Constant Power Solution of Hill’s Equation | Book Publisher International

British Nobel laureate A.V. Hill invented 1938 the famous muscle mechanics equation which is commonly known as the force-velocity relationship of muscle contraction.  Hill’s equation is a constant power equation. Hill’s equation can be presented in a form in which it shows Hill’s equation in three different power components (paragraph 1.4). The first power component is the power which is done against external force. Force multiplied by velocity is power. Second is the power of friction. Third term has no velocity variable, and therefore it can be concluded that it has no effect on the motion. It is the power consumption of muscle’s operational ability. This is the beginning of the solution of Hill’s equation. This book requires the ability of high school mathematics and mechanics. With that ability it is possible to reach high level of applied mechanics and mathematics which in this study is the level of Nobel price. Although this book signifies high level of science, the special concern has been taken to present the whole solution process as easy as possible. Most important part of the iteration process is in hand written form. In hand written form it is easy to differentiate from the other part of iteration process, and furthermore it signifies that hand work is necessary to learn and understand this kind of research process. The solution process consists of 73 equations, but they are in easy form, and most of them are closely related, and therefore easy to understand.  This book could be (for instance) a study book for applied mechanics. The solution of Hill’s equation in this book is founded on the research papers which are published in scientific journals (paragraph 1.5). Because the contents of articles are limited in these research papers, the iteration process of curve fitting is missing. In this book the fitting processes of these papers are referred as First fitting, and the total fitting processes have been presented here, and they are referred as Second fitting. The fitting processes of First Fitting have been continued in this book in order to obtain more accurate values and to confirm the theory of muscle contraction. In Second fitting the theory of muscle contraction in arm rotation movement (Maximum rotational moment → Maximum power → Maximum velocity) was used to determine value of Maximum power in three different manners.  These three Maximum power values must be the same value, and using this fact the total solution of Hill’s equation has been proved to be true. The bold letters have been written to differentiate the most important basic things.

Biography of author(s)

Ahti Rahikainen
Faculty of Sport and Health Sciences, Biology of Physical Activity, University of Jyväskylä, P.O.Box 35, 40014 Jyväskylä, Finland.