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

Chapter 3.0 Vehicle Design
3.1 Wing Sizing
determine the individual effect on lift and power. With the insight provided by this single-variable
analysis, a multivariable analysis will be performed to produce an optimized vehicle
configuration.
As shown in Figure 3-5, the loading on the wing will vary depending on the wing geometry and
operational conditions. Because the wing structure mass is based on the loading experienced by
the wing, the mass of the wing structure will also change. This will affect the relative lifting
capacity of the vehicle. Relative lifting capacity (m r ) is defined as the total mass the Entomopter
can lift (m t ) minus the mass of the wings (m w ).
mr = mt - mw
Equation 3-7
The mass the Entomopter can lift is the vertical lift component of the resultant lift shown in
Figure 3-5. The lift generated by the wings is also used as the means of forward propulsion for
the Entomopter. Therefore, when calculating the total lift generated by the Entomopter based on
the resultant velocity, given by Equation 3-6, the drag-force vector must be subtracted to calculate
the portion of lift used to maintain the vehicle in flight. The drag on the vehicle due to forward
motion (D) is given by Equation 3-8.
D = 1 2 ρV 2 c d S w
Equation 3-8
The total vehicle wetted surface area (S w ) is given by Equation 3-9, where the area of the Entomopter
body was assumed to be 0.5 m 2 . The total drag coefficient (c d ) for the vehicle was
assumed to be 0.3. Based on this drag calculation the effective lift (L e ) of the Entomopter is
given by Equation 3-10.
S w = 2A w (4) + 0.05
Equation 3-9
L e = L 2 − D 2
Equation 3-10
A relative lifting capacity is a much more useful characteristic of Entomopter performance than
the total lift generated by the wings. By factoring out the wing mass a truer representation of the
vehicle’s relative performance under various operating conditions is achieved. Wing mass is
dependent on the structural analysis described in the Entomopter wing structure section. The
biggest effect on wing mass is the size of the wing. The relation between wing mass and size is
shown in Figure 3-8.
To examine the effect of the various operational parameters on the lift and power requirement
for the Entomopter, a base operating configuration must be established. From this base operating
point the variables, such as flapping rate, flapping angle, and wing length will be individually
varied. Initially in-flight cruise conditions were examined. This assumed a flight speed (V) for
the vehicle of 15 m/s and a C L generated by the wings of 10. This lift coefficient was based on
the baseline lift coefficient of 5 for the flapping wing and the estimated doubling or tripling
enhancement due to active boundary layer blowing at the trailing edge of the wing. The analysis
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