A Study of Scale Effects in Discrete Scaled Dynamic Systems

Scaled experimentation is an important experimental approach for the investigation of complex systems. Unfortunately, scaling suffers scale effects, where changes in behaviour with scale can be so significant to undermine any scaled investigation. The state-of-the-art in scaled experimentation remains dimensional analysis, which unfortunately offers no solution to scale effects and consequently scaled experiments although important provide only limited usefulness at the present time. This paper is concerned with a new approach to scaled experimentation founded on the theory of finite similitude applied to discrete mechanical systems. The new theory applies the metaphysical concept of space scaling, where objects, prototypes, systems, experimental apparatus and facilities are scaled by the means of space contraction or expansion. Although space scaling is clearly practically impossible, what is possible is an assessment of the effects of space scaling on the governing physics and a comparison with real experimental behaviours. It is shown in the paper how the new theory accounts for all scale dependencies and unlike dimensional analysis is able to accommodate known scale effects. It provides also alternative scale-invariances that cater for the situation where scale effects are present but unknown. This aspect is the focus here with application of first-order finite similitude to simple mechanical-dynamic systems, an approach that requires two scaled experiments at two distinct scales. It is demonstrated how it is possible by means of two scaled experiments to represent behaviours at the full scaled that hitherto would have been deemed impossible with traditional dimensional analysis.