Variable versus constant power strategies during cycling time-trials: Prediction of time savings using an up-to-date mathematical model

Abstract

Swain (1997 Swain, D. P. 1997. A model for optimizing cycling performance by varying power on hills and in wind. Medicine and Science in Sports and Exercise, 29: 1104–1108. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) employed the mathematical model of Di Prampero et al. (1979 Di Prampero, P. E., Cortili, G., Mognoni, P. and Saibene, F. 1979. Equation of motion of a cyclist. Journal of Applied Physiology, 47: 201–206. [PubMed], [Web of Science ®] , [Google Scholar]) to predict that, for cycling time-trials, the optimal pacing strategy is to vary power in parallel with the changes experienced in gradient and wind speed. We used a more up-to-date mathematical model with validated coefficients (Martin et al., 1998 Martin, J. C., Milliken, D. L., Cobb, J. E., McFadden, K. L. and Coggan, A. R. 1998. Validation of a mathematical model for road cycling power. Journal of Applied Biomechanics, 14: 276–291. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) to quantify the time savings that would result from such optimization of pacing strategy. A hypothetical cyclist (mass = 70 kg) and bicycle (mass = 10 kg) were studied under varying hypothetical wind velocities (?10 to 10 m · s^?1), gradients (?10 to 10%), and pacing strategies. Mean rider power outputs of 164, 289, and 394 W were chosen to mirror baseline performances studied previously. The three race scenarios were: (i) a 10-km time-trial with alternating 1-km sections of 10% and ?10% gradient; (ii) a 40-km time-trial with alternating 5-km sections of 4.4 and ?4.4 m · s^?1 wind (Swain, 1997 Swain, D. P. 1997. A model for optimizing cycling performance by varying power on hills and in wind. Medicine and Science in Sports and Exercise, 29: 1104–1108. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]); and (iii) the 40-km time-trial delimited by Jeukendrup and Martin (2001 Jeukendrup, A. E. and Martin, J. 2001. Improving cycling performance: How should we spend our time and money?. Sports Medicine, 31: 559–569. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Varying a mean power of 289 W by ± 10% during Swain's (1997 Swain, D. P. 1997. A model for optimizing cycling performance by varying power on hills and in wind. Medicine and Science in Sports and Exercise, 29: 1104–1108. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) hilly and windy courses resulted in time savings of 126 and 51 s, respectively. Time savings for most race scenarios were greater than those suggested by Swain (1997 Swain, D. P. 1997. A model for optimizing cycling performance by varying power on hills and in wind. Medicine and Science in Sports and Exercise, 29: 1104–1108. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). For a mean power of 289 W over the “standard” 40-km time-trial, a time saving of 26 s was observed with a power variability of 10%. The largest time savings were found for the hypothetical riders with the lowest mean power output who could vary power to the greatest extent. Our findings confirm that time savings are possible in cycling time-trials if the rider varies power in parallel with hill gradient and wind direction. With a more recent mathematical model, we found slightly greater time savings than those reported by Swain (1997 Swain, D. P. 1997. A model for optimizing cycling performance by varying power on hills and in wind. Medicine and Science in Sports and Exercise, 29: 1104–1108. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). These time savings compared favourably with the predicted benefits of interventions such as altitude training or ingestion of carbohydrate-electrolyte drinks. Nevertheless, the extent to which such power output variations can be tolerated by a cyclist during a time-trial is still unclear.     

Age and gender differences in children's and adolescents' adaptation to sexual abuse

OBJECTIVE: How children manifest psychological distress following the discovery of sexual abuse requires a better understanding of individual differences in developmental capacities and vulnerabilities. This study examined how age at the time of the abuse discovery and gender of victim are related to psychological distress. METHOD: One hundred and sixty-nine participants (96 children, 73 adolescents) were interviewed within 8 weeks of discovery of the abuse. Multivariate analyses were used to examine how age at discovery, and gender, with abuse characteristics as covariates, were related to shame, attribution style, depression, self-esteem, and traumatic events sequelae. RESULTS: Adolescents compared to children report a higher level of depressive symptoms, negative reactions by others, and lower levels of self-esteem, social support, and sexual anxiety. Girls compared to boys report higher levels of intrusive thoughts, hyperarousal, sexual anxiety, personal vulnerability, and perceiving the world as a dangerous place and lower levels of eroticism. CONCLUSIONS: These findings suggest the importance of considering individual differences in age and gender for understanding patterns of symptom expression. Treatment strategies need to reflect these individual differences in adjustment, such as targeting issues of sexual anxiety for girls and self-esteem for adolescents.     

“Doing What I can,but I got no Magic Wand:” A Snapshot of Early Childhood Educator Experiences and Efforts to Ensure Quality During the COVID-19 Pandemic

Early Childhood Education Journal - The COVID-19 pandemic impacted early childhood programs serving infants, toddlers, and preschoolers in dramatic ways. After temporarily closing, many educators...     

Symbolic Management of the Degree of Information Security by Integer Splitting

This paper demonstrates the application of module arithmetic for controlling the level of information security by a new technique referred as integer splitting. The basic definitions and concepts of the method are provided. The mathematical function of arising transformation is described in detail; its properties were studied and the basic theorems were proven that justify the use of splitting in practical applications. An active system was designed and characteristic cases of its operation are considered.     

超高含水原油混合流动及初始沉积特性

使用自行设计的实验装置,对超高含水原油的流动特性和初始沉积过程进行探究。系统研究实验温度、混合流速和体积含水率对超高含水原油初始沉积过程的影响,分析不同温度下原油的运动形态和初始沉积方式。初始沉积过程可分为蔓延沉积过程和粘连沉积过程,根据沉积特点和压降曲线的变化趋势将初始沉积过程分为3个阶段：沉积诱导期、快速沉积期和沉积动态平衡期。通过对沉积物碳数分布的分析,得知超高含水原油初始沉积过程中,同时存在剪切剥离作用、胶凝作用和分子扩散作用。实验温度和体积含水率主要通过改变胶凝作用和分子扩散来影响初始沉积过程,混合流速通过改变剪切剥离强度来影响初始沉积过程。     

一个统一混沌系统及其研究

发现了一个新的混沌系统,它是介于著名的Lorenz系统和Chen系统之间的临界系统.同时,提出了一个单参数的统一混沌系统--Lorenz系统族,它包含Lorenz系统和Chen系统作为参数区间的两个极端系统,临界系统作为一个过渡系统.基于线性耦合多振子互同步问题的研究,提出了研究这一类问题的新方法--模式分解法,并首次从理论上给出了上述3个典型系统混沌同步的几个严格的充分条件.还提出了一类新的简单的切换分段线性反控制器,它能够使一个简单的线性系统在三维空间中同时产生n个,或一个具有多吸引域融合的复杂混沌吸引子.     

Reducing adolescents' involvement with relational aggression: Evaluating the effectiveness of the Creating A Safe School (CASS) intervention

This study examined the effectiveness of a comprehensive, school‐based intervention program, Creating A Safe School (CASS; The Ophelia Project) designed to reduce relational aggression (RA) and relational victimization (RV). Sixth‐grade students (N = 406) were surveyed before and after the intervention. Program effects were tested using a repeated‐measures design. Results revealed significant reductions in RA and RV among students who reported initially high levels of involvement. Findings also showed that decreasing approval of RA accounted for a significant amount of variance in changes in RA between pre‐ and posttest. These results provide initial evidence of the effectiveness of the CASS intervention model in reducing RA among early adolescents. © 2010 Wiley Periodicals, Inc.