Aerodynamics and Design for Ultra-Low Reynolds Number Flight

4.2.7 The Distinction Between the Analysis and Design Problems
Chapter 4
The four relations for thrust and torque (Eqns. 4.18 - 4.21) yield two equations for two
unknowns (u, v i ) for each differential blade element. The other three unknown
quantities (Γ, κ, and v v ) are treated as dependent functions of the input parameters: the
lift distribution, rotor speed, ascent rate, number of blades, and chord distribution.
Details of these models are presented in the following sections of this chapter. With
values for u and v i , the required blade pitch distribution, θ(r) may be found as:
The determination of θ(r) is the last step in what can be described as the design case.
The geometry of the rotor is only partially defined with the remaining aspects of the
geometry revealed as part of the solution. The problem can be solved directly without
iteration, but has limited applicability.
Single point design is useful, but solving analysis problems, such as assessing a new
(4.28)
design at multiple operating points, or the performance of an existing design, is also an
essential capability for developing rotors for practical application. Unfortunately, this
requires some form of iteration with this rotor model. Rather than develop a separate
method for analysis, a simple modification in the definition of the subsequent
optimization problem is described in Section 4.6. This allows a single unified method to
be used for analysis and design.
U∞ + u
θ( r
⎞
) =
α ⎛
geo + atan ---------------------------
⎝ ⎠
Ωr– vi– vv 57