Phase II Final Report - NASA's Institute for Advanced Concepts

Chapter 3.0 Vehicle Design
3.2 Wing Motion and Structure Analysis
Figure 3-15: Entomopter Wing Structural Geometry
The inner ellipse, that represents the empty area, is of slightly different proportions then the
outer ellipse. This provides for increased mass on the upper and lower wing surfaces to increase
the structural rigidity and minimizes the mass at the front and trailing edges where it is needed
the least. The thickness taper for the wing was assumed to be a linear function from the root to
the tip.
I = (π / 64) (a 1 b 1
3 – a2 b 2
3 ) Equation 3-27
A = (π /4) (a 1 b 1 – a 2 b 2 ) Equation 3-28
To quantify the benefit of using a hollow wing and taper, the above analysis was performed for
four different structural designs. The maximum tip bending of each case was held constant and
the mass of the wing section was determined based on a configuration that would not exceed the
set bending limit. The results of this are shown in Figure 3-16. This bending limit was chosen
for comparison between the different geometries and may not represent the actual bending limit
required by the Entomopter. Because of the aerodynamics of the wing operation it may be desirable
to actually have a greater tip bending then what was used in this analysis. If this is the case
then this will reduce the wing section mass from what is presented here. However the trends
regarding the geometry impacts on the wing mass will still be valid regardless of the desired
wing bending limit.
The mass distribution curves are generated by plotting the mass of wing sections, each 1/100 of
the total wing section length. Each curve in Figure 3-16 represents the mass distribution necessary
to maintain a maximum wing tip deflection of 0.015 m. Depending on the case the taper
ratio, inner hollow ellipse or both were varied until the wing was able to achieve the minimum
deflection required. The details of the wing geometry and total mass are shown in Table 3-4.
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