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Meridian Curve
Geometry of the hull
Meunseir elliptical
separation of boundary layers in positive pressure gradients
"Goodyear" modified elliptical
![{\displaystyle r(x)=r_{max}(a-b{\frac {2x}{L}})[1-({\frac {2x}{L}}-c)^{2}]^{\frac {1}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f2061467179e284fdfd71ebaf39d3b09d0620bb)
NACA/Göttingen
![{\displaystyle r(x)=a_{0}{\sqrt {x}}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b3f557d964846190279aa3a7532b05cffbe20f25)
![{\displaystyle r(x)=d_{0}+d_{1}(1-x)+d_{2}(1-x)^{2}+d_{3}(1-x)^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a9f86f7a89d51437fd8920766309825b6cb2d8a)
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...
![{\displaystyle L=(vol)\delta g}](https://wikimedia.org/api/rest_v1/media/math/render/svg/170bfd57eaecaa3c8a591d0b385b910a2791455b)
where
![{\displaystyle \delta =\rho _{air}-\rho _{helium}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c6ad891bef2ef74155a51269bd9b04086af3707)
![{\displaystyle D=q_{0}C_{D_{0}}(vol)^{\frac {2}{3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/23e3febff7a9b66ee880b34bab16cc4f76b5c09c)
![{\displaystyle (L/D)={\frac {(vol)\delta g}{q_{0}C_{D_{0}}(vol)^{\frac {2}{3}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d3aa3447337a5fee1630545af323848557489d3b)
![{\displaystyle C_{D_{0}}=0.19Re_{vol}^{-0.15}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2dee0ce7c6f9e8138d643ca242df587c36440af9)
![{\displaystyle C_{D_{0}}=0.24Re_{vol}^{-0.15}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb86c34971e4189f686fa7ec36f1fde587a5378d)
where
![{\displaystyle Re_{vol}={\frac {V(vol)^{\frac {1}{3}}}{\nu }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d2a2c0fac233ff0936a969a6c6579cb383433779)
Aerodynamics of Static Heaviness or Buoyant Conditions
![{\displaystyle L=(vol)\delta g+q_{0}C_{L}(vol)^{\frac {2}{3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3da273f6e9751752930d5af0951cac0e44c4816b)
![{\displaystyle D=q_{0}(C_{D_{0}}+KC_{L}^{2})(vol)^{\frac {2}{3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/835c89848a171a75cddf78592c4d0ad82581dd7c)
![{\displaystyle (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}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4f4e4fdc6ee0e48f7578f794147bb6ea0ee4c3a0)
![{\displaystyle K=1.4-0.035\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/05060db09e0922841c454bd057aee0800b3206cf)
![{\displaystyle C_{L_{\alpha }}=0.021}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe2a82b5068384a7f9ac63306748ce70baa4f2d1)
References