# Mechanical Properties of Sugar Beet Roots under Impact Loading Conditions

^{*}

## Abstract

**:**

_{imp}= 0.5, 1.0 and 1.5 m·s

^{−1}. The measurements of local root curvatures in three chosen impact areas and the deformation (d

_{max}) allowed modelling of the volume of contact (CV) by means of the ellipsoid cap. These investigations enabled the determination of the relations between the maximal impact force, F

_{max}, the impact energy, E

_{imp}, and the absorbed energy, E

_{abs}, as well as the contact volume and impact velocity, taking into account the root storage time, S

_{t}. It was found that the maximal impact force increased with increasing impact velocity and decreased with the storage time for each group of roots. With increasing velocity, there were also increases in the following: impact energy, absorbed energy, contact volume and maximal deformation, as well as absorbed energy, referred to as the mass E

_{abs-v}from V

_{imp}. The mean values of the stresses (σ

_{max}), being the quotients of the impact force (F

_{max}) and the surface area of the ellipsoid cap base (A

_{BE}), were 0.81–1.17 MPa, 1.064–1.59 MPa and 1.45–1.77 MPa for the velocities of 0.5, 1.0 and 1.5 m·s

^{−1}, respectively. It was confirmed that the statistical significance of the mentioned parameters changes depending on the impact velocity.

## 1. Introduction

^{−1}, and their size can increase with increasing motion velocity that is caused by, e.g., picking up, sorting, transport mechanisms or drop height during transshipment [10,11,12]. The identification of root defects in the forms of cracks, breakages (fractures) and abraded surfaces during a beet’s movement inside a harvester, e.g., on transporters and cleaning turbines, is discussed in [13,14,15], along with the necessity to avoid these defects. Methods allowing the obtaining of information about biological material responses to mechanical loads, particularly impact loads, have been searched for. The literature reports the descriptions of various impact tests, which are divided into a small number of types. Experiments using a physical pendulum can be conducted on samples [16] or on whole fruits. Experiments that involve striking a fruit placed at the end of an arm against a flat surface [17,18,19,20,21] or striking an immobile fruit with an impactor fixed to the pendulum [22,23,24] are more frequently applied. Another type of test involves free dropping from a chosen height; this is used for estimations of the fruit’s characteristics, e.g., guava ripeness [25] or apples’ resistance to damages [26]. Such investigations have determined the results of loads during the impact of various materials against surface areas [27] and the elasticity modulus and maximal forces using a triaxial acceleration sensor for potato tubers [28].

- Time courses of the beet root’s reaction and force response to the impact.
- The course of deformation during the impact in time as a sequence of images.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Research Stand

#### 2.3. Volume of Deformation of the Root

_{E}

_{1}, b

_{E}

_{2}half-axes (Figure 2a).

_{1}–D

_{4}(Figure 2b) using a radius measuring device. Such interpretation allows reconstruction of local root geometry as a prolate ellipsoid on the half-axes a and b (Figure 2c), whose characteristic features are circular cross-sections in the plane perpendicular to the large half-axis b.

_{1}. During impact, the root curvature is in contact with the flat resistant surface of the sensor (Figure 3a). The value of the formed deformation, d

_{max}, can be determined in millimeters during the test (Figure 3b,c). Figure 3c presents the impact in the final phase in which the deformation reaches the maximal value d

_{max}. The value b

_{E}in the picture corresponds to this deformation. In order to show the maximal deformation d

_{max}= c

_{E}, the deformation was moved to Figure 3b, which presents the beginning of the root surface contact with the sensor-resistant plane.

_{E}, b

_{E}and d

_{max}= c

_{E}(in millimeters)—are much smaller than the half-axes a and b of the prolate ellipsoid used for reproduction of the local root shape (Figure 4a). In this paper, there was an attempt to model contact volume (CV), total deformation during the impact, as the ellipsoid cap (Figure 4), which can be expressed using the following dependence:

_{E}= d

_{max}—the horizontal deformation, mm; a—the small ellipsoid half-axis; 2a = D

_{1}mm, b—the large ellipsoid half-axis, mm.

_{max}= c

_{E}which can be obtained from direct measurements, e.g., 2a = D

_{1}, and based on the results of impact tests as the maximal deformation d

_{max}= c

_{E}(Figure 3b). However, the value of the large half-axis b of the prolate ellipsoid presented in Figure 4a can be calculated from the dependence determining the position of point M fulfilling the ellipse equation. Figure 5 presents the ellipse, which is also the largest longitudinal cross-section. The ellipse equation is as follows:

_{E}, y =

**½**b

_{E}—the coordinates of the ellipse M point position.

_{E}and y = ½·b

_{E}, were used for determination of the value of large half-axis b from the following equation:

_{E}—the maximal deformation.

_{E}, because the exact volume of their occurrence is not known due to the lack of visible blue spots on the root tissue. Cross-section area of ellipsoid based on ellipse (A

_{BE}) with the main axes a

_{E}and b

_{E}, presented in Figure 4b, was obtained from the following equation:

_{E}—the width of the ellipsoid section; b

_{E}—the height of the ellipsoid section.

_{max}) for the mechanical impact obtained from the tests as well as A

_{BE}determined from the relation (4), normal compressive stresses of a dynamic character formed during the root impact against the plate surface were calculated:

_{max}—the maximal stress, MPa; F

_{max}—the maximal value of impact force obtained from the tests, N; A

_{BE}—the area of ellipsoid based on ellipse, mm

^{2}.

#### 2.4. Moisture Content

_{k}—the mass of root sample in grams before drying, g; M

_{b}—the mass of the sample after drying, g.

#### 2.5. Apparatus and Slotted Section

^{−1}(0.44 mV·N

^{−1}—typical voltage sensitivity) and measurement range of 2200 N—which is a piezoelectric transducer that generates an analog signal proportional to the force being measured. The signal from the force sensor was transmitted using the recorder LMS SCADAS Mobile (Siemens, Munich, Germany) to a computer equipped with LMS Test.Xpress 8A software for registration and analysis of the data, which could then be visualized, processed and recorded to a hard disk in real time. The measurement initiation took place when the value of root reaction force exceeded 0.5 N at the frequency of 10.24 kHz. A Phantom Miro M320 camera (Vision Research, Wayne, NJ, USA) with a lens with 25 mm focal length was used for recording the course of root impact against the plate surface perpendicular to the direction of pendulum movement. The sequence of images was analyzed using Phantom Camera Control (PCC-2) software with pixel resolving power of 1024 × 768 at the velocity of 3413 frames per second. Figure 3 presents time-lapse photos obtained by means of the camera showing the beet root before and during the impact against the flat immovable surface of the plate fixed to the force sensor. The course of root velocity and its deformation in time were determined using Tema Motion Vision 3.8 software (Image Systems, Linköping, Sweden).

#### 2.6. Measurements

^{−1}, respectively. In a single research cycle involving 5 beets, the values of reaction and deformation forces in the root surface were obtained, and their exemplary courses in time are presented in Figure 6.

_{imp}) and elastic rebound (E

_{el}) energies as well as absorbed energy (E

_{abs}) by the root using the following formulae:

- E
_{imp}—The energy of the mechanical impact J, - E
_{el}—The energy of beet material response to the mechanical impact J, - E
_{abs}—The energy absorbed during the mechanical impact (the surface area between the curves F_{imp(d)}and F_{reb(d)}in the part from d = 0 to d = d_{max}).

**Figure 7.**Typical relationship between the force response and the deformation during the impact and the rebound of sugar beet root.

_{abs-v}, which is the quotient of E

_{abs}and the root mass m, was proposed:

_{ab-v}—the absorbed energy related to the mass, J·g

^{−1}; m—the root mass, g.

## 3. Results and Discussion

^{2}= 0.94 was found.

_{max}on the impact velocity V

_{imp}, taking the storage time into account. An increase in maximal values of forces with increasing impact velocity was found for all groups of roots stored from 0 to 5 days. The maximal impact force reached the following mean values for fresh roots: 389.3 N for 0.5 m·s

^{−1}velocity, 870.5 N for 1.0 m·s

^{−1}and 1274.4 N for 1.5 m·s

^{−1}. The values of forces decreased on successive days for all impact velocities, and F

_{max}reached the following mean values for 5-day-old roots: 259.0 N for the velocity 0.5 m·s

^{−1}, 552.2 N for 1.0 m·s

^{−1}and 799.5 N for 1.5 m·s

^{−1}. The dependence of the maximal value of force, F

_{max}, on the velocity, V

_{imp}, and the day of storage, S

_{t}, was statistically significant and the determination coefficients were R

^{2}= 0.87–0.98 and R

^{2}= 0.49–0.79, respectively. The increase in the value of the maximal impact force with increasing impact velocity was confirmed by impact studies carried out not only for beets [24,33], but also for potatoes [44], peaches [45], corn [46], blueberries [47], apples [27,48,49,50], pears [29], kiwifruit [51] and guava [25]. This results from the viscoelastic nature of plant materials that are vegetables and fruits, and is connected with the loss of turgor in the tissues.

_{imp}increased with the increasing impact velocity V

_{imp}for all groups of stored roots in the period of time from 0 to 5 days (Figure 10). The impact energies E

_{imp}, e.g., for fresh roots, had the values 0.188–0.249 J, 0.578–0.801 J and 1.223–1.778 J, respectively, depending on whether the drop velocity V

_{imp}was 0.5, 1.0 or 1.5 m·s

^{−1}, and were statistically significant, whereby R

^{2}= 0.85–0.95. For the dependence shown in Figure 11 concerning the increase in the absorbed energy E

_{abs}with the increasing impact velocity V

_{imp}, statistical significance was found for all groups of stored roots (R

^{2}= 0.63–0.95). The similar relationship is observed in case of E

_{abs-v}quantity (Figure 12). The presented research results can be compared with the effects of experiments on impacts involving pomegranate, based on which Shafie et al. [41] found that the energy absorbed during the impact had the greatest effect on the bruising volume.

_{imp}for sugar beets is presented in Figure 13. A CV increase with increasing impact velocity was observed for all analyzed groups of roots, and this dependence was statistically significant (R

^{2}= 0.68–0.93). From the dependence of the absorbed energy referred to as the mass E

_{abs-v}on the impact velocity V

_{imp}calculated from Formula (9), an increase in values (0.110–0.137 J·g

^{−1}, 0.317–0.527 J·g

^{−1}and 0.645–1.044 J·g

^{−1}) was obtained for successive impact velocities. Statistical significance for the analyzed dependence E

_{abs-v}on V

_{imp}(R

^{2}= 0.66–0.90) and for V

_{imp}= 1.0–1.5 m·s

^{−1}was also found on the storage day S

_{t}. From analyzing the effect of impact velocity V

_{imp}on the amount of maximal deformation, d

_{max}, the results presented in Figure 14 were obtained. With the increasing impact velocity, the deformation increased for all groups of stored beets. The statistical significance of the effect of the impact velocity V

_{imp}on the amount of maximal deformation, d

_{max}(R

^{2}= 0.74–0.92), was observed. This tendency presented in beets has been confirmed by other investigations. Ahmadi et al. [53] analyzed the behavior of various layers (skin, flesh and seed chamber) during impacts of an apple against another apple and apples against a rigid object using the finite elements method. The maximal deformation was larger at higher impact velocities in each tested layer of apples. Lu and Wang [54] determined the limit for bruising of “Gala” apples to be in the drop height range of 0.04–0.7 m. The maximal deformation increased with increasing drop height. The characteristic feature of these studies was finding the zero values of deformation at the drop height of 0.04 m, which was interpreted as the critical height at which damage takes place. The increase in maximal deformation with increasing impact velocity was found for three varieties of apples and two varieties of pears [19,55].

_{max}with increasing impact velocity V

_{imp}(R

^{2}= 0.47–0.69). In the case of fresh roots, a slight increase in stress was observed between velocities of 1.0 and 1.5 m·s

^{−1}. This is consistent with the results of studies on pears and potatoes, for which the stress increase tends to stabilize after exceeding a certain impact velocity [19,45]. The calculated mean values, σ

_{max}, decreased with the storage time, S

_{t}, and were in the ranges of 1.170–0.804 MPa, 1.589–1.063 MPa and 1.769–1.450 MPa for velocities of 0.5, 1.0 and 1.5 m·s

^{−1}, respectively. This dependence was statistically significant and the determined general tendency towards a decrease in maximal stress with increasing storage time is confirmed in a paper by Vursavus and Ozguven [56].

_{abs-v}with increasing velocity indicates the possibility of exceeding the elasticity limit in some areas of the root and the appearance of plastic deformations. Similar conclusions can be drawn by observing the tendency towards stabilization of the impact stress values with the increasing impact velocity. In this case, this can evidence the approximation of the mean stress values to the critical value, which should be stable and independent of the impact velocity (dynamic yield pressure). The precise determination of critical stress values under impact load conditions, including stress propagation in the wave form, requires further detailed investigations.

## 4. Conclusions

^{−1}, 870.5 N for 1.0 m·s

^{−1}and 1274.4 N for 1.5 m·s

^{−1}. In the successive days of storage, F

_{max}decreased, achieving the following mean values for the 5-day-old roots: 259.0 N for the velocity 0.5 m·s

^{−1}, 552.2 N for 1.0 m·s

^{−1}and 799.5 N for 1.5 m·s

^{−1}. The increase in the maximal value of the root force response F

_{max}with the increasing impact velocity V

_{imp}is evidence of the viscoelastic properties of the studied material.

_{imp}increased with increasing impact velocity and decreased for each storage day. The mean values in the period of 0–5 days were in the following range: 233.6–149.0 (10

^{−3}J) for the velocity 0.5 m·s

^{−1}, 787.7–547.2 (10

^{−3}J) for 1.0 m·s

^{−1}and 1656.6–1022.1(10

^{−3}J) for 1.5 m·s

^{−1}. The value of absorbed energy increased depending on the impact velocity. The energy, E

_{abs}, reached a mean of 208.6–128.9 (10

^{−3}J) for the velocity of 0.5 m·s

^{−1}, 678.5–447.8 (10

^{−3}J) for 1.0 m·s

^{−1}and 1288.2–938.1 (10

^{−3}J) for 1.5 m·s

^{−1}. With increasing impact velocity, an increase in the root maximal deformation was observed, with the following values: 1.16–1.45 mm for V

_{imp}= 0.5 m·s

^{−1}, 1.94–2.41 mm for 1.0 m·s

^{−1}and 2.67–3.09 mm for V

_{imp}= 1.5 m·s

^{−1}. A similar dependence was found in the case of contact volume CV. An increase in CV was observed with the increasing impact velocity for all analyzed groups of roots, and this dependence was statistically significant (R

^{2}= 0.68–0.93).

_{abs-v}on the impact velocity V

_{imp}calculated from Formula (9), increased values were obtained in the ranges of 0.110–0.137 J·g

^{−1}, 0.317–0.527 J·g

^{−1}and 0.645–1.044 J·g

^{−1}for successive impact velocities (R

^{2}= 0.66–0.90). It was found that the values of maximal stresses, σ

_{max}, increased with the increasing impact velocity and decreased depending on the storage day. The calculated mean values of σ

_{max}decreased with the storage time, being 1.170–0.804 MPa, 1.589–1.063 MPa and 1.769–1.450 MPa for the velocities 0.5, 1.0 and 1.5 m·s

^{−1}, respectively.

_{max}) against the impact as well as the changes in the impact energy (E

_{imp}), absorbed energy (E

_{abs}) or maximal stress (σ

_{max}) are directly connected with the loss of water in the root surface part.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Jarimopas, B.; Singh, S.P.; Sayasoonthorn, S.; Singh, J. Comparison of package cushioning materials to protect postharvest impact damage to apples. Packag. Technol. Sci.
**2007**, 20, 315–324. [Google Scholar] [CrossRef] - Van Zeebroeck, M.; Van Linden, V.; Ramon, H.; De Baerdemaeker, J.; Nicolai, B.M.; Tijskens, E. Impact damage of apples during transport and handling. Postharvest Biol. Technol.
**2007**, 45, 157–167. [Google Scholar] [CrossRef] - Opara, U.L.; Fadiji, T. Compression damage susceptibility of apple fruit packed inside ventilated corrugated paperboard package. Sci. Hortic.
**2018**, 227, 154–161. [Google Scholar] [CrossRef] - Van Zeebroeck, M.; Van Linden, V.; Darius, P.; De Ketelaere, B.; Ramon, H.; Tijskens, E. The effects of fruit factors on the bruise susceptibility of apples. Postharvest Biol. Technol.
**2007**, 46, 10–19. [Google Scholar] [CrossRef] - Valero, C.; Crisosto, C.H.; Slaughter, D. Relationship between nondestructive firmness measurements and commercially important ripening fruit stages for peaches, nectarines and plums. Postharvest Biol. Technol.
**2007**, 44, 248–253. [Google Scholar] [CrossRef] - Van Linden, V.; De Ketelaere, B.; Desmet, M.; De Baerdemaeker, J. Determination of bruise susceptibility of tomato fruit means of an instrumented pendulum. Postharvest Biol. Technol.
**2006**, 40, 7–14. [Google Scholar] [CrossRef] - Blahovec, J. Shape of bruise spots in impacted potatoes. Postharvest Biol. Technol.
**2006**, 38, 278–284. [Google Scholar] [CrossRef] - Spackman, V.M.T.; Cobb, A.H. An enzyme-based method for the rapid determination of sucrose, glucose and fructose in sugar beet roots and the effects of impact damage and postharvest storage in clamps. J. Sci. Food Agric.
**2001**, 82, 80–86. [Google Scholar] [CrossRef] - Hoffmann, C.M. Sugar beet from field clamps-harvest quality and storage loss. Sugar Ind.
**2018**, 143, 639–647. [Google Scholar] [CrossRef] - He, L.; Fu, H.; Xia, H.; Manoj, K.; Zhang, Q.; Whiting, M. Evaluation of a localized shake-and-catch harvesting system for fresh market apples. Agric. Eng. Int. CIGR J.
**2018**, 19, 36–44. [Google Scholar] - Tabatabaekoloor, R. Engineering properties and bruise susceptibility of peach fruits (Prunus persica). Agric. Eng. Int. CIGR J.
**2013**, 15, 244–252. [Google Scholar] - Hussein, Z.; Fawole, O.A.; Opara, U.L. Investigating bruise susceptibility of pomegranate cultivars during postharvest handling. AFJRD
**2017**, 2, 33–39. [Google Scholar] - Hoffmann, C.M.; Schnepel, K. Susceptibility to root tip breakage increases storage losses of sugar beet genotypes. Sugar Ind.
**2016**, 141, 625–632. [Google Scholar] [CrossRef] - Hoffmann, C.M.; Engelhardt, M.; Gallmeier, M.; Gruber, M.; Märländer, B. Importance of harvesting system and variety for storage losses of sugar beet. Sugar Ind.
**2018**, 143, 474–484. [Google Scholar] [CrossRef] - Nasirahmadi, A.; Wilczek, U.; Hensel, O. Sugar Beet Damage Detection during Harvesting Using Different Convolutional Neural Network Models. Agriculture
**2021**, 11, 1111. [Google Scholar] [CrossRef] - Stropek, Z.; Gołacki, K. Response of Apple Flesh to Compression under the Quasi-Static and Impact Loading Conditions. Materials
**2022**, 15, 7743. [Google Scholar] [CrossRef] - Van Zeebroeck, M.; Tijskens, E.; Van Liedekerke, P.; Deli, V.; De Baerdemaeker, J.; Ramon, H. Determination of the dynamical behaviour of biological materials during impacts using pendulum device. J. Sound Vib.
**2003**, 266, 465–480. [Google Scholar] [CrossRef] - Stropek, Z.; Gołacki, K. Methodological aspects of determining apple mechanical properties during impact. Int. J. Food Prop.
**2016**, 19, 1325–1334. [Google Scholar] [CrossRef] - Stropek, Z.; Gołacki, K. Impact characteristics of pears. Postharvest Biol. Technol.
**2019**, 147, 100–106. [Google Scholar] [CrossRef] - Stropek, Z.; Gołacki, K. Stress relaxation of the apples at different deformation velocities and temperature. Trans. ASABE
**2019**, 62, 115–121. [Google Scholar] [CrossRef] - Polat, R.; Aktas, T.; Ikinci, A. Selected Mechanical Properties and Bruise Susceptibility of Nectarine Fruit. Int. J. Food Prop.
**2012**, 15, 1369–1380. [Google Scholar] [CrossRef] - Ahmadi, E. Bruise susceptibilities of kiwifruit as affected by impact and fruit properties. Res. Agric. Eng.
**2012**, 58, 107–113. [Google Scholar] [CrossRef] - Abedi, G.; Ahmadi, E. Design and evaluation a pendulum device to study postharvest mechanical damage in fruits: Bruise modeling of red delicious apple. AJCS
**2013**, 7, 962–968. [Google Scholar] - Gorzelany, J.; Puchalski, C. Application of the non-desctructive method to investigations of mechanical properties of sugar beet roots. Acta Agrophys.
**2003**, 2, 61–71. [Google Scholar] - Lien, C.C.; Ting, C.H. Assessing guava maturity by statistical analyses of dropped fruit impact responses. Postharvest Biol. Technol.
**2014**, 95, 20–27. [Google Scholar] [CrossRef] - Słupska, M.; Syguła, E.; Komarnicki, P.; Szulczewski, W.; Stopa, R. Simple Method for Apples’ Bruise Area Prediction. Materials
**2022**, 15, 139. [Google Scholar] [CrossRef] - Komarnicki, P.; Stopa, R.; Szyjewicz, D.; Kuta, Ł.; Klimza, T. Influence of Contact Surface Type on the Mechanical Damages of Apples Under Impact Loads. Food Bioproc. Tech.
**2017**, 10, 1479–1494. [Google Scholar] [CrossRef] - Geyer, M.O.; Praeger, U.; Konig, C.; Graf, A.; Truppel, I.; Schluter, O.; Herold, B. Measuring behavior of an acceleration measuring unit implanted in potatoes. Trans. ASABE
**2009**, 52, 1267–1274. [Google Scholar] [CrossRef] - Komarnicki, P.; Stopa, R.; Szyjewicz, D.; Młotek, M. Evaluation of bruise resistance of pears to impact load. Postharvest Biol. Technol.
**2016**, 114, 36–44. [Google Scholar] [CrossRef] - Kabas, O. Methods of Measuring Bruise Volume of Pear (Pyrus Communis L.). Int. J. Food Prop.
**2010**, 13, 1178–1186. [Google Scholar] [CrossRef] - Opara, U.L.; Pathare, P.B. Bruise damage measurement and analysis of fresh horticultural produce—A review. Postharvest Biol. Technol.
**2014**, 91, 9–24. [Google Scholar] [CrossRef] - Alizadeh, H.; Segerlind, L.J. Some material properties of sugar beet roots. Appl. Eng. Agric.
**1997**, 13, 507–510. [Google Scholar] [CrossRef] - Bentini, M.; Caprara, C.; Rondelli, V. Mechanical properties of sugar beet roots. Trans. ASAE
**2005**, 48, 1429–1439. [Google Scholar] [CrossRef] - Wang, F.; Zhang, D. Experimental Study on Compression Property of Sugar Beet; Paper number 141905757, Montreal, Quebec Canada July 13–16; American Society of Agricultural and Biological Engineers: St. Joseph, MI, USA, 2014. [Google Scholar] [CrossRef]
- Nedomova, Š.; Kumbar, V.; Pytel, R.; Buchar, J. Mechanical properties of sugar beet root during storage. Int. Agrophys.
**2017**, 31, 507–513. [Google Scholar] [CrossRef] [Green Version] - Kleuker, G.; Hoffmann, C.M. Method development for the determination of textural properties of sugar beet roots. Sugar Ind.
**2019**, 144, 392–400. [Google Scholar] [CrossRef] - Kleuker, G.; Hoffmann, C.M. Influence of tissue strength on root damage and storage losses of sugar beet. Sugar Ind.
**2020**, 145, 435–443. [Google Scholar] [CrossRef] - Kołodziej, P.; Gołacki, K.; Boryga, M. Impact characteristics of sugar beet root during postharvest storage. Int. Agrophys.
**2019**, 33, 355–361. [Google Scholar] [CrossRef] - Trnka, J.; Kumbár, V.; Nedomova, Š.; Pytel, R.; Buchar, J. Influence of sugar beet storage duration on root response to non-destructive impacts. Int. Agrophys.
**2018**, 32, 421–428. [Google Scholar] [CrossRef] - Pan, L.; Lu, R.; Zhu, Q.; McGarth, J.M.; Tu, K. Measurement of moisture, soluble solids, sucrose content and mechanical properties in sugar beet using portable visible and near-infrared spectroscopy. Postharvest Biol. Technol.
**2015**, 102, 42–50. [Google Scholar] [CrossRef] - Shafie, M.M.; Rajabipour, A.; Castro-García, S.; Jiménez-Jiménez, F.; Mobli, H. Effect of Fruit Properties on Pomegranate Bruising. Int. J. Food Prop.
**2015**, 18, 1837–1846. [Google Scholar] [CrossRef] - Kitthawee, U.; Pathaveerat, S.; Srirungruang, T.; Slaughter, D. Mechanical bruising of young coconut. Biosyst. Eng.
**2011**, 109, 211–219. [Google Scholar] [CrossRef] - ASAE. Moisture measurement-forages. In ASAE Standards; ASAE: St. Joseph, MI, USA, 1992; Volume 406, Chapter S358.2. [Google Scholar]
- Stropek, Z.; Gołacki, K. Studies concerning the response of potatoes to impact. Int. Agrophys.
**2022**, 36, 115–122. [Google Scholar] [CrossRef] - Brusewitz, G.H.; McCollum, T.G.; Zhang, X. Impact bruise resistance of peaches. Trans. ASAE
**1991**, 34, 962–965. [Google Scholar] [CrossRef] - Fu, Q.; Fu, J.; Chen, Z.; Han, L.; Ren, L. Effect of impact parameters and moisture content on kernel loss during corn snapping. Int. Agrophys.
**2019**, 33, 493–502. [Google Scholar] [CrossRef] - Yu, P.; Li, C.; Takeda, F.; Krewer, G. Visual bruise assessment and analysis of mechanical impact measurement in southern highbush blueberries. Appl. Eng. Agric.
**2014**, 30, 29–37. [Google Scholar] [CrossRef] - Scheffler, O.C.; Coetzee, C.J.; Opara, U.L. A discrete element model (DEM) for predicting apple damage during handling. Biosyst. Eng.
**2018**, 172, 29–48. [Google Scholar] [CrossRef] - Stropek, Z.; Gołacki, K. Viscoelastic response of apple flesh in a wide range of mechanical loading rates. Int. Agrophys.
**2018**, 32, 335–340. [Google Scholar] [CrossRef] - De Kleine, M.E.; Karkee, M. Evaluating a non-newtonian shear-thickening surface during fruit impacts. Trans. ASABE
**2015**, 58, 907–915. [Google Scholar] [CrossRef] - Du, D.; Wang, B.; Wang, J.; Yao, F.; Hong, X. Prediction of bruise susceptibility of harvested kiwifruit (Actinidia chinensis) using finite element method. Postharvest Biol. Technol.
**2019**, 152, 36–44. [Google Scholar] [CrossRef] - Azam, M.M.; Eissa, A.H. Comprehensive Evaluation of Dynamic Impact as a Measure of Potato Quality. Eur. J. Biophys.
**2015**, 3, 59–68. [Google Scholar] [CrossRef] - Ahmadi, E.; Barikloo, H.; Kashafi, M. Viscoelastic finite element analysis of the dynamic behavior of apple under impact loading with regard its different layers. Comput. Electron. Agric.
**2016**, 121, 1–11. [Google Scholar] [CrossRef] - Lu, L.X.; Wang, Z.W. Dropping bruise fragility and bruise boundary of apple fruit. Trans. ASABE
**2007**, 50, 1323–1329. [Google Scholar] [CrossRef] - Stropek, Z.; Gołacki, K. A new method for measuring impact related bruises in fruits. Postharvest Biol. Technol.
**2015**, 110, 131–139. [Google Scholar] [CrossRef] - Vursavus, K.; Ozguven, F. Determining the strength properties of the Dixired peach variety. Turk. J. Agric. For.
**2003**, 27, 155–160. [Google Scholar]

**Figure 2.**Three-dimensional scans of the sugar beet. (

**a**) View in the plane parallel to the main axis with large half-axes (b

_{E}

_{1}, b

_{E}

_{2}) of the ellipses describing the vertical root curvatures; (

**b**) view in the plane perpendicular to the main axis and diameters (D

_{1}–D

_{4}); (

**c**) local beet surface curvatures modelled by the prolate ellipsoid of the dimensions; half-axes—small a and large b.

**Figure 3.**Image sequences of the root using the camera Phantom Miro M320 during the impact test. (

**a**) The beet and resistance plate fixed to the force sensor; (

**b**) the impact start; (

**c**) the impact end; d

_{max}—the pictorial determination of maximal deformation d

_{max}= c

_{E}.

**Figure 4.**Modelling the contact volume (CV) as the ellipsoidal cap. (

**a**) The ellipsoid dimensions; (

**b**) the ellipsoid cross-section dimensions: a

_{E}, b

_{E}, d

_{max}= c

_{E}.

**Figure 5.**The largest ellipsoid cross-section with auxiliary denotations for determination of the large half-axis b value.

**Figure 6.**Typical force response in time and deformation in time curves during the impact of sugar beet root against the rigid plate.

**Figure 8.**Average water content, WSB%, in the beet roots in the surrounding impact sites depending on the storage day.

**Figure 9.**Diagram of maximal impact force (F

_{max}) dependence on impact velocity (V

_{imp}) for the stored beets.

**Figure 10.**Dependence of impact energy (E

_{imp}) on the impact velocity (V

_{imp}) for the stored beets.

**Figure 11.**Dependence of absorbed energy (E

_{abs}) on the impact velocity (V

_{imp}) for the stored beets.

**Figure 12.**Dependence of absorbed energy related to mass (E

_{imp-v}) on the impact velocity (V

_{imp}) for the stored beets.

**Figure 13.**Dependence of the contact volume (CV) on the impact velocity (V

_{imp}) for the stored beets.

**Figure 14.**Dependence of the maximal deformation (d

_{max}) on the impact velocity (V

_{imp}), taking the storage time (S

_{t}) into account.

**Figure 15.**Dependence of the maximal impact stress (σ

_{imp}) on the impact velocity (V

_{imp}), taking the storage time (S

_{t}) into account.

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## Share and Cite

**MDPI and ACS Style**

Kołodziej, P.; Stropek, Z.; Gołacki, K.
Mechanical Properties of Sugar Beet Roots under Impact Loading Conditions. *Materials* **2023**, *16*, 1281.
https://doi.org/10.3390/ma16031281

**AMA Style**

Kołodziej P, Stropek Z, Gołacki K.
Mechanical Properties of Sugar Beet Roots under Impact Loading Conditions. *Materials*. 2023; 16(3):1281.
https://doi.org/10.3390/ma16031281

**Chicago/Turabian Style**

Kołodziej, Paweł, Zbigniew Stropek, and Krzysztof Gołacki.
2023. "Mechanical Properties of Sugar Beet Roots under Impact Loading Conditions" *Materials* 16, no. 3: 1281.
https://doi.org/10.3390/ma16031281