The strip-theory equations of flow through a ducted fan were the basis of a method of designing a fan for a given performance. The merit of the method was that it amounted to an explicit solution of the design problem, no iteration being necessary.
In the inverse problem, of determining the flow past a given fan in conditions other than those of the design, two relations—the motor or tunnel characteristics, for example—will be given between the four quantities P, Ω, η, u (the motor power and angular velocity, the fan efficiency and the air speed at the fan). The problem is to determine the values of these four quantities together with details of the flow past any blade element.
This paper shows that to a high degree of accuracy the performance of a ducted fan can be summed up by saying that P/Ω3 and η are both functions of Ω/u only, functions which depend only on the fan shape. Solution by graphical means is therefore almost instantaneous.
The fan-tunnel combination is shown to be governed by extremely simple equations which amount to saying that the tunnel power factor is a function of Ω/u only which, again, can be calculated once for all for a given fan and tunnel.