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The Curvature Constant Parameter of the Power-Duration Curve for Varied-Power Exercise

FUKUBA, YOSHIYUKI1; MIURA, AKIRA1; ENDO, MASAKO1; KAN, AKIRA1; YANAGAWA, KAZUMASA1; WHIPP, BRIAN J.2

Medicine & Science in Sports & Exercise: August 2003 - Volume 35 - Issue 8 - p 1413-1418
doi: 10.1249/01.MSS.0000079047.84364.70
APPLIED SCIENCES: Biodynamics

FUKUBA, Y., A. MIURA, M. ENDO, A. KAN, K. YANAGAWA, and B. J. WHIPP. The Curvature Constant Parameter of the Power-Duration Curve for Varied-Power Exercise. Med. Sci. Sports Exerc., Vol. 35, No. 8, pp. 1413–1418, 2003.

Introduction The tolerable duration (t) for high-intensity cycle ergometry bears a hyperbolic relationship to the power output (P) with an asymptote termed the critical power (CP), and a curvature constant (W′) that is numerically equivalent to an amount of work that can be performed above CP. The physiological nature of W′ has received little consideration compared with CP, e.g., whether the total amount of work above CP remains constant when the power actually changes during the high-intensity task.

Purpose The purpose of this study was to compare W′ derived from the standard estimation method, consisting of several different constant-P tests, and the total amount of work above CP during an exhausting exercise bout using a variable-P protocol.

Methods Eleven healthy male subjects (age: 21–40 yr) volunteered to participate in this study. Each initially performed four-to-six high-intensity square-wave exercise bouts for estimation of CP [mean (SD); 213.3 (22.4) W] and W′ [12.68 (3.08) kJ]. The subjects subsequently performed two variable-P tests to the limit of tolerance. During the first part, P was 117% or 134% of CP for a duration that expended approximately half of W′. The work rate was then abruptly increased to 134% (UP protocol) or decreased to 117% (DOWN protocol) of CP for the second part.

Results There were no significant differences between W′ [12.68 (3.08) kJ] and the total amount of work above CP during the UP [12.14 (4.18) kJ] and DOWN [12.72 (4.05) kJ] protocols (P > 0.05).

Conclusion We conclude that the work equivalent of W′ is not affected by power variations during exhausting cycle ergometry, at least in the P range of 100–134% of CP.

1Department of Exercise Science and Physiology, School of Health Sciences, Hiroshima Prefectural Women’s University, Hiroshima, JAPAN; and

2Division of Respiratory and Critical Care Physiology and Medicine, Harbor-UCLA Medical Center, Torrance, CA

Address for correspondence: Yoshiyuki Fukuba, Ph.D., FACSM, Professor of Human Physiology, Department of Exercise Science and Physiology, School of Health Science, Hiroshima Prefectural Women’s University, 1-1-71, Ujina-higashi, Minami-ku, Hiroshima 734-8558 Japan; E-mail: address: fukuba@hirojo-u.ac.jp.

Submitted for publication October 2002.

Accepted for publication April 2003.

©2003The American College of Sports Medicine