How to make diamond rings at Mach speed

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I am almost every time put in a trance whilst spectating an aircraft/jet takeoff. There is always something interesting in the occurrence that makes me go nuts!

And this time around, there are these series of rings that one can see in the exhaust plume of a jet engine when it takes off (usually when the afterburner is on).

I had no clue about the phenomenon nor did I know how to express it in ‘search engine’ terms to find a match.

But upon discussion with some of friends, I was shown this video of a space shuttle launch that seemed to produce a similar pattern.

Hmm.. Interesting

Shock Diamonds

These set of rings/disks that are formed in the exhaust plume are known as Shock Diamonds or Mach discs (and by many more names).

These usually form at low altitudes when the pressure of the exhaust plume is lower than the atmospheric pressure.

How does it form ?

Since the atmospheric pressure is higher than the exhaust, it will squeeze it inward. This compresses the exhaust increasing its pressure.

The increased pressure also instills an increase in temperature.

As a result, this ignites any excess fuel present in the exhaust making it burn. It is this burning that makes the shock diamond glow.

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The pressure is now more than the atmospheric pressure, and the exhaust gases start to expand out.

Over time, the process of compression and expansion repeats itself until the exhaust pressure becomes the same as the ambient atmospheric pressure.

In other words, the flow will repeatedly contract and expand while gradually equalizing the pressure difference between the exhaust and the atmosphere.

The same occurs in rocket engines as well.

What if?

What if the atmospheric pressure is less than the exhaust plume ( like at higher altitudes ), would we still see shock diamonds?

Yup, we would! And here’s a picture of it too (The Bell X-1 at speeds close to Mach 1).

The same phenomenon as discussed above occurs except that the cycle starts with the exhaust gases expanding to atmospheric pressure first.

Did you enjoy this post?

There is an extensive explanation of shock diamonds given by shock waves which this post does not cover.

And this beckons the start of Supersonic Fluid Dynamics – a marvelous field of its own. If this captivated you, it is definitely worth a google search.

Cheers!

How to build Beijng’s Forbidden City with 100-tonne stone blocks tens of miles away

(c) Wiki Commons

This “How to” may not be that relevant in modern times, but in the XIV and XV century, I could think of a few civilizations that would have loved to learn how Chinese engineers moved huge volumes of rock from quarries tens of miles away. Such blocks of stone, weighing at least 100 tonnes, were used to build the splendid Forbidden City, which resides in the traditional Beijing center. There were no high power machines during that time, and using brute force alone meant that construction would take forever. Instead, historical documents and a recent computation made by scientists at the University of Science and Technology Beijing, show that raw material for the palace was brought  on wooden sledges along ice roads. Basically, the Chinese engineers took advantage of natural lubrication conditions.

One of the biggest attractions at the Forbidden Palace is the “Large Stone Carving” that graces the stairway to the Hall of Preserving Harmony. Impressive and beautiful figurines and decorations are littered throughout the stone, however the huge monolith is one single block, and it weighs no less then 272 metric tonnes. How on earth did they move this kind of material, considering it came from tens and tens of miles away? Maybe even farther.

The wheel was invented in China well before that, since the 4th century BC actually. Even in the late 1500s, however, Chinese wheeled vehicles could not carry loads exceeding around 86 tonnes, says Thomas Stone, a fluid mechanicist at Princeton University in New Jersey, and a member of the team that performed the study. For great loads,  the use of wooden sledges was required.

Imagine whole tree trunks the size say of a telegraph pole lined up one after the other. The stone, pulled by many men and burden animals, would slide along these tree trunks. In practice, however, this theory is met with a lot of challenges. This would only work on smooth, hard surface to prevent the rollers from becoming mired.  So, again, how did they do it?

Building a palace one (big) stone at a time

Photo by Jakub Hałun.

Luckily, the Chinese kept a lot of documents for their projects be them agriculture, arts or, of course, construction. The researchers found a 500-year-old Chinese record claiming that in 1557,  112-metric-tonne stone was transported over 28 days to the Forbidden City from a quarry by ice sledge. This quarry was located 70 kilometers away from Beijing.

The team of scientists decided to test this historical documentation and they computed the friction, power and delivery time for the same amount of load under various scenarios. Dragging a 112-tonne sledge over bare ground would require more than 1,500 men, however the   same sled across bare ice or across wet, wooden rails would require 330 men to pull. Here’s the interesting part, though: when a thin film of water is poured on top of the ice during the winter when most transports would take place,  fewer than 50 men would be needed to tow the load. Lubricated in this fashion, the stones would have slid along at a stately 0.18 miles (0.29 kilometers) an hour, the analysis finds.\

“I’m not surprised. If you get enough people, enough rope, and enough time, you can move just about anything,” says archaeologist Charles Faulkner of the University of Tennessee, Knoxville, who was not on the study team. “And they had a lot of time. And a lot of people.”

And certainly, we couldn’t have expected anything less from the people who built the Great Wall of China. Findings and results were reported in a paper published in the journal  Proceedings of the National Academy of Sciences .

Fluid dynamics shapes beautiful hexagon honeycombs, not the bees themselves

Honeybees are exquisite and majestic beings, which have always caught the imagination of people. Bees are typically associated with feminine energy, because they are ruled by queens, particularly with the roman goddess Venus. In some cultures, bees also represent wisdom. From a biological point of view however, bees could be definitely associated with motherhood. Without bees, a myriad of plants would die out due to lack of pollination. It’s clear that honeybees are of the utmost importance for the biosphere’s delicate balance.

There’s one more thing honeybees are cherished and appreciated by humans for: their display of biological engineering, namely for producing hexagon honeycombs. This may be the only thing people overly credit bees for, though. The perfect hexagonal honeycombs which have awed and inspired people for thousands of years may primarily result from the physics of surface tension, the honeybees themselves being responsible only for laying the foundations.

The findings come after researchers at University of Cardiff, UK,  led by engineer Bhushan Karihaloo, closely studied a colony of bees. After they flushed the colony out by smoking the hive, the researchers examined the honeycomb structures, some in their last stage of development, while other in their first incipient form. The scientists found that bees first produce cells that are circular in cross section, which eventually build up like a layer of bubbles. The wax, heated by  the bees’ bodies, then gets pulled into hexagonal cells by surface tension at the junctions where three walls meet. Both experiments and models have confirmed these findings.

When first made, the comb cells of the Italian honeybee (Apis mellifera Ligustica) are circular (top), but after two days they already look more hexagonal (bottom). (c) Nature

Why hexagon of all shapes? Well, a geometric array of identical cells with simple polygonal cross sections can take only one of three forms: triangular, square or hexagonal. Of these, in this particular situation, the hexagon shape takes the least amount of wall area, thus using less wax. Nature , as always, is guided by efficiency.

But wax is solid, right? Yes, and for the wax to flow, this is why the bees heat up the cells – to be more precise, to 45 oC or warm enough to flow like a viscous liquid. Not all bees heat up the wax, of course, otherwise the whole colony would collapse. A median ambient temperature of 25 degrees in the hive supports this idea. As an interesting fact, one of the greatest foreseeing minds, Charles Darwin, also had the idea that the bees might first make circular cells, which become hexagonal subsequently, but lacked evidence to support his proposal.

Still with knowing this, bees still can be seen as excellent engineers of the animal kingdom. For one, it’s they who lay out the ground work, and make sure physics takes its course by heating the wax. They also use their head as a plumb-line to measure the vertical, tilt the axis of the cells very slightly up from the horizontal to prevent the honey from flowing out, and measure cell wall thicknesses with extreme precision. Really, bees are so amazing!

The study was reported in the Journal of the Royal Society Interface