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

Planetary Exploration Using Biomimetics
An Entomopter for Flight on Mars
The forces generated are dependent on the operational conditions and geometry of the Entomopter
wing. From the subsequent sizing analysis a baseline set of conditions was established
representing the most desired operating conditions. These are listed in Table 3-3.
Table 3-3: Baseline Operating Conditions
Flapping Frequency
Maximum Wing Motion Angle
Wing Section Length
6 Hz
± 75 o
0.6 m
It was assumed that the change in θ, or wing position, with respect to time follows a cosine function.
This motion is shown in Figure 3-11. This curve is for a 6 Hz wing flapping frequency and
a ±75° wing motion. The cycle starts with the wing in the maximum upward position.
100
80
60
40
20
0
-20
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
-40
-60
-80
-100
Time (sec)
Figure 3-11: Wing Motion Represented by Angle Change with Time
In general the equation for θ (shown in Figure 3-11) can be represented by Equations 3-13 and
3-14. Where a is the absolute value of θ at its maximum point, the constant b is set by the wing
flapping frequency (f) given by Equation 3-14 and c sets the starting point for the cycle (c is 0 in
this case). By changing c the curve will shift to the left or right. For this analysis the wing starts
at the maximum upward position at time 0 and begins its flap with a downward stroke.
θ = a cos(bt + c) Equation 3-13
b = 2 π / (1/f) Equation 3-14
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Phase II Final Report