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

Chapter 3.0 Vehicle Design
3.2 Wing Motion and Structure Analysis
This initial analysis looks at the loading on the wing due to its motion and the gravitational force
on Mars. For the time, the lifting loads on the wings have been ignored. A simplified two dimensional
analysis can be performed based on the wing platform geometry. It is initially assumed
that the wing thickness is uniform over the entire wing. As the analysis progresses more detail
will be added to accurately represent the wing geometry and extend the analysis to three dimensions.
The forces exerted on a uniform two-dimensional wing are shown in Figure 3-10, where F g is
the force due to gravity, F t is the tangential force at a point a distance r along the wing, and F r is
the radial force at that same point. These forces can be represented by the following equations:
Figure 3-10: Forces Acting on a Given Point Along the Way
F t = m (r (d 2 θ / dt 2 )+ 2 (dr / dt) θ) + m g Cos (θ) Equation 3-11
F r = m ( (d 2 r / dt 2 ) – 2 r ( dθ / dt) 2 ) + m g Sin (θ) Equation 3-12
In these equations θ represents the angle of the wing with respect to the horizontal at a given
point in time, r is the radius along the wing where the forces being calculated act, m is the mass
of the wing section at r, t is the time, and g is the gravitational force on Mars (-3.75 m/s 2 ).
Because the wing cannot change length the derivatives of radius with respect to time (dr/dt and
d 2 r/dt 2 ) are zero.
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