Feed-Time Distribution in Pneumatic Feeding of Softwood Seedlings

Transcription

1 Journal of Forest Engineering 49 FeedTime Distribution in Pneumati Feeding of Softwood Seedlings Ulf Hallonborg The Forestry Researh Institute of Sweden Uppsala, Sweden ABSTRACT Long seedling feed times an restrit the performane of a planting mahine. In this study feed times were measured in a pneumati feed test rig. Test variables were seedling type, air veloity and hose diameter. Feed time histograms were then tested against hi square distributions. Eah aepted distribution was used for alulating the proportion of seedlings that ould reah a planting head in time and the proportion arriving late, with respet to the mahine yle time. The mean feed times for those two ategories were then weighted together to obtain a total feed time. Two models for desribing the total feed time, one for normal seedlings and one for butt ended seedlings were onstruted, with mahine yle time, air veloity and fullness quotient as input variables. Keywords: Mehanized planting, pneumati feeding, seedling transport, feed distribution. INTRODUCTION Mahines for planting softwood seedlings an be equipped with different types of seedling feed systems. When a pneumati feeding system is used, that is when the seedlings are blown or suked through a hose, feed times annot be fully ontrolled. Sine seedling feed times an restrit planting apaity, both their mean value and distribution are of interest [1]. The aim of this investigation was to determine whether hi square distributions (1b) an provide a good model for seedling feed times, and if so, determine a model for the resulting feed time. f(x)=.x (X 1).e ax 1(a) f( x) 2.T(r\ 1(b) x.e 2 As hi square distributions are only defined for integer values (degrees of freedom) on r and real values are used. They are in reality gamma distributions 1(a) withvalues of λ = 0.5 r and x = 0.5 that are used. Nevertheless here they will be alled hi square distributions, mainly beause they are single parametri. The distributions were used to alulate the proportion of seedlings that reah the planting head in time with respet to the planting head yle time and the proportion that arrive too late and ause a derease in planting apaity. The only known ommerial tree planting mahine equipped with a pneumati seedling feed system is the Swedish Silva Nova. Therefore the feed tests were arried out in a rig with a hose onfiguration and diameters similar to those of the Silva Nova. Seedlings were sampled from prodution stores in the field. Some samples onsisted of pine seedlings only, while others onsisted of sprue only, and a third type ontained both pine and sprue seedlings. Although Larsson [3] reported a slight differene in frition oeffiient between pine and sprue, no systemati differene between speies was found in this study. This fator was therefore disregarded. Feed time histograms were obtained experimentally for different types of seedlings. They were fed through hoses with different diameters at ontrolled air veloities. Histograms obtained were ompared with hi square distributions, and the best fitting urve was used to alulate the proportion of seedlings that reah the planting head within the mahine s yle time and the proportion of late seedlings. Mean feed times for the on time and late seedling groups were then used to alulate a total feed time as a proportion weighted mean. A linear model for prediting total feed time was then onstruted using the data from eah seedling bath as input. The author is a researher in the Mehanial Engineering at the Forestry Researh Institute of Sweden.

2 Journal of Forest Engineering MATERIALS AND METHODS Seedlings Seedlings of five types were sampled from prodution during the 1993 planting season (Table 1). In addition, Plantek seedlings were obtained diretly from a new nursery system and thus had smaller green parts owing to their shorter period of growth. Test rig The test rig (Figure 1) was quite simple, onsisting mainly of an eletri fan that suked air through a hose. Photoells measured the time it took for a seedling to move 4.2 m with a height differene of 1.5 m between two time measurement points. Measures and onfiguration of the hose were hosen to resemble the onditions on a Silva Nova. Likewise, hose type and inside diameters of, and mm were hosen. The hoses were made of transparent PVC with an inserted steel spiral that prevents flattening. The seedlings were inserted vertially into the hose. The bottom of the ontainer passed the first photoell, starting the lok one the whole seedling was well inside the hose. After a onave up bow the seedling passed a point of inflexion and then a onave down bow before going down to the seond photoell, whih stopped the lok. The highest point in the last bow was level with the first photoell and thus 1.5 m above the seond photoell. Further downstream there was a box where the seedlings stopped on ushioning material, and the air was led away to the fan. The box ould be opened and the seedling taken out for further examination. Time measurements were taken in hundredths of seonds and ould be read from a digital display that was reset between seedlings. Air veloities of, and m/s were hosen to over the range used in pratie. The veloity was measured with a propeller meter (Shiltkneht Miniair 2) and adjusted with a shunt on the abovementioned box. Measurements were taken in the enter of the hose at steady state with no seedling in the hose. Some seedlingtype/hosediameter ombinations were not tested. For very high or low fullness quotients, seedlings ould not be properly transported. Statistial methods Briefly the idea behind the method is to find hisquare distributions that fit the feedtime histograms well enough to allow alulation of the proportion of seedlings on the right wing that will not reah the planting head in due time aording to the yle time of the mahine. First time readings for eah ombination of seedling type, hose diameter and air veloity were represented in a number of histograms with different lass widths by rounding (Figure 2). For eah lass i, the histograms were then transformed from the realtime axis t to an x axis by multiplying by a sale fator s and translating aording to equation (2). At this point the sale fator is still an unknown variable xi=s (titm) (2) in whih t m is the shortest feed time. The transformed Table 1. Type and number of tested seedlings, their ontainer volume and largest ross setional area. Weight and length are mean values and ranges for the seedling type. Seedling type Number Container volume, m 3 Container rosssetional area, m 2 Total weight, g Green length, m Blokplant 121 Blokplant Hiko V Planta Plantek 121 Plantek

3 Journal of Forest Engineering 51 Figure 1. Test rig onfiguration. a) 0 t m t 4 k m im b) ) Figure 2. Original feedtime histogram (a), translated and multiplied histogram by a sale fator (b) and the adapted hisquare distribution () that starts at zero.

4 52 Journal of Forest Engineering histogram for a speifi lass width was then ompared with hi square distributions (Figure 3). To be able to alulate the seedling proportions, the planting head yle time t must be transformed to the x axis. This value, x, is given by (4) x =s (t t ) (4) m Figure 3. Chi square distribution with rank 4.97 (solid) fitted to observed values (dashed) with lass width 0.18 for Blokplant 100 at m/s in mm hose. The sum of squared differenes for eah bar in the histogram was alulated and divided by the number of bars. This LS mean value, (obs hi) 2 /n, was minimized by stepwise manual interative adjustment of the rank r of the hi square distribution and t m under the ondition that the mean value t M of the histogram equaled the rank of the hi square distribution, that is ( tm tm ) For every minimized LS mean value a hi square test was arried out to determine whether there was a signifiant differene between the histogram and the hi square distribution funtion. Bars were augmented so that no more than two bars had theoretial values lower than 5. The number of degrees of freedom in the test was alulated as the resulting number of bars minus one. The signifiane level was set at The minimum LS mean values form a regression urve that has its minimum for the lass width that gives the best fit. Regression lines for rank, sale fator and lowest value give values for these, orresponding to the best lass width (Figure 4). The regression model for LS mean was a seond order polynomial and for rank, sale fator and lowest value a straight line. (3) Figure 4. Regression lines over lass width for Planta 80 at m/s in a mm hose. Remaining on the x axis the proportion of seedlings that reah the planting head at times shorter than or equal to t is s (ttm) d = f(x)dx in whih f(x) is the frequeny funtion for the fitted hi square distribution. The late arriving proportion is 1 d, and their mean feed time t t l = 1d x f s (t tm) The late feed time an be transformed bak to the real time axis and the resulting total feed time, T, for all plants alulated as the weighted mean of t and t l as (5) (6)

5 Journal of Forest Engineering 53 T = d t +(1d) (tl /s + t m ) (7) Transformation bak to the real time axis by t = x / s + t m (8) gives the resulting distribution urve in real time (Figure 5). [2], were tried in order to find the best lass width. Methods based on the number of observations, n and standard deviation did not work well. Standard deviation is sensitive to extreme values whih are not wanted in this ase, espeially not on the left wing of the distribution. A more resistant measure is the IQR, the interquartile range. Working on the basis of that riterion Freedman and Diaonis arrive at: h = 2 IQR / 3 n (9) in whih h is the lass width. This method was evaluated RESULTS Figure 5. Resulting real time distribution urve for Planta 80 at m/s in a mm hose. Calulations aording to equation (7) were arried through for eah ombination of seedling type, hose diameter and air veloity at yle times of,, and seonds. If the perentage of seedlings arriving in time reahed 100 at yle times shorter than seonds, the shorter yle time was used in onstruting the model. The 100perent limit turned out to be very diffuse due to the smooth asymptoti harater of the right wings of the distributions; therefore two values were used: One value where the rounded total feed time equaled t and one value where the rounded total feed time was one hundredth of a seond longer than t. This way eah bath that ould be used in onstruting the model generated at least two sets of input data. A linear model was then formed with mahine yle time, air veloity and the quotient of fullness q (ontainer ross setional area divided by hose ross setional area) as independent variables and the total feed time T as dependent variable. In fat, the test results indued the onstrution of two separate models by separating the seedling bathes into two groups. More diret methods by Sott and Freedman and Diaonis, reviewed by Hoaglin, Mosteller and Tukey Seedling transport did not work for three out of 33 test bathes. All three failures ourred at an air veloity of m/s, whih evidently did not provide the drag fore on the seedling required to overome frition and gravity. Test data for the different seedling bathes are given in Table 2. Results of the optimization and goodnessoffit tests are given in table 3. Rank sale fator and lowest value are the regression values orresponding to the minimum point of the regression line for the LSmean values. Sine the shortest feed time, t m was only used as a start value in the optimization the resulting lowest value in table 3 is different. Due to the regression proedure the resulting mean feed times an also differ from those in table 2. The regression values do not orrespond exatly. These mean feed times are alulated by inserting r for x in eq. (8). Rsquare values for the regressions were greater than 0.84 for LSmean and rank exept in one ase where it was 0.67 for LSmean and two ases where it was for rank. For the sale fator, Rsquared values were at least in all ases. A signifiant differene between the feedtime distribution and hisquare distributions at the 5% level was only found in six of 30 ases. This indiates that hisquare distributions an be used as an approximation of feedtime distributions. Four of the six exeptions involve Hiko seedlings. The pine bath run at m/s with mm hose (p=0.002) is adjaent to one for whih the transport failed. Moreover, it was the only bath with negative skewness. All three sprue bathes had high

6 54 Journal of Forest Engineering skewness ompared with the rest of the bathes. The m/s bath is a limit ase (p= 7), but the other two show a highly signifiant disagreement with hi square distributions with = 0.5 r. The fifth bath that did not agree with a hi square distribution was Blokplant 100 at m/s, whih also had a high skewness. This bath and the two Hiko bathes with high skewness derease too rapidly to the right of their maximum to agree with distributions with lambda values as high as 0.5 r. Lower values on lambda would give a narrower distribution and better agreement. The sixth bath that disagreed (p=0.011) was Plantek 121 at m/s. No reason for this ould be found based on its skewness. Table 2. Feed test data for the different seedling bathes. The quotient of fullness, q, is the inside hose ross setional area divided by the largest ontainer ross setional area. Q Q is the range 3 1 between the 1st and 3rd quartile. Feed time Seedling type Speies n Quotient Air of full vel. Hose ness, q m/s min, mean, Std Skewdev. t m t M ness Q3Q1 Plantek 121 Planta 80 Pine/ Sprue Sprue HIKO V Sprue Pine Plantek 81 Blokplant 121 Blokplant 100 Pine/ Sprue Sprue Pine

7 Journal of Forest Engineering 55 Table 3. Results from optimization and goodness of fit test. The three rightmost olumns ontain lass widths obtained by optimization and by using the Freedman and Diaonis formula with exponent and respetively. Seedling type r ank r Sale fator s G of p Feed times, seond lowest mean Class width, seonds FD FD optimal (0.333) (0.268) Plantek 121 Planta 80 HIKO V Plantek 81 Blokplant 121 Blokplant Treating all bathes as one homogenous group was not suessful beause the harateristis of the individual bathes differed too muh. By ontrast, it was useful to divide the seedling bathes into two groups: Group A, ontaining Plantek 121, Planta 80 and Hiko seedlings, and Group B, ontaining Plantek 81 and Blokplant seedlings. One strong indiation that this was a valid partitioning was the differene in mean feed times (Table 2 and 3). In both groups the slopes of the lines were signifiantly different from zero (p < 0.003) and from eah other (p < 0.004). R square values were rather low, i.e (Figure 6).

8 56 Journal of Forest Engineering In both models the oeffiients were signifiantly different from zero (p < for all exept the quotient of fullness for group A, for whih p = 0.005). The R squared value is 0.98 for both models and the standard error for T less than 1.5%. Figure 6. Mean feed times for seedling bathes in group A (diamonds) and group B (squares), and their regression lines over air veloity. For seedling group A the resulting model was:... T = t v q and for group B: (10) In the Freedman and Diaonis formula, equation (9), 2. IQR orresponds to Q Q in table 2. The 3 1 third olumn from the right in table 3 gives the lass widths obtained in the optimizing proess. Class widths, h, aording to (9) are given in the next olumn. If the exponent in the Freedman and Diaonis formula is altered from to lass widths will be equal to those shown in the rightmost olumn. Equations like (10) and (11) an be used to study how a speifi planting mahine with a given yle time is influened by different seedling types or to determine expeted feed times at different yle times for a speifi type of seedling. In the first ase t is held onstant and tables like Table 4 are obtained. In the seond ase qis held onstant, and tables like Table 5 are obtained.... T = t v q (11) Table 4. Total feed times, T, for quotients of fullness, q, between 0.3 and 0.9 for group A seedlings at mahine yle time t = seonds and air veloities of m/s. Air veloity, m/ s q

9 Journal of Forest Engineering 57 Table 5. Total feed times, T, for mahine yle times, t, between 2 and 3 seonds for Planta 80 (q = ) from group A in a mm hose. Air veloity, m/s t, s In both tables model estimates lower than the mahine yle time are set equal to the mahine yle time. DISCUSSION Chisquare distributions an be used as a model to desribe the feedtime distribution for many ombinations of seedling type, air veloity and hose diameter in the pneumati feeding of softwood seedlings. Real values for the rank of the hisquare distribution must be used in order to ahieve an aeptably high degree of resolution. A full expansion of the model to gamma distributions would probably give signifiant agreement for all the bathes in this study. In that ase a omputer program would have to be used to handle the stepwise adaption of lambda, rank and lowest value. The test rig onfiguration has been fixed throughout this study. The fat that standard deviation as well as Q 3 Q 1 are proportional to the mean value for both seedling groups onfirms that there is no reason to believe that the feed time pattern would be radially different if the hose length or alignment were slightly altered. Feed times for other hose lengths would then be roughly proportional to the length. Division of the seedling bathes into two groups made it possible to onstrut good models. There are three main differenes between the models: Feed times are generally lower for model A. Model A is less dependent on air veloity. Model A has a negative oeffiient for dependene on quotient of fullness, whereas model B has a positive one. The first two mentioned differenes are not unusual. The third however, a positive oeffiient for dependene on quotient of fullness is not logial. A reason for this outome ould be differenes in the aerodynamis around the ontainer bottom [4]. All seedling types in group B have a rather large buttend area perpendiular to the ontainer axis. Furthermore Blokplant seedlings have an equally thik ontainer. As a result, eddies form at the ontainer end. Under ertain onditions the eddies are ontinuously shed alternately from different sides of the ontainer, ausing the seedling to wobble. The ontainer would be flung from one side of the hose to the other, resulting in a prolongation of the feed time. Wobbling was observed visually during the study, and wobbling seedlings were ounted. Wobbling was rare at m/s. At or m/s the perentage of wobbling seedlings was learly higher for group B seedlings (1075%) ompared with group A seedlings (at most %). For several bathes the wobbline perentage was highest at m/s, whih suggests that there is a maximum at some intermediate air veloity. In any ase, wobbling ould not be inluded in either of the two linear models. Still wobbling may be an important fator responsible for differenes in seedling behavior between A and B.

10 58 Journal of Forest Engineering Finding the best lass width for adaptation of the hi square distribution through optimization requires a lot of alulations. The Freedman and Diaonis formula provides a good start irrespetive of whether the traditional exponent is hanged slightly. It is standard pratie to use lass widths of the form 1, 2 or 5 times a power of 10. Diret use of the formula gave 12 hits out of 30 bathes. For all exept one of the other bathes, lass widths were one step narrower. When was used as the exponent instead of the number of hits reahed a maximum of 21. Three out of four misses in seedling group A involved bathes without a mathing hi square distribution. The fourth was due to double rounding. Some pratial problems were enountered during the feed tests. For instane, some seedlings did not stop the time measurement, espeially at low quotients of fullness, resulting in a redued number of observations. At low quotients of fullness and low air speeds some seedlings have feed times that are three or four times the mahine yle time. What should the longest allowable feed time be? Some types of seedling ontainers tend to release peat whih moves ahead of the seedling and shuts off the time measurement too early. Therefore it is important to srutinize raw data, espeially the left wing of the obtained distribution. SUMMARY Feed time distributions in pneumati seedling feed equipment an be satisfatorily desribed by hi square distributions. For very fast seedling types (Hiko) values smaller than = 0.5 r should be used. Though butt ended seedling types show an illogial behavior, probably due to wobbling, their feed time distributions an also be obtained with the desribed method. The proportion of late seedlings alulated from the hi square distributions agree rather well with those observed within the range of interest. Differenes in behavior between seedling types led to the development of two models for desribing the total feed time. These two models an be used to simulate the produtivity of planting mahines with pneumati seedling feed systems or to analyze suh systems in other ways. REFERENCES [1] Hallonborg, U Limiting fators in mehanized tree planting. Journal of Forest Engineering. Vol 7, No.2, January [2] Hoaglin, D.C., F. Mosteller, and J.W. Tukey. Understanding robust and exploratory data analysis. John Wiley & Sons, In. 27. [3] Larsson, T Försök med rörtransport av rotade plantor. Forsningsstiftelsen Skogsarbeten, Teknik nr 5, [4] Massey, B.S. Mehanis of fluids. Van Nostrand Reinhold Company LTD,