Dr.Hab. V.D. Kryazhev¹
Dr. Hab., Professor V.Y. Karpov²
PhD, Professor K.K. Skorosov³
PhD, Associate Professor V.I. Sharagin^4
1Federal Scientific Center for Physical Culture and Sports, Moscow
²Russian State Social University, Moscow
³Penza State University, Penza
⁴Moscow State University of Psychology and Education, Moscow

Corresponding author: kryzev@mail.ru

Keywords: long-distance running, mathematical modeling, run energy cost, run energy efficiency.

Background. Di Prampero (Italy) [4] and F. Peronne, G. Thibault (Canada) [7] have developed a middle-/ long-distance run energy cost rating method based on the aerobic/ anaerobic metabolism capacity and kinetics rating formulae, with the resulting values calculated with only 0.68% error. Their calculations of VO2max were only 2-3 mm/kg/min different from the published individual long-distance running elite test data. It is commonly assumed that the long-distance running elite energy cost varies at around 3.86 J/kg/m, and the maximal oxygen consumption at 80 ml/kg/min [7]. Later it was found, however, that the East African long-distance running elite (from Ethiopia, Kenya and other nations) runs in much more energy efficient manner that the Europeans [5, 6]. We believe that it may be pertinent in this context to have the common long-distance running energy efficiency analysis and findings revised.

Objective of the study was to analyze, on a mathematical and statistical basis, the African and European long-distance running elite energy efficiency.

Methods and structure of the study. We collected for analysis the individual competitive performance data of the top-five European and top-five African runners from the 2019 top-100 list: see Table 1.

Table 1. Individual competitive performance data of the top-five European and top-five African competitors in 3000m, 5000m and 10000m  

Sports results (LnT times) were converted into mean distance speed (V) and processed in Excel to produce V-LnT correlations. The critical running speed (Vcrit) was found based on the seventh-minute LnT (Ln 420 = 6.04) [7, 8]. Based on the critical running speed concept [1] and using the ∆MAP = Crtot ∙ Vcrit, W ratio, we computed the maximum aerobic power (MAP) above the quiescent level (∆MAP) using the equation VO2max = (∆MAP + 1.2) ∙ 2.87 ml/kg/min. Note that Crtot means the run energy cost net of the air resistance. Run energy efficiency (net energy cost Cr) was estimated at 3.76 J/kg/m for the Europeans and 3.30 J/kg/m for the Ethiopians [4, 5]. Note that the aerobic maximum aerobic power, run energy cost and endurance ratio (E, rated by the regression curve tilt angle V - LnT [8] as provided by Péronnet-Thibault model [7]) may be used to compute the individual energy efficiency [2].

Results and discussion. Given on Figure hereunder are the regression equations for the African and European runners with virtually the same tilt angles indicative of the similar E ratios and endurance indices EI. The critical speeds generated by the regression equations show advantage of the African group. Thus the Ethiopian runners demonstrate higher energy efficiencies i.e. energy costs per meter net of the air resistance; and, hence, lower metabolic demand (MD) on the distances. It should be emphasized that the African runners are generally more successful than the Europeans in spite of the lower aerobic maximums. The mathematical models that we applied give fairly accurate energy efficiency rates based on the known energy costs [2, 7].

Figure 1. Elite long-distance runners’ distance speed variations on three distances

Note that the mean values for the European/ African long-distance running elites vary within the range of around 7% [4, 6], although the intergroup energy efficiencies are quite significant.

Table 2. Calculated energy cost and performance test data of the European and African elite long-distance runners on 3000m distance

Note: р≤0.05; V – running speed; Pv – metabolic demand; VO2max – maximum oxygen consumption; Vcrit – critical running speed; Cr – energy cost per meter net of air resistance

The high run energy efficiencies of the world leading Ethiopian and Kenyan middle- and long-distance runners may be due to the genetically predetermined lower limb metrics and habitual high-altitude living conditions [3] that develop more energy efficient aerobic metabolism. The shorter shin circumference (minus 3 cm on average) secures more efficient mass-inertial performance of the distal leg segments and eases the mechanical work [6]; plus the lower shoulder of forces acting in the Achilles tendon contributes to the energy efficiency of the elastic elements in the musculoskeletal system [3].

Conclusion. Mathematical analysis of the competitive performance data and energy efficiency of elite long-distance runners demonstrated serious advantages of the East African runners over their European competitors secured by the lower metabolic demands on the distances and, hence, better energy efficiencies as a sound basis for their great competitive accomplishments despite the relatively lower aerobic maximums.

References

1. Kryazhev V.D., Volodin R.N., Solovyev V.B. et al. Critical running speed concept and its assessment in middle distance runners. Vestnik sportivnoy nauki. 2019. No. 6. pp. 4-6.
2. Kryazhev V.D., Kryazhev S.V. Individual rating of bioenergetic indicators of middle distance runners. Vestnik sportivnoy nauki. 2019. No. 1. pp. 15-20.
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