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

$r(x)=a_{0}{\sqrt {x}}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}$

$r(x)=d_{0}+d_{1}(1-x)+d_{2}(1-x)^{2}+d_{3}(1-x)^{3}$

Optimal Fineness Ratios

Airship Hull Drag vs. Fineness Ratio at Constant Reynolds No.

Neutral Buoyancy Aerodynamics

Log Law Boundary Layer Theory vs. Experiement - Airship Hulls

Log Law Boundary Layer Theory vs. Experiement - Complete Airships

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

$L=(vol)\delta g$

where

$\delta =\rho _{air}-\rho _{helium}$

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

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

$C_{D_{0}}=0.19Re_{vol}^{-0.15}$

$C_{D_{0}}=0.24Re_{vol}^{-0.15}$

where

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

Aerodynamics of Static Heaviness or Buoyant Conditions

$L=(vol)\delta g+q_{0}C_{L}(vol)^{\frac {2}{3}}$

$D=q_{0}(C_{D_{0}}+KC_{L}^{2})(vol)^{\frac {2}{3}}$

$(L/D)={\frac {(vol)\lambda g+q_{0}C_{L}(vol)^{\frac {2}{3}}}{q_{0}(C_{D_{0}}+KC_{L}^{2})(vol)^{\frac {2}{3}}}}$

$K=1.4-0.035\alpha$

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