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

Chapter 3.0 Vehicle Design
3.1 Wing Sizing
Chapter 3.0 Vehicle Design
3.1 Wing Sizing
3.1.1 Engine Energy Production Requirements
The energy consumed by the wing motion during each flap can be broken down into two main
components: The energy needed to move the wing mass, acceleration and deceleration, at the
desired flapping rate, and the energy needed to overcome the drag on the wing due to the lift produced
during flapping. The energy due to motion is much greater than that due to lift generation.
Initially, therefore, only the energy due to motion will be evaluated.
3.1.2 Energy Required Due to Motion
The energy required to move
the mass of the wing can be
easily calculated based on
the geometry of the wing,
mass distribution along the
wing, and the flapping rate.
These parameters, which
include wing length, flapping
frequency, and the
angle through which the
wing moves during the flap
cycle, are shown in
Figure 3-1. They can be varied
to try to optimize wing
design and operation. The
optimization consists of
maximizing lift while minimizing
the power required.
From the structural analysis
the mass distribution along a
wing section length was
determined. Utilizing this
Figure 3-1: Parameters for Power Consumption
Optimization
mass distribution. Loading on the wing due to its acceleration can be determined using the mass
distribution. The mass distribution and corresponding loading are shown in Figure 3-2.
The wing loading shown in Figure 3-2 is due to the acceleration of the wing mass; aerodynamics
and other loads are not included at this point. The force (F) was based on Equation 3-1, where
mi is the mass of an incremental piece of the wing corresponding to a mean radial distance of ri,
q is the angle through which the wing will move during the acceleration (this is equal to the
maximum deflection angle used during the structural analysis), and f is the flapping frequency in
cycles per second. Wing acceleration was assumed to be a constant from the beginning of the
stroke where the wing is in its full upward position to the wing in a horizontal position. The
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