Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Chapter 4
lift distribution, and rotational speed are treated as the free design variables with the
primary constraint that the power required matches the motor's power available. The
motor model is flexible in that the code requires a user supplied subroutine that returns
the power available for a given RPM. The overall structure is pictured in Figure 4.7.
As mentioned earlier, the analysis mode is a different problem and requires the ability to
input only the geometry of the rotor, chord distribution, incidence, and the rotor speed.
Rather than create a second iterative rotor analysis code for this problem, this case is also
solved using the same rotor analysis code and non-linear optimizer, but the problem
posed to the optimizer is modified. The specified incidence angle at each station is
treated as an equality constraint. This drives the geometry to the specified incidence
angles. The optimal solution that satisfies the incidence constraints provides the correct
lift distribution for the analysis of rotor performance. With RPM as an input, the
constraint on the power required is removed. It is assumed in the analysis mode that the
case represents a realizable operating point. The design code produces an optimal
solution at a single operating point. The analysis code allows these solutions to be
evaluated over a range of operating conditions. It also provides a means of validating the
method by comparing predicted performance with experimental results for existing
rotors and propellers. The next chapter discusses the effectiveness of the various
enhancement models and the validation of the overall method.
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