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Kinematics of marathon running tactics
Human Movement Science xxx (2013) xxx–xxx
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Human Movement Science journal homepage: www.elsevier.com/locate/humov
Kinematics of marathon running tactics Wlodzimierz S. Erdmann ⇑, Patrycja Lipinska J. Sniadecki University School of Physical Education and Sport, Gdansk, Poland
a r t i c l e
i n f o
a b s t r a c t
Article history: Available online xxxx
Ó 2013 Elsevier B.V. All rights reserved.
PsycINFO classification: 3720 Keywords: Marathon running Tactics Kinematics Pacing Top runners Gebrselassie
1. Introduction Many human activities requiring strenuous effort are often performed in an incorrect manner, with may lead to early exhaustion. Among other factors, this may be caused by an inappropriate distribution of effort over the course of an event, as is in long-distance running. Long-distance runners usually have the following general aims in mind in designing their running tactics: (1) to end first at the finish line (not necessarily with the best time ever), usually in regular championships, or (2) to run the best possible time so as to break a record. Studies of running tactics are very helpful for both runner and coach in determining the ideal tactics for a particular future run (Arska, 1972; Gabrys & Celeban, 1996; Sozanski, 2007). Noakes (2000, 2003), Lucia, Olivan, Bravo, Gonzales-Freire, and Foster (2008) and Joyner, Ruiz, and Lucia (2011) all investigated the efficiency of running. They concluded that in order to achieve a very good result in marathon running (42,195 m), running economy constitutes one of the most important
⇑ Corresponding author. Address: Department of Biomechanics and Sport Engineering, J. Sniadecki University School of Physical Education and Sport, 1 Gorskiego Str., Gdansk 80-336, Poland. Tel.: +48 60 5304939 (mobile), +48 58 5547105 (office), fax: +48 58 5547166. E-mail address: [email protected] (W.S. Erdmann). 0167-9457/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.humov.2013.07.006
Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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features defining the successful runner. According to Williams (2007), it is not easy to identify and universally apply patterns of efficient movement for runners. These patterns still not to be found. Erdmann and Lipinska (2003a, 2003b, 2006), Lipinska (2006), Lipinska and Erdmann (2007) investigated marathon running at the highest competitive level by examining the velocity distribution during marathon running. The following example illustrates the kind of data and insights obtained. In the Berlin 2002 marathon, the female runner Takahashi attempted to break the world record. She ran the first 5 km at a mean velocity higher than 5.00 m/s. This was too fast since the mean velocity for the female marathon world’s best run was at that time 5.07 m/s. Her velocity gradually decreased in the course of the race, resulting in a lower velocity during the second part of the run than during the first. Her mission to break the world record failed (Erdmann & Lipinska, 2003b). Within the theory of a particular sport discipline different models are employed, among which scientific models are crucial. A scientific model incorporates a theoretical approach, which takes into account all the necessary quantities and their values that scientists believe must be included in the perfect competitor (a master). Scientific models may be rooted in exercise physiology, biomechanics, psychology and other disciplines (Shephard & Astrand, 2000; Noakes, 2000; Sadowski, 2009; Sozanski, 2007). Practically meaningful scientific models for long-distance running speak to issues of strategy and tactics. Strategy, among other important problems, takes into account which players the team will comprise during a race, or which runners will participate in the competition as leading runners or as pacemakers. Different pacemakers are chosen for different races. Unfortunately, they are usually selected a short time before a run and sometimes there is not enough time to prepare properly for the run in case of an initiative to establish a new record time. In addition to biomechanical quantities (work and power), runners use an index called ‘‘pacing’’, which indicates how many minutes a runner should take to run one or more kilometers. During competition this index helps runners to adopt proper tactics by taking into account the load distribution during the event. The load is measured as the velocity at which runners run the distance. For long-distance running, especially for a marathon run, a group model is available at present, based on Ethiopians and Kenyans. For over 10 years, the world long-distance running model of a master, especially in marathon running, has been personified in Haile Gebre Selassie or Gebrselassie (Ethiopia). He is considered by many to be the greatest long-distance runner of all time.
2. Concept of the work The aims of the present research were: (1) to examine pacing protocols, i.e., manners of load (velocity) distribution along the course by elite marathon runners, (2) to formulate recommendations for proper running tactics through proper load distribution, (3) to investigate the pacing of running of the long-time world’s best long-distance runner. We had the following hypotheses: (1) distribution of a load (velocity) during a marathon run should resemble an ascending line through the entire course; (2) fewer and smaller deviations from the line of running velocity are characterized by better results; (3) the world’s top long-distance runner runs with similar tactics in different runs when attempting to break the world record. We were further interested in finding answers to the following questions: (1) What are the characteristics of the pacing for the first runners at the finish line and for those further back? (2) What is a runner’s tactical approach to the first and last kilometers of the run? (3) What is the difference between velocities for the first and second parts of the run? (4) What are the velocity deviations, i.e., what accelerations and decelerations are made during the entire run? (5) Can the end results be predicted from the early stages of the run? (6) What are the differences between male and female marathon running? (7) How does the world’s top runner run consecutive stages of a marathon run when breaking or seeking to break the world record? (8) Does the world’s top runner run different races in the same manner?
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(9) What are the best tactics for breaking a world record in a marathon run? (10) What is the role of pacemakers in a run aimed at breaking a world record? 3. Methods There are millions of long-distance runners worldwide. In order to learn more about how the best of them run, 50 male and 50 female runners who finished first in four marathons were studied (EBBA runs). Furthermore, the marathon runs of the world’s best long-distance runner, Haile Gebrselassie, along with his pacemakers (different for each run), were investigated (BDBD runs). Runners of EBBA marathons were divided into groups (male and female): (A) first three at the finish line, (B) places 4 to 10, (C) places 11 to 50, (D) first 10 at finish line, (E) first 50 at finish line. For the BDBD runs, for the investigated stages of the distance, the time of the leading runner was taken into account. Gebrselassie was always among the leading group and finished first. The following EBBA marathon runs were investigated: (1) IAAF World Championships, Edmonton, 2001, (2) Boston Marathon, 2002, (3) Berlin Marathon, 2002, (4) Olympic Games, Athens, 2004. In Edmonton, during the male run (on August 3, 2001) it was cloudy, with a temperature of 19 °C. The start was at 6.45 pm. During the female run (on August 10, 2001) it was also cloudy, with a temperature of 16 °C. The start was at 8.00 am. During the Boston run (15 April 2002) the temperature was 21 °C, and it was partly cloudy, with a light headwind facing the runners. The start was at noon. The Berlin marathon took place on September 29, 2002. The temperature was 14 °C, and it was cloudy and windless. The start was at 10.00 am. In Berlin few world records were established. In 2004, at the time of the research, the male world record was 2:04:55 (2003, Paul Tergat, Kenya) and the female world record was 2:19:46 (2000, Tegla Loroupe, Kenya). During 2007–2009 the male world marathon record was established by Gebrselassie in Berlin 2007 and 2008 with runs of 2:04:23 and 2:03:59 respectively. The Olympic marathon in Athens 2004 took place along a historical course from the city of Marathon to the Olympic Stadium in Athens. The female marathon took place on 22 August 2004. The start was at 6.00 pm. There was a high temperature of 35 °C, and it was sunny, with no wind. The male marathon took place on August 29, 2004. The start was at 6.00 pm. The temperature reached 30 °C, and it was partly cloudy with a gentle wind. The following BDBD marathon runs were investigated: (1) Berlin 2007, (2) Dubai 2008, (3) Berlin 2008, (4) Dubai 2009. On the last Sunday of September about 40,000 runners (among them 30,000 foot runners) participate each year in the Berlin marathon. They start at 9.00 am. In 2007 and 2008 the temperature was 17 °C and 19 °C, respectively. Since 2000, every January, about 10,000 runners have participated in the Dubai marathon. They used to start at 7.00 am – now they start at 6.00 am. In 2008, at the start it was 15 °C and at the finish it was 20 °C. In 2009, there was light rain and the temperature was 16 °C. This is the marathon in the world with the highest price money. The winning runner is awarded a sum of 250,000 US dollars. Both Berlin and Dubai marathons meet the IAAF standards required for a run to qualify as a world record. New world records in Dubai would be rewarded with a prize of 1 million US dollars. This is an indicator of a high volitional involvement by the runner. Time data for every 5000 m, for the last 2195 m, for halves and for the entire distance were obtained from the websites of IAAF and organizing committees (www.iaaf (2001); www.bostonmarathon (2002); www.berlinmarathon (2002), 2007, 2008; www.athens, (2004), www.dubaimarathon, 2008, 2009). In addition, time data for every kilometer of the BDBD runs were gathered by Sean Hartnett of the University of Wisconsin – Eau Claire, who worked on behalf of the organizing committees (he was sitting in the car preceding the front runners). The data were given to the authors as openaccess data. Also, pace (minutes and seconds per 1 km) was obtained for different stages of the run. Distance and time data, velocities and accelerations were calculated: /1, 2/. Mean data for all groups and standard deviations and variations for groups of 50 runners were obtained.
Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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v ¼ Ddi =Dti
ð1Þ
a ¼ Dvi =Dti
ð2Þ
where D is difference, d is distance (m), t is time (s), v is velocity (m/s), a is acceleration (m/ks2), i is (a) from 1 to 9 for 5000 m and 2195 m sections and (b) from 1 to 42 for 1000 and 1195 m sections (note: since acceleration data were very small a unit of 1/ks2 = 1/1000 s2 was introduced, e.g., Dvi = 5.76 m/s5.67 m/ s = 0.09 m/s (velocity difference between two consecutive 5 km sections); Dti = 900 s (sum of half times of two consecutive 5 km sections); a = Dvi/Dti = 0.09 m/s/900 s = 0.0001 m/s2 = 100.0 m/ks2). In order to predict the end results of a run from the data of previous sections of the same run, correlation coefficients were calculated between the time of consecutive n 5 km (where n = 1. . .8) sections of the distance and the end time of the entire marathon distance obtained by the first ten runners at the finish. In terms of mechanical and steering approaches, as well as from the physiological point of view of optimal running, a long-distance run should be performed at a steady velocity (Foster, Schrager, Sny_ der, & Thompson, 1994; Maronski, 1996; Rapoport, 2010). Wazny and Sadowski (1974) stated that in endurance disciplines all deviations, if any, from that steady velocity should be within ±2%. In order to assess this assumption, an additional quantity, i.e., quotient of deviations of velocity, was established. This quotation was defined as the absolute value of the acceleration divided by the mean velocity of the distance: /3/. The smaller the quotient, the better.
Qvd ¼ jamean j=vmean
ð3Þ
where Qvd is quotient of velocity deviations, jamean is mean absolute acceleration of 9 consecutive 5000 m and 2195 m sections (m/ks2), and vmean is mean velocity of the entire distance (m/s). Mean and standard deviations were calculated for all runs. Pearson’s coefficients were calculated between: (a) time of consecutive stages of the course and end time of the first ten runners; (b) quotient of velocity deviations and place at the finish. Welch’s t-test was used to support inequality of means of the end times of the EBBA runs for groups: A (1. . .3 runners at the finish line) and B (4. . .10), A (1. . .3) and C (11. . .50), B (4. . .10) and C (11. . .50), A+B (1. . .10) and C (11. . .50). A significance level of a = .01 was adopted. 4. Results 4.1. Times of runs 4.1.1. Times of EBBA marathons For male runners the best times, when comparing all four runs, for the first, third and tenth at the finish line were obtained at the Berlin course where the profile is the easiest among all EBBA courses. Also, data for the groups of the first 3, 10 and 50 at the finish line were the best in Berlin. Among women the best times for the first, third and tenth at the finish were obtained in Boston where the first fragment of the course runs downhill. Data for the first 3 at the finish were the best in Boston, but for the first 10 and the first 50 were the best in Edmonton. Table 1 Male time data (upper line, h:min:s) and mean pace data (lower line, min:s/km) of the 1st, 3rd, 10th and 50th runners at the finish and of the groups of the first 3, 10 and 50 runners at the finish of the marathon run. Runners Courses
1st
Edmonton
2:12:42 3:08.7 2:09:02 3:03.5 2:06:47 3:00.3 2:10:56 3:06.2
Boston Berlin Athens
3rd 2:13:18 3:09.5 2:09:45 3:04.5 2:06:52 3:00.4 2:12:11 3:08.0
10th 2:17:35 3:15.6 2:12:28 3:08.4 2:10:56 3:06.2 2:14:45 3:11.6
50th 2:31:42 3:35.7 2:29:47 3:33.0 2:24:55 3:26.1 2:22:37 3:22.8
3 mean
10 mean
mean
2:12:54 3:09.0 2:09:17 3:03.8 2:06:49 3:00.3 2:11:32 3:07.0
2:15:08 3:12.2 2:10:38 3:05.8 2:09:01 3:03.5 2:13:04 3:09.2
2:23:28 3:24.0 2:20:17 3:19.5 2:16:29 3:24.1 2:17:39 3:15.7
50 SD
var.
05:32
3.86
07:02
5.01
05:30
4.03
03:27
2.51
Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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Table 2 Female time data (upper line, h:min:s) and mean pace data (lower line, min:s/km) of the 1st, 3rd, 10th and 50th runners at the finish and of the groups of the first 3, 10 and 50 runners at the finish of the marathon run. Runners Courses
1st
Edmonton
2:26:01 3:27.6 2:20:43 3:20.1 2:21:49 3:21.7 2:26:20 3:28.1
Boston Berlin Athens
3rd 2:26:18 3:28.0 2:26:01 3:27.6 2:26:10 3:27.8 2:27:20 3:29.5
10th 2:30:38 3:34.2 2:35:34 3:41.2 2:39:37 3:47.0 2:32:50 3:37.3
50th 3:14:29 4:36.5 3:00:56 4:17.3 2:58:18 4:13.5 2:50:01 4:01.8
3 mean
10 mean
mean
2:26:08 3:27.8 2:22:38 3:22.8 2:24:03 3:24.8 2:26:44 3:28.27
2:28:00 3:30.5 2:28:32 3:31.2 2:31:27 3:35.4 2:29:42 3:32.9
2:39:37 3:47.0 2:47:10 3:57.7 2:53:23 4:06.5 2:44:33 3:54.0
1
0..5 0..10 0..15 0..20 0..25 0..30 0..35 0..42
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
Correlation coefficient
Distance, km
6.85
21:36
12.46
20:24
12.40
Distance, km
Athens 2004 marathon Correlation coefficient
0..5 0..10 0..15 0..20 0..25 0..30 0..35 0..42
11:27
0..5 0..10 0..15 0..20 0..25 0..30 0..35 0..42
Berlin 2002 marathon
1
7.11
1
Distance, km
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
var.
11:20
Boston 2002 marathon Correlation coefficient
Correlation coefficient
Edmonton 2001 marathon 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
50 SD
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
1
0..5 0..10 0..15 0..20 0..25 0..30 0..35 0..42
Distance, km
Fig. 1. Correlation coefficients between time of consecutive n 5 km (where: n = 1..8) fragments of the distance and end time of the whole marathon distance obtained by the first ten runners at the finish line; dark gray – female, light gray – male data.
Since the Edmonton marathon was run for a championship and not for a record time, the results obtained among male runners were the worst for mean values of the first 3, 10 and 50 at the finish comparing all four investigated marathon runs. Among women the slowest marathon run, taking into account the first 10 and 50 competitors at the finish, was the Berlin run. Detailed data of times and pace of runners obtained at the analyzed courses are presented in Table 1 (males) and Table 2 (females). Analysis of correlation coefficients between times at consecutive sections (for every 5 km) from the start and the finish time revealed different distributions of overcoming a load. In males during the first half of the distance it is hard to predict who will be in the first ten places at the finish. Correlation coefficients are low. In Edmonton the situation became clearer only after the 25th km when runners started to run the ascending fragment of terrain. A similar situation occurred in Boston where the ascending part of the distance came between the 26th and 33rd km. In Berlin the situation started to be more predictable after half the distance. In Athens the situation became more predictable after overcoming the huge hill around the 32nd km. Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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In female runs, those in Edmonton, Boston and Berlin were predictable from the first few kilometers onwards, especially in Boston and Berlin where correlation coefficients were already high (about .8) after the first 5 km. In Athens the situation was clearer after the first half of the distance, and especially during the long ascending fragment of the run during the second half of the distance. See Fig. 1 for details. The mean end time data of the runs of the investigated groups A, B and C differed significantly. For female groups A (1. . .3 runners at the finish line) and B (4. . .10 runners) in the Boston marathon 2002 and for male groups A and B in the Athens marathon 2004, the p-value was <.01. For all other comparisons, the p-value was <.001. 4.1.2. Times of BDBD marathons At the Berlin 2007 marathon Gebrselassie ran with a few pacemakers. The last one ran with the leader up to the 30th km. Gebrselassie won the marathon with a new world record of 2 h 4 min 26 s (mean pace: 2 min 56.9 s per 1 km). At the Berlin 2008 marathon the last pacemaker ran with Gebrselassie again up to the 30th km. Gebrselassie won the run again with a new world record of 2 h 03 min 59 s (pace: 2:56.3). In the Dubai 2008 marathon Gebrselassie set out to break the world record once more. Pacemakers helped him through about 3/4 of the distance. He finished in 2 h 04 min 53 s (pace: 2:57.6). Also in the Dubai 2009 marathon Gebrselassie wanted to break the world record. Once more pacemakers helped him through about 3/4 of the distance. He won with a time of 2 h 05 min 29 s (pace: 2:58.4). 4.2. Velocity of the runs 4.2.1. Velocities of EBBA marathons Velocity curves among the men and women groups of the first 3, first 10 and first 50 runners differed significantly. Velocity curves for consecutive sections of the run were more or less ascending for the first 3 male runners, more or less horizontal for the first 10, and descending for the first 50 runners. Women’s curves were characterized by a constant descent from start to finish (except in the Athens 2004 marathon). This picture becomes even clearer if the groups of runners are ordered according to their places at the finish: 1. . .3, 4. . .10, 11. . .50 (Fig. 2). The difference in velocity between each consecutive 5000 m and the mean velocity for the entire distance was not greater than 1.5% for the first three males during the Berlin 2002 marathon. The highest difference in velocity between each consecutive 5000 m and the mean velocity for the entire distance occurred for the first three females during the Edmonton 2001 run (4.8%). But one should take into account that the course in Edmonton had a depression of about 60 m between 22 and 29 km, which affected these results. 4.2.2. Velocities of BDBD marathons At the Berlin 2007 marathon the leading group began the run with a mean velocity of 5.67 m/s (pace: 2:56.6), which was lower to 5.58 (pace: 2:59.2) during the 20th and 25th km of the run. At this point the group quickened its pace and Gebrselassie, finishing alone, obtained the peak mean velocity of 5.79 m/s (pace: 2:52.6) for the last 2.195 km. At the Berlin 2008 marathon the leading group started the run (first 5 km) with a mean velocity of 5.66 m/s (pace: 2:56.6), near the mean velocity of the entire distance. The next 5 km was run faster, i.e., with a mean velocity of 5.75 m/s (pace: 2:54.0). The next 15 km they ran with the lowest velocity of the entire run, i.e., 5.62 m/s (pace: 2:57.9). Then the velocity gradually increased to the highest value of 5.76 m/s (pace: 2:53.6) for the 35–40 km fragment of the run. At the Dubai 2008 marathon the leading group began the run with a mean velocity of 5.83 m/s (pace: 2:51.4) for the first 5 km and 5.80 m/s (pace: 2:52.4) for the second 5 km. The group then decreased its velocity to 5.49 m/s (pace: 3:02.2) between the 30th and 35th km of the run. For the last 7 km the velocity increased to 5.58 m/s (pace: 3:00.8). The following year in the Dubai 2009 marathon the leading group started the run with a velocity of 5.62 m/s (pace: 2:58.0), which was an appropriate speed, but the next 5 km were run with an average Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8
Edmonton 2001, 1..3, 4..10, 11..50 females
Velocity, m/s
Velocity, m/s
Edmonton 2001, 1..3, 4..10, 11..50 males
123456789 5 10 15
20
25
30
35
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8 123456789 5 10 15
40 43
Velocity, m/s
Velocity, m/s
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8 25
30
35
5 10 15 123456789
40 43
Velocity, m/s
Velocity, m/s 30
35
40 43
123456789 5 10
20
25
35
40 43
15
20
25
30
35
40 43
Athens 2004, 1..3, 4..10, 11..50 females
Velocity, m/s
Velocity, m/s
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8
Distance, km
30
Distance, km
Athens 2004, 1..3, 4..10, 11..50 males
15
25
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8
Distance, km
123456789 5 10
20
Berlin 2002, 1..3, 4..10, 11..50 females
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8 25
40 43
Distance, km
Berlin 2002, 1..3, 4..10, 11..50 males
20
35
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8
Distance, km
5 10 15 123456789
30
Boston 2002, 1..3, 4..10, 11..50 females
Boston 2002, 1..3, 4..10, 11..50 males
20
25
Distance, km
Distance, km
123456789 5 10 15
20
30
35
40 43
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8 123456789 5 10 15
20
25
30
35
40 43
Distance, km
Fig. 2. Velocity of the male and female runners: 1..3 – triangles and black line; 4..10 – squares and dark gray line; 11..50 – diamonds and light gray line.
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B
Marathon Berlin 2007 & 2008
5.9
5.9
5.85
5.85
5.8
5.8
5.75
5.75
Velocity (m s)
Velocity (m /s)
A
5.7 5.65 5.6
Marathon Dubai 2008 & 2009
5.7 5.65 5.6
5.55
5.55
5.5
5.5
5.45
5.45
5.4 0
1 5
5.4
2 10 3 15 4 20 5 25 6 30 7 35 8 40 9 43
0 1 5
2 10 3 15 4 20 5
25 6 30 7 35 8 40 9 43
Distance (km)
Distance (km)
Fig. 3. Gebrselassie and his pacemakers’ runs: mean velocity for 5 km fragments with trend lines are presented in A (Berlin 2007, 2008) and B (Dubai 2008, 2009). Mean data of velocity for the whole distance in Berlin 2007 and Berlin 2008 were 5.652 m/s and 5.672 m/s, respectively (both world records). Mean data of velocity for the whole distance in Dubai 2008 and Dubai 2009 were 5.631 m/s and 5.604 m/s, respectively.
A
Marathon Berlin 2007. Gebrselassie
B
6.2
Marathon Berlin 2008. Gebrselassie 6.2 6
5.8
Velocity, m/s
Velocity, m /s
6
5.6 5.4 5.2
5.8 5.6 5.4 5.2
5
5
4.8
4.8
1
4
1
7 10 13 16 19 22 25 28 31 34 37 40 43
C
Marathon Dubai 2008. Gebrselassie
D
6.2
7 10 13 16 19 22 25 28 31 34 37 40 43
Marathon Dubai 2009. Gebrselassie
6.2
6
6
Velocity, m /s
Velocity, m /s
4
Distance. km
Distance. km
5.8 5.6 5.4 5.2
5.8 5.6 5.4 5.2
5
5
4.8
4.8 1
4
7 10 13 16 19 22 25 28 31 34 37 40 43
Distance. km
1
4
7 10 13 16 19 22 25 28 31 34 37 40 43
Distance. km
Fig. 4. Gebrselassie and his pacemakers’ runs: mean velocity for 1 km fragments with mean velocity of the whole distance are presented in A and B (Berlin 2007, 2008) and C and D (Dubai 2008, 2009). The ascending mean data of velocity gave faster end time in both Berlin runs compared to those in Dubai. In all four runs there was unnecessary dispersion of 1 km fragments’ velocity values even up to 6 m/s.
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A
B
Berlin 2002, the first 3 males
Edmonton 2001, the first 3 females 400
Acceleration, m/ks2
Acceleration, m/ks2
400 300 200 100 0 1
-100
2
3
4
5
6
7
8
-200 -300 -400
300 200 100 0 -100
1
2
3
5
10
15
4
5
6
7
8
20
25
30
35
40
-200 -300 -400
5
10
15
20
25
30
35
40
Distance, km
Distance, km
Fig. 5. Acceleration of: A – the first 3 males in Berlin 2002; an example of low values of up to about 100 m/ks2 (with flat profile of the course), and B – the first 3 females in Edmonton 2001; an example of high values of up to 400 m/ks2 (with partly descending and ascending profile of the course in the middle of the distance).
velocity of 5.80 m/s (pace: 2:52.0), which was too high. Thereafter, the velocity gradually decreased up to the end of the marathon. Detailed views of the distribution of velocities of Haile Gebrselassie and his pacemakers during the BDBD marathon runs are presented in Fig. 3 for 5 km intervals and in Fig. 4 for 1 km intervals. For 1 km sections the standard deviation of 42 arguments (41 mean data of velocity of 1 km sections and the last of 1.195 km) equaled 0.085 m/s for the Berlin 2007 marathon and 0.135 m/s for the Berlin 2008 marathon. The standard deviation of 42 arguments equaled 0.136 m/s for the Dubai 2008 marathon and 0.173 m/s for the Dubai 2009 marathon.
B
Berlin 2002, 50 males
Quotient of velocity dev.
Quotient of velocity dev.
A 80 70 60 50 40 30 20 10 0 0
5
10
15
20
25
30
35
Berlin 2002, 50 females 80 70 60 50 40 30 20 10 0
43
0
5
10
D
Berlin 2002, 50 males
Quotient of velocity dev.
Quotient of velocity dev.
C 80 70 60 50 40 30 20 10 0 0
10
20
30
Place at the finish
15
20
25
30
35
43
Distance, km
Distance, km
40
50
Berlin 2002, 50 females 80 70 60 50 40 30 20 10 0 0
10
20
30
40
50
Place at the finish
Fig. 6. Quotient of velocity deviations of Berlin 2002 run: A and B along the whole distance – note that males had high values of deceleration at the beginning and at the end of a run while females had deceleration only at the end of a run; C and D according to the place at the finish – high correlation in males (r = 0.701) and no correlation in females.
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Table 3 Male and female velocity data of the first ten runners at the finish; with the velocity of the second half of the distance faster (bold), equal (normal) and slower (gray) than the first half of the distance; note that except females in Berlin 2002 always the first runners at the finish had the second half run faster than the first one.
No.
Edmonton 2001
Boston 2002
1st half
1st half
2nd half
males 1 2 3 4 5 6 7 8 9 10
5.25 5.25 5.25 5.25 5.25 5.25 5.25 5.25 5.25 5.25
males 5.35 5.35 5.30 5.25 5.24 5.12 5.03 5.02 4.99 4.98
5.38 5.38 5.38 5.38 5.38 5.38 5.38 5.38 5.38 5.38
4.89 4.89 4.87 4.89 4.77 4.72 4.72 4.70 4.64 4.49
4.97 4.97 4.97 4.97 4.89 4.83 4.93 4.63 4.71 4.73
females 11 12 13 14 15 16 17 18 19 20
4.74 4.74 4.74 4.74 4.71 4.74 4.74 4.74 4.74 4.86
Berlin 2002 2nd half
1st half
Athens 2004 2nd half
males 5.52 5.52 5.46 5.46 5.40 5.38 .5.30 5.30 5.29 5.24
5.52 5.52 5.52 5.52 5.52 5.52 5.38 5.41 5.52 5.52
5.02 4.99 4.67 4.58 4.62 4.61 4.45 4.63 4.37 4.33
4.98 4.98 4.86 4.86 4.62 4.71 4.60 4.64 4.59 4.38
females
1st half
2nd half
males 5.57 5.57 5.56 5.48 5.43 5.26 5.39 5.36 5.25 5.23
5.20 5.20 5.22 5.20 5.20 5.20 5.20 5.20 5.18 5.20
4.94 4.78 4.77 4.76 4.59 4.42 4.52 4.35 4.29 4.43
4.75 4.75 4.65 4.75 4.75 4.75 4.75 4.65 4.65 4.55
females
5.56 5.51 5.43 5.43 5.36 5.35 5.34 5.28 5.27 5.24
females 4.86 4.85 4.91 4.74 4.71 4.55 4.53 4.61 4.60 4.66
4.3. Acceleration and quotient of velocity deviations 4.3.1. Acceleration and Qvd of EBBA marathons Mean absolute acceleration data for the first 50 males in the Berlin 2002 marathon, taking into account 5 km intervals, were 176 m/ks2 (SD = 83) for the first 50 runners and less than 100 m/ks2 for the first 3 males were. For the first 50 females in the Berlin 2002 marathon the absolute acceleration reached the value of 85 (69) m/ks2. For the first three females similar values were obtained. Fig. 5 shows data for the first 3 males in the Berlin 2002 marathon (low values) and for the first 3 females in Edmonton (high values). Taking into account the acceleration relative to the mean velocity, i.e., the quotient of velocity deviation, in the Berlin 2002 marathon at the beginning of the run (0..10 km) around 1/3 out of 50 of the investigated male competitors who were the first at the finish line ran the first 5 km slower than the second 5 km; within the middle third some ran faster and some ran slower; and around the last third some ran faster and then slowed down after realizing they were running too fast. Female runners ran the second 5 km at almost the same velocity as the first. Well before the finish (at 35.42 km) around 2/3 of male runners and around 3/4 of female runners decelerated. Even the psychological influence of approaching the finish line did not help to at least maintain the velocity at the same level as before (Fig. 6A and B). Taking into account the mean quotient of velocity deviation for the entire run according to the place at the finish, there was a positive correlation in males and a lack of correlation in females (Fig. 6C and D). 4.3.2. Acceleration and Qvd of BDBD marathons Accelerations in the BDBD marathon runs of Haile Gebrselassie were small. In the Berlin 2007 and 2008 marathons they were 48 (SD = 29) and 70 (43) m/ks2, respectively, for 5 km intervals and 432 (471) and 753 (695) m/ks2, respectively, for 1 km intervals. In the Dubai 2008 and 2009 marathons they were 67 (48) and 82 (59) m/ks2, respectively, for 5 km intervals and 428 (400) and 504 (522) m/ks2, respectively, for 1 km intervals. Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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Marathon Dubai 2008. Gebrselassie. end data cumulative time. pace and velocity from the start hrs:min:sec 2:00:32 2:00:53 2:01:54 2:02:43 2:03:19 2:03:48 2:04:15 2:04:50 2:04:53 min:sec 2:51.4 2:51.9 2:53.3 2:54.5 2:55.4 2:56.0 2:56.9 2:57.5 2:57.6
5.9 5.85 Velocity. m/s
5.8 5.75
.
5.7 5.65 5.6 5.55 5.5
1 0..5
2 0..10
3 0..15
4 0..20
5 0..25
6 0..30
7 0..35
8 0..40
9 0..42
Distance. km
Fig. 7. Cumulative time, pace and velocity of Dubai 2008 run. Up to the 15th km Gebrselassie and his pacemakers ran for a new world record below 2 h and 2 min which was at that time not affordable.
Quotients of velocity deviation for the Berlin 2007 and 2008 marathons were 8.4 and 7.7, respectively, for 5 km intervals and 76.5 and 132.8, respectively, for 1 km intervals. In the Dubai 2008 and 2009 marathons they were 8.6 and 10.4, respectively, for 5 km and 76.0 and 93.0, respectively, for 1 km intervals. 5. Discussion Martin and Gynn (2000) presented Olympic marathon data for 100 years. From all participants (around 1500 runners, among whom 221 women) 26.5% of men and 15.9% of women did not complete their race. One contestant even died while running. It is supposed in most cases that the reason for this large number of failures was improper running tactics, i.e., too intense running from the beginning of the run and unsteady running during the entire course of the event. De Koning et al. (2011), investigating a Hazard score (dealing with changes of velocity during an event) problem, presented an acceleration/deceleration curve (change in pace) showing a steady lowering of data from above to below 0% (which was defined as the steady pace). This shape of curve was obtained for good runners but not for the best. It agrees with the shape of curves obtained in this work for runners worse than the first ten at the finish. The best runners at the finish, in particular male runners, showed a more or less increasing velocity in almost all marathons under investigation (Table 3). This kind of velocity distribution seems to be best for running long distances. Runners who were among the first three at the finish line had a more or less ascending velocity line, while those finishing 4th to 10th were more or less stable, and those finishing 11th to 50th had a descending line. The present data provide evidence for the hypothesis that the smaller the deviations of the mean velocity during the marathon, the better. The quotient of velocity deviations equaled about 10 or less for the best runners, especially for male runners. Absolute acceleration and the quotient of velocity deviation were higher for the first and last stages of the Berlin 2002 marathon, where the profile of the course was flat and did not influence the velocity and acceleration of the running. The highest values of absolute acceleration and quotient of velocity deviation were associated with the worst runners. Male marathon running is characterized by a higher velocity (which is good) and by higher deviations of velocity, i.e., by higher acceleration (which is not good), than female marathon running. More males than females ran the second leg faster than the first. The female runs are more predictable than male runs when one takes into account time results from consecutive sections of the distance. The quotient of velocity deviation was high in male runners and close to zero in female runners. Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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A
Marathon. males. predicted time 2:03:00
min:sec 2:56.1 2:55.7 2:55.4 2:55.1 2:54.8 2:54.5 2:54.2 2:53.9 2:53.6 5.8
Velocity, m/s
5.7 5.6 5.5 5.4 5.3 5.2 5.1 1 0..5
2 5..10
3 4 10..15 15..20
5 6 7 8 9 20..25 25..30 30..35 35..40 40..42
Distance. km
B
Marathon. females. predicted time 2:15:00
min:sec 3:13.4 3:13.1 3:12.7 3:12.3 3:11.9 3:11.6 3:10.8 3:10.5 3:10.5 5.8
Velocity. m/s
5.7 5.6 5.5 5.4 5.3 5.2 5.1 1 0..5
2 5..10
3 4 10..15 15..20
5 6 7 8 9 20..25 25..30 30..35 35..40 40..42
Distance. km Fig. 8. Distribution of velocity and pace for prediction of the new world records with times of 2 h:03 min for males (A) and 2 h:15 min for females (B).
Haile Gebrselassie and his pacemakers provided telling examples of both good and bad running tactics. The world’s top long-distance runner ran with different tactics in different runs when attempting to break the current world record. Record runs during the Berlin 2007 and 2008 marathon had a lower velocity during the first half and a higher velocity in the second half of the course. Also, the velocity during every 1 km section deviated only very little from the mean velocity during the entire marathon. In contrast, the Dubai runs were performed in an incorrect manner, i.e., with too high a velocity at the start followed by a decrease in velocity. Velocity deviations for every 1 km section were higher in Dubai than in Berlin. Taking into account the actual velocity of the run and prediction of the end time based on that velocity, Berlin end times (calculated for the 2007 and 2008 runs) were similar to those of real end times. Unfortunately, in Dubai the end time predicted from the current velocity deviated strongly from the actual end time. If a runner in 2008 would have run the entire marathon with the velocity of the first 5 kilometers up, he would have established a highly improbable new world record of 2 h 00 min 32 s. Also, the next stages were run at a much too high velocity (see Fig. 7). It is important to establish proper tactics with pacemakers. Even if they feel well on the day of running and want to run faster, it is not recommended to do so over the first stages of the marathon. Instead, they need to run at the established velocity. Before the run, runners should establish by themselves, or with the help of their coach, suitable tactics for the particular run based on the purpose of the run, their overall fitness and specific fitness on the day of the run, the weather conditions, the profile of the course, and the level of other runners. Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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The role of pacemakers is to assist the main runner along the course for physical and psychological purposes. The former takes into account the lowering of air drag. Here pacemakers should run just in front of the main runner in order to form a shield against air drag for the main runner. Unfortunately, pacemakers do not always run this way. The latter takes into account better mobilization for a run if someone runs within a group of other runners. Neville and Whyte (2005) presented a paper on future world records in middle- and long-distance running. In their prediction they used extrapolation of a curve based on records recorded throughout the 20th century. The new record model presented in this article applies a proposal of a distribution of a load (velocity) which would be characterized by constant slow acceleration of a movement with very small deviations from the main ascending line. Fig. 8 presents the proposed distribution of velocity and pace along a course in order for male and female runners to achieve a new world record. 6. Final remarks In marathon running – and the same applies to other long-distance runs – the mean velocity should be a little bit lower for the first half than for the second half of the run. Deviations of the ascending line of velocity should be minimized, i.e., acceleration needs to be always low and positive, and not exceed a value of 50 m/ks2. In order to get feedback on how the run is being performed, it is recommended that runners wear instruments, based on global navigation satellite system technology, which provide all the necessary information (velocity or pace, distance to the end, etc.) that allow them to run in accordance with the recommendations that follow from this study. Results obtained within the field of long-distance running may be extrapolated to other sports and physiological activities involved sustained high effort, e.g., competitions for triathletes, racewalkers, swimmers, rowers and other sportspersons. Likewise, workers in construction, forestry, metallurgy and in other heavy industries, as well as tourists, explorers and military personnel, are all well advised to start their work or locomotion with a moderate level of effort before raising it gradually in order to ensure a lower first-stage effort level and a higher second-stage effort level. References Arska, M. (1972). Distribution of times in marathon and race walking (in Polish). Sport Wyczynowy (Competetive Sport), 1, 48–49. de Koning, J. J., Foster, C., Bakkum, A., Kloppenburg, S., Thiel, Ch., Joseph, T., et al (2011). Regulation of pacing strategy during athletic competition. PLoS One, 6(1), e15863. Erdmann, W. S., & Lipinska, P. (2003b). Investigations of women marathon Berlin 2002 based on time and velocity and track profile (in Polish, English summary). Acta of Bioengineering and Biomechanics, 5(Suppl. 1), 144–149. Erdmann, W. S., & Lipinska, P. (2006). Kinematics of marathon running’s tactics. Part one: Course profile. In H. Schwameder, G. Strutzenberger, V. Fastenbauer, S. Lindinger, & E. Müller (Eds.). XXIV International Symposium on Biomechanics in Sports. Proceedings (Vol. 2, pp. 689–692). Salzburg, Austria: University of Salzburg. Erdmann, W. S., & Lipinska, P. (2003a). Analysis of tactics of women’s marathon run in Boston 2002 based on mean velocity of runners and profile of a track (in Polish). In K. Prusik (Ed.), Athletics in theory and practice (pp. 283–288). Bydgoszcz: Sport Editors. Foster, C., Schrager, M., Snyder, A. C., & Thompson, N. N. (1994). Pacing strategy and athletic performance. Sports Medicine, 17, 77–85. Gabrys, T., & Celeban, A. (1996). Velocity and tactical approach in long distance running of 5000 and 10,000 m (in Polish). Lekkoatleta (Track and Field Athlete), 7(8), 49–52. Joyner, M. J., Ruiz, J. R., & Lucia, A. (2011). The two-hour marathon: Who and when? Journal of Applied Physiology, 110, 275–277. Lipinska, P. (2006). Kinematic quantities and geometry of a course and tactics of marathon run (in Polish). Doctoral dissertation, Gdansk: J. Sniadecki University of Physical Education and Sport. Lipinska, P., & Erdmann, W. S. (2007). Kinematics of marathon running. Part two: Distribution of velocity. In H. Menzel & M. H. Chagas (Eds.), XXV International Symposium on Biomechanics in Sports. Proceedings (pp. 483–486). Belo Horizonte, M.G.: University of Minas Gerais. Lucia, A., Olivan, J., Bravo, J., Gonzales-Freire, M., & Foster, C. (2008). The key to top-level endurance running performance: A unique example. British Journal of Sports Medicine, 42, 172–174. Maronski, R. (1996). Minimum-time running and swimming: An optimal control approach. Journal of Biomechanics, 29, 245–249. Martin, D. E., & Gynn, R. W. H. (2000). The Olympic marathon. Champaign, Ill.: Human Kinetics. Neville, A. M., & Whyte, G. (2005). Are there limits to running world records? Medicine & Science in Sport & Exercise, 37, 1785–1788. Noakes, T. (2000). Physiological models to understand exercise fatigue and the adaptations that predict or enhance athletic performance. Scandinavion Journal of Medicine and Science in Sports, 10, 123–145.
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Noakes, T. (2003). Lore of running (4th ed.). Human Kinetics: Champaign, Ill. Rapoport, B. I. (2010). Metabolic factors limiting performance in marathon runners. PLoS Computational Biology, 6(10), e1000960. Sadowski, J. (2009). Science in Olympic preparations – inter-disciplinarity, trend to innovations. In J. Czerwinski & H. Sozanski (Eds.), Contemporary Olympic sport (pp. 95–111). Gdansk, Poland: J. Sniadecki University School of Physical Education and Sport. Shephard, R. J., & Åstrand, P.-O. (Eds.). (2000). Endurance in sport (2nd ed.). International Olympic Committee Medical Commission, International Federation of Sports Medicine. Oxford, UK: Blackwell Science. Sozanski, H. (2007). Science in sport – theory and practice. Wychowanie Fizyczne i Sport/Physical Education and Sport, 51, 141–147. _ Wazny, Z., & Sadowski, G. (1974). Problems of tactics in endurance disciplines of cyclical character of movements (in Polish). Kultura Fizyczna (Physical Culture), 10, 439–443. Williams, K. R. (2007). Biomechanical factors contributing to marathon race success. Sports Medicine, 37, 420–423.
Web pages www.aims-association.org (1997) Yearbook (pp. 49–52). Association of International Road Races – retrieved 2004. www.athens2004.com/results (2004) – retrieved 2004. www.berlinmarathon.de (2002) – retrieved 2004. www.bostonmarathon.org (2002) – retrieved 2004. www.iaaf.results (2001) – retrieved 2004. www.iaaf.rules (2009) Competition Rules 2010–2011 (pp. 224–225). Monte Carlo, Monaco: International Association of Athletic Federations – retrieved 2011.
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Kinematics of marathon running tactics Wlodzimierz S. Erdmann ⇑, Patrycja Lipinska J. Sniadecki University School of Physical Education and Sport, Gdansk, Poland
a r t i c l e
i n f o
a b s t r a c t
Article history: Available online xxxx
Ó 2013 Elsevier B.V. All rights reserved.
PsycINFO classification: 3720 Keywords: Marathon running Tactics Kinematics Pacing Top runners Gebrselassie
1. Introduction Many human activities requiring strenuous effort are often performed in an incorrect manner, with may lead to early exhaustion. Among other factors, this may be caused by an inappropriate distribution of effort over the course of an event, as is in long-distance running. Long-distance runners usually have the following general aims in mind in designing their running tactics: (1) to end first at the finish line (not necessarily with the best time ever), usually in regular championships, or (2) to run the best possible time so as to break a record. Studies of running tactics are very helpful for both runner and coach in determining the ideal tactics for a particular future run (Arska, 1972; Gabrys & Celeban, 1996; Sozanski, 2007). Noakes (2000, 2003), Lucia, Olivan, Bravo, Gonzales-Freire, and Foster (2008) and Joyner, Ruiz, and Lucia (2011) all investigated the efficiency of running. They concluded that in order to achieve a very good result in marathon running (42,195 m), running economy constitutes one of the most important
⇑ Corresponding author. Address: Department of Biomechanics and Sport Engineering, J. Sniadecki University School of Physical Education and Sport, 1 Gorskiego Str., Gdansk 80-336, Poland. Tel.: +48 60 5304939 (mobile), +48 58 5547105 (office), fax: +48 58 5547166. E-mail address: [email protected] (W.S. Erdmann). 0167-9457/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.humov.2013.07.006
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features defining the successful runner. According to Williams (2007), it is not easy to identify and universally apply patterns of efficient movement for runners. These patterns still not to be found. Erdmann and Lipinska (2003a, 2003b, 2006), Lipinska (2006), Lipinska and Erdmann (2007) investigated marathon running at the highest competitive level by examining the velocity distribution during marathon running. The following example illustrates the kind of data and insights obtained. In the Berlin 2002 marathon, the female runner Takahashi attempted to break the world record. She ran the first 5 km at a mean velocity higher than 5.00 m/s. This was too fast since the mean velocity for the female marathon world’s best run was at that time 5.07 m/s. Her velocity gradually decreased in the course of the race, resulting in a lower velocity during the second part of the run than during the first. Her mission to break the world record failed (Erdmann & Lipinska, 2003b). Within the theory of a particular sport discipline different models are employed, among which scientific models are crucial. A scientific model incorporates a theoretical approach, which takes into account all the necessary quantities and their values that scientists believe must be included in the perfect competitor (a master). Scientific models may be rooted in exercise physiology, biomechanics, psychology and other disciplines (Shephard & Astrand, 2000; Noakes, 2000; Sadowski, 2009; Sozanski, 2007). Practically meaningful scientific models for long-distance running speak to issues of strategy and tactics. Strategy, among other important problems, takes into account which players the team will comprise during a race, or which runners will participate in the competition as leading runners or as pacemakers. Different pacemakers are chosen for different races. Unfortunately, they are usually selected a short time before a run and sometimes there is not enough time to prepare properly for the run in case of an initiative to establish a new record time. In addition to biomechanical quantities (work and power), runners use an index called ‘‘pacing’’, which indicates how many minutes a runner should take to run one or more kilometers. During competition this index helps runners to adopt proper tactics by taking into account the load distribution during the event. The load is measured as the velocity at which runners run the distance. For long-distance running, especially for a marathon run, a group model is available at present, based on Ethiopians and Kenyans. For over 10 years, the world long-distance running model of a master, especially in marathon running, has been personified in Haile Gebre Selassie or Gebrselassie (Ethiopia). He is considered by many to be the greatest long-distance runner of all time.
2. Concept of the work The aims of the present research were: (1) to examine pacing protocols, i.e., manners of load (velocity) distribution along the course by elite marathon runners, (2) to formulate recommendations for proper running tactics through proper load distribution, (3) to investigate the pacing of running of the long-time world’s best long-distance runner. We had the following hypotheses: (1) distribution of a load (velocity) during a marathon run should resemble an ascending line through the entire course; (2) fewer and smaller deviations from the line of running velocity are characterized by better results; (3) the world’s top long-distance runner runs with similar tactics in different runs when attempting to break the world record. We were further interested in finding answers to the following questions: (1) What are the characteristics of the pacing for the first runners at the finish line and for those further back? (2) What is a runner’s tactical approach to the first and last kilometers of the run? (3) What is the difference between velocities for the first and second parts of the run? (4) What are the velocity deviations, i.e., what accelerations and decelerations are made during the entire run? (5) Can the end results be predicted from the early stages of the run? (6) What are the differences between male and female marathon running? (7) How does the world’s top runner run consecutive stages of a marathon run when breaking or seeking to break the world record? (8) Does the world’s top runner run different races in the same manner?
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(9) What are the best tactics for breaking a world record in a marathon run? (10) What is the role of pacemakers in a run aimed at breaking a world record? 3. Methods There are millions of long-distance runners worldwide. In order to learn more about how the best of them run, 50 male and 50 female runners who finished first in four marathons were studied (EBBA runs). Furthermore, the marathon runs of the world’s best long-distance runner, Haile Gebrselassie, along with his pacemakers (different for each run), were investigated (BDBD runs). Runners of EBBA marathons were divided into groups (male and female): (A) first three at the finish line, (B) places 4 to 10, (C) places 11 to 50, (D) first 10 at finish line, (E) first 50 at finish line. For the BDBD runs, for the investigated stages of the distance, the time of the leading runner was taken into account. Gebrselassie was always among the leading group and finished first. The following EBBA marathon runs were investigated: (1) IAAF World Championships, Edmonton, 2001, (2) Boston Marathon, 2002, (3) Berlin Marathon, 2002, (4) Olympic Games, Athens, 2004. In Edmonton, during the male run (on August 3, 2001) it was cloudy, with a temperature of 19 °C. The start was at 6.45 pm. During the female run (on August 10, 2001) it was also cloudy, with a temperature of 16 °C. The start was at 8.00 am. During the Boston run (15 April 2002) the temperature was 21 °C, and it was partly cloudy, with a light headwind facing the runners. The start was at noon. The Berlin marathon took place on September 29, 2002. The temperature was 14 °C, and it was cloudy and windless. The start was at 10.00 am. In Berlin few world records were established. In 2004, at the time of the research, the male world record was 2:04:55 (2003, Paul Tergat, Kenya) and the female world record was 2:19:46 (2000, Tegla Loroupe, Kenya). During 2007–2009 the male world marathon record was established by Gebrselassie in Berlin 2007 and 2008 with runs of 2:04:23 and 2:03:59 respectively. The Olympic marathon in Athens 2004 took place along a historical course from the city of Marathon to the Olympic Stadium in Athens. The female marathon took place on 22 August 2004. The start was at 6.00 pm. There was a high temperature of 35 °C, and it was sunny, with no wind. The male marathon took place on August 29, 2004. The start was at 6.00 pm. The temperature reached 30 °C, and it was partly cloudy with a gentle wind. The following BDBD marathon runs were investigated: (1) Berlin 2007, (2) Dubai 2008, (3) Berlin 2008, (4) Dubai 2009. On the last Sunday of September about 40,000 runners (among them 30,000 foot runners) participate each year in the Berlin marathon. They start at 9.00 am. In 2007 and 2008 the temperature was 17 °C and 19 °C, respectively. Since 2000, every January, about 10,000 runners have participated in the Dubai marathon. They used to start at 7.00 am – now they start at 6.00 am. In 2008, at the start it was 15 °C and at the finish it was 20 °C. In 2009, there was light rain and the temperature was 16 °C. This is the marathon in the world with the highest price money. The winning runner is awarded a sum of 250,000 US dollars. Both Berlin and Dubai marathons meet the IAAF standards required for a run to qualify as a world record. New world records in Dubai would be rewarded with a prize of 1 million US dollars. This is an indicator of a high volitional involvement by the runner. Time data for every 5000 m, for the last 2195 m, for halves and for the entire distance were obtained from the websites of IAAF and organizing committees (www.iaaf (2001); www.bostonmarathon (2002); www.berlinmarathon (2002), 2007, 2008; www.athens, (2004), www.dubaimarathon, 2008, 2009). In addition, time data for every kilometer of the BDBD runs were gathered by Sean Hartnett of the University of Wisconsin – Eau Claire, who worked on behalf of the organizing committees (he was sitting in the car preceding the front runners). The data were given to the authors as openaccess data. Also, pace (minutes and seconds per 1 km) was obtained for different stages of the run. Distance and time data, velocities and accelerations were calculated: /1, 2/. Mean data for all groups and standard deviations and variations for groups of 50 runners were obtained.
Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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W.S. Erdmann, P. Lipinska / Human Movement Science xxx (2013) xxx–xxx
v ¼ Ddi =Dti
ð1Þ
a ¼ Dvi =Dti
ð2Þ
where D is difference, d is distance (m), t is time (s), v is velocity (m/s), a is acceleration (m/ks2), i is (a) from 1 to 9 for 5000 m and 2195 m sections and (b) from 1 to 42 for 1000 and 1195 m sections (note: since acceleration data were very small a unit of 1/ks2 = 1/1000 s2 was introduced, e.g., Dvi = 5.76 m/s5.67 m/ s = 0.09 m/s (velocity difference between two consecutive 5 km sections); Dti = 900 s (sum of half times of two consecutive 5 km sections); a = Dvi/Dti = 0.09 m/s/900 s = 0.0001 m/s2 = 100.0 m/ks2). In order to predict the end results of a run from the data of previous sections of the same run, correlation coefficients were calculated between the time of consecutive n 5 km (where n = 1. . .8) sections of the distance and the end time of the entire marathon distance obtained by the first ten runners at the finish. In terms of mechanical and steering approaches, as well as from the physiological point of view of optimal running, a long-distance run should be performed at a steady velocity (Foster, Schrager, Sny_ der, & Thompson, 1994; Maronski, 1996; Rapoport, 2010). Wazny and Sadowski (1974) stated that in endurance disciplines all deviations, if any, from that steady velocity should be within ±2%. In order to assess this assumption, an additional quantity, i.e., quotient of deviations of velocity, was established. This quotation was defined as the absolute value of the acceleration divided by the mean velocity of the distance: /3/. The smaller the quotient, the better.
Qvd ¼ jamean j=vmean
ð3Þ
where Qvd is quotient of velocity deviations, jamean is mean absolute acceleration of 9 consecutive 5000 m and 2195 m sections (m/ks2), and vmean is mean velocity of the entire distance (m/s). Mean and standard deviations were calculated for all runs. Pearson’s coefficients were calculated between: (a) time of consecutive stages of the course and end time of the first ten runners; (b) quotient of velocity deviations and place at the finish. Welch’s t-test was used to support inequality of means of the end times of the EBBA runs for groups: A (1. . .3 runners at the finish line) and B (4. . .10), A (1. . .3) and C (11. . .50), B (4. . .10) and C (11. . .50), A+B (1. . .10) and C (11. . .50). A significance level of a = .01 was adopted. 4. Results 4.1. Times of runs 4.1.1. Times of EBBA marathons For male runners the best times, when comparing all four runs, for the first, third and tenth at the finish line were obtained at the Berlin course where the profile is the easiest among all EBBA courses. Also, data for the groups of the first 3, 10 and 50 at the finish line were the best in Berlin. Among women the best times for the first, third and tenth at the finish were obtained in Boston where the first fragment of the course runs downhill. Data for the first 3 at the finish were the best in Boston, but for the first 10 and the first 50 were the best in Edmonton. Table 1 Male time data (upper line, h:min:s) and mean pace data (lower line, min:s/km) of the 1st, 3rd, 10th and 50th runners at the finish and of the groups of the first 3, 10 and 50 runners at the finish of the marathon run. Runners Courses
1st
Edmonton
2:12:42 3:08.7 2:09:02 3:03.5 2:06:47 3:00.3 2:10:56 3:06.2
Boston Berlin Athens
3rd 2:13:18 3:09.5 2:09:45 3:04.5 2:06:52 3:00.4 2:12:11 3:08.0
10th 2:17:35 3:15.6 2:12:28 3:08.4 2:10:56 3:06.2 2:14:45 3:11.6
50th 2:31:42 3:35.7 2:29:47 3:33.0 2:24:55 3:26.1 2:22:37 3:22.8
3 mean
10 mean
mean
2:12:54 3:09.0 2:09:17 3:03.8 2:06:49 3:00.3 2:11:32 3:07.0
2:15:08 3:12.2 2:10:38 3:05.8 2:09:01 3:03.5 2:13:04 3:09.2
2:23:28 3:24.0 2:20:17 3:19.5 2:16:29 3:24.1 2:17:39 3:15.7
50 SD
var.
05:32
3.86
07:02
5.01
05:30
4.03
03:27
2.51
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Table 2 Female time data (upper line, h:min:s) and mean pace data (lower line, min:s/km) of the 1st, 3rd, 10th and 50th runners at the finish and of the groups of the first 3, 10 and 50 runners at the finish of the marathon run. Runners Courses
1st
Edmonton
2:26:01 3:27.6 2:20:43 3:20.1 2:21:49 3:21.7 2:26:20 3:28.1
Boston Berlin Athens
3rd 2:26:18 3:28.0 2:26:01 3:27.6 2:26:10 3:27.8 2:27:20 3:29.5
10th 2:30:38 3:34.2 2:35:34 3:41.2 2:39:37 3:47.0 2:32:50 3:37.3
50th 3:14:29 4:36.5 3:00:56 4:17.3 2:58:18 4:13.5 2:50:01 4:01.8
3 mean
10 mean
mean
2:26:08 3:27.8 2:22:38 3:22.8 2:24:03 3:24.8 2:26:44 3:28.27
2:28:00 3:30.5 2:28:32 3:31.2 2:31:27 3:35.4 2:29:42 3:32.9
2:39:37 3:47.0 2:47:10 3:57.7 2:53:23 4:06.5 2:44:33 3:54.0
1
0..5 0..10 0..15 0..20 0..25 0..30 0..35 0..42
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
Correlation coefficient
Distance, km
6.85
21:36
12.46
20:24
12.40
Distance, km
Athens 2004 marathon Correlation coefficient
0..5 0..10 0..15 0..20 0..25 0..30 0..35 0..42
11:27
0..5 0..10 0..15 0..20 0..25 0..30 0..35 0..42
Berlin 2002 marathon
1
7.11
1
Distance, km
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
var.
11:20
Boston 2002 marathon Correlation coefficient
Correlation coefficient
Edmonton 2001 marathon 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
50 SD
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
1
0..5 0..10 0..15 0..20 0..25 0..30 0..35 0..42
Distance, km
Fig. 1. Correlation coefficients between time of consecutive n 5 km (where: n = 1..8) fragments of the distance and end time of the whole marathon distance obtained by the first ten runners at the finish line; dark gray – female, light gray – male data.
Since the Edmonton marathon was run for a championship and not for a record time, the results obtained among male runners were the worst for mean values of the first 3, 10 and 50 at the finish comparing all four investigated marathon runs. Among women the slowest marathon run, taking into account the first 10 and 50 competitors at the finish, was the Berlin run. Detailed data of times and pace of runners obtained at the analyzed courses are presented in Table 1 (males) and Table 2 (females). Analysis of correlation coefficients between times at consecutive sections (for every 5 km) from the start and the finish time revealed different distributions of overcoming a load. In males during the first half of the distance it is hard to predict who will be in the first ten places at the finish. Correlation coefficients are low. In Edmonton the situation became clearer only after the 25th km when runners started to run the ascending fragment of terrain. A similar situation occurred in Boston where the ascending part of the distance came between the 26th and 33rd km. In Berlin the situation started to be more predictable after half the distance. In Athens the situation became more predictable after overcoming the huge hill around the 32nd km. Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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W.S. Erdmann, P. Lipinska / Human Movement Science xxx (2013) xxx–xxx
In female runs, those in Edmonton, Boston and Berlin were predictable from the first few kilometers onwards, especially in Boston and Berlin where correlation coefficients were already high (about .8) after the first 5 km. In Athens the situation was clearer after the first half of the distance, and especially during the long ascending fragment of the run during the second half of the distance. See Fig. 1 for details. The mean end time data of the runs of the investigated groups A, B and C differed significantly. For female groups A (1. . .3 runners at the finish line) and B (4. . .10 runners) in the Boston marathon 2002 and for male groups A and B in the Athens marathon 2004, the p-value was <.01. For all other comparisons, the p-value was <.001. 4.1.2. Times of BDBD marathons At the Berlin 2007 marathon Gebrselassie ran with a few pacemakers. The last one ran with the leader up to the 30th km. Gebrselassie won the marathon with a new world record of 2 h 4 min 26 s (mean pace: 2 min 56.9 s per 1 km). At the Berlin 2008 marathon the last pacemaker ran with Gebrselassie again up to the 30th km. Gebrselassie won the run again with a new world record of 2 h 03 min 59 s (pace: 2:56.3). In the Dubai 2008 marathon Gebrselassie set out to break the world record once more. Pacemakers helped him through about 3/4 of the distance. He finished in 2 h 04 min 53 s (pace: 2:57.6). Also in the Dubai 2009 marathon Gebrselassie wanted to break the world record. Once more pacemakers helped him through about 3/4 of the distance. He won with a time of 2 h 05 min 29 s (pace: 2:58.4). 4.2. Velocity of the runs 4.2.1. Velocities of EBBA marathons Velocity curves among the men and women groups of the first 3, first 10 and first 50 runners differed significantly. Velocity curves for consecutive sections of the run were more or less ascending for the first 3 male runners, more or less horizontal for the first 10, and descending for the first 50 runners. Women’s curves were characterized by a constant descent from start to finish (except in the Athens 2004 marathon). This picture becomes even clearer if the groups of runners are ordered according to their places at the finish: 1. . .3, 4. . .10, 11. . .50 (Fig. 2). The difference in velocity between each consecutive 5000 m and the mean velocity for the entire distance was not greater than 1.5% for the first three males during the Berlin 2002 marathon. The highest difference in velocity between each consecutive 5000 m and the mean velocity for the entire distance occurred for the first three females during the Edmonton 2001 run (4.8%). But one should take into account that the course in Edmonton had a depression of about 60 m between 22 and 29 km, which affected these results. 4.2.2. Velocities of BDBD marathons At the Berlin 2007 marathon the leading group began the run with a mean velocity of 5.67 m/s (pace: 2:56.6), which was lower to 5.58 (pace: 2:59.2) during the 20th and 25th km of the run. At this point the group quickened its pace and Gebrselassie, finishing alone, obtained the peak mean velocity of 5.79 m/s (pace: 2:52.6) for the last 2.195 km. At the Berlin 2008 marathon the leading group started the run (first 5 km) with a mean velocity of 5.66 m/s (pace: 2:56.6), near the mean velocity of the entire distance. The next 5 km was run faster, i.e., with a mean velocity of 5.75 m/s (pace: 2:54.0). The next 15 km they ran with the lowest velocity of the entire run, i.e., 5.62 m/s (pace: 2:57.9). Then the velocity gradually increased to the highest value of 5.76 m/s (pace: 2:53.6) for the 35–40 km fragment of the run. At the Dubai 2008 marathon the leading group began the run with a mean velocity of 5.83 m/s (pace: 2:51.4) for the first 5 km and 5.80 m/s (pace: 2:52.4) for the second 5 km. The group then decreased its velocity to 5.49 m/s (pace: 3:02.2) between the 30th and 35th km of the run. For the last 7 km the velocity increased to 5.58 m/s (pace: 3:00.8). The following year in the Dubai 2009 marathon the leading group started the run with a velocity of 5.62 m/s (pace: 2:58.0), which was an appropriate speed, but the next 5 km were run with an average Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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W.S. Erdmann, P. Lipinska / Human Movement Science xxx (2013) xxx–xxx
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8
Edmonton 2001, 1..3, 4..10, 11..50 females
Velocity, m/s
Velocity, m/s
Edmonton 2001, 1..3, 4..10, 11..50 males
123456789 5 10 15
20
25
30
35
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8 123456789 5 10 15
40 43
Velocity, m/s
Velocity, m/s
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8 25
30
35
5 10 15 123456789
40 43
Velocity, m/s
Velocity, m/s 30
35
40 43
123456789 5 10
20
25
35
40 43
15
20
25
30
35
40 43
Athens 2004, 1..3, 4..10, 11..50 females
Velocity, m/s
Velocity, m/s
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8
Distance, km
30
Distance, km
Athens 2004, 1..3, 4..10, 11..50 males
15
25
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8
Distance, km
123456789 5 10
20
Berlin 2002, 1..3, 4..10, 11..50 females
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8 25
40 43
Distance, km
Berlin 2002, 1..3, 4..10, 11..50 males
20
35
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8
Distance, km
5 10 15 123456789
30
Boston 2002, 1..3, 4..10, 11..50 females
Boston 2002, 1..3, 4..10, 11..50 males
20
25
Distance, km
Distance, km
123456789 5 10 15
20
30
35
40 43
5.8 5.6 5.4 5.2 5 4.8 4.6 4.4 4.2 4 3.8 123456789 5 10 15
20
25
30
35
40 43
Distance, km
Fig. 2. Velocity of the male and female runners: 1..3 – triangles and black line; 4..10 – squares and dark gray line; 11..50 – diamonds and light gray line.
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W.S. Erdmann, P. Lipinska / Human Movement Science xxx (2013) xxx–xxx
B
Marathon Berlin 2007 & 2008
5.9
5.9
5.85
5.85
5.8
5.8
5.75
5.75
Velocity (m s)
Velocity (m /s)
A
5.7 5.65 5.6
Marathon Dubai 2008 & 2009
5.7 5.65 5.6
5.55
5.55
5.5
5.5
5.45
5.45
5.4 0
1 5
5.4
2 10 3 15 4 20 5 25 6 30 7 35 8 40 9 43
0 1 5
2 10 3 15 4 20 5
25 6 30 7 35 8 40 9 43
Distance (km)
Distance (km)
Fig. 3. Gebrselassie and his pacemakers’ runs: mean velocity for 5 km fragments with trend lines are presented in A (Berlin 2007, 2008) and B (Dubai 2008, 2009). Mean data of velocity for the whole distance in Berlin 2007 and Berlin 2008 were 5.652 m/s and 5.672 m/s, respectively (both world records). Mean data of velocity for the whole distance in Dubai 2008 and Dubai 2009 were 5.631 m/s and 5.604 m/s, respectively.
A
Marathon Berlin 2007. Gebrselassie
B
6.2
Marathon Berlin 2008. Gebrselassie 6.2 6
5.8
Velocity, m/s
Velocity, m /s
6
5.6 5.4 5.2
5.8 5.6 5.4 5.2
5
5
4.8
4.8
1
4
1
7 10 13 16 19 22 25 28 31 34 37 40 43
C
Marathon Dubai 2008. Gebrselassie
D
6.2
7 10 13 16 19 22 25 28 31 34 37 40 43
Marathon Dubai 2009. Gebrselassie
6.2
6
6
Velocity, m /s
Velocity, m /s
4
Distance. km
Distance. km
5.8 5.6 5.4 5.2
5.8 5.6 5.4 5.2
5
5
4.8
4.8 1
4
7 10 13 16 19 22 25 28 31 34 37 40 43
Distance. km
1
4
7 10 13 16 19 22 25 28 31 34 37 40 43
Distance. km
Fig. 4. Gebrselassie and his pacemakers’ runs: mean velocity for 1 km fragments with mean velocity of the whole distance are presented in A and B (Berlin 2007, 2008) and C and D (Dubai 2008, 2009). The ascending mean data of velocity gave faster end time in both Berlin runs compared to those in Dubai. In all four runs there was unnecessary dispersion of 1 km fragments’ velocity values even up to 6 m/s.
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W.S. Erdmann, P. Lipinska / Human Movement Science xxx (2013) xxx–xxx
A
B
Berlin 2002, the first 3 males
Edmonton 2001, the first 3 females 400
Acceleration, m/ks2
Acceleration, m/ks2
400 300 200 100 0 1
-100
2
3
4
5
6
7
8
-200 -300 -400
300 200 100 0 -100
1
2
3
5
10
15
4
5
6
7
8
20
25
30
35
40
-200 -300 -400
5
10
15
20
25
30
35
40
Distance, km
Distance, km
Fig. 5. Acceleration of: A – the first 3 males in Berlin 2002; an example of low values of up to about 100 m/ks2 (with flat profile of the course), and B – the first 3 females in Edmonton 2001; an example of high values of up to 400 m/ks2 (with partly descending and ascending profile of the course in the middle of the distance).
velocity of 5.80 m/s (pace: 2:52.0), which was too high. Thereafter, the velocity gradually decreased up to the end of the marathon. Detailed views of the distribution of velocities of Haile Gebrselassie and his pacemakers during the BDBD marathon runs are presented in Fig. 3 for 5 km intervals and in Fig. 4 for 1 km intervals. For 1 km sections the standard deviation of 42 arguments (41 mean data of velocity of 1 km sections and the last of 1.195 km) equaled 0.085 m/s for the Berlin 2007 marathon and 0.135 m/s for the Berlin 2008 marathon. The standard deviation of 42 arguments equaled 0.136 m/s for the Dubai 2008 marathon and 0.173 m/s for the Dubai 2009 marathon.
B
Berlin 2002, 50 males
Quotient of velocity dev.
Quotient of velocity dev.
A 80 70 60 50 40 30 20 10 0 0
5
10
15
20
25
30
35
Berlin 2002, 50 females 80 70 60 50 40 30 20 10 0
43
0
5
10
D
Berlin 2002, 50 males
Quotient of velocity dev.
Quotient of velocity dev.
C 80 70 60 50 40 30 20 10 0 0
10
20
30
Place at the finish
15
20
25
30
35
43
Distance, km
Distance, km
40
50
Berlin 2002, 50 females 80 70 60 50 40 30 20 10 0 0
10
20
30
40
50
Place at the finish
Fig. 6. Quotient of velocity deviations of Berlin 2002 run: A and B along the whole distance – note that males had high values of deceleration at the beginning and at the end of a run while females had deceleration only at the end of a run; C and D according to the place at the finish – high correlation in males (r = 0.701) and no correlation in females.
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W.S. Erdmann, P. Lipinska / Human Movement Science xxx (2013) xxx–xxx
Table 3 Male and female velocity data of the first ten runners at the finish; with the velocity of the second half of the distance faster (bold), equal (normal) and slower (gray) than the first half of the distance; note that except females in Berlin 2002 always the first runners at the finish had the second half run faster than the first one.
No.
Edmonton 2001
Boston 2002
1st half
1st half
2nd half
males 1 2 3 4 5 6 7 8 9 10
5.25 5.25 5.25 5.25 5.25 5.25 5.25 5.25 5.25 5.25
males 5.35 5.35 5.30 5.25 5.24 5.12 5.03 5.02 4.99 4.98
5.38 5.38 5.38 5.38 5.38 5.38 5.38 5.38 5.38 5.38
4.89 4.89 4.87 4.89 4.77 4.72 4.72 4.70 4.64 4.49
4.97 4.97 4.97 4.97 4.89 4.83 4.93 4.63 4.71 4.73
females 11 12 13 14 15 16 17 18 19 20
4.74 4.74 4.74 4.74 4.71 4.74 4.74 4.74 4.74 4.86
Berlin 2002 2nd half
1st half
Athens 2004 2nd half
males 5.52 5.52 5.46 5.46 5.40 5.38 .5.30 5.30 5.29 5.24
5.52 5.52 5.52 5.52 5.52 5.52 5.38 5.41 5.52 5.52
5.02 4.99 4.67 4.58 4.62 4.61 4.45 4.63 4.37 4.33
4.98 4.98 4.86 4.86 4.62 4.71 4.60 4.64 4.59 4.38
females
1st half
2nd half
males 5.57 5.57 5.56 5.48 5.43 5.26 5.39 5.36 5.25 5.23
5.20 5.20 5.22 5.20 5.20 5.20 5.20 5.20 5.18 5.20
4.94 4.78 4.77 4.76 4.59 4.42 4.52 4.35 4.29 4.43
4.75 4.75 4.65 4.75 4.75 4.75 4.75 4.65 4.65 4.55
females
5.56 5.51 5.43 5.43 5.36 5.35 5.34 5.28 5.27 5.24
females 4.86 4.85 4.91 4.74 4.71 4.55 4.53 4.61 4.60 4.66
4.3. Acceleration and quotient of velocity deviations 4.3.1. Acceleration and Qvd of EBBA marathons Mean absolute acceleration data for the first 50 males in the Berlin 2002 marathon, taking into account 5 km intervals, were 176 m/ks2 (SD = 83) for the first 50 runners and less than 100 m/ks2 for the first 3 males were. For the first 50 females in the Berlin 2002 marathon the absolute acceleration reached the value of 85 (69) m/ks2. For the first three females similar values were obtained. Fig. 5 shows data for the first 3 males in the Berlin 2002 marathon (low values) and for the first 3 females in Edmonton (high values). Taking into account the acceleration relative to the mean velocity, i.e., the quotient of velocity deviation, in the Berlin 2002 marathon at the beginning of the run (0..10 km) around 1/3 out of 50 of the investigated male competitors who were the first at the finish line ran the first 5 km slower than the second 5 km; within the middle third some ran faster and some ran slower; and around the last third some ran faster and then slowed down after realizing they were running too fast. Female runners ran the second 5 km at almost the same velocity as the first. Well before the finish (at 35.42 km) around 2/3 of male runners and around 3/4 of female runners decelerated. Even the psychological influence of approaching the finish line did not help to at least maintain the velocity at the same level as before (Fig. 6A and B). Taking into account the mean quotient of velocity deviation for the entire run according to the place at the finish, there was a positive correlation in males and a lack of correlation in females (Fig. 6C and D). 4.3.2. Acceleration and Qvd of BDBD marathons Accelerations in the BDBD marathon runs of Haile Gebrselassie were small. In the Berlin 2007 and 2008 marathons they were 48 (SD = 29) and 70 (43) m/ks2, respectively, for 5 km intervals and 432 (471) and 753 (695) m/ks2, respectively, for 1 km intervals. In the Dubai 2008 and 2009 marathons they were 67 (48) and 82 (59) m/ks2, respectively, for 5 km intervals and 428 (400) and 504 (522) m/ks2, respectively, for 1 km intervals. Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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Marathon Dubai 2008. Gebrselassie. end data cumulative time. pace and velocity from the start hrs:min:sec 2:00:32 2:00:53 2:01:54 2:02:43 2:03:19 2:03:48 2:04:15 2:04:50 2:04:53 min:sec 2:51.4 2:51.9 2:53.3 2:54.5 2:55.4 2:56.0 2:56.9 2:57.5 2:57.6
5.9 5.85 Velocity. m/s
5.8 5.75
.
5.7 5.65 5.6 5.55 5.5
1 0..5
2 0..10
3 0..15
4 0..20
5 0..25
6 0..30
7 0..35
8 0..40
9 0..42
Distance. km
Fig. 7. Cumulative time, pace and velocity of Dubai 2008 run. Up to the 15th km Gebrselassie and his pacemakers ran for a new world record below 2 h and 2 min which was at that time not affordable.
Quotients of velocity deviation for the Berlin 2007 and 2008 marathons were 8.4 and 7.7, respectively, for 5 km intervals and 76.5 and 132.8, respectively, for 1 km intervals. In the Dubai 2008 and 2009 marathons they were 8.6 and 10.4, respectively, for 5 km and 76.0 and 93.0, respectively, for 1 km intervals. 5. Discussion Martin and Gynn (2000) presented Olympic marathon data for 100 years. From all participants (around 1500 runners, among whom 221 women) 26.5% of men and 15.9% of women did not complete their race. One contestant even died while running. It is supposed in most cases that the reason for this large number of failures was improper running tactics, i.e., too intense running from the beginning of the run and unsteady running during the entire course of the event. De Koning et al. (2011), investigating a Hazard score (dealing with changes of velocity during an event) problem, presented an acceleration/deceleration curve (change in pace) showing a steady lowering of data from above to below 0% (which was defined as the steady pace). This shape of curve was obtained for good runners but not for the best. It agrees with the shape of curves obtained in this work for runners worse than the first ten at the finish. The best runners at the finish, in particular male runners, showed a more or less increasing velocity in almost all marathons under investigation (Table 3). This kind of velocity distribution seems to be best for running long distances. Runners who were among the first three at the finish line had a more or less ascending velocity line, while those finishing 4th to 10th were more or less stable, and those finishing 11th to 50th had a descending line. The present data provide evidence for the hypothesis that the smaller the deviations of the mean velocity during the marathon, the better. The quotient of velocity deviations equaled about 10 or less for the best runners, especially for male runners. Absolute acceleration and the quotient of velocity deviation were higher for the first and last stages of the Berlin 2002 marathon, where the profile of the course was flat and did not influence the velocity and acceleration of the running. The highest values of absolute acceleration and quotient of velocity deviation were associated with the worst runners. Male marathon running is characterized by a higher velocity (which is good) and by higher deviations of velocity, i.e., by higher acceleration (which is not good), than female marathon running. More males than females ran the second leg faster than the first. The female runs are more predictable than male runs when one takes into account time results from consecutive sections of the distance. The quotient of velocity deviation was high in male runners and close to zero in female runners. Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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A
Marathon. males. predicted time 2:03:00
min:sec 2:56.1 2:55.7 2:55.4 2:55.1 2:54.8 2:54.5 2:54.2 2:53.9 2:53.6 5.8
Velocity, m/s
5.7 5.6 5.5 5.4 5.3 5.2 5.1 1 0..5
2 5..10
3 4 10..15 15..20
5 6 7 8 9 20..25 25..30 30..35 35..40 40..42
Distance. km
B
Marathon. females. predicted time 2:15:00
min:sec 3:13.4 3:13.1 3:12.7 3:12.3 3:11.9 3:11.6 3:10.8 3:10.5 3:10.5 5.8
Velocity. m/s
5.7 5.6 5.5 5.4 5.3 5.2 5.1 1 0..5
2 5..10
3 4 10..15 15..20
5 6 7 8 9 20..25 25..30 30..35 35..40 40..42
Distance. km Fig. 8. Distribution of velocity and pace for prediction of the new world records with times of 2 h:03 min for males (A) and 2 h:15 min for females (B).
Haile Gebrselassie and his pacemakers provided telling examples of both good and bad running tactics. The world’s top long-distance runner ran with different tactics in different runs when attempting to break the current world record. Record runs during the Berlin 2007 and 2008 marathon had a lower velocity during the first half and a higher velocity in the second half of the course. Also, the velocity during every 1 km section deviated only very little from the mean velocity during the entire marathon. In contrast, the Dubai runs were performed in an incorrect manner, i.e., with too high a velocity at the start followed by a decrease in velocity. Velocity deviations for every 1 km section were higher in Dubai than in Berlin. Taking into account the actual velocity of the run and prediction of the end time based on that velocity, Berlin end times (calculated for the 2007 and 2008 runs) were similar to those of real end times. Unfortunately, in Dubai the end time predicted from the current velocity deviated strongly from the actual end time. If a runner in 2008 would have run the entire marathon with the velocity of the first 5 kilometers up, he would have established a highly improbable new world record of 2 h 00 min 32 s. Also, the next stages were run at a much too high velocity (see Fig. 7). It is important to establish proper tactics with pacemakers. Even if they feel well on the day of running and want to run faster, it is not recommended to do so over the first stages of the marathon. Instead, they need to run at the established velocity. Before the run, runners should establish by themselves, or with the help of their coach, suitable tactics for the particular run based on the purpose of the run, their overall fitness and specific fitness on the day of the run, the weather conditions, the profile of the course, and the level of other runners. Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006
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The role of pacemakers is to assist the main runner along the course for physical and psychological purposes. The former takes into account the lowering of air drag. Here pacemakers should run just in front of the main runner in order to form a shield against air drag for the main runner. Unfortunately, pacemakers do not always run this way. The latter takes into account better mobilization for a run if someone runs within a group of other runners. Neville and Whyte (2005) presented a paper on future world records in middle- and long-distance running. In their prediction they used extrapolation of a curve based on records recorded throughout the 20th century. The new record model presented in this article applies a proposal of a distribution of a load (velocity) which would be characterized by constant slow acceleration of a movement with very small deviations from the main ascending line. Fig. 8 presents the proposed distribution of velocity and pace along a course in order for male and female runners to achieve a new world record. 6. Final remarks In marathon running – and the same applies to other long-distance runs – the mean velocity should be a little bit lower for the first half than for the second half of the run. Deviations of the ascending line of velocity should be minimized, i.e., acceleration needs to be always low and positive, and not exceed a value of 50 m/ks2. In order to get feedback on how the run is being performed, it is recommended that runners wear instruments, based on global navigation satellite system technology, which provide all the necessary information (velocity or pace, distance to the end, etc.) that allow them to run in accordance with the recommendations that follow from this study. 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Please cite this article in press as: Erdmann, W. S., & Lipinska, P. Kinematics of marathon running tactics. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2013.07.006