Question 5.2: Calculate the wing-geometry parameters for the Space Shuttle......
Calculate the wing-geometry parameters for the Space Shuttle Orbiter
To calculate the wing-geometry parameters for the Space Shuttle Orbiter, the complex shape of the actual wing is replaced by a swept, trapezoidal wing, as shown in Fig. 5.9. For the reference wing of the Orbiter, the root chord (c_{r}) , is 57.44 ft, the tip chord (c_{t}) is 11.48 ft, and the span (b) is 78.056 ft. Using these values which define the reference wing, calculate (a) the wing area (S), (b) the aspect ratio (AR), (c) the taper ratio (λ), and (d) the mean aerodynamic chord (mac).
(a) The area for the trapezoidal reference wing is
S\,=\,\left({\frac{c_{t}+c_{r}}{2}}\right){\frac{b}{2}}2\,=\,2690\,\mathrm{ft}^{2}(b)The aspect ratio for this swept, trapezoidal wing is
A R={\frac{b^{2}}{S}}={\frac{(78.056)^{2}}{2690}}=2.265(c) The taper ratio is
\lambda={\frac{c_{t}}{c_{r}}}={\frac{11.48}{57.44}}=0.20(d) To calculate the mean aerodynamic chord, we will first need an expression for the chord as a function of the distance from the plane of symmetry [i.e., c(y)].The required expression is
c(y)\,=\,c_{r}+{\frac{11.48-57.44}{39.028}}y\,=\,57.44\,-\,1.1776ySubstituting this expression for the chord as a function of y into the equation for the mean aerodynamic chord, we obtain
m a c={\frac{2}{S}}\int_{0}^{0.5b}\left[c(y)\right]^{2}d y={\frac{2}{2690}}\int_{0}^{39.028}\left(57.44-1.1776y\right)^{2}d yIntegrating this expression, we obtain
mac = 39.57 ft