Distances used in the computation of the parametres. 1.5-3 km. Fractions of S ..... 4000 5000 6000 7000 8000 9000. 0. 10000. 20000. 30000. 40000. Zatopek.
Modelling of running performances in elite endurance runners
Part two Nurmi
Zatopek
Väätäinen
Virén
Eastbourne 10/07/2017
Aouita
Gebrselassie
Are the results of the models independent of the range of distances ?
Scherrer and Monod, 1960, J Physiol (Paris) 52:419-501
“ La relation T = f(t) n’est pas strictement linéaire comme le montre d’ailleurs la figure 2A où les courbes tendent à s’infléchir vers l’abscisse au delà d’une trentaine de minutes.” “The relationship W = f(t) is not perfectly linear as shown on figure 2A, where the curves tend towards abscissa beyond 30 minutes” Scherrer and Monod, 1960, J Physiol (Paris) 52:419-501
D lim (m)
Zatopek
20000
15000
10000 SCrit 1.5-5 km SCrit 1.5-10 km SCrit 1.5-20 km
5000
0 0
500 1000 1500 2000 2500 3000 3500 4000
t lim (s)
D lim (m)
Gebrselassie
20000
15000
10000 SCrit 1.5-5 km SCrit 1.5-10 km SCrit 1.5-21.09 km
5000
0 0
500 1000 1500 2000 2500 3000 3500 4000
t lim (s)
Critical speed (SCrit) computed from different distances 1.5 &3 km
3 &5 km
5 &10 km
Nurmi Zatopek Väätäinen Virén Aouita Gebrsellasie
5.62 5.88 6.02 6.22 6.25 6.49
5.43 5.73 5.97 6.01 6.08 6.37
5.33 5.57 5.79 5.80 5.76 6.07
Means
6.08
5.93
5.72
Anaerobic Distance Capacity (ADC) computed from different distances 1.5 & 3 km
3 &5 km
5 &10 km
Nurmi Zatopek Vääitäinen Virén Aouita Gebrsellasie
191 129 151 118 194 110
283 203 176 219 270 166
373 334 324 383 518 394
Means
149
220
388
Fractions of SCrit and ADC computed from 1.5-3-5-10 km 1.6
ADC
1.4 1.2 1.0
SCrit
0.8 0.6 0.4
1.5-3 km
3-5 km
5-10 km
Distances used in the computation of the parametres
-1
S (m.s ) 7.4
1.5 km
7.2 7.0 3 km
6.8
5 km
6.6 10 km
6.4 6.2
Gebrselassie Aouita Virén Väätäinen Zatopek Nurmi
20 km
6.0 5.8 5.6 5.4 0.000
0.001
0.002
0.003
1/t lim
0.004
0.005
SCrit (model with 1/tlim) computed from different distances 1.5&3 k 5.62
3&5 k 5.43
5&10 km 5.33
Zatopek
5.88
5.73
5.57
Väätäinen
6.02
5.97
5.79
Virén
6.22
6.01
5.80
Aouita
6.25
6.08
5.76
Gebrselassie
6.49
6.34
6.07
Means
6.08
5.93
5.72
Nurmi
Parametre ADC (model with 1/tlim) computed from different distances 1.5&3 k
5&10 km
Nurmi Zatopek Väätäinen Virén Aouita Gebrselassie
191 129 151 118 194 110
3&5 k
Means
149
220
388
283 203 176 219 271 166
373 334 324 383 518 394
The relationship between tlim and Dlim is not perfectly linear. Therefore: - the slope of the tlim-Dlim relationship depends of tlim; - the value of SCrit depends on the range of tlim;
“… he (A. V. Hill) showed that the relationship was hyperbolic... This relationship remains evident when today's world record performances are plotted in the same way. This is of interest because it indicates that the human power–duration relationship is hyperbolic in its nature...” Poole, Burnley, Vanhatalo, Rossiter, Jones Med. Sci. Sports Exerc., Vol. 48, No. 11, 2016
Exponent g (Kennelly) computed from different distances 1.5 & 3 km
3 & 5 km
5 & 10 km
Nurmi Väätäinen Virén Aouita Gebrselassie
0.908 0.926 0.942 0.908 0.947
0.926 0.955 0.943 0.930 0.957
0.946 0.953 0.945 0.926 0.943
Means
0.926
0.942
0.943
Fractions of g, Scrit and E computed from 1.5-3-5-10 km 1.25 1.20 1.15 1.10 1.05
g
1.00
SCrit
0.95 0.90
0.85
1.5-3 km
3-5 km
5-10 km
Distances used in the computation of the parametres
Endurance Index E (Péronnet-Thibault) computed from different distances
1.5 &3 km
5 &10 km
Nurmi Vaatainen Virén Aouita Gebrselassie
0.573 0.473 0.377 0.649 0.366
3 &5 km
Means
0.488
0.368
0.354
0.434 0.289 0.366 0.464 0.288
0.305 0.285 0.341 0.469 0.368
Fractions of g, Scrit and E computed from 1.5-3-5-10 km 1.25 1.20 1.15 1.10 1.05
g
1.00
SCrit
0.95 0.90
E
0.85
1.5-3 km
3-5 km
5-10 km
Distances used in the computation of the parametres
Parametre S∞ (exponential decay. Hopkins)
computed from different distances
Nurmi Väätäinen Virén Aouita Gebrselassie
Means
ALL
1.5-3-5 km
3-5-10 km
5.52 5.97 5.96 6.03 6.23
5.64 6.13 6.11 6.31 6.50
5.48 5.86 5.91 5.87 5.99
5.94
6.14
5.82
-1
S (m.s )
Zatopek
6,8
1.5- 3-5-10-20 km 3-5-10-20 km 5-10-20 km
6,4 6,0 5,6
11%
5,2
42.19 km road
4,8 0
1500
3000
4500
t lim (s)
6000
7500
9000
Is it possible to predict Marathon performances from track performances ?
-1
S (m.s )
Gebrselassie Virén Zatopek Nurmi
7.0 6.6 6.2 5.8 5.4 5.0 4.6 500
1000
5000
10000
tlim (s) the prediction of the Marathon performances from performances on track is not accurate
-1
S (m.s )
Péronnet-Thibault model
7,2 7,0 6,8 6,6 6,4 6,2 6,0 5,8 5,6 5,4 5,2 5,0 4,8 4,6
Gebrselassie Virén Zatopek Radcliffe
0
1000 2000 3000 4000 5000 6000 7000 8000 9000
tlim (s) the prediction of the Marathon performances from performances on track is not accurate
Péronnet-Thibault model -1
S (m.s )
Paula Radcliffe
7.0 6.6 6.2
3000 m
5.8
10000 m 5000 m
5.4
Marathon
5.0 4.6 500
1000
tlim (s)
5000
10000
Péronnet-Thibault model -1
S (m.s )
Paula Radcliffe
7.0 6.6 6.2
3000 m
5.8
10000 m 5000 m
5.4
Marathon
5.0 4.6 500
1000
tlim (s)
5000
10000
Péronnet-Thibault model -1
S (m.s )
Paula Radcliffe
7.0 6.6 6.2
3000 m
5.8
10000 m 5000 m
5.4
Marathon
5.0 4.6 500
1000
tlim (s)
5000
10000
-1
Average Running Speed during the race (m.s ) 7.0
1.5 km
Mathematical models computed from 1.5-3-5-10 km (empty circles)
3 km 5 km 6.5 10 km
Hill-Scherrer Hopkins 6.0
Kennelly Péronnet-Thibault
21.09 km
5.5
42.19 km
Running performances of H. Gebrselassie 5.0
1000 2000 3000 4000 5000 6000 7000
Duration of the race(s)
In elite endurance runners accustomed to track and marathon
races
Radcliffe),
both
Péronnet-Thibault
(for the
example, models
accurately
of
Gebrselassie Kennelly describe
or and the
performances over distances ranging from 1500 m to 42.195 km.
-1
S (m.s ) 7.2 7.0 6.8 6.6 6.4 6.2 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6
Péronnet-Thibault Kennelly
1.5 km 3 km 5 km 10 km 1.5 km 3 km 5 km 10 km
Gebrselassie half-marathon Marathon
Marathon
Radcliffe
0
1000 2000 3000 4000 5000 6000 7000 8000 9000
tlim (s)
0.94
D = 9.719 tlim
Application of Kennely’s model to the performances of Gebrselassie including half-marathon and marathon.
In riders considerably more accustomed to runs on track than in the marathon (for example, Virén or Zatopek), the modelling of the performances over the distances ranging from 1500 m to 42,195 km is less accurate.
-1
S (m.s ) 7.2 7.0 6.8 6.6 6.4 6.2 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6
Péronnet-Thibault Kennelly
1.5 km 3 km 1.5
5 km 10 km
3 5 km
Virén
10 km
Marathon 20 km
Zatopek Marathon
0
1000
3000
5000
tlim (s)
7000
9000
-1
S (m.s ) 7.2 7.0 6.8 6.6 6.4 6.2 6..0 5.8 5.6 5.4 5.2 5.0 4.8 4.6
Péronnet Thibault Hopkins
* *
performance not included in computation
Gebrselassie
Radcliffe
0
1000
3000
5000
tlim (s)
7000
9000
-1
S (m.s ) 7.2 7.0 6.8 6.6 6.4 6.2 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6
Péronnet Thibault Hopkins
*
performance not included in computation
Virén
* Zatopek
0
1000
3000
5000
tlim (s)
7000
9000
The modelling is even worse with the model of the critical speed for distances rangeing from 1500 m to 42,195 km.
-1
S (m.s ) 7.2 7.0 6.8 6.6 6.4 6.2 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6
Péronnet-Thibault
SCrit
* *
performance not included in computation
Gebrselassie
Radcliffe
0
1000
3000
5000
tlim (s)
7000
9000
S (m.s ) 7.2 7.0 6.8 6.6 6.4 6.2 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6
Péronnet-Thibault
SCrit
*
performance not included in computation
Virén
* Zatopek
0
1000
3000
5000
tlim (s)
7000
9000
However… The Dlim-tlim relationships seem linear even after the inclusion of marathon performances.
Dlim (m) 40000 Gebrselassie
30000
20000
Radcliffe
10000
0 0
1000 2000 3000 4000 5000 6000 7000 8000 9000
tlim (s)
Dlim (m) 40000
30000
Virén Zatopek
20000
10000
0 0
1000 2000 3000 4000 5000 6000 7000 8000 9000
tlim (s)
The differences between the actual performances in the Marathon and extrapolated estimates from track events could be explained by the effects of ground (track vs road, slopes...). The limiting factors in Marathon could be different than those limiting the performances in shorter track races. The modelling of running performances assumed that the performances correspond to the same training and the same fitness level.
-1
S (m.s )
Exponential decay Hopkins et al. 1989
1999
7.0
Gebrselassie
1998 1998
6.6
3-5-10-20 km 1998
6.2 2006 half marathon
5.8
2007
2008 Marathon
5.4 0
1000 2000 3000 4000 5000 6000 7000 8000
t lim (s)
100 %
100 Aerobic
80
80
About 2 minutes
60 40
60
Adapted from Astrand and Rodhal
20
40 20
Anaerobic
0
0 0
20
40
time (min)
Aerobic and anaerobic contributions to exhausting exercises
1.5
3
5
10 km
100 %
100 Aerobic
80
80
60
60
40
40
20
20
Anaerobic
0
0 0
20
40
time (min)
Aerobic and anaerobic contributions to exhausting exercises
mmol / L 12
mg / 100 ml 100 Adapted from Costill 1970
10
80 8 60 6 40
4
20
2
Rest 00
0
4
8
12
16
20
24
28
32
36
Competitive running distance (km)
40
44
0
Endurance capability probably depends on a combination of the following factors: - a high percentage of type I muscle fibers, - the capacity to store large amounts of muscle and/or liver glycogen, - the capacity to spare carbohydrate reserves by using more free fatty acids as energy substrate, - the capacity to efficiently dissipate heat. Péronnet and Thibault 1989
It is likely than endurance capability also depends on psychological and neurological factors, which explains the effects of several doping substances (amphetamine…).
Comparisons between the models
Excepted the dimensionless exponent g of Kennelly's model, the parameters of the other models (E, SCrit and S ) depend : - not only on endurance capability - but also on maximal aerobic speed. Therefore the correlations between these parameters are generally not significant.
-1
S Crit (m.s ) 6.4 6.2 6.0 5.8 5.6 3-5-10 km
5.4
1.5-3-5-10 km
5.2 0.25
0.30
0.35
0.40
E
0.45
0.50
0.55
However the correlations between g, E, SCrit and S become highly significant when these parameters are normalized to an estimate of maximal aerobic speed (S 420).
S Crit /S420 0.94 0.92
G
Vä Z
0.90
Y = 0.995 - 1.599 X 2 r = 0.991
V
0.88 N A
0.86
1.5-3-5-10 km
0.84 0.050
0.055
0.060
0.065
E/S420
0.070
0.075
0.080
-1
SCrit (m.s ) 6.4 6.2 6.0 5.8 5.6 5.4
3-5-10 km
5.2
1.5-3-5-10 km
5.0 0.92
0.93
0.94
g (Kennelly)
0.95
0.96
S Crit /S 420 0.92 Vä
G
0.91 V Z
0.90 0.89 0.88
N
0.87
Y = - 0.588 + 1.585 X 2 r = 0.990
A
1.5-3-5-10 km
0.86 0.92
0.93
0.94
g
0.95
0.96
6.4 6.2 6.0 5.8 5.6 3-5-10 km
5.4
1.5-3-5-10 km
5.2 0.25
0.30
0.35
0.40
0.45
0.50
0.55
S
Hopkins / S 420
0.93
Y = 0.982 - 1.144 X 2 r = 0.879
Vä Z
1.5-3-5-10 km
0.92 G V 0.91
N
0.90
A 0.89 0.050
0.055
0.060
0.065
E / S 420
0.070
0.075
0.080
S
Hopkins (m.s
-1
)
6.4 6.2 6.0 5.8 5.6 3-5-10 km
5.4
1.5-3-5-10 km
5.2 5.2
5.4
5.6
5.8
6.0 -1
S Crit (m.s )
6.2
6.4
S
Hopkins / S 420
0.93
Vä Z
0.92
G
V
0.91 N
0.90
Y = 0.256 + 0.731 X 2 r = 0.925 1.5-3-5-10 km
A
0.89 0.86
0.87
0.88
0.89
SCrit / S 420
0.90
0.91
0.92
E 0.6
3-5-10 km
0.5
1.5-3-5-10 km
0.4
0.3
0.2 0.92
0.93
0.94
g (Kennelly)
0.95
0.96
E/ S420 0.080
A
Y = 0.989 - 0.990 X 2 r = 0.997
0.075 N 0.070
1.5-3-5-10 km
0.065 0.060 V
0.055
Vä Z
0.050 0.92
0.93
0.94
g
G 0.95
0.96
Are the relationships between the parameters of the different models the same for high-level athletes and normal athletes? A simulation study
S/MAS
g
1.0 0.9
0.95
0.8 0.90
0.7 0.6
0.80
0.5
0.70
0.4 0.3
Kennelly
0.2
0.60
S / MAS = k(tlim / tMAS)
g -1
0.1 0.0 0
2
4
6
8
10
12
tlim / tMAS
14
16
18
20
S/MAS 1.0
E/MAS
0.9
0.046
0.8 0.086
0.7 0.6
0.15
0.5
0.20
0.4 0.3
Péronnet-Thibault
0.2
0.23
S / MAS = 1 - E ln(tlim / tMAS)
0.1 0.0 0
2
4
6
8
10
12
tlim / tMAS
14
16
18
20
S/MAS
almost equal
E/MAS g
1.0 0.9
0.95 0.046
0.8 0.90 0.086
0.7 0.6
0.80 0.15
0.5
0.70 0.20
0.4 0.3
Kennelly Péronnet-Thibault
0.2
0.60 0.23
0.1 0.0 0
2
4
6
8
10
12
tlim / tMAS
14
16
18
20
Let two runners whose characteristics are: -
VO2max = 60 ml O2.kg -1; -1 -1 running economy = 3.5 ml O2.min .(km/h) ; -1 MAS (maximal aerobic speed) = 60/3.5 = 17 km.h ; E/MAS (Péronnet-Thibault) = 0.05 -1
VO2max = 60 ml O2.kg ; -1 -1 running economy = 3.5 ml O2.min .(km/h) ; MAS (maximal aerobic speed) = 60/3.5 = 17 km.h-1; E/MAS (Péronnet-Thibault) = 0.10
Dlim (m) 40000
30000
E/MAS = 0.05 MAS = 17km.h
-1
E/MAS = 0.10
20000
MAS = 17km.h
-1
10000
0
0
2000
4000
6000
8000
tlim (s)
10000
12000
14000
-1
Speed (m.s )
Kennelly Péronnet-Thibault
5.0 1.5 km 3 km
4.5 3 km
5 km 10 km
E/MAS = 0.05 half-marathon
5 km
Marathon
4.0 10 km
3.5 half-marathon
Marathon
3.0 0
2000 4000 6000 8000 10000 12000 14000
tlim (s)
-1
Speed (m.s )
Hopkins Péronnet-Thibault
5.0 1.5 km 3 km
4.5 3 km
5 km 10 km
E/MAS = 0.05 half-marathon
5 km
Marathon
4.0 10 km
E/MAS = 0.1
3.5 half-marathon
Marathon
3.0 0
2000 4000 6000 8000 10000 12000 14000
tlim (s)
-1
Speed (m.s ) 5.0
4.5
Effects of distance range on Hopkins model E/MAS = 0.05 1.5 to 5 km 1.5 to 10 km 1.5 to 21.1 km
4.0
1.5 to 42.2 km
3.5
3.0 0
2000 4000 6000 8000 10000 12000 14000
tlim (s)
-1
Speed (m.s ) 5.0
Effects of distance range on Hopkins model
4.5 E/MAS = 0.1 1.5 to 5 km
4.0
1.5 to 10 km
3.5
1.5 to 21.1 km 1.5 to 42.2 km
3.0 0
2000 4000 6000 8000 10000 12000 14000
tlim (s)
Value of exponent g Range
for E/MAS = 0.05
for E/MAS = 0.10
1500-Marathon
0.946
0.879
1500-Half Marathon
0.947
0.885
1500 – 10000
0.948
0.891
1500 – 5000
0.949
0.896
1500 – 3000
0.950
0.899
Values of exponent g as a function of the range of running distances for two values of E/MAS in the case where the model of Péronnet-Thibault is assumed to be perfect and the best one.
Value of S∞ (Hopkins) Range
for E/MAS = 0.05
for E/MAS = 0.10
1500-Marathon
3.98
3.13
1500-Half Marathon
4.11
3.41
1500 – 10000
4.26
3.76
1500 – 5000
4.38
4.01
Values of exponent S∞ as a function of the range of running distances for two values of E/MAS in the case where the model of Péronnet-Thibault is assumed to be perfect and the best one.
Value of index E/MAS Range
for g = 0.95
for g = 0.85
1500-Marathon
0.047
0.118
1500-Half Marathon
0.047
0.126
1500 – 10000
0.048
0.134
1500 – 5000
0.049
0.142
1500 – 3000
0.050
0.148
Values of index E/MAS as a function of the range of running distances for two values of g in the case where the model of Kennelly is assumed to be perfect and the best one.
