Featured Research

from universities, journals, and other organizations

What is the best way of stacking apples?

Date:
April 25, 2012
Source:
CNRS (Délégation Paris Michel-Ange)
Summary:
When stacking apples on a market stall, fruit sellers “naturally” adopt a particular arrangement: a regular pyramid with a triangular base. Scientists have now demonstrated that this arrangement is favored for reasons of mechanical stability. This work could contribute to the design of organized porous materials.

Top: Face centre cubic (FCC) stacking in which the same layer arrangement is repeated every three layers. Bottom: Hexagonally close packed (HCP) stacking in which the same layer arrangement is repeated every two layers.
Credit: © S. Heitkam; Image courtesy of CNRS

When stacking apples on a market stall, fruit sellers "naturally" adopt a particular arrangement: a regular pyramid with a triangular base. A French-German team, which includes in particular the Laboratoire de Physique des Solides (Université Paris-Sud / CNRS), has demonstrated that this arrangement is favored for reasons of mechanical stability. This work, which is published on the Physical Review Letters (PRL) website, could contribute to the design of organized porous materials.

Take apples or marbles. The best way to stack them consists in erecting a pyramid layer by layer, which ensures the maximum number of spheres is fitted into the minimum amount of space. There are several arrangements for stacking such identical spheres (of the same volume) with the same, optimal density. Two, in particular, are well known: a structure known as face centered cubic (FCC), whose base is necessarily a triangle for the smallest possible pyramid, and a hexagonally close-packed (HCP) structure with a hexagonal base, also when constructing the smallest possible pyramid. The first arrangement consists of a periodic repetition of three different positions of layers: ABCABC…. In the second, two different positions of layers are periodically repeated: ABABAB.... As early as 1611, while studying the stacking of canon balls, the scientist Johannes Kepler proposed the FCC arrangement as being the most efficient. It is moreover the arrangement used by stall holders to stack their fruit and vegetables.

In addition, the FCC structure turns out to last longer than the HCP arrangement, particularly during the spontaneous formation of stacks of bubbles, drops or solid grains of equal volume. Why is there such a preference when both structures result in the same compactness? That is the question the researchers set themselves to solve. One of the explanations put forward so far is a higher disorder (or entropy) in FCC stacking than in an HCP arrangement. But this argument, which could be true for very small objects of nano- or microscopic size, no longer holds for macroscopic objects such as bubbles or drops.

The researchers carried out numerical simulations and experiments with macroscopic spheres of different sizes (greater than 10-6 meters). After throwing the spheres into a box, they observed how they formed into stacks and then subjected the system to mechanical tests. The researchers demonstrated that the two arrangements, FCC and HCP, formed with the same probability. However, the hexagonally close-packed structure is more frequently destroyed when new spheres are added and it is then converted into a more stable face centered cubic structure. In this way, they demonstrated that the FCC arrangement is mechanically more stable than any other compact hexagonal structure. Why is that? At the surface of a pyramidal stacking, several neighboring spheres are missing1. In FCC structures, since the forces are transferred via straight lines, this does not cause an imbalance of the system. However, in other stacking arrangements, a resulting force is exerted towards the exterior on the spheres situated at the edges, which pushes them away from the stack.

If this force is not compensated by a sufficient force of gravity or friction, the HCP structure collapses. Thus, a pyramid comprising four layers of spheres without friction in an HCP arrangement can collapse under its own weight. Conversely, layers can be stacked indefinitely in a FCC structure. External phenomena, such as hustle and bustle or constant passing-by near the edifice, can destabilize the structure and thereby induce the formation of the FCC arrangement. The scientists are now attempting to determine whether this mechanism is involved in other situations: shearing of the edifice, use of "soft" spheres, etc. It could play a significant role in certain porous materials organized into regular arrays.

1 -- Within a complete stack (which would occupy the whole volume of a box), it plays no role: all of the forces are compensated by neighboring spheres.


Story Source:

The above story is based on materials provided by CNRS (Délégation Paris Michel-Ange). Note: Materials may be edited for content and length.


Journal Reference:

  1. S. Heitkam, W. Drenckhan, J. Fröhlich. Packing Spheres Tightly: Influence of Mechanical Stability on Close-Packed Sphere Structures. Physical Review Letters, 2012; 108 (14) DOI: 10.1103/PhysRevLett.108.148302

Cite This Page:

CNRS (Délégation Paris Michel-Ange). "What is the best way of stacking apples?." ScienceDaily. ScienceDaily, 25 April 2012. <www.sciencedaily.com/releases/2012/04/120425094304.htm>.
CNRS (Délégation Paris Michel-Ange). (2012, April 25). What is the best way of stacking apples?. ScienceDaily. Retrieved July 22, 2014 from www.sciencedaily.com/releases/2012/04/120425094304.htm
CNRS (Délégation Paris Michel-Ange). "What is the best way of stacking apples?." ScienceDaily. www.sciencedaily.com/releases/2012/04/120425094304.htm (accessed July 22, 2014).

Share This




More Matter & Energy News

Tuesday, July 22, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Government Approves East Coast Oil Exploration

Government Approves East Coast Oil Exploration

AP (July 18, 2014) — The Obama administration approved the use of sonic cannons to discover deposits under the ocean floor by shooting sound waves 100 times louder than a jet engine through waters shared by endangered whales and turtles. (July 18) Video provided by AP
Powered by NewsLook.com
Sunken German U-Boat Clearly Visible For First Time

Sunken German U-Boat Clearly Visible For First Time

Newsy (July 18, 2014) — The wreckage of the German submarine U-166 has become clearly visible for the first time since it was discovered in 2001. Video provided by Newsy
Powered by NewsLook.com
Obama: U.S. Must Have "smartest Airports, Best Power Grid"

Obama: U.S. Must Have "smartest Airports, Best Power Grid"

Reuters - US Online Video (July 17, 2014) — President Barak Obama stopped by at a lunch counter in Delaware before making remarks about boosting the nation's infrastructure. Mana Rabiee reports. Video provided by Reuters
Powered by NewsLook.com
Crude Oil Prices Bounce Back After Falling Below $100 a Barrel

Crude Oil Prices Bounce Back After Falling Below $100 a Barrel

TheStreet (July 16, 2014) — Oil Futures are bouncing back after tumbling below $100 a barrel for the first time since May yesterday. Jeff Grossman is the president of BRG Brokerage and trades at the NYMEX. Grossman tells TheStreet the Middle East is always a concern for oil traders. Oil prices were pushed down in recent weeks on Libya increasing its production. Supply disruptions in Iraq fading also contributed to prices falling. News from China's economic front showing a growth for the second quarter also calmed fears on its slowdown. Jeff Grossman talks to TheStreet's Susannah Lee on this and more on the Energy Department's Energy Information Administration (EIA) report. Video provided by TheStreet
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
 
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:  

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:  

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile iPhone Android Web
Follow Facebook Twitter Google+
Subscribe RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins