Katz J S, Katz L
Science Policy Research Unit, University of Sussex, Brighton, UK.
J Sports Sci. 1999 Jun;17(6):467-76. doi: 10.1080/026404199365777.
In a previous study, we showed that the 1992 men's world record running times in the 100 m to 200 km could be represented accurately by the equation T = cDn, where T is the calculated record time for distance D, and c and n are positive constants. Here, we extend that to cover the years 1925-65 at 10-year intervals and 1970-95 in 5-year intervals for distances of 100 m to 10 km. Values of n for all years lie along a straight line with a small negative slope. A regression analysis yields an equation for values of n covering the period 1925-95. Values of c from 1925 to 1995 were fitted by a quadratic equation. These two equations define a surface in three-dimensional space (log(T), log(D), data) for all men's world record runs over the 70-year period for distances of 100 m to 10 km. We also demonstrated previously that event times, t, do not scatter randomly with respect to the values of T but form a consistent pattern about the straight lines in log(T) versus log(D) plots. In this study, we show that the pattern of (t-T)/t as a function of date has remained constant for the past 70 years.
在之前的一项研究中，我们表明1992年男子100米到200公里的世界纪录跑步时间可以用方程T = cDⁿ准确表示，其中T是距离D的计算记录时间，c和n是正的常数。在此，我们将其扩展到涵盖1925年至1965年，以10年为间隔，以及1970年至1995年，以5年为间隔，距离为100米到10公里的情况。所有年份的n值沿一条具有小负斜率的直线分布。回归分析得出了涵盖1925年至1995年期间n值的方程。1925年至1995年的c值用二次方程拟合。这两个方程在三维空间（log(T)、log(D)、数据）中定义了一个曲面，该曲面涵盖了70年期间所有男子100米到10公里距离的世界纪录跑步情况。我们之前还证明，比赛时间t相对于T值并非随机散布，而是在log(T)对log(D)的图中围绕直线形成一致的模式。在本研究中，我们表明在过去70年中，(t - T)/t作为日期的函数模式保持不变。
