Several large-scale anthropometric studies were conducted in the 1960s and 1970s, mostly in industrialized countries. Contemporary studies are typically of smaller scope, with the exception of the ongoing CAESAR (Civilian American and European Surface Anthropometry Resource) project (http: / / store.sae.org/ caesar / ). Anthropometric data are generally presented in tabular form, with some combination of means, standard deviations, and population percentiles. A normal statistical distribution is usually assumed, a simplification which is reasonable in most cases, though which also leads to larger magnitudes of errors at extremes
of populations (e.g., the largest and smallest individuals).
Standard statistical methods can be employed directly for a number of applications. If, for example, we wish to design the height of a doorway to allow 99% of males to pass through unimpeded, we can estimate this height from the mean ( ) and standard deviation ( ) as follows (again assuming a normal distribution). Male stature has, roughly, 175.58 and 6.68 cm. The standard normal variate, z, is then used along with a table of cumulative normal probabilities to obtain the desired value:
where zA is the z value corresponding to a cumulative area A and Y is the value to be estimated. Here, z0.99 2.326, and thus Y 191.1 cm, or the height of a 99th percentile male. Clearly, however, further consideration is needed to address a number of practical issues. These include the relevance of the tabular values, whether this static value is applicable to a functional situation, and if /how allowances should be made for clothing, gait, etc.
Percentile calculations, as given above, are straightforward only for single measures. With multiple dimensions, such as several contiguous body segments, the associated procedures become more involved. To combine anthropometric measures, it is necessary to create a new distribution for the combination. In general, means add, but variances (or standard deviations) do not. Equations are given below for two measures, X and Y (a statistics source should be consulted for methods appropriate for n 2 values):
where indicates addition if measures are to be added and subtraction otherwise, cov is the covariance, and r is the correlation coefficient. As can be seen from these equations, the variance ( 2) of the combined measure reduces to the sum of the individual variances when the two measures are independent, or cov(X,Y) rXY 0. Human measures are generally moderately correlated, however, with r on the order of 0.2–0.8 depending on the specific measures.
Maury A. Nussbaum
Industrial and Systems Engineering
Virginia Polytechnic Institute and State University
Blacksburg, Virginia
Jaap H. van Diee¨n
Faculty of Human Movement Sciences
Vrije Universiteit
Amsterdam, The Netherlands
Mechanical Engineers’ Handbook: Materials and Mechanical Design, Volume 1, Third Edition.
Edited by Myer Kutz
Copyright 2006 by John Wiley & Sons, Inc.
