73 
 

 American Scientific Research Journal for Engineering, Technology,  and Sciences  (ASRJETS) 

ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 

 

http://asrjetsjournal.org/  
 

Determining the Optimal Sowing Frequency and Sowing 

Norm of Cereal Crops   

Natroshvili D.*a, Lomishvili M.b 

aDimitri natroshvili - Professor, Doctor of Technical Sciences, Department of Agro-Engineering, Georgian 

Technical University, Georgia, 0192, Tbilisi, 17 D. Guramishvili Street 

bMaia Lomishvili - PhD, Department of Agro-Engineering, Georgian Technical University, Georgia, 0192, 

Tbilisi, 17 D. Guramishvili Street 

aEmail: d.natroshvili@agruni.edu.ge  

bEmail: makomako429@mail.ru 

 

Abstract 

Anyone interested in growing crops ¬ knows that all crops need favorable conditions to get a good crop. In 

particular, the yield of cereal crops depends on many random factors, the complex consideration of which is 

associated with great difficulties.  

Optimal plant distribution and grain crop nutrition conditions can only be achieved during sowing. The main 

calculation values of sowing of cereal crops are the determination of the optimal sowing frequency and the 

sowing norm per hectare. Through the nomogram given in the paper it is possible to determine the required 

number of plants in the open sowing trail depending on the distance between the given rows and the optimal 

plant frequency. There is also a nomogram defining the sowing norm, through which it is possible to determine 

the sowing norm of the desired crop by considering the absolute mass of the grain and its ability to emerge. 

Keywords:  Optimal frequency; The sowing norm; Distance between rows; Productivity. 

1. Introduction 

The basis for sowing crops is to achieve the optimal sowing frequency. The sowing rate of the plant should be 

higher than the calculated one due to the not so high rate of field crop emergence and the negative impact of 

weeds and pests. 

Figure 1. shows the effect of plant frequency on corn yield [1,2]. 

------------------------------------------------------------------------ 

* Corresponding author.  

http://asrjetsjournal.org/


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2. Materials and methods. 

Depending on soil and natural-climatic conditions, the optimum frequency of maize sowing varies within the 

limits of 𝟐𝟓 ∙ 𝟏𝟎𝟑 … . . 𝟒𝟐 ∙ 𝟏𝟎𝟑 pieces/ ha., and for sunflower 𝟐𝟖 ∙ 𝟏𝟎𝟑 … . 𝟓𝟓 ∙ 𝟏𝟎𝟑pieces / ha. 

Here   Table 1: shows the number of plants during the sowing of corn and sunflower in the open sowing trace 

in different soil conditions depending on the sowing scheme. 

 

Figure 1: Plant frequency (H) Impact of maize on plant frequency Yield (Q kg / ha) according to the sowing 

Figur. 

According to the given sowing scheme, it is necessary to determine the number of grains sown in the open 

sowing trace, so that the number of missed (not emerged) sown sowing traces does not exceed the permissible 

deviation from the normal value of plant frequency and also the locate optimal number of plants in the open 

sowing trace [3].  

The number of opened sowing traces (z, thousand pieces / ha) considering the distance between the plants in the 

rows and the distances between rows themselves  is determined by the following formula: 

                                                         𝑧 =
104

𝑎𝑏
                                                   (1) 

Where 𝒂 is the distance between rows, (m); 

            𝒃 - Distance between opened sowing tracks in a row, m; 



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Table 1: Number of plants in the opened sowing  trace during the sowing of corn and sunflowers depending on 

the sowing scheme 

Agricultural 

Culture 

Zone 

Number of 

plants  

pieces / ha 

Distance 

between rows 

m. 

Sowing 

scheme 

m. 

Number of plants 

In the 

footsteps 

of an open 

sower 

On the 

longitudin

al meter 

2 3 4 5 6 7 8 

Cor n as grain 

and silage 

Moist 40...42 

0,7 

0,9 

0.7x0.7     

0.9x0.9 

2                

2...3 
2.8      3.7 

Less moist 28...32 0.9 0.9x0.9 2...3 2.7 

Dry 25...28 0.9 0.9x0.9 2 2.4 

sunflower 

Moist 50...55 0.7 0.7x0.7 2...3 3.7 

Less moist 38...40 

0.7 

0.9 

0.7x0.7  

0.9x0.7 

2...3        

2...3 
3.5       2.6 

Dry 28...30 0.9 0.9x0.9 2...3 2.6 

 

The number of plants in the open sowing track depending on the frequency is determined by the formula:                                                              

                                                𝑘 =
104

𝐻𝑎𝑏
                                             (2) 

Where 𝑯 is the plant frequency (thousand pieces / ha);  

The values of the distances between the rows, quantity of the opened sowing tracks, quantity of the plants in the 

opened sowing tracks during different frequencies is given in the chart 2 and were defined by formulas (1) and 

(2) With the nomogram in figure 2, it is possible to determine the number of plants required for open sowing 

traces depending on the distance between rows and the optimum plant frequency [4]. 

Determine the required number of sowing grains that are needed to achieve a given number of plants. In order to 

solve this task, the ability of the seed material to emerge from the field, pests, diseases and other factors that 

hinder the growth and development of plants during the vegetation period must be taken into account.Taking 

into account the ability of the seed emergence in the field try to solve the task using the probability theory, 

namely by the binominal law of the distribution, which for this particular case can be defined as follows. At the 

time of sowing, it is possible to emerge seeds with probability P at each sowing track, The probability of any 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 78, No  1, pp 73-82 

 

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number of occurrences corresponds to the degree of members of the Newton binomial decay, Which is equal to 

the number of seeds sown in the sowing track: 

 

 

Figure 2: Nomogram for defining sowing as studies. 

(𝑝 + 𝑞)𝑛 = 𝑝𝑛 + 𝐶𝑛
1𝑝𝑛−1q+𝐶𝑛

2𝑝𝑛−2𝑞2+...+𝑐𝑛
𝑚𝑝𝑛−𝑚𝑞𝑚 + ⋯ + 𝑞𝑚            (3) 

Where P is the seed grow up probability; 

           q - non-Probability of grow up of seeds; 

𝑪𝒏
𝒎-n The number of samples selected from the 𝒎  seeds and grow up of plants;  

The probability of the grow up of ,,m" number from ,,n" number of seeds is determined by the Bernoulli 

equation: 

                     𝑝𝑛
(𝑚)

=𝐶𝑛
𝑚 ∙ 𝑝𝑚 ∙ 𝑞𝑛−𝑚                                                        (4) 

where  𝐶𝑛
𝑚 =

𝑛!

𝑚!(𝑛−𝑚)!
 

 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 78, No  1, pp 73-82 

 

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3. Results 

(4) Using the formula, the probability of sowing tracks creation according to the number of the grains (N=3) and 

their B dependent field emergence ability was defined, according to which the nomogram was Figure (Fig. 3). 

This monogram determines the number of plants emerging in the footsteps of trace 𝑴, % the field emergence 

capacity for a specific value of 𝑩. 

The nomogram in Figure 3 gives a complete picture of the distribution of grains in the sowing trail, using it it is 

possible to select the required number of grains in the sowing trail, in our case 𝒏 =  𝟑 is selected for the corn 

crop when its field emergence capacity is 𝑩 =  𝟗𝟎%. For a particular case according to the nomogram (Chart 

3.) we will have: number of sowing tracks without plants -2.4%, with one plant -8.6%, with two plants -13.5% 

and with three plants -75.5%. 

When sowing arable crops, we know the distance between rows (0.7) according to the graph given in Figure 2, 

we determine the number of sowing traces per -20 000 1 hectare. In case of sowing three grains during sowing 

per trace and field emergence, considering field emergence ability (B) we get 54 000 plants per 1 hectare. From 

which we will have sowing traces without plants - 1296, with one plant - 4 644 sowing traces, with two plants - 

7 290 sowing traces, and with three plants - 40 770. 

The assumptions obtained in determining the optimal sowing frequency incompletely reflect the distribution of 

seeds and germination during sowing, so that modern sowing machines and compaction devices give a 

significant deviation and in many cases the sowing scheme is infringed. Therefore, to achieve optimal plant 

distribution, we need to have real data on grain distribution in the row [5]. 

Optimal plant distribution and grain nutrition is possible only during sowing, so the main calculation value of 

sowing of grain crops is the sowing norm per hectare, the main determinants of which are the following 

indicators. plant variety, natural-climatic conditions, soil condition, soil quality, soil Type of sowing, depth of 

sowing of grain in the soil, agro-terms of sowing. Plant feeding and weeding the plot [4]. 

Agronomic science and practice under these conditions gives the sowing norm for all zones of the country. 

In order to increase the yield of agricultural crops, it is necessary to carry out soil improvement works, as well 

as to maintain the optimal distribution of grains in the soil in both horizontal and vertical planes. Under such 

conditions the sowing rate can be significantly reduced. 

Improving the sowing technology of grain crops requires strict adherence to the defined sowing norm. 

The sowing norm can be defined by the following formula: 

                                                       𝑋 =
𝑄∙𝐴

П∙104                                                       (5) 

Where 𝑸 𝑖s the number of grains per hectare, pieces / hectare; 



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𝑨 - absolute mass of grains, grams; 

П - ability to germinate grains,%;  

(5) The values in the formula are defined as follows: 

Q - refers to the number of grains per hectare, the variability limits of which are given below. 

𝐀 - To determine the absolute mass of a grain we must understand the mass of 1 000 grains, it will be the 

absolutely dry substance in the grain with its own hygroscopic water. 

The absolute mass of a grain is called the mass of an absolutely dry substance of 1,000 grains, and the 

percentage of moisture in the grain must also be taken into account during the study, as it can affect the mass of 

1,000 grains [3, 4, 6].  

 

Figure 3: Determining the number of plants in the sowing Trace Nogram (n = 3). 

The absolute mass should always be expressed according to the dried grain. It is calculated by the formula:       

                                                                   𝐴 =
(100−𝑐)∙𝑎

100
 𝑔𝑟.                                                        (6) 

Where 𝐂 is the grain moisture content in%. 

  𝑎 - air dry mass of 1 000 grains. 



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In order to determine the ability of grain to germinate П it is necessary to take the seeds of the "main crop". 

The grain sowing rate is best determined by nomographic means, which can be constructed using formula (5). 

To construct the sowing norm nomogram, we need to obtain the following limits for the values 𝑸, and П: 

3 ∙ 106 < Q < 8 ∙ 106 

0.01< A <0.06 

60 < П < 85 

If we calculate formula (5) we get the following image: 

𝑙𝑔𝑋 − 𝑙𝑔𝐴 + 𝑙𝑔𝑄 − 𝑙𝑔П ∙ 104 

Or 

                                                                         𝑙𝑔𝑋 − 𝑙𝑔𝐴 = 𝑙𝑔𝑄 − 𝑙𝑔П ∙ 104                                          (7) 

This image is suitable for calculating the proportional nomogram: 

                                                    𝑓1(𝑢) − 𝑓2(𝑣) = 𝑓3(𝜔) − 𝑓4(𝑡)                                              (8) 

To get the nomogram, we need to construct the scale of the function in Chart (8) with the following equations: 

𝑥 = λ1𝑓1(𝑢);     y=λ2𝑓2(𝑣); 

𝑧 = λ3𝑓3(𝜔);   𝜇 = λ4𝑓4(𝑡) 

Or 

    𝑥 = λ1(𝑙𝑔𝑋𝑚𝑎𝑥 −lg𝑋𝑚𝑖𝑛.);         y=λ2(𝑙𝑔𝐴𝑚𝑎𝑥 − 𝑙𝑔𝐴𝑚𝑖𝑛);                              (9) 

𝑧 = λ3(𝑙𝑔𝑄𝑚𝑎𝑥. − 𝑙𝑔𝑄𝑚𝑖𝑛.);     𝜇 = λ4(𝑙𝑔П𝑚𝑎𝑥. ∙ 104 − 𝑙𝑔П𝑚𝑖𝑛 ∙ 104; 

Where 𝛌𝟏, 𝛌𝟐,  𝛌𝟑,  𝛌𝟒  are the values that determine the length of the corresponding function scale on the 

nomogram. 

Determine the sowing norm - 𝑋 (kg / ha) according to the formula for the absolute grain mass 𝐴, the grain 

germination capacity P and the specific value Q for the number of grains per hectare (5). 

            We know that                                  5< X < 565 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 78, No  1, pp 73-82 

 

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             Let's get it                          λ1 = 120 მმ.,    λ2 = 250 მმ. 

Let the distance between the scales 𝑥 (𝑋) and 𝑦 (𝐴) be ℎ1 = 50 mm, and let the distance between the scales 

𝑧 (𝑄) and 𝜇 (П) be ℎ2, the value of which can be determined from the following dependencies: 

ℎ1

ℎ2
=

λ2

λ1
 

from where                                                 λ2 = ℎ1
λ2

λ1
=

50∙260

120
= 108 მმ. 

The values of 𝒙, 𝒚, 𝒛 and μ scales can be determined using formula (9): 

𝐿𝑥 = 120(𝑙𝑔565 − 𝑙𝑔50) = 123.9 მმ. 

 

𝐿𝑦 = 120(𝑙𝑔0.06 − 𝑙𝑔0.01) = 93.4 მმ. 

 

𝐿𝑧 = 260(𝑙𝑔8 ∙ 106 − 𝑙𝑔3 ∙ 106) = 110.7 მმ. 

 

𝐿𝜇 = 120(𝑙𝑔85 − 𝑙𝑔60) = 39.2მმ. 

Construct a scale of function 𝒚 when 𝐴 changes in the limits 𝐴1 = 10  grams from 𝐴 =  60 grams. 

𝑄 varies from 𝑄1 = 3 ∙ 106  to 𝑄2 = 8 ∙ 106 per/ hectar; 

П varies - П1 = 60 from П2=85%. 

𝑋 varies - 𝑋1 = 50 to 𝑋2 = 500  kg / ha. 

It is then possible to construct scales of values 𝑿, , 𝑨,П and 𝑸, followed by a nomogram on which the scales 

𝑿 𝑎nd 𝑨 are parallel to each other, and also the scales П and 𝐐 are parallel to each other (Chart. 4). 

4. Conclusion.  

The nomogram given in Chart - 4 makes it possible to determine the grain sowing rate per hectare for the 

specific conditions mentioned above: 

Suppose we have the following values [4]: 

                                         𝑄 = 4 ∙ 106 pieces / hectare; П = 70%; 𝐴 = 50 gr. 



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We connect the points 𝑸 and П on the scale accordingly. On the 𝑨 scale we will find the corresponding point of 

30 gr and from this point we will let it run on the 𝒂𝒃  line until it crosses the X scale. The crossing point on theX  

scale indicates the sowing norm 𝐗  =  200 𝑘𝑔/ℎ𝑒. 

This nomogram can be used to determine the sowing rate of a desired crop, taking into account the absolute 

mass of the grain and its germination capacity. 

 

Figure 4: Determination of sowing rate of cereal crops by nomogram. 

 

References 

[1] Cherniavsky A. A, Tretyak A. N - the advantages of soil-cultivation M. Agriculture # 8, 1989, pp 34-

40. 

[2] Natroshvili D., Lobzhanidze  Z.  - Analysis of machine technologies for care and cultivation of cereals, 

Ts. Georgian Technical University, Ts. Collection of scientific works of Mirtskhulava Institute of 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 78, No  1, pp 73-82 

 

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Water Management # 72. Tbilisi, 2017, pp 135. 

[3] Shapakidze E., Natroshvili D.-  Lecture course, methodical instructions for practical work, Tbilisi, 

2010, pp 234.   

[4]  Natroshvili D. (PhD dissertation overview) - "Development and improvement of a complex of 

machine technologies for sowing cereals and a complex of combined machines for small plots",. 2003, 

252 pp. 

[5] Natroshvili D., Zangaladze N. -  Some results of an experimental study of mining combined sowing, 

SSAU, Scientific Papers, Tbilisi,  1989, pp 58-63.     

[6] Natroshvili D. - Determining some of the indicators of a combined corn sowing machine, SSAU, 

Scientific Publications, Tbilisi,  1997, pp 32-29.