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No. 88: Jul-Aug 1993

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Bruised Apples

A serious problem has cropped up in supermarkets, where fresh, ripe apples are piled up high in beckoning pyramids. Surely, as the heights of the pyramids increase, the bottom-most apples will be crushed, particularly those in the center under the apexes. Common sense tells us that crushing forces will be greatest at Position #4 in the illustration.

Pyramid of apples
But grocers need not be concerned about Apple #4. Two Czech researchers, J. Schmid and J. Novosad, using pressure sensors, found that in a horizontal plane through a stacked pyramid the maximum pressure actually occurs in a ring of objects (apples) some distance from the pyramid's vertical axis. How come?

(Watson, A.; "The Perplexing Puzzle Posed by a Pile of Apples," New Scientist, p. 19, December 14, 1991.)

A theoretical analysis of the problem by J. Grindlay doesn't help much. He analyzed a two-dimensional pile of disks, as shown, and calculated that maximum bruising forces should occur at the outermost disks instead of at the center, (Grindlay, J.; "Bruised Apples," American Journal of Physics, 61:469, 1993.)

Comment. Thus, common-sense expectations, experimental measurements, and theoretical calculations lead to three different results. Much more work needs to be done here.

From Science Frontiers #88, JUL-AUG 1993. 1993-2000 William R. Corliss

Science Frontiers Sourcebook Project Reviewed in:


  • "A sourcebook of unexplained phenomena is therefore a valuable addition to a collection of scientific literature. William R. Corliss has provided this in the past with his source books of scientific anomalies in several subjects, and now he has provided it for astronomy. He has done an excellent job of collecting and editing a large amount of material, taken in part from scientific journals and in part from scientific reporting in the popular or semi-scientific press." -- "The Mysterious Universe: A Handbook of Astronomical Anomalies", reviwed by Thomas Gold, Cornell University, in Icarus, vol.41, 1980

  • "An interesting, systematic presentation of unusual weather [..] This book is recommended for a general audience" --"Corliss, William R., Tornados, Dark Days, Anomalous Precipitation, and Related Weather Phenomena, Sourcebook Project, 1983.", revieweed in Choice, September 1983
  • "..the science is necessarily somewhat speculative, but Corliss's symthesis is based on reputable sources." -- "Corliss, William R. (Compiler). Lightning, Auroras, Nocturnal Lights, and Related Luminous Phenomena" reviwed by Joseph M. Moran, Univ. of Wisconsin in Science Books and Films, Sep/Oct 1983

  • "Before opening the book, I set certain standards that a volume which treads into dangerous grounds grounds like this must meet. The author scrupulously met, or even exceeded those standards. Each phenomenon is exhaustively documented, with references to scientific journals [..] and extensive quotations" -- "Book Review: The moon and planets: a catalog of astronomical anomalies", The Sourcebook Project, 1985., Corliss, W. R., Journal of the Royal Astronomical Society of Canada, Vol. 81, no. 1 (1987), p. 24., 02/1987