Main results

• It has been shown that, within the framework of a local interaction model, the drag of bodies with the given base area has the lower bound D*, which is attained by bodies formed by combinations of surface parts, whose normal makes a constant optimum angle with the direction of motion. The velocity and medium characteristics in terms of constants of the drag law determine this angle independently of the base area.
  

• For any specified limitations on the body size, a method of optimum shape design, based on combining the surface parts of the optimum cone and planes tangent to it, has been proposed. In particular, this method allows one to construct optimum starbodies, optimum asymmetrical and nonconical bodies like missiles and optimum bodies with a circular base (see Figures below).
  

• It has been shown that all bodies constructed have the same total drag D*, minimal for the given base area and independent of the body length, and that, even for asymmetrical bodies, the acting force has no component in a plane perpendicular to the direction of motion.
  

• To verify the benefits of the proposed design, the optimum drag characteristics, found in Newtonian flow, have been compared with the drag of other shapes of equivalent length and base area. The results show that, in most cases, the proposed shapes are more effective in providing drag reduction than bodies found in earlier studies (see reference [4] in Selected Publications).
  

• Also within the framework of a local interaction model a solution of the problem of constructing three-dimensional bodies of maximum penetration depth has been found. It has been proved that the desired shapes ( as well as minimal drag bodies) are formed by combination of the surface parts whose normal makes a constant optimum angle with the direction of the motion. In general case this optimal angle differs from the optimal angle found for minimal drag bodies. Hence, the method of optimum shape design, proposed for minimal drag bodies, can be used to construct the body providing the maximum penetration depth .
  

• It has been shown that, for the given base area all bodies constructed have the same total drag and the same penetration depth during their rectilinear motion, but they have different dynamics characteristics when the rectilinear motion is disturbed. The stability criterion of the optimum pyramidal body motion has been found.
  

• Simulation of 3D-motion of the optimum shapes is in a good accordance with theoretical estimations.