on the drag coefficient and the attempts that have been made to relate irregular shapes to spheres. From the equation of motion (4) for an object falling in still air, the relationship between displacement, time and terminal velocity is derived as (Bilanski £2. 31., 1962). S = 25? lllcosh g_ t (6) VI: 00 If one measures the time for an object to fall over a distance 3, then the terminal velocity can be calculated from (6) or read from a terminal velocity versus falling time graph for a particular distance as in Figure 2. Figure 2 shows that the accuracy in measuring the falling time is very important for objects with high terminal velocities. Improvement could be sought from using a higher falling distance but unreasonable heights are required to obtain dependable results once the terminal velocity exceeds fifty to sixty ft/sec. Another way to obtain more accurate values for the terminal velocity is to drop the object in an airstream.apposite to the falling direction and measuring the falling time and the air velo- city. The velocity calculated from equation (6) is then added to the measured air velocity to obtain the terminal velocity. Other methods have been used to determine terminal velocities of agricultural products. Perhaps the most important is the one in which the object is floated in an airstream, the velocity of which then is measured. The main difficulty with this method is to get the object flotating because of the rotation resulting from an irregular shape. Terminal Velocity (ft/sec) 100 80 60 4O 20 Figure 2 Terminal Velocity Versus Falling Time Falling Distance Falling Distance 24 ft. 16 ft. 1.0 1.1 1.2 1.3 1.4 1.5 I 1 J J I Falling time (sec.) IV EXPERIMENTAL PROCEDURE The terminal velocity of strawberries was initially determined in the dropping test and compared with the results from the flotation method. The dropping test did not give consistent values for terminal velocity because the terminal velocity of strawberries is too high. It lies in that part of the curve (Figure 2) where small time errors give large velocity variations. The dropping method was thus abandonned and terminal velocities were determined from flotation. The equipment used to determine the terminal velocity is shown in Figure 3. It consists basically of a motor to drive the fan, a vertical cylindrical plexiglass tunnel connected to a plenum chamber which in turn was connected to the inlet of the fan. generating the airstream by aspiration. The air velocity was controlled by changing the outlet cross-sectional area of the fan. A flow straightener was mounted at the entrance of the tunnel and a wire screen was mounted about six inches above the straightener. The strawberries were placed on the wire screen at the start of the test. Higher in the tunnel was another wire screen to prevent the loss of strawberries once they were lifted. The strawberries were placed in the tunnel through an opening in the side which then was carefully closed in order to minimize any disturbance of the airstream due to leaks or surface irregularities at that place. 10 11 P lenum Plexiglas tube L= 10 in. 6 F to manometer I wire screen _,,. ...... _. to inlet of fan flow straightener l MW Figure 3 Aerodynamic Properties Testing Apparatus 12 The air velocity was calculated from static pressure readings. Therefore, a thin tube with small holes was vertically mounted in the middle of the tunnel and connected to a micromanometer in parallel with another small hole in the tunnel wall to average the static pressure in the tunnel. Pressure losses due to the straightener and the friction with the tunnel wall were neglected. The air velocity was calculated using Bernouilli's equation __P_9_ + Y_9_2_ ___ _£1_ + 11.2. Keir 2g [air 23 (7) Where: Po and p1 are the static pressure outside and inside the tunnel respectively, V0 and V1 are the air velocities outside and inside the tunnel respectively, and gait is the density of the air. Since Vo = 0 at a distance far removed from the tunnel (7) reduces to y_3 PQ-P] (8) 2g - Hair The equation for the manometer reading is Po’Pl = h lfluid (9) Where: (yfluid is the density of the manometer fluid and h is the manometer reading (inches). Substitution of (9) into (8) gives the flotation velocity as v1 =V/é'g""_z£1fii’d [h- = 66.75 h ft/sec. (10) The smallest division on the manometer scale was .05 inch with possible interpolation to .01 inch. The terminal velocity of the strawberries was determined on an individual basis. A strawberry was placed in the tunnel and the 13 air velocity was increased until the strawberry started flotating. The manometer reading at the initial flotation was recorded. Other physical parameters useful in classification of strawberries which were recorded are: 1. Color, five color groups visually distinguished, green, white, pink-white, pink, red. Weight and volume. A METTLER balance type P1200 was used to measure the weight of the strawberries in air and the weight of the displaced water. The volume and specific gravity were then calculated as (Mohsenin, 1970): weight of displaced water VOlume = weight density of water Weight in air x specific gravity of water weight of displaced water specific gravity = The specific gravity for each color group is given in Table 1. Dimensions. The height and two orthogonal diameters at two different locations on the strawberry were measured with a caliper as indicated in Figure 5. Figure 4 Measured Dimensions of Strawberries ’N 14 V EXPERIMENTAL RESULTS AND DISCUSSION Terminal Velocity The terminal velocity of 568 strawberries was determined with approximately 100 strawberries in each color group. The strawberries were all of the Midway variety. Very small straw- berries (less than one gram) were not included. A statistical analysis of the data was performed using the LS-Stat routines of the Michigan State University, Agricultural Experiment Station. The first regression analysis was performed using the linear model Vt=ao+a1W+aZSG Where: Vt is the terminal velocity, W is the weight of the strawberry and SC is the specific gravity. Beta-weights of 0.707 and 0.006 were obtained for the weight and specific gravity variables respectively. (Beta-weights are used as a means of indicating the contribution of each independent variable above that accounted for by its mean). Consequently, the density was omitted in the second analysis which used a linear model Vt = a + b W A summary of the results for this model is given in Table 2. The equations are represented in Figure 5. 15 16 Equation (5) indicates that the terminal velocity is a function of the square root of the weight, therefore, the data were also analyzed using the model: Vt = a1 + b1 w’é (11) The coefficients for this model are given in Table 3. The equations for the different color groups are also shown in Figure 6. The correlation coefficients indicate that using the square root of the weight does result in a more accurate model. Also comparing the equations for each color group with the equations for the total group as in Figure 6 shows that the terminal velocity of strawberries can be satisfactorily expressed as a function of weight while disregarding the color. However, the multiple correlation coefficients of .8205 indicate that a fairly large amount of the variation of the terminal velocity is caused by factors other than the weight. The shape of the strawberries cannot be overlooked as a factor causing the previously discussed variation in terminal velocity. Indeed, Hallee (1972) in his potato studies and Soule (1970) for blueberries found that terminal velocity can be related to the ratio weight/projected area. However, the projected area varies with orientation and with shape. Since orientation is difficult to exactly determine, the projected area was not cal- culated. However, some shape parameters and their variations were calculated from the dimension measurements of about 80 strawberries. The ratio of the maximum thickness in two orthogonal directions, the thickness versus height ratio and the slope of the cone are given hereafter in Table 4 (see also Figure 4). These shape 17 Table 1 Specific Gravity of Strawberries Color Specific Gravity Standard Deviation Green .886 .0562 White .898 .0409 White-Pink .907 .0769 Pink .918 .0367 Red .921 .0405 variations would have to be combined with the variation in orientation to make an estimation of the projected area possible. Another factor is the presence of the cap. How this affects the terminal velocity of different sizes of strawberries was not investigated in this experiment. Strawberries initially laying horizontally on the wire screen slowly moved into a vertical orientation with increasing air velocity and remained in this position (Figure 7). The air velocity had to be increased by about 25 to 47 feet per second before the strawberry was lifted which happened so suddenly that no flotation could be observed. The strawberry was usually found in a horizontal position against the top wire screen. A possible explanation of this phenomenon is that as soon as the strawberry is lifted it starts rotating and assumes an orientation such that the terminal velocity is less than the actual air velocity. It was found that this problem in determining the flotation velocity could 18 was. moo. mne. OH.~ mw.wm mm.o no.wH mH.H mom HHmuo>o mob. MNH. moo.a ¢¢.H om.mo mw.n m¢.wH oo.~ mmH com awn. NmH. o¢o.~ mn.H wm.um mm.~ nm.ma mN.~ NHH xeem #mm. mna. mo~.H mo.~ om.mm Hn.o nH.eH on.H NHH xowmuouwaz dun. oma. ooa.H mm.~ Ho.wm om.n mm.ma mw.H mm cages nun. mom. mam. mo.m o¢.mm om.m mo.oH mH.H mod compo ucoaoawwoou n m :oquoaouuoo mo uouum «0 scene a m emoz. Sofiexmz Enaeawz 333:2 oumocmum unmoamum manna «unwamz .oz @395 H300 N «Heme 3n+muu>eoeoz 3 uswemz msmum> u> huwooao> HmawaumH we mfimhfimee eowmmouwom 19 Hum. mmm. wNm. 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Figure 6 Linear Model Vt = a1 +»b1 W35 for each Color Group 22 Table 4 Ratio's of the Dimensions of Strawberries in Different Directions (For Symbols see Figure 5) Ratio Mean Standard Deviation B_= Dmax Y A Dmax X .928 .0693 A__ Dmax X H — H .771 .0879 A-C _ Dmax X-Dmin X L 7 2L .198 .113 B-D _ Dmax Y-Dmin Y L " 2L .210 .111 be overcome by slightly vibrating the tunnel such that the strawberry did not stay in the same position but was moving across the wire screen. The orientation of a flotating strawberry varied with the shape. The more a shape approximated a sphere, the more likely the strawberry would remain vertical. With shapes approaching cones more rotation about a vertical and horizontal axis was observed, and usually the axis of the cone would make an angle with the vertical. If the cross section was not circular but elliptical it seemed that the largest diameter of the cross section was oriented normal to the direction of the airflow. 23 Figure 7 Strawberry Orientation before Lifting I IL A VI FEASIBILITY OF PNEUMATIC SORTING OF STRAWBERRIES The quality of a sorting operation can be measured in the following way, a) the percentage of the undesired material, in this case unripe strawberries, removed, and b) the composition of the final product. the sorting performance can be estimated from the terminal velocity In the case of pneumatic sorting of strawberries, of the various maturity levels.' The regression analysis in the previous section showed that the terminal velocity of strawberries is primarily a function of weight. Other factors such as density, shape, etc., result in a velocity distribution for a particular weight. weight groups, each covering one gram. In this study the strawberries were divided in discrete The velocity distribution for the 4-5 gram weight group is given in Figure 8 along with the cumulative distribution. The cumulative distribution is also the percent of the weight group that is lifted at a certain velocity. Estimation of the Removal Percentages Note that discrete values were also used for the velocity. Once the strawberries are divided in weight groups and the distribution of the terminal velocity for the different weight groups is known, the percentage of each maturity that is lifted can be calculated from: Percent of one maturity level lifted at a certain air velocity weight groups ‘I’ Percent of the maturity level in each weight group ' 24 fl F Percent of that at a certain velocity weight group lifted 7 25 Figure 8 Frequency Distribution and Cumulative Frequency Distribution of Strawberries Lifted at Different Air Velocities (4-5 gram weight group) Frequency -— Distribution Cumulative an... Frequency 100 .— Distribution | I I 90 — : 1 I . . q, 80 .. I . 3 . ' ‘H 70 . I I w-I u | I 5 60 I a 3 _ I ' e “ I I m I 50 " . . I . I I ' I 40 - . . ' I I | I 30 _ . I . ' i : 0 - I 2 . . : 10 ' . I I 5 Air Velocity (ft/sec) 26 This can also be written in matrix notation as: {R}: [Q [P] {v} (12) Where: {R} gives the percentage of each color group removed at a certain velocity [AJI relates the color group (rows) to the weight groups (columns) for a field sample. A co- h color efficient aij is the percent of the it group which fall in the weight group j. For example, if green is the first color group and 4-5 grams is the fifth weight group then a15 is the percent of green strawberries weighing between four and five grams. [13] contains the percentage of each weight group (rows) lifted at different air velocities (columns) {V} is a triggering matrix, i.e. all the coefficients are zero except the velocity under investigation which has a value of one. The color levels used are l=green, 2=green-white, 3=white-pink, 4=pink, and S=ripe. The weight groups were 0-1, 1-2, etc., up through l9-20 grams. The determination of [A] and [B] is discussed in detail later in this section. The Composition of the Final Product The maturity distribution of the final product can be estimated from: — .m.- I I‘M reach color- group in percent of total remaining after using a certain velocity L. ‘ 27 r. .- .— Number or total I Percent of weight of berries that weight in a weight group group not = that have that X lifted at weight maturity the given airj groups .L J I.velocity (total number or weight remaining at that velocity) This can again be written using matrix notation as: {F}=c V (13) £101 V Where: {F} is the maturity distribution of the final product [CI after passing through an airstream with a given velocity contains the total number or weight of each color group in each weight group as obtained from dividing a field sample in color groups and weight groups. A coefficient cij is the number (or total weight) of the strawberries with color i that are in the jth weight group. [M] contains the percentage of each weight group (rows) not lifted at different air velocities (columns). The relationship between mij and bij is m.. = 1 - bij (14) 13 {V} again is the velocity triggering matrix. Evaluation of the Removal Matrix LB] The air velocities at which the sorting performance will be evaluated range from 55 ft/sec up to and including 100 ft/sec in steps of 5 ft/sec. The percentage of strawberries in each weight group that has a lifting velocity below a given air velocity was 5... 28 ooo.~ oom. ooe. cow. mHINH ooo.H ooo.H mmm. owm. NHIHH ooo.H ooo.H omw. mmm. qua. mwo. HauoH ooo.H ooo.H mum. mam. wqa. nmo. caum ooo.H ooo.H mma. non. mom. meo. mum ooo.H 0mm. mum. mam. wmd. woo. «Ho. mun ooo.H dam. «mm. «mm. wow. mea. 0H0. n-o ooo.H ooo.H ooo.H woe. mew. oom. eha. «Ho. mus ooo.H ooo.H ooo.a mnm. mwm. man. mad. use. aum ooo.H ooo.H ooo.~ ooo.H coo.H qu. mam. Noe. mmo. MIN ooo.H ooo.H ooo.a ooo.H ooo.a mma. mmo. new. mmm. 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NON. omnma mauwa wanna mHumH oHTnH mHTQH aauma manna Awmncwucouv o manna 32 Table 7 Mean and Standard Deviation of the Weight and the Terminal Velocity of the Different Weight Groups Weight No. of 2 Weight (ggams), Terminal Velocity Group Strawberries Mean Standard Mean Standard* Grams Deviation Deviation 1-2 15 1.74 .236 56.72 4.939 2-3 52 2.48 .298 60.98 4.343 3-4 65 3.52 .259 65.88 4.498 4-5 86 4.49 .300 69. 57 5.041 5-6 80 5.50 .275 71.60 4.941 6-7 63 6.49 .277 73.64 4.728 7-8 73 7.53 .317 75.67 4.497 8-9 61 8.55 .325 77.71 4.465 9-10 27 9.62 .298 79.33 4.015 10-11 23 10.47 .239 80.19 5.714 11-12 16 11.52 .258 81.51 2.750 12-13 10 12.69 .222 85.26 4.255 13-14 5 13.59 .284 81.55 4.330 14-15 5 14.28 .293 88.03 2.068 15-16 5 15.41 .407 86.91 1.811 stw *Average standard deviation for group 1-2 through 9-10 is 4.607 calculated as shown in Figure 7. These percentages are bij can be expressed either as a percent by number or as a percent by weight. Tables 5 and 6 give the coefficients of the sorting matrix as calculated from the experimental data. Table 5 gives the percentage by number while Table 6 gives the percentage by weight. 411‘ r 11 a r .a K acutely . .P 34. s .134... .4 “I. q - 3 3 macho uawwos some you huwooHo> HmeHEuoH use mo use: can Baum omnqmuno euamdoaumfiom unwwmzuuhuaooao> HmaHSHoH Amamumv uswaoz a shaman mH ImH IIBH ea ma ea ma NH HH DH m h. e n a m m H 7 a _ u . - — q _ u - & T u i _ d on.. mm.1 09.1 mm.1 24 AV m~.1 .I O O 8.. mm.1 om.| (ass/3;) KaroolaA {surmaal 34 ooo.H ooo.H ooo.H mam. mom. emu. mam. one. NHIHH Goo!" 0004 0004 000.." Nwm. cow. and. mNH. Mao. SIOH ooo.H ooo.H ooo.H ooo.H mom. Ham. moo. mom. mmo. ofium ooo.H ooo.H ooo.H ooo.~ 5mm. mmm. Hun. mom. nmo. mum ooo.H ooo.H ooo.H ooo.H ooo.H mum. mam. qu. eoH. oHo. mun ooo.H ooo.H ooo.H ooo.H ooo.H 0mm. mmm. mum. an. «No. ~10 ooo.H ooo.H ooo.H ooo.H ooo.H 5mm. wmm. men. Nmm. «co. cum ooo.H ooo.H ooo.H ooo.a ooo.H ooo.H com. 0mm. mom. Hwa. mmo. mud ooo.H ooo.H ooo.H ooo.H ooo.H ooo.H coo.H owm. 0mm. nme. mHH. HHo. «um ooo.~ ooo.a ooo.H ooo.H ooo.H ooo.H ooo.H ooo.H onm. mam. Mme. aoH. mum ooo.H ooo.H ooo.H ooo.H ooo.H ooo.H ooo.H ooo.~ ooo.H mwo. Hmm. mmq. NIH ooo.~ ooo.H ooo.H ooo.H ooo.H ooo.H ooo.H ooo.H ooo.H ooo.H ooo.a ooo.~ H10 268 One moH ooH mm om mm om me on me co mm asouu eeooom ammumm$.huwuoau> HmcHEHoH unwwoz mmmflcmoumm 0>flumasfino ”mmw Kahuna wowuuom omumHnuamu 05H m eases 35 ooo.H ooo.H ooo.H ooo.H ooo.H ooo.H ooo.~ ooo.H Nmm. Nam. ooo.H ooo.~ ooo.H ooo.H ooo.H ooo.H Ham. mmm. mum. mwm. omo. ooo.a ooo.H ooo.a moo. ANN. mam. Now. Hao. Hum. Nwm. «mm. mON. mom. fine. oom. mwo. own. on. NNm. mNo. nmo. aoH. 0H0. mNH. NNo. NNN. mao. mmm. omo. Ram. mqa. NH0. «#0. NmN. omo. ONumH mHan manna NHIQH manna manna «HINH MHINH Aomsewucoov w magma 36 These tables have some inaccuracies for higher weight groups due to the small number of strawberries in these groups. The terminal velocity data available for lower weight groups was used to extrapolate coefficients of the sorting matrix for the higher weight groups. The mean and the standard deviations of the weight and of the terminal velocity Vt for each weight group was calculated (Table 7). A graph of the terminal velocity versus weight was plotted using the calculated means (Figure 9). The terminal velocity for the midpoint of each weight group was determined from Figure 9. The standard deviation of the velocity in each weight group was assumed equal to the average standard deviations for the weight groups one through nine. Cumulative distributions at the air velocities previously mentioned were calculated from the normal distribution of the terminal velocity of a weight group. Table 8 gives the results of these calculations which are also the coefficients bij of the removal matrix [B] . For example, 12.5 percent of the strawberries weighing between 10 and 11 grams are removed by a lifting velocity of 75 feet/second. Since [B] , Table 8 is based on the midpoint value of the weight groups, the coefficients are both a percentage by number and a percentage by weight. Therefore,[:B] can be used in calculating removal both by number and by weight. The Field Data A sample of machine harvested strawberries was divided into color groups and each individual strawberry was weighed. The matricies [Cg] and.[Cvj were obtained, where the subscripts n and w indicate that the coefficients Cij are the total number or total 37 weight in the color group i and weight group j. The weight distri- butions per color group, cij’ were calculated in percentages both by count and by weight giving the matricesEAé] and [Ag] , where the subscripts n.and w'indicate that aij are percentages by count and by weight respectively. The matrices [AEJ and [Aw] are given in Tables 9 and 10. For clarification, a15 in Table 9 is the percent (10.3) by number of the greens in the 4-5 gram weight group while a15 in Table 10 is the percent (15.9) by weight of the greens in the 405 gram weight group. The matrices [CE] and [Célare shown in Tables 11 and 12. Results Tables 13 and 14 summarize the results of the estimation of the percent of material removed in an airstream and the composition of the final product. Tables 13 and 14 are in percentages by number. Tables 15 and 16 are in percentage by weight. The initial composition of the field sample was, in percentages by number; 47.7 green, 12.6 white-pink, 9.2 pink, and 30.5 ripe. After using an airstream with a velocity of 70 ft/sec, the composition of the remaining product, Table 14 is 16.3 percent green, 17.1 percent white-pink, 12.2 percent pink and 54.4 percent ripe. Table 12 shows that in this sorting process 85.5 percent of the greens were removed but also 26.3 percent of the ripe strawberries were lost. Sorting performances by weight are shown in Tables 15 and 16. It is clear that both Tables 13 and 14, or 15 and 16 are necessary to evaluate a sorting performance. They show that 38 omo. oNo. OHo. oHo. ONO. one. one. Hmo. Hmo. Hmo. HoH. Hmo. HNH. Hmo. HoH. Hmo. QNo. 0N0. com ooH. moo. mmo. mmH. com. ooH. moo. OON. HeHm xaHm eNo. eNo. mno. oNN. wmo. 00H. oaH. NNH. ooH. uouH£3 coo. Nmo. Nmo. moH. mmN. meN. HNN. HNo. comma oN mH mH NH 0H mH «H mH NH. -mH -wH -NH -oH -mH ueH -mH -NH -HH HHuoH oHum auw mun hum 01m muq aum muN NIH Huo esouo Agaouuv mmsouo newHoz uoHoo Andeanz he mmwwuemoummvneHQ onEmm onHm Ho oHooe 41 w¢.wn ooém 8.3 8.2 8.8 2.8 orom ormoaommm 2.2 ooom moon 2.: mnoo 3.3 mom do om.m Bo so.om mm.oa ma.m om.om Hm.oo ma.mH mm.m Ho.oH seam mo.ma om.o Ho.mm oH.oo oo.mm oo.mm mm.om Ho.AH mo.m acne -ooaaz o~.o mm.am Ho.mm mH.oo o.amo Hm.oo oo.oo mo.o cameo oNan aHan wHuNH NHueH oHunH mHuqH «HumH mHuNH NHuHH HHnOH oHum mum AnemHUv asouo ustos mum m-o o-m m-o o-m m-m m-H H-o macho uoHoo f Wombats: 3:30: on mesouu uoHou new uanoz ouaH movH>Ha oHeEmm oHon NH mHLMH 42 Table 13 Strawberries of each Color Group Sorted out at Different Air Velocities (Percentage by Number) Air Velocity White- (ft/sec) Green Pink Pink Red 55 .230 .072 .022 .013 60 .437 .142 .096 .039 65 .669 .240 .235 .106 70 .855 .426 .438 .243 75 .958 .685 .697 .454 80 .993 .894 .883 .685 85 .999 .979 .969 .854 90 1.000 1.000 1.000 .941 95 1.000 1.000 1.000 .981 100 1.000 1.000 1.000 .997 105 1.000 1.000 1.000 1.000 Table 14 Composition of the Final Product after Using an Airstream at Different Velocities (Percentages by Number) Air Velocity Green White- Pink Red (ft/sec) Pink 55 .420 .134 .103 .344 60 .356 .144 .111 .389 65 .265 .161 .118 .456 70 .163 .171 .122 .544 75 .079 .156 .110 .655 80 .029 .108 .887 .776 85 .007 .052 .056 .885 90 .000 .015 .020 .965 95 0.000 .003 .003 .994 100 0.000 0.000 0.000 1.000 105 0.000 0.000 0.000 1.000 Table 15 Strawberries of each Color Group Sorted out at Different Air Velocities (Percentages by Weight) — fi _ __- Air Velocity Green White— Pink Red (ft/sec) Pink 55 .119 .019 .010 .003 60 .282 .044 .047 .012 65 .519 .110 .133 .044 70 .758 .280 .305 .128 75 .918 .569 .570 .298 80 .983 .838 .804 .533 85 .998 .963 .942 .745 90 1.000 .995 .992 .881 95 1.000 1.000 1.000 .959 100 1.000 1.000 1.000 .992 105 1.000 1.000 1.000 .999 110 1.000 1.000 1.000 1.000 Table 16 Composition of the Final Product after Using an Airstream at Different Velocities(Percentage by Weight) 45 Air Velocity Green White- Pink Red (ft/sec) Pink 55 .240 .139 .106 .515 60 .207 .144 .109 .540 65 .155 .150 .110 .585 70 .095 .148 .108 .649 75 .046 .124 .094 .736 80 .016 .079 .073 .832 85 .003 .036 .043 .917 90 .011 .014 .976 95 .002 .002 .996 100 1.000 105 1.000 110 0.000 Initial Composition .262 .137 .104 .497 46 sorting of the machine harvested strawberries under investigation is not possible without the loss of the major part of the ripe strawberries. However, these results depend on the actual maturity stage of the strawberries, the uniformity of ripening. This information would be required for determining the optimum time for machine harvesting as well as for estimating the pneumatic sorting performance. The sorting matrix [B] in Table 8 gives the percentages of each weight group lifted at different air velocities. The obtained results are an estimation of the size of strawberries that are sorted out. The decision to work with a certain air velocity depends upon how desirable small ripe strawberries are and what labor is required to remove remaining bigger green strawberries. V II CONCLUS IONS The objectives of this study were to obtain information on aerodynamic properties of strawberries and to investigate the feasibility of pneumatic sorting. The conclusions are: l. The terminal velocity Vt of strawberries is primarily a function of the square root of the weight W. Terminal velocity and weight can be related by a regression equation of the form Vt = 44.74 + 11.22 (W)%. There is no indication that green and red strawberries with the same weight have different terminal velocities. The feasibility of pneumatic sorting is highly dependent upon the color and weight distribution of the strawberries in the machine harvested product. Since the probability of having only small green and large red strawberries is low, complete sorting of the color groups is unlikely. It was observed that some strawberries can be oriented in an airstream before they are lifted. These strawberries generally were conical in shape. 47 SUGGESTIONS FOR FURTHER WORK The terminal velocity was determined for each strawberry individually. It would be desirable to know how straw- berries behave in a group and if the sorting performance would be the same. Information on how the shape of strawberries changes with maturity could improve the sorting matrix since the shape affects the range of the terminal velocity in a specific weight group. The influence of the cap on the terminal velocity of different sizes of strawberries and the behavior of strawberries still in a cluster needs attention. Information is needed on how color and weight distri- bution in the field evolves during the ripening and how this is reflected in the machine harvested product. 48 BIBLIOGRAPHY Aristimabal, L., E. E. Burns and 0. R. Kunze. Physical, Chemical and Organoleptic Properties of Peanuts Separated in a Controlled Airstream. ASAE Transactions, 1969. Vol. 12, p. 298. Bilanski, W. K., S. H. Collins and P. Chu. Aerodynamic Properties of Seed Grains, Agricultural Engineering, 1962. Vol. 63, No. 6, pp. 216-219. Booster, D. E., Kirk, D. E. and G. E. Nelson. "State of the Art and Future Outlook for Mechanical Strawberry Harvesting" in "Fruit and Vegetable Harvest Mechanization: Technological Implications." B. F. Cargill and G. E. Rossmiller, editors. Rural Manpower Center Report No. 16, East Lansing, Michigan, 1969. Crowther A. I. and G. Gilfillan. The Behavior of Potatoes, Stones and Clods in a Vertical Airstream. Journal of Agricultural Engineering Research, 1959. Vol. 4, p. 9. German, R. F. and I. H. A. Lee. Grain Separation on an Oscillating Sieve as Affected by Air Volume and Frequency. ASAE Transactions, 1972. Vol. 15, p. 303. Haller, N. D. Aerodynamic Properties of Potatoes and Associated Soil Materials. ASAE Transactions, 1972. Vol. 15, p. 303. Idell, J. H., Holmes R. G., and E. G. Humphries. Resonance Frequencies and Drag Coefficients: Design Criteria for the Deve10pment of an Air Suspension-Vibration Strawberry Harvester. ASAE Paper No. 71-692, 1971, ASAE, St. Joseph, Michigan. Igbeka, J. and R. Sagi. Physical and Aerodynamic Properties of Dropped Citrus Flower Particles. ASAE Transactions, 1971. Vol. 14, p. 844. Kashyap, M. M., and A. C. Pandya. Air Velocity Requirement for Winnowing Operations. Journal of Agricultural Engineering Research, 1966. Vol. 11, p. 24. Lapple, L. E. Fluid and Particle Mechanics. University of Delaware, Newark, Delaware, 1956. Larsen, R. Paul. A Fruit and Vegetable Harvesting Mechanization: Technological Implications. B. F. Cargill and G. E. Rossmiller, editors. Rural Manpower Center Report No. 16, East Lansing, Michigan, 1969. 49 50 Mohsenin, N. N. Physical Properties of Plant and Animal Materials. Gordon and Breach, Science Publishers, New York, 1970. Nelson, G. S. and A. A. Rattan. A Mechanical Harvester for Strawberries, Arkansas Farm Research, 1967. Vol. XVI, No. 4. Nelson, G. S. and A. A. Kattan. Grading Mechanically Harvested Strawberries, Arkansas Farms Research, 1969. Vol. XVIII. No. 2. Soule, H. M. Investigation of Some Aerodynamic Properties of Lowbush Blueberries, ASAE Transactions, 1970. Vol. 13, p. 114. Tiwari, S. N. Aerodynamic Behavior of Dry Edible Beans and Associated Materials in Pneumatic Separation. Unpublished MB thesis, University of Maine, 1962. Torobin, L. B. and W. H. Gauvin. Fundamental Aspects of Solids-Gas Flow, Part IV: The Effects of Particle Rotation, Roughness and Shape. Canadian Journal of Chemical_§ggineering, 1960. Vol. 38, p. 142. Uhl, I. B. and B. I. Lamp. Pneumatic Separation of Grain and Straw Mixtures, ASAE Transactions, 1966. Vol. 9, p. 264. MICHIGAN STQTE UNIV. III 6 I I III I III | 31293007 IIII 6 LIBRQRIES 7185