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Proportionality Constants


Proportionality Constants were one of the earliest methods developed to predict human anthropometry. They are typically calculated by taking a large sample of anthropometric data and determining either the mean or 50th percentile ratio of the length of each measure of interest to stature. Drillis and Contini were among the first to publish mathematical ratios of many body dimensions to stature (Drillis and Contini, 1966). See figure below for a simplified diagram of Drillis and Contini’s proportionality constants.


These values have been extensively used as a design tool because they provide a means of estimating the lengths of many body segments while knowing only the stature of an individual. An example design process using proportionality constants works like this:

  1. Determine which body dimension can be used to most accurately predict adjustability levels. For example, trochanteric height (leg length) may be used to predict seat height adjustability range on a stationary exercise bike.
  2. Determine the cutoff percentiles for the desired accommodation level for the artifact. If 95% accommodation is desired, the 2.5th and 97.5th percentiles are used.
  3. Find the accommodation range. To do this, multiply the proportionality constant of the body dimension determined in step 1 by the stature corresponding to the low cutoff percentile determined in step 2. This provides the smallest body dimension length that will be accommodated. Multiply the same proportionality constant by the stature corresponding to the high cutoff percentile to obtain the largest body dimension that will be accommodated. The difference between these two lengths is the accommodation range.

Boundary Ratios

While simple to use, proportionality constants have many limitations. Those from Drillis and Contini were calculated from a population that has never been validated, and they did not provide formal definitions of the body dimensions each ratio predicted. Furthermore, proportionality constants are used under the false assumption that an nth percentile person by stature is composed of nth percentile body segments. A recent study (see Fromuth, 2008) has overcome the above drawbacks by developing a set of Boundary Ratios. There are however, drawbacks to all proportionality constant models that cannot be overcome. In DfHV, posture and user preference heavily influence accommodation levels and these often do not correlate with anthropometry. Proportionality constant models assume that two people of the same size will interact with a designed artifact in the same way. Due to these limitations, it is best to gather data from a study of the target population to obtain more accurate estimates of accommodation levels using either population or hybrid models.

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Posted on

September 28, 2017