Thermal Transfer Analysis for Sports Footwear, for Performance Athletes, during Volleyball Training

Abstract

The purpose of this paper is a social one, to present various experimental thermal analyses of sports footwear to identify the areas that ensure the best foot ventilation for comfort in movement. The mechanical properties of the analyzed footwear were determined on the Nano Indenter Agilent G200, with the help of which Young’s modulus was determined according to ISO 14577. Thermography measurements were performed at the Oradea University Sports Club. The FLIR SC 640 thermal imaging camera was used, which is a portable thermographic scanning equipment. The measurements were performed on eight athletes (subjects) in a volleyball training session, wearing sports footwear (Asics and Mizuno). Thermographic recordings were made during training at five different times: moment zero (before the start of training), moment one (2 min of training), moment two (5 min of training), moment three (15 min of training), and moment four (at the end of the volleyball training session). For the other three subjects, although having different models of the same sports footwear, the analysis of the thermal distribution values shows they are within the minimum and maximum limits of the five subjects analyzed in the paper. Based on the thermographic recording values obtained, a mathematical model was determined using polynomial regression to predict temperature values outside the range of the experimental data. In the present paper, research was carried out in order to identify the thermal variations of indoor sports shoes used in volleyball training so as to detect the heat exchange between the foot and the outdoor environment. Whether we are talking about winter sports or sports that take place in other atmospheric conditions, the comfort given by the optimal temperature at the level of each body segment is certainly reflected in the level of performance achieved.

1. Introduction

The growing concern of consumers about the comfort of footwear has motivated manufacturers to design footwear with optimal thermal comfort [1,2].

Although the legs represent only 7% of the body surface [3], their exposure to extreme environments can cause discomfort, fatigue, and decreased performance [4,5].

Many of the problems that arise in the foot are directly related to footwear, so it is very important to choose the right footwear [6,7,8].

Regarding the scientific studies based on thermography, a series of papers has been published that analyzes various important aspects regarding heat transfer; this research was conducted with the help of the infrared thermal imaging camera [9,10,11,12].

There is not much research on how, when, and where sports footwear are heated during sports training; there are only a few results regarding the fact that shoe temperatures can rise up to 50 °C during exercise in the summer [13], and the temperature of the footwear must be maintained between 27 °C and 30 °C for optimal thermal comfort [14]. An extreme microclimate inside the footwear contributes to discomfort during wear and decreased performance [15].

In sports, and especially in elite sports, these aspects can have significant effects on the performance obtained by athletes; in their involvement in training and competitions, the superior comfort offered by a quality product is a favorable premise for the aforementioned aspects [16,17,18,19].

The shape of the foot can also affect the comfort degree of the footwear, with high levels of friction in some parts that can lead to increased discomfort due to rising temperatures at the points of contact, with a direct effect on the skin and wounds that may occur at this level. Thus, the structure of the footwear can be brought into discussion, along with its assembly, how foot ventilation is attained, but also the quality of the materials used in the manufacturing process.

Depending on the specific characteristics of the diversity of indoor sports disciplines [20,21,22], the footwear is adapted according to the type of sport practiced; in this case, the athletic setting is volleyball training [23,24,25,26,27,28,29]. In view of this, there are specialized and renowned companies for the manufacture of indoor volleyball footwear that do studies and research in this direction [30,31,32,33].

Lately, however, more and more sports equipment manufacturers who were well-known and recognized for being familiar with a particular sport have begun to diversify in several directions (handball, football, volleyball, fashion, etc.).

Hummel, Mikasa, Craft, Kempa, Nike, New Balance, and Armani are just a few companies that strengthen the idea mentioned above.

In this sense, this study aims to analyze the way and establish the extent to which heat transfers between the foot and the external environment during the training of athletes who practice volleyball, equipped with some models of sports shoes produced for the details of this sport and used by a large majority of players.

The research hypothesis is in line with this goal and seeks to clarify to some extent the influence of materials used in shoe manufacturing on the comfort of athletes, with a direct effect on the level of performance achieved in training and competitions.

2. Materials and Methods

Experimental Research on Footwear Temperature

The infrared thermography examination method [34,35,36] has recently entered the practice of non-destructive examinations, being a method of measuring the thermal field by recording infrared radiation and visualizing the temperature distribution on the observed surfaces [37,38,39].

Thermography measurements were performed at the University Sports Club in Oradea. The FLIR SC 640 thermal imaging camera was used, which is a piece of portable thermographic scanning equipment, ”without cooling”, which has the strongest existing IR detector, with a resolution of 640 × 480 pixels and with a thermal sensitivity encountered so far only by cameras with cooling systems (<0.04 °C).

As can be seen from Figure 1, the thermal imaging camera is equipped with a laser pointer, germanium lens, SD card, USB, and video connector.

A great advantage of the FLIR SC 640 thermal imaging camera is that it allows scanning objects remotely, with no contact, the testing being non-destructive for the objects to be measured; it ensures predictive maintenance of equipment and the detection of defects in the early stages to reduce costs. FLIR RESEARCH IR MAX 4.40 software is used for research and development, allowing real-time analysis of the video sequence.

It is well-known that research in the field has led to the emergence of new materials used in sports, footwear with higher elasticity, and optimal forms of footwear that offer customized aerodynamic heel sock lining for the best possible pressure distribution and the insertion of attractive colors, to induce different emotional states, using knowledge of chromotherapy [40,41].

Thermal analysis of sports footwear was performed on 8 subjects during volleyball training, as shown in Figure 2.

In this paper the data for the 5 subjects presented are relevant because they represent the values of the minimum and maximum thermal distribution in the 2 types of sports footwear (Asics and Mizuno) chosen as the most representative of the 8 subjects analyzed participating in volleyball training.

Analysis of the other 3 subjects, although having different models of the same sports footwear, shows that the thermal distribution values are within the minimum and maximum limits of the 5 subjects analyzed in the paper.

Thermography measurements were performed on five athletes (subjects) who wore Asics (subjects 1 and 2) and Mizuno (subjects 3, 4, and 5) sports shoes in a volleyball training session, as shown in Figure 3; footwear image and material characteristics for Asics and Mizuno shoes are shown in Figure 4. Polynomial regression is used to create a mathematical model and to predict temperature values outside the range of the experimental data.

The mechanical properties of the analyzed footwear were determined on the Nano Indenter Agilent G200, with the help of which Young’s modulus, Hardness at Maximum Load, Displacement at Maximum Load, Drift Correction, and Load at Max Load were determined according to ISO 14577 [42]. The external synthetic leather layer was analyzed (exposed to stress). Among the mechanical and thermal methods suffered, the Young’s modulus is modified. For future research, variation in Young’s modulus can be examined at other temperatures analyzed in the present article, both on synthetic leather and on synthetic fibers. The two pairs of footwear were exposed to the same temperature variations; one of the reasons why the heat transfer is different between the two models is due to mechanical properties of the two materials, which are differentiated by their different Young’s modulus values, shown in

Table 1. Mechanical proprieties for Asics footwear.

Test	Modulus at Max Load GPa	Hardness at Max Load GPa	Drift Correction Nm/s	Displacement at Max Load Nm	Load at Max Load mN
Mean	0.061	0.007	−0.417	2084.76	0.348
Standard Deviation	0.018	0.005	0.223	77.11	0.193
% Coefficient of Variation	46.95	66.63	−53.47	3.7	55.57

for Asics and in

Table 2. Mechanical proprieties for Mizuno footwear.

Test	Modulus at Max Load GPa	Hardness at Max Load GPa	Drift Correction Nm/s	Displacement at Max Load Nm	Load at Max Load mN
Mean	0.039	0.01	−0.198	2115.856	0.495
Standard Deviation	0.016	0.006	0.335	30.382	0.184
% Coefficient of Variation	26.46	62.13	−169.17	1.44	37.24

for Mizuno.

Based on the determined Young’s Modulus, it can be seen that the increase in the temperature in the range of 23.1 °C–32.7 °C on the shoe surface influences the increase in Young’s modulus linearly with the increase in the temperature in the range of 40 °C–100 °C [43]. In the research reviewed in the paper [43] on textile fibers, temperature has an influence on Young’s modulus; it can be observed that increasing temperature in the range of 40 °C–100 °C on textile fibers influences the increase in Young’s modulus. With increasing temperature, the structure of the material changes, influencing its mechanical properties.

In the research carried out in the present work on the textile material of the two types of footwear, it can be observed that the increase in temperature in the range 23.1 °C–32.7 °C influences the increase in Young’s modulus.

The Young’s modulus values shown in Table 1 and Table 2 are average values; Figure 5 and Figure 6 show the evolution of Young’s modulus for Asics footwear and Mizuno footwear as a function of temperature for the 23.1 °C–32.7 °C range.

The relationship obtained between temperature and Young’s modulus in the range 23.1 °C–32.7 °C as shown in Figure 5 for Asics footwear is a polynomial function of degree two (1).

y = 3 × 10⁻⁵x² + 0.0023x + 0.0376

(1)

The coefficient of determining R² established by the regression procedure is:

R² = 0.974

(2)

The relationship obtained between temperature and Young’s modulus in the range 23.1 °C–32.7 °C as shown in Figure 6 for Mizuno footwear is a polynomial function of degree two (3).

y = 7 × 10⁻⁶x² + 0.0023x + 0.0232

(3)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9785

(4)

3. Results and Discussion

Thermographic recordings on sports shoes were made during training at five different times: moment zero (before starting the training), moment one at 2 min of training, moment two at 5 min of training, moment three at 15 min of training, and moment four at the end of the volleyball training. These recordings were made to identify the areas that ensure the best ventilation of the foot for comfort in movement.

As shown in Figure 7 for the right foot of subject 1 at time zero (before the start of volleyball training), the maximum temperature along the line Li1, which is positioned on the central part of the foot, is 28.1 °C, and the minimum temperature is 23.8 °C.

The temperature variation along the Li1 line is 4.3 °C, and the emissivity is 0.83, at time zero for subject 1.

On the side along the Li2 line, the maximum temperature is 26.6 °C, and the minimum temperature is 23.1 °C, at time zero for subject 1. The temperature variation along the Li2 line is 3.5 °C, and the emissivity is 0.86 at time zero for subject 1.

For the left foot of subject 1 at time zero, the maximum temperature along the Li3 line positioned on the central side is 28.4 °C, and the minimum temperature is 23.2 °C.

The temperature variation along the Li3 line is 5.2 °C, and the emissivity is 0.81, at time zero for subject 1.

On the side along the Li4 line, the maximum temperature is 27.3 °C, and the minimum temperature is 24.0 °C, at time zero for subject 1.

The temperature variation along the line Li4 is 3.3 °C, and the emissivity is 0.83, at time zero for subject 1.

In Figure 7, for the right foot of subject 2 at time zero (before starting the volleyball training), the maximum temperature along the line Li5, which is positioned on the central part of the leg, is 29.1 °C, and the minimum temperature is 24.9 °C.

The temperature variation along the Li5 line is 4.2 °C, and the emissivity is 0.83, at time zero for subject 2.

On the side along the Li6 line, the maximum temperature is 28.5 °C, and the minimum temperature is 24.5 °C, at time zero for subject 2.

The temperature variation along the line Li6 is 4.0 °C, and the emissivity is 0.83, at time zero for subject 2.

For the left foot of subject 2 at time zero, the maximum temperature along the Li7 line positioned on the central side is 28.2 °C, and the minimum temperature is 24.8 °C.

The temperature variation along the Li7 line is 3.4 °C, and the emissivity is 0.83, at time zero for subject 2.

On the side along the Li8 line, the maximum temperature is 27.8 °C, and the minimum temperature is 23.6 °C, at time zero for subject 2.

The temperature variation along the line Li8 is 4.2 °C, and the emissivity is 0.83, at time zero for subject 2.

Thermography measurements for subject 3 for the right foot at time zero (before starting the volleyball training) show that the maximum temperature along the Li1 line, which is positioned on the center of the foot, is 27.1 °C, and the minimum temperature is 22.9 °C. The temperature variation along the Li1 line is 4.2 °C, and the emissivity is 0.83, at time zero for subject 3. On the side along the Li2 line, the maximum temperature is 26.1 °C, and the minimum temperature is 25.0 °C, at moment zero for subject 3. The temperature variation along the Li2 line is 1.1 °C, and the emissivity is 0.83, at moment zero for subject 3. For the left foot of subject 3 at time zero, the maximum temperature along the Li3 line positioned on the central side is 27.0 °C, and the minimum temperature is 24.0 °C. The temperature variation along the Li3 line is 3.0 °C, and the emissivity is 0.83, at time zero for subject 3. On the side along the Li4 line, the maximum temperature is 26.1 °C, and the minimum temperature is 24.1 °C, at time zero for subject 3.

The temperature variation along the line Li4 is 2.0 °C, and the emissivity is 0.83, at time zero for subject 3.

In Figure 7, for the right foot of subject 4 at time zero (before starting the volleyball training), the maximum temperature along the Li5 line, which is positioned on the center of the foot, is 26.7 °C, and the minimum temperature is 23.2 °C. The temperature variation along the Li5 line is 3.5 °C, and the emissivity is 0.83, at time zero for subject 4. On the side along the Li6 line, the maximum temperature is 25.5 °C, and the minimum temperature is 23.1 °C, at time zero for subject 4.

The temperature variation along the line is 2.4 °C, and the emissivity is 0.83, at time zero for subject 4.

For the left foot of subject 4 at time zero, the maximum temperature along the Li7 line positioned on the central side is 25.9 °C, and the minimum temperature is 23.0 °C.

The temperature variation along the Li7 line is 2.9 °C, and the emissivity is 0.83, at time zero for subject 4. On the side along the Li8 line, the maximum temperature is 25.4 °C, and the minimum temperature is 24.0 °C, at time zero for subject 4. The temperature variation along the line Li8 is 1.4 °C, and the emissivity is 0.83, at time zero for subject 4.

In Figure 7, for the right foot of subject 5 at time zero (before starting the volleyball training), the maximum temperature along the line Li9, which is positioned on the center of the foot, is 27.9 °C, and the minimum temperature is 23.7 °C. The temperature variation along the Li9 line is 4.2 °C, and the emissivity is 0.83, at time zero for subject 5. On the side along the Li10 line, the maximum temperature is 27.0 °C, and the minimum temperature is 24.6 °C, at time zero for subject 5. The temperature variation along the line Li10 is 2.4 °C, and the emissivity is 0.83, at time zero for subject 5. For the left foot of subject 5 at time zero, the maximum temperature along the Li11 line positioned on the central side is 26.0 °C, and the minimum temperature is 22.8 °C.

The temperature variation along the Li11 line is 3.2 °C, and the emissivity is 0.83, at time zero for subject 5. On the side along the Li12 line, the maximum temperature is 26.2 °C, and the minimum temperature is 24.7 °C, at zero time for subject 5. The temperature variation along the Li12 line is 1.4 °C, and the emissivity is 0.83, at zero time for subject 5. (Figure 8) shows the temperature variation along the subject lines on each footwear at time zero.

In the case of subject 1 at time zero, as shown in Figure 9, the relation obtained is a polynomial function of degree four (5).

Y = 0.0073x⁴ − 0.2275x³ + 2.0874x² − 5.9588x + 28.002

(5)

The coefficient of determining R² established by the regression procedure is:

R² = 0.8659

(6)

In the case of subject 2 at time zero as shown in Figure 10, the relation obtained is a polynomial function of degree five (7).

Y = 0.0258x⁵ − 0.583x⁴ + 4.7504x³ − 16.831x² + 25.227x + 12.25

(7)

The coefficient of determining R² established by the regression procedure is:

R² = 0.8298

(8)

In the case of subject 3 at time zero, as shown in Figure 11, the relation obtained is a polynomial function of degree six (9).

Y= −0.0112x⁶ + 0.3202x⁵ − 3.6246x⁴ + 20.466x³ − 59.556x² + 82.822x − 17.538

(9)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9086

(10)

In the case of subject 4 at time zero, as shown in Figure 12, the relation obtained is a polynomial function of degree six (11).

Y = −0.0093x⁶ + 0.2621x⁵ − 2.8882x⁴ + 15.629x³ − 42.674x² + 54.437x − 1.575

(11)

The coefficient of determining R² established by the regression procedure is:

R² = 0.930

(12)

In the case of subject 5 at time zero, as shown in Figure 13, the relation obtained is a polynomial function of degree five (13).

Y = 0.0336x⁵ − 0.7404x⁴ + 5.9279x³ − 20.914x² + 31.876x + 7.575

(13)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9273

(14)

As shown in Figure 14, for the right foot of subject 1 at time one (two minutes of training), the maximum temperature along the line Li1, which is positioned on the center of the foot, is 28.9 °C, and the minimum temperature is 22.3 °C. The temperature variation along the Li1 line is 6.6 °C, and the emissivity is 0.83 at time one. On the side along the Li2 line, the maximum temperature is 29.6 °C, and the minimum temperature is 22.8 °C at time one. The temperature variation along the Li2 line is 6.9 °C, and the emissivity is 0.83 at time one.

For the left foot of subject 1 at time one, the maximum temperature along the Li3 line positioned on the central side is 28.3 °C, and the minimum temperature is 23.6 °C. The temperature variation along the Li3 line is 4.6 °C, and the emissivity is 0.83, for subject 1 at time one. On the side along the Li4 line, the maximum temperature is 27.2 °C, and the minimum temperature is 22.9 °C, for subject 1 at time one. The temperature variation along the Li4 line is 4.2 °C, and the emissivity is 0.83, for subject 1 at time one.

In Figure 14, for the right foot of subject 2 at time one (two minutes of training), the maximum temperature along the line Li5, which is positioned on the central part of the leg, is 30.1 °C, and the minimum temperature is 24.0 °C. The temperature variation along the Li5 line is 6.2 °C, and the emissivity is 0.83 at time one. On the side along the Li6 line, the maximum temperature is 28.9 °C, and the minimum temperature is 23.9 °C at time one. The temperature variation along the Li6 line is 4.9 °C, and the emissivity is 0.83 at time one.

For the left leg of subject 2 at time one, the maximum temperature along the Li7 line positioned on the central side is 28.8 °C, and the minimum temperature is 23.6 °C. The temperature variation along the Li7 line is 5.2 °C, and the emissivity is 0.83 at time one. On the side along the Li8 line, the maximum temperature is 28.1 °C, and the minimum temperature is 23.5 °C at time one. The temperature variation along the Li8 line is 4.6 °C, and the emissivity is 0.83 at time one.

Thermography measurements afferent for subject 3 for the right foot at time one (two minutes of training) show that the maximum temperature along the Li1 line, which is positioned on the center of the foot, is 28.6 °C, and the minimum temperature is 23.4 °C. The temperature variation along the Li1 line is 5.2 °C, and the emissivity is 0.83 at time one. On the side along the Li2 line, the maximum temperature is 27.9 °C, and the minimum temperature is 22.9 °C, at time one. The temperature variation along the Li2 line is 4.9 °C, and the emissivity is 0.83 at time one.

For the left foot of subject 3 at time one, the maximum temperature along the Li3 line positioned on the central side is 27.6 °C, and the minimum temperature is 22.4 °C. The temperature variation along the Li3 line is 5.2 °C, and the emissivity is 0.83 at time one.

On the side along the Li4 line, the maximum temperature is 26.6 °C, and the minimum temperature is 23.8 °C, at time one. The temperature variation along the Li4 line is 2.8 °C, and the emissivity is 0.83 at time one.

In Figure 14, for the right foot of subject 4 at time one (two minutes of training), the maximum temperature along the Li5 line, which is positioned on the center of the foot, is 26.4 °C, and the minimum temperature is 22.3 °C.

The temperature variation along the Li5 line is 4.1 °C, and the emissivity is 0.83 at time one.

On the side along the Li6 line, the maximum temperature is 26.1 °C, and the minimum temperature is 22.6 °C, at time one.

The temperature variation along the line is 3.6 °C, and the emissivity is 0.83, at time one.

For the left foot of subject 4 at time one, the maximum temperature along the Li7 line positioned on the central side is 26.7 °C, and the minimum temperature is 22.0 °C.

The temperature variation along the Li7 line is 4.6 °C, and the emissivity is 0.83 at time one. On the side along the Li8 line, the maximum temperature is 25.9 °C, and the minimum temperature is 22.2 °C at time one.

The temperature variation along the Li8 line is 3.7 °C, and the emissivity is 0.83 at time one.

In Figure 14, for the right foot of subject 5 at time one (two minutes of training), the maximum temperature along the line Li9, which is positioned on the central part of the foot, is 28.3 °C, and the minimum temperature is 23.0 °C.

The temperature variation along the Li9 line is 5.2 °C, and the emissivity is 0.83 at time one. On the side along the Li10 line, the maximum temperature is 28.0 °C, and the minimum temperature is 23.0 °C, at time one. The temperature variation along the Li10 line is 5.0 °C, and the emissivity is 0.83 at time one.

For the left foot of subject 5 at time one, the maximum temperature along the Li11 line positioned on the central side is 26.7 ° C, and the minimum temperature is 22.9 °C.

The temperature variation along the Li11 line is 3.8 °C, and the emissivity is 0.83 at time one. On the side along the Li12 line, the maximum temperature is 27.0 °C, and the minimum temperature is 23.3 °C, at moment one. The temperature variation along the Li12 line is 3.6 °C, and the emissivity is 0.83 at time one.

Figure 15 shows the temperature variation along the subject lines on each footwear at time one.

In the case of subject 1 at time one, as shown in Figure 16, the relation obtained is a polynomial function of degree five (15).

Y = 0.032x⁵ − 0.7303x⁴ + 6.0275x³ − 21.775x² + 34.185x + 4.475

(15)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9287

(16)

In the case of subject 2 at time one, as shown in Figure 17, the relation obtained is a polynomial function of degree five (17).

Y = 0.0337x⁵ − 0.7537x⁴ + 6.0782x³ − 21.284x² + 31.658x + 8.25

(17)

The coefficient of determining R² established by the regression procedure is:

R² = 0.8816

(18)

In the case of subject 3 at time one, as shown in Figure 18, the relation obtained is a polynomial function of degree five (19).

Y = 0.0256x⁵ − 0.562x⁴ + 4.3959x³ − 14.611x² + 20.122x + 14.05

(19)

The coefficient of determining R² established by the regression procedure is:

R² = 0.944

(20)

In the case of subject 4 at time one as shown in (Figure 19), the relation obtained is a polynomial function of degree five (21).

Y = 0.0204x⁵ − 0.4685x⁴ + 3.89x³ − 14.045x² + 21.61x + 11.3

(21)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9256

(22)

In the case of subject 5 at time one, as shown in Figure 20, the relation obtained is a polynomial function of degree five (23).

Y = 0.0335x⁵ − 0.7396x⁴ + 5.8882x³ − 20.439x² + 30.4x + 7.825

(23)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9431

(24)

As shown in Figure 21, for the right foot of subject 1 at time two (five minutes of training), the maximum temperature along the line Li1, which is positioned on the center of the foot, is 29.0 °C, and the minimum temperature is 22.1 °C. The temperature variation along the Li1 line is 6.9 °C, and the emissivity is 0.83 at time two. On the side along the Li2 line, the maximum temperature is 30.1 °C, and the minimum temperature is 22.5 °C at time two. The temperature variation along the Li2 line is 7.6 °C, and the emissivity is 0.83 at time two. For the left foot of subject 1 at time two, the maximum temperature along the Li3 line positioned on the central side is 28.9 °C, and the minimum temperature is 23.5 °C.

The temperature variation along the Li3 line is 5.5 °C, and the emissivity is 0.83, for subject 1 at time two. On the side along the Li4 line, the maximum temperature is 29.5 °C, and the minimum temperature is 23.0 °C, for subject 1 at time two. The temperature variation along the Li4 line is 6.5 °C, and the emissivity is 0.83, for subject 1 at time two.

In Figure 21, for the right foot of subject 2 at time two (five minutes of training), the maximum temperature along the Li5 line, which is positioned on the center of the foot, is 29.6 °C, and the minimum temperature is 23.3 °C. The temperature variation along the Li5 line is 6.2 °C, and the emissivity is 0.83 at time two. On the side along the Li6 line, the maximum temperature is 31.4 °C, and the minimum temperature is 25.8 °C at time two.

The temperature variation along the Li6 line is 5.6 °C, and the emissivity is 0.83 at time two. For the left foot of subject 2 at time two, the maximum temperature along the Li7 line positioned on the central side is 30.6 °C, and the minimum temperature is 25.5 °C.

The temperature variation along the Li7 line is 5.1 °C, and the emissivity is 0.83 at time two. On the side along the Li8 line, the maximum temperature is 29.7 °C, and the minimum temperature is 24.9 °C, at time two. The temperature variation along the Li8 line is 4.8 °C, and the emissivity is 0.83 at the second moment. Thermography measurements afferent for subject 3 for the right foot at time two (five minutes of training) show that the maximum temperature along the Li1 line, which is positioned on the central part of the foot, is 29.5 °C, and the minimum temperature is 23.0 °C. The temperature variation along the Li1 line is 6.6 °C, and the emissivity is 0.83 at time two. On the side along the Li2 line, the maximum temperature is 27.5 °C, and the minimum temperature is 22.5 °C at time two. The temperature variation along the Li2 line is 5.0 °C, and the emissivity is 0.83 at time two. For the left leg of subject 3 at time two, the maximum temperature along the Li3 line positioned on the central side is 29.0 °C, and the minimum temperature is 23.5 °C. The temperature variation along the Li3 line is 5.5 °C, and the emissivity is 0.83 at time two. On the side along the Li4 line, the maximum temperature is 27.7 °C, and the minimum temperature is 25.2 °C, at time two. The temperature variation along the Li4 line is 2.5 °C, and the emissivity is 0.83 at the second moment.

In Figure 21, for the right foot of subject 4 at time two (five minutes of training), the maximum temperature along the Li5 line, which is positioned on the central part of the foot, is 29.5 °C, and the minimum temperature is 23.6 °C. The temperature variation along the Li5 line is 5.9 °C, and the emissivity is 0.83 at time two. On the side along the Li6 line, the maximum temperature is 27.0 °C, and the minimum temperature is 23.2 °C, at time two. The temperature variation along the line is 3.7 °C, and the emissivity is 0.83 at time two. For the left foot of subject 4 at time two, the maximum temperature along the Li7 line positioned on the central side of the foot is 27.7 °C, and the minimum temperature is 22.6 °C. The temperature variation along the Li7 line is 5.1 °C, and the emissivity is 0.83 at time two. On the side along the Li8 line, the maximum temperature is 27.4 °C, and the minimum temperature is 22.5 °C, at time two. The temperature variation along the Li8 line is 4.9 °C, and the emissivity is 0.83 at time two.

In Figure 21, for the right foot of subject 5 at time two (five minutes of training), the maximum temperature along the line Li9, which is positioned on the central part of the foot, is 30.0 °C, and the minimum temperature is 23.3 °C. The temperature variation along the Li9 line is 6.8 °C, and the emissivity is 0.83 at time two. On the side along the Li10 line, the maximum temperature is 28.0 °C, and the minimum temperature is 23.0 °C, at time two. The temperature variation along the Li10 line is 5.0 °C, and the emissivity is 0.83 at time two. For the left foot of subject 5 at time two, the maximum temperature along the Li11 line positioned on the central side of the foot is 28.3 °C, and the minimum temperature is 23.2 °C. The temperature variation along the Li11 line is 5.1 °C, and the emissivity is 0.83 at time two. On the side along the Li12 line, the maximum temperature is 26.5 °C, and the minimum temperature is 22.6 °C at time two. The temperature variation along the Li12 line is 3.9 °C, and the emissivity is 0.83 at time two.

Figure 22 shows the temperature variation along the subject lines on each footwear at time two.

The graphs in Figure 23 show the temperature variation along the subject lines on each shoe at time two.

In the case of subject 1 at time two, as shown in Figure 23, the relation obtained is a polynomial function of degree five (25).

Y = 0.0342x⁵ − 0.77x⁴ + 6.2742x³ − 22.391x² + 34.781x + 4.075

(25)

The coefficient of determining R² established by the regression procedure is:

R² = 0.949

(26)

In the case of subject 2 at time two, as shown in Figure 24, the relation obtained is a polynomial function of degree five (23).

Y = 0.0337x⁵ − 0.7988x⁴ + 6.9294x³ − 26.798x² + 45.724x − 1.85

(27)

The coefficient of determining R² established by the regression procedure is:

R² = 0.973

(28)

In the case of subject 3 at time two, as shown in Figure 25, the relation obtained is a polynomial function of degree four (29).

Y = 0.0234x⁴ − 0.5233x³ + 3.8039x² − 9.0518x + 28.848

(29)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9048

(30)

In the case of subject 4 at time two, as shown in Figure 26, the relation obtained is a polynomial function of degree six (31).

Y = −0.004x⁶ + 0.1371x⁵ − 1.7876x⁴ + 11.182x³ − 34.259x² + 47.197x + 1.1

(31)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9084

(32)

In the case of subject 5 at time two, as shown in Figure 27, the relation obtained is a polynomial function of degree five (33).

Y = 0.0246x⁵ − 0.5619x⁴ + 4.6153x³ − 16.352x² + 24.455x + 11.075

(33)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9011

(34)

As shown in Figure 28, for the right foot of subject 1 at time three (15 min of training), the maximum temperature along the line Li1, which is positioned on the center of the foot, is 30.6 °C, and the minimum temperature is 25.4 °C.

The temperature variation along the Li1 line is 5.2 °C, and the emissivity is 0.83 at time three. On the side along the Li2 line, the maximum temperature is 30.4 °C, and the minimum temperature is 23.7 °C, at time three. The temperature variation along the Li2 line is 6.7 °C, and the emissivity is 0.83 at time three. For the left foot of subject 1 at time three, the maximum temperature along the Li3 line positioned on the central side is 30.1 °C, and the minimum temperature is 23.2 °C. The temperature variation along the Li3 line is 6.9 °C, and the emissivity is 0.83, for subject 1 at time three. On the side along the Li4 line, the maximum temperature is 29.0 °C, and the minimum temperature is 23.5 °C, for subject 1 at time three. The temperature variation along the Li4 line is 5.6 °C, and the emissivity is 0.83, for subject 1 at time three.

In Figure 28, for the right foot of subject 2 at time three (15 min of training), the maximum temperature along the Li5 line, which is positioned on the center of the leg, is 31.3 °C, and the minimum temperature is 27.1 °C. The temperature variation along the Li5 line is 4.2 °C, and the emissivity is 0.83 at time three. On the side along the Li6 line, the maximum temperature is 31.6 °C, and the minimum temperature is 26.6 °C at time three.

The temperature variation along the Li6 line is 5.0 °C, and the emissivity is 0.83 at time three. For the left foot of subject 2 at time three, the maximum temperature along the Li7 line positioned on the central side is 30.9 °C, and the minimum temperature is 23.8 °C. The temperature variation along the Li7 line is 7.1 °C, and the emissivity is 0.83 at time three.

On the side along the Li8 line, the maximum temperature is 31.3 °C, and the minimum temperature is 26.6 °C at time three. The temperature variation along the Li8 line is 4.7 °C, and the emissivity is 0.83 at time three.

Thermography measurements for subject 3 for the right foot at time three (15 min of training) show that the maximum temperature along the Li1 line, which is positioned on the center of the foot, is 31.3 °C, and the minimum temperature is 25.9 °C.

The temperature variation along the Li1 line is 5.4 °C, and the emissivity is 0.83 at time three.

On the side along the Li2 line, the maximum temperature is 30.2 °C, and the minimum temperature is 26.1 °C at time three. The temperature variation along the Li2 line is 4.1 °C, and the emissivity is 0.83 at time three.

For the left foot of subject 3 at time three, the maximum temperature along the Li3 line positioned on the central side is 30.4 °C, and the minimum temperature is 25.4 °C. The temperature variation along the Li3 line is 5.0 °C, and the emissivity is 0.83 at time three.

On the side along the Li4 line, the maximum temperature is 30.2 °C, and the minimum temperature is 26.5 °C at time three. The temperature variation along the Li4 line is 3.5 °C, and the emissivity is 0.83 at time three.

In Figure 28, for the right foot of subject 4 at time three (15 min of training), the maximum temperature along the Li5 line, which is positioned on the central part of the leg, is 31.0 °C, and the minimum temperature is 24.2 °C.

The temperature variation along the Li5 line is 6.8 °C, and the emissivity is 0.83 at time three. On the side along the Li6 line, the maximum temperature is 29.6 °C, and the minimum temperature is 25.8 °C, at time three. The temperature variation along the line is 3.8 °C, and the emissivity is 0.83, at time three.

For the left foot of subject 4 at time three, the maximum temperature along the Li7 line positioned on the central side is 29.5 °C, and the minimum temperature is 24.1 °C. The temperature variation along the Li7 line is 5.4 °C, and the emissivity is 0.83 at time three.

On the side along the Li8 line, the maximum temperature is 29.4 °C, and the minimum temperature is 25.0 °C, at time three. The temperature variation along the Li8 line is 4.5 °C, and the emissivity is 0.83 at time three.

In Figure 28, for the right foot of subject 5 at time three (15 min of training), the maximum temperature along the Li9 line, which is positioned on the center of the leg, is 31.9 °C, and the minimum temperature is 23.8 °C.

The temperature variation along the Li9 line is 8.0 °C, and the emissivity is 0.83 at time three. On the side along the Li10 line, the maximum temperature is 30.5 °C, and the minimum temperature is 25.9 °C at time three. The temperature variation along the Li10 line is 4.6 °C, and the emissivity is 0.83 at time three.

For the left foot of subject 5 at time three, the maximum temperature along the Li11 line positioned on the central side is 29.5 °C, and the minimum temperature is 27.3 °C. The temperature variation along the Li11 line is 2.2 °C, and the emissivity is 0.83 at time three.

On the side along the Li12 line, the maximum temperature is 29.9 °C, and the minimum temperature is 27.1 °C, at time three. The temperature variation along the Li12 line is 2.7 °C, and the emissivity is 0.83 at time three.

Figure 29 shows the temperature variation along the subject lines on each shoe at time three.

In the case of subject 1 at time three, as shown in Figure 30, the relation obtained is a polynomial function of degree six (35).

Y = −0.0019x⁶ + 0.0849x⁵ − 1.299x₄ + 8.8694x³ − 27.942x² + 37.336x + 8.3125

(35)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9286

(36)

In the case of subject 2 at time three, as shown in Figure 31, the relation obtained is a polynomial function of degree five (37).

Y = 0.0428x⁵ − 0.9481x⁴ + 7.5635x³ − 26.064x² + 37.249x + 9.325

(37)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9723

(38)

In the case of subject 3 at time three as shown in Figure 32, the relation obtained is a polynomial function of degree five (39).

Y = 0.0267x⁵ − 0.5918x⁴ + 4.7128x³ − 16.251x² + 23.884x + 14.15

(39)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9191

(40)

In the case of subject 4 at time three, as shown in Figure 33, the relation obtained is a polynomial function of degree six (41).

Y = −0.0136x⁶ + 0.4107x⁵ − 4.8582x⁴ + 28.305x³ − 83.495x² + 115.22x − 31.4

(41)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9305

(42)

In the case of subject 5 at time three, as shown in Figure 34, the relation obtained is a polynomial function of degree six (43).

Y = 0.0013x⁶ − 0.008x⁵ − 0.2331x⁴ + 2.9358x³ − 12.446x² + 22.828x + 10.687

(43)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9166

(44)

As shown in Figure 35, for the right foot of subject 1 at time four (at the end of volleyball training), the maximum temperature along the line Li1, which is positioned on the center of the foot, is 31.8 °C, and the minimum temperature is 26.1 °C. The temperature variation along the Li1 line is 5.7 °C, and the emissivity is 0.83 at time four. On the side along the Li2 line, the maximum temperature is 29.6 °C, and the minimum temperature is 25.1 °C at time four. The temperature variation along the Li2 line is 4.5 °C, and the emissivity is 0.83 at time four.

For the left foot of subject 1 at time four, the maximum temperature along the Li3 line positioned on the central side is 30.4 °C, and the minimum temperature is 26.8 °C. The temperature variation along the Li3 line is 3.5 °C, and the emissivity is 0.83, for subject 1 at time four. On the side along the Li4 line, the maximum temperature is 29.3 °C, and the minimum temperature is 25.6 °C, for subject 1 at time four. The temperature variation along the Li4 line is 3.7 °C, and the emissivity is 0.83, for subject 1 at time four.

In Figure 35, for the right foot of subject 2 at time four (at the end of the volleyball training), the maximum temperature along the line Li5, which is positioned on the central part of the foot, is 32.7 °C, and the minimum temperature is 25.6 °C.

The temperature variation along the Li5 line is 7.1 °C, and the emissivity is 0.83 at time four. On the side along the Li6 line, the maximum temperature is 30.4 °C, and the minimum temperature is 23.9 °C at time four. The temperature variation along the Li6 line is 6.5 °C, and the emissivity is 0.83 at time four.

For the left foot of subject 2 at time four, the maximum temperature along the Li7 line positioned on the central side is 31.8 °C, and the minimum temperature is 25.7 °C.

The temperature variation along the Li7 line is 6.0 °C, and the emissivity is 0.83 at time four.

On the side along the Li8 line, the maximum temperature is 31.1 °C, and the minimum temperature is 25.1 °C at time four. The temperature variation along the Li8 line is 5.9 °C, and the emissivity is 0.83 at time four.

Thermography measurements afferent for subject 3 for the right foot at time four (at the end of volleyball training) show that the maximum temperature along the Li1 line, which is positioned on the center of the foot, is 30.8 °C, and the minimum temperature is 26.8 °C.

The temperature variation along the Li1 line is 4.0 °C, and the emissivity is 0.83 at time four. On the side along the Li2 line, the maximum temperature is 29.4 °C, and the minimum temperature is 26.7 °C at time four.

The temperature variation along the Li2 line is 2.7 °C, and the emissivity is 0.83 at time four.

For the left foot of subject 3 at time four, the maximum temperature along the Li3 line positioned on the central side is 30.9 °C, and the minimum temperature is 26.9 °C.

The temperature variation along the Li3 line is 3.9 °C, and the emissivity is 0.83 at time four.

On the side along the Li4 line, the maximum temperature is 30.0 °C, and the minimum temperature is 27.5 °C, at moment four. The temperature variation along the Li4 line is 2.5 °C, and the emissivity is 0.83 at time four.

In Figure 35, for the right foot of subject 4 at time four (at the end of volleyball training), the maximum temperature along the Li5 line, which is positioned on the center of the leg, is 32.5 °C, and the minimum temperature is 26.7 °C.

The temperature variation along the Li5 line is 5.8 °C, and the emissivity is 0.83 at time four. On the side along the Li6 line, the maximum temperature is 31.2 °C, and the minimum temperature is 26.6 °C at time four.

The temperature variation along the line is 4.6 °C, and the emissivity is 0.83 at time four. For the left foot of subject 4 at time four, the maximum temperature along the Li7 line positioned on the central side is 30.8 °C, and the minimum temperature is 24.9 °C.

The temperature variation along the Li7 line is 5.9 °C, and the emissivity is 0.83 at time four.

On the side along the Li8 line, the maximum temperature is 30.6 °C, and the minimum temperature is 27.3 °C at time four.

The temperature variation along the Li8 line is 3.3 °C, and the emissivity is 0.83 at time four.

In Figure 35, for the right foot of subject 5 at time four (at the end of the volleyball training), the maximum temperature along the line Li9, which is positioned on the central part of the foot, is 32.0 °C, and the minimum temperature is 25.8 °C.

The temperature variation along the Li9 line is 6.2 °C, and the emissivity is 0.83 at time four.

On the side along the Li10 line, the maximum temperature is 31.9 °C, and the minimum temperature is 27.2 °C at time four. The temperature variation along the Li10 line is 4.7 °C, and the emissivity is 0.83 at time four.

For the left foot of subject 5 at time four, the maximum temperature along the Li11 line positioned on the central side is 31.1 °C, and the minimum temperature is 29.6 °C.

The temperature variation along the Li11 line is 1.4 °C, and the emissivity is 0.83 at time four. On the side along the Li12 line, the maximum temperature is 31.2 °C, and the minimum temperature is 28.6 °C at time four.

The temperature variation along the Li12 line is 2.6 °C, and the emissivity is 0.83 at time four (at the end of the volleyball training).

Figure 36 shows the temperature variation along the subject lines on each footwear at time four.

In the case of subject 1 at time four, as shown in Figure 37, the relation obtained is a polynomial function of degree five (45).

Y = 0.0132x⁵ − 0.2834x⁴ + 2.1186x³ − 6.4126x² + 7.6639x + 22.95

(45)

The coefficient of determining R² established by the regression procedure is:

R² = 0.7532

(46)

In the case of subject 2 at time four, as shown in Figure 38, the relation obtained is a polynomial function of degree four (47).

Y = 0.0234x⁴ − 0.5642x³ + 4.4478x² − 11.769x + 33.584

(47)

The coefficient of determining R² established by the regression procedure is:

R² = 0.8281

(48)

In the case of subject 3 at time four, as shown in Figure 39, the relation obtained is a polynomial function of degree six (49).

Y = −0.0111x⁶ + 0.3057x⁵ − 3.2957x⁴ + 17.512x³ − 47.164x² + 59.678x − 0.25

(49)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9021

(50)

In the case of subject 4 at time four, as shown in Figure 40, the relation obtained is a polynomial function of degree five (51).

Y = 0.0371x⁵ − 0.8116x⁴ + 6.3706x³ − 21.567x² + 30.664x + 12.075

(51)

The coefficient of determining R² established by the regression procedure is:

R² = 0.929

(52)

In the case of subject 5 at time four, as shown in Figure 41, the relation obtained is a polynomial function of degree six (53).

Y = 0.0111x⁶ − 0.2878x⁵ + 2.8981x⁴ − 14.36x³ + 36.273x² − 41.937x + 43.175

(53)

The coefficient of determining R² established by the regression procedure is:

R² = 0.9325

(54)

Polynomial regression is used to create a mathematical model based on polynomials of degree four, five, and six by processing the experimental data and to predict the temperature values outside this range for each individual subject; this method is sensible because, based on the analysis of the polynomial type, a difference in the degree of the polynomial was observed when comparing the shoes of subjects 1 and 2 with the shoes of subjects 3, 4, 5.

It is observed from this analysis that for subjects 1 and 2, wearing the same type of footwear, the degree of the polynomials for moments one and two is the same (of degree five), and for moments zero, three, and four, the difference is small (of one degree between them).

For subject 3, the degree of the polynomials for moments zero and four is the same (of degree six), and for moments one, two, and three, the difference is small (of one degree between them).

For subject 4, the degree of the polynomials for moments zero, two, and three is the same (of degree six); it is also the same for moments one and four (of degree five).

For subject 5, the degree of the polynomials for moments zero, one, and two is the same (of degree 5); it is also the same for moments three and four (of degree six).

It can be seen from this analysis that the difference in the degrees of the polynomials from one shoe to the other is greater than the difference between them.

Considering that these analyses have been done by other researchers in the field in different settings, in research laboratories on unused sports footwear intended for indoor sports activities, the authors wanted to analyze whether there are significant differences in temperature distribution compared to those studied in laboratory conditions where the environment is much better controlled.

The authors studied indoor volleyball footwear in real time on several subjects during several volleyball training sessions to monitor the heat exchange between the foot and the outdoor environment at different times of training intensity, since most research is conducted in research laboratories [40].

The authors measured the variation in sports footwear temperature during volleyball training for the eight subjects analyzed, of which three subjects had a different model of the same sports footwear.

The analysis shows that the thermal distribution values are within the minimum and maximum limits of the five subjects analyzed in the paper, and they are presented in

Table 3. Variation of the sports footwear temperature during volleyball training at the time of measurements for the 5 selected subjects from 8 analyzed.

Subject	Time Zero	Time One	Time Two	Time Three	Time Four
Subject 1	Li1 max 28.1 °C	Li1 max 28.9 °C	Li1 max 29.0 °C	Li1 max 30.6 °C	Li1 max 31.8 °C
	Li1 min 23.8 °C	Li1 min 22.3 °C	Li1 min 22.1 °C	Li1 min 25.4 °C	Li1 min 26.1 °C
	Li2 max 26.6 °C	Li2 max 29.6 °C	Li2 max 30.1 °C	Li2 max 30.4 °C	Li2 max 29.6 °C
	Li2 min 23.1 °C	Li2 min 22.8 °C	Li2 min 22.5 °C	Li2 min 23.7 °C	Li2 min 25.1 °C
	Li3 max 28.4 °C	Li3 max 28.3 °C	Li3 max 28.9 °C	Li3 max 30.1 °C	Li3 max 30.4 °C
	Li3 min 23.2 °C	Li3 min 23.6 °C	Li3 min 23.5 °C	Li3 min 23.2 °C	Li3 min 26.8 °C
	Li4 max 27.3 °C	Li4 max 27.2 °C	Li4 max 29.5 °C	Li4 max 29.0 °C	Li4 max 29.3 °C
	Li4 min 24.0 °C	Li4 min 22.9 °C	Li4 min 23.0 °C	Li4 min 23.5 °C	Li4 min 25.6 °C
Subject 2	Li5 max 29.1 °C	Li5 max 30.1 °C	Li5 max 29.6 °C	Li5 max 31.3 °C	Li5 max 32.7 °C
	Li5 min 24.9 °C	Li5 min 24.0 °C	Li5 min 23.3 °C	Li5 min 27.1 °C	Li5 min 25.6 °C
	Li6 max 28.5 °C	Li6 max 28.9 °C	Li6 max 31.4 °C	Li6 max 31.6 °C	Li6 max 30.4 °C
	Li6 min 24.5 °C	Li6 min 23.9 °C	Li6 min 25.8 °C	Li6 min 26.6 °C	Li6 min 23.9 °C
	Li7 max 28.2 °C	Li7 max 28.8 °C	Li7 max 30.6 °C	Li7 max 30.9 °C	Li7 max 31.8 °C
	Li7 min 24.8 °C	Li7 min 23.6 °C	Li7 min 25.5 °C	Li7 min 23.8 °C	Li7 min 25.7 °C
	Li8 max 27.8 °C	Li8 max 28.1 °C	Li8 max 29.7 °C	Li8 max 31.3 °C	Li8 max 31.1 °C
	Li8 min 23.6 °C	Li8 min 23.5 °C	Li8 min 24.9 °C	Li8 min 26.6 °C	Li8 min 25.1 °C
Subject 3	Li1 max 27.1 °C	Li1 max 28.6 °C	Li1 max 29.5 °C	Li1 max 31.3 °C	Li1 max 30.8 °C
	Li1 min 22.9 °C	Li1 min 23.4 °C	Li1 min 23.0 °C	Li1 min 25.9 °C	Li1 min 26.8 °C
	Li2 max 26.1 °C	Li2 max 27.9 °C	Li2 max 27.5 °C	Li2 max 30.2 °C	Li2 max 29.4 °C
	Li2 min 25.0 °C	Li2 min 22.9 °C	Li2 min 22.5 °C	Li2 min 26.1 °C	Li2 min 26.7 °C
	Li3 max 27.0 °C	Li3 max 27.6 °C	Li3 max 29.0 °C	Li3 max 30.4 °C	Li3 max 30.9 °C
	Li3 min 24.0 °C	Li3 min 22.4 °C	Li3 min 23.5 °C	Li3 min 25.4 °C	Li3 min 26.9 °C
	Li4 max 26.1 °C	Li4 max 26.6 °C	Li4 max 27.7 °C	Li4 max 30.2 °C	Li4 max 30.0 °C
	Li4 min 24.1 °C	Li4 min 23.8 °C	Li4 min 25.2 °C	Li4 min 26.5 °C	Li4 min 27.5 °C
Subject 4	Li5 max 26.7 °C	Li5 max 26.4 °C	Li5 max 29.5 °C	Li5 max 31.0 °C	Li5 max 32.5 °C
	Li5 min 23.2 °C	Li5 min 22.3 °C	Li5 min 23.6 °C	Li5 min 24.2 °C	Li5 min 26.7 °C
	Li6 max 25.5 °C	Li6 max 26.1 °C	Li6 max 27.0 °C	Li6 max 29.6 °C	Li6 max 31.2 °C
	Li6 min 23.1 °C	Li6 min 22.6 °C	Li6 min 23.2 °C	Li6 min 25.8 °C	Li6 min 26.6 °C
	Li7 max 25.9 °C	Li7 max 26.7 °C	Li7 max 27.7 °C	Li7 max 29.5 °C	Li7 max 30.8 °C
	Li7 min 23.0 °C	Li7 min 22.0 °C	Li7 min 22.6 °C	Li7 min 24.1 °C	Li7 min 24.9 °C
	Li8 max 25.4 °C	Li8 max 25.9 °C	Li8 max 27.4 °C	Li8 max 29.4 °C	Li8 max 30.6 °C
	Li8 min 24.0 °C	Li8 min 22.2 °C	Li8 min 22.5 °C	Li8 min 25.0 °C	Li8 min 27.3 °C
Subject 5	Li9 max 27.9 °C	Li9 max 28.3 °C	Li9 max 30.0 °C	Li9 max 31.9 °C	Li9 max 32.0 °C
	Li9 min 23.7 °C	Li9 min 23.0 °C	Li9 min 23.3 °C	Li9 min 23.8 °C	Li9 min 25.8 °C
	Li10 max 27.0 °C	Li10 max 28.0 °C	Li10 max 28.0 °C	Li10 max 30.5 °C	Li10 max 31.9 °C
	Li10 min 24.6 °C	Li10 min 23.0 °C	Li10 min 23.0 °C	Li10 min 25.9 °C	Li10 min 27.2 °C
	Li11 max 26.0 °C	Li11 max 26.7 °C	Li11 max 28.3 °C	Li11 max 29.5 °C	Li11 max 31.1 °C
	Li11 min 22.8 °C	Li11 min 22.9 °C	Li11 min 23.2 °C	Li11 min 27.3 °C	Li11 min 29.6 °C
	Li12 max 26.2 °C	Li12 max 27.0 °C	Li12 max 26.5 °C	Li12 max 29.9 °C	Li12 max 31.2 °C
	Li12 min 24.7 °C	Li12 min 23.3 °C	Li12 min 22.6 °C	Li12 min 27.1 °C	Li12 min 28.6 °C

.

Sustainability in sports footwear includes many factors, such as design, supply chain, waste reduction, minimizing energy consumption, recycling, waste, and further innovation.

Based on the Young’s Modulus determined by 0.061 GPa for Asics sports footwear, it can be seen that the increase in temperature in the range of 23.1 °C–32.7 °C on the surface of the shoe influences the increase in Young’s modulus, which varies linearly with the increase in the temperature. Based on the Young’s Modulus determined by 0.039 GPa for Mizuno sports footwear, it can be observed that the temperature increase in the range of 23.1 °C–32.7 °C on the surface of the shoe influences the increase in Young’s modulus, which varies linearly with the increase in the temperature.

The polynomial regression is used to create a mathematical model based on processing the experimental data and to predict temperature values outside this domain.

In the mentioned cases when the regression of the polynomial function R2 has a value of less than 0.9, the mathematical model is less representative of the real situation, and the heat distribution on the analyzed surfaces of sports footwear is higher in the analyzed moments.

In the cases mentioned when the polynomial function regression R2 has a value higher than 0.9, the mathematical model represents the real situation, and the heat distribution on the analyzed areas of the sports footwear is higher.

In the case of subjects 1 and 2 using Asics footwear, it can be observed that the regression of the polynomial function R2 has a value of less than 0.9 at time zero (before starting the training). Following the measurements performed at time one (two minutes of training), only in the case of subject 2 did the regression of the polynomial function R2 have a value less than 0.9. In the case of time four (at the end of volleyball training), the regression of the polynomial function R2 had a value of less than 0.9 for subjects 1 and 2.

In the aforementioned cases, when the regression of the polynomial function R2 has a value of less than 0.9, the mathematical model is less representative of the real situation, and the heat distribution on the analyzed surfaces of sports footwear (Asics) is higher in the analyzed moments.

In the case of subjects 1 and 2 who use Asics sports footwear, there is an uneven distribution of temperature variation along the analyzed lines Li1, Li2, Li3, Li4, Li5, Li6, Li 7, and Li8 within the four moments in which the measurements were performed.

In the case of subjects 3, 4, and 5 who use Mizuno sports footwear, it can be observed that the polynomial function regression R² has a value greater than 0.9 within the four moments analyzed.

In the cases mentioned when the polynomial function regression R² has a value higher than 0.9, the mathematical model represents the real situation, and the heat distribution on the analyzed areas of the sports footwear (Mizuno) is higher only at moment four.

In the case of subjects 3, 4, and 5 who use Mizuno sports shoes, there is a uniform distribution of temperature variation along the analyzed lines Li1, Li2, Li3, Li4, Li5, Li6, Li 7, Li8, Li9, Li10, Li11, and Li12 during the four moments when the measurements were performed.

4. Conclusions

In the present paper, research was carried out in order to identify the thermal variation of indoor sports shoes used in volleyball training so as to detect the heat exchange between the foot and the outdoor environment.

Based on the values obtained from the research on the eight subjects, of which five subjects are relevant to this paper, we can conclude that the sole of the shoes is the coldest area, and for these reasons, we did not include these values in the data analysis, although subjects 3, 4, and 5 had footwear with ventilation in the sole, and the temperature distribution values were small in comparisons between them and subjects 1 and 2, whose soles were not ventilated (not significant).

The two pairs of footwear were exposed to the same temperature variations; one of the reasons why the heat transfer is different between the two models is due to the mechanical properties of the two materials, which are differentiated by their different Young’s modulus values.

Therefore, the test was valuable for showing the temperature distribution along the lines for each shoe and showing the strengths and weaknesses of the design of the tested footwear compared to the research done in the field. The authors conducted in the present research measurements from each angle of the room in which the volleyball training occurred, using a thermographic camera that was mounted on a tripod to capture the image in real time and from the same distance in static and dynamic moments.

Following the research and the data analyzed on sports footwear for the five tested subjects, it can be concluded that the sole of each shoe tested is the most insulating part, and the part that supports the heel shows the lowest heat transfer rates.

In future research, the variation in the Young’s modulus values can be examined at other temperatures analyzed in the present article, both on synthetic leather and on synthetic fibers.

The present research differs when compared to the majority of studies in the field, which are performed in a stationary configuration, despite the fact that it is well-known that the shoes of a real volleyball player are rarely stationary during training, where all the subsets are subjected to the same type of physical effort.

The authors of this paper aim to perform temperature measurements during a men’s volleyball training session to examine the distribution along temperature lines between subjects in the same environmental conditions and the advantages obtained by examining each shoe.