Mathematical Modelling and Optimization of Seed Metering Unit Performance in Precision Peanut Seeding

Abstract

The objective of this study was to determine, develop mathematical models, and optimize the in-row seed distribution uniformity performance of a vacuum-type seed metering unit in peanut seeding under different operating conditions. The greased belt stand trials based on the Central Composite Design (CCD) were. Quality of feed index, multiple index, miss index, precision, and coefficient of precision were examined as dependent variables, while the peripheral speed of the seed plate, hole diameter of the seed plate, and vacuum pressure were selected as independent variables. Based on the analysis of experimental data from five different levels of each independent variable, performed using the CCD, a meaningful mathematical model was developed in cubic form for the quality of feed index for peanut seeding, and the model was optimized. The ideal conditions were determined from the model as 0.079 ms⁻¹, 6.94 mm, and 7.07 kPa for peripheral speed of the seed plate, hole diameter, and vacuum pressure, respectively. Based on the findings, quality in seeding by selecting the parameters that affect the performance of precision peanut seeding can be enhanced, resulting in valuable information that can be used as a useful guide to farmers, machine manufacturers, and researchers.

1. Introduction

Peanut (Arachis hypogaea) comes from the legume family, being an annual and summer plant grown in warm climates. It has great economic importance as an oilseed and is farmed in many parts of the world, including South America, Europe, Africa, and Asia. It is a cultured plant that grows well in different temperatures, climates, and soil conditions but requires special care to have a good yield.

Peanut is highly linked to the food due to its high nutritional value with rich fat and protein content. It is used for a variety of purposes, such as fresh consumption, roasting, confectionery, oil extraction in the food industry, and even bran production for animal feed, making it a vital food source in many countries. Peanut production, including for its oil, peanut butter, roasted, and snack, has been increasing consistently, having a total of 44,041,913 tons of annual volume throughout the world [1].

While peanut planting is still performed manually in underdeveloped countries or some developing countries, planters are commonly used for seeding in developed countries. In planting, seed-machine-soil harmony is very important for an efficient and effective production as well as yield. It is possible to increase planting success by depositing qualified seeds on a well-prepared seed bed using the appropriate seeder. Therefore, problems that could arise from the seeder should be identified and eliminated before planting.

It is possible to plant many different seeds with the same seeder. However, since each seed has its own characteristics, working conditions could also be different. For example, cotton seeds will need less vacuum pressure than corn seeds, and the planter disc to be used will also be different. It is possible to achieve quality planting by determining the optimum working conditions related to the seed type.

In a previous study [2], the optimum vacuum pressure of a precision vacuum seeder was determined to develop mathematical models using different kinds of seeds with various physical properties. It was found that the thousand kernel mass, projected area, sphericity, and kernel density of seeds varied from 4.3 to 372.5 g, 5–77 mm², 38.4–85.8%, and 440–1310 kg m⁻³, respectively. The optimum vacuum pressure was determined as 4.0 kPa for maize; 3.0 kPa for cotton, soy bean, and watermelon-I; 2.5 kPa for watermelon-II; melon and cucumber; 2.0 kPa for sugar beet; and 1.5 kPa for onion seeds.

Singh et al. [3] conducted research using cotton seeds by a vacuum-type precision metering unit with the conclusion that a vacuum level of 2 kPa produced superior results, providing a quality of feed index of 94.7% and a coefficient of variation in spacing of 8.6% in cotton seeding.

Gomes [4] evaluated planting quality as a function of different forward speeds and seed distribution systems by using soybean seeds. The mechanical seed metering unit was run at forward speeds of 5, 6, and 7 km h⁻¹, while the vacuum-type seed metering unit was at 8, 10, and 12 km h⁻¹. It was emphasized by the researchers that the mechanical seed metering unit provided the best performance at a forward speed of 5 km h^−1, and the vacuum type metering unit was at the forward speed of 12 km h⁻¹.

Boydak and Kara [5] investigated saving of machinery utilization and energy input to optimize the germination and emergence process of the peanut plant. Four different tillage methods were evaluated, namely traditional tillage; T1 (plough, disc harrow, harrow), reduced tillage; T2 (combined rototiller and chisel, ribbed rollers, planting), reduced tillage; T3 (chisel, goblet disc harrow, planting), and ridge sowing; T4. Results of this study revealed that the best soil tillage method was T2 for the optimization of minimum machinery and energy input.

Baran et al. [6] determined the relationship between various inputs used in peanut production and the outputs obtained. As a result of field experiments, it was observed that irrigation energy had the highest rate in the production inputs, followed by fuel oil, fertilizer, seed, pesticide, machinery, and human labor energies, respectively.

Waldaho et al. [7] evaluated the performance of a single-row peanut planter drawn by animals with a simple structure that can be easily operated and maintained by farmers. The experiments were conducted in two field conditions by using manual operation and the peanut planter. Planting depth, planting speed, and row and row distance measurements were determined, and it was found that animal-drawn peanut planters had a great advantage in terms of planting quality, seed, planting time, and labor compared to hand planting. The seed rates were 82 kg ha⁻¹ and 93 kg ha⁻¹ for peanut planters and hand planting, respectively. The field efficiency was found as 0.08 ha h⁻¹ for the planter.

The main objective of the research conducted by Noor et al. [8] was to investigate the effect of four soil tillage systems on main crop peanut, wheat, and second crop peanut in order to evaluate crop yield and fuel consumption to perform an effective economic analysis. It was found that the highest yield for peanut under different tillage methods was 2097.8 kg ha⁻¹, while the lowest yield was observed as 1649.9 kg ha⁻¹. The highest and lowest fuel consumption levels of different soil tillages for main and second crop peanuts were 62.61 and 34.08 l ha⁻¹ and 33.09 and 61.82 l ha⁻¹, respectively.

It is a known fact that selection of machine construction and working conditions play a significant role on planting quality and yield in single peanut planting. It is also important to minimize errors that could arise from the seeder and optimize the working parameters in precision peanut planting so that in-row seed distribution uniformity can be enhanced. There is still limited information on such issues mentioned above, although it is possible to find lots of studies on precision seeding of corn, cotton, soybeans, sunflowers, etc. using precision seeders. The objective of this study planned to fill this gap in the literature was to determine, develop mathematical models, and optimize the in-row seed distribution uniformity performance of a vacuum-type seed metering unit in peanut seeding under different operating conditions.

2. Materials and Methods

A vacuum type seed metering unit equipped with a 26-hole seed disk was employed for the seeding of peanut seeds for the experiment. The vacuum pressure was provided by an electronic driving system while the metering unit was driven by a reductor, and it was measured at the nearest position to the disk. All of the experiments were conducted using a greased belt test stand, as depicted in Figure 1. Some physical properties of the peanut seeds used in the experiments are displayed in

Table 1. Some physical properties of the peanut seeds.

Physical Property	Average	Standard Error
Length (l), mm	19.61	2.55
Width (w), mm	11.04	1.02
Thickness (t), mm	9.23	0.81
Sphericity (Φ), %	64.21	5.54
Thousand seed mass, (m1000), g	1042	2.03

.

The seed spacing data were collected by using a computerized seed spacing measurement system (CMS) aided with a laser beam [9]. CMS was used for the measurement of seed spacing on the sticky belt test stand. It is hardware consisted of a high precision optical mouse aided with a laser pointer and a computer. The software of the CMS stored coordinate data of the seeds using a simple user interface and saved data to Microsoft Excel 2021 for further statistical analysis. The data were collected by mouse click when the laser aligned with the seed.

The response surface problem usually centers on an interest in some response Y, which is a function of k independent variables ξ₁, ξ₂, …, ξ_k, that is,

Y = f (ξ₁, ξ₂, …, ξ_k)

(1)

The response surface designs require coding of independent variables. The coding of independent variables into X_i is expressed by the following equation:

$$X_i={\displaystyle \frac{{\xi }_i-{\xi }^{*}}{d_s}}$$

(2)

where ξ_i is the actual value in original units; ξ* is the mean value (centre point); and d_s is the step value [10].

Metering unit performance of the seeder was tested based on the Three-Variable Central Composite Design (CCD) that one of the response surface methodology designs. Peripheral speed of the seed disk (X₁), hole diameter of the seed disk (X₂), and vacuum pressure (X₃) were chosen as independent variables, while quality of feed index (I_qf), multiple index (I_mult), miss index (I_miss), precision (CV_m), and coefficient of precision (CP3) were considered as dependent variables.

The quality of feed index is the percentage of spacings that are more than half but no more than 1.5 times the theoretical spacing. The multiple index is the percentage of spacings that are less than or equal to half of the theoretical spacing. The miss index is the percentage of spacings greater than 1.5 times the theoretical spacing. The quality of feed index is a measure of how often the spacings were close to the theoretical spacing. The sum of multiple index, miss index, and quality of feed index forms the theoretical spacing. In an ideal precision seeding process, no multiples and skips occur, and the quality of feed index is 100%. Precision is a measure of the variability in spacing between plants after accounting for variability due to both multiples and skips. The precision is the coefficient of variation of the spacings that are classified as singles. The CP3, known as the 3-cm mode range, was used to determine the ability of the precision seeder to space seeds and includes only spacings within ±1.5 cm of the theoretical spacing.

The performance criterion I_qf, I_mult, and I_miss indices were evaluated based on [11], CP3 was evaluated by [12], and CV_m was evaluated using [13]. The acceptable limits of >90.5%, <4.75%, <4.75% [14], >40% [15], and <29% [11] were applied for I_qf, I_mult, I_miss, CP3, and Precision evaluations, respectively.

Three-variable CCD requires five levels for each independent variable. These levels were coded as ±1.682 (star points), ±1, and 0 (center point) [10]. A list of independent variables and their coded and uncoded factor levels can be seen in

Table 2. Independent variables and their coded factor levels.

Independent Variable	Step Value	Coded and Uncoded (Reel) Values
		−1.682	−1	0	1	1.682
Peripheral speed of the seed disk (X1, ms−1)	0.04	0.053	0.08	0.12	0.16	0.187
Hole diameter of the seed disk (X2, mm)	1.2	2.98	3.8	5.0	6.2	7.02
Vacuum pressure (X3, kPa)	2.2	2.8	4.3	6.5	8.7	10.2

. The metering unit was operated at five peripheral speeds of the seed disk, five hole diameters of the seed disk, and five vacuum pressures for seeding of peanut seeds. The experiments were conducted based on the CCD experimental design principles, having three replications with 15 cm of seed spacing.

The factor levels were chosen based on different limitations. In this context, hole diameter levels were determined based on peanut seed properties, and 5 different seed disks with 5 different hole diameters were manufactured. Five different vacuum pressures were applied based on the minimum vacuum requirement for keeping the seed in the hole and the capacity of the fan that provides vacuum pressure. Five different peripheral speeds of the seed disk were preferred at a range between 0 and 0.2 ms⁻¹. Greased belt stand was run at the forward speed from 0 to 2 ms⁻¹ only, without any skating. For the metering unit, the peripheral speed of the seed disk was 10 times smaller than the forward speed for the transmission ratio used for the seed spacing of 15 cm.

Microsoft Excel and Minitab Release 18.0 Trial Version were used to analyze the data and its modeling. The stepwise multiple regression procedure was used for the selection of the variables as they entered the model in linear, interaction, and cubic form at the probability level of 99%. Maple 17.0 Single User Profile Trial Version was also used to have optimum values of the independent variables derived from the model equation having its set up in cubic form. Optimum values were determined by taking derivatives of the model equations using the Maple program.

The seed metering unit used in the experiments had two single devices, as be seen from Figure 2. The single device (1) is positioned on the right set to position 10 of the scale based on the size of the peanut seeds. The single device (2) positioned behind the seed disk was disabled since it caused seed damage, as illustrated in Figure 2. Especially dicotyledonous seeds such as peanuts can easily be damaged by mechanical friction, which possibly decreases the overall yield. The seed damage was prevented by disabling the device.

3. Results and Discussion

3.1. Performance Indicators

Depending on the CCD principles, the data obtained from experiments conducted by using 5 different seed plate peripheral speeds, seed plate hole diameters, and vacuum pressures were examined as I_qf, I_mult, I_miss, CV_m, and CP3. The results are given in

Table 3. The results of seed spacing uniformity performance of the seed metering unit.

Run #	Repetition	Independent Variables			Dependent Variables (Performance Indicators)
		X1	X2	X3	Iqf, %	Imult, %	Imiss, %	CVm, %	CP3, %
	1	−1	−1	−1	0.00	0.00	100.00	10.17	61.67
1	2	−1	−1	−1	0.00	0.00	100.00	12.88	50.00
	3	−1	−1	−1	0.00	0.00	100.00	9.18	51.00
	1	−1	1	−1	79.55	6.82	13.63	13.35	52,27
2	2	−1	1	−1	72.34	4.26	23.40	13.43	44.68
	3	−1	1	−1	75.56	4.44	20.00	13.04	44.44
	1	1	−1	−1	0.00	0.00	100.00	9.22	57,78
3	2	1	−1	−1	0.00	0.00	100.00	10.70	54.55
	3	1	−1	−1	0.00	0.00	100.00	9.10	54.35
	1	1	1	−1	58.82	1.88	40.00	18.29	35.29
4	2	1	1	−1	58.82	0.00	41.18	22.18	29.41
	3	1	1	−1	60.00	1.18	38.82	13.44	22.86
	1	−1	−1	1	58.82	2.94	38.24	17.60	38.24
5	2	−1	−1	1	60.61	3.03	36.36	15.76	36.36
	3	−1	−1	1	57.14	0.00	42.86	11.15	42.86
	1	−1	1	1	97.96	2.04	0.00	17.45	48.98
6	2	−1	1	1	98.00	0.00	2.00	14.19	56.00
	3	−1	1	1	96.08	3.92	0.00	16.23	45.10
	1	1	−1	1	61.76	5.89	32.35	22.23	32.35
7	2	1	−1	1	57.58	6.06	36.36	16.77	39.39
	3	1	−1	1	61.76	2.95	35.29	23.28	32.35
	1	1	1	1	87.23	0.00	12.77	17.54	42.55
8	2	1	1	1	86.96	2.17	10.87	15.80	47.83
	3	1	1	1	89.13	2.17	8.70	16.48	47.83
	1	−1.682	0	0	78.26	4.35	17.39	20.05	23.91
9	2	−1.682	0	0	76.07	3.00	20.93	20.08	23.26
	3	−1.682	0	0	78.57	3.43	18.00	28.17	21.43
	1	1.682	0	0	53.85	3.00	43.15	27.27	15.38
10	2	1.682	0	0	54.29	0.00	45.71	21.23	25.71
	3	1.682	0	0	55.88	2.94	41.18	17.68	32.35
	1	0	−1.682	0	0.00	0.00	100.00	13.43	48.89
11	2	0	−1.682	0	0.00	0.00	100.00	12.87	56.82
	3	0	−1.682	0	0.00	0.00	100.00	12.87	53.33
	1	0	1.682	0	93.63	2.13	4.24	19.30	38.30
12	2	0	1.682	0	95.75	0.00	4.26	16.88	44.68
	3	0	1.682	0	95.74	0.00	4.26	12.87	53.19
	1	0	0	−1.682	0.00	0.00	100.00	13.65	39.19
13	2	0	0	−1.682	0.00	0.00	100.00	10.53	51.11
	3	0	0	−1.682	0.00	0.00	100.00	12.69	46.67
	1	0	0	1.682	92.86	0.00	7.14	21.71	50.00
14	2	0	0	1.682	89.74	0.00	10.26	21.48	38.46
	3	0	0	1.682	92.68	0.00	7.32	22.51	26.83
	1	0	0	0	69.70	0.00	30.30	14.14	45.45
15	2	0	0	0	71.43	0.00	28.57	16.86	37.14
	3	0	0	0	71.88	0.00	28.12	19.44	40.63
	1	0	0	0	74.29	0.00	25.71	15.60	40.00
16	2	0	0	0	77.14	2.78	20.08	15.30	54.29
	3	0	0	0	75.00	2.86	22.14	16.77	38.89
	1	0	0	0	69.44	2.78	27.78	13.61	47.22
17	2	0	0	0	71.43	2.86	25.71	19.63	42.86
	3	0	0	0	68.75	0.00	31.25	19.36	34.38
	1	0	0	0	72.41	0.00	27.59	12.91	41.38
18	2	0	0	0	71.43	0.00	28.57	10.56	54.29
	3	0	0	0	68.75	0.00	31.25	18.48	31.25
	1	0	0	0	74.29	2.86	22.85	14.48	42.86
19	2	0	0	0	71.43	2.86	25.71	13.49	40.00
	3	0	0	0	74.29	0.00	25.71	14.15	51.43
	1	0	0	0	70.97	6.45	22.58	14.33	41.94
20	2	0	0	0	76.76	7.42	15.79	16.02	42.42
	3	0	0	0	69.70	6.06	24.24	18.04	47.37

for all performance indicators. CCD requires 20 runs, and each run is conducted at its own dependent values. For example, Run#1 was conducted at coded values of −1, −1 −1 conditions that represented peripheral speed of 0.08 ms⁻¹, hole diameter of 3.8 mm, and vacuum pressure of 4.3 kPa in the study (Table 2).

In ideal seeding, the metering unit should release all the seeds into the soil at theoretical seed spacing without any doubling or missing. However, as can be seen from Table 3, different results were determined for each type of experiment. It means that the system resulted in the response for different working conditions, revealing that such findings are satisfactory for modeling. Consequently, it can be stated that the factors that affect the system were accurately chosen. Furthermore, repetitions were found very close to each other, as can be observed in Table 3. Especially considering the compatibility results of runs 15, 16, 17, 18, 19, and 20, which were carried out at central values in accordance with the CCD, resulting in consistent findings with the experiments (Table 3).

The performance values varied 0–98.0%, 0–100%, 0–7.42%, 9.1–28.17%, and 15.38–57.78% for I_qf, I_miss, I_mult, CV_m, and CP3, respectively, as displayed in Table 3.

Depending on the working conditions specified in the experimental design, it was observed that no seeds were kept in the seed disk in runs 1, 3, 11, and 13, especially due to working under low vacuum pressure and high peripheral speed conditions. For the experiments, I_qf and I_miss values were evaluated as 0% and 100%, respectively. At run# 1, all independent variables were studied with the coded value of “−1” and such values close to the second smallest one. Although this situation might be evaluated positively in terms of peripheral speed of disk, it was not possible to keep the seeds in the hole due to the seed disk having very small hole diameter and low vacuum pressure. Similarly, because run# 3 was conducted at the lowest hole diameter and vacuum pressure, the seeds could not be retained in the hole. Run #11 and run #13 were also carried out using the lowest hole diameter and vacuum pressure, and no seeds were kept in the holes, either.

These results, which were perceived as a negative point in the experiments, should actually be considered positively in terms of optimization studies carried out by RSM. In this way, it can be easily stated that the system responded to the planned operating conditions and that the selected parameters were effective parameters on the system.

Among 20 runs, only the runs 6, 12, and 14 resulted in appropriate seeding quality (>90.5%) in terms of I_qf values. Except for 1, 3, 11, and 13, the runs conducted at low vacuum pressure and small hole diameter had low I_qf values (<90.5%) since there were not enough seeds kept in discs.

As mentioned previously, the main objective of this work was to determine the optimum working conditions for quality peanut seeding using a metering unit. Therefore, determining the working conditions makes I_qf = 100% an important parameter.

It was determined that multiples were not encountered often with the metering unit, resulting in only a few attempts with the limit value of above 4.75% as displayed in Table 3. It has been observed that mostly one seed is kept in the holes due to the shape of the peanut seed and the effect of the singling device. It has also been observed that multiplies occurred while the seeds fell onto the greased belt surface due to the centrifugal force on the disk and the physical properties of the seed. Consequently, seeds could not stick to the belt approaching the other seed due to the rolling effect.

Based on the results, it was found that the metering unit tended to work with misses when operations were carried out under the specified conditions. Especially that was the case when low vacuum pressure was used so that hole diameter values and gaps occurred due to the inability to hold a seed in all holes, and therefore the I_qf value decreased depending on the void ratio.

Especially when seeding big seeds, it is of great importance that all holes on the seed plate are filled with at least one seed, in terms of seeding quality and providing equal living space for each seed. For this reason, selection of appropriate hole diameter of seed plate and vacuum pressure were parameters that directly affect the planting quality, as can be seen from the results.

According to the results regarding CV_m, it is seen that the values obtained under all operating conditions were found below the 30% limit value (Table 3). This means that all seeds within the acceptable seed range were deposited on the belt in a precise seed distribution.

Considering the CP3 values, it is seen that all repetitions of runs 4, 7, 9, and 10 were below the 40% limit value, and the working conditions applied were not appropriate in terms of this performance indicator (Table 3). It can be seen that the I_qf results of run 9, which had almost the lowest CP3 values among these runs, were found to be higher than the other runs. As seen in Table 3, the I_qf values in the second and third repetitions of run 12 were found to be 95.75% and 95.74%, respectively. It can be seen that the CP3 values may be quite different from each other (44.46% and 53.19%, respectively).

These results given above about CV_m and CP3 confirmed that they should be interpreted together with other performance indicators instead of a single evaluation of them when evaluating them as performance indicators.

3.2. Performance Modelling

One of the most important targets of this study was to determine the optimum working conditions for qualified peanut seeding using the vacuum-type seed metering unit. Optimization analyses were carried out using the data presented in Table 3.

Model equations were developed by preparing data sets in quadratic and cubic form for all performance indicators, namely, I_qf, I _mult, I_miss, CV_m, and CP3. Based on detailed analyses carried out in the Minitab statistical package program, a statistically significant cubic at the 3rd degree model was reached only for I_qf at the 99% significance level. As a result of the analysis using stepwise regression analysis, the following model equation (y_Iqf) with a 99.5% coefficient of determination (R²) for the quality of feed index (I_qf,%) in peanut seeding was developed. Minitab results are given in Figure 3.

y_Iqf = 72.081 + 28.251X₂ + 17.822X₃ − 3.461X₁X₂ − 1.519X₁² − 8.642X₂X₃ − 8.106X₂² − 8.685X₃² − 3.135X₁²X₂ − 2.513X₁³ + 3.342X₃³

(3)

As can be seen from the model equation, which was established with 19 variables in cubic form, including 10 variables as a result of stepwise regression analysis. Among these variables, X₁ was included in the equation alone in quadratic (X₁²) and cubic (X₁³) forms, whereas it was not as in first degree (X₁) form. The hole diameter variable entered the model equation alone in simple form (X₂) and quadratic form (X₂²), while the vacuum pressure variable was included in the equation in three forms, namely, simple (X₃), quadratic (X₃²), and cubic (X₃³).

Based on the stepwise regression analysis, the binary interactions of X₁X₂ (peripheral speed x hole diameter) and X₂X₃ (hole diameter x vacuum pressure) entered the model, but the interaction of X₁X₃ (peripheral speed x vacuum pressure) was not in the model. The triple interaction of X₁, X_2, and X₃ also did not enter the model.

The resulting model equation is valid for the system for the following constraint values, and it should be taken into consideration that the predictability of the model could reduce in different values.

0.053 ≤ Peripheral speed of the seed plate ≤ 0.187 ms⁻¹

2.98 ≤ Hole diameter of the seed plate ≤ 7.02 mm

2.8 ≤ Vacuum pressure ≤ 10.2 kPa

3.3. Optimization of Seed Metering Unit Performance in Peanut Seeding

The model equation was transferred to the Maple program to find the optimum values of the I_qf model equation obtained from the experiments carried out using peanut seeds. Since it is not possible to solve the equation manually because the model equation is in cubic form, the Maple program was used for derivation of the equation. For this purpose, the small software seen in Figure 4 was used. The roots of the 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 equation depending on each independent variable and equating the obtained values to zero, the optimum values of the independent variables were calculated as coded values of −1.0249, 1.62, and 0.2582 for X₁, X₂, and X₃, respectively, as depicted in Figure 4.

The coded optimum values obtained from the model equation were converted to real values, and 0.079 ms⁻¹, 6.94 mm; and 7.07 kPa were calculated for the peripheral speed of the seed plate, hole diameter, and vacuum pressure, respectively.

Based on the optimum values for peanut seeding, it was determined that the optimum hole diameter of the seed plate in peanut seeding, which is a particularly large seed, was found almost at the highest limit value. There was a high vacuum pressure requirement, and the peanut could be planted with high seeding quality when the lowest forward speed is used.

With the graphical representations given in Figure 5, Figure 6 and Figure 7, the effects of the variables taken into consideration in this study using peanut seeds on the performance of the metering unit had become even more obvious and meaningful. It is particularly clear how the plate hole diameter and vacuum pressure changed the overall planting quality.

It was determined that the hole diameter of the seed plate suitable for the seed to be planted and providing the appropriate vacuum were the most prioritized design criteria. In a past study conducted by [16], similar findings were found in the planting of some different seeds except peanut.

A generalized hole dimeter and vacuum pressure models were also developed based on some physical properties of the seeds in the same work. Using their generalized models, the hole diameter and vacuum pressure were calculated for the peanut seeds as 8.16 mm and 6.84 kPa, respectively. As compared the results, vacuum pressure values were found very close to each other (7.07 kPa from this study and 6.84 kPa from [16], while the hole diameters had 1.22 mm differ from each other. As can be seen from these results, the models could give precise information since mathematical models have a prediction rate.

The predicted values from the model equation were compared with the measured data for sensitivity analysis, as illustrated in Figure 8. In this figure, the diagonal line drawn on each figure represents a perfect fit with a correlation coefficient of 100%. The measured data and predictions from the model showed similarity to each other (r = 0.986).

The optimum level of the models was tested in the laboratory in order to carry out the subject tests. The seeder was operated using a plate with a hole diameter of 6.9 mm, the vacuum was adjusted to a value of 7.07 kPa, and the greased belt was run at 0.79 ms⁻¹. (The peripheral speed of the seed plate was adjusted to 0.079 ms⁻¹ that corresponds to 0.79 ms⁻¹ forward speed of the seeder in the field.) For the verification test, three replications were achieved, and the quality of the feed index was found to be 100% for all replications. The seed spacing results obtained from the verification test are tabulated in

Table 4. The verification test results at optimal conditions as seed spacings in cm (peripheral speed of the seed plate (X₁) of 0.079 ms⁻¹, hole diameter (X₂) of 6.94 mm, and vacuum pressure (X₃) of 7.07 kPa).

Run # 1		Run # 2		Run # 3
14.40	17.76	17.52	14.00	14.80	15.84
12.88	15.04	12.64	10.80	16.16	10.00
12.72	15.20	13.12	12.32	12.72	14.56
14.48	13.20	18.64	13.44	13.52	18.40
12.80	15.04	11.60	12.48	16.40	13.04
16.64	8.88	16.16	15.28	13.60	12.96
15.20	17.12	11.20	11.60	13.12	14.16
12.00	11.92	12.72	14.48	15.28	12.00
15.60	17.28	15.68	14.56	13.04	15.44
9.84	12.40	14.80	11.60	14.00	13.28
13.28	13.76	12.32	13.52	14.32	12.96
16.40	12.08	16.80	14.08	12.24	13.28
12.00	12.96	15.28	15.52	15.76	11.76
16.56	12.56	14.00	13.76	15.84	15.20
12.80	16.88	14.32	13.76	15.28	14.88
13.68	12.40	13.76	12.80	12.16	13.44
13.04	15.68	13.44	14.56	12.24	13.04
14.40	12.64	13.28	13.44	16.00	13.52
15.92	13.20	10.96	16.32	13.28	13.84
15.44	12.48	12.96	14.08	14.72	13.28
11.28	12.56	14.96	12.72	13.60	14.16
16.00	16.88	16.64	13.20	12.88	13.84
10.40	16.64	10.96	13.52	14.64	16.48
9.68	10.48	13.28	13.04	12.40	11.60
14.40	13.36	17.52	15.36	14.80	12.48
Iqf = 100%		Iqf = 100%		Iqf = 100%

.

The validation of the model and the optimum level of the variables were also controlled at two different theoretical seed spacings, namely 7.5 cm and 12.5 cm. These spacings were selected since they were shorter than 15 cm, and it appears that seed spacing accuracy performance might decrease with decreasing seed spacing. The average of three replications for the quality of feed index was found to be 96.1% and 100% for 7.5 cm and 12.5 cm of theoretical seed spacings, respectively. Apparently, the model was valid for not only the seed spacing of 15 cm but also the seed spacings that were shorter than 15 cm.

4. Conclusions

Based on the results found in this study, precision of peanut seeding could be defined as a function of different independent variables, namely the peripheral speed of the seed plate, hole diameter, and vacuum pressure. The results showed that the peanut seeds could be successfully planted with metering unit performance of 100% at optimized values of these independent variables of 0.079 ms⁻¹, 6.94 mm, and 7.07 kPa at seed spacing of 15 cm.

The validity of the models and the optimum level of the variables were also checked at two different theoretical seed spacings. It was determined that the model was appropriate for the seed spacing, which was shorter than the seed spacing of 15 cm. It is expected that data from the experiments and developed model to increase the quality in seeding by selecting the parameters affecting the performance in precision peanut seeding could have valuable information and important guidance to farmers, machine manufacturers, and researchers.