PERIODICUM BIOLOGORUM Vol. 83, No 1,153-155, 1981 THE FORCE-VELOCITY RELATION IN QUADRICEPS MUSCLE SHORTENING S. JARIC, D. RISTANOVIC and P. GAVRILOVIC School for Physical Education, Department of Biophysics, Faculty Medicine, and Institute for Physical Education, Belgrade, Yugoslavia Received October IS, 1980 One of the basic features of muscle mechanics is the relation between the maximum force exerted by muscle contraction and the velocity of muscle shortening. This force-velocity relation is adequately represented by a rectangular hyperbola, the charac- teristic equation of which for muscle has been deter- mined by A.V. Hill (4) as follows: (F + a)(v + b) = b (Fo + a)= C. (I) Here , F is force, v is velocity of muscle shortening, Fo is maximum isometric force at zero speed. C is a constant, while a and b are constants chosen to give the best fit of eq. ( 1) to a series of observed values for v and F. The main aim of the present work was to evaluate the Hill equation by studying the voluntary isometric contraction of the quadri- ceps femoris muscle in man. The mechanics of muscle shortening were de- scribed by means of two-dimensional analysis and force-platform technique. Two young males were used as subjects in these experiments. Subject I was a graduate student of the School for Physical Education in Belgrade and Subject 2 was a highly skilled jumper. The subject stood on a force-platform (Kistler) used to measure vertical ground reaction force exer- ted during ·contact with it. Since the major force producer for upward movement is the knee extensor and the second most important force producer is the ankle plantar flexion (6), the subject's feet were in UDC 57 : 61 CODEN : PDBI-A YU ISSN 0031 - 5362 Conference paper a plantar flexion position. From this fixed starting position with the knee joint angle flexed at 70 ± 4 degrees. he made a vertical jump exerting maximum effort. Such a knee angle allowed the muscle to reach a fully active state before taking the first experimental value from the record. Prior to jum- ping, both coordinates of the subject lateral malleolus were registered by means of a light-emitting diode attached to the malleolus. All the measured forces were reduced for 20% of the body weight. This force approximately corresponds to that measured by the platform when the quadriceps muscle shortening control is stopped at any stage of movement. The movement of the hip joint center was registered two-dimensionally with the use of a diode attached to the trochanter projection on to a sagittal plane. The diode position was registered with a Selspot sys- tem camera (Selcom AB) and referred to the lateral malleolus record. The signals from the camera were amplified and graphed on a Honeywell multichannel X-Y plotter along with the amplified signals from the platform. The force and both coordinates were shown simultaneously against the time. They were measured only for the feet contact period. Both the component of the force and that of the resultant velocity were studied along a line extending from the greater trochanter to the lateral malleolus. This line made a small angle with the vertical. Therefore , un- der a given set of experimental conditions. the quadri- ceps muscle was the only one to act in such a move- ment. The experiment consisted of three jumps on the platform: one was analyzed when the quadriceps muscle was contracted against no load , and the other when two additional loads (of 20 kg and 40 kg. respectively) were applied. Actually. in order to broaden the ranges for values of the forces and velocities and to obtain some more data points to fit them to eq. (!). we used these two additional loads. Rest periods of five min were used bet ween successive runs. From the plot. the values for the distance between the diode and the reference point (allowing the knee joint angle choice and calculation of the correspon- ding muscle contraction velocities) , and for the force Reprint requests to: D. Ristanovic, Department of Biophysics,Faculty of Medicine, Visegradska 26/2, 11000 Bel- grade , Yugoslavia Perio d. bioi., Vol. 83, No 1, 1981 153