Читать книгу Planning and Executing Credible Experiments - Robert J. Moffat - Страница 30

Shape cannot be measured – not even simple shapes, such as circles. Simple shapes can be described by names that we all understand by experience, but they cannot be measured. For example, a “circle” is defined as the locus of points lying in a plane and at the same distance from a common point, called “the center.” Given that definition and a value for the radius, you can draw a circle and look at it, and you know exactly what was meant – but that does not constitute measuring the shape of the circle. The shape information was conveyed using the reserved word “circle”; only the size was described by the radius and location by the center.

Shape can have a delicious impact, when tested by experiment! For example, the design of rice cookers has made it possible to make chef‐quality rice at home. A few years ago, product design engineers in Japan focused on the cooking profile of rice (not the shape of the device). By experiment, they found the shape of the temperature versus time curve, T = f (t), as shown in Figure 2.1, which optimizes rice taste when the ingredient is washed white, short‐grain rice. They also found a different shape that is best for unwashed rice and yet another shape for brown rice. Although aspects of the shape can be measured, such as the time at each temperature, it is the shape of the cooking profile that enhances the taste of the rice. By offering more delicious rice, manufacturers gained market share over older cookers that merely boiled rice.³

Another example comes from the physics of fluid flows. In boundary layer studies, the shape of the velocity profile is of considerable interest and often needs to be recorded. One way to deal with this is to present u = f (y), a set of ordered pairs (u, y). This allows the viewer to draw the shape and look at it. Another way, conveying less information but sometimes enough, is to present the shape factor: the ratio of two integral measures of the boundary layer thickness, the displacement thickness divided by the momentum thickness. Turbulent boundary layers have larger values of the shape factor than laminar boundary layers. Researchers who know approximately what the velocity profile looks like (i.e. what family of shapes to which it belongs) can communicate quite a bit of information to one another by quoting shape factor values. Yet the value of the shape factor itself is not a measure of shape. Only if the boundary layer is known to be laminar or turbulent or somewhere in between does the shape factor convey information. If the family of possible shapes is not specified either explicitly or implicitly, then it takes a very large number of scalar pairs to describe shape – enough data points to plot the shape so it can be looked at. Presenting u(y) throughout the boundary layer allows the viewer to see the shape, but that does not constitute a measurement of shape any more than a photograph of a face is a measurement of the shape of that face. The derived scalar “measures” of shape, such as displacement thickness, momentum thickness, and shape factor, can convey significantly wrong impressions of the shape of a boundary layer velocity distribution when they are reported for a “pathological boundary layer,” i.e. one whose velocity distribution is significantly different than usual. They convey the right information only when they are applied to boundary layers with generally typical velocity distributions.

Figure 2.1 Rice cooker design trajectory.