Critical Velocity obtained using Simplified Models of the Railway Track: Viability and Applicability

Increased demands on the capacity of the railway network gave rise to new issues related to the dynamic response of railway tracks subjected to moving vehicles. Thus, it becomes important to evaluate the applicability of traditionally used simplified models which have a closed form solution. Regarding simplified models, transversal vibrations of a beam on a visco-elastic foundation subjected to a moving load are considered. Governing equations are obtained by Hamilton’s principle. Shear distortion, rotary inertia and effect of axial force are accounted for. The load is introduced as a time varying force moving at a constant velocity. Transversal vibrations induced by the load are solved by the normal-mode analysis. Reflected waves at the extremities of the full beam are avoided by introduction of semi-infinite elements. Firstly, the critical velocity obtained from this model is compared with results of an undamped Euler- Bernoulli formulation with zero axial force. Secondly, a finite element model in ABAQUS is examined. The new contribution lies in the introduction of semi- infinite elements and in the first step to a systematic comparison, which have not been published so fa

Relationships and significance of lactate minimum, critical velocity, heart rate deflection and 3 000 m track-tests for running

The running velocities associated to lactate minimum (V-lm), heart rate deflection (V-HRd), critical velocity (CV), 3000 M (V-3000) and 10000 m performance (V-10km) were compared. Additionally the ability of V-lm and VHRd on identifying sustainable velocities was investigated.Methods. Twenty runners (28.5 +/- 5.9 y) performed 1) 3000 m running test for V3000; 2) an all-out 500 in sprint followed by 6x800 m incremental bouts with blood lactate ([lac]) measurements for V-lm; 3) a continuous velocity-incremented test with heart rate measurements at each 200 m for V-HRd; 4) participants attempted to 30 min of endurance test both at V-lm(ETVlm) and V-HRd(ETVHRd). Additionally, the distance-time and velocity-1/time relationships produced CV by 2 (500 m and 3000 m) or 3 predictive trials (500 m, 3000 m and distance reached before exhaustion during ETVHRd), and a 10 km race was recorded for V-10km.Results. The CV identified by different methods did not differ to each other. The results (m(.)min(-1)) revealed that V-.(lm) (281 +/- 14.8)< CV (292.1 +/- 17.5)=V-10km (291.7 +/- 19.3)< V-HRd (300.8 +/- 18.7)=V-3000 (304 +/- 17.5) with high correlation among parameters (P < 0.001). During ETVlm participants completed 30 min of running while on the ETVHRd they lasted only 12.5 +/- 8.2 min with increasing [lac].Conclusion. We evidenced that CV and Vim track-protocols are valid for running evaluation and performance prediction and the parameters studied have different significance. The V-lm reflects the moderate-high intensity domain (below CV), can be sustained without [lac] accumulation and may be used for long-term exercise while the V-HRd overestimates a running intensity that can be sustained for long-time. Additionally, V-3000 and V-HRd reflect the severe intensity domain (above CV).

The relationship between onset of blood lactate accumulation, critical velocity, and maximal lactate steady state in soccer players

The objective of this study was to analyze the validity of the velocity corresponding to the onset of blood lactate accumulation (OBLA) and critical velocity (CV) to determine the maximal lactate steady state (MLSS) in soccer players. Twelve male soccer players (21.5 ± 1.0 years) performed an incremental treadmill test for the determination of OBLA. The velocity corresponding to OBLA (3.5 mM of blood lactate) was determined through linear interpolation. The subjects returned to the laboratory on 7 occasions for the determination of MLSS and CV. The MLSS was determined from 5 treadmill runs of up to 30-minute duration and defined as the highest velocity at which blood lactate did not increase by more than 1 mM between minutes 10 and 30 of the constant velocity runs. The CV was determined by 2 maximal running efforts of 1,500 and 3,000 m performed on a 400-m running track. The CV was calculated as the slope of the linear regression of distance run versus time. Analysis of variance revealed no significant differences between OBLA (13.6 ± 1.4 km·h-1) and MLSS (13.1 ± 1.2 km·h-1) and between OBLA and CV (14.4 ± 1.1 km·h-1). The CV was significantly higher than the MLSS. There was a significant correlation between MLSS and OBLA (r = 0.80), MLSS and CV (r = 0.90), and OBLA and CV (r = 0.80). We can conclude that the OBLA can be utilized in soccer players to estimate the MLSS. In this group of athletes, however, CV does not represent a sustainable steady-state exercise intensity. © 2005 National Strength & Conditioning Association.

Determination of critical velocity and anaerobic capacity of running rats

The aim of this study was to validate a non-invasive protocol to determine aerobic and anaerobic capacity of treadmill running rats. Thirteen male Wistar rats (90 days old) were submitted to 4 exercise tests, consisting of running at 25, 30, 35 and 40 m min-1, continuously until exhaustion. For the critical velocity (CV) and anaerobic running capacity (ARC) estimations, the hyperbolic curve (velocity versus time to exhaustion (tlim)) was linearized to V= CV+ARC/tlim, where the CV and ARC were linear and slope coefficients, respectively. In order to verify if the CV was the maximal aerobic intensity, the rats were submitted to the maximal lactate steady state test (MLSS) composed of three 25-minute tests of continuous running trials at 15, 20 and 25 m min-1, with blood collection every 5 minutes. The CV was obtained at 22.8±0.7 m min-1 and the ARC, at 26.80±2.77 m. The MLSS was observed at 20m min-1, with blood lactate 3.84 ± 0.31 mmol L-1. There was a progressive increase in lactate concentration at 25 m min-1. The CV and MLSS were different, but presented a high and significant correlation (r=0.81). These results indicate that the non-invasive protocol can be used for physical evaluation of aerobic running rats, but the ARC should still be further investigated.

Anaerobic running capacity determined from the critical velocity model is not significantly associated with maximal accumulated oxygen deficit in army runners

Purpose: The aim of this study was to verify whether there is an association between anaerobic running capacity (ARC) values, estimated from two-parameter models, and maximal accumulated oxygen deficit (MAOD) in army runners. Methods: Eleven, trained, middle distance runners who are members of the armed forces were recruited for the study (20 ± 1 years). They performed a critical velocity test (CV) for ARC estimation using three mathematical models and an MAOD test, both tests were applied on a motorized treadmill. Results: The MAOD was 61.6 ± 5.2 mL/kg (4.1 ± 0.3 L). The ARC values were 240.4 ± 18.6 m from the linear velocity-inverse time model, 254.0 ± 13.0 m from the linear distance-time model, and 275.2 ± 9.1 m from the hyperbolic time-velocity relationship (nonlinear 2-parameter model), whereas critical velocity values were 3.91 ± 0.07 m/s, 3.86 ± 0.08 m/s and 3.80 ± 0.09 m/s, respectively. There were differences (P < 0.05) for both the ARC and the CV values when compared between velocity-inverse time linear and nonlinear 2-parameter mathematical models. The different values of ARC did not significantly correlate with MAOD. Conclusion: In conclusion, estimated ARC did not correlate with MAOD, and should not be considered as an anaerobic measure of capacity for treadmill running. © 2013 Elsevier Masson SAS. All rights reserved.

BONA FIDE, STRONG-VARIABLE GALACTIC LUMINOUS BLUE VARIABLE STARS ARE FAST ROTATORS: DETECTION OF A HIGH ROTATIONAL VELOCITY IN HR CARINAE

We report optical observations of the luminous blue variable (LBV) HR Carinae which show that the star has reached a visual minimum phase in 2009. More importantly, we detected absorptions due to Si lambda lambda 4088-4116. To match their observed line profiles from 2009 May, a high rotational velocity of nu(rot) similar or equal to 150 +/- 20 km s(-1) is needed (assuming an inclination angle of 30 degrees), implying that HR Car rotates at similar or equal to 0.88 +/- 0.2 of its critical velocity for breakup (nu(crit)). Our results suggest that fast rotation is typical in all strong-variable, bona fide galactic LBVs, which present S-Dor-type variability. Strong-variable LBVs are located in a well-defined region of the HR diagram during visual minimum (the ""LBV minimum instability strip""). We suggest this region corresponds to where nu(crit) is reached. To the left of this strip, a forbidden zone with nu(rot)/nu(crit) > 1 is present, explaining why no LBVs are detected in this zone. Since dormant/ex LBVs like P Cygni and HD 168625 have low nu(rot), we propose that LBVs can be separated into two groups: fast-rotating, strong-variable stars showing S-Dor cycles (such as AG Car and HR Car) and slow-rotating stars with much less variability (such as P Cygni and HD 168625). We speculate that supernova (SN) progenitors which had S-Dor cycles before exploding (such as in SN 2001ig, SN 2003bg, and SN 2005gj) could have been fast rotators. We suggest that the potential difficulty of fast-rotating Galactic LBVs to lose angular momentum is additional evidence that such stars could explode during the LBV phase.

Evaluation of an innovative critical power model in intermittent vertical jump

The aim of this study was to test if the critical power model can be used to determine the critical rest interval (CRI) between vertical jumps. Ten males performed intermittent countermovement jumps on a force platform with different resting periods (4.1 +/- 0.3 s, 5.0 +/- 0.4 s, 5.9 +/- 0.6 s). Jump trials were interrupted when participants could no longer maintain 95% of their maximal jump height. After interruption, number of jumps, total exercise duration and total external work were computed. Time to exhaustion (s) and total external work (J) were used to solve the equation Work = a + b . time. The CRI (corresponding to the shortest resting interval that allowed jump height to be maintained for a long time without fatigue) was determined dividing the average external work needed to jump at a fixed height (J) by b parameter (J/s). in the final session, participants jumped at their calculated CRI. A high coefficient of determination (0.995 +/- 0.007) and the CRI (7.5 +/- 1.6 s) were obtained. In addition, the longer the resting period, the greater the number of jumps (44 13, 71 28, 105 30, 169 53 jumps; p<0.0001), time to exhaustion (179 +/- 50, 351 +/- 120, 610 +/- 141, 1,282 +/- 417 s; p<0.0001) and total external work (28.0 +/- 8.3, 45.0 +/- 16.6, 67.6 +/- 17.8, 111.9 +/- 34.6 kJ; p<0.0001). Therefore, the critical power model may be an alternative approach to determine the CRI during intermittent vertical jumps.

Ramp and constant power trials produce equivalent critical power estimates

The standard critical power test protocol on the cycle prescribes a series of trials to exhaustion, each at a different but constant power setting. Recently the protocol has been modified and applied to a series of trials to exhaustion each at a different ramp incremental rate. This study was undertaken to compare critical power and anaerobic work capacity estimates in the same group of subjects when derived from the two protocols. Ten male subjects of mixed athletic ability cycled to exhaustion on eight occasions in randomized order over a 3-wk period. Four trials were performed at differing constant power settings and four trials on differing ramp incremental rates. Both critical power and anaerobic work capacity were estimated for each subject by curve fitting of the ramp model and of three versions of the constant power model. After adjusting for inter-subject variability, no significant differences were detected between critical power estimates or between anaerobic work capacity estimates from any model formulation or from the two protocols. It is concluded that both the ramp and constant power protocols produce equivalent estimates for critical power and anaerobic work capacity.

Adaptação de protocolos invasivos e não invasivos para avaliações aeróbias e anaeróbias específicas ao basquetebol feminino

OBJECTIVE: To adapted the critical velocity (CV), RAST test and lactate minimum (LM) to evaluation of female basketball players. METHODS: Twelve well-trained female basketball players (19 ± 1yrs) were submitted to four intensities running (10 - 14 km/h) at shuttle exercise until exhaustion, applied on alternate days. The linear model 'velocity vs. 1/tlim' was adopted to determine the aerobic (CV) and anaerobic (CCA) parameters. The lactate minimum test consisted of two phases: 1) hiperlactatemia induction using the RAST test and 2) incremental test composed by five shuttle run (20-m) at 7, 8, 9, 10, and 12 km/h. Blood samples were collected at the end of each stage. RESULTS: The velocity (vLM) and blood lactate concentration at LM were obtained by two polynomial adjustments: lactate vs. intensity (LM1) and lactate vs. time (LM2). ANOVA one-way, Student t-test and Pearson correlation were used for statistical analysis. The CV was obtained at 10.3 ± 0.2 km/h and the CCA estimated at 73.0 ± 3.4 m. The RAST was capable to induce the hiperlactatemia and to determine the Pmax (3.6 ± 0.2 W/kg), Pmed (2.8 ± 0.1 W/kg), Pmin (2.3 ± 0.1 W/kg) and FI (30 ± 3%). The vLM1 and vLM2 were obtained, respectively, at 9.47 ±0.13 km/h and 9.8 ± 0.13 km/h, and CV was higher than vLM1. CONCLUSION: The results suggest that the non-invasive model can be used to determine the aerobic and anaerobic parameters. Furthermore, the LM test adapted to basketball using RAST and progressive phase was effective to evaluate female athletes considering the specificity of modality, with high success rates observed in polynomial adjustment 'lactate vs. time' (LM2).