Experimental Modelling in Engineering by F. W. David

By F. W. David

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The second relation is derived from the first by the relaxation of certain conditions in the model design, resulting in the so-called "distorted model". Both relations will be dealt with in the subsequent sections. The principles involved will be discussed with reference to the example of the bending beam, used before, and to a number of other examples of simple situations in Mechanics. 1 Complete Similarity The meaning of complete similarity is readily explained by considering the beam problem of Chapter 3.

Establish by DA all iT-factors . List the given values and/or ranges of the prototype variables. Establish the scaling factors for all variables from the conditions X^ = 1 . e. where special conditions, not arising out of DA, must be considered, or where certain constraints are imposed. In such cases modelling proceeds along a different course. 2. 1 Modelling of Functional Relations Quite frequently cases are encountered where the effects of one or several prescribed inputs on a prototype system are to be examined by model tests.

For prototype-model relationship this condition expresses linearity between respective variables which can be defined by a constant of proportionality. This non-dimensional constant is given the name scaling factor, X , being the ratio magnitude of variable x. in prototype magnitude of variable x. 4) 39 Section AA (a) prototype (elevation view ) MfflfflfflA (b) model (elevation and plan views) FIG. 1 (a) (b) Prototype variable cross-section beam. Model beam (in plan v i e w ) . e. magnitude of IT .

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