Aerodynamics and Design for Ultra-Low Reynolds Number Flight
Aerodynamics and Design for Ultra-Low Reynolds Number Flight
Aerodynamics and Design for Ultra-Low Reynolds Number Flight
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Chapter 6<br />
The importance of the operational deflections <strong>for</strong> micro-rotors becomes apparent if<br />
Eqn.6.1 is considered with the restrictions of constant chord <strong>and</strong> thickness along a blade:<br />
This may be further manipulated to show a predominant dependence of θ on ωR (the tip<br />
speed) <strong>and</strong> the inverse of the thickness ratio squared. The tip speeds of the micro-rotors<br />
presented here are roughly one third to one fourth those of full scale helicopter rotors,<br />
but t/c is reduced by a factor of three to four <strong>and</strong> dominates. This effect is also seen on<br />
large scale rotors, but <strong>for</strong> the development of small rotors it should be considered an<br />
essential component of design. Large rotors typically have some <strong>for</strong>m of collective<br />
control that can be used to partially compensate <strong>for</strong> the loss of incidence, but the only<br />
control available to the micro-rotors is RPM.<br />
The effects of the aerodynamic <strong>for</strong>ces are not negligible <strong>and</strong> are strongly coupled to the<br />
structural de<strong>for</strong>mations. The pitching moment coefficient is typically insensitive to<br />
angle of attack <strong>and</strong> provides a relatively small nose down moment that works in unison<br />
with the structural moment due to rotation. However, the local lift coefficient is<br />
obviously very sensitive to the incidence angle <strong>and</strong>, <strong>for</strong> a positive lift coefficient,<br />
opposes the inertial effects of rotation. The correct deflected rotor solution would be at<br />
structural equilibrium <strong>and</strong> operating at lift coefficients representative of the equilibrium<br />
geometry. This requires some <strong>for</strong>m of iteration. Ideally this would be integrated into the<br />
design process, but at this time that has not been implemented. For the purpose of the<br />
analyses presented here, several iterations have been carried out manually at each rotor<br />
speed, but the solutions are not fully converged, meaning that the assumed lift<br />
coefficients used <strong>for</strong> the structural analyses do not precisely match the predicted value<br />
from the final per<strong>for</strong>mance analyses.<br />
122<br />
dθ 3 2<br />
( r)<br />
-----ρ<br />
1<br />
–<br />
dR<br />
12 matω<br />
---<br />
1<br />
G(<br />
t ⁄ c)<br />
2<br />
=<br />
-------------- cos(<br />
ζ+ θ)<br />
sin(<br />
ζ+ θ)<br />
dR<br />
tip<br />
∫<br />
r<br />
(6.6)
Change language