Measure for Measure

The physicist Lord Kelvin (1824-1907) wrote:

I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind.

This wonderfully arrogant bit of Victorian certainty was somewhat diminished by twentieth-century physics, but the search for accurate measurements continues, as such measurements are the means of testing the predictions of science. In forensic science and engineering, measurements have a slightly different use--here we use measurements not to predict the future, but to reconstruct the past. Still, many of the tools and techniques of measurement are the same, and in this article we'll discuss a few of them.

First, a bit of nomenclature. In everyday use, the terms accuracy and precision are used almost interchangeably, but when used to discuss measurements they have distinct meanings. Accuracy refers to how close a measured value is to the true value, while precision refers to the degree of fineness of the measurement. For example, if a measuring tool or technique is used incorrectly, the value obtained may be stated with great precision ("1.3263 inches") without being accurate. On the other hand, there are many situations where a useful and accurate statement of measurement ("between 3 and 4 feet") is relatively imprecise. Accuracy should always be strived for; the level of precision needed depends on the situation and what the measurement is to be used for.

Most of the tools used to determine the positions and orientations of objects (equipment, people, etc.) involved in a failure or accident are commonplace: rulers, tape measures, protractors, levels, plumb lines. Less common, but certainly not exotic are surveyors' and machinists' tools: theodolites, total stations, micrometers, depth gages. Special purpose tools--weld profile gauges, stage micrometers for microscopes, optical comparators--also find their way into the technical investigator's kit.

Measurement techniques are as important as the tools used. How do you determine the diameter of a part that has broken into several pieces, none of which are big enough to allow for direct diametral measurement? Several techniques are available. For example, you could measure the chord and arc lengths between two points on the part and then use the geometric properties of a circle to calculate the diameter. You could also trace the part on a piece of graph paper, get the coordinates of a few points, and calculate the diameter by plugging the coordinates into the mathematical formula for a circle. If you didn't want to do a lot of calculations, you could cut circle templates of various sizes until you get one that fits snugly against the part. There are other methods--the choice should be based on the nature of the part (it may be too big to be traced) and the level of precision required.

Photographs can be a good source of geometric data. In fact, the science of making measurements from photographs has its own name--photogrammetry--and many forensic photographs are taken for the express purpose of making measurements. Photogrammetry is typically used when direct measurement is impossible or impractical. In situations where an accident scene has been altered, or a failed piece of equipment has been scrapped, photographs are often the only source of geometric data. Recent improvements and lowered costs for digitizing photographs have made some photogrammetric measurements much easier to perform.

Witness marks--such as scratches, dents, and paint transfer--are an excellent source of positional data. Properly interpreted, they give an absolute indication of contact between parts as well as some indication of the parts' relative movement before and after contact.

This article has touched on only a few aspects of geometric measurement, and we haven't discussed at all the measurement of force, temperature, or time. But, according to the word processor, this article is now over 650 words long, which, by any measure, is long enough.