Novel Thermal Analysis Model of the Foot-Shoe Sole Interface during Gait Motion

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1 Proceedings Novel Thermal Analysis Model o the Foot-Shoe Sole Interace during Gait Motion Yasuhiro Shimazaki * and Kazutoshi Aisaka Department o Human Inormation Engineering, Okayama Preectural University, Soja , Japan; cd9001c@ss.oka-pu.ac.jp * Correspondence: shimazaki@ss.oka-pu.ac.jp; Tel.: Presented at the 1th conerence o the International Sports Engineering Association, Brisbane, Queensland, Australia, 6 8 March 018. Published: 14 February 018 Abstract: Excessive heat at the oot-shoe sole interace negatively aects a human s thermal comort. An understanding o the thermal behavior at this interace is important or alleviating this discomort. During gait motion, a human s body weight cyclically compresses a shoe sole (commonly constructed o viscoelastic materials), generating heat during loading. To evaluate the thermal eects o this internal heat generation on oot comort, we developed and empirically validated a thermal analysis model during gait motion. A simple, one-dimensional prediction model or heat conduction with heat generation during compressive loading was used. Heat generation was estimated as a unction o the shoe sole s material properties (e.g., elastic modulus) and various gait parameters. When compared with experimental results, the proposed model proved eective in predicting thermal behavior at the oot-shoe sole interace under various conditions and shows potential or improving a human s thermal comort during gait motion through inormed ootwear design. Keywords: heat transer; ootwear; comort; ethylene-vinyl acetate (EVA) rubber; oot contact; modeling; walking 1. Introduction Footwear designs have continued to advance in an eort to improve comort and perormance in routine daily or specialized sports applications. Despite these known advancements, ew studies were uncovered that considered the thermal comort o ootwear. A human oot acts as a thermal radiator or the body [1]. When a oot is conined in a shoe, the heat that is prevented rom releasing can negatively aect a human s thermal comort. This eect is exacerbated during gait motion. Shoe soles are commonly constructed rom viscoelastic materials, such as ethylene-vinyl acetate (EVA), to provide shock buering. These same materials generate heat when they are compressed by loading [], adding to a human s discomort. An understanding o the thermal behavior at the oot-shoe sole interace is important or alleviating this discomort. Thus, the objective o this study was to investigate the microclimatic thermal eects attributable to internal heat generation at the oot-shoe sole interace during gait motion. First, we determined the mechanical parameters associated with gait. Next, we developed a simple heat transer model or predicting temperature at the oot-shoe sole interace by considering both the human s metabolic heat generation and the shoe sole s heat generation under contact loading. Finally, we validated the proposed heat transer model empirically. Proceedings 018,, 78; doi: /proceedings

2 Proceedings 018,, 78 o 7. Materials and Methods.1. Analysis o Gait Motion As a irst step in this study, we determined the mechanical parameters associated with gait. When a oot contacts a shoe sole, the mechanical energy o loading is transormed into thermal energy associated with the shoe sole deormation. To determine the eects o gait on this phenomenon, parameters related to oot loading were directly measured. As previously reported, the oot contact loading and contact area are time-dependent [3]. As such, we irst considered the eects o gait speed on time-dependent changes in the amount o loading orce, contact area, and timing. The loading orce and contact area were measured using the pressure sensors (Nitta, F-scan System). Gait speeds o 3 (walking), 6 (walking), and 9 km/h (running) were tested... Development o the Proposed Thermal Analysis Model Ater determining the mechanical parameters associated with gait, we developed a simple heat transer model or predicting temperature at the oot-shoe sole interace during gait motion. Figure 1 shows the one-dimensional coordinate system used in the model. In the proposed model, heat is primarily transerred by conduction. Especially or human body, Penne s bioheat transer equation was used. The unsteady-state heat transer relationships or the shoe sole (constructed o EVA rubber) under contact loading and the human are expressed as ollows: Tr Tr ρ rc r = kr + q (or shoe sole with EVA rubber) (1) r t z T T ρ c = k + ρ c ω ( Ta T ) + q (or human oot) () met t z where T is the temperature [K], t is the time [s], ρ is the density [kg/m 3 ], c is the speciic heat [J/(kgK)], k is the thermal conductivity [W/(mK)], qr is the shoe sole s heat generation under contact loading [W/m 3 ] and q is the human s metabolic heat generation [W/m 3 ]. The subscripts r,, and a indicate met the shoe sole with EVA rubber, the human oot, and the arteria, respectively. Figure 1. One-dimensional coordinate system used in the proposed thermal analyses model. The heat gain at the oot-shoe sole interace attributable to loading is equal to the energy loss caused by shoe sole deormation during oot contact. During swing, heat is released rom the rubber sole by orced convection due to oot movement. Because gait motion is cyclic, the heat generated during a single gait cycle can be expressed as ollows [3]: W q r = (during oot contact) (3) SL q r W = πε E (4) [ h ( T T )] = r z=0 env 0 (during swing) (5)

3 Proceedings 018,, 78 3 o 7 where W is the per gait cycle energy loss [N], S is the oot contact area [m ], L is the oot contact duration [s], ε0 is the strain amplitude, E is the elastic modulus loss [Pa], and h is the convective heat transer coeicient [W/(m K)]. The subscripts env indicates ambient environment. The energy loss is assumed to be ully transormed into thermal energy. Using the proposed thermal analysis model, heat generation was estimated as a unction o various gait parameters and the shoe sole s material properties (e.g., elastic modulus). Table 1 details the three shoe sole materials considered in the study. Each was a specially blended EVA with known material properties. In general, EVA08 is a harder material while EVA16 is a soter material. The materials strain during gait motion is also an important parameter or predicting heat generation based on Equation (4). As such, strain was measured or each material during gait motion using a three-dimensional motion and deormation sensor (GOM, ARAMIS) with a sampling requency o 15 Hz. Table 1. Shoe sole material properties. EVA08 EVA1 EVA16 Hardness (JIS Durometer A) A45 A35 A Thermal conductivity [W/(m K)] Speciic heat [J/(kg K)] Density [kg/m 3 ] Expansion ratio (N.D.) tan δ Elastic modulus storage (E ) [MPa] Elastic modulus loss (E ) [MPa] Empirical Validation o the Proposed Thermal Analysis Model Following development o the proposed thermal analysis model, its ability to predict thermal behavior (speciically heat transer and vertical temperature distributions) at the oot-shoe sole interace during gait motion was empirically validated. Nine human subjects with heights o 1.70 ± 0.04 m, weights o 59.8 ± 5.4 kg, and ages o 3.0 ± 0.8 years provided inormed consent to participate in this study. Body weights among the participants were roughly equivalent, minimizing the eects o body weight on the degree o loading and allowing or results averaging across all participants. Experiments were conducted in an artiicial climate chamber that enabled arbitrary climatic conditions. To limit a shoe s insulating eects, a 15-mm thick EVA rubber sole sans shoe was prepared and attached to each participant s oot. Temperatures were measured vertically using thermocouples in 5-mm increments. To support averaging, temperatures were measured at three points along each surace. For the human oot, the ball, arch, and heel were selected or measurement. Figure conceptually depicts these temperature measurement locations. Participants O intake and CO production were also measured to support metabolic heat generation estimation. Figure. Conceptual diagram o temperature measurement locations.

4 Proceedings 018,, 78 4 o 7 3. Results 3.1. Input Parameters or the Proposed Thermal Analysis Model The proposed thermal analysis model requires both gait motion and material property parameters to predict heat transer and generation. Required gait motion parameters include the oot contact area, oot contact duration, and gait cycle duration. Required material property parameters include the strain Gait Motion Parameters In this study, the required gait motion parameters were determined empirically. Figure 3 shows the mean contact area under loading [Figure 3a] and the stance and swing durations [Figure 3b] as a unction o gait requency. This study ocuses on the orce-thermal energy interaction. The use o gait requencies better supports consideration o heat generation in equations ocused on contact loading. In this study, gait speeds o 3, 6, and 9 km/h corresponded to gait requencies o 45, 60, and 75 beats/min rom preliminary experiments. In general, gait requency increases linearly with gait speed. (a) (b) Figure 3. Measured mean gait parameters as a unction o gait requency: (a) Contact area; (b) Stance and swing durations. Experimental results indicated that the contact area increased as gait speed increased, measuring , 0.007, and m at gait requencies o 45, 60, and 75 beats/min, respectively. Signiicant contact area dierences were conirmed between the 45 and 60 beats/min and the 45 and 75 beats/min gait requencies. Conversely, the stance and swing durations decreased as gait speed increased. For example, stance time was 0.46, 0.34, and 0.7 s at gait requencies o 45, 60, and 75 beats/min, respectively Material Property Parameters In this study, the required material property parameters were also determined empirically. Table lists the mean maximum strains or the dierent EVA materials and gait requencies considered. The strain increased as the EVA rubber sotness and gait requency increased. Figure 4 shows the measured strain or the EVA16 material at a gait requency o 60 beats/min. A negative value indicates compression. The upper layers o the sole exhibited the highest strains. The maximum measured strain was approximately.0 mm. Table. Measured mean maximum strains or dierent EVA materials and gait requencies. EVA Material Mean Maximum Strain [mm] 45 Beats/min 60 Beats/min 75 Beats/min EVA EVA EVA

5 Proceedings 018,, 78 5 o Thermal Analysis Figure 4. Measured strain or the EVA16 material at a gait requency o 60 beats/min Empirical Temperature Distributions Time-dependent temperature distributions at the oot-show sole interace were determined empirically in this study. Figure 5 show the time-dependent temperature distribution or the EVA08 material under a neutral thermal environment o C and or various gait requencies. The values presented are obtained as the mean values o all participants. As a baseline reerence, Figure 5a shows the temperature distributions at a requency gait o 0 km/h (seated position). When the human subject was seated, all temperatures remained constant and a thermally neutral state was reached. When the human subject began walking, temperatures increased over time and increased with gait requency. A aster gait resulted in higher temperatures. The upper layers o the sole exhibited higher temperatures because o the higher deormations (higher strains) and direct contact with the human oot. For example, temperatures measured 0.5 and.6 C at the bottom (z = 0) and top (z = 0.0) o the shoe sole at a gait requency o 75 beats/min. Temperature distributions or the other EVA materials showed similar trends Foot z = z = 0.01 z = z = Foot z = z = 0.01 z = z = 0 (a) (b) (c) Foot z = z = 0.01 z = z = 0 Figure 5. Measured time-dependent temperature distributions or the EVA08 material at C: (a) 0 beats/min gait requency (seated position); (b) 45 beats/min gait requency; (c) 75 beats/min gait requency.

6 Proceedings 018,, 78 6 o Comparative Measured and Predicted Temperature Distributions As a inal step in this study, we compared the time-dependent temperature distributions obtained empirically with the temperature distributions predicted by the proposed thermal analysis model. Figure 6 compares the measured and predicted time-dependent temperature distributions on the bottom o human oot or the EVA08 material at C and various gait requencies. As noted previously, the required parameters to support the model, including the prediction o initial temperatures, were obtained empirically. In this comparison, data rom a single individual were used. Both measured and predicted temperatures increased over time. Ater min, predicted temperatures were elevated 3.6 and 6. C or gait requencies o 45 and 75 beats/min, respectively. Comparatively, measured temperatures were elevated 3.9 and 7.0 C or gait requencies o 45 and 75 beats/min, respectively. This same level o agreement was observed across all conditions considered in this study. Thus, the proposed model proved eective in predicting thermal behavior at the oot-shoe sole interace during gait motion under various conditions Experiment (a) Numerical simulation Experiment (b) Numerical simulation Figure 6. Comparative measured and predicted time-dependent temperature distributions or the EVA08 material at C: (a) 45 beats/min gait requency; (b) 75 beats/min gait requency. 4. Conclusions Thermal comort is an important but oten overlooked eature when designing ootwear. In this study, we developed and empirically validated a thermal analysis model during gait motion. First, we determined the mechanical parameters associated with gait. Next, we developed a simple heat transer model or predicting temperature at the oot-shoe sole interace by considering both the human s metabolic heat generation and the shoe sole s heat generation under contact loading. Finally, we validated the proposed heat transer model empirically. When compared with experimental results, the proposed model proved eective in predicting thermal behavior at the oot-shoe sole interace under various conditions. This development is signiicant because o its potential or improving a human s thermal comort during gait motion through inormed ootwear design. Future research will consider the overall ootwear comort including the inner and the upper areas but not limited to the oot-shoe sole interace. Acknowledgments: The authors would like to acknowledge Chugoku Rubber Industry Co., Ltd. or providing sample materials and relevant technical assistance in support o this study. Conlicts o Interest: The authors declare no conlicts o interest. Reerences 1. Taylor, N.A.S.; Machado-Moreira, C.A.; van den Heuvel, A.M.J.; Caldwell, J.N. Hands and eet: physiological insulators, radiators and evaporators. Eur. J. Appl. Physiol. 014, 114, , doi: /s

7 Proceedings 018,, 78 7 o 7. Terasaki, K.; Okada, M.; Matsuura, K.; Kawashimo, K.; Maeda, Y.; Kitazawa, K. Heat generation and transient heat conduction o rubber under cyclic compressing. Trans. Jpn. Soc. Mech. Eng. 1976, 4, , doi:10.199/kikai (In Japanese) 3. Shimazaki, Y.; Murata, M. Eect o gait on ormation o thermal environment inside ootwear. Appl. Ergon. 015, 49, 55 6, doi: /j.apergo by the authors; Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions o the Creative Commons Attribution (CC BY) license (