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

Planetary Exploration Using Biomimetics
An Entomopter for Flight on Mars
Cm = Coefficient of Moment
Cp = Coefficient of Power Required.
Table 3-8: List of Symbols (Continued)
3.3.3.7 Model Formulation for Baseline Case
It was assumed that the planform shape of the Entomopter wing is fixed in three dimensions and
for parametric analysis, as we change the span of the wing, the chord length will vary all along
the wing, so the shape of the planform is just defined by one parameter: span. Also it is assumed
that the axis of rotation ("a") is constant. Hence, the total number of variables considered reduce
to five: span, velocity, flapping frequency, flapping amplitude, and pitch amplitude. A cycle is
defined as one complete upbeat and one downbeat, starting with h = 0 at t = 0, and then it moves
(upwards) to -hamp at 1/4 time period, and then starts the down beat, continuing until the 3/4
time period. In the final 1/4 time period, it comes back to the zero position. The angle of attack
stays constant during the upbeat and downbeat and it flips during the 1/20th portion of time
period at the extremes of the upbeat and down beat. A computer code was written in Mathcad
2000 to evaluate these results. The values and equations used for baseline case are as follows:
(NOTE: the notation used below ":=" means "defined as".)
V:= 14 freq := 16 Plamp := 75 Pitamp := 8
sspan
span
:=
2
a:= −0.25
ω :=
4⋅
freq
⋅ Plamp ⋅
⎛
⎜
⎝
π
180
hamp := sspan ⋅ sin Plamp ⋅
αamp := Pitamp ⋅
t :=
0
,
100⋅
freq
π
180
1
100⋅
freq
π
180
⎞
⎠
1
..
freq
Since the instantaneous flapping height changes linearly, it was decided that different coefficients
would be calculated for the first quarter cycle, then from 1/4 until 3/4 and finally for the
last quarter of the cycle. This will give close to linear change effects. A similar approach was
adopted for pitching motion coefficients and different coefficients were evaluated for flipping
from positive to negative and vice versa. These coefficients were determined by solving a system
of nonlinear simultaneous equations.
( )
h01 + h11 ⋅ cos φh1 0
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Phase II Final Report