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Influence of Tube Configuration on Seed Delivery to a Coulter
J. agric. Engng Res. (1999) 74, 177}184 Article No. jaer.1999.0449, available on line at http://www.idealibrary.com on
In#uence of Tube Con"guration on Seed Delivery to a Coulter Hans Christian Endrerud Agricultural University of Norway, Department of Agricultural Engineering, P.O. Box 5065, N-1432 As s, Norway; e-mail: [email protected] (Received 6 June 1998; accepted in revised form 4 June 1999)
An investigation has been carried out in order to "nd how the kinetic energy of seeds sliding and falling down a seed tube was in#uenced by tube diameter, inclination of the tube and radius of coulter bend in a simulation of a tube and coulter system. The kinetic coe$cient of friction found by elevating the tube until the seed velocity was constant was only valid for tube inclinations up to 253. At higher tube inclinations, the coe$cient of kinetic friction had to be replaced with a new apparent coe$cient of friction with a higher value. Ideally, the delivery tube leading to the bend should be inclined at 603 to the horizontal plane. Delivery tubes at inclinations of 903 and 453 were tested in the laboratory. The results showed that the seeds lose a considerable kinetic energy when running through a 903 bend. Seeds dropped in a vertical tube or into a bend of small radius, lost almost all their kinetic energy when colliding with the horizontal or low inclination part of the bend. To lower the impact of collisions in the bend, the ratio of the bend radius to the tube diameter should be as large as possible. Tube diameter had no in#uence on the energy loss when the delivery tube was inclined to 453. Inclined tubes into the bend were favourable, because collision energy was minimized. The results of this investigation were used in designing a new seed tube and coulter assembly for direct drilling. 1999 Silsoe Research Institute
1. Introduction Many seed drills deliver seeds from the hopper to the coulters by gravitation. The seed is accelerated by gravity as it leaves the seed hopper, but its velocity is in#uenced by the frictional characteristics of the seed in the seed tube and coulter. It is important that the seed tube and coulter are designed in such a way that the seeds do not stop, or lose too much velocity prior to deposition. The layout of the seed delivery system can consist of one or more bends, and di!erent inclinations of the tubes. Bends and gentle inclination sections of the seed delivery system reduce the seed velocity, or in the worst case stop the seed. The consequence of this may be gaps in the seed row or the blocking of the delivery tube. Few scienti"c papers cover the gravitational fall of seeds in tube systems and coulters. MuK ller and KoK ller (1996) found that seeds sliding in a coulter with a V-shaped duct system improved seed spacing in the row. Three ducts with an inclination of 40 or 503 were found optimal for the best seed placement. The authors point out that even for drills utilizing high-quality seed metering device, high friction components and non-optimal layout of tubes and bends 0021-8634/99/100177#08 $30.00/0
in the seed transport system can aggravate the longitudinal seed distribution in the seed rows. Nogtikov and Sazonov (1995) made a mathematical analysis of the con"guration of seed tubes in a seed drill. Optimum velocity of the seeds was found for a 0)25 m wide coulter design, using a 0)3 m long delivery tube at 703 inclination, leading to a bend radius of 0)3 m. Some references exist on seeds falling in a natural environment in biological physics and in agricultural materials engineering. Allen et al. (1996) have formulated and analysed models for seed dispersal and competition among species of plants. Greene and Johnson (1996) have developed a model for seed dispersal from a forest into a clearing. In agricultural engineering, several references exist on physical and aerodynamical properties of seeds. Suthar and Das (1996) have examined seeds of karingda (Citrullus lanatus) falling in air, and found a terminal velocity of 4)5}6)5 m/s depending on seed moisture. In the same investigation, the static coe$cient of friction was found to be 0)154#0)016 M for seeds starting to slide on mild steel, where M was the moisture content as a percentage. At seed moisture content of 10%, the static coe$cient of friction was 0)314, Singh and Goswami (1996) examined
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cumin (Cuminum cyminum) seeds, and found a terminal velocity of 2)6}4)8 m/s dependent on seed moisture content that ranged from 7 to 22%. The increase in terminal velocity was due to increase in mass of each seed per unit cross-sectional area. The static coe$cient of friction was found to be 0)476#0)01 M for seeds starting to slide on mild steel, and 0)26#0)016 M for seeds starting to slide on stainless steel. At 10% seed moisture, the static coe$cients of friction were 0)576 and 0)420 for seeds on mild steel and stainless steel, respectively. harman (1996) examined lentil (¸ens culinaris) seeds, and found the terminal velocity to increase linearly with moisture content, from 11 to 12 m/s for a moisture content increase from 6 to 32)5%. The kinetic coe$cient of friction k increased from 0)27 to 0)4 as seed moisture contents increased from 6 to 33% for seeds sliding on galvanized steel. At 10% moisture content, the kinetic coe$cient of friction was close to a value of 0)30. Harmond et al. (1965) found terminal velocities of 6)3, 7)0 and 9)0 m/s for oats, barley and wheat, respectively. When designing a tube and coulter assembly for a drill, the tube and bend parameters should be chosen in such a way that maximum seed velocity and exit trajectory is obtained at the outlet of the assembly. The objective of this investigation was to reveal factors contributing to the loss of seed kinetic energy in a tube and coulter assembly, and to determine optimal tube inclination, tube diameter and bend radius of such an assembly, using both mathematical modelling and laboratory experiments
2. Seed transport in a tube system
where l is the terminal velocity in m/s, i is a function of fall height and initial velocity, m is the seed mass in kg, o is the density fair (1)205 kg/m at 203C), c is the air U resistance coe$cient or drag, and A is the cross-sectional area of the seed. Values for c were not established U experimentally, but based on equations for a falling sphere, c for a sphere-shaped seed was estimated to be in U the range 0)2}0)47 (Vogel, 1981; Bosch, 1984; Ward-Smith, 1984), depending on the Reynolds number. The drag decreases with increasing Reynolds number (Daugherty et al., 1985). Sitkei (1986) states c values of 0)47}0)51 for U oats, and 0)5 for wheat and barley. Terminal velocity is given as 6)6, 7)6 and 9)6 m/s for oats, barley and wheat, respectively. Gravitational delivery of seeds from hopper to coulter in a ordinary drill, normally occurs over a height of 1)0}1)7 . In Fig. 1, the seed velocities using di!erent values for the air resistance coe$cient are compared. Height values from 1)0 to 1)7 m were used in Eqn (2). Seed velocity was calculated for values of the coe$cient of air resistance, c of 0, 0)1, 0)3 and 0)5. Using U Eqn (2), the terminal velocity for barley was estimated to be 12)2 m/s, for a c value of 0)5, a seed mass of 4)2; U 10\ kg and a cross-sectional area of 8)79;10\ m. This shows clearly that the maximum seed velocity in the tube between hopper and coulter would not reach the terminal velocity. The di!erence in calculated velocity between free fall in vacuum and when using the c values U mentioned is quite small. If the fall height is 1 m, a seed with a value for c of 0)5 has a "nal velocity 3)23% lower U than that for a seed in vacuum. Dropping through a height of 1)7 m, the di!erence in velocity would be 5)39% under the same conditions. The e!ect due to air resistance is therefore neglected in this paper.
2.1. Free fall and air resistance, a theoretical approach Under ideal conditions, a seed falling in a tube obtains a velocity given by Eqn (1), where l is the terminal velocity in m/s, g is the acceleration due to gravity, 9)81 m/s, and h is the vertical height in m. l"(2gh
2.2. Conservation of energy When a seed is dropped from rest, the initial velocity is zero and the total energy equals the potential energy
(1)
In this equation, air resistance and friction between the seed and the tube have been neglected. Air resistance and friction reduces seed air velocity under practical conditions, and Eqn (1) give higher values for l than actually are observed. If air resistance is taken into account, seed velocity is obtained using Eqn (2), (Bosch, 1984). l"l
1 2mg 1! where l " and i"eEF l K oc A U (2)
Fig. 1. Velocity of seeds for diwerent values of height and coezcient of air resistance c : , vacuum; , c "0)1; U U , c "0)30; , c "0)5 U U
T U BE C O N FI GU R A T IO N O N S EE D D E LIV ER Y
= expressed in Eqn (3). Any initial velocity of the seed caused by the metering device of the hopper, would increase the total energy, but is neglected in this paper. = "mgh (3) For a seed sliding in a non-vertical tube, the velocity is in#uenced by friction between tube and seed. The transfer of energy by the bouncing of seeds in the tube and coulter assembly, can reduce the seed velocity signi"cantly. The friction force is dependent on the coe$cient of kinetic friction k between the tube and the seed, the mass of the seed m and the tube inclination a. Values for the kinetic friction depend on seed moisture (Sitkei, 1986). Barley seeds with a moisture content of 10}20%, sliding on steel, are given a friction coe$cient equal to 0)38. The seed acceleration a is given by a"g sin a!gk cos a"g sin a!k cos a
(4)
The total acceleration force F of the seed is given by F"ma"mg (sin a!k cos a)
(5)
Equation (5) shows that the acceleration force F acting on the seed increases with the weight of the seed mg and as the inclination a of the delivery tube increases towards 903. The seed velocity is found by substituting Eqn (4) into the following expression: h l"2as"2a sin a
(6)
where s is the tube length, yielding l"2gh
sin a!k cos a "2gh (1!k cot a) sin a
(7)
The kinetic energy = after a free fall of h metres is given by = "mgh
sin a!k cos a "mgh (1!k cot a) (8) sin a
After a vertical fall through the pipe of h metres, the potential energy of the seed at the start of the fall = , is converted to an energy loss caused by friction and kinetic energy = as it enters the bend. Under ideal conditions, no collisions between the seed and the gradual inclination of the bend occur. But under real conditions, the seed collides with the walls of the bend, bounces and is exposed to forces causing a change in velocity and direction. When the seed leaves the bend, it has a kinetic energy = , where the di!erence between = and = is the loss of energy in the bend. The loss of energy is composed of losses due to collisions and friction. The loss of energy in the bend can be described as the ratio R : @ = != (9) R" @ =
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The ratio R yields a measure of the energy retained by C the seed upon exiting the bend. This ratio compares the kinetic energy leaving the bend with the potential energy in the start position, and depends on the con"guration of the seed tube and coulter assembly. This ratio R conC tains losses both in the tube and coulter. The kinetic energy of the seeds when leaving the bend ensures delivery of the seeds when the coulter is in the soil, determines proper seed placement and prevents blockage of seeds in the tube. = R" (10) C = When seeds are placed in the soil, both the seed velocity and the kinetic energy is zero. When the seed enters the bend, a third force acts on the seed in addition to the gravitation and friction components. This force exposes the seed to a centripetal acceleration, directed perpendicular to the curve of the bend. The centripetal acceleration increases with the square of the velocity, and inversely with the radius, The seed is exposed to a total acceleration in the bend given in Eqn (11). In this equation, the "rst two contributions are from the translational situation, and the third part is due to the centripetal acceleration. dl l a" "g sin h!kg cos h!k dt r
(11)
where dl is a small change in velocity measured in m/s, dt is a small change in time, h is the slope of the bend and r is the radius of the bend in m. As the seed travelled through the bend, the inclination h varied from the tube inclination of a to horizontal at the outlet. Rewriting Eqn (11), exchanging dt with dh as shown in Eqn (12), a new equation is given for bend acceleration for a given velocity and position in the bend in Eqn (13). ds dh r l"! "!r and dt"! dh dt dt l
(12)
dl gr kgr a" "! sin h# cos h#kl dh l l
(13)
The last equation, in addition to Eqn (7), is the basis for a theoretical calculation of velocity in any combination of tube and coulter assembly.
3. Materials and methods In order to examine how the seed losses its energy in the tube and coulter assembly, a laboratory experiment was conducted. The kinetic energy of seeds leaving the bend was measured as a stopping distance in a horizontal tube with the same dimensions as the acceleration zone
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Table 2 Weight of seeds and largest cross-sectional area for the seeds used in the experiment Seed Oats Barley Wheat
Seed mass, kg
Cross-sectional area, m
4)0;10\ 4)2;10\ 3)9;10\
6)38;10\ 8)79;10\ 6)90;10\
3.1. Experimental design Fig. 2. Laboratory arrangement of tubes and bend with acceleration zone, bend and stopping zone. The arrangement for the vertical acceleration zone is shown with solid lines and the acceleration zone with a 453 inclination with dashed lines
tube and bend (Fig. 2). The total stopping distance was measured from the joint between the bend and the horizontal zone, to where the seed had come to rest. The seed velocity was not measured in this experiment. All seeds were dropped from a height of 1 m above the horizontal stopping zone. The delivery tube had one of the two positions, vertical or with a 453 inclination. The end of the tube was attached to the bend. The tubes were made of transparent PMMA acrylic plastic with inner diameters of 20, 30 and 40 mm. The bends were made of PVC plastic, and the seed path had outside radius of curvature of 0)5,1 and 1)5 times the diameter of the tube. The types of seeds used were oats, barley and wheat. Table 1 shows the radius for the combinations of tubes and bends used in the experiment. The seeds of barley (Pernilla), oats (Mustang) and wheat (Folke) had di!erent masses and cross-sectional areas as shown in Table 2. The kinetic coe$cient of friction of the seeds in the tubes was found placing seeds in the tube, and elevating the tube until the seed velocity was constant. The coe$cient of friction was found for oats, barley and wheat using Eqn (14). F mg sin a "tan a k" Q" N mg cos a
(14)
where F is the frictional force and N is the normal force. Q Table 1 Radius for di4erent combinations of tubes and bends Tube diameter (D), mm 20 30 40
Bend radius, mm Small, 0)5 D
Medium, 1 D
Large, 1)5 D
10 15 20
20 30 40
30 45 60
Combinations of tube diameter, delivery tube inclination and seed types described were tested in the laboratory experiment. For every tube diameter, three di!erent bends with di!erent radii were tested as shown in Table 1. Every combination of tube diameter, bend, delivery tube inclination and seed type had 10 independent seed drops. Statistical analysis of the stopping distances was carried out with standard anova.
4. Results and discussion 4.1. Forces due to friction between the tube and the seed The coe$cients of friction between the tube and the various seeds of oats, barley and wheat used in the experiment are shown in Table 3. For inclinations of the delivery tube larger than the corresponding dynamic coe$cient of friction, it was observed that the seeds not only had a transversal movement, but also a rotating and bouncing movement during their travel down the tube. This is analogous to turbulent #ow in a #uid, and yields a higher loss of energy than in the laminar #ow. In this case, the path of the seed in the tube was longer than for pure translational movement. The kinetic energy was not only converted into frictional resistance, but also to losses due to rotation in any of the three possible axes, collisions and extra friction due to a longer path. These factors contribute to a new apparent coe$cient of friction k*, valid when the seed movement was not solely translational. The apparent coe$cient of friction k* was found measuring the time elapsed for a seed travel of 1)9 m in the delivery tube, using di!erent inclinations a of Table 3 Coe7cients of friction for oats, barley and wheat in the plastic tubes used in the experiment Seed Oats Barley Wheat
Inclination (a), degree
Coezcient of friction, k
16)65 15)30 13)50
0)300 0)274 0)240
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the tube. For each inclination of the tube, the acceleration of the seed was calculated, and the apparent coe$cient of friction was given, Eqn (15). a k*"tan a! g cos a
(15)
where a was the seed acceleration in the delivery tube. It was assumed that the acceleration was constant during the fall. This coe$cient was only calculated for barley, because the discussion on energy was for barley only. The value of a was calculated by means of an interactive method:
2 s !s !l a" *t *t
(16)
where l was the velocity after a tube distance travel of s "0)1 m, and l the velocity after s "1)9 m distance. The time taken *t for the seed to fall from s to s was measured for four di!erent inclinations. As an initial condition in the iteration, l "0 m/s was used. The ap parent coe$cient of friction k* is given in Table 4 for inclinations of 203, 253, 303 and 453 only.
4.2. Energy considerations Equations (5) and (11) were used for calculating the seed velocity, and the value for R for any possible C inclination of the delivery tube. The change of velocity in the bend was found using 200 iterations. The value of the apparent coe$cient of friction was k*"0)497, and was assumed to be valid for all inclination angles of the acceleration zone tube in the range 45}853. The mass of the barley seed was 4)2;10\ kg. Figure 3 shows the results for R for the inclinations where k* was assumed C to be valid. In the model, the seed drop height was 1 m above the lower, inner bend section and the horizontal stop zone. The results are given for the smallest and the largest bend used in the experiment, 10 and 60 mm inner bend radius. The results shown in Fig. 3 indicate that the smallest losses of energy occurred for an inclination of about 603 for the delivery tube. For inclinations greater than 603, the bend friction was dominant. For lower Table 4 Apparent coe7cient of friction l* for seeds of barley at four di4erent tube inclinations Tube inclination (a), degree
Apparent coezcient of friciton (k*)
20 25 30 45
0)250 0)294 0)304 0)497
Fig. 3. Seed kinetic energy when leaving the bend shown as a percentage of the initial potential energy R versus diwerent C values of the delivery tube inclination: , bend radius of 10 mm; , bend radius of 60 mm
inclination values, friction in the delivery tube was dominant. The di!erences in seed kinetic energy between the two bends in Fig. 3 was due to a slightly higher entry velocity in the smaller bend than in the larger bend. The loss of energy in the bend for a given inclination was independent of the bend radius, assuming that no collisions occurred. In an ideal system, the tube and bend should be constructed in such a way that losses are signi"cantly reduced or eliminated in critical zones. In a practical system with a coulter, this may be di$cult to achieve, but the losses should be reduced as much as possible. For an exact adjusted vertical delivery tube, friction is non-existent, when it is assumed that the air resistance can be neglected. When a non-vertical tube is used, the kinetic energy of the seed is dependent on friction and the tube inclination. In the laboratory experiment with a tube inclination of 453, energy e$ciency was less than optimal. The choice of coe$cient of friction has a signi"cant e!ect on the calculated velocity of the seed. The kinetic coe$cients of friction are given in Table 3, whereas the apparent coe$cient of friction was higher due to the rotating and bouncing movement. The losses in the delivery tube can be quite signi"cant as shown in Fig. 4. Here, the relative loss of energy is shown as a percentage of the total potential energy at the start of the tube. Steep delivery tubes would reduce the losses, and reduce the di!erence between the friction values for a given inclination.
4.3. Stopping distance The stopping distance was used to calculate the losses of energy in the tubes and the bend. The analysis showed that all of the factors tube diameter, bend radius, delivery tube inclination and type of seed were signi"cant at a 1% level. The vertical tube gave a stopping distance of 0)445 m, and the tube with a 453 inclination gave a
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Fig. 4. Loss of energy in the delivery tube relative to the potential energy for diwerent values of inclination, and four values for the apparent coezcients of friction k*: , k*"0)497; , k*"0)4; , k*"0)3; , k*"0)25
stopping distance of 0)802 m. Increasing tube diameters gave longer stopping distances. For a 20 mm diameter tube, the distance was 0)510 m; for 30 mm tube 0)615 m; and for the largest tube used, 40 mm, the stopping distance was 0)745 m. Di!erent seeds gave di!erent stopping distances as well. Oats had the shortest stopping distance of 0)539 m. Barley had an average of 0)605 m, and wheat the highest value of 0)726 m. The results for stopping distances for the di!erent seeds, showed a clear correlation with the coe$cient of friction. In the subsequent discussion, the di!erent seeds are handled as one group. The bend radius had a clear e!ect on the stopping distance. The small bend gave a stopping distance of 0)301 m, the medium bend gave a stopping distance of 0)599 m and the largest bend a stopping distance of 0)970 m. The real bend radius of curvature was dependent on tube diameter, as shown in Table 1. The stopping distances for the di!erent combinations of tube diameters, delivery tube inclinations and bend radii are shown in Fig. 5. A model for the stopping distance valid only for the given range of bend radii r and tube diameters d used in the experiment is expressed in Eqn (17) for the inclined tube, and in Eqn (18) for the vertical tube: s "!0)4618#0)3869 ln(r) G 0)6855(r!8)7898) s" T d
Fig. 5. Stopping distances for diwerent combinations of delivery tube inclination, tube diameters and bend radii: , 453 , 453 inclined, 30 mm tube; , 453 inclined, 20 mm tube; inclined, 40 mm tube; , vertical, 20 mm tube; , vertical, 30 mm tube; , vertical, 40 mm tube
of a collision between the seed and the inner parts of the bend is small. For a 20 mm bend radius, the value of the ratio r/d was, in this case, 1 for the 20 mm tube, and 0)5 for the 40 mm tube. A low r/d value increased the probability of a collision between seed and bend. For the 453 inclined delivery tube and small bend radii, stopping distance were of the same level as that for the di!erent tube diameters. This indicated that the bend section was free of collisions, and the friction was the only means of energy loss.
4.4. Energy loss in the tube and the bend The loss of energy in the bend R was dependent on the @ bend radius, the delivery tube inclination and the tube diameter. Figure 6 shows that the loss was approximately 25% under the best conditions that appeared at a 453 inclination of the tube, a 40 mm tube diameter and a large bend radius. When a vertical tube and a small bend radius were used, almost all of the energy was lost in the bend. The parameter R describing the kinetic energy C leaving the acceleration zone and the bend, showed that a larger bend radius resulted in a better energy utilization
(17) (18)
where s and s were the stopping distances for the tubes G T of 453 and vertical inclination, respectively. The results showed a distinct di!erence in stopping distance between a vertical delivery tube and a delivery tube with a 453 inclination, at small values of the bend radius. For larger bend radii, the two delivery tube inclinations approached similar stopping distances. For a small bend radius and a vertical delivery tube, the stopping distance was the largest for the tube with the smallest diameter. This case occurs with a coulter where space often is the limiting factor. The explanation to this can be that the likelihood
Fig. 6. Loss of energy through the bend relative to the potential energy, R for diwerent combinations of delivery tube inclinations, @ tube diameters and bend radii: , 453 inclined, 20 mm tube; , 453 inclined, 30 mm tube; , 453 inclined, 40 mm tube; , vertical, 20 mm tube; , vertical, 30 mm tube; , vertical, 40 mm tube
T U BE C O N FI GU R A T IO N O N S EE D D E LIV ER Y
Fig. 7. Amount of energy out of the bend as a percentage of the initial potential energy, R for diwerent combinations of delivery C tube inclinations, tube diameters and bend radii: , 453 inclined, 20 mm tube; , 453 inclined, 30 mm tube; , 453 inclined, 40 mm tube; , vertical, 20 mm tube; , vertical, 30 mm tube; , vertical, 40 mm tube
in the system, as shown in Fig. 7. For a small bend radius it was quite favourable to select a delivery tube section with 453 inclination rather than a vertical one, but this di!erence was reduced for a larger bend radius. For the largest bend with 60 mm radius, both vertical and inclined tubes gave the same level of energy utilization. Figure 7 also shows that the energy ratio R for a tilted C delivery tube tended to approach a horizontal asymptotic value for the highest values for bend radius. It appears that an upper limit for the energy ratio R exists C for these tubes. It was assumed that the friction in the tube and the bend were the same, and that no collisions occurred. The experiment did not indicate any upper limit for R for vertical delivery tubes, but values tended C to approach those for the tilted delivery tubes.
5. A practical application The analysis described was used in designing a coulter at the Department of Agricultural Engineering in 1994.
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The objective was to build a coulter for a new direct drill concept, each coulter sowing two rows of seeds. The coulter was of a goose-foot type shown in Fig. 8. The rows of seeds are placed on either side of the centre of the coulter, and the coulter was constructed for sowing depths of 25 mm or more. The goose-foot shape lifted the soil over the wings, and placed the seeds in each of the two rows. The coulter had two vertical delivery tubes, each leading the seeds to the separate rows. Each tube ended in a bend, with the seed exists facing opposite directions, and adjusted slightly backwards in the direction of travel. The inner tube diameter was 20 mm, and the bend radius was 30 mm. The drop height of the seeds was 1)05 m, where the "rst distance of 0)69 m was through a plastic tube, and the lower section of 0)36 m was through the vertical tube of the tube and coulter assembly. The outlet of each bend was placed approximately 25 mm to the side of the centre of the coulter. The two tubes were welded together, and were part of the structure "xing the coulter assembly to the mounting attachment of the drill. If the assumption that the coe$cient of friction is the same for the steel structure of this coulter and the plastic material in the arrangement is valid, the factor R would be slightly lesser than 35%. In C practical use, the coulter sowed two bands of seeds, each with a mean internal distance of 55 mm to the side of the centre line of the coulter. This meant that the seeds had travelled approximately 30 mm after exiting the bend of the tube and coulter attachment. This distance was limited by the soil roughness and the reduced gap under the wing of the coulter. Obviously, no seeds could penetrate outside the width of the goose-foot share. The friction between the soil and the seed was also greater than that between the tube and the seed in the stopping zone of the laboratory experiment. With this coulter, it was the shape and design of the coulter, not the seed velocity that a!ected the distance between the two rows sown by the same coulter. The calculations shown in Fig. 7 shows clearly that even a small reduction in bend
Fig. 8. Coulter for direct drilling developed at the Agricultural University of Norway, Department of Agricultural Engineering. Front view to the left, and rear view to the right
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Fig. 9. Seed placement using a goose-foot coulter for direct drilling
radius, can result in a dramatically reduced energy utilization. If the coulter had been equipped with a 20 mm bend radius, the expected value of R would have been C approximately 10%. This would clearly a!ect the interrow distance produced by the coulter given a sub-optimal seed distribution. Figure 9 shows an illustration of the seed placement when the seeds left the tube bends. The "gure also shows how the soil was lifted over the share of the coulter as the seeds were placed underneath. The sowing depth was controlled by means of a combined packing and depth control wheel, following the coulter.
6. Conclusion The maximum calculated seed velocity in a conventional drill delivery tube is expected to be lower than the calculated terminal velocity for the seeds of oats, barley and wheat. The coe$cients of friction were in the range 0)24}0)3 for these seed types, where wheat had the lowest sliding friction in the plastic tube. These coe$cients of friction corresponded with tube inclinations in the range 13)5}16)653. When the inclination of the delivery tube was larger than 253, the seed was also subjected to additional energy losses because of rotation, collision and extra friction due to a longer sliding path. The total energy loss at these quite steep inclination could therefore not be described properly by the coe$cient of kinetic friction. Hence a new apparent coe$cient of friction was calculated. This coe$cient increased with tube inclination and, for an inclination of 453, was about twice the value of the measured kinetic coe$cient of friction. Based on this new apparent coe$cient of friction, the optimal inclination of the delivery tube leading into a bend was calculated to be about 603. For inclinations of less than 603, the friction in the delivery tube was dominant, but at inclinations higher than 603, the friction in the bend was dominant. The transport of barley seeds in a tube and coulter assembly, simulating the arrangement on a drill, exposed the seeds to large energy losses in the tubes. The seed kinetic energy when leaving the bend, expressed as the stopping distance, was greater for the tube with an
inclination of 453, than for the vertical tube. With the inclined tube, the stopping distance was only dependent on bend radius, and with the vertical tube, both bend radius and tube diameter was signi"cant. At a given bend radius, the stopping distance was larger for a delivery tube of 453 inclination than for a vertical tube. In the latter situation, seed collisions in the tube and coulter arrangement was likely to occur, and caused a great energy loss. The tube diameter was critical for the vertical delivery tube. The stopping distance decreased with increasing tube diameter, and a small tube diameter was favourable in this case.
Acknowledgements The author would like to thank Professor Peder Tyvand and Associate Professor Bj+rn Berre for valuable help with discussion on theory and analysis of the results. This paper was made possible by funding from the Research Council of Norway.
References Allen E J; Allen L J S; Gilliam X (1996). Dispersal and competition models for plants. Journal of Mathematical Biology. 34(4), 455}481 Bosch GmbH (1984). Kraftfahr Technisches Tashenbuch. VDIVerlag, DuK sseldorf, Germany xarman K (1996). Some physical properties of lentil seeds. Journal of Agricultural Engineering Research, 63, 87}92 Daugherty R; Franzini J B; Finnemore E J (1985). Fluid mechanics with engineering applications. McGraw-Hill, New York, United States Greene D J; Johnson E A (1996). Wind dispersal of seeds from a forest into a clearing. Ecology, 77(2), 595}609 Harmond J E; Brandenburg N R; Jensen L A (1965). Physical properties of seed. Transactions of the ASAE, 8(1), 30}32 MuK ller J; KoK ller K (1996). Improvement of seed spacing for seed drills. AgEng'96 Conference on Agricultural Engineering. Madrid, Spain Nogtikov A A ; Sazonov S N (1995). Determination of the parameters of the seed-duct for coulters distributing seed in the soil. Tekhnika Selskom Khozyaistve, 3, 29}31 Singh K K; Goswami T K (1996). Physical properties of cumin seed. Journal of Agricultural Engineering Research, 64, 93}98 Sitkei G (1986). Mechanics of agricultural materials. Developments in Agricultural Engineering: 8. Elsevier, Amsterdam, the Netherlands Suthar S H; Das S K (1996). Some physical properties of karingda [Citrullus lanatus (thumb) mansf] seeds. Journal of Agricultural Engineering Research, 65, 15}22 Vogel S (1981). Life in Moving Fluids. Willard Grant Press, Boston, United States Ward-Smith A J (1984). Biophysical Aerodynamics and the Natural Environment. Wiley, Chichester, US
In#uence of Tube Con"guration on Seed Delivery to a Coulter Hans Christian Endrerud Agricultural University of Norway, Department of Agricultural Engineering, P.O. Box 5065, N-1432 As s, Norway; e-mail: [email protected] (Received 6 June 1998; accepted in revised form 4 June 1999)
An investigation has been carried out in order to "nd how the kinetic energy of seeds sliding and falling down a seed tube was in#uenced by tube diameter, inclination of the tube and radius of coulter bend in a simulation of a tube and coulter system. The kinetic coe$cient of friction found by elevating the tube until the seed velocity was constant was only valid for tube inclinations up to 253. At higher tube inclinations, the coe$cient of kinetic friction had to be replaced with a new apparent coe$cient of friction with a higher value. Ideally, the delivery tube leading to the bend should be inclined at 603 to the horizontal plane. Delivery tubes at inclinations of 903 and 453 were tested in the laboratory. The results showed that the seeds lose a considerable kinetic energy when running through a 903 bend. Seeds dropped in a vertical tube or into a bend of small radius, lost almost all their kinetic energy when colliding with the horizontal or low inclination part of the bend. To lower the impact of collisions in the bend, the ratio of the bend radius to the tube diameter should be as large as possible. Tube diameter had no in#uence on the energy loss when the delivery tube was inclined to 453. Inclined tubes into the bend were favourable, because collision energy was minimized. The results of this investigation were used in designing a new seed tube and coulter assembly for direct drilling. 1999 Silsoe Research Institute
1. Introduction Many seed drills deliver seeds from the hopper to the coulters by gravitation. The seed is accelerated by gravity as it leaves the seed hopper, but its velocity is in#uenced by the frictional characteristics of the seed in the seed tube and coulter. It is important that the seed tube and coulter are designed in such a way that the seeds do not stop, or lose too much velocity prior to deposition. The layout of the seed delivery system can consist of one or more bends, and di!erent inclinations of the tubes. Bends and gentle inclination sections of the seed delivery system reduce the seed velocity, or in the worst case stop the seed. The consequence of this may be gaps in the seed row or the blocking of the delivery tube. Few scienti"c papers cover the gravitational fall of seeds in tube systems and coulters. MuK ller and KoK ller (1996) found that seeds sliding in a coulter with a V-shaped duct system improved seed spacing in the row. Three ducts with an inclination of 40 or 503 were found optimal for the best seed placement. The authors point out that even for drills utilizing high-quality seed metering device, high friction components and non-optimal layout of tubes and bends 0021-8634/99/100177#08 $30.00/0
in the seed transport system can aggravate the longitudinal seed distribution in the seed rows. Nogtikov and Sazonov (1995) made a mathematical analysis of the con"guration of seed tubes in a seed drill. Optimum velocity of the seeds was found for a 0)25 m wide coulter design, using a 0)3 m long delivery tube at 703 inclination, leading to a bend radius of 0)3 m. Some references exist on seeds falling in a natural environment in biological physics and in agricultural materials engineering. Allen et al. (1996) have formulated and analysed models for seed dispersal and competition among species of plants. Greene and Johnson (1996) have developed a model for seed dispersal from a forest into a clearing. In agricultural engineering, several references exist on physical and aerodynamical properties of seeds. Suthar and Das (1996) have examined seeds of karingda (Citrullus lanatus) falling in air, and found a terminal velocity of 4)5}6)5 m/s depending on seed moisture. In the same investigation, the static coe$cient of friction was found to be 0)154#0)016 M for seeds starting to slide on mild steel, where M was the moisture content as a percentage. At seed moisture content of 10%, the static coe$cient of friction was 0)314, Singh and Goswami (1996) examined
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cumin (Cuminum cyminum) seeds, and found a terminal velocity of 2)6}4)8 m/s dependent on seed moisture content that ranged from 7 to 22%. The increase in terminal velocity was due to increase in mass of each seed per unit cross-sectional area. The static coe$cient of friction was found to be 0)476#0)01 M for seeds starting to slide on mild steel, and 0)26#0)016 M for seeds starting to slide on stainless steel. At 10% seed moisture, the static coe$cients of friction were 0)576 and 0)420 for seeds on mild steel and stainless steel, respectively. harman (1996) examined lentil (¸ens culinaris) seeds, and found the terminal velocity to increase linearly with moisture content, from 11 to 12 m/s for a moisture content increase from 6 to 32)5%. The kinetic coe$cient of friction k increased from 0)27 to 0)4 as seed moisture contents increased from 6 to 33% for seeds sliding on galvanized steel. At 10% moisture content, the kinetic coe$cient of friction was close to a value of 0)30. Harmond et al. (1965) found terminal velocities of 6)3, 7)0 and 9)0 m/s for oats, barley and wheat, respectively. When designing a tube and coulter assembly for a drill, the tube and bend parameters should be chosen in such a way that maximum seed velocity and exit trajectory is obtained at the outlet of the assembly. The objective of this investigation was to reveal factors contributing to the loss of seed kinetic energy in a tube and coulter assembly, and to determine optimal tube inclination, tube diameter and bend radius of such an assembly, using both mathematical modelling and laboratory experiments
2. Seed transport in a tube system
where l is the terminal velocity in m/s, i is a function of fall height and initial velocity, m is the seed mass in kg, o is the density fair (1)205 kg/m at 203C), c is the air U resistance coe$cient or drag, and A is the cross-sectional area of the seed. Values for c were not established U experimentally, but based on equations for a falling sphere, c for a sphere-shaped seed was estimated to be in U the range 0)2}0)47 (Vogel, 1981; Bosch, 1984; Ward-Smith, 1984), depending on the Reynolds number. The drag decreases with increasing Reynolds number (Daugherty et al., 1985). Sitkei (1986) states c values of 0)47}0)51 for U oats, and 0)5 for wheat and barley. Terminal velocity is given as 6)6, 7)6 and 9)6 m/s for oats, barley and wheat, respectively. Gravitational delivery of seeds from hopper to coulter in a ordinary drill, normally occurs over a height of 1)0}1)7 . In Fig. 1, the seed velocities using di!erent values for the air resistance coe$cient are compared. Height values from 1)0 to 1)7 m were used in Eqn (2). Seed velocity was calculated for values of the coe$cient of air resistance, c of 0, 0)1, 0)3 and 0)5. Using U Eqn (2), the terminal velocity for barley was estimated to be 12)2 m/s, for a c value of 0)5, a seed mass of 4)2; U 10\ kg and a cross-sectional area of 8)79;10\ m. This shows clearly that the maximum seed velocity in the tube between hopper and coulter would not reach the terminal velocity. The di!erence in calculated velocity between free fall in vacuum and when using the c values U mentioned is quite small. If the fall height is 1 m, a seed with a value for c of 0)5 has a "nal velocity 3)23% lower U than that for a seed in vacuum. Dropping through a height of 1)7 m, the di!erence in velocity would be 5)39% under the same conditions. The e!ect due to air resistance is therefore neglected in this paper.
2.1. Free fall and air resistance, a theoretical approach Under ideal conditions, a seed falling in a tube obtains a velocity given by Eqn (1), where l is the terminal velocity in m/s, g is the acceleration due to gravity, 9)81 m/s, and h is the vertical height in m. l"(2gh
2.2. Conservation of energy When a seed is dropped from rest, the initial velocity is zero and the total energy equals the potential energy
(1)
In this equation, air resistance and friction between the seed and the tube have been neglected. Air resistance and friction reduces seed air velocity under practical conditions, and Eqn (1) give higher values for l than actually are observed. If air resistance is taken into account, seed velocity is obtained using Eqn (2), (Bosch, 1984). l"l
1 2mg 1! where l " and i"eEF l K oc A U (2)
Fig. 1. Velocity of seeds for diwerent values of height and coezcient of air resistance c : , vacuum; , c "0)1; U U , c "0)30; , c "0)5 U U
T U BE C O N FI GU R A T IO N O N S EE D D E LIV ER Y
= expressed in Eqn (3). Any initial velocity of the seed caused by the metering device of the hopper, would increase the total energy, but is neglected in this paper. = "mgh (3) For a seed sliding in a non-vertical tube, the velocity is in#uenced by friction between tube and seed. The transfer of energy by the bouncing of seeds in the tube and coulter assembly, can reduce the seed velocity signi"cantly. The friction force is dependent on the coe$cient of kinetic friction k between the tube and the seed, the mass of the seed m and the tube inclination a. Values for the kinetic friction depend on seed moisture (Sitkei, 1986). Barley seeds with a moisture content of 10}20%, sliding on steel, are given a friction coe$cient equal to 0)38. The seed acceleration a is given by a"g sin a!gk cos a"g sin a!k cos a
(4)
The total acceleration force F of the seed is given by F"ma"mg (sin a!k cos a)
(5)
Equation (5) shows that the acceleration force F acting on the seed increases with the weight of the seed mg and as the inclination a of the delivery tube increases towards 903. The seed velocity is found by substituting Eqn (4) into the following expression: h l"2as"2a sin a
(6)
where s is the tube length, yielding l"2gh
sin a!k cos a "2gh (1!k cot a) sin a
(7)
The kinetic energy = after a free fall of h metres is given by = "mgh
sin a!k cos a "mgh (1!k cot a) (8) sin a
After a vertical fall through the pipe of h metres, the potential energy of the seed at the start of the fall = , is converted to an energy loss caused by friction and kinetic energy = as it enters the bend. Under ideal conditions, no collisions between the seed and the gradual inclination of the bend occur. But under real conditions, the seed collides with the walls of the bend, bounces and is exposed to forces causing a change in velocity and direction. When the seed leaves the bend, it has a kinetic energy = , where the di!erence between = and = is the loss of energy in the bend. The loss of energy is composed of losses due to collisions and friction. The loss of energy in the bend can be described as the ratio R : @ = != (9) R" @ =
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The ratio R yields a measure of the energy retained by C the seed upon exiting the bend. This ratio compares the kinetic energy leaving the bend with the potential energy in the start position, and depends on the con"guration of the seed tube and coulter assembly. This ratio R conC tains losses both in the tube and coulter. The kinetic energy of the seeds when leaving the bend ensures delivery of the seeds when the coulter is in the soil, determines proper seed placement and prevents blockage of seeds in the tube. = R" (10) C = When seeds are placed in the soil, both the seed velocity and the kinetic energy is zero. When the seed enters the bend, a third force acts on the seed in addition to the gravitation and friction components. This force exposes the seed to a centripetal acceleration, directed perpendicular to the curve of the bend. The centripetal acceleration increases with the square of the velocity, and inversely with the radius, The seed is exposed to a total acceleration in the bend given in Eqn (11). In this equation, the "rst two contributions are from the translational situation, and the third part is due to the centripetal acceleration. dl l a" "g sin h!kg cos h!k dt r
(11)
where dl is a small change in velocity measured in m/s, dt is a small change in time, h is the slope of the bend and r is the radius of the bend in m. As the seed travelled through the bend, the inclination h varied from the tube inclination of a to horizontal at the outlet. Rewriting Eqn (11), exchanging dt with dh as shown in Eqn (12), a new equation is given for bend acceleration for a given velocity and position in the bend in Eqn (13). ds dh r l"! "!r and dt"! dh dt dt l
(12)
dl gr kgr a" "! sin h# cos h#kl dh l l
(13)
The last equation, in addition to Eqn (7), is the basis for a theoretical calculation of velocity in any combination of tube and coulter assembly.
3. Materials and methods In order to examine how the seed losses its energy in the tube and coulter assembly, a laboratory experiment was conducted. The kinetic energy of seeds leaving the bend was measured as a stopping distance in a horizontal tube with the same dimensions as the acceleration zone
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Table 2 Weight of seeds and largest cross-sectional area for the seeds used in the experiment Seed Oats Barley Wheat
Seed mass, kg
Cross-sectional area, m
4)0;10\ 4)2;10\ 3)9;10\
6)38;10\ 8)79;10\ 6)90;10\
3.1. Experimental design Fig. 2. Laboratory arrangement of tubes and bend with acceleration zone, bend and stopping zone. The arrangement for the vertical acceleration zone is shown with solid lines and the acceleration zone with a 453 inclination with dashed lines
tube and bend (Fig. 2). The total stopping distance was measured from the joint between the bend and the horizontal zone, to where the seed had come to rest. The seed velocity was not measured in this experiment. All seeds were dropped from a height of 1 m above the horizontal stopping zone. The delivery tube had one of the two positions, vertical or with a 453 inclination. The end of the tube was attached to the bend. The tubes were made of transparent PMMA acrylic plastic with inner diameters of 20, 30 and 40 mm. The bends were made of PVC plastic, and the seed path had outside radius of curvature of 0)5,1 and 1)5 times the diameter of the tube. The types of seeds used were oats, barley and wheat. Table 1 shows the radius for the combinations of tubes and bends used in the experiment. The seeds of barley (Pernilla), oats (Mustang) and wheat (Folke) had di!erent masses and cross-sectional areas as shown in Table 2. The kinetic coe$cient of friction of the seeds in the tubes was found placing seeds in the tube, and elevating the tube until the seed velocity was constant. The coe$cient of friction was found for oats, barley and wheat using Eqn (14). F mg sin a "tan a k" Q" N mg cos a
(14)
where F is the frictional force and N is the normal force. Q Table 1 Radius for di4erent combinations of tubes and bends Tube diameter (D), mm 20 30 40
Bend radius, mm Small, 0)5 D
Medium, 1 D
Large, 1)5 D
10 15 20
20 30 40
30 45 60
Combinations of tube diameter, delivery tube inclination and seed types described were tested in the laboratory experiment. For every tube diameter, three di!erent bends with di!erent radii were tested as shown in Table 1. Every combination of tube diameter, bend, delivery tube inclination and seed type had 10 independent seed drops. Statistical analysis of the stopping distances was carried out with standard anova.
4. Results and discussion 4.1. Forces due to friction between the tube and the seed The coe$cients of friction between the tube and the various seeds of oats, barley and wheat used in the experiment are shown in Table 3. For inclinations of the delivery tube larger than the corresponding dynamic coe$cient of friction, it was observed that the seeds not only had a transversal movement, but also a rotating and bouncing movement during their travel down the tube. This is analogous to turbulent #ow in a #uid, and yields a higher loss of energy than in the laminar #ow. In this case, the path of the seed in the tube was longer than for pure translational movement. The kinetic energy was not only converted into frictional resistance, but also to losses due to rotation in any of the three possible axes, collisions and extra friction due to a longer path. These factors contribute to a new apparent coe$cient of friction k*, valid when the seed movement was not solely translational. The apparent coe$cient of friction k* was found measuring the time elapsed for a seed travel of 1)9 m in the delivery tube, using di!erent inclinations a of Table 3 Coe7cients of friction for oats, barley and wheat in the plastic tubes used in the experiment Seed Oats Barley Wheat
Inclination (a), degree
Coezcient of friction, k
16)65 15)30 13)50
0)300 0)274 0)240
T U BE C O N FI GU R A T IO N O N S EE D D E LIV ER Y
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the tube. For each inclination of the tube, the acceleration of the seed was calculated, and the apparent coe$cient of friction was given, Eqn (15). a k*"tan a! g cos a
(15)
where a was the seed acceleration in the delivery tube. It was assumed that the acceleration was constant during the fall. This coe$cient was only calculated for barley, because the discussion on energy was for barley only. The value of a was calculated by means of an interactive method:
2 s !s !l a" *t *t
(16)
where l was the velocity after a tube distance travel of s "0)1 m, and l the velocity after s "1)9 m distance. The time taken *t for the seed to fall from s to s was measured for four di!erent inclinations. As an initial condition in the iteration, l "0 m/s was used. The ap parent coe$cient of friction k* is given in Table 4 for inclinations of 203, 253, 303 and 453 only.
4.2. Energy considerations Equations (5) and (11) were used for calculating the seed velocity, and the value for R for any possible C inclination of the delivery tube. The change of velocity in the bend was found using 200 iterations. The value of the apparent coe$cient of friction was k*"0)497, and was assumed to be valid for all inclination angles of the acceleration zone tube in the range 45}853. The mass of the barley seed was 4)2;10\ kg. Figure 3 shows the results for R for the inclinations where k* was assumed C to be valid. In the model, the seed drop height was 1 m above the lower, inner bend section and the horizontal stop zone. The results are given for the smallest and the largest bend used in the experiment, 10 and 60 mm inner bend radius. The results shown in Fig. 3 indicate that the smallest losses of energy occurred for an inclination of about 603 for the delivery tube. For inclinations greater than 603, the bend friction was dominant. For lower Table 4 Apparent coe7cient of friction l* for seeds of barley at four di4erent tube inclinations Tube inclination (a), degree
Apparent coezcient of friciton (k*)
20 25 30 45
0)250 0)294 0)304 0)497
Fig. 3. Seed kinetic energy when leaving the bend shown as a percentage of the initial potential energy R versus diwerent C values of the delivery tube inclination: , bend radius of 10 mm; , bend radius of 60 mm
inclination values, friction in the delivery tube was dominant. The di!erences in seed kinetic energy between the two bends in Fig. 3 was due to a slightly higher entry velocity in the smaller bend than in the larger bend. The loss of energy in the bend for a given inclination was independent of the bend radius, assuming that no collisions occurred. In an ideal system, the tube and bend should be constructed in such a way that losses are signi"cantly reduced or eliminated in critical zones. In a practical system with a coulter, this may be di$cult to achieve, but the losses should be reduced as much as possible. For an exact adjusted vertical delivery tube, friction is non-existent, when it is assumed that the air resistance can be neglected. When a non-vertical tube is used, the kinetic energy of the seed is dependent on friction and the tube inclination. In the laboratory experiment with a tube inclination of 453, energy e$ciency was less than optimal. The choice of coe$cient of friction has a signi"cant e!ect on the calculated velocity of the seed. The kinetic coe$cients of friction are given in Table 3, whereas the apparent coe$cient of friction was higher due to the rotating and bouncing movement. The losses in the delivery tube can be quite signi"cant as shown in Fig. 4. Here, the relative loss of energy is shown as a percentage of the total potential energy at the start of the tube. Steep delivery tubes would reduce the losses, and reduce the di!erence between the friction values for a given inclination.
4.3. Stopping distance The stopping distance was used to calculate the losses of energy in the tubes and the bend. The analysis showed that all of the factors tube diameter, bend radius, delivery tube inclination and type of seed were signi"cant at a 1% level. The vertical tube gave a stopping distance of 0)445 m, and the tube with a 453 inclination gave a
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Fig. 4. Loss of energy in the delivery tube relative to the potential energy for diwerent values of inclination, and four values for the apparent coezcients of friction k*: , k*"0)497; , k*"0)4; , k*"0)3; , k*"0)25
stopping distance of 0)802 m. Increasing tube diameters gave longer stopping distances. For a 20 mm diameter tube, the distance was 0)510 m; for 30 mm tube 0)615 m; and for the largest tube used, 40 mm, the stopping distance was 0)745 m. Di!erent seeds gave di!erent stopping distances as well. Oats had the shortest stopping distance of 0)539 m. Barley had an average of 0)605 m, and wheat the highest value of 0)726 m. The results for stopping distances for the di!erent seeds, showed a clear correlation with the coe$cient of friction. In the subsequent discussion, the di!erent seeds are handled as one group. The bend radius had a clear e!ect on the stopping distance. The small bend gave a stopping distance of 0)301 m, the medium bend gave a stopping distance of 0)599 m and the largest bend a stopping distance of 0)970 m. The real bend radius of curvature was dependent on tube diameter, as shown in Table 1. The stopping distances for the di!erent combinations of tube diameters, delivery tube inclinations and bend radii are shown in Fig. 5. A model for the stopping distance valid only for the given range of bend radii r and tube diameters d used in the experiment is expressed in Eqn (17) for the inclined tube, and in Eqn (18) for the vertical tube: s "!0)4618#0)3869 ln(r) G 0)6855(r!8)7898) s" T d
Fig. 5. Stopping distances for diwerent combinations of delivery tube inclination, tube diameters and bend radii: , 453 , 453 inclined, 30 mm tube; , 453 inclined, 20 mm tube; inclined, 40 mm tube; , vertical, 20 mm tube; , vertical, 30 mm tube; , vertical, 40 mm tube
of a collision between the seed and the inner parts of the bend is small. For a 20 mm bend radius, the value of the ratio r/d was, in this case, 1 for the 20 mm tube, and 0)5 for the 40 mm tube. A low r/d value increased the probability of a collision between seed and bend. For the 453 inclined delivery tube and small bend radii, stopping distance were of the same level as that for the di!erent tube diameters. This indicated that the bend section was free of collisions, and the friction was the only means of energy loss.
4.4. Energy loss in the tube and the bend The loss of energy in the bend R was dependent on the @ bend radius, the delivery tube inclination and the tube diameter. Figure 6 shows that the loss was approximately 25% under the best conditions that appeared at a 453 inclination of the tube, a 40 mm tube diameter and a large bend radius. When a vertical tube and a small bend radius were used, almost all of the energy was lost in the bend. The parameter R describing the kinetic energy C leaving the acceleration zone and the bend, showed that a larger bend radius resulted in a better energy utilization
(17) (18)
where s and s were the stopping distances for the tubes G T of 453 and vertical inclination, respectively. The results showed a distinct di!erence in stopping distance between a vertical delivery tube and a delivery tube with a 453 inclination, at small values of the bend radius. For larger bend radii, the two delivery tube inclinations approached similar stopping distances. For a small bend radius and a vertical delivery tube, the stopping distance was the largest for the tube with the smallest diameter. This case occurs with a coulter where space often is the limiting factor. The explanation to this can be that the likelihood
Fig. 6. Loss of energy through the bend relative to the potential energy, R for diwerent combinations of delivery tube inclinations, @ tube diameters and bend radii: , 453 inclined, 20 mm tube; , 453 inclined, 30 mm tube; , 453 inclined, 40 mm tube; , vertical, 20 mm tube; , vertical, 30 mm tube; , vertical, 40 mm tube
T U BE C O N FI GU R A T IO N O N S EE D D E LIV ER Y
Fig. 7. Amount of energy out of the bend as a percentage of the initial potential energy, R for diwerent combinations of delivery C tube inclinations, tube diameters and bend radii: , 453 inclined, 20 mm tube; , 453 inclined, 30 mm tube; , 453 inclined, 40 mm tube; , vertical, 20 mm tube; , vertical, 30 mm tube; , vertical, 40 mm tube
in the system, as shown in Fig. 7. For a small bend radius it was quite favourable to select a delivery tube section with 453 inclination rather than a vertical one, but this di!erence was reduced for a larger bend radius. For the largest bend with 60 mm radius, both vertical and inclined tubes gave the same level of energy utilization. Figure 7 also shows that the energy ratio R for a tilted C delivery tube tended to approach a horizontal asymptotic value for the highest values for bend radius. It appears that an upper limit for the energy ratio R exists C for these tubes. It was assumed that the friction in the tube and the bend were the same, and that no collisions occurred. The experiment did not indicate any upper limit for R for vertical delivery tubes, but values tended C to approach those for the tilted delivery tubes.
5. A practical application The analysis described was used in designing a coulter at the Department of Agricultural Engineering in 1994.
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The objective was to build a coulter for a new direct drill concept, each coulter sowing two rows of seeds. The coulter was of a goose-foot type shown in Fig. 8. The rows of seeds are placed on either side of the centre of the coulter, and the coulter was constructed for sowing depths of 25 mm or more. The goose-foot shape lifted the soil over the wings, and placed the seeds in each of the two rows. The coulter had two vertical delivery tubes, each leading the seeds to the separate rows. Each tube ended in a bend, with the seed exists facing opposite directions, and adjusted slightly backwards in the direction of travel. The inner tube diameter was 20 mm, and the bend radius was 30 mm. The drop height of the seeds was 1)05 m, where the "rst distance of 0)69 m was through a plastic tube, and the lower section of 0)36 m was through the vertical tube of the tube and coulter assembly. The outlet of each bend was placed approximately 25 mm to the side of the centre of the coulter. The two tubes were welded together, and were part of the structure "xing the coulter assembly to the mounting attachment of the drill. If the assumption that the coe$cient of friction is the same for the steel structure of this coulter and the plastic material in the arrangement is valid, the factor R would be slightly lesser than 35%. In C practical use, the coulter sowed two bands of seeds, each with a mean internal distance of 55 mm to the side of the centre line of the coulter. This meant that the seeds had travelled approximately 30 mm after exiting the bend of the tube and coulter attachment. This distance was limited by the soil roughness and the reduced gap under the wing of the coulter. Obviously, no seeds could penetrate outside the width of the goose-foot share. The friction between the soil and the seed was also greater than that between the tube and the seed in the stopping zone of the laboratory experiment. With this coulter, it was the shape and design of the coulter, not the seed velocity that a!ected the distance between the two rows sown by the same coulter. The calculations shown in Fig. 7 shows clearly that even a small reduction in bend
Fig. 8. Coulter for direct drilling developed at the Agricultural University of Norway, Department of Agricultural Engineering. Front view to the left, and rear view to the right
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Fig. 9. Seed placement using a goose-foot coulter for direct drilling
radius, can result in a dramatically reduced energy utilization. If the coulter had been equipped with a 20 mm bend radius, the expected value of R would have been C approximately 10%. This would clearly a!ect the interrow distance produced by the coulter given a sub-optimal seed distribution. Figure 9 shows an illustration of the seed placement when the seeds left the tube bends. The "gure also shows how the soil was lifted over the share of the coulter as the seeds were placed underneath. The sowing depth was controlled by means of a combined packing and depth control wheel, following the coulter.
6. Conclusion The maximum calculated seed velocity in a conventional drill delivery tube is expected to be lower than the calculated terminal velocity for the seeds of oats, barley and wheat. The coe$cients of friction were in the range 0)24}0)3 for these seed types, where wheat had the lowest sliding friction in the plastic tube. These coe$cients of friction corresponded with tube inclinations in the range 13)5}16)653. When the inclination of the delivery tube was larger than 253, the seed was also subjected to additional energy losses because of rotation, collision and extra friction due to a longer sliding path. The total energy loss at these quite steep inclination could therefore not be described properly by the coe$cient of kinetic friction. Hence a new apparent coe$cient of friction was calculated. This coe$cient increased with tube inclination and, for an inclination of 453, was about twice the value of the measured kinetic coe$cient of friction. Based on this new apparent coe$cient of friction, the optimal inclination of the delivery tube leading into a bend was calculated to be about 603. For inclinations of less than 603, the friction in the delivery tube was dominant, but at inclinations higher than 603, the friction in the bend was dominant. The transport of barley seeds in a tube and coulter assembly, simulating the arrangement on a drill, exposed the seeds to large energy losses in the tubes. The seed kinetic energy when leaving the bend, expressed as the stopping distance, was greater for the tube with an
inclination of 453, than for the vertical tube. With the inclined tube, the stopping distance was only dependent on bend radius, and with the vertical tube, both bend radius and tube diameter was signi"cant. At a given bend radius, the stopping distance was larger for a delivery tube of 453 inclination than for a vertical tube. In the latter situation, seed collisions in the tube and coulter arrangement was likely to occur, and caused a great energy loss. The tube diameter was critical for the vertical delivery tube. The stopping distance decreased with increasing tube diameter, and a small tube diameter was favourable in this case.
Acknowledgements The author would like to thank Professor Peder Tyvand and Associate Professor Bj+rn Berre for valuable help with discussion on theory and analysis of the results. This paper was made possible by funding from the Research Council of Norway.
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