The problem of the body of revolution of minimal resistance

Details The problem of the body of revolution of minimal resistance The problem of the body of revolution of minimal resistance

2008-04-24

arxiv.org/abs/0804.4020v1

Mathematics

Optimization and Control

Scientific paper

Newton's problem of the body of minimal aerodynamic resistance is traditionally stated in the class of {\it convex} axially symmetric bodies with fixed length and width. We state and solve the minimal resistance problem in the wider class of axially symmetric but {\it generally nonconvex} bodies. The infimum in this problem is not attained. We construct a sequence of bodies minimizing the resistance. This sequence approximates a convex body with smooth front surface, while the surface of approximating bodies becomes more and more complicated. The shape of the resulting convex body and the value of minimal resistance are compared with the corresponding results for Newton's problem and for the problem in the intermediate class of axisymmetric bodies satisfying the {\it single impact} assumption \cite{CL1}. In particular, the minimal resistance in our class is smaller than in Newton's problem; the ratio goes to 1/2 as (length)/(width of the body) $\to 0$, and to 1/4 as (length)/(width) $\to +\infty$.

Affiliated with

Also associated with

No associations

Rating

The problem of the body of revolution of minimal resistance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The problem of the body of revolution of minimal resistance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The problem of the body of revolution of minimal resistance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-728063