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Energy supply and influencing 
factors of mountain marathon 
runners from Baiyin marathon 
accident in China
Jichao Sun
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.
Sports is an activity developed to meet the needs of human production, military, and  health1. Physical fitness is 
the premise to maintain and complete the human body’s essential life activities and physical skills. Marathon runs 
for a long time and consumes much energy. The performance of athletes is closely related to physical  fitness2. 
Physical performance is also affected by the surrounding environment, including temperature, humidity, road 
slope, road friction, and so  on3, 4. The relationship between human energy expenditure and the external environ-
ment needs to be studied to assess the individual strength of marathon runners. The war between Russia and 
Ukraine is going on, and now ordinary Ukrainian residents are also participating in the war. These people lack 
military training and actual combat experience and have limited combat power to participate in the war. Obtain-
ing the maximum energy supply of the human body also helps assess the combat effectiveness of a  soldier5 and 
ordinary people to participate in war.
For many years, sports researchers around the world have been conducting similar studies, including pre-
competition hypothermia, post-competition hypothermia, and pre-competition and post-competition warm-
ing  studies6 at the cold Winter Olympics, as well as various Oxygen inhalation, high-intensity training at high 
 altitudes7–10, etc., these studies have achieved positive results.
High temperature impacts the performance of marathon athletes, and hypothermia harms  athletes11, 12. The 
research on the limited energy supply means the final limit of the human body’s skills, and it is the research at the 
expense of the human body’s death. When evaluating the energy supply of marathon runners or ordinary people, 
especially their limited energy supply, it is impossible to carry out limit tests to ensure personnel safety. At the 
same time, there is still a lack of published literature on this kind of extreme energy supply research. From some 
marathon fatalities, we can get some trial-like results. Analyzing these marathon accidents, one can obtain data on 
the extreme energy supply of the personnel. Although these tests are not obtained from actual tests, these data are 
relatively close to the limits of the human body and are very precious. At the same time, such data is essential to 
the military and sports. After obtaining such data, it is possible to design better the marathon running route and 
guide the athletes to conduct self-assessments whether they can refer to relevant competitions, which will have 
positive significance and value. It is also a good guide for evaluating ordinary people who participated in the war.
OPEN
School of Water Resource & Environment, China University of Geosciences, Beijing 100083, China. email: sunjc@
cugb.edu.cn
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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  respectively13. As of March 19, 2022, 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  times14.
But there have been very individual race accidents, such as the marathon accident in Baiyin, Gansu of  China15. 
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, pre-
cipitation, and strong wind, resulting in the death of 21 participants and the injury of  815. 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  leaders15.
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 
 media16. However, low temperature also does great harm to  athletes17. 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 devel-
opment, 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  tragedy18. 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 sugges-
tions 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.
Figure 1.  Many marathons held in China.
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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.
Figure 2.  Baiyin marathon photos of pre-race, disaster, and rescue. (a–c) Baiyin marathon on May 20, 2018. (d) 
cave-dwelling, some runners were warming themselves by the fire on May 22, 2021.
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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 inter-
mountain 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 
Figure 3.  Marathon route and start, check, supply and endpoint and pictures along the route. (a) Photo of 
the race route on CP1. (b,c) photos of the race route on CP2–CP3. ‘Start’ is the starting point, CP1–CP9 is the 
checkpoint, SP is the supply point, and EP is the endpoint.
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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 require-
ments.
At the general running speed, the prediction formula of human exercise energy  consumption19, 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  road21. When going downhill, 
the energy consumption  decreases22, but with the increase of the descending slope, the energy consumption 
also increases to improve the friction and reduce the risk of  falling23. 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  exposed24–26. The heat dissipation is,
where Wci is the air-cooling index (kcal/m2/h), F is the wind speed (m/s), T is the air temperature (℃). It repre-
sents 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 intra-
muscular glycogen and lipids to a lesser  extent27, 28. Therefore, there is no need to distinguish between carbohy-
drate and lipid metabolism and their percentages.
At the same temperature, the energy consumption positively correlates with the maximum oxygen  uptake29. 
According to the test  results30, 31, perform linear formula fitting at the same temperature to obtain the energy 
consumption at 100%  VO2max, namely the maximum energy supply rate. Table 1 lists the data. In  reference29, 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 tem-
peratures of 100%VO2max and temperature is not significant. On the contrary, the total energy consumption at 
different temperatures remains  stable32. 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.
(1)
M = 1.5W + 2.0(W + L)
 L
W
2
+ η(W + L)[1.5V2 + 0.35VG],
(2)
Wci = (10.45 + 10
√
F − F) × (33 − T),
Table 1.  Reference data of human of Chinese male athletes’ energy supply.
Intensity (% of  VO2max)
Total energy consumption (cal/min/kg)
Temperature (°C)
References
65%VO2max
240.0
12
30
80%VO2max
290.0
100%VO2max
356.7
This research
40%VO2max
134.8
23
31
60%VO2max
185.4
80%VO2max
239.8
100%VO2max
291.7
This research
40%VO2max
126.6
33
31
60%VO2max
188.3
80%VO2max
236.7
100%VO2max
294.0
This research
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Liang Jing, China’s leading marathon runner who died in the accident, ran at 100 km for 7 h in previous com-
petitions 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  m2, and the temperature comes from Baiyin meteorological observation station.
Reference15 provides the temperature data of the day at point CP3. Baiyin Weather Station and  Reference33 
offer the average temperature, maximum and minimum temperature of 21 days before the competition. Figure 4 
lists the temperature  curves15.
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. Accord-
ing 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 
Figure 4.  The temperature of Baiyin and CP3 on race day and the average temperature, maximum and 
minimum temperature of 21 days before the competition, Baiyin Weather Station.
Figure 5.  Marathon route altitude, maximum energy supply, and energy demand curve, replenishment points, 
and check-in points. Calculate the energy required according to the actual temperature at CP3. Since there is no 
temperature data later, the following data is vacant.
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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  long34.
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 the last three marathons, the competition time is May 20, 2018, June 8, 2019, and September 29, 2020. 
The maximum and minimum temperatures in these three times are 14–27 ℃, 15–29 ℃, 14–20 ℃. Choose the 
minimum value of temperature for calculation. In each interval, calculate the ratio of the total energy consumed 
to the maximum supply energy according to Eqs. (1) and (2), shown in Fig. 6.
C1 is from the Start point to CP1 point [Start CP1]. C2: [CP1, CP2]. C3: [CP2, CP3]. C4: [CP3, CP4]. C5: 
[CP4, SP]. C6: [SP, CP5]. C7: [CP5, CP6]. C8: [CP6, CP7]. C9: [CP7, CP8]. C10: [CP8, CP9].C11: [CP9, End 
point]. The CP3 T is missing from C9 to C11 from the CP7 to the end. Baiyin T is the temperature of Baiyin. CP3 
T is the temperature of CP3 point. The lowest temperature is 14 °C, 15 °C, and 14 °C on the 1st, the competition 
on May 20, 2018, the second on June 8, 2019, and the third on September 29, 2020. The horizontal black line is 
90%.
Section C3 in Fig. 6, that is, from CP2 to CP3, the calculation on the day of the first, second, and third mara-
thon 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 °C35, 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 danger-
ous 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%  VO2max. 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.
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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 Gz is the comprehensive slope; ΔLi is the ist distance, in the research, ΔLi = 200 m; Gi is the slope of the ist 
distance, only Gi > 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 Gi > 0 and Gi < 0, and take − Gi for Gi < 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 Gi for 
Gi < 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% 
 VO2max. 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 tem-
perature 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  temperature15. 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 
(3)
Gz =
 GiLi
 Li
× 100%,
Figure 7.  The dangerous risk zones of wind speed and temperature in the CP2–CP3 section of the Baiyin 
marathon.
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leads to insufficient physical strength to resist a sudden low temperature, resulting in  hypothermia36. Runners 
used fire to keep warm in a cave-dwelling, shown in Fig. 2d.
There are many  reasons15 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  literature34 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 calcula-
tion 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.
Received: 17 December 2021; Accepted: 3 May 2022
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Acknowledgements
Thank Zhang Xiaotao and Dongbei Lowang 01 for the pictures.
Author contributions
S.J. did and finished all the work.
Competing interests 
The author declares no competing interests.
Additional information
Correspondence and requests for materials should be addressed to J.S.
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© The Author(s) 2022

Energy supply and influencing factors of mountain marathon runners from Baiyin marathon accident in China.
Sun, Jichao