# Simulation of the Rollover Angle of a Self-Propelled Radish Harvester for Different Load Conditions
## 1 Introduction  
In Korea, radish is the third-largest vegetable crop [1] and is used as a typical side dish with the traditional Korean food kimchi. Korean radish kimchi has six categories: kkakttugi, seokkabiki (or nabakkimchi), dongchimi, jianji, jangachi, and jangkwa [2]. Generally, vegetables are classified according to the parts used and their function into six types: flavor, root, leaf, stem, fruit, and western vegetables. Among them, flavor vegetables cover almost 44.9% of the cultivation area [3], which has been decreasing at an average rate of around 0.8% per year. According to Korean statistics, radish cultivation is decreasing day by day. The growing area dropped by 12.3% from 2018 to 2019, almost 752 ha [4]. In addition, the number of farmers decreased by 22% from 2,962,000 in 2011 to 2,317,000 in 2020 [5] in Korea. In particular, the proportion of farmers aged 65 and over increased by 26% from 33.7% in 2011 to 42.5% in 2020 [6,7]. The solution to the problem of aging farm labor could lie with machinery. In Korea, in 2020, almost all paddy fields were mechanized (98.6%), but the upland field mechanization rate was lower (61.9%) [8]. In particular, in case of the radish harvest, the mechanization rate in 2020 was very low (11.3%) [9]. To date, a machine for harvesting radish has not yet been made commercially available, yet mechanization is required to address the growing shortage of workforce and to minimize labor costs and time. Radish is an upland field crop [1], and more than 90% of Korea's upland fields have a slope of 2\({}^{\circ}\) or more, with 23% of all upland fields having a slope of 15\({}^{\circ}\) or more [10]. Generally, these fields are very uneven, and the slope affects the stability and performance of agricultural machinery [11]. [PERSON] [12] reported that about 50% of all farm accidents occurred because of machinery instability including the rollover. According to [PERSON] et al. [13], the stability of a machine fails when the slope angle is higher than the rollover angle, and they noted that the most frequent cause of death and injury from farm machinery accidents in Australia were caused by rollover. Similar findings were made by [PERSON] [14], who also pointed out a good understanding of slope stability is essential for safe and stable commercialized agricultural machinery. [PERSON] [15] stated that, in addition to serious injury and economic losses, rollover accidents create mental stress. Therefore, it is important to make agricultural machinery stable to avoid unwanted agricultural accidents. Various parameters of agricultural machinery affect stability, such as static, dynamic, and operational parameters. The static parameters include the wheelbase, the width, and the center of gravity (CoG) of the machine, while the operating parameters are considered among the dynamic parameters. Some agricultural machinery (e.g., tractors) have a rollover protective structure (ROPS) [16; 17; 18], which according to [PERSON] et al. [19] is designed to avoid or minimize the risks to the driver in case of a rollover during field operation. They mentioned that the ROPS is characterized by having a large enough clearance space to protect the driver. Generally, rollovers occur under static or operational conditions in the lateral or longitudinal directions. Stability angles vary from 15 to 45\({}^{\circ}\) for different agricultural machinery according to ISO 16231-2 [20]. In Korea and Japan, the slope operation limit in stability evaluation is 15\({}^{\circ}\) to minimize overturning [21]. However, the stability angle also varies on the basis of the weight balance [22]. [PERSON] [23] found that the lateral load transfer ratio (LTR) is a main cause of machine instability. It was also mentioned that LTR has a high impact on the front wheel of the machine and causes longitudinal rollover accidents. Therefore, weight balance is another important aspect to consider when analyzing the stability or rollover angle in the manufacturing of a stable and safe machine.