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

Planetary Exploration Using Biomimetics
An Entomopter for Flight on Mars
from 0 to i. Where I(r) is the moment of inertia of the wing section and E is the modulus of elasticity.
θ =
M(r)
∫ dr =
I(r)E
Lastly the deflection of the wing can be calculated by integrating the tangent angle (θ). This
integration is given below.
∫
i
∑
y = θ(r)dr = θ i ∆r
i
∑
0
0
M i ∆r
I i E
Equation 3-25
Equation 3-26
Utilizing the above analysis the geometry of the wing structure was examined to determine what
geometry would provide the greatest stiffness with a minimum amount of weight for the base
line operating conditions given in Table 3-3. The initial structural design was a solid wing with
an elliptical cross section of uniform thickness from the root to the tip. Variations from this
geometry were then tried in order to reduce mass while maintaining the same amount of deflection.
To reduce structural mass a hollow ellipse for the wing cross section was used. Since the
majority of the strength in the wing comes from the material furthest form the center (core) of
the wing, this type of structure enabled the wing to be light-weight while providing sufficient
structural rigidity. The reasoning behind this type of cross section can be seen in the moment of
inertia (I) equation for an ellipse, given in Equation 3-27. To minimize deflection the moment of
inertia has to be as large as possible. This can be accomplished by increasing the thickness of the
wing (b). However you also want to minimize mass. This is accomplished by utilizing the smallest
cross sectional area (of material) as possible. The cross sectional area for the wing section
(A) is given in Equation 3-28. To accommodate these two somewhat contradictory requirements
mass is moved from the center of the ellipse to the edges by making it hollow and thicker. Since
the moment of inertia for the ellipse is proportional to the thickness cubed, any small increase in
thickness can have a large increase in wing strength.
To further optimize the wing geometry the thickness was tapered from the root to the tip. This
allowed more mass to be utilized near the root where the bending and shear loads are the greatest.
This geometry is shown in Figure 3-15. The effect of utilizing a hollow wing and tapering it
toward the tip has a substantial effect on the overall mass of the wing and therefore the structural
loading.
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Phase II Final Report