Energy supply and influencing factors of mountain marathon runners from Baiyin marathon accident in China

High temperature impacts the performance of marathon athletes, and hypothermia harms athletes. Twenty-one runners died, and eight were injured in the China Baiyin marathon on May 22, 2021. It’s a typical human life test. The energy equations are combined with the maximum energy supply of Chinese male athletes to study this accident. We analyze the human body’s route slope, travel speed, and heat dissipation under low temperatures in this marathon. The study shows that the large slope and long-distance of CP2 to CP3 section and the low temperature during the competition are the main reasons for the accident. The method of quantifying the slope and temperature and calculating the percentage of athletes’ physical consumption proposed in this paper can evaluate the route design of field marathons. We suggest that the physical energy consumption ratio of 90%, i.e. 315 cal/min/kg, should be taken as the maximum energy supply for Chinese male marathon runners. Dangerous risk zones for wind speed and temperature on dangerous path sections are also formulated for athletes to make their assessments. This paper’s theories and methods can effectively help design the marathon route and determine the race time.

To increase the influence and popularity of the city, local governments in China have held marathons one after another and invited famous runners from all over the world to participate, which has indeed boosted the local economy in China. In 2018 and 2019, there were 278, 330, and 27, 61 registrations for Category A and Category B events of the Chinese Athletics Association respectively 13 . As of , the running competitions held in China include various walks, half marathons, 50 km, 30 km, 28 km, 21 km, 16 km, 15 km, 10 km, 8, 8 km, 3.8 km, and so on to 2625 times 14 .
But there have been very individual race accidents, such as the marathon accident in Baiyin, Gansu of China 15 . On May 22, 2021, the fourth Yellow River Shilin Mountain Marathon 100 km cross-country race (Abbreviated as Baiyin marathon) was held in Jingtai County, Baiyin City of China. 172 participants took part in the 100-km cross-country race. During the race, public safety responsibility events occurred due to sudden cooling, precipitation, and strong wind, resulting in the death of 21 participants and the injury of 8 15 . China's State Sports Administration issued a notice on May 28 to comprehensively 'one-on-one' check road running (including marathon, half marathon, 10 km, 5 km) and suspend the competitions that do not meet the requirements. On June 25, the government arrested five officials and dismissed, removed, demoted, warned, and demerit recorded twenty-seven leaders 15 .
It can be seen from Fig. 1 that due to COVID-19, the number of marathons has significantly been reduced since 2020. Due to the Baiyin marathon accident in 2021, the State Sport General Administration of China immediately stopped many marathons, so the number of races in 2021 was reduced. Data for 2022 is not final yet, and complete data will be available in 2023.
On the one hand, marathon accidents are not good for the development of marathon sports, and on the other hand, it is also bad for the health of the athletes participating in the competition. The high temperature in this kind of competition, like a marathon, or long-distance races, has attracted the attention of athletes and relevant media 16 . However, low temperature also does great harm to athletes 17 . There are many reasons for the accident in the Baiyin marathon. However, the low temperature and the energy supply of the athletes' bodies are less than the energy dissipation is one of the main reasons.
Because of this severe sports accident, it is necessary to conduct scientific research, analyze the causes of the accident, and avoid such accidents. Local governments hold various competitions to promote tourism development, stimulate the economy, and improve local popularity. Ignoring the potential hazards is an important reason why many Gansu province officials were held accountable for an ultramarathon tragedy 18 . At the same time, the Baiyin marathon accident also has several adverse natural conditions: high altitude, large slope, and low temperature.
This paper studies the route slope and temperature from the human body's heat dissipation and energy supply to reveal the cause of the accident.
In this accident, the athlete's death has already shown that the energy supply has reached its limit. It is simply a life experiment of the human body, which is very cruel. Therefore, it is necessary to study the energy supply limit of athletes in this competition through this marathon accident and analyze the cause of the accident from the human energy supply limit. Therefore, the main goal of this paper is to study and obtain the human body's limited supply of energy for remote mobilization and combine the slope of the track and the temperature of the environment to study and analyze the setting of the way.
Avoid recurrence of such accidents through research. At the same time, we also put forward some suggestions for athletes to participate in similar competitions. We set up a self-assessment chart for whether sports can participate based on temperature, slope, and speed during the competition. It is hoped that casualties in future competitions can be avoided through this accident analysis.

Methods
The elevation and landform of the Biayin marathon. Baiyin marathon in Gansu of China was held four times in 2018 ( Fig. 2a-c), 2019, 2020, and 2021. The first three sessions went well, and an accident occurred in the fourth session (some runners were warming themselves in the cave-dwelling, Fig. 2d). According to the race route of the Baiyin marathon, the elevation map in the race route area is drawn, and a map of vegetation along the way is attached (as shown in Fig. 3). Baiyin city is mountainous primarily, and a broad valley plain coexists. The northern part is an alluvial diluvial inclined plain, the central part is a low hill, and the southern part is loess beam, replat, and tableland landform. www.nature.com/scientificreports/ The climate of Baiyin city is a transition zone from a middle temperate semi-arid zone to an arid zone in China. The annual average temperature is 6-9 ℃, and the yearly rainfall is 180-450 mm, mainly in July, August, and September, accounting for more than 60% of the annual precipitation. It belongs to the northwest margin of the southeast monsoon climate, and the yearly evaporation reaches 1500-1600 mm, 4.5 times the average precipitation. Jingtai County in the north has maximum annual evaporation of 3390 mm. Baiyin has four seasons with plenty of sunshine, no hot summer, and no cold winter.
The topographic features of Baiyin City are mainly bedrock mountains (as shown in Figs. 2c, 3a) and intermountain basins. The horizontal distribution of vegetation in the city gradually transitions from south to north to grassland deserts (as shown in Fig. 3b), and the transition between zones is not apparent. The tectonic structure in the northwest belongs to the eastward extension of the Qilian Mountains, with bare ground bedrock (as shown in Fig. 2c) and natural vegetation on the shady slopes (as shown in Figs. 2a,b, 3c). The southeast is dominated www.nature.com/scientificreports/ by loess beam, replat and tableland landform, rivers, flats, and valleys. The tectonic structure belongs to the Longzhong Basin. Except for a few bedrock mountains, the ground is covered by loess (Fig. 2d).

Energy consumption at a particular slope and speed. Marathon runner's energy consumption
includes heat dissipation and kinetic energy consumption of the human body. The athletes need to supply more energy to meet heat dissipation and kinetic energy consumption when the temperature is lower, the travel speed is faster, and the road is steeper. The athlete can complete sports at low temperatures, large slopes, and high speeds only when the speed and intensity of the energy supplied by the human body meet these energy requirements.
At the general running speed, the prediction formula of human exercise energy consumption 19,20 is: where M is the energy consumption rate of the human body (w), W is the body weight (kg), L is the bear load (kg), V is the running speed (m/s), G is the slope (%), η is the surface condition coefficient, η = 1 in the case of horizontal hard road and η = 2 on loose sand. Figures 2a-c and 3a-c, η = 1.2. People move slower on a 12° gradient slope uphill and downhill than on a flat road 21 . When going downhill, the energy consumption decreases 22 , but with the increase of the descending slope, the energy consumption also increases to improve the friction and reduce the risk of falling 23 . But the increase is not as significant as the upslope walking. This paper selects the positive slope for calculation.
Human body surface heat dissipation. Baiyin Marathon runners are not equipped for the cold, wearing simple clothes or directly exposed [24][25][26] . The heat dissipation is, where Wci is the air-cooling index (kcal/m 2 /h), F is the wind speed (m/s), T is the air temperature (℃). It represents the heat dissipation rate of the human body surface with a skin temperature of 33 ℃.
The maximum energy supply of Chinese runners. Accurate measurement of lipid or carbohydrate metabolism during exercise is also complex. Marathon running is fueled principally by the oxidation of intramuscular glycogen and lipids to a lesser extent 27,28 . Therefore, there is no need to distinguish between carbohydrate and lipid metabolism and their percentages.
At the same temperature, the energy consumption positively correlates with the maximum oxygen uptake 29 . According to the test results 30,31 , perform linear formula fitting at the same temperature to obtain the energy consumption at 100% VO 2max , namely the maximum energy supply rate. Table 1 lists the data. In reference 29 , the performance at different temperatures shows a similar and linear relationship.
Rising and falling external temperatures increase the body's energy expenditure ( Table 1). The linear relationship between the total energy consumption of Chinese male athletes at different temperatures of 100%VO 2max and temperature is not significant. On the contrary, the total energy consumption at different temperatures remains stable 32 . It isn't easy to obtain data on the maximum energy supply at different temperatures. Therefore, this paper takes the full energy supply as a fixed value. The energy supply range of Chinese male athletes is 291.7-356.7 cal/min/kg. Therefore, this paper considers that Chinese male athletes' maximum energy supply rate is 350 cal/min/kg. Other data. Select terrain data from ASTERGDEMv2.0, land DEM, with an accuracy of about 30 m, and the download address is https:// earth explo rer. usgs. gov/. Figure 3 is generated by ArcGIS V10.3. www.nature.com/scientificreports/ Liang Jing, China's leading marathon runner who died in the accident, ran at 100 km for 7 h in previous competitions at a speed of 4 m/s. This research takes the value of 1.5 m/s according to the running speed of ordinary athletes. The weight of male athletes is 70 kg, the wind speed is 0, the height is 170 cm, the body surface area is 1.82 m 2 , and the temperature comes from Baiyin meteorological observation station.
Reference 15 provides the temperature data of the day at point CP3. Baiyin Weather Station and Reference 33 offer the average temperature, maximum and minimum temperature of 21 days before the competition. Figure 4 lists the temperature curves 15 .

Results
According to Eqs. (1) and (2) calculate the total energy required by running energy consumption and surface heat dissipation along the elevation of the running route. And the energy supply rate is 350 cal/min/kg (1715 J/s, max supply energy) according to the maximum oxygen uptake. Figure 5 lists the results.
The slope increases significantly in the CP2-CP3 section (24-32.5 km), and the required energy rises. According to the speed of 1.5 m/s, runners run in this section from 13:26 to 15:01. At this time, the temperature in Baiyin is 6.9-8.2 ℃. In Fig. 5, many parts of the blue curve of CP2-CP3 section are more significant than the pink curve, indicating that the energy demand is greater than the energy supply. The external performance is that the athletes gradually lose temperature and enter a dangerous state. In the section before CP1 (5-10 km), there is also a part where the energy demand is greater than the energy supply. Still, this section is at the initial running stage, and the gap between energy demand and energy supply is not too large. Athletes can well avoid temperature loss in this section by unconscious deceleration. The energy demand is greater than the energy supply from CP4 to SP and SP to CP5, but the two sections are mainly the downhill section. Since calculating in  www.nature.com/scientificreports/ this paper is based on the absolute value of the slope, athletes can slow down and travel downhill slowly. At the same time, the distance is not long, and the actual energy demand is not high. Therefore, we believe that the design of the route is seriously unreasonable and unscientific in CP2-CP3. And the design at 5-10 km is also absurd. The main reason is that the slope is too large, and the distance with a significant slope is too long 34 .
From Fig. 4, when passing through CP2-CP3, the temperature is lower than the minimum temperature in the previous 21 days, which is also a significant factor leading to the accident. Therefore, it is necessary to design the running route with the local historical temperature and avoid the month with the lowest temperature and the continuous path with a steep slope.
In Section C3 in Fig. 6, that is, from CP2 to CP3, the calculation on the day of the first, second, and third marathon shows that the ratio is close to 90%. Calculate these three results according to the minimum temperatures of 14 °C, 15 °C and 14 °C on the day of the competition. The temperature of the race day is higher than and not constant equal to this minimum temperature. The energy consumption rate in this competition period is less than 90%. At the same time, the span of the minimum and maximum temperature is close to the optimal temperature of 18.6 °C 35 , so the athletes can pass smoothly.
In Fig. 6, in Section C3, according to the temperature at Baiyin meteorological station and CP3 on the day of the fourth competition in 2021, the physical energy consumption of athletes on the race day has been greater than 90%, or even reached 113%, indicating that the physical energy consumption of athletes is too large. This distance is 8.5 km, which takes 1.6 h according to the speed of 1.5 m/s. At this time, the athletes are in danger.
In section C11, in 2021, the physical consumption of athletes has also reached 94%, which is also a dangerous section. In other areas (C1, C2, C4-C10), the physical consumption of athletes does not exceed 90%, and athletes are in a safe state.
The first three were safe from the four Baiyin marathons in 2018, 2019, 2020, and 2021, and the fourth had accidents. Combining Fig. 6 with the above analysis, we conclude that choosing 350 cal/min/kg as Chinese male athletes' maximum energy supply rate is reasonable under 100% VO 2 max. It is reasonable to take 90% of the energy consumption ratio as Chinese marathon athletes' maximum energy supply rate 315 cal/min/kg.

Discussion
The purpose of this study is to prevent the recurrence of such accidents.
The energy consumption of the human body: First, the heat dissipation on the surface of the body is directly related to the outside air temperature. The body heat dissipation is significant when the outside air temperature is low. The second is the path slope. The large slope requires large energy. The third is the moving speed. The speed is large, and the energy required is large. The speed is small, and the energy required is small. The fourth is the wind speed, in Eq. (2). The lost energy is large when the wind speed is large, and the heat loss is slight when the wind speed is negligible. Figure 6. The ratio of the total energy consumed for a marathon to the maximum energy supply T is the temperature, and LT is the lowest temperature. www.nature.com/scientificreports/ If completely avoid such accidents, one needs to limit the temperature, slope, moving speed, and wind speed. The above analysis is based on the fact that the long-distance moving speed of ordinary people is 1.5 m/s. The previous analysis has determined that the limit energy supply of personnel is 350 cal/min/kg. According to the calculation of 90%, the maximum energy supply is 315 cal/min/kg to be calculated.
The marathon path is ups and downs with different slopes. The comprehensive slope characterizes the overall slope of the path, which is as follows: where G z is the comprehensive slope; ΔL i is the ist distance, in the research, ΔL i = 200 m; G i is the slope of the ist distance, only G i > 0 is selected for calculation.
The slop of the CP2-CP3 is the largest in the entire marathon route (Fig. 4). This part is chosen to calculate the comprehensive slope according to Eq. (2). The comprehensive slope of the CP2-CP3 is 0.17197. Suppose we determine all the slopes, including the G i > 0 and G i < 0, and take − G i for G i < 0, the comprehensive slope is 0.21152. It doesn't take much energy to go downhill, so we don't take downhill into account. If we take G i for G i < 0, the comprehensive slope is 0.132424. This calculation ignores the difficulty of the climb. So we choose 0.17197 to evaluate.
When the temperature is 15 °C, the travel speed is 1.5 m/s, and the wind speed is 0, the required energy is 1546.3 w, which is close to 315 cal/min/kg of the energy supplied by the ordinary human body, and the calculated energy supply rate is 1543.5w.
According to Eqs. (1), (2), and (3), in the CP2-CP3 section, the slope value is 0.17197, and the temperature and wind speed risk zoning of this section is shown in Fig. 7.
The athlete's speed is 0, 0.5 m/s, and the maximum energy supply is 1543.5 w, according to 70% and 100% VO 2max . It is roughly divided into three zones: danger zone, transition zone, and safety zone.
When the Baiyin Marathon was held on May 22, 2021, the temperature range was [− 4.1 ℃, − 1.2 ℃]. Because this paper could not get the wind speed data at that time, according to the photos of the participating remote mobilizers, the wind speed was very large. The wind speed F is greater than 5.5-8 m/s, or greater than 14-17 m/s. The dangerous risk zones in CP2-CP3 were shown in "Baiyin CP2-CP3" in Fig. 7. The rectangular area shown in the figure indicates that the site is hazardous, and as the wind speed increases, the danger increases.
In CP2-CP3, marathon runners can make adjustments and actions by assessing their zone based on the temperature and wind speed at that time. Figure 7 has good instructive value and is very actionable. It is convenient for athletes to evaluate whether they can participate in the marathon according to their situation and prepare corresponding equipment.

Conclusions
'522' Baiyin marathon is a typical 'human life test' and an 'energy supply human experiment' . The lessons of the marathon accident can provide a reference for the marathon.
In the first three Baiyin marathons, no accidents occurred. The main reason is that the temperature on the race day is relatively high, which is 14-29 °C. The energy consumption rate of athletes is lower than or temporarily reaches 90%, and the athletes are in a safe state all the time.
An important reason for the accident of the fourth silver marathon in 2021 is the low temperature 15 . In the marathon route design, from CP2 to CP3, the terrain is continuously uphill at a large angle, and the athletes consume much physical energy. From CP2 to CP3, with the most accidents, the athletes' physical consumption rate is greater than 90% or even 113%, and the athletes are in a dangerous state, resulting in hypothermia. Fatigue www.nature.com/scientificreports/ leads to insufficient physical strength to resist a sudden low temperature, resulting in hypothermia 36 . Runners used fire to keep warm in a cave-dwelling, shown in Fig. 2d. There are many reasons 15 for the 2021 marathon accident, including unscientific route design, unreasonable holding time, etc. These complex factors bring great trouble to the route designer, which is challenging. The method proposed in this paper, which fully considers the slope and temperature, quantitatively calculates the percentage of athletes' physical consumption, and then designs the route design and evaluation of field marathons through the physical consumption ratio, is a valuable method. The physical energy consumption ratio of 90%, i.e., 315 cal/min/kg, should be taken as the maximum energy supply rate of Chinese marathon athletes and the maximum energy supply rate at the maximum oxygen intake of Chinese male athletes is 350 cal/min/kg.
When designing the marathon route in the future, avoiding continuous uphill with a large slope is necessary. Designers can refer to this literature 34 for route design. At the same time, the race time should entirely avoid high temperatures and, more importantly, avoid low-temperature times.
At the same time, the dangerous risk zones for the wind speed and temperature of marathon runners are established on the most hazardous path section so that the runners can evaluate whether they can participate in the marathon according to their conditions and prepare corresponding equipment.
Since it is an accident-based analysis, much data is lacking, and life experiments are impossible. The calculation involves a lot of content and is very complex. Nonetheless, such a limited analysis of life is valuable. The guiding significance of the paper is that the organizer needs to calculate the current situation synchronously according to the real-time situation, and broadcast the information in real time. www.nature.com/scientificreports/