Re: Weighing Freight Car Models with Liquid Gravity

Dave Parker


My comments on this have always included the caveat that spheres the have to small enough to achieve something at least close to idealized spherical packing.

If you had a center-sill space with a 1 x 1 cm cross-section, and you carefully filled it with 1-cm diameter spheres, you would indeed have about 52% sphere and 48% void space (just the ratio of the volume of a sphere and a cube of the same size).  Obviously, if the spheres are say 0.75 cm in dia, then you can't pack them in there efficiently, and you'll get less weight.

But if the spheres were say 1 mm, or even 2, then you are going to get something at least close to idealized packing (74-26).  Going to 0.1 mm spheres is only going gain you something on the order of one or a few percent (maybe), hardly worth worrying about. 

Concerning Tony's comment, I agree but only in theory.  If you start mixing smaller spheres in with bigger ones, then the little ones can get in the way of the dense packing of the big ones.  The gain in density will likely be rather minimal in most cases, and it may even reduce the density.  This is a very common observation in soil science -- things like dune sands usually have higher (dry) densities than do other soils that have a range of particle sizes.

Dave Parker
Riverside, CA

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