From an empirical choice of the shadowing of one control-plate element by another, expressions are derived for the reactivity worth of systems of circumferential control plates. The expressions contain three parameters which are determined when independent calculations of three control systems have been made. The parameters can be expressed in terms of the worth of the complete control plate, the increase in reactivity due to unshadowing of an end of a control plate and the decay constant of the assumed exponentially decaying shadowing function. Application of the expressions to a particular reactor design, where circumferential control plates separate core from radial reflector, shows that the analysis is accurate for those situations where the number of control plates is not large. The analysis neglects neutron absorption by the edge of a control plate so that it underestimates reactivity worth in situations involving large numbers of control plates where the surface area of the plate edges becomes significant.
