An arithmetic function f is said to be multiplicative if f(1) = 1 and f(mn) = f(m)f(n) whenever (m, n) = 1, where (m, n) denotes as usual the greatest common divisor of m and n. Furthermore an arithmetic function is said to be linear (or completely multiplicative) if f(1) = 1 and f(mn) = f(m)f(n) for all positive integers m and n.The Dirichlet convolution of two arithmetic functions f and g is defined by for all n∈Z+. Recall that the set of all multiplicative functions, denoted by M, with this operation is an abelian group.

A model is presented for the aerodynamic performance prediction of fixed-pitch rotors for small unmanned aerial vehicles. The method uses a blade element momentum theory based approach that is formulated specifically for small rotors operating in hover and edgewise flight. In order to validate the model, a rotor test stand is used to measure the performance of a commercially available rotor for several inflow angles and advance ratios. The predictions agree with measurements for operating conditions excluding conditions with suspected vortex ring state. The model is incorporated into a numerical optimization scheme to demonstrate its potential as a design tool. Designs are presented that minimize the power loading for single- and multi-point operating conditions. The optimized designs have hyperbolic twist distributions, higher solidities, and operate at lower tip-speeds than existing designs. A potential flow based model is also presented to predict the wake interactions between multiple rotors in configuration.

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A model is presented for the aerodynamic performance prediction of fixed-pitch rotors for small unmanned aerial vehicles. The method uses a blade element momentum theory based approach that is formulated specifically for small rotors operating in hover and edgewise flight. In order to validate the model, a rotor test stand is used to measure the performance of a commercially available rotor for several inflow angles and advance ratios. The predictions agree with measurements for operating conditions excluding conditions with suspected vortex ring state. The model is incorporated into a numerical optimization scheme to demonstrate its potential as a design tool. Designs are presented that minimize the power loading for single- and multi-point operating conditions. The optimized designs have hyperbolic twist distributions, higher solidities, and operate at lower tip-speeds than existing designs. A potential flow based model is also presented to predict the wake interactions between multiple rotors in configuration.