Critical torque, estimated time to exhaustion, and anaerobic work capacity from linear and nonlinear mathematical models

C. Russell Hendrix, Terry J. Housh, Michelle Mielke, Jorge M. Zuniga, Clayton L. Camic, Glen O. Johnson, Richard J. Schmidt

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Theoretically, critical torque (CT) is the maximal isometric torque that can be maintained without fatigue, and anaerobic work capacity (AWC) is the total "isometric work" associated with stored energy sources within the muscle. PURPOSE: The purpose of this study was twofold: 1) to determine whether there were differences among the estimates of CT and AWC from linear and nonlinear mathematical models and 2) to compare the estimated time to exhaustion (ETTE) values associated with the CT estimates from the linear and nonlinear mathematical models. METHODS: Nine adult subjects (mean ± SD age = 21.6 ± 1.2 yr) performed three or four continuous, fatiguing, isometric muscle actions of the leg extensors at 30%, 45%, 60%, and 75% of maximum voluntary isometric contraction to determine the time to exhaustion (Tlim) values. Five mathematical models (two linear, two nonlinear, and one exponential) were used to estimate CT and AWC (the exponential model did not estimate AWC) from the relationships between "isometric work" or torque and Tlim. Individual torque versus Tlim curves was also generated from the fatiguing isometric muscle actions to calculate the ETTE values. RESULTS: The exponential model resulted in greater mean CT and lower ETTE values than the other models. There were no significant differences, however, between models for AWC. CONCLUSION: Torque-curve analyses indicated that the mean ETTE values range from 7.26 to 16.98 min, and therefore all five CT models (23.0 to 37.0 N•m) overestimated the torque levels that could be maintained for an extended period without fatigue.

Original languageEnglish (US)
Pages (from-to)2185-2190
Number of pages6
JournalMedicine and science in sports and exercise
Issue number12
StatePublished - Dec 2009


  • Anaerobic work capacity (awc)
  • Critical torque (ct)
  • Estimated time to exhaustion (ette)
  • Isometric work (w )
  • Limit time (t)

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine
  • Physical Therapy, Sports Therapy and Rehabilitation

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