Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

The Platonic Form Of Stalactites

07.12.2004


No matter whether they’re big, little, long, short, skinny or fat -- classic stalactites have the same singular shape.

Almost everyone knows that stalactites, formations that hang from the roof of caves, are generally long, slender and pointy. But the uniqueness of their form had gone unrecognized. "There’s only one shape that all stalactites tend to be. The difference is one of magnification -- it’s either big or it’s small, but it’s still the same shape," said researcher Martin Short of the University of Arizona in Tucson.

Short and his colleagues have developed a mathematical theory that explains how stalactites get their shape. "It’s an ideal shape in nature and in mathematics that had not been known before," said Raymond Goldstein, a UA physics professor and senior author on the research report. "The Greek philosopher Plato had the concept that there are ideal forms underlying what we see in nature. Although any particular stalactite may have some bumps and ridges that deform it, one might say that within all stalactites is a idealized form trying to get out."

The universality of stalactites had probably been overlooked because the cave formations vary so much in size, said Short, a doctoral candidate in physics at UA. "The result was a surprise," he said. "We had no idea going into this that we’d find this basic shape."

An article detailing the findings of Short, Goldstein and their colleagues will be published in an upcoming issue of Physical Review Letters. The Research Corporation and the National Science Foundation funded the research. Other authors on the article are James C. Baygents, a UA associate professor of chemical and environmental engineering; J. Warren Beck, a research scientist in UA’s department of physics; David A. Stone, a doctoral candidate in UA’s department of soil, water and environmental science; and Rickard S. Toomey, III, science and research manager for Arizona State Parks.

Although people have investigated how cave formations grow, few scientists examined why stalactites have their characteristic shape. After someone suggested that the tubules David Stone was growing in the laboratory resembled some cave formations, Goldstein became intrigued by caves.

He and his colleagues took a field trip to the famed Kartchner Caverns State Park in Benson, Ariz. and were floored by the variety of forms, especially the ripples many structures possess. So Goldstein suggested that his student Martin Short investigate the formation of ripples on stalactites. That task turned out to be extremely difficult, Short said. First he had to learn about the underlying dynamics of stalactite growth.

Stalactites grow when water laden with carbon dioxide and calcium carbonate drips from cracks or holes in the cave’s ceiling. As a water droplet hangs from the crack, the carbon dioxide escapes, much as a bottle of sparkling water fizzes when opened. As a result, the calcium carbonate comes out of solution and is left behind as a tiny bit of solid calcium carbonate. As each successive drip flows over the minute mineral deposit, the sequence repeats, ultimately forming a stalactite. Because the shape stems from the flow of water over the surface of the growing stalactite, the team turned to the field of fluid dynamics. The researchers developed an equation to describe how a stalactite’s shape evolves. "It’s a general equation of motion for the growth of stalactites," Goldstein said. "It’s a geometric law of motion."

Then the researchers plugged the equation into a computer and asked it to "grow" some shapes. To the team’s surprise, no matter what shape was used as a starting point, the computer’s formations lengthened and thickened in a universal manner. The results looked strikingly like classic stalactites. "The computer told us there was something unique to look for, this ideal form," Goldstein said. The researchers then solved their equation of motion and obtained a specific mathematical expression that describes the carrot-like shape of stalactites.

The next step was to test their model against the real thing, so the researchers returned to Kartchner Caverns. "We spent four hours in the cave with cameras and strobe lights and laptops. We took dozens of pictures," said Goldstein.

Because cave formations are delicate, the researchers could not stomp around measuring the stalactites by hand. Instead, the scientists used lasers to project a pair of green dots onto the stalactites from afar and then took pictures of the stalactites. The researchers knew how far apart the green dots were, so the dots served as a scale bar for the pictures. Then the researchers could garner the stalactites’ dimensions from the pictures. Back in the lab, the researchers analyzed the actual stalactites and compared their shapes to the ideal form predicted by the mathematics. The real and the ideal differed by less than 5 percent. "We calculated the shape mathematically and said, well, we have to go see if this is right," Goldstein said. "And we did. And it was."

Kartchner’s Toomey said, "It’s cool because the research contributes to learning new things about this cave that apply as well to other caves throughout the world," adding, "Missions of state parks include preservation, understanding and education. To have Kartchner and other state parks available for these types of studies helps further these missions." Now, Short and Goldstein say, they finally know enough to figure out what gives stalactites their ripples.

Mari N. Jensen | University of Arizona
Further information:
http://www.arizona.edu
http://www.physics.arizona.edu/~gold/
http://www.pr.state.az.us/Parks/parkhtml/kartchner.html

More articles from Earth Sciences:

nachricht Climate change weakens Walker circulation
20.10.2017 | MARUM - Zentrum für Marine Umweltwissenschaften an der Universität Bremen

nachricht Shallow soils promote savannas in South America
20.10.2017 | Senckenberg Forschungsinstitut und Naturmuseen

All articles from Earth Sciences >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Neutron star merger directly observed for the first time

University of Maryland researchers contribute to historic detection of gravitational waves and light created by event

On August 17, 2017, at 12:41:04 UTC, scientists made the first direct observation of a merger between two neutron stars--the dense, collapsed cores that remain...

Im Focus: Breaking: the first light from two neutron stars merging

Seven new papers describe the first-ever detection of light from a gravitational wave source. The event, caused by two neutron stars colliding and merging together, was dubbed GW170817 because it sent ripples through space-time that reached Earth on 2017 August 17. Around the world, hundreds of excited astronomers mobilized quickly and were able to observe the event using numerous telescopes, providing a wealth of new data.

Previous detections of gravitational waves have all involved the merger of two black holes, a feat that won the 2017 Nobel Prize in Physics earlier this month....

Im Focus: Smart sensors for efficient processes

Material defects in end products can quickly result in failures in many areas of industry, and have a massive impact on the safe use of their products. This is why, in the field of quality assurance, intelligent, nondestructive sensor systems play a key role. They allow testing components and parts in a rapid and cost-efficient manner without destroying the actual product or changing its surface. Experts from the Fraunhofer IZFP in Saarbrücken will be presenting two exhibits at the Blechexpo in Stuttgart from 7–10 November 2017 that allow fast, reliable, and automated characterization of materials and detection of defects (Hall 5, Booth 5306).

When quality testing uses time-consuming destructive test methods, it can result in enormous costs due to damaging or destroying the products. And given that...

Im Focus: Cold molecules on collision course

Using a new cooling technique MPQ scientists succeed at observing collisions in a dense beam of cold and slow dipolar molecules.

How do chemical reactions proceed at extremely low temperatures? The answer requires the investigation of molecular samples that are cold, dense, and slow at...

Im Focus: Shrinking the proton again!

Scientists from the Max Planck Institute of Quantum Optics, using high precision laser spectroscopy of atomic hydrogen, confirm the surprisingly small value of the proton radius determined from muonic hydrogen.

It was one of the breakthroughs of the year 2010: Laser spectroscopy of muonic hydrogen resulted in a value for the proton charge radius that was significantly...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

ASEAN Member States discuss the future role of renewable energy

17.10.2017 | Event News

World Health Summit 2017: International experts set the course for the future of Global Health

10.10.2017 | Event News

Climate Engineering Conference 2017 Opens in Berlin

10.10.2017 | Event News

 
Latest News

Terahertz spectroscopy goes nano

20.10.2017 | Information Technology

Strange but true: Turning a material upside down can sometimes make it softer

20.10.2017 | Materials Sciences

NRL clarifies valley polarization for electronic and optoelectronic technologies

20.10.2017 | Interdisciplinary Research

VideoLinks
B2B-VideoLinks
More VideoLinks >>>