From: tkoenig@netcologne.de   
      
   alexandru_trofin@yahoo.com  schrieb:   
   >> The pressurized crew section would, of course, occupy only a relatively   
   small portion of the vessel's internal volume.  Any other compartments outside   
   of this pressure hull would either be totally unpressurized or would contain   
   compressed fluid or    
   reaction mass.   
   >   
   > Why? You could pressurize the whole ship without requiring too   
   > much extra mass for the pressure bottle. The larger the volume, the   
   > more efficient (mass-wise) it is to pressurize it, since envelope   
   > mass grows with radius squared, but volume grows with radius cubed.   
      
   The material has to be thicker to withstand the pressure, too.   
      
   For a thin spherical shell (the optimum pressure vessel and also   
   the one most easy to model) with a pressure difference delta_p   
   to the outside, a radius R and a thickness s << R where   
   sigma is the stress in the shell, the force from the pressure   
   is   
      
   F_p = pi * R^2 * delta_p   
      
   and the force from the mechanical stress in the shell is   
      
   F_s = 2 * pi * R * s * sigma   
      
   so the stress from F_p = F_s then is   
      
   sigma = delta_p * R/(2*s)   
      
   so it increases linearly with the radius.   
      
   If you want to keep the stress constant when choosing a different   
   radius, you get   
      
   s = R/2 * delta_p / sigma   
      
   so the thickness scales linearly with the radius.   
      
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