Mathematical Modeling and Optimization of Seed Distribution Uniformity in Planting of Sage Seeds Using a Micro-Granular Applicator

Abstract

The objective of this study was to determine the seed flow characteristics and in-row seed distribution uniformity under different operating conditions to develop mathematical models and to optimize the seed distribution uniformity in the seeding of sage seeds by a micro-granule applicator equipped with a conveyor belt seed-metering unit. In this study, weighing tests were used to determine the seed flow characteristics, while sticky belt tests were used to determine the in-row seed distribution uniformity. While the evaluations of flow uniformity were carried out depending on the coefficient of variation values (CVs), in-row seed distribution uniformity evaluations were carried out using the values of the variation factor (V_f) and goodness criterion (λ). Central Composite Design (CCD) was used as the experimental design. Based on the analysis of data obtained from the experiments, the polynomial functions were developed for V_f and λ values and the models were optimized. The forward speed was determined as 2.14 m s⁻¹, the seed rate was 13.9 kg ha⁻¹, and the seed falling angle was 42.73° for the V_f model, while these values were determined as 2.43 m s⁻¹, 14.7 kg ha⁻¹, and 33.11°, respectively, for the λ model. All these findings reveal that the metering unit equipped with conveyor belt could be used for the seeding of sage seeds successfully. Data and information found in this work would have great potential to be used as a guide for farmers, manufacturers, and scientists who work in such areas.

1. Introduction

Medicinal and aromatic plants have been used in many industries such as medicine, food, chemistry, cosmetics, beverages, and soft drinks for many years. They are also of great importance in terms of agriculture and trade, especially in countries with suitable climate conditions for the cultivation of these plants.

The demand for medicinal and aromatic plants in world marketing has an increasing trend. China, India, the USA, Germany, Mexico, Egypt, Bulgaria, Chile, Singapore, Morocco, Pakistan, and Turkey are among the countries that import and export the most medicinal and aromatic plants in the world.

The increasing demand for medicinal and aromatic plants brings the need for agricultural practices that will increase the quality and yield of these plants. Even the smallest improvement in planting practices, which is one of the most important steps in the plant production chain, may have a major impact on the quality and yield of the product to be harvested and may be an important added value for producers.

Studies conducted on medicinal and aromatic plants around the world generally focus on issues such as the effect of climatic conditions on these plants [1], determining different usage areas of these plants [2], and the harvesting and drying of the plants [3,4,5,6,7].

Studies involving seeding, harvesting, and drying mechanizations have generally been conducted by agronomists. In these studies, seeds were mostly placed in the soil by hand, and plants were harvested and evaluated in terms of yield and quality parameters [8,9]. Currently, there is a limited number of studies conducted using seeders when only considering evaluating machine performance [10,11].

When studies using sage are examined, the situation is similar. For instance, in previous work [12], applications that increase germination and emergence performance in sage species were revealed. For this purpose, nine different coating techniques were applied to sage seeds and germination, and emergence degrees were observed. Based on the statistical analysis, it was found that the coating processes affected the seeds positively and germination and emergence degrees were improved.

In previous work [13], a new harvester prototype was developed for cutting and collecting different types of aromatic and medical plants. To test this harvester, sage, rosemary, and winter savory were used. Based on the results, it was found that the working time taken by the machine to collect sage was the highest compared to other plants. The average value of fuel consumption for sage was also found to be the highest one with 0.32 kg kWh⁻¹. The machine working efficiency ranged from 28.5 to 36.9 m² min⁻¹ for all plants. Generally, the performance of the prototype demonstrated clear results regarding harvesting different kinds of plants successfully.

The optimization studies conducted with medicinal and aromatic plants mostly focus on oil or mineral extraction. There are also studies using sage in this area.

In a previous study [14], response-surface methodology was applied for the optimization of hydrocolloid extraction from wild sage seed. In this study, the effect of temperatures of 25–80 °C; a water-to-seed rate of 25:1–85:1; and a pH of 3–9 on the yield, apparent viscosity, and emulsion stability index of hydrocolloid extracted from wild sage seed was investigated. Based on the experimental results, a quadratic model was developed. The optimum conditions for maximizing the responses were realized when the temperature was 25 °C, the water-to-seed rate was 51:1, and the pH was 5.5. All hydrocolloid solutions (1% w/v) showed shear thinning behavior in different extraction conditions, and the consistency coefficient and flow behavior index varied from 4.455 to 9.435 (Pa.sn) and from 0.317 to 0.374, respectively.

A study [15] was conducted on the extraction of minerals from garden sage using water as a solvent using different extraction conditions. They used a three-factor full factorial design and investigated the effects of these factors, namely, the liquid/solid ratio, extraction temperature, and extraction time, and their interactions. The generated prediction functions resulted in a good fit to the experimental data (R² > 99%). The optimum values of the factors were as follows: a liquid/solid ratio of 15 mL/g, an extraction temperature of 100 °C, and an extraction time of 80 min.

In another study [16], the authors developed a dry extraction method for sage seed gum using friction-based techniques. This research demonstrates how process parameters can be optimized using experimental design techniques to maximize performance. The rotor speed, angle of friction, and friction distance were used as dependent variables. The effects of these variables on extraction yield, protein content, and viscosity were evaluated. Optimum conditions for a maximum extraction yield, viscosity, and minimum protein content were determined to be 900 rpm of rotor speed, 6.9 degrees of angle of friction, and 2.2 mm of friction distance. Under these optimized conditions, the extraction yield, protein content, and viscosity were found to be 10.61%, 7.02%, and 112 mPa∙s, respectively.

The influence of the extraction techniques on the quality of the sage essential oil was investigated in a study [17]. The experimental samples were analyzed for chemical composition, thermal properties, and biological activity. Chemical composition showed that viridiflorol was the principal compound in all samples. Camphor, thujones, and verticiol followed this parameter. MWD 400 W was the most potent antioxidant agent, and D 200 W and MWD 400 W were the most potent antimicrobial agents, while hydrodistallates (D 200 W and D 400 W) were the most potent cytotoxic agents. An artificial neural network model was developed for the antioxidant activity of the analyzed samples. This resulted in a good fit to the experimental data (R² = 0.998).

Although various studies have been conducted on optimizing the extraction process in medicinal and aromatic plants, seed flow uniformity, and seed distribution uniformity on the row, no study has been conducted on the seeding optimization of these plants. Moreover, the common point of the seeding studies is also that these studies are carried out with a universal machine equipped with a fluted roller.

Unlike other studies, this study aimed to define the seeding possibility of sage seeds by using a micro-granule applicator equipped with a conveyor belt seed-metering unit that can be precisely adjusted for seed rate, revealing the seed flow uniformity and optimizing the in-row seed distribution uniformity of the seeder. For this purpose, the responses of the micro-granule applicator to different working conditions in sage planting were determined and the optimum working conditions for sage seeds were investigated.

2. Materials and Methods

In the experiments, a micro-granule applicator equipped with a conveyor belt seed-metering unit was used for seeding sage seeds. The micro-granule applicator is offered as optional equipment on precision seeders. The metering unit has such a mechanism that it can be easily adjusted to the desired seed rate values. There are two different seed outlets to provide seed flow in the applicator as depicted in Figure 1. The seed hopper had a 25 L capacity. Some physical properties of the sage seeds used in the experiments are displayed in

Table 1. Some physical properties of the sage seeds.

Physical Property	Average	Standard Error
Length (l), mm	2.68	0.20
Width (w), mm	2.45	0.14
Thickness (t), mm	2.19	0.13
Sphericity (Φ), %	90.81	3.14
Thousand-seed mass, (m1000), g	8.95	0.01

.

In the experiments, the conveyor belt was driven by a computer-controlled stepper motor. The stepper motor control unit consists of Arduino Uno R3, Arduino CNC Shield, DRV8825 stepper motor driver, DC power supply (19 V, 4.74 A), data cable, and Nema 23 stepper motor (0.55 Nm). The micro-granule applicator was placed on a frame specially designed for this study, the connection height of which can be steplessly adjusted.

The performance of the micro-granular applicator was investigated under laboratory conditions in terms of seed rate, flow uniformity, and in-row seed distribution uniformity [18,19]. In the study, weighing tests were used to determine the seed rate and seed flow characteristics, while sticky belt tests were used to determine in-row seed distribution uniformity.

The procedures for maintaining precise weight measurements and the sticky belt test stand, which ensures uniformity in in-row seed distribution, are effectively demonstrated in Figure 2.

The weighing experiments were conducted at various levels and positions of the micro-granule applicator seed-metering unit with sage seeds to determine the seed rate values. The metering unit had 20 different scale values between 0 and 9.5 (by horizontal scale) at each position from 0 to 3 (by vertical scale) (Figure 3). The seed rate-setting mechanism had a precise position control device. When the horizontal roller rotates, the vertical roller rotates and the device adjusts the desired scale values, precisely (Figure 3). While the horizontal roller had 20 notches that were numbered from 0 to 9 with a step value of 0.5, the vertical roller had 3 notches. When the horizontal roller rotates one turn, the vertical roller rotates from a 0 to 1 scale position.

Containers were placed under the seed pipes of the micro-granule applicator equipped with a conveyor belt seed-metering unit in order to determine the seed flow characteristics (seed rate and flow uniformity). Seed flow was provided for 1 min in each experiment using a weighing test stand (Figure 2). The experiments were carried out with 3 replications.

Seed weights obtained from seed pipes were measured by a digital scale with a precision of 0.01 g and were recorded in Microsoft Excel. For the determination of seed rate values, the seed-metering unit was set to a forward speed of 1.0 ms⁻¹ and tested at different seed rate positions. For flow uniformity evaluation, the seed-metering unit was tested based on the experimental design parameters. The data were evaluated as the coefficient of variation (CV, %) values based on [18], as shown in

Table 2. Qualitative evaluation adjectives corresponding to values of seed flow uniformity.

CV, %	Evaluation
<1	Very good
1–2	Good
2–3	Moderate
3–4	Sufficient
>4	Insufficient

.

While the evaluations of flow uniformity were carried out depending on the coefficients of variation values (CV), in-row seed distribution uniformity evaluations were carried out on the values of variation factor (V_f) and goodness criterion (λ).

The in-row seed distribution uniformity obtained by computer-aided classification was defined by the values of variation factor (V_f) and the goodness criterion (λ). While the Vf value describes how well the data fit a Poisson distribution, the λ value defines the percentage of segments with 1, 2, and 3 seeds or plants.

The calculation of the variation factor (V_f) and variance (S²) of the seed distribution were given below as Equations (1) and (2) given by [20]. In the equations, μ is the average number of seeds per segment, x_i is the expected number of seeds or plants in the segment, f_i is the segment ratio which is the percentage of the segments with different numbers of seeds or plants, and n is the total sample number.

$${\mathrm{V}}_{\mathrm{f}}={\displaystyle \frac{{\mathrm{S}}^2}{\mathsf{\mu }}}$$

(1)

$${\mathrm{S}}^2={\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{i}}^2{\mathrm{f}}_{\mathrm{i}}-({\left({\mathrm{x}}_{\mathrm{i}}{\mathrm{f}}_{\mathrm{i}}\right)}^2/\mathrm{n})}{\mathrm{n}-1}}$$

(2)

The seed row spacing pattern was determined based on the “V_f” values obtained during the experiments. In this definition, if V_f > 1.1, it indicates there are undesired misses and multiples within the in-row seed spacing. If 0.9 <V_f < 1.1, this indicates the in-row seed spacing matches the Poisson distribution. If V_f < 0.9, this indicates the in-row seed spacing may be characterized as precision seeding.

The uniformity quality of the in-row seed spacing was determined by a goodness criterion. In this definition,, if λ ≥ 72, it indicates the seeding uniformity quality is “very good”; if 65 ≤ λ < 72, this indicates the seeding uniformity quality is “good”; if 55 ≤ λ < 65, this indicates the seeding uniformity quality is “moderate”; and if λ < 55, this indicates the seeding uniformity quality is “insufficient”.

In the goodness criteria evaluation, the average of number of seeds/plants per segment, μ, was chosen to be μ = 2, and the segment length, a, was calculated according to Equation (3) given by the study [18].

$$\mathrm{a}={\displaystyle \frac{100 \mathsf{\mu } \mathsf{\sigma }}{\mathrm{b} \mathrm{N}}}$$

(3)

where σ is the thousand-seed mass (g/1000 seeds), b is the row spacing (cm), and N is the seed rate (kg ha⁻¹). In the sticky belt experiments, the segment length was calculated to be μ = 2.

The metering-unit performance in the form of flow uniformity and seed distribution uniformity of the micro-granule applicator were tested based on the three-variable Central Composite Design (CCD), one of the response-surface methodology designs. Forward speed (X₁), seed rate (X₂), and seed falling angle (X₃) were chosen as independent variables, while variation factor and goodness criteria, which are seed distribution uniformity indices, and also flow uniformity were considered as dependent variables. The seed falling angle is the angle that the seed tube axis makes with the vertical plane.

Three-variable CCD requires five levels for each independent variable. These levels were coded as ±1.682 (star points), ±1, and 0 (center point) [21]. A list of independent variables, and their coded and uncoded factor levels, can be seen in

Table 3. Independent variables along with their coded factor levels.

Independent Variable	Step Value	Coded and Uncoded (Reel) Values
		−1.682	−1	0	1	1.682
Forward speed (X1, ms−1)	0.6	1.01	1.4	2.0	2.6	3.01
Seed rate (X2, kg ha−1)	5.0	6.6	10	15	20	23.4
Seed falling angle (X3, °)	20	1.36	15	35	55	68.64

. The metering unit was operated at five forward speeds, five seed rates, and five seed falling angles for seeding of sage seeds. The experiments were conducted based on the CCD experimental design principles having three replications for determining flow uniformity and seed distribution uniformity.

Microsoft Excel and the Minitab Release 18.0 Trial Version were used for data analysis and mathematical modeling. The Maple 17.0 Single User Profile Trial Version was also used to obtain optimum values of the independent variables derived from the model equation specified in cubic form.

3. Results and Discussion

3.1. Seed Rate Evaluation of the Samples

Flow tests were conducted at various positions of the micro-granule applicator to determine the seed rate values of sage at a forward speed of 1.0 ms⁻¹ for 60 s in three replications. The flow test results of the seed rate provided by seed-metering are given in

Table 4. Seed rate results obtained from weighing experiments.

Seed Rate-Setting Main Position (Vertical Roller)	Seed Rate-Setting Precise Position (Horizontal Roller)	Seed Weight (g)			Average (g)	Seed Rate (kg ha−1)	CV (%)
		Rep# 1	Rep# 2	Rep# 3
	0.0	-	-	-	-	-	-
	1.0	-	-	-	-	-	-
	2.0	-	-	-	-	-	-
	3.0	1.79	1.49	1.55	1.61	2.7	9.86
0	4.0	3.68	3.86	4.09	3.88	6.5	5.30
	5.0	6.37	6.54	8.00	6.97	11.6	12.86
	6.0	10.85	10.43	10.48	10.59	17.6	2.17
	7.0	11.28	11.69	12.11	11.69	19.5	3.55
	8.0	13.65	13.92	13.87	13.81	23.0	1.04
	9.0	16.02	15.91	15.92	15.95	26.6	0.38
	0.0	17.42	17.18	17.11	17.24	28.7	0.94
	1.0	19.34	19.22	18.87	19.14	31.9	1.28
	2.0	20.50	20.41	20.47	20.46	34.1	0.22
	3.0	22.21	22.84	22.08	22.38	37.3	1.82
1	4.0	23.55	22.66	22.99	23.07	38.4	1.95
	5.0	23.22	23.33	22.74	23.10	38.5	1.36
	6.0	24.35	24.58	24.91	24.61	41.0	1.14
	7.0	26.31	26.26	26.07	26.21	43.7	0.48
	8.0	26.63	26.69	27.04	26.79	44.6	0.83
	9.0	28.50	28.05	28.27	28.27	47.1	0.80
	0.0	31.33	31.31	30.56	31.07	51.8	1.41
	1.0	31.67	33.55	32.61	32.61	54.4	2.88
	2.0	34.27	34.25	34.25	34.26	57.1	0.03
	3.0	35.47	33.62	34.08	34.39	57.3	2.80
2	4.0	35.96	34.72	34.72	35.13	58.6	2.04
	5.0	35.77	36.28	36.67	36.24	60.4	1.25
	6.0	37.14	37.32	36.84	37.10	61.8	0.65
	7.0	39.53	37.01	37.78	38.11	63.5	3.39
	8.0	39.61	38.96	39.23	39.27	65.4	0.83
	9.0	40.14	39.51	40.85	40.17	66.9	1.67
	0.0	41.62	40.69	40.53	40.95	68.2	1.44
	1.0	40.68	40.42	41.27	40.79	68.0	1.07
	2.0	42.13	42.54	42.14	42.27	70.5	0.55
	3.0	42.64	43.82	42.29	42.92	71.5	1.87
3	4.0	44.00	44.72	42.58	43.77	72.9	2.49
	5.0	44.33	44.87	44.36	44.52	74.2	0.68
	6.0	45.14	45.36	44.80	45.10	75.2	0.63
	7.0	44.65	44.39	44.11	44.38	74.0	0.61
	8.0	43.98	43.94	42.82	43.58	72.6	1.51
	9.0	45.09	44.43	43.56	44.36	73.9	1.73

.

As seen from Table 4, depending on the scale value, the increasing seed rate values showed an increasing trend. The relationship between the scale value and seed rate was found in the polynomial form with the coefficient of determination value (R²) of 0.9953 (Figure 4). It was thought that because the shape of the seed hopper exit hole was circular, the relation was found in polynomial form and not in linear form.

The seeding rates varied from 2.7 kg ha⁻¹ to 73.9 kg ha⁻¹ with very low CV values between replicates (Table 4). Considering that the seeding rate of sage seeds is typically 10–20 kg ha⁻¹, the values obtained in the experiments were found to be appropriate.

In the seed rate determination experiments using sage, the experiments started from the third position of the zero stage. Because of the low exit hole cross-section, the seed passage and flow could not be achieved in the stages before the third stage. Experiments were carried out in 10 various positions for each stage except for the zero stage.

3.2. Flow Uniformity Evaluation of the Samples

To evaluate the uniformity of sage seed flow, experiments were conducted based on the CCD principles by using five different forward speeds, seeding rates, and seed falling angles with three replicates for each experiment. All independent variables were coded based on the CCD principles at −1.682, −1, 0, +1, and +1.682 using step values.

While the experimental design and the coded and uncoded values of the independent variables are given in

Table 5. Experimental design and coded and uncoded values of the independent variables.

Experiment Number	Forward Speed (X1)		Seed Rate (X2)		Seed Falling Angle (X3)
	Coded	Uncoded (ms−1)	Coded	Uncoded (kg ha−1)	Coded	Uncoded (°)
1	−1	1.4	−1	10	−1	15
2	−1	1.4	1	20	−1	15
3	1	2.6	−1	10	−1	15
4	1	2.6	1	20	−1	15
5	−1	1.4	−1	10	1	55
6	−1	1.4	1	20	1	55
7	1	2.6	−1	10	1	55
8	1	2.6	1	20	1	55
9	−1.682	1.01	0	15	0	35
10	1.682	3.01	0	15	0	35
11	0	2.0	−1.682	6.6	0	35
12	0	2.0	1.682	23.4	0	35
13	0	2.0	0	15	−1.682	1.36
14	0	2.0	0	15	1.682	68.64
15	0	2.0	0	15	0	35
16	0	2.0	0	15	0	35
17	0	2.0	0	15	0	35
18	0	2.0	0	15	0	35
19	0	2.0	0	15	0	35
20	0	2.0	0	15	0	35

, the flow uniformity results obtained from the experiments conducted using CCD are given in

Table 6. The results of the flow uniformity performance of the seed-metering unit.

Run #	Independent Variables			Seed Weight (g)			Average (g)	CVfu *, % (Evaluation)	Standard Deviation
	X1	X2	X3	Rep #1	Rep #2	Rep #3
1	−1	−1	−1	11.11	11.51	11.65	11.42	2.45 (moderate)	0.28
2	−1	1	−1	18.43	18.24	18.38	18.35	0.54 (very good)	0.10
3	1	−1	−1	17.53	17.24	17.54	17.44	0.98 (very good)	0.17
4	1	1	−1	32.11	32.16	32.01	32.09	0.24 (very good)	0.08
5	−1	−1	1	10.55	10.53	10.91	10.66	2.01 (moderate)	0.21
6	−1	1	1	19.30	19.11	19.20	19.20	0.49 (very good)	0.10
7	1	−1	1	16.01	16.44	15.54	16.00	2.81 (moderate)	0.45
8	1	1	1	31.58	31.95	31.08	31.54	1.38 (good)	0.44
9	−1.682	0	0	13.09	12.82	13.14	13.02	1.32 (good)	0.17
10	1.682	0	0	28.22	28.18	28.15	28.18	0.12 (very good)	0.04
11	0	−1.682	0	7.69	7.79	8.72	8.07	7.04 (insufficient)	0.57
12	0	1.682	0	28.31	29.06	28.40	28.59	1.43 (good)	0.41
13	0	0	−1.682	18.45	18.20	18.95	18.53	2.06 (moderate)	0.38
14	0	0	1.682	20.06	19.53	20.42	20.00	2.24 (moderate)	0.45
15	0	0	0	19.05	18.96	19.31	19.11	0.95 (very good)	0.18
16	0	0	0	19.82	20.05	19.30	19.72	1.95 (good)	0.38
17	0	0	0	19.61	19.06	19.96	19.54	2.32 (moderate)	0.45
18	0	0	0	20.10	20.65	19.55	20.10	2.74 (moderate)	0.55
19	0	0	0	19.80	19.78	19.34	19.64	1.32 (good)	0.26
20	0	0	0	19.23	19.79	19.63	19.55	1.48 (good)	0.29

* CV_fu: Coefficient of variation for flow uniformity.

.

Each experiment was conducted with its own independent values. For instance, the second experiment was conducted at 1.4 ms⁻¹ of forward speed, 20 kg ha⁻¹ of seed rate, and 15° of seed falling angle that corresponded the coded values at −1, 1, and −1, respectively. The flow uniformity results were evaluated based on the CV% values given in Table 2.

As can be seen from Table 6, depending on the experimental design, the average flow rates of weighing trials conducted for sage seeds ranged from 8.07 to 32.09 g. However, they varied depending on each experimental condition, and the lowest and highest CV_fu values in the replicates were 0.12% and 7.04%. respectively. When the standard deviation values obtained under in all conditions were examined, these values were found to be quite low. This indicated that the agreement between replications was very high.

The results from the flow uniformity tests on sage seeds indicated that the overall flow quality was generally classified as “medium”. However, in Experiment 11, where the forward speed was 2.0 ms⁻¹, the seed rate was 6.6 kg ha⁻¹, and the seed falling angle was 35°, the flow quality was additionally categorized as "insufficient" based on the coefficient of variation (CV_fu%).

In Experiment 10, where the forward speed and seeding rate were higher despite the same seed falling angle, the lowest CV_fu value of 0.12% was obtained and the flow uniformity was found to be of “very good” quality. Based on these results, it can be said that increasing the forward speed and seeding rate had a positive effect on flow uniformity.

Similar findings were determined in a previous study [10] conducted using a fluted roller with different kinds of cereal seeds and medicinal and aromatic plant seeds. It was determined that the most important factor affecting the flow uniformity of sage seeds was the forward speed, while the seed rate and seed falling angle were more effective parameters in the flow uniformity of black cumin and coriander seeds.

Another study [11] was conducted using a seed-metering unit equipped with a fluted roller and coriander seeds. In the study, CV values for flow uniformity ranged from 0.28% to 1.05%. These values were observed at forward speeds of 1.0, 1.5, and 2.0 ms⁻¹ and seed rates of 15, 20, and 25 kg ha⁻¹.

Different types of seed-metering units and seeds were used in this study, which may differ from ours.

3.3. In-Row Seed Distribution Uniformity Evaluation

The sticky belt experiments were conducted using the same design outlined in Table 5, which was also used in the flow uniformity experiments. The results of the sticky belt experiments can be found in

Table 7. The results of the in-row seed distribution uniformity performance of the seed-metering unit.

Run #	Independent Variables			S2	Vf	Evaluation	μ	λ	Evaluation
	X1	X2	X3
1	−1	−1	−1	5.03	2.52	NBD *	4.12	40.33	Insufficient
2	−1	1	−1	4.01	2.01	NBD	3.62	51.67	Insufficient
3	1	−1	−1	3.43	1.72	NBD	3.36	53.33	Insufficient
4	1	1	−1	3.59	1.79	NBD	3.46	53.33	Insufficient
5	−1	−1	1	4.26	2.13	NBD	3.73	47.00	Insufficient
6	−1	1	1	3.98	1.99	NBD	3.67	47.67	Insufficient
7	1	−1	1	4.64	2.32	NBD	3.94	41.67	Insufficient
8	1	1	1	3.73	1.87	NBD	3.49	49.33	Insufficient
9	−1.682	0	0	4.35	2.17	NBD	3.66	40.00	Insufficient
10	1.682	0	0	3.94	1.97	NBD	3.46	47.00	Insufficient
11	0	−1.682	0	6.63	3.31	NBD	4.67	30.33	Insufficient
12	0	1.682	0	3.10	1.55	NBD	3.07	58.00	Moderate
13	0	0	−1.682	3.05	1.53	NBD	3.13	58.00	Moderate
14	0	0	1.682	4.04	2.02	NBD	3.59	48.67	Insufficient
15	0	0	0	4.28	2.14	NBD	3.76	46.67	Insufficient
16	0	0	0	3.82	1.91	NBD	3.45	52.33	Insufficient
17	0	0	0	4.04	2.02	NBD	3.59	48.67	Insufficient
18	0	0	0	3.92	1.96	NBD	3.59	50.67	Insufficient
19	0	0	0	4.00	2.00	NBD	3.54	50.67	Insufficient
20	0	0	0	4.12	2.06	NBD	3.55	49.33	Insufficient

* NBD: Negative binomial distribution.

, where we evaluated the variation factor (V_f) and goodness criteria (λ) discussed in previous sections. Based on the experimental results, values of S², V_f, μ, and λ were calculated.

While the highest V_f value obtained from the sticky belt experiments with sage seeds was 3.31 in experiment 11 (at a forward speed of 2 ms⁻¹, seed rate of 6.6 kg ha⁻¹, and seed falling angle of 35°), the lowest V_f value was 1.53 in experiment 13 (at a forward speed of 2 ms⁻¹, seed rate of 15 kg ha⁻¹, and seed falling angle of 1.36°).

In all experiments, including those conducted under conditions numbered 11 and 13, the in-row seed distribution uniformity in sage planting exhibited characteristics of a negative binomial distribution based on the V_f values. The obtained λ values also supported this finding indicating that the seeding quality, in terms of in-row seed distribution uniformity, was largely classified as “insufficient”.

The highest λ values recorded were 58.00% (medium) from experiment 12 (forward speed of 2 ms⁻¹, seed rate of 23.4 kg ha⁻¹ and seed falling angle of 35°), and experiment 13 (forward speed of 2.0 ms⁻¹, seed rate of 15 kg ha⁻¹ and seed falling angle of 1.36°), the lowest λ value was obtained as 30.33% (insufficient) from experiment 11 (forward speed of 2 ms⁻¹, seed rate of 6.6 kg ha⁻¹ and seed falling angle of 35°).

3.4. Performance Modeling

One of the most important objectives of this study was to determine the optimum working conditions for qualified sage seeding using a micro-granule applicator equipped with the conveyor belt seed-metering unit. For this purpose, model equations were developed by preparing data sets in cubic form for in-row seed distribution uniformity (as V_f and λ) based on the data given in Table 6 and Table 7.

Detailed analyses conducted using the Minitab statistical package program, a statistically significant cubic at the third-degree models were developed for CV_fu and for V_f at the 99% significance level, while the third-degree model was developed for λ was at the 90% significance level.

Based on the analysis conducted using stepwise regression, we developed model equations for flow uniformity (y_CVfu), variation factor (y_Vf), and goodness criteria (y_λ) in sage seeding with a micro-granule applicator equipped with a conveyor belt seed-metering unit. The results from Minitab for these equations are presented in

Table 8. The statistical analysis results in Minitab for the y_CVfu model.

Step No	Model Predictors	Model Coefficient	Standard Deviation	R2 Variation (%)
-	Model Constant	0.5507	-	-
1	X12	−0.576	0.753	31.82
2	X2	−0.565	0.589	59.00
3	X13	−0.365	0.462	75.17
4	X1 X3	0.387	0.390	82.64
5	X12 X3	0.313	0.334	87.53
6	X22	0.158	0.305	89.79
7	X1	0.321	0.279	91.61

,

Table 9. The statistical analysis results in Minitab for the y_Vf model.

Step No	Model Predictors	Model Coefficient	Standard Deviation	R2 Variation (%)
-	Model Constant	2.020	-	-
1	X23	−0.216	0.231	61.58
2	X22	0.1297	0.200	71.73
3	X33	0.0622	0.173	79.38
4	X1 X3	0.136	0.149	84.89
5	X1	−0.059	0.126	89.38
6	X1 X2 X3	−0.111	0.103	93.06
7	X32	−0.0753	0.0777	96.12
8	X2	0.087	0.0700	96.91
9	X1 X22	−0.059	0.0655	97.34

and

Table 10. The statistical analysis results in Minitab for the y_λ model.

Step No	Model Predictors	Model Coefficient	Standard Deviation	R2 Variation (%)
-	Model Constant	2.020	-	-
1	X23	2.84	5.55	41.93
2	X33	−3.28	3.65	75.37
3	X1 X3	−2.29	3.36	79.47
4	X1 X2 X3	2.29	3.03	83.56
5	X1	1.67	2.69	87.26
6	X12	−1.34	2.50	89.22
7	X22	−1.10	2.34	90.72
8	X32	−0.75	2.26	91.51
9	X3	1.66	2.18	92.27

.

$${\mathrm{l}\mathrm{n}\mathrm{y}}_{\mathrm{C}\mathrm{V}\mathrm{f}\mathrm{u}}=0.5507-0.576{\mathrm{X}}_1^2-0.565{\mathrm{X}}_2-0.365{\mathrm{X}}_1^3+0.387{\mathrm{X}}_1{\mathrm{X}}_3+0.313{\mathrm{X}}_1^2{\mathrm{X}}_3+0.158{\mathrm{X}}_2^2+0.321{\mathrm{X}}_1({\mathrm{R}}_2=91.61\%)$$

(4)

$${\mathrm{y}}_{{\mathrm{V}}_{\mathrm{f}}}=2.020-0.216{\mathrm{X}}_2^3+0.1297{\mathrm{X}}_2^2+0.0622{\mathrm{X}}_3^3+0.136{\mathrm{X}}_1{\mathrm{X}}_3-0.059{\mathrm{X}}_1-0.111{\mathrm{X}}_1{\mathrm{X}}_2{\mathrm{X}}_3-0.0753{\mathrm{X}}_3^2+0.087{\mathrm{X}}_2-0.059{\mathrm{X}}_1{\mathrm{X}}_2^2({\mathrm{R}}_2=97.34\%)$$

(5)

$${\mathrm{y}}_{\mathsf{\lambda }}=49.59+2.84{\mathrm{X}}_2^3-3.28{\mathrm{X}}_3^3-2.29{\mathrm{X}}_1{\mathrm{X}}_3+2.29{\mathrm{X}}_1{\mathrm{X}}_2{\mathrm{X}}_3+1.67{\mathrm{X}}_1-1.34{\mathrm{X}}_1^2-1.10{\mathrm{X}}_2^2-0.75{\mathrm{X}}_3^2+1.66{\mathrm{X}}_3({\mathrm{R}}_2=92.27\%)$$

(6)

Based on the model equations, which were established with 19 variables in cubic form, the results of the stepwise regression analysis included 7, 9, and 9 variables considered for CV_fu, V_f, and λ, respectively.

As shown in Table 8, the predictor that entered the CV_fu model in the first step was X₁², which individually explained approximately 32% of the system. The predictor added in the second step was X₂, which accounted for approximately 27% of the system. The forward speed variable, which was included in the model singularly and in the form of interactions from the third step onwards, was found as the independent variable that affected the “CV_fu model” the most for sage seeding. The predictors X₂³ and X₂², which were included in the V_f model at the first and second steps, represent the cubic and quadratic forms of the seed rate. Notably, the seed rate as the independent variable accounted for the majority of the system’s explanation, contributing 71.73% on its own. The independent variables of seed falling angle and forward speed, which came in the following steps, contribute to the model to a small extent. Although all three independent variables interacted with each other through double or triple interactions, these interactions did not significantly impact the system as shown in Table 9.

As seen from Table 10, while the predictor of X₂³ entered the λ model in the first step and could be explained by 41.93% of the system, the predictor of X₃³ entered the model in the second step and affected approximately 33% of the system. Although the interactions that entered the model in the third and fourth steps were not as effective as the seed rate and seed falling angle on the system, they were included in the model equation in terms of their tendency to increase the R² value. The terms that entered into the equation from the fifth step onwards affected the system with a decreasing rate as R² increased.

The resulting model equations are valid for the system under the specified constraint values, and it should be noted that the predictability of the models may decrease with different values.

1.01 ms⁻¹ ≤ Forward speed ≤ 3.01 ms⁻¹

6.6 kg ha⁻¹ ≤ Seed rate ≤ 23.4 kg ha⁻¹

1.36° ≤ Seed falling angle ≤ 68.64°

3.5. Performance Optimization

One of the most important objectives of this study was to determine the optimum working parameters that affect qualified sage seeding. For this target, the model equations obtained for in-row seed distribution uniformity were transferred to the Maple program to find the optimum values of the model equations. The roots of each model equation were found and the optimum values for all independent variables were calculated as coded values. As a result of taking the derivatives of the model equations depending on each independent variable and equating the obtained values to zero, the optimum values of the independent variables were calculated as coded values for V_f and λ, respectively. The coded optimum values obtained from the model equations were converted to real values.

The optimum coded values for V_f were determined to be 0.1902, −0.2109, and 0.3865 for X₁, X₂, and X₃, respectively. The coded optimum values obtained from the model equation were then converted to real values, and 2.114 ms⁻¹, 13.945 kg ha⁻¹, and 42.73° were calculated for the forward speed, seed rate, and seed falling angle, respectively.

The optimum coded values for λ were also determined as 0.7082, −0.0569, and −0.0942 for X₁, X₂, and X₃, respectively. The corresponding real values were 2.425 ms⁻¹, 14.715 kg ha⁻¹, and 33.11°, respectively.

The optimum values obtained from the V_f and λ models were found to be similar. Based on these results, if a seed rate is chosen approximately 14 kg ha⁻¹ and is set to a seed falling angle at a low degree, it could be possible to operate the seeder at a high forward speed.

The sticky belt experiments were applied once again to the seed-metering unit using optimum values of 2.114 ms⁻¹, 13.945 kg ha⁻¹, and 42.73° which were obtained from the V_f model, and also of 2.425 ms⁻¹, 14.715 kg ha⁻¹, and 33.11° which were obtained from optimization of the λ model. For these verification tests, three replications were conducted, and the in-row seed distribution uniformity performances of the seed-metering unit were assessed. The results for seed uniformity obtained from these verification tests are presented in

Table 11. The verification test results under optimal conditions.

Model	Optimum Conditions	μ	Vf	λ (%)
Vf model	2.114 ms−1 13.945 kg ha−1 42.73°	2.24	0.73	88.33
λ model	2.425 ms−1 14.715 kg ha−1 33.11°	2.23	0.71	89.00

. The highest λ value obtained from the experiments conducted in the CCD experimental design was 58.00% (medium) (Table 7). In contrast, the λ values reached 88.33% and 89% (very good) in the experiments conducted under the optimal conditions determined by the optimization of V_f model and λ model, respectively. This indicates that the planting quality will improve under these optimal conditions, leading to an increase in the proportion of one-, two-, and three-seed strips relative to the total number of strips.

Similarly, in the CCD experiments given in Table 7, the V_f value was found to be the lowest at 1.53 (negative binomial distribution), while when working at optimum points, this value was found to be 0.73 and 0.71 in the V_f model and λ model, respectively (Table 11). These values are characterized as precision seeding (V_f < 0.9). This means that it is possible to seed sage seeds by using the seed-metering device in precision-seeding characterization if the correct working conditions are chosen.

In the experiments conducted under optimum conditions, the μ values were found to be close to the desired theoretically value of two for two models. In previous experiments, this value was also found to be above three (Table 7). This improvement also demonstrates the success of the optimization.

The graphical representations in Figure 5 and Figure 6 clearly demonstrate the effects of the variables considered in this study which were used to evaluate the in-row seed distribution uniformity of the metering unit. These graphs illustrate how the goodness criteria and variation factors are influenced when one independent variable is maintained at its optimum value while the other two independent variables change. It is particularly evident that how the forward speed, seed rate, and seed falling angle impact the overall seeding quality.

The predicted values from the model equations were compared with the measured data for sensitivity analysis as illustrated in Figure 7, which presents both the V_f model and the λ model. In this figure, the diagonal line drawn on each figure represents a perfect fit indicating a correlation coefficient of 100%. The measured data and predictive data from the models demonstrated a high level of similarity, with the V_f model similarity being r = 0.98 and the λ model similarity being r = 0.87.

As a result of all the evaluations mentioned above, it was concluded that the V_f and λ models were suitable models in terms of in-row seed distribution uniformity in sage seeding.

4. Conclusions

The results demonstrated that the sage seeds can be effectively planted using a micro-granule applicator equipped with a conveyor belt seed-metering unit. This metering unit was proven to be highly useful for sage seeding because of the possibility of a wide-ranging seed rate which variated from 2.7 kg ha⁻¹ to 73.9 kg ha⁻¹ with the very lowest CV values. Considering that the seed rate of sage seed is generally between 10 and 20 kg ha⁻¹, the values obtained from the experiments were found to be appropriate.

The system was optimized based on the sticky belt experimental results. Before optimization, the goodness-of-fit criteria was found to be 58.00% (medium), which improved to 89% (very good) after optimization. Similarly, the variation factor decreased from 1.53 (negative binomial distribution) to 0.71 (precision seeding) by optimizing.

The validity of the models and the optimal levels of the variables were assessed through sensitivity analysis and additional experiments conducted under optimal conditions. It was determined that the models were appropriate for the in-row seed distribution uniformity performance. This study on sage seeding is expected to provide valuable insights for farmers, machine manufacturers, and researchers.