Comparative Analysis of Static Rollover Stability Between Conventional and Electric Tractor

Abstract

As the development of electric tractors progresses, battery systems have become a key component, accounting for a significant portion of the vehicle’s total weight. With rollover accidents remaining a leading cause of fatal injuries in agricultural machinery, the stability of electric tractors is drawing increasing attention. In particular, battery placement may critically affect the overall mass distribution and rollover behavior, highlighting the need for safety-focused design optimization. This study evaluates the static rollover stability of a 55 kW electric tractor by analyzing the effect of battery mounting position and comparing it with a conventional tractor. Three tractor models were considered: an electric tractor with a front-mounted battery, one with a center-mounted battery, and a conventional tractor. Multibody dynamic simulations were conducted using RecurDyn, and a total of 24 orientations, at 15° intervals, were simulated to determine the tipping angles in all directions. The results revealed that battery placement had a significant impact on rollover stability. The front-mounted battery type exhibited up to 30% higher tipping angles than the conventional tractor in the forward pitch direction near 90°, indicating improved stability. In contrast, the center-mounted battery type showed a tipping angle distribution generally similar to that of the conventional tractor, with smaller variations across directions. These findings demonstrate the influence of mass distribution on rollover safety and provide valuable insight for structural design of electric tractors.

1. Introduction

The increasing use of agricultural tractors has significantly enhanced productivity and reduced labor intensity in modern farming [1]. However, their growing prevalence has been accompanied by a persistent incidence of safety-related accidents, particularly rollovers. Rollover accidents are among the most fatal types of agricultural machinery incidents. They commonly occur when tractors operate on uneven terrains, field boundaries, or sloped surfaces, and these incidents are often triggered by a combination of structural imbalance and loss of wheel traction [2,3,4].

As the global agricultural sector transitions toward decarbonization, the electrification of agricultural machinery is gaining momentum [5,6,7]. Electric tractors are being actively developed and partially commercialized in regions such as Europe and the United States, offering benefits including reduced emissions, lower operating noise, and simplified powertrains [8,9]. However, their widespread adoption faces significant practical hurdles, such as the lack of charging infrastructure in remote agricultural settings and concerns about limited operating time. These challenges underscore the need for highly optimized and safe designs. In South Korea, the electrification of agricultural machinery is in progress, and development efforts have reached the prototype phase for mid-power electric tractors [10,11]. A key structural distinction between conventional tractors and their electric counterparts lies in the configuration of their powertrains, as conventional models are typically equipped with diesel engines, whereas electric tractors employ battery-powered electric motors [12]. Conventional tractors typically house heavy engine components and fuel tanks toward the front, yielding a forward-biased center of gravity (CoG). Conversely, the higher energy density and compact design of battery systems relative to diesel engines can substantially alter both the overall vehicle mass and the CoG position [6,13]. Such differences highlight a fundamental departure from conventional platforms and underscore the need to critically reassess rollover stability evaluation methods. While previous studies have examined stability in diesel- or hydrogen-powered tractors [14,15,16], limited research has specifically addressed how battery placement uniquely influences the rollover behavior of electric tractors [17,18]. This study addresses this research gap by directly comparing conventional and electric tractor architectures, thereby providing novel insights into safety-oriented design optimization for electrified agricultural machinery.

Previous studies have established analytical and simulation-based frameworks to assess rollover risk in conventional tractors [19,20,21,22,23]. Watanabe et al. modeled the influence of steering-induced bounce on traction distribution under slope driving [15], while Choi et al. explored lateral stability by quantifying the CoG’s role in rollover dynamics [14]. More recent research by Son et al. examined how power source differences, specifically in hydrogen-powered tractors, affect static rollover behavior through comparative simulation analysis with conventional tractors [16]. Although Son’s methodology offered valuable insights into the impact of component layout on rollover angles, its generalizability to electric tractor platforms, which present distinct design architectures and mass characteristics, remains unverified.

Therefore, this study aims to critically evaluate the applicability of static rollover angle analysis methods to electric tractors. By simulating and comparing a conventional tractor and an electric tractor of equivalent rated output, this research investigates how battery placement influences rollover stability under various orientation scenarios. Two battery layouts (front-mounted and centrally embedded) were examined to determine their effects on CoG positioning and rollover angles. The resulting data provide a comparative perspective on rollover performance between drivetrain types and offer foundational insights for developing stability guidelines suited to the evolving landscape of electrified agricultural machinery. These findings are expected to guide safer structural design practices for future electric tractors and support the development of updated rollover stability standards.

This paper is organized as follows: Section 2 of this paper introduces the tractor models used, simulation analysis conditions, variable configurations, and analysis methods. Section 3 compares and analyzes the static rollover angles, traction distribution, and changes in center of gravity position under different conditions. Section 4 presents the optimal structural conditions and future design directions from the perspective of rollover stability.

2. Materials and Methods

2.1. Modeling of Electric and Conventional Tractor

The tractor models used in this study consisted of an electric tractor currently under development and a conventional tractor with an equivalent rated output, both designed for comparative analysis under identical conditions. The electric tractor model was designed based on specifications provided by the manufacturer, while the conventional tractor model reflected the structure of commonly available commercial models using Autodesk Inventor (Autodesk Inc., San Rafael, CA, USA) (

Table 1. Specifications of Electric and Conventional Tractors Used for Simulation Modeling.

Parameters	Electric Tractor	Conventional Tractor
Length [mm]	3840	3920
Width [mm]	1880	1940
Height [mm]	2415	2710
Mass [kg]	2800	3065
Rated power [kW(ps)]	55 (75)	55 (75)
Minimum ground clearance [mm]	493	450
Wheelbase [mm]	2143	2200

).

The total mass of the electric tractor specified in Table 1 includes the battery pack. Its lower mass compared to the conventional model is due to the replacement of the heavy internal combustion powertrain, including the engine and transmission, with a lighter and simpler electric drive system.

2.2. Placement of Powertrain Components in Each Model

The position of the battery in electric tractors was identified as a key structural design variable in this study, as it plays a decisive role in determining the vehicle’s mass distribution and COG [17]. In electric tractors, the battery, and in conventional models, the engine, are the heaviest components and thus exert a significant influence on stability-related parameters [1,13].

To investigate the impact of battery placement, two electric tractor configurations were developed: one with a front-mounted battery (Figure 1a) and the other with a centrally mounted battery (Figure 1b).

Table 2. Specifications of Battery and Engine.

Parameters	Battery	Engine
Length [mm]	514.9	1352.3
Width [mm]	630.0	1003.0
Height [mm]	783.7	1487.5
Mass [kg]	500.0	461.0

presents the specifications of the power sources for each configuration, and the internal component layout was calculated and compared through 3D modeling. Additionally, the overall center of gravity coordinates for each configuration are presented in

Table 3. Center of Mass Coordinates for Each Tractor Models.

Parameters	Front-Mounted	Center-Mounted	Conventional
X coordinate [mm]	−86.22	−15.06	−11.14
Y coordinate [mm]	913.63	893.84	906.00
Z coordinate [mm]	1253.14	773.23	868.99

, illustrating the shift in the center of mass based on the position of the battery or engine (Figure 2 and Figure 3).

The conventional tractor model, used as a reference, adopts the typical front-engine configuration commonly observed in commercial tractors with the engine mass of 3065 kg (Table 2 and Table 3).

2.3. Mathematical Modeling of Static Tipping and Deviation Calculation

In this study, three static tipping angle models were considered to analyze the rollover characteristics of the tractor: lateral rollover (rollover around the front axle pivot), and pitch-over events in both forward and backward directions, based on the rollover modeling approach proposed by Andrew L. Guzzomi (2012) [24]. These are defined as the angular threshold at which the center of gravity (COG) of the tractor crosses the tipping axis (P), resulting in a loss of contact at one of the wheels.

As shown in Figure 4, the lateral tipping model considers the front axle pivot (P) as the hinge about which the tractor rotates when placed on an inclined surface. The rollover angle ${\theta }_r$ is computed using Equation (1), as proposed by Guzzomi [24]:

$${\theta }_r [°]={\tan }^{-1}{\displaystyle \frac{2(hs-h_1{l}_1)}{w(s-s_1)}}$$

(1)

where w is the track width, $l$ is the wheelbase, $l_1$ is the horizontal distance from the rear axle to the COG, h is the vertical height of the COG from the ground, and h₁ is the height of the front axle pivot.

In contrast, pitch-over events are analyzed with respect to rotation about the front or rear wheel contact points. The forward pitch-over angle θ_pf and backward pitch-over angle θ_pb are calculated using simple geometric relationships, also based on the model in [24], as follows:

$${\theta }_{pf} [°]={\tan }^{-1}{\displaystyle \frac{l-l_1}{h}}$$

(2)

$${\theta }_{pb} [°]={\tan }^{-1}{\displaystyle \frac{l_1}{h}}$$

(3)

where $l$ is the wheelbase, $l_1$ is the horizontal distance from the rear axle to the COG, and h is the vertical height of the COG from the ground.

These three tipping angles serve as static stability indicators for different tipping directions, and they are later used to quantify the rollover safety of electric and conventional tractors under various design configurations.

In the simulation analysis, the static tipping angle of a tractor is defined as the point at which the grounding force of one wheel becomes zero on an inclined surface. This follows the criterion proposed by Andrew et al., which considers “the moment when one wheel loses its grounding force as the beginning of tipping,” and is established as a judgment criterion for static tipping analysis [24,25].

After simulating tipping events for each tractor model, the resulting tipping angles were compared to evaluate the relative stability between electric and conventional tractors. To quantitatively compare the rollover angles between the electric tractor and the conventional engine tractor, the relative directional deviation was calculated using the electric tractor as a reference, as shown in Equation (4):

$$Deviation \left[\%\right]= {\displaystyle \frac{{\theta }_{EV}-{\theta }_{conventional}}{{\theta }_{conventional}}}\times 100$$

(4)

where θ_EV and θ_Conventional represent the rollover angles of the electric and conventional tractors, respectively.

This equation enables a direction-specific comparison of rollover stability between the two tractor types under identical driving conditions, and it is particularly useful for evaluating the influence of battery mounting position (Figure 5).

2.4. Simulation Framework for Rollover Stability Analysis

This study employed a multi-body dynamics simulation to evaluate the structure design variations between electric and conventional tractor influence static rollover stability. Tractor models were configured to have an equivalent rated power of 55 kW to ensure a consistent basis for comparison. For the electric tractor, two distinct configurations were developed according to the battery’s location, one at the front and the other at the middle. The conventional tractor model was constructed based on the layout of a commercially available model, reflecting the conventional front mounted engine and rear fuel tank arrangement [16].

Rollover stability was assessed under static conditions using a dynamic simulation program Recurdyn 2025 (FunctionBay, Seongnam, Republic of Korea), the ground surface was initially set to a horizontal position, and its inclination was gradually increased at a constant angular velocity during each simulation set. Moreover, total of 24 directional test cases were established by incrementally rotating the tractor’s heading in 15° steps, covering a full 360° range relative to its forward direction. For each case, the tractor was assumed to be placed on a rigid, inclined surface. To prevent the tractor from slipping during the rollover simulation on the ground, the coefficient of dynamic friction between the tires and the ground was set to 1.2. In addition, the ground stiffness and damping coefficients were set to 105 and 10, respectively, to reflect realistic contact behavior [16,19]. The tire’s radial stiffness and damping coefficients were set to 4080 N/mm⁻¹ and 2.8, respectively, based on parameters from existing literature [19].

Since an unloaded tractor is not expected to roll over at slope angles below 30 degrees, the simulation time was set to 25 s, and the total number of steps was set to 750, considering the angular velocity of the rotating ground. As the slope angle increased, the point of rollover was determined based on the loss of ground reaction force at any of the wheels. This methodology followed the approach outlined by Son et al. (2024), which was originally developed for evaluating rollover risk in high-powered tractors exceeding 100 kW, and its applicability under these different structural conditions was critically examined [16].

2.5. Validation of the Simulation Model

To validate the simulation methodology employed in this study, the analysis from a previous study by Son et al. [16] was replicated. A validation model was developed by matching the principal specifications of the reference study, such as the tractor’s mass, center of gravity, and key simulation variables. The model’s Center of Gravity was established using the X and Z coordinates reported by the reference study, while the lateral Y coordinate was calculated from the provided weight distribution ratio.

Table 4. Model specifications, parameters, and rollover angle results for validation.

Category	Front-Mounted	Son et al.	Validation Model
Specifications	Mass (kg)	5100	5100
	Center of Gravity [mm]	(1355.72, 66, 1356.59)	(1355.72, 66, 1356.59)
Conditions	Dynamic Friction Coefficient	1.2	1.2
	Stiffness Coefficient [N/mm3]	105	105
	Damping Coefficient [N·s/mm]	10	10
Result	Rollover Angle [°]	35.89	37.92

presents a side-by-side comparison of the replicated parameters and the resulting static tipping angles.

As shown in Table 4, the static tipping angle from the validation model (37.92°) shows good agreement with the result from the reference study (35.89°). The relative deviation of approximately 5.7% confirms that the simulation methodology employed in this study is valid.

3. Results

3.1. Observation of Initial Wheel Lift-Off and Rollover Onset

For each slope direction, the tire that first lost ground contact was identified by monitoring the normal contact force at each wheel. Ground contact was considered lost when the normal force decreased to zero, which defined the initial point of lateral instability. This criterion was used to establish the onset of rollover, and the corresponding wheel position served as an indicator of rollover tendency and direction.

Figure 6 indicates the variation in normal contact forces for all four wheels of the electric tractor with a center-mounted battery as the slope angle increases in the 0° orientation. As the slope increases, a clear redistribution of vertical loads is observed. The front-left tire exhibits a progressive decrease in contact force, reaching zero at a slope angle of 28.9°. Simultaneously, the right-side tires show a compensatory increase in load, while the left-side tires maintain relatively moderate changes. This pattern reflects a lateral shift in load toward the uphill side, which becomes more nonlinear beyond 20°, indicating increasing instability (Figure 6).

Once one tire loses ground contact, the remaining three—or sometimes only two—tires must support the entire load. This load concentration often produces local oscillations or fluctuations in the contact force data, appearing as noise in the graph. This behavior is characteristic of dynamic systems approaching the transition from stable to unstable states. When two tires (front-left and rear-left) completely lift off and their contact forces simultaneously reach zero, the center of gravity rapidly shifts beyond the support base, leading to a sudden drop in the contact force on the remaining wheels. In the simulation, this point coincided with the physical rollover of the tractor model.

These findings emphasize the significance of rear wheel loading and load symmetry in rollover prevention, and offer practical implications for optimizing mass distribution, ballast placement, and battery configuration in the structural design of electric tractors operating on sloped terrain.

3.2. Variation in First Ground Contact Loss According to Vehicle Orientation and Structural Type

To characterize the onset of rollover instability across different tractor types, variations in vertical contact force at the wheel that first exhibited ground detachment were analyzed (

Table 5. Contact force trends of first-losing wheels by vehicle orientation and tractor type.

Orientation	Front-Mounted	Center-Mounted	Conventional
0–75
90–165
180–255
270–345

). In all cases, the contact force at this critical wheel progressively declined with increasing slope angle, and the slope angle at which it reached zero was defined as the rollover threshold. The specific wheel initiating contact failure differed depending on tractor type, primarily due to variations in load distribution arising from battery placement and structural layout. At 90° and 270° orientations, representing frontal and rearward slope ascents, pitch induced rollover was observed. The front left wheel lifted first at 90° due to a forward incline, whereas the rear right wheel detached first at 270° under rearward ascent. These directional differences are driven by a rightward shift in the center of gravity common to all types, causing the inner wheel to lift as the center of mass exceeds the lateral support base. A comparable mechanism was observed at 0° and 180°, orientations associated with lateral rollover vulnerability. Here, the lateral offset of the center of gravity led to asymmetric load distribution and dictated which wheel experienced initial contact failure. Additionally, the initial ground contact forces varied markedly depending on wheel position and heading orientation. These disparities stemmed from non-uniform mass distribution and differing moment arms between each wheel and the center of gravity. As the vehicle enters a slope, gravitational loading is unevenly distributed across the wheels, directly influencing both initial contact conditions and rollover sensitivity.

3.3. Comparison of Directional Rollover Stability

The rollover angles of each tractor type (front-mounted battery, center-mounted battery, and conventional) was evaluated under 24 directional conditions at 15° intervals, covering the full range of 360°. As a result, the directional distribution of rollover angles in polar coordinates for each type is presented in Figure 7. The electric tractor with the front-mounted battery exhibited a forward-shifted center of gravity, resulting in higher rollover angles in the 0–180° range where the tractor’s front faced uphill. In contrast, the center-mounted battery type demonstrated increased rollover angles in the 180–360° range, where the rear of the tractor was oriented upslope. These findings indicate that directional rollover stability is strongly influenced by the longitudinal placement of the center of mass which is directly affected by battery location. The center-mounted type appears to offer more balanced stability characteristics, whereas the front-mounted type enhances resistance primarily in forward facing conditions. Notably, none of the types consistently outperformed the others across all directions implying an inherent tradeoff between slope orientation and optimal mass distribution. In perspective of design, these results underscore the importance of considering directional terrain effects when determining battery placement in electric tractors. Integration of adjustable or modular battery systems could allow dynamic mass redistribution in response to terrain conditions, potentially enhancing rollover safety and operational flexibility in sloped agricultural environments.

3.4. Rollover Angle Error Analysis Between Electric and Internal Combustion Tractors

To quantitatively assess the effect of battery placement on directional rollover stability, the relative differences in rollover threshold angles between each electric tractor type and the conventional model were calculated using Equation (1) and the results are presented in Figure 8. The front-mounted battery type exhibited substantial improvements in rollover angles within the 0–180° range with a peak increase of 29.9% at the 90° orientation during head-on uphill travel. This suggests that forward oriented mass concentration can significantly enhance stability in uphill conditions. However, it exhibited decreased rollover stability in the 180–315° orientation range with reductions reaching up to 20% compared to the conventional type. This directional sensitivity suggests that front-mounted mass concentration may compromise stability when the rear of the tractor faces uphill. The rapid increase in rollover angle difference between 60° and 90° further suggests that the vehicle’s stability response is particularly sensitive to forward facing slope inclinations. In contrast, the center-mounted battery type produced smaller deviations from the conventional type across all directions. Although it did not achieve the peak performance as the front-mounted setup, it provided more uniform rollover performance, especially in the 180–270° range where rearward and lateral slopes are encountered. Notably, both types intersected the zero-difference line at specific orientation angles, representing directional points where rollover performance was equivalent to that of the conventional design. These transitional angles may correspond to equilibrium conditions in which the influence of battery mass distribution on stability is minimized. Overall, these results underscore a trade-off between directional performance and generalized stability, which should be carefully considered in the design of mass distribution strategies for electric tractors operating on varied slope conditions.

4. Discussion

This study quantitatively analyzed changes in rollover stability according to the battery mounting position of electric tractors and evaluated their structural stability characteristics through comparison with a conventional tractor. The simulation results showed that the contact force of the tires located on the downhill side gradually increased, while that of the tires facing the slope decreased until reaching 0 N, at which point rollover was initiated. In this study, the slope angle at that moment was defined as the rollover angle.

The electric tractor with a front-mounted battery showed higher rollover angles in the 0–180° range, where the driving direction faced uphill, compared to the conventional tractor. This result indicates improved rollover stability and is interpreted as the effect of the front-concentrated battery mass increasing the stabilizing moment acting opposite to the slope [26]. Conversely, in the 180–360° range, where the rear of the tractor faced the slope, the center-mounted battery configuration showed relatively higher rollover angles, suggesting that rearward weight distribution contributed positively to rollover resistance in that orientation.

In accordance with South Korea’s national certification standards for agricultural machinery, tractors are required to maintain rollover stability on slopes up to 30°, which serves as a critical safety threshold under typical domestic field conditions [27]. Both front and center-mounted battery electric tractor types achieved rollover angles exceeding this benchmark in most directional orientations, indicating general compliance with the regu-latory criterion while suggesting the need for further refinement in specific conditions. However, internationally recognized standards, such as the OECD Tractor Codes and ISO 5700, focus not only on static stability but also on the structural integrity of the Roll-Over Protective Structure (ROPS) based on energy and load tests [28,29]. A critical point is that these existing standards were developed based on the mass distribution and rollover dynamics of conventional front-engine tractors. As demonstrated in this study, the center of gravity and rollover behavior of electric tractors can differ significantly depending on battery placement. This suggests that as electric tractors become more prevalent, a revision of existing standards or the development of new safety criteria that account for the unique and variable mass distributions of electric tractors is necessary. The 360-degree stability profiles presented in this research could serve as crucial foundational data for establishing such future policy and standards.

Rollover was defined as occurring when any wheel that reaches zero of contact force, following the methodology proposed by Son et al. [16], which was originally developed for a hydrogen tractor. In his study, computational analysis for rollover of a hydrogen tractor revealed that centrally positioning the high-mass hydrogen storage tank beneath the chassis yielded the most favorable stability performance. This observation is consistent with the current findings for the center-mounted battery type, thereby reinforcing the methodological validity and suggesting its applicability to electric tractors with alternative mass distributions. In addition, Lee’s study reported that the battery accounts for a significant portion of the vehicle’s total weight and that its position has a substantial impact on rollover stability (Lee et al., 2023) [18]. In particular, it was shown that the risk of rearward rollover decreases as the center of gravity shifts forward. Although the study was conducted under a single directional condition, the results were consistent with those observed under similar conditions in the present study.

Meanwhile, this study was based on static simulation conditions, and dynamic factors such as driving speed and implement attachment, which may occur in actual field operations, were not considered. Therefore, future research should include dynamic simulation analysis that reflects various field conditions and ground characteristics and comprehensively assess the effects of variables such as battery mass, wheel arrangement and actual operation conditions on rollover stability [30,31]. Additionally, as this study focused on a specific 55 kW prototype currently under development, future work could explore how these findings apply to other tractor types, such as compact or large-scale models, which have different mass and geometric characteristics.

5. Conclusions

This study investigated the effect of battery placement on the directional rollover stability of electric tractors through multibody dynamic simulations conducted across 24 slope orientations. The results revealed that battery location significantly influences rollover behavior: the front-mounted battery type enhanced stability during uphill travel (0–180°), while the center-mounted type demonstrated superior performance on rearward slopes (180–360°). These findings reinforce the principle that rollover resistance improves when the center of gravity is positioned opposite to the direction of slope ascent. The outcomes highlight battery mounting location as a key design parameter in the structural safety of electric tractors and underscore the importance of incorporating directional slope conditions into early-stage design strategies. As the deployment of electric tractors continues to grow in agricultural operations, ensuring rollover stability across diverse terrains and working conditions will become increasingly critical. This study provides a structural basis for battery placement optimization in electric tractor design, and future research should further investigate dynamic operating scenarios, variable load distributions, and heterogeneous field conditions to enhance real world applicability.