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

Chapter 3.0 Vehicle Design
3.2 Wing Motion and Structure Analysis
the base operating conditions of 6 Hz, 75° Maximum angle and a 0.6 m wing section length
(shown in Equation 3-19) the shear loading can be calculated as follows.
Figure 3-14: Load Diagram and Coordinate System for Wing Loading
∫
V ( r)
= W ( r)
dr
Equation 3-18
W(r) = -554.63+1.0608E5 r – 60373 r 2 –2.2389E5 r 3 Equation 3-19
Integrating yields
V(r) = -554.63 r + 53040 r 2 – 20124.33 r 3 – 55972.5 r 4 + C 1 Equation 3-20
The boundary conditions used to determine C 1 are; r = 0. 5 (the wing tip) the shear must be equal
to; V = 0.
1 = -6968.86 Equation 3-21
The bending moment along the wing is the integral of the shear load given by Equations 3-20
and 3-21. This is represented by the following equations.
M(r) =
∫V (r) dr
M(r) = -277.315 r 2 + 17680 r 3 – 5031.08 r 4 – 11194.5 r 5 – 6968.66 r + C 2
Where C 2 is determined from the boundary conditions; M = 0 at r = 0.5.
Equation 3-22
Equation 3-23
C 2 = -2007.93 Equation 3-24
Based on this analysis the shear loading and bending moment for the various flight conditions is
shown in Figure 3-18.
The tangent angle to the bending curve (q) is the next quantity that can be calculated by integrating
the moment (Equation 3-23). This angle can be represented by the following equation. Since
the wing geometry changes from the root to the tip the moment of inertia (I) is not a constant and
therefore varies along the wing length. This integral can be approximated by an infinite series
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