The design of ducted fans, and the estimation of their performance for conditions other than those of the design, are usually based on the equations of the so-called strip-theory. Existing methods of solution invariably employ some form of iteration which is more or less rapidly convergent according to the experience of the computer and the detail of the method.

In this note, a solution is given which, although it is strictly an iteration, is explicit in the sense that in practice no iteration is necessary. It is shown how both design for a given performance and performance for a given fan can be calculated in one direct step.

Conditions for maximum efficiency are considered in an Appendix. Here a suggestion of R. Baldur's is used to give a simple approximate solution of the strip-theory equations which can be developed to give conditions for maximum efficiency, for the special case of a constant pressure rise through the fan.