Determination of Moving Speed of School Age Children

School age children (pedestrians) can move at different speeds, which are conditioned by certain parameters. Not all parameters have the same effect on the pedestrian speed. According to the literature, gender and age are the most researched parameters that have an impact on the speed of pedestrians. However, a small number of authors have dealt with the influence of movement regimes (slow, normal, fast, run, and rush) on pedestrian speed, while at the same time taking into account age and gender. For that reason, this article measured the speed of movement of school age children by movement regimes, taking into account age and gender. Within the same movement regime, the influence of age, sex, height, and weight on the speed of movement was investigated. Experimental measurements of the speed of movement of pedestrians aged 7 to 20 years were performed. Based on the results of measurements and statistical analyzes, recommendations on the average speed of movement regimes, age, and gender are given.


Introduction
e speed of pedestrians depends on a number of parameters. is article primarily deals with the research of the speed of pedestrian movement according to the movement regimes combined with the knowledge of age and gender. A review of previous research in this area shows that there are certain gaps: (i) A small number of authors have dealt with measuring pedestrian speeds depending on the regime of movement, taking into account gender and age (ii) Majority of the previous work dealt with only one usual (normal) movement regime, taking into account both age and gender (iii) Sample sizes by categories are relatively small, so the question of statistical reliability of the obtained results arises (iv) During measurement, age was not always known (v) When measuring in advance, the movement regime of pedestrians was not known (vi) e accuracy of the measuring equipment affected the obtained results (vii) Wide speed limit (min-max) for the same movement regime (viii) In the presentation of measured results, the minimum, maximum, and average values are given, without statistical analyzes and conclusions about the reliability of the obtained results, etc.
Having in mind all the above, it is clear that in the previous research on the speed of movement of school age children, there are gaps that need to be explored. Research (measurements) of the speed of movement of school age children were performed in experimental conditions, on the test area. During the preparation of the experiment, the aim was to eliminate the gaps and shortcomings that have been observed in previous research.
Pedestrian speed in practice is used as an input data in many situations (studies). Very often, the speed of pedestrians cannot be determined by known engineering methods, so in these cases, the recommendations given in the literature are used. e previously stated fact clearly speaks of the importance of the reliable speed measurements.
e main goal of this article is to measure the speed of movement of school age children, with predefined movement regimes with the knowledge of key parameters that affect it within the same mode, in order to obtain more reliable results and give recommendations regarding speed in different regimes.
In addition to the presentation of measured results, the article describes in detail the measurement procedure and the used measuring equipment. e literature review provides an overview of articles that have dealt with similar issues and the results obtained by other authors. Statistical analysis showed that there is a relationship between the pedestrians' speed of movement of certain age and gender within the same movement regime. In the discussion and conclusion, recommendations were given regarding the pedestrian speed, depending on the movement regime, taking into account gender and age.

Literature Overview
A large number of authors have researched and measured the parameters of pedestrian flows, and the obtained results can be used for various purposes. e basic parameters of pedestrian flows are flow density and speed [1]. e speed of pedestrian depends on the characteristics of pedestrians (age, gender, and physical abilities), infrastructure (length, width, type of pedestrian object) as well as weather and other external conditions [2]. Similar conclusions were reached by Peters et al. [3] and Xie et al. [4]. Based on the results of research conducted in India, Subramanyam and Prasanna Kumar [5] showed that the speed of movement of male pedestrians is higher by 0.17 m/s compared with the speed of movement of female pedestrians. Bansal et al. [6] concluded that pedestrian speed is affected by age, group size, and crossing patterns. In their work, they linked pedestrian crossing speed and crosswalk characteristics (the classification of road, length, and width of the crosswalk and the width of the pedestrian island). In his research, Tarawneh [7] showed that group size, age, and gander significantly affect pedestrian speed. Some researchers have concluded that age and body height are the factors that have the greatest impact on pedestrian movement [8][9][10]. It is necessary to know the speed of pedestrians when designing traffic lights, designing pedestrian facilities, for traffic accidents expertise, and the like. Risks related to transportation activities include not only driver-based accidents in a transportation process but also error-based accidents in goods traffic [11]. Pedestrians are the most vulnerable participants in traffic, and pedestrian traffic is affected by a number of factors [12]. e research conducted in Beijing included measuring pedestrian crossing speed [13]. Zhuang and Wu used previously obtained speeds to analyze crossing speed at crosswalks with countdown timers [14]. Stollof et al. also investigated pedestrian crossing speed at crosswalks with countdown timers, but they also investigated pedestrian crossing speed at ordinary signalized crosswalks [15]. In their work, Iryo-Asano and Alhajyaseen [16] modelled changes in pedestrian speeds when crossing signalized crosswalks. e speed of pedestrians is a direct consequence of the regime, i.e., the way pedestrians move. It is common to use the speed of a normal pedestrian in the analysis of pedestrian movement; however, when examining traffic accidents, it is necessary to know the speed of pedestrian movement for different regimes. It is usually not possible to determine the speed of pedestrians technically, based on the available physical traces. It is common for the speed of pedestrians to be adopted according to the recommendations from the literature, depending on the movement regime [17]. Some researchers have developed models to calculate the pedestrians speed at the time of contact with the vehicle [18]. Otković et al. [19] have developed models that predict children crossing speed, covering children aged 5 to 15 years. Earlier researches in the United Kingdom show that average crossing speed for younger pedestrians is between 1.32 and 1.72 m/s [20][21][22][23]. e pedestrian crossing speed for younger pedestrian in the Netherlands is 1.5 m/s [24]. To date, in some research, it has been found that the results of measuring pedestrian speeds have a normal distribution regardless of gender and age [25], that pedestrian speeds are affected by various factors, including street width, weather conditions, number of pedestrians crossing in a group, curbs, road markings, etc. [26], and that the speed of pedestrians is a direct consequence of the pedestrian age and the density of pedestrian flow at pedestrian crossings [1,27]. Recommendations regarding the speed of pedestrians are different depending on the purpose for which the speeds are used. us, the recommendations on changing the speed of pedestrians at signaled pedestrian crossings state that it is necessary to reduce the speed from 1.2 m/s to 0.9 m/s [28]. Table values of pedestrian speeds are usually given within certain limits for the same regime. It is common in the literature to give the upper and lower speed limits for a particular regime. e speed ranges for the same moving regime are often too large to reliably determine the speed of pedestrians. In the same traffic situation, by adopting the lower or upper speed limit in a certain mode, different conclusions can be reached.
Statistical analyses of pedestrian speeds shown in the tables usually do not exist, so the reliability of the obtained data is unknown. In addition to the above, it is not known in which conditions and in what manner the measurements were performed and by which measuring devices. In addition to not knowing the technical parameters that could have influenced the obtained results, the characteristics of the respondents themselves are not known, i.e., their weight, height, etc. are not known. Most of the experiments were conducted during the 70s and 80s of the last century, so it is necessary to analyze the compliance of known data with the measured ones [17]. A special problem is the changes in growing up, on which the key influence chronologically has television, computers, and in the last decade, smartphones. e consequences on psychophysical and psychomotor development have long been known: primarily obesity [29,30], cardiac, muscular, and skeletal changes [31][32][33] that, so far, have not been placed in the context of traffic safety, primarily pedestrian's safety. is influence is especially pronounced in highly developed countries. In the case of Serbia, numerous studies show intensive application and perspectives of IT sector development [34][35][36]. e context of the COVID-19 pandemic superimposes the use of television, computers, and smartphones, and the negative consequences of the physical development of children and adolescents will certainly be investigated in the context of the impact of the pandemic.

Research Method
It is not possible to clearly define certain movement regimes of pedestrians or school age children with technical parameters. For that reason, in order to determine the speed of movement of school age children, measurements of movement speeds were performed in precisely defined conditions and for certain regimes of movement. e defined movement regimes are identical to the tables in the existing literature, as follows: Bearing in mind that the research covered school children, the measurements were performed on the grounds of primary and secondary schools, for each age group of school children, on a sample of at least 100 respondents. In this way, categories of respondents were formed and are shown in Table 1.
e conducted research was performed on a preformed test area. e test included measurements of children's movement speeds according to predefined regimes. e statistical data obtained by the performed measurement were processed and systematized according to the data given in the literature.

Measuring Devices Used in the Experiment.
e Newtest Powertimer 300-series testing system device was used to determine the speed of school children. e device is designed for the accurate assessment of biomechanical and physiological explosive power, speed, reaction time, and quickness. e Newtest Powertimer 300-series is used to test athletic performance in about 20 different athletic disciplines.
is device enables precise measurements and tests that can be easily translated into numerical values. One of the most important features of this device is that the measurements are performed with an accuracy of 0.001 s.
A PC is used to control the Newtest Powertimer 300series (Figure 1.), and it is recommended to use a laptop due to the portability of the device itself. Newtest Powertimer Analyzer (version 1.00.137) application allows easy protocol selection and testing control. e measured results obtained in this way are automatically saved and can be downloaded from the Newtest Powertimer database at any time.
e Newtest Powertimer 300-series consists of a main console with five inputs for sensors, an audible alarm, a USB output, and a power connector. e Newtest Powertimer 300-series sensors are photocells and a weight-sensitive pad that can also detect some other parameters. Depending on the discipline being measured, a combination of sensors or the use of only one sensor type is possible.
Photocells belong to the IP 67 class, and as such, they enable measurements with an accuracy of ±0.001 seconds when measuring time and ±1 mm when measuring jump height. e sensor range can be adjusted in the range of 0.2-3 m. Photocells can be used in the temperature range from −20°C to +40°C. Experimental measurement of pedestrian movement parameters can also be performed via video surveillance.
One of the abilities of the Newtest Powertimer 300-series device is to measure the speed of the subjects. To determine the speed of school children, for the purpose of research, the so-called "Speed test" was used.

Measurement
Procedure. Due to the specific categories examined in this research, data collection during the research was performed on the grounds of a primary and secondary schools. In the primary school, the test area ( Figure 2.) was formed on a sports field with a concrete base, and during the research, it was flat, dry, and clean. In high school, the research was conducted in a sports gymnasium with parquet flooring. Measurements were performed in May 2019 in daylight conditions. e outside temperature ranged from 15°C to 20°C; the weather was sunny. e procedure for measuring the speed of movement of school-aged pedestrians consisted of three phases:

Mathematical Problems in Engineering 3
(1) Forming the test area (2) Training of respondents (3) Measurement of speed depending on the mode e test area is organized into three spatial units. In the first part of the test area, the respondents formed a line in accordance with the list and the ordinal number of the respondents. For each respondent, the following is known: gender, age, height, and weight. In the second part of the test area, the speed of movement was measured and sensors were placed there; three photocells with the range set at 3 m were used for this research. e test area was formed in such a way as to more accurately reflect the usual width of the road with two traffic lanes. e start of the test is marked by the starting line, which is located 1 m in front of the first sensor. e sensors are placed in a line at a distance of 3 m from each other. e last sensor also represents the finish line. e third part of the test area is parallel to the second part, and it was used to return the respondents to the back of the line.
Before the start of the measurements, a short training was performed, and the respondents were informed about the research that is being performed, as well as the regimes of moving through the test zone. e regimes of movement were demonstratively shown by the researchers, and then after the roll call, a line of respondents was formed. e passage of the subjects through the test zone was controlled by the researchers, while technical characteristics of the Newtest Powertimer 300-series device limit the number of persons in the test zone to one. Hence, the next respondent needs to wait for the previous respondent to leave the test zone in order for the next measurement to start.
e controlled passage of the subjects next to the sensor provides data in the Newtest Powertimer Analyzer (version 1.00.137) software package. Each passage is defined by the time needed to pass between the first and second sensors and the total time of passage between the sensors. In addition to the time needed to pass the course, the Newtest Powertimer Analyzer provides the ability to calculate the passage speed for the previously specified times. Data obtained by the measurement were transferred to the Microsoft Office Excel software package, in which a database was formed for additional analysis, such as categorization of participants, expansion of the database on age, height, weight, respondents, etc.

Results of the Measurements and
Statistical Analysis e obtained results of the measurement are presented by movement regimes, defined by age groups and gender. A comparative analysis of the results led to the conclusion that the distance covered did not affect the measured speed values. e time for which the subjects crossed the first three and the second three meters on the measuring range was very similar, and the oscillations were insignificant and were represented as positive and negative, for the same regime of movement (Table 2).
Due to the absence of significant differences in times it took the respondents to cross the first and second part of the testing area, all the presented results are expressed for crossing across the entire test area. Based on the conducted research, it can be concluded that the length of the covered distance does not affect the speed of pedestrians within the same regime of the same age and gender. e mean value, standard deviation, and the minimum and maximum speed values were determined by measuring individual pedestrian speeds. Table 2 shows results of measuring the pedestrian speeds by gender, age, and movement regimes. Tables 3-7 show the values of parametric characteristics (mathematical expectation and standard deviation), the type of speed distribution for all regimes for both genders, and the verification of the hypothesis of the established distribution. All hypotheses on the nonparametric distribution characteristic were verified by the χ 2 test with a significance threshold greater than p � 0.05 (from Tables 3-7). e verification parameters are given in the graphs (in Appendix, Figures 3-8).  Using the t test for dependent samples in the group of male children aged 8 to 10 years, there are significant differences between the average values of speeds in all regimes (p ≤ 0.0001). Using the t test for dependent        vertical of the movement regime (abscissas and ordinates of the histogram are identical) for male (blue) and female (red) children aged 10 to 12 years are given in Appendix in Figure 5.
Using the t test for dependent samples in the group of male children aged 12 to 15 years, there are significant differences between the average values of speeds in all regimes (p ≤ 0.0001). Using the t test for dependent Values 0,0 y07 y08 y08 y10 y10 y12 y12 y15 y15 y20 Male Ygroup y07 y08 y08 y10 y10 y12 y12 y15 y15 y20 Female Ygroup  For all ages and for both genders, movement regimes are clearly differentiated by absolute statistical differences in movement speeds. With this outcome, a reliable statistical basis for examining the influence of gender and age on the average speed of movement was set.

Influence of Gender on Movement Speeds for Identical Movement Regimes and Ages.
Based on all normal distributions, the mean values from Tables 3-7 by gender, age, and movement regimes were compared using the t test. Results with significance thresholds are given in Table 8.
For the whole interval of age groups, there are no significant differences between male and female children in two movement regimes: "slow" and "normal." By age, differences in faster regimes were found, as follows: (i) For ages 7 to 8, male children are faster only in "rush" regime. (ii) For ages 8 to 10, female children are faster in "fast" regime and male children are faster in "rush" regime. (iii) For ages 10 to 12, male children are faster in two regimes: "fast" and "rush." (iv) For ages 12 to 15, male children are faster in three regimes: "fast." "run," and "rush." (v) For ages 15 to 20, male children are faster in three regimes: "fast," "run," and "rush." In conclusion, the influence of gender exists to a lesser extent at younger ages and becomes moderately significant at older ages, for all faster regimes of walking or running, there are significant differences in average speeds in favor of male subjects.

Influence of Age on Pedestrian Speeds within the Same Regime and Same Genders.
e variance analysis of the influence of age groups by regimes and gender was done by the Dunckan test. e presentation of obtained results is shown in Tables 9 and 10. e influence of age on the average speed of movement within the same regime was statistically moderate in younger subjects and pronounced in older subjects. Differentiation is more pronounced in male respondents, and for them, it becomes absolute with age. As for the age of the female respondents, their differentiation ends at the age of 12 years, after which, the average speeds in the "fast," "run," and "rush" modes do not differ significantly.

Discussion
e obtained results, primarily the verified nonparametric characteristics of the normal distributions of speed, are consistent with some of the previous studies. Together with these researches, the presented results make the basis for more reliable application of the existing tabularly presented standards where the type of distributions of pedestrian speeds is not emphasized. ese results can significantly increase the accuracy of spatiotemporal analyses in traffic accidents involving pedestrians. With the reconstruction of the movement regime, the known age, and gender, the expertise can be conducted with credible speeds of pedestrians. As with the design of security systems in order to reduce risk, the following results must be taken into account.
(i) At all ages for both genders, movement regimes are clearly differentiated by absolute statistical differences in movement speeds. (ii) e influence of gender exists to a lesser extent at a younger age and becomes moderately significant at an older age. (iii) Significant differences in average speeds of the pedestrian movement by regimes were found in male subjects. In female subjects, the preadolescent limit (10 to 12 years) was expressed as meritorious.  0,0000 0,0000 0,0000 0,0000 Y08 Y10 0,0000 0,0084 0,0000 0,0000 Y10 Y12 0,0000 0,0084 0,0012 0,0000 Y12 Y15 0,0000 0,0000 0,0012 0,0000 Y15 Y20 0,0000 0,0000 0,0000 0,0000 (iv) Speeds of movement do not depend on the length of the distance covered for the conditions of the set test area. (v) e weight and height of the respondents did not show statistical significance that can be related to the speed of movement according to defined regimes and age limits. (vi) Period of the research is an important basis for a long-term study and the basis for future pedestrian speed standards, primarily due to the expected negative impact of the COVID-19 pandemic on the psychophysical development of children and adolescents.

Conclusions
In this article, the speed of movement of school age children in experimental conditions was measured. e measurement was performed both for male and female children by age groups in defined movement regimes. Movement regimes are defined as slow, normal, fast, run, and rush. e age groups are divided into classes of 7-8, 8-10, 10-12, 12-15, and 15-20 years. Based on the measurement of movement speeds of school age children, it was determined that the movement regime has the greatest influence on speed. For the same movement regime, age shows a significant effect on speed especially in younger age groups. e standard deviation of the measured speeds has a lower value in the slow and normal modes compared with fast, run, and rush. A comparative analysis of the measured mean values of the speed of movement of school age children with the values from the literature showed certain similarities, along with the difference between the minimum and maximum values. It is possible that this difference was due to the sample size used in the measurement or the conditions under which the experiment was performed.
Analyzes have shown that measured pedestrian speeds have the normal distribution regardless of the movement regime, age, and gender, which is in accordance with the conclusions of previous aticle [25]. Comparative analysis of measured speeds in the normal regime for all age categories, regardless of gender coincided with the results given in [20][21][22][23][24].
Measurement of pedestrian speeds in children aged 7 to 20 years show good agreement with the recommendations given for pedestrian speeds on pedestrian traffic lights crossings in previous study [28].
Further research should focus on measuring speeds in real conditions, intersections, pedestrian crossings, etc., which would make it possible to perform a comparative analysis with the results obtained in this article. e obtained mean values of speeds, taking into account the standard deviation, can be used as reliable input data in various analyzes.

Data Availability
e numerical data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.