Force- and Power-Velocity Relationships in a Multi-Joint Movement

Open Access
Hardyk, Andrew T. T.
Graduate Program:
Exercise and Sport Science
Doctor of Philosophy
Document Type:
Date of Defense:
October 30, 2000
Committee Members:
  • H Joseph Sommer Iii, Committee Member
  • William J Kraemer, Committee Member
  • Richard Carroll Nelson, Committee Member
  • Vladimir M Zatsiorsky, Committee Chair
  • vertical jump
  • force
  • multi-joint
  • force ellipses
  • velocity ellipses
  • power
  • velocity
Force-velocity characteristics in multi-joint movements, specifically the vertical jump, have been relatively unexplored in the literature. There were five main goals in this study: 1) to accurately define the force-velocity relationships for a multi-joint movement and compare them to Hill's classic force-velocity curve, 2) to compare several options for presenting force-velocity curves in a multi-joint movement, 3) to accurately define the power-load and power-velocity relationships in a multi-joint movement for the ranges of force and velocity that were obtainable, 4) since the entire theoretical power-velocity curve was not obtainable because of physical limitations, to determine whether the data in this experiment lies in the ascending or descending portion of the theoretical power-velocity curve, and 5) to determine the load and velocity at which maximum power was produced. Ten well-trained subjects were asked to perform maximum effort, noncountermovement vertical jumps with a range (80% of bodyweight unloading to 125% of bodyweight additional loading) of external loads applied. Each subject performed 28-34 trials with two trials at each condition. The instant of the maximum levels of the various velocity measures was used as the time to measure all of the other variables and the trial with the highest maximum center of mass velocity was selected for analysis. Relationships were identified as 'Hill-like' if they were descending, had upward concavity, and 0<a/Fo<1. All of the variables studied in this investigation (maximum velocity of the center of mass, maximum knee angular velocity, maximum leg extension velocity, ground reaction force, and knee moment) were plotted against load. None of these relationships compared well with Hill's curve. Various logical combinations of these variables were compared to each other and to Hill's curve. Only ground reaction force vs. maximum center of mass velocity (video), vs. maximum knee angular velocity, and vs. maximum leg extension velocity were Hill-like. The best fit was the ground reaction force vs. maximum center of mass velocity (video) relationship, mathematically fit with Hill's curve. Power, calculated by multiplying ground reaction force and maximum center of mass velocity, varied as expected with maximum center of mass velocity and was on the descending part of the theoretical power-velocity curve. Maximum power corresponded to approximately 37-61% of the maximum squat lift of the subjects and 56% of maximum velocity. This was higher than predicted from theoretical models, but was similar to weightlifting studies. This study successfully determined the force-velocity and power-velocity relationships for a multi-joint movement. Theoretical reasons why there was limited agreement with Hill's curve were discussed. No other study known by the author covers as wide a range of forces and velocities in vertical jumping.