User:Cronkurleigh/sandbox

Meridian Curve
Geometry of the hull

Meunseir elliptical

separation of boundary layers in positive pressure gradients

"Goodyear" modified elliptical


 * $$r(x) = r_{max}(a-b\frac{2x}{L})[1-(\frac{2x}{L}-c)^2]^\frac{1}{2}$$

NACA/Göttingen


 * $$r(x) = a_0\sqrt{x} + a_1 x + a_2 x^2 + a_3 x^3$$
 * $$r(x) = d_0 + d_1(1-x) +d_2(1-x)^2 + d_3(1-x)^3$$

Neutral Buoyancy Aerodynamics




Navier-Stokes equations - low speed aerodynamics - typically neglect the buoyancy of the vehicle...


 * $$ L = (vol) \delta g$$

where


 * $$ \delta = \rho_{air} - \rho_{helium}$$


 * $$ D = q_0 C_{D_{0}} (vol)^\frac{2}{3}$$


 * $$ (L/D) = \frac{(vol) \delta g}{q_0 C_{D_{0}} (vol)^\frac{2}{3}}$$


 * $$C_{D_0} = 0.19 Re_{vol}^{-0.15}$$


 * $$C_{D_0} = 0.24 Re_{vol}^{-0.15}$$

where
 * $$ Re_{vol} = \frac{V (vol)^\frac{1}{3}}{\nu}$$

Aerodynamics of Static Heaviness or Buoyant Conditions

 * $$L = (vol) \delta g + q_0 C_L (vol)^\frac{2}{3}$$


 * $$D = q_0 (C_{D_0} + K C_L^2)(vol)^\frac{2}{3}$$


 * $$(L/D) = \frac{(vol) \lambda g + q_0 C_L (vol)^\frac{2}{3}}{q_0 (C_{D_0} + K C_L^2)(vol)^\frac{2}{3}}$$


 * $$K = 1.4 - 0.035\alpha$$


 * $$C_{L_\alpha} = 0.021$$