Applications of matrix manipulation in dimensional analysis involving large numbers of variables

Abstract Many methods of dimensional analysis are tedious and time consuming if a large number of variables is involved. This is typically the case in analysing marine structures for model testing in wave tanks. When structural response is important the model must reproduce the dynamic behaviour of both fluid and structure and variables describing fluid, structure and wave properties are all important. It is suggested here that such a large number of variables is best handled in any dimensional analysis by the matrix method. This is a rigorous method in which variables are manipulated by simple, well defined, rules to formulate the dimensionless π terms. Codes for computer analysis, together with sample input and output data files, are provided in an appendix.