Aerodynamics and Design for Ultra-Low Reynolds Number Flight

The static deformations described in this section account for some of the detailed
Chapter 6
behavior of particular rotor samples and emphasize the potential problems associated
with precision manufacturing at this scale. This is particularly true of any aerodynamic
surface where structural variations of only a few degrees can have a distinct effect on
performance. While in this section deformations were examined on a case by case basis
in a necessarily qualitative manner, the next section considers, in detail, deformations
that are systemic in nature and broadly, and somewhat uniquely, affect rotor design at
these small physical scales.
6.5.2 Operational Deformations
Rotors spinning from 30,000 to over 50,000 RPM experience tremendous inertial forces
due to centripetal acceleration. At the design speed of 47,000 RPM the tip of the four-
blade 2.5cm rotor experiences centripetal accelerations 30,000 times the force of gravity.
These forces should be beneficial axially, stiffening the blade against longitudinal
bending, but the thin structures coupled with the incidence of blades has the potential for
strong torsional effects.
Thin Plate Beam Torsion Model
The magnitude of torsional deflections due to rotation have been modeled using beam
torsion theory. The thin blade sections and relatively high aspect ratio of the blades
make use of this simple model acceptable. The local blade cross-section is reduced to a
flat plate with the structural axis at mid-chord. This simplifies the derivation of a closed
form for the local torsional moment and is reasonable considering the thin and lightly
cambered, constant thickness airfoils being used, and the fact that both the four-blade
and five-blade rotors have zero sweep at mid-chord. Other than these simplifications,
the full rotor geometry is modeled, with chord, thickness, and design incidence permitted
to vary along the span.
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