Comparison of Radial Ply and Cross Ply Tire in Terms of Achieved Rolling Resistance and Soil Compaction in a Soil Test Channel

Abstract

Many literature sources state that radial ply tires achieve lower rolling resistance values than cross ply tires. From a certain point of view, radial ply tires are gentler on the ground than cross ply tires. The effort was therefore to experimentally verify this statement for two radial ply and cross ply tires similar in shape and size. The work deals with the diagnostics of rolling resistance levels achieved by radial ply and cross ply tires on selected forest soil under the laboratory conditions of a soil test channel. BKT 210/95 R16 Agrimax RT 855 and Özka 7.50-16 8PR KNK 50 were chosen as radial ply and cross ply tires, respectively, and had approximately the same dimensions. The soil in the soil test channel can be characterized as a loamy sand with an average moisture content of 30% and an initial bulk density of 1445.07 kg·m⁻³. Another monitored parameter was the diagnostics of changes in soil density caused by tire movement in order to assess the degree of soil compaction. From the results of the work, it follows that there is no statistically significant difference between radial ply and cross ply tires in terms of the achieved levels of rolling resistance on the soil. The observed tires also caused intense compaction of the soil in the soil test channel, especially at higher tire pressures and higher vertical loads. The analysis of the results also shows that changes in tire pressure in both tires cause more energy loss and soil compaction than changes in the vertical load.

1. Introduction

The main component of energy loss in wheeled machines with a wheeled gear is rolling resistance. Because wheeled machines often move not only on paved roads but especially in fields, the rolling resistance of wheels consists of two components. The first is internal rolling resistance, which is related to deformation of the tire casing itself. It is the dominant type of resistance when driving on paved roads. The second component is external rolling resistance related to deformation of the soil in the contact patch when driving on unpaved roads or on the ground. The magnitude of deformation is significantly influenced by the type of soil and especially its immediate moisture [1,2].

A significant factor affecting the rolling resistance of a tire wheel is tire pressure. It is advisable to use the highest possible pressure on firm, unyielding surfaces while, of course, considering the permissible rate of wear and achieving optimal tire life [3,4]. On the other hand, lower tire pressure is more suitable for soil or unpaved surfaces, while minimum rolling resistance values can be achieved at a certain pressure level. A lower pressure in the tire means larger contact area with the surface and thus lower mean contact pressure causing less deformation of the soil and less engagement of the wheel [5]. However, it is necessary to observe the prescribed technical parameters of a given tire, especially the ratio of tire pressure and radial load. Low tire pressure below the permissible limit of a loaded tire can cause it to collapse and incur irreparable damage. Therefore, it is necessary to approach the choice of tire pressure with caution.

The construction of tires of wheeled machines can basically be divided into radial ply and cross ply. Cross ply tires are characterized by the fact that the fibres of the carcass are oriented diagonally, in such a way that the fibres of the individual layers of the carcass cross each other on different planes. Under the tread are buffer layers that soften shocks when crossing obstacles. In some cross ply casings, this layer is made of steel cord that protects the frame from being punctured by sharp objects [6].

Tires with a radial ply frame are characterized by a zero angle of cord fibres in the frame and a rigid buffer layer that runs in the form of a belt around the perimeter of the tire. This gives these coats specific properties. The advantages of radial ply tires, in general, include longer service life compared to cross ply tires, better off-road handling, less rolling resistance and partly better suspension [7]. The basic disadvantages of radial ply tires include less lateral stability and less shock absorption.

Due to the aforementioned disadvantages, the use of casings with a radial carcass in some wheeled machines is questionable. They adversely affect the longitudinal and transverse stability of the machine, especially when driving or performing work [8]. The environmental impact of pneumatic wheels are also significant. Wheeled means in agriculture and forestry negatively impact the soil surface by compacting the soil, creating ruts and removing organic material from the soil surface caused primarily by their passage [9]. Soil deformation is influenced by a number of factors such as initial volumetric weight, size of soil particles and their distribution, content of soil organic matter, soil moisture and number of passes by wheeled vehicles [10]. However, in general, the lower the bulk density of the soil, the more prone it is to compaction [11]. Forest soils, in most cases, have bulk density values lower than 1.4 g·cm⁻³ in their upper layer due to a higher proportion of organic matter and biotic activity [12]. An increase in the water content in the soil causes a reduction in the frictional forces between the soil particles, a reduction in the soil’s bearing capacity and a higher susceptibility to compaction. The susceptibility of soil to compaction increases up to a certain critical moisture content. In fact, the higher the moisture content, the higher the proportion of water-filled pores that cannot be compressed [13]. After exceeding the critical moisture in the soil, the wheeled means cause changes in the top layer of the soil by their movement and thus subsequently compress the soil and cause the formation of ruts [14]. Fine-grained soils are generally more susceptible to damage than coarse-grained soils [15]. The distribution and size of soil particles plays a significant role in soil water retention and soil compaction during the passage of wheeled vehicles. The influence of the passage of wheeled means on the volumetric weight of the soil decreases with increasing depth [16]. Susceptibility of soil to damage strictly depends on soil structure and the ability of soil aggregates to withstand pressure without damage [17].

Our department has been investigating tire rolling resistance research under laboratory conditions using a soil test channel for a long period of time. Due to the proportions of experimental equipment, these are mainly small tractor and municipal tires. As mentioned above, radial ply tires are generally considered in the literature to be more advantageous than cross ply tires in terms of rolling resistance. For this reason, we decided to experimentally verify this claim on selected tires of similar shape and size.

The entire experiment focused on the conditions of the soil test channel. Detailed technical parameters and information regarding construction are specified in the work of Helexa et al. [18]. During implementation of the aforementioned experimental measurements, changes in soil compaction were also monitored by monitoring changes in bulk density of the surface horizon from 0 to 5 cm. Based on assessment of the aforementioned two parameters, it is possible to evaluate the properties of the tested tires not only from the point of view of energy demand during operation but also from the environmental point of view.

2. Materials and Methods

Two tires of approximately the same proportions were chosen for testing: one having cross ply construction (Özka 7.50-16 8PR KNK 50) and the other having radial ply construction (BKT 210/95 R16 Agrimax RT 855), both with an arrow pattern. Their basic technical parameters and carrying capacities are listed in

Table 1. Basic technical parameters of the tested tires.

	Özka 7.50-16 8PR KNK 50	BKT 210/95 R16 Agrimax RT 855
Parameter	Value	Value
Overall Diameter	805 mm	806 mm
Section Width	205 mm	214 mm
Maximum load on towed tire	Not specified by the manufacturer	1275 kg
Maximum load on the drive tire	875 kg in speed 10 km·h−1	1020 kg in speed 10 km·h−1
Maximum tire pressure	275 kPa	240 kPa
Tire weight with rim	31.00 kg	35.40 kg
Construction	Cross ply	Radial ply

and Table S1.

The testing of the aforementioned tires was carried out under the laboratory conditions of the soil test channel. The soil test channel is shown in the following figure (Figure 1). The soil test channel is a box structure with an effective length of 6550 mm, a width of 690 mm and a depth of 500 mm. Its working volume is therefore 2.26 m³. The construction is designed in a modular way, so that it can be extended as necessary to the required length.

The soil in the soil test channel came from a beech stand in the Turová forest district and was provided by the University Forest Enterprise of the Technical University in Zvolen. From a granulometric point of view, it is possible to characterize this soil as loamy sand on the basis of a laboratory grain size analysis. For a more detailed specification, Figure 2 shows the grain size curve of the given soil constructed according to the Slovak Technical Standard [19]. The granulometric analysis as well as the grain size curve were carried out by the staff of the Faculty of Civil Engineering of the University of Žilina. The following table (

Table 2. Basic parameters of the used soil.

Parameter	Value
Soil type	Loamy sand
Gravel	12.90%
Sand	36.06%
Silt	46.74%
Clay	4.3%
Volumetric weight of soil	1445.07 kg·m−3 in the horizon (0 to 5 cm)
Angle of internal friction	37.75°
Cohesion	11.6 kPa
Moisture content	30.00%
Plasticity number Ip	13.26
Limit of plasticity Wp	23.55%
Liquid limit WL	36.81%

) shows the basic mechanical properties of the soil obtained from samples taken from the upper soil horizon (0 to 15 cm) after moistening with water to a moisture content of 30%. This soil moisture value was maintained on average during the entire process of the measurements. The stated characteristic values of the soil were obtained on the basis of laboratory analyses of the samples performed at the Faculty of Civil Engineering of the University of Žilina.

The methodology for measuring the rolling resistance of the tires in question was simple and basically involved pulling the main frame 3 (Figure 1a) with the tire along the prepared ground surface in the soil test channel using the rope of the braking and winding device 5 (Figure 1a). An HBM S9M/10kN tensile and compressive force sensor with a nominal size of 10 kN was used to measure the tensile force. The signal from the sensor was subsequently recorded by the HBM Quantum X MX 840 A measuring centre, which is controlled via a computer using HBM Catman Easy software (5.0.1 version). This enables the subsequent transfer of recorded files to MS Excel, in which the results were measured and evaluated. Due to the cramped conditions and dimensions, the speed of pulling the tire on the ground in the soil test channel was at the level of 0.1 m·s⁻¹.

The measurement of the rolling resistance of the tires was carried out at tire pressures of 100 kPa, 150 kPa, 200 kPa and 240 kPa due to the mutual diagnostics of both constructions of the tires in question. Five levels of vertical tire load were chosen: 220 kg (the weight of the main frame 3 without the wheel drive mechanism and without weights), 346.80 kg, 473.60 kg, 600.40 kg and 727.20 kg. For the Özka 7.50-16 8PR KNK 50 tire, the load level of 727.20 kg at a tire pressure of 100 kPa was omitted, as the permissible tire load given by the manufacturer for the given tire pressure levels would be exceeded. Mechanical weights consisting of steel plates weighing 31.70 kg were used to load the tires. During the realisation of the measurement, the sizes of the contact surfaces of the tires with the soil in the soil test channel were not monitored.

Because the wheel drive system was dismantled from the device to maximally reduce the weight acting on the tire. The main frame with the tested tire was transferred to the starting position by handling crane (Figure 1a). The pressures in the tires and their vertical load were chosen in such a way as to meet the technical requirements set by the tire manufacturers and to avoid unnecessary overloading, which reduces their service life.

In this way of measuring the rolling resistance of tires, the total measured tensile force consists not only of the rolling resistance component itself but also other resistance forces, which must be taken into account in the calculation itself (Figure 3). Total resistance force is given by:

$${\mathrm{F}}_{\mathrm{c}}={\mathrm{F}}_{\mathrm{v}}+{\mathrm{F}}_{\mathrm{v}\mathrm{v}}+{\mathrm{F}}_{\mathrm{m}\mathrm{t}}\left[\mathrm{N}\right]$$

(1)

where F_v is rolling resistance of the towed tire (N), F_vv is resistance in the guiding frame (N) and F_mt is friction resistance force in bearings (N).

From Equation (1), it is possible to express the rolling resistance value in the following form:

$${\mathrm{F}}_{\mathrm{v}}={\mathrm{F}}_{\mathrm{c}}-{\mathrm{F}}_{\mathrm{v}\mathrm{v}}-{\mathrm{F}}_{\mathrm{m}\mathrm{t}}\left[\mathrm{N}\right]$$

(2)

Based on the free pulling of the guiding frame without the attached main frame with the wheel, the frictional resistance in the guiding frame F_vv was calculated. Using the measuring apparatus mentioned above, this measurement was performed even before the rolling resistance of the tires was really measured. Its value was found at 79.82 N. Based on the conducted computations, the frictional resistance force in the tire wheel bearings is relatively small, with a maximum value of 1.5 N. The wheel housing’s bearing houses are not fitted with a contact seal to lessen this resistance. Thus, the bearings themselves only experience friction.

For every load level and tire pressure, rolling resistance measurement was performed three times. The final value was calculated as the arithmetic mean of these measured values. No relationships between tire slip, load and tire pressure were observed when evaluating the rolling resistance of the tires under observation.

It is natural that the rolling resistance values obtained in this way for the individual monitored tires represent the total resistance component on the monitored ground. Due to the fact that we did not measure the rolling resistance of the monitored tires on a concrete (non-yielding) base, we were not able to determine the purely internal component of total rolling resistance related to deformation of the tire or the external component of rolling resistance related to soil deformation. Therefore, all stated values of the measured rolling resistances represent only the overall total component.

In addition to monitoring the rolling resistance curves of the tires in question, changes in soil density were also monitored after each run of the tires at a given tire pressure and vertical load. We consider changes in soil density as a determining parameter affecting soil compaction, which results in the reduction of pores in the soil necessary for gas exchange and affecting the water regime of soils. On the other hand, the detection of changes in bulk density in the surface layer of the soil is technically relatively simple and can be implemented using a simple methodology.

Changes in soil density were determined by weighing soil samples taken using sampling cylinders with an internal diameter of 59.50 mm and a height of 37.20 mm. The volume of these take-up rollers was therefore 103.40 cm³. Changes in soil density were monitored at the bottoms of the tire tracks, where the greatest force action and thus the greatest compression (compaction) of soil mass is assumed to occur. The pressed ring was then excavated from the sampling site and levelled according to the faces with a knife for further weighing. Subsequently, the sample was weighed on an Axis AG 2000 C laboratory scale with a weighing capacity of 2000 g; from the measured values of the weight of the sample, the weight and volume of the sampling roller itself, the value of the volumetric weight of the soil was calculated according to the equation:

$${\mathrm{m}}_{\mathrm{o}\mathrm{z}}={\displaystyle \frac{{\mathrm{m}}_{\mathrm{v}\mathrm{z}}-{\mathrm{m}}_{\mathrm{v}}}{{\mathrm{V}}_{\mathrm{v}}}}={\displaystyle \frac{{\mathrm{m}}_{\mathrm{z}}.1000}{{\mathrm{V}}_{\mathrm{v}}}}\left[\mathrm{g}·\mathrm{c}{\mathrm{m}}^{-3}\right]$$

(3)

where m_oz is the volumetric weight of soil (g·cm⁻³), m_vz is the weight of the soil sample taken with the sampling roller (g), m_v is the weight of the sampling roller (g), m_z is the weight of the soil sample taken (g) and V_v is the volume of the sampling roller (cm³).

Modification of the soil after passage of a wheel was carried out manually by digging and levelling with the help of hand tools, so that the starting volumetric weight of the observed soil was always on average at the same level. After each soil modification, the mechanical parameters of the soil were verified using a hand-held Eijkelkamp penetrometer with a nominal range of 1000 N load cell. During these measurements, soil moisture was checked using a hand-held instrument for measuring soil moisture (IMKO HD2 with an IMKO Trime-Pico 64/32 sensor) and was on average at the level of 30%.

During measurements, the traction resistance of the trailed wheel (F_c—total resistance force when pulling) was recorded using the HBM S9M/10kN force sensor with a sampling frequency of 5 Hz (Figure 3). The stated value of the sampling frequency was chosen based on the work of Bauer and Sedlák [20], who used the stated value of the sampling frequency in the measurement of traction indicators of tractors. The measured data were transferred to a computer via the HBM Quantum X MX 840 A measurement recorder and via the HBM Catman Easy measurement software (5.0.1 version) into MS Excel, in which they were subsequently processed. The speed of the towed wheel was 0.1 m·s⁻¹. The sets of measured tensile resistances F_c at individual values of the vertical load and the corresponding values of pressures of the monitored tires were then statistically processed in the Statistica 12 CZ program.

The aforementioned functional dependencies could be described well by linear regression equations. The question is whether there are differences between the individual regression curves for the rolling resistance achieved F_v with radial ply and cross ply tires. This is important in order to be able to say exactly whether there are noticeable differences in the achieved rolling resistances and thus energy savings for one or the other tested tire.

For this purpose, we subjected the fitted regression functions to a test of the agreement of the regression coefficients of the two basic sets [21]. This test assumes two basic sets, while the dependence of the Y variable on the X variable in the first basic set is described by the regression model y_i1 = b₀₁ + b₁₁.x_i1 and in the second basic set by the model y_i2 = b₀₂ + b₁₂.x_i2. On the basis of n₁ sample data from the first basic set using the method of least squares, we obtained an equalization function with residual variance s_rez1², and using n₂ sample data from the second basic set, we obtained an equalization function with residual variance s_rez2². To determine whether the response variables in both basic sets respond in the same way to changes in the explanatory variable, we test the null hypothesis H₀: b₁₁ = b₁₂ against the alternative hypothesis H₁: b₁₁ ≠ b₁₂. The test characteristic assumes the validity of the null hypothesis Student’s probability distribution with the number of degrees of freedom (n₁ + n₂ − 4). If the test characteristic is from the critical area |t| > t_{1 − (α/2)} (n₁ + n₂ − 4), we reject the null hypothesis about the coincidence of the regression coefficients. In such a case, we have to consider the slope of the regression lines as being different (b₁₁ ≠ b₁₂)—i.e., that the regression lines are different and that we cannot assume that a unit change in the explanatory variable will cause the same change in the response variable in the first and in the second basic sets.

3. Results

An example of the course of the measured tensile strength for the BKT 210/95 R16 Agrimax RT 855 radial ply tire at a tire pressure of 150 kPa and a vertical load of 220 kg is shown in the figure (Figure 4).

The specific values of the rolling resistance of the monitored tires were subsequently calculated from the stated values of traction forces, after taking into account the resistance forces mentioned above when pulling the wheel on the soil in the soil test channel. During the statistical processing of the already calculated rolling resistance values, the following quantities were calculated: mean, median, mode, maximum and minimum values of tensile force, range, variance, standard deviation, variation coefficient, skewness and sharpness. Subsequently, the data sets were subjected to a normality test. The normality of data distribution was assessed by the Shapiro-Wilk test. An example of statistical data processing of the already calculated rolling resistance is shown in the figure (Figure 5) for the BKT 210/95 R16 Agrimax RT 855 radial ply tire with a tire pressure of 150 kPa and a vertical load of 220 kg.

The Shapiro-Wilk test does not reject the hypothesis about the normality of the distribution of the measured data at a significance level of 0.05 (p = 0.20110). Similar results were also obtained when processing other measured values of tensile force. As the results of the experiments, the following figures (Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10) show graphical dependences of the measured rolling resistance courses and changes in soil density caused by the movement of the monitored tires. For the purposes of mutual comparison, the dependencies of both tires are presented together in the same graph.

Figure 6 shows examples of the dependence of achieved rolling resistances on vertical load for both tested tires at constant tire pressure (100 kPa and 240 kPa).

Figure 7 shows the dependence of rolling resistance of the monitored tires on tire pressure under constant load (220.00 kg and 727.20 kg).

All graphic dependencies were subjected to the aforementioned tests. Table S2 shows partial results of these tests applied to the dependence of the course of rolling resistance of the monitored tires on vertical load at constant tire pressures of 100 kPa, 150 kPa, 200 kPa and 240 kPa.

Figure 8 shows the dependence of rolling resistance coefficients on tire pressure under constant vertical load (220.00 kg and 727.20 kg).

Figure 9 presents two mutual comparisons of the achieved changes in bulk density of the soil under different vertical tire loads at constant tire pressures (100 kPa and 240 kPa). The initial volume density of the soil in the soil test channel reached a value of 1445.07 kg·m⁻³ in the 0 to 5-cm horizon, and the average soil moisture reached a value of 30%.

Figure 10 presents two mutual comparisons of the achieved changes in bulk density of soil at different tire pressures under constant vertical load (220 kg and 600.40 kg).

As can also be seen from the second part of the graphed dependencies presenting the changes in volumetric weight of the soil under different vertical loads (Figure 9) and at different tire pressures (Figure 10), these can also be described relatively well by linear regression functions. Here, too, the question arises regard the extent to which the individual regression functions for radial ply and cross ply tires are independent of each other. For this reason, in this case as well, the above-described test for the regression coefficients of the two basic sets was performed. As an example of the results of this test, Table S3 shows the results obtained for the dependence of the change in bulk density of the soil on vertical load of the monitored tires at constant tire pressure.

When monitoring the rolling resistance and the compaction effect of the observed radial ply and cross ply tires, it was also interesting how growth in vertical load and tire pressure affects the achieved rolling resistance and volumetric weight of the monitored soil. Therefore, all the regression equations for individual functional dependencies plotted above were gathered, and the changes in the directions of these regression lines were monitored. The slopes of these regression lines can be used to determine the direction of these dependencies and thus determine whether the given function is increasing or decreasing. Since all slopes of regression lines are positive, all regression dependencies are increasing functions (Tables S4–S7). Their average values were calculated from the individual guidelines of the regression lines and thus the average value of the change of the relevant observed factor on the variable quantity was determined.

Table S4 expresses the average increase in rolling resistance of the monitored tires as a function of vertical load at constant tire pressure. Table S5 shows the average increase in rolling resistance of the monitored tires as a function of tire pressure under constant vertical load.

Table S6 expresses the average increase in volumetric weight of the soil as a function of vertical load of the monitored tires at constant tire pressure. Table S7 shows the average increase in volumetric weight of the soil as a function of tire pressure of the monitored tires under constant vertical load.

4. Discussion

Figure 6 illustrates how the rolling resistances of the sample tires vary with vertical load, keeping the tire pressure constant. Conversely, Figure 7 demonstrates how rolling resistances changes with tire pressure when the load remains constant. Since both tires were compared with each other, their visual representations are always plotted together.

It is clear from the dependency waveforms that the plotted points closely align with linear regression functions. From the graphical dependencies in Figure 6 and Figure 7, it is obvious that the values of rolling resistance increase both with an increase in tire load and with an increase in tire pressure. When considering the absolute values of rolling resistance, the radial ply tire BKT 210/95 R16 Agrimax RT 855 showed marginally lower rolling resistance (with the exception of the dependency shown in Figure 6a) compared to the cross ply tire Özka 7.50-16 8PR KNK 50. Certain deviations were detected in the dependence of rolling resistance on the vertical load of the tires at a pressure of 100 kPa (Figure 6a). It is clear from the graph that the cross ply tire had a slightly higher rolling resistance than the radial ply tire. In this context, it should be noted that despite the fact that tire manufacturers in their technical materials allow the operation of tires at pressures lower than 100 kPa (Table 1, Table S1) with a relatively high vertical load, the reality confirmed by our measurements is different. Already at an operating pressure of 100 kPa and the prescribed permissible vertical load, relatively large deformations of the tire structure can be observed, accompanied by various sound effects related to excessive deformation of the tire structure and probably also to the movement of the tire bead on the rim. It follows from the above that classic radial ply and cross ply tires are not structurally suitable for operation at low tire pressures (100 kPa and below).

Plotted regression functions (Figure 6 and Figure 7) were subjected to the test of conformity of regression coefficients. The method is explained in more detail in the previous chapter. Considering that the computed criterion of this test method, denoted as |t|_off is smaller than the critical tabulated criterion value of t_0.975 for all regression models, we cannot reject the hypothesis that the regression coefficients for the translated radial and cross ply tire functional dependencies agree. Therefore, statistically speaking, there is no distinction between them, and the groupings of plotted points from each dependency could essentially be substituted with a single, unified regression function. This implies that the rolling resistances measured for the tested radial and cross ply tires do not exhibit a statistically significant disparity. As an illustration of the outcomes from the test method, Table S2 presents the results of calculating the concurrence of the regression coefficients of the linear functions, which represent rolling resistance against load at a constant tire pressure for the sample tires.

For both tires, there is a progressive increase in rolling resistance as a result of both escalating tire pressure and rising vertical load when the tires are in operation on the ground. These changes are attributed [22,23] to a steady rise in contact pressure and, in the case of escalating vertical load, to enhanced penetration into soft soil [24].

A more precise representation of rolling resistance can be achieved by transforming the absolute values for rolling resistance provided into corresponding coefficients of rolling resistance. Hence, Figure 8 illustrates how the computed values of the obtained rolling resistance coefficients are dependent on the tire pressure of the sample tires, while keeping the load constant. The points plotted once again closely align with the linear regression functions. On the observed terrain, the computed rolling resistance coefficients varied, with values ranging from 0.24 at a tire pressure of 100 kPa up to 0.35 at a pressure of 240 kPa. The values of rolling resistance coefficients above are associated with specific conditions. For example, a coefficient of 0.24 is typical for a loamy forest soil covered with a coniferous forest floor or a slightly saturated meadow, while a coefficient of 0.35 is characteristic of vegetated peatland [25]. The resulting values of the rolling resistance coefficients that were achieved are generally found at the upper boundary of the coefficients listed in the tables. This implies that the soil was quite malleable at the time of measurement, leading to substantial sinking of the sample tires into the terrain. Cross ply tires achieved slightly higher values than radial tires. Nonetheless, upon re-examining the closeness of data points for the two tire types, we still observe no distinction between radial and cross ply tires.

Another key aspect to oversee when assessing agricultural and forestry tires is their impact on the environment, specifically on the soil. The impact was evaluated for the sample tires, considering the alterations in soil bulk density following the passage of the tires. Alterations in the bulk density can be viewed as an indicator of soil compaction [26].

The results obtained from the changes in soil bulk density were once again visualized according to two functional dependencies: one focusing on varying vertical loads at constant tire pressure (Figure 9) and the other on varying tire pressures under constant load (Figure 10). The plotted values once more closely align with linear regression models. The changes in the bulk density of the soil under investigation, in absolute terms, varied. The lowest recorded value was 1460.00 kg·m⁻³, observed with the radial BKT tire, inflated to a pressure of 100 kPa and subjected to a wheel load of 220 kg. On the other hand, the highest value recorded was 1898.65 kg·m⁻³, which was observed for the cross ply Özka tire, inflated to a pressure of 240 kPa and bearing a vertical load of 727.2 kg. From the visual representation, it is evident that the radial BKT tire exhibited a slower rate of change in volumetric mass relative to the cross ply Özka tire. Upon examining the individual waveforms of the approximation functions, it can be observed that the individual measured values and the regression functions are relatively distinct and widely spaced. Hence, one could infer that, in this scenario, the functional dependencies for each tire are mutually exclusive. Moreover, some statistically meaningful disparities between the radial and cross ply tires would be likely. Nonetheless, the statistical analysis conducted for this scenario did not reveal any significant difference between the sample tires. Similar to the previous instance, the individual regression functions were once again evaluated using the goodness-of-fit test for regression coefficients. Considering that the computed criterion of this test method (denoted as |t|_off) is smaller than the critical tabulated criterion value of t_0.975 for all regression models, we cannot reject the hypothesis that the regression coefficients of the translated radial and cross ply tire functional dependencies agree. Therefore, statistically speaking, there is no distinction between the two tire types, and the groupings of plotted points from each dependency could essentially be substituted with a single unified regression function again. This implies that there is no statistically significant disparity in the changes in soil bulk density induced by radial and cross ply tires. To exemplify the results from the testing method, Table S3 showcases the outcomes of determining the alignment of the regression coefficients of the linear functions. These functions depict rolling resistance as a function of load at a steady tire pressure for the sample tires.

As previously discussed, our examination of the radial and cross ply tires’ rolling resistance and compaction effect also included an interest in understanding how increases in vertical load and tire pressure influence the rise in both the achieved rolling resistance and bulk density of the soil sample. To achieve this, all the regression equations from each functional dependency depicted above were combined, and alterations in the trajectories of these regression lines were monitored (Tables S4–S7).

Table S4 illustrates the mean increase in rolling resistance of the examined tires as a function of vertical load, maintaining a constant tire pressure. The mean slope of these plotted regression functions for the BKT 210/95 R16 Agrimax RT 855 radial tire is 2.01. This signifies a rise in rolling resistance of 2.01 N·kg⁻¹. An increase of 100 kg in the wheel’s vertical load results in a rise in rolling resistance by 201 N. For the cross ply tire Özka 7.50-16 8PR KNK 50, the mean value of the regression line slopes is 1.92, signifying a rise in rolling resistance of 1.92 N·kg⁻¹. An increase of 100 kg in vertical load corresponds to a 192 N rise in the tire’s rolling resistance.

The values above, which represent the increase in rolling resistance due to the variation in load of the sample tires at a constant tire pressure, do not exhibit substantial differences in the increase in rolling resistance between the two types of tires. The difference in absolute rate is only 9 N·kg⁻¹ or a relative rate of 4.48%. In this respect, the sample tires can therefore be considered equivalent.

Table S5 showcases the average increase in rolling resistance of the sample tires, depicted as a function of vertical load, while keeping tire pressure constant. The average slope of these wave formed regression functions for the BKT 210/95 R16 Agrimax RT 855 radial tire is 0.93. This indicates an increase in rolling resistance of 0.93 N·kPa⁻¹. A 100-kg increase in the wheel’s vertical load leads to a 93 N increase in rolling resistance. For the cross ply tire, specifically the Özka 7.50-16 8PR KNK 50, the average value of the slopes of the regression lines is 3.07. This indicates an increase in rolling resistance of 307 N·kPa⁻¹ for each kilogram. When the tire’s pressure is boosted by 100 kPa, a rise in the tire’s rolling resistance by 307 N is noted. In this instance, the increase in the radial tire’s rolling resistance due to the alteration in tire pressure is minor, even 53.73% less than the increase caused by the change in vertical load. However, the scenario is different for a cross ply tire, where a variation in tire pressure results in comparatively significant change in the attained rolling resistance values. This value represents a 37.46% increase compared to the rise resulting from the augmentation in vertical load.

Not only is it crucial to track change in rolling resistance values of tires traversing the soil, but it is also vital to evaluate how these changes impact the soil’s degradation. In this study, the evaluation is conducted based on changes in the soil’s bulk density being examined in the soil test channel.

Table S6 depicts the mean rise in soil sample bulk density, represented as a function of vertical load on the tire, while the tire pressure remains constant. The average slope of the charted regression functions for the BKT 210/95 R16 Agrimax RT 855 radial tire stands at 0.39. This indicates an increase in rolling resistance of 0.39 kg·m⁻³·kg⁻¹. An increase in the wheel’s vertical load by 100 kg corresponds to a rise in bulk mass of 39 kg.m⁻³. For the cross ply tire, Özka 7.50-16 8PR KNK 50, the mean value of the regression line slopes is 0.40. This signifies a rise in the soil’s bulk density by 0.40 kg·m⁻³·kg⁻¹. This means that a 40 kg·m⁻³ increase in the soil’s bulk density corresponds to a 100-kg increase in vertical wheel load. From this perspective, the differences can be deemed virtually insignificant, and the two tires can be regarded as comparable in relation to their compaction effect.

Table S7 illustrates the mean rise in the soil’s bulk density at the compaction pressure, maintaining a constant vertical load. The average slope of the charted regression functions for the BKT 210/95 R16 Agrimax RT 855 radial tire stands at 0.83. This indicates an increase in rolling resistance of 0.83 kg·m⁻³·kPa⁻¹. An increase in the tire’s pressure by 100 kPa corresponds to a rise in the soil’s bulk density of 83 kg·m⁻³. For the cross ply tire, Özka 7.50-16 8PR KNK 50, the mean value of the regression line slopes is 1.05. This signifies a rise in the soil’s bulk density by 1.05 kg·m⁻³·kg⁻¹. An increase in the tire’s pressure by 100 kPa results in a rise in the soil’s bulk density of 105 kg·m⁻³. In this scenario, the compaction impact of the cross ply tire exceeds that of the radial tire by 22 kg·m⁻³ for each increment of 100 kPa in tire pressure. Expressed in terms of percentage, this represents a variation of 20.95%.

From the results obtained, it can be concluded that altering the tire pressure of the tires has a more pronounced impact on changes in rolling resistance (3.07 N·kPa⁻¹ for the cross ply Özka tire) or bulk soil mass (1.05 kg·m⁻³·kPa⁻¹ for the cross ply Özka tire and 0.83 kg·m⁻³·kPa⁻¹ for the radial BKT tire), compared to the effect of modifying the vertical load of the sample tires. The impact of variations in vertical load on the alterations in rolling resistance and soil bulk density is evenly distributed for both sample tires. From this perspective, there are virtually no distinctions between the radial and cross ply designs of the sample tires.

The literature commonly suggests that radial tires tend to exhibit less rolling resistance compared to cross ply tires. The sidewalls of radial tires are more flexible, which allows for more radial deflection and consequently results in a broader contact area with the pad. The increased contact surface of the radial tire leads to reduced pressure exerted on the soil and a lesser degree of soil compaction, as partially evidenced in our study. For cross ply tires, the losses attributed to tread compression escalate with the square of radial deflection. This rate of increase is typically much quicker compared to radial tires [27]. Nonetheless, for minor deformations, there are no notable disparities in energy loss between radial and cross ply tires [28]. In our situation, we did not stress the tires to their maximum potential load for a given pressure, especially not at elevated tire pressure levels. This was mainly due to technical limitations of the soil channel apparatus. The levels of rolling resistance attained in tires are also influenced by the characteristics of the cord material utilized. This includes losses within the cord material due to hysteresis as well as the impact of the deformation mode of the employed rubber [29]. The angles at which the individual cord threads are routed in the carcass of the tire have a significant effect on the tire’s final properties.

Of course, the rolling resistance of tires is also related to the viscoelastic properties of the rubber used. The tread itself has the greatest influence on viscoelastic losses in tires. Its duty cycle is a combination of radial compression, bending, and internal friction. The results of individual studies are often contradictory in this respect, probably because the effects of tread rubber and casing carcass do not accumulate. Rather, it appears that there is a strong interaction between these components, which may result in actual energy losses being greater than expected [30].

While the observed data suggests certain advantages of radial tires over cross ply tires from an absolute perspective (such as reduced rolling resistance and soil compression), from a strict statistical perspective, we were unable to establish a significant difference between the two in the parameters we studied. The reasons why this is the case can be found in the causes mentioned above. The primary information that tire manufacturers provide to consumers predominantly pertains to the immediate functioning of the tires. Details about the casing structure, carcass construction, cord materials used, or the viscoelastic characteristics of the rubber compounds are understandably proprietary to the manufacturer.

5. Conclusions

It is clear that the sample tire designs and sizes are not very soil friendly. These needs are more likely to be fulfilled by wide, low-pressure tires that can bear heavy loads even at reduced tire pressures. However, the results also show that the question of the correct choice of tire pressure is not negligible even for conventional tires of radial or cross ply construction. The results show clearly how markedly increased tire pressure translates into increased soil compaction as well as increased rolling resistance. Instead of increasing with the weight on each wheel, this process becomes more intense as the tire’s pressure rises. Regarding the requirement for appropriate tire pressure, modern mobile equipment service technicians do not need to find this task labour-intensive or physically taxing. Currently, users of mobile equipment may choose and modify the tire pressure of each tire from the driver’s seat, either manually or automatically, based on the load and design of the tire, using a system called the Central Tire Inflation System or CTIS.

If we were to briefly summarize the results and findings achieved in our experiment, we could summarize them in the following few points:

• Be careful when choosing the tire pressure of wheeled work equipment. By calculation, simulation or experiment, determine the maximum load values of individual wheels in the most critical working phases of the mechanical device. Based on the obtained results, choose the appropriate tire pressure of individual wheels.
• If it is necessary to change the tire pressure frequently to optimize the reduction of rolling resistance and the reduction of damage to the road surface, consider equipping the wheeled work equipment with a CTIS system.
• If the agrotechnical and operational conditions allow, choose double mounting of tires. Double assembly allows further reduction of tire pressure and distribution of the wheel load over a larger contact area, which has a beneficial effect on the resulting level of ground compaction.
• In the case of common designs of radial ply and cross ply tires, do not choose a tire pressure of 100 kPa or lower, even though tire manufacturers often allow this in their technical materials.
• If possible, use radial ply tires with slightly lower levels of rolling resistance from the point of view of reducing the rolling resistance of wheeled work equipment.
• For wheeled mechanized equipment where directional stability is important and standard stabilization cannot be used, choose cross ply tires, as they show better lateral stability. Similarly, in the case of constructions of the driving systems of forestry wheeled tractors, it is more advantageous to use cross ply tires, which are more resistant in the heel part against the penetration of branches.