Mathematical analysis of running performance and world running records

The objective of this study was to develop an empirical model relating human running performance to some characteristics of metabolic energy-yielding processes using A, the capacity of anaerobic metabolism (J/kg); MAP, the maximal aerobic power (W/kg); and E, the reduction in peak aerobic power with the natural logarithm of race duration T, when T greater than TMAP = 420 s. Accordingly, the model developed describes the average power output PT (W/kg) sustained over any T as PT = [S/T(1 - e-T/k2)] + 1/T integral of T O [BMR + B(1 - e-t/k1)]dt where S = A and B = MAP - BMR (basal metabolic rate) when T less than TMAP; and S = A + [Af ln(T/TMAP)] and B = (MAP - BMR) + [E ln(T/TMAP)] when T greater than TMAP; k1 = 30 s and k2 = 20 s are time constants describing the kinetics of aerobic and anaerobic metabolism, respectively, at the beginning of exercise; f is a constant describing the reduction in the amount of energy provided from anaerobic metabolism with increasing T; and t is the time from the onset of the race. This model accurately estimates actual power outputs sustained over a wide range of events, e.g., average absolute error between actual and estimated T for men's 1987 world records from 60 m to the marathon = 0.73%. In addition, satisfactory estimations of the metabolic characteristics of world-class male runners were made as follows: A = 1,658 J/kg; MAP = 83.5 ml O2.kg-1.min-1; 83.5% MAP sustained over the marathon distance. Application of the model to analysis of the evolution of A, MAP, and E, and of the progression of men's and women's world records over the years, is presented.     

Relationship between distance running mechanics, running economy, and performance

The relationships between biocmechanical aspects of distance running, running economy (VO2 submax), and performance were investigated. A variety of biomechanical measures for 31 subjects running at 3.6 m/s was obtained, including three-dimensional angular and translational kinematics, ground reaction forces and center of pressure patterns, mechanical power, and anthropometric measures. Physiological measures obtained included maximal and submaximal O2 consumption, muscle fiber composition, and measures of the ability to store and return elastic energy during knee bends. A subset of 16 runners was also evaluated in relation to performance in a 10-km run. Biomechanical variables were identified which showed significant differences or consistent trends between groups separated on the basis of VO2 submax, establishing the importance of biomechanical influences on running economy. It appears that no single variable or small subset of variables can explain differences in economy between individuals but rather that economy is related to a weighted sum of the influences of many variables.     

Prerequisites in distance running performance of female runners

We investigated which attribute or what combination of attributes would best account for distance running performance of female runners. The subjects were 30 well-trained female distance runners, aged 19 to 23 years. Anthropometric and body composition characteristics, pulmonary function characteristics, blood properties, and cardiorespiratory function characteristics were measured at rest or during submaximal and maximal exercise. Analyses of the data showed that the relationship of oxygen uptake corresponding to lactate threshold (VO2T, ml.kg-1.min-1) with each distance running performance was substantially higher as compared with the relationship of other independent variables including maximal oxygen uptake (VO2max). Furthermore, multiple regression analysis indicated that running performances in 3,000m, 5,000m, and 10,000m are best accounted for by a combination of VO2/LT (X1), fat-free weight (X2), and/or mean corpuscular volume (X3). A multiple regression equation for predicting the 5,000m (Y, s) running performance was formulated as Y = -14.75X1-3. 03X2-5.79X3 + 2282.1. We suggest that VO2max would not stand alone as a decisive factor of distance running success in female runners, and that the distance running performance could be better accounted for by a combination of several attributes relating to lactate threshold, body composition, and/or hematological status. The linear regression of the predicted running performance on the actually measured running performance can be accepted in the range of 986-1197s.     

Assessment of middle-distance running performance in sub-elite young runners using energy cost of running

The purpose of this study was to assess the validity of v _amax as an indicator of middle-distance running performance in sub-elite young runners, _amax being defined as the quotient maximal oxygen uptake (V˙O _2max) divided by the net energy cost of running (C _r) on a treadmill at a submaximal running velocity (280 m · min⁻¹). The V˙O _2max, ventilatory threshold, _amax, and C _r were assessed in 39 young male sub-elite runners having only small variations in performance level. The relationship between each variable and running performance (at 1500 m, 3000 m, and 5000 m) was evaluated. A trend toward a negative correlation existed between C _r and performance although this was not significant. The V˙O _2max and _amax were significantly related to performance. The _amax accounted for around 50% of the variability in performance whereas other physiological variables selected in this study were responsible, at best, for approximately 39%. The results presented in this study suggested that _amax was a useful indicator of middle-distance running performance in sub-elite young runners with similar performance levels as well as in top elite athletes. Accepted: 19 August 1997     

Predicting running velocity at blood lactate threshold from running performance tests in adolescent boys

The purpose of this study was to investigate the relationship between running velocity at blood lactate threshold (VLT) and running performance (50 m, 40 s and 5 min) in boys aged 14 years at puberty (n = 30) and young men aged 16-20 years (n = 39), and to examine the possibility of predicting VLT from running performances in boys during adolescence. Special attention was also paid as to whether these parameters are related to bone maturity in boys at puberty. After allowing for chronological age, height, weight and fat content, all the running performances were positively correlated to bone maturity in non-active boys at puberty. In contrast, VLT was negatively correlated to bone maturity. In spite of these results, VLT was significantly related to performance in the 5 min run in both the boys and the young men. However, the correlation coefficient for the former was significantly lower than that for the latter. The 5 min and 40 s runs were selected by stepwise regression analysis for predicting VLT in the two groups. The same predictor was selected from the combined data from both groups using the following equation: VLT(m X min-1) = 124 - 0.83 X 40 s run(m) + 0.202 X 5 min run(m). The correlation between actual and estimated VLT, and the standard error of the estimate of this formula were 0.726 and - 5 + 15 m X min-1 in the boys, and 0.880 and 4 + 11 m X min-1 in the young men, respectively. This formula was similar in precision to the formulae obtained from the data in each individual group.(ABSTRACT TRUNCATED AT 250 WORDS)     

Creatine supplementation and multiple sprint running performance

The aim of this study was to examine the effects of short-term creatine monohydrate supplementation on multiple sprint running performance. Using a double-blind research design, 42 physically active men completed a series of 3 indoor multiple sprint running trials (15 x 30 m repeated at 35-second intervals). After the first 2 trials (familiarization and baseline), subjects were matched for fatigue score before being randomly assigned to 5 days of either creatine (4 x d(-1) x 5 g creatine monohydrate + 1 g maltodextrin) or placebo (4 x d(-1) x 6 g maltodextrin) supplementation. Sprint times were recorded via twin-beam photocells, and earlobe blood samples were drawn to evaluate posttest lactate concentrations. Relative to placebo, creatine supplementation resulted in a 0.7 kg increase in body mass (95% likely range: 0.02 to 1.3 kg) and a 0.4% reduction in body fat (95% likely range: -0.2 to 0.9%). There were no significant (p > 0.05) between-group differences in multiple sprint measures of fastest time, mean time, fatigue, or posttest blood lactate concentration. Despite widespread use as an ergogenic aid in sport, the results of this study suggest that creatine monohydrate supplementation conveys no benefit to multiple sprint running performance.     

Physiological determinants of three-kilometer running performance in experienced triathletes

The present investigation examined the physiological parameters that contribute to 3-km running performance. Following 2 familiarization sessions, 16 experienced male triathletes (Vo(2)max = 55.7 +/- 4.9 ml.kg(-1).min(-1), age = 31.3 +/- 11.7 years) performed a 3-km time trial (3kmTT) and were assessed for selected physiological and anthropometrical characteristics. Stepwise multiple regression and correlation analysis was used to determine the variables that significantly related to 3kmTT. The analysis revealed that 82.3% of the adjusted variance in 3kmTT performance could be explained by peak treadmill running velocity during a Vo(2)max test (Vmax) alone. The addition of the running velocity at lactate threshold (LT(vel)) and peak lactate concentration ([BLa(-)](peak)) to the prediction equation allowed for 93.6% of the adjusted variance in 3kmTT to be predicted (Y = -13.64 Vmax - 25.61 LT(vel) - 5.40 [BLa(-)](peak) + 1358.5). Correlation analysis revealed that Vmax (r = -0.91), LT(vel) (r = -0.90), and Vo(2)max (r = -0.80) were significantly related to running performance. These results show that Vmax was the single best predictor of 3-km running performance in experienced male triathletes and that both aerobic and anaerobic abilities are related to improved 3kmTT performance. Since the assessment of Vmax is relatively simple to implement, we suggest that determining Vmax may be a practical method for monitoring performance changes in short-term endurance running events.     

Calcaneus length determines running economy: implications for endurance running performance in modern humans and Neandertals

The endurance running (ER) hypothesis suggests that distance running played an important role in the evolution of the genus Homo. Most researchers have focused on ER performance in modern humans, or on reconstructing ER performance in Homo erectus, however, few studies have examined ER capabilities in other members of the genus Homo. Here, we examine skeletal correlates of ER performance in modern humans in order to evaluate the energetics of running in Neandertals and early Homo sapiens. Recent research suggests that running economy (the energy cost of running at a given speed) is strongly related to the length of the Achilles tendon moment arm. Shorter moment arms allow for greater storage and release of elastic strain energy, reducing energy costs. Here, we show that a skeletal correlate of Achilles tendon moment arm length, the length of the calcaneal tuber, does not correlate with walking economy, but correlates significantly with running economy and explains a high proportion of the variance (80%) in cost between individuals. Neandertals had relatively longer calcaneal tubers than modern humans, which would have increased their energy costs of running. Calcaneal tuber lengths in early H. sapiens do not significantly differ from those of extant modern humans, suggesting Neandertal ER economy was reduced relative to contemporaneous anatomically modern humans. Endurance running is generally thought to be beneficial for gaining access to meat in hot environments, where hominins could have used pursuit hunting to run prey taxa into hyperthermia. We hypothesize that ER performance may have been reduced in Neandertals because they lived in cold climates.     

Effects of specific versus cross-training on running performance

The cross-training (XT) hypothesis suggests that despite the principle of specificity of training, athletes may improve performance in one mode of exercise by training using another mode. To test this hypothesis we studied 30 well-trained individuals (10 men, 20 women) in a randomized longitudinal trail. Subjects were evaluated before and after 8 weeks of enhanced training (+10%/week), accomplished by adding either running (R) or swimming (XT) to baseline running, versus continued baseline running (C). Both R ( – 26.4s) and XT (– 13.2s) improved time trial (3.2 km) performance, whereas C did not (– 5.4s). There were no significant changes during treadmill running in maximum oxygen uptake (O_2peak; – 0.2, – 6.0, and + 2.7%), steady state submaximal O₂ at 2.68 m · s^–1 ( – 1.2, – 3.3 and + 0.2 ml · kg^–1 · min^–1), velocity at O_2peak (+0.05, +0.25 and +0.09 m · s^–1) or accumulated O₂ deficit (+ 11.2, – 6.1 and + 9.4%) in the R, XT or C groups, respectively. There was a significant increase in velocity associated with a blood lactate concentration of 4 mmol · l^–1 in R but not in XT or C ( + 0.32, + 0.07 and + 0.08 m · s^–1). There were significant changes in arm crank O_2peak ( + 5%) and arm crank O₂ at 4 mmol · l^–1 ( + 6.4%) in XT. There was no significant changes in arm crank O_2peak ( + 1.3 and – 7.7%) or arm crank O₂ at 4 mmol · l^–1 ( + 0.8 and + 0.4%) in R or C, respectively. The data suggest that muscularly non-similar XT may contribute to improved running performance but not to the same degree as increased specific tranining.     

Can cycle power predict sprint running performance?

A major criticism of present models of the energetics and mechanics of sprint running concerns the application of estimates of parameters which seem to be adapted from measurements of running during actual competitions. This study presents a model which does not perpetuate this solecism. Using data obtained during supra-maximal cycle ergometer tests of highly trained athletes, the kinetics of the anaerobic and aerobic pathways were modelled. Internal power wasted in the acceleration and deceleration of body limbs and the power necessary to overcome air friction was calculated from data in the literature. Assuming a mechanical efficiency as found during submaximal cycling, a power equation was constructed which also included the power necessary to accelerate the body at the start of movement. The differential equation thus obtained was solved through simulation. The model appeared to predict realistic times at 100 m (10.47 s), 200 m (19.63 s) and 400 m (42.99 s) distances. By comparison with other methods it is argued that power equations of locomotion should include the concept of mechanical efficiency.     

The role of anaerobic ability in middle distance running performance

The purpose of this study was to assess the relationship between anaerobic ability and middle distance running performance. Ten runners of similar performance capacities (5 km times: 16.72, SE 0.2 min) were examined during 4 weeks of controlled training. The runners performed a battery of tests each week [maximum oxygen consumption (VO2max), vertical jump, and Margaria power run] and raced 5 km three times (weeks 1, 2, 4) on an indoor 200-m track (all subjects competing). Regression analysis revealed that the combination of time to exhaustion (TTE) during the VO2max test (r2 = 0.63) and measures from the Margaria power test (W.kg-1, r2 = 0.18; W, r2 = 0.05) accounted for 86% of the total variance in race times (P less than 0.05). Regression analysis demonstrated that TTE was influenced by both anaerobic ability [vertical jump, power (W.kg-1) and aerobic capacity (VO2max, ml.kg-1.min-1)]. These results indicate that the anaerobic systems influence middle distance performance in runners of similar abilities.     

Physiological parameters related to running performance in college trackmen.

Submaximal and maximal oxygen consumption (VO2) and heart rate (HR) were correlated with running performance in events ranging from 100 yards to 2 miles, using as subjects 20 members of a college track team. In the first of two studies (n=11) a multi-stage walking test was used to determine VO2 and HR. Max VO2 expressed in ml/kg/min, was significantly related to 1 mile run performance but not to any of the other runs. Submaximal HR was significantly related to performance in both the 1 mile and 2 mile runs. Correlations between these physiological parameters and performance in the 220, 440, and 880 yard runs were nonsignificant. Multiple R's using max VO2 (ml/kg/min) and submaximal H were .758 and 9671, respectively, for the 1 and 2 mile runs. In study two (n=9) a running test for VO2 and HR was used, which resulted in a mean max VO2 about 7 ml higher than than elicited in the walking test, implying that for trained runners a running test was a more valid test of aerobic power. Marked relationships were found between body weight and performance, positive for the 100 yard dash and negative for the 2 mile run. Submaximal HR was again significantly related to performance in the 1 and 2 mile runs. Max VO2 was positively related to 2 mile performance and negatively related to 100 yard dash performance. Multiple R's using max VO2 and submaximal HR were .799 and .925 for the 1 and 2 mile runs, respectively. Using submaximal HR and weight the multiple R's were .777 and .945, showing that these two can account for a large amount of the variance in distance running performance. In neither study was submaximal VO2 significantly related to running performance.     

The effects of static stretching on running economy and endurance performance in female distance runners during treadmill running

Stretching can lead to decreased muscle stiffness and has been associated with decreased force and power production. The purpose of this study was to investigate the acute effects of static stretching (SS) on running economy and endurance performance in trained female distance runners. Twelve long distance female (30 ± 9 years) runners were assessed for height (159.4 ± 7.4 cm), weight (54.8 ± 7.2 kg), % body fat (19.7 ± 2.8%), and maximal oxygen consumption (VO2max: 48.4 ± 5.1 ml·kg(-1)·min(-1)). Participants performed 2 sessions of 60-minute treadmill runs following a randomly assigned SS protocol or quiet sitting (QS). During the first 30 minutes (running economy), expired gases, heart rate (HR), and rating of perceived exertion (RPE) were recorded while the participant ran at 65% VO2max. During the final 30 minutes (endurance performance), distance covered, speed, HR, and RPE were recorded while the participant attempted to cover as much distance as possible. Repeated measures analyses of variance were performed on the data. Significance was accepted at p < 0.05. The SS measured by sit-and-reach increased flexibility (SS: 29.8 ± 8.3 vs. QS: 33.1 ± 8.1 cm) but had no effect on running economy (VO2: 33.7 ± 3.2 vs. 33.8 ± 2.3 ml·kg(-1)·min(-1)), calorie expenditure (270 ± 41 vs. 270 ± 41 kcal), HR (157 ± 10 vs. 160 ± 12 b·min(-1)), or endurance performance (5.5 ± 0.6 vs. 5.5 ± 0.7 km). These findings indicated that stretching did not have an adverse effect on endurance performance in trained women. This suggests that the performance decrements previously associated with stretching may not occur in trained women.     

Effects of a concurrent strength and endurance training on running performance and running economy in recreational marathon runners

The purpose of this study was to investigate the effects of a concurrent strength and endurance training program on running performance and running economy of middle-aged runners during their marathon preparation. Twenty-two (8 women and 14 men) recreational runners (mean ± SD: age 40.0 ± 11.7 years; body mass index 22.6 ± 2.1 kg·m?2) were separated into 2 groups (n = 11; combined endurance running and strength training program [ES]: 9 men, 2 women and endurance running [E]: 7 men, and 4 women). Both completed an 8-week intervention period that consisted of either endurance training (E: 276 ± 108 minute running per week) or a combined endurance and strength training program (ES: 240 ± 121-minute running plus 2 strength training sessions per week [120 minutes]). Strength training was focused on trunk (strength endurance program) and leg muscles (high-intensity program). Before and after the intervention, subjects completed an incremental treadmill run and maximal isometric strength tests. The initial values for VO2peak (ES: 52.0 ± 6.1 vs. E: 51.1 ± 7.5 ml·kg?1·min?1) and anaerobic threshold (ES: 3.5 ± 0.4 vs. E: 3.4 ± 0.5 m·s?1) were identical in both groups. A significant time × intervention effect was found for maximal isometric force of knee extension (ES: from 4.6 ± 1.4 to 6.2 ± 1.0 N·kg?1, p < 0.01), whereas no changes in body mass occurred. No significant differences between the groups and no significant interaction (time × intervention) were found for VO2 (absolute and relative to VO2peak) at defined marathon running velocities (2.4 and 2.8 m·s?1) and submaximal blood lactate thresholds (2.0, 3.0, and 4.0 mmol·L?1). Stride length and stride frequency also remained unchanged. The results suggest no benefits of an 8-week concurrent strength training for running economy and coordination of recreational marathon runners despite a clear improvement in leg strength, maybe because of an insufficient sample size or a short intervention period.