Great circles and flight paths

It is an often repeated cliché that the easiest way to become a millionaire is to start out a billionaire then go into the airline business. It is a tough and competitive business which means that we can be fairly certain that planes do fly the shortest possible way between point A and B. Sure, there are many complicating factors but let’s leave them at the moment.

It is an amusing experience to take a globe or Google Earth and find out how an airplane should fly between two points to spend the smallest amount of fuel possible. In order to do that, an airplane should follow a great circle. What is this? It is an imaginary line on the surface of the Earth which is an intersection of the surface and a geometrical plane which is determined by three points: departure and arrival airfields and the center of the Earth.

When we open Google Earth and measure the distance between two points, this distance is measured exactly along a great circle. There is nothing very special about that if these points are relatively close to each other (few thousand kilometers) or if they are roughly on the same meridian (all meridians are great circles). However, things get somewhat surprising when these conditions are not met.

The result is surprising because our Earth is round but we prefer flat maps for practical reasons. Unfortunately, there are no ways to project a spherical surface onto flat map without generating distortions. It is a matter of choice which distortions and where we prefer but we can not go without them. We should keep this in mind or otherwise we may live in illusions which have not much to do with the real world.

This post is motivated by my upcoming trip to Hawaii. I live in Estonia which is a small country in northern Europe. Now let’s imagine how should an airplane fly in order to cover the smallest possible distance. Is it something like this:

flight path
Actually no, this is not the shortest distance between Estonia and Hawaii. We should not believe this map because it is a two-dimensional representation of a three-dimensional object. Hence, it is unavoidably faulty and limited. In reality, the shortest flight route between Estonia and Hawaii goes almost straight over the north pole:
Estonia Hawaii great circle
Although there are few countries that have more northerly position than Estonia and Hawaii is not too far from the equator but still the shortest way to Hawaii from Estonia is to head straight towards the north pole. This world is sometimes really weird. Or I should say “round”?

I said in the previous post that after the trip Hawaii would be the most distant place on Earth where I have ever been. This is really nothing to brag about because Hawaii is only 11,000 kilometers away from my home. The circumference of the Earth is 40,000 kilometers. We should travel approximately 20,000 kilometers and then we can say that it really is not possible to go any further, unless we are leaving the Earth entirely.

But let’s come back to the real world. It would be very nice to fly straight from Estonia to Hawaii but this is not to be. It is odd and very unfortunate. Both are fine places for living but surprisingly small number of people are apparently sharing my view. I have to first go to places where more people live and where there is a real market for airlines. In my case, instead of heading north, I will go south. I will go to Istanbul in Turkey from where my plane should fly to Los Angeles. The distance between these two cities is also 11,000 kilometers and the flight will last 14 hours. I already feel that these are going to be frustratingly long 14 hours. Anyway, here is how the route from Istanbul to Los Angeles should theoretically look like:

Istanbul Los Angeles flight path shortest
I know what great circles are and how bizarre the shortest route on globe may look. However, I still find it unexpected that one should fly north of Iceland over the Greenland ice shield in order to fly along the shortest route from Istanbul to Los Angeles.

I am not sure that this is the actual route because there are other factors that should be taken into account. Jet streams, for example, are powerful winds high in the atmosphere which airlines try to use when flying in the same direction with wind and avoid when flying in the opposite direction. However, one thing is clear. The third image is much better representation of the actual flight route than the first one.

First time in America

I am happy to announce that I will soon leave home to discover new and interesting places. I have never been that far from home. I plan to visit two world-class geological destinations: Big Island of Hawaii and Death Valley in USA. I will go in the second half of this month and the whole trip will last about one month.

I will spend most of the time in Hawaii and about 10 days in southern California on the way back. This is not much. I know that California has interesting hiking trails and outcrops for more than a lifetime of travels. However, I have to try to take the best out of these days. I am sure some of you live in California or have been there and can recommend places worth visiting. I will arrive to Los Angeles and plan to rent a car to go to Death Valley and visit geologically interesting places along the way. I have no idea at the moment which places these are. You can help me to make the best selection.

I will try to make my best to take you along by posting pictures of interesting geology I will see there. I am really looking forward to this trip.

Conchoidal Fracture: What It Is and Why It Matters

Obsidian

Conchoidal fracture is a smoothly curving fracture surface of fine-grained materials which have no planar surfaces of internal weakness or planes of separation (no cleavage). Such a curving fracture surface is characteristic of glass and other brittle materials with no crystal structure. However, conchoidal fracture is common in crystalline materials also if they have no cleavage (like mineral quartz), or if they are composed of very small mineral grains so that the fracture surface which is actually zigzagging between the grains appears smooth to our eyes. This is the case with many fine-grained (aphanitic) rocks.

Obsidian
Obsidian is famous for its conchoidal fracture surface. This rock type was highly valued during the Stone Age because it makes a fine cutting blade if treated (fractured by precise and forceful blows) correctly. Width of sample is 11 cm.

Smoothly curving fracture surface develops when force is rapidly applied to brittle objects like hitting a piece of obsidian (volcanic glass) with a hard pointy object. If the force is applied correctly, a flake of obsidian is peeled away leaving obsidian with a smoothly curving fracture surface and sharp edges. It was the way our ancestors made sharp cutting tools.

Why is the fracture surface smoothly curving? Because we apply a force to only one point. This is where the brittle deformation starts. The energy of the blow spreads in the material like seismic waves travels through the Earth. So the curving lines are like the fronts of seismic energy recorded on the fracture surface. The fracture can occur only if the blow is energetic enough to peel off a flake. We need to apply more force if we want to shatter a large piece of material and much less if we just want to peel off a small flake from the edge.

Obsidian
Another piece of obsidian with nicely curving conchoidal fracture surfaces. Width of sample from Armenia is 11 cm.
Gilsonite
This rock sample looks very much like obsidian but it is actually an amorphous fine-grained asphalt known as gilsonite. It has no crystalline structure and it is brittle at room temperature when force is applied rapidly. The sample from Mexico is 11 cm in width.
Basalt rock sample
Even crystalline rocks like basalt may display conchoidal fracture if they are fine-grained enough. However, the fracture surface is not as smooth and shiny because microscopically it is pretty rough. Width of the sample is 12 cm.
Chert and chalk
Chert is another rock type that commonly exhibits a conchoidal fracture. It was also widely used as a tool-making material by our ancestors. The width of the sample from Cyprus: 7 cm.
Smoky quartz
Quartz is a mineral with crystalline structure, but there are no planes of weakness inside the crystal. Hence, it has no preferred planar surfaces along which to break. Quartz is not the only mineral without cleavage, but it is the best known and most widespread of them. Smoky quartz on the picture. Width of sample 11 cm.
Conchoidal fracture
Chalcedony is a very fine-grained rock type that is compositionally close to quartz and chert. There is a red variety of chalcedony which is known as carnelian on the picture above. Red color is given by hematite impurities. The sample from Kazakhstan is 14 cm in width.
Phosphorite
“Conchoidal fracture” is named so because the curved lines on the fracture surface resemble the rippling growth lines on the shells of clams or conchs. The sample above is sandstone with abundant phosphatic brachiopod (Lingulata) shells from the Ordovician of Estonia. Brachiopods look similar to clams. Their shells have similar growth ripples. Pay attention to the fact that conchoidal fracture only looks similar to the appearance of clam shells. Their origin is completely different. Width of sample is 12 cm.

Blue, black and white

Today is a birthday. Not my birthday but my dear home country Estonia is 95 years old now. I wish her a prosperous future. May it be much brighter than the past.

Estonia’s national colors are blue, black and white and this post is inspired by these colors.

Hematite
This is a sample of hematite. Hematite is an oxide of iron. It is extremely widespread mineral, especially in sedimentary rocks. Many reddish rocks and minerals owe their color to hematite. Ironically, there is nothing red in this picture of a pure sample of hematite but it would be red if powdered.

The colors that dominate on the picture above are dark brown with white and bluish spots — the approximate colors of the national flag of Estonia. Dark brown is the natural color of hematite, white spots are reflections from the light source but what about the blue spots?

I have to say that I am really not sure. Some minerals possess a very beautiful play of colors called iridescence. Especially well-known example is a plagioclase feldspar mineral labradorite:

Spectrolite
Plagioclase crystals in this sample of anorthosite look bluish when viewed from a certain angle. Plagioclase crystals allow some light to penetrate into the crystal which is made of many alternating slabs of different composition which act like mirrors and reflect the light back. Reflected lightwaves combine (this is called interference) and create interesting bluish play of colors.

Is the same effect responsible for the bluish spots on hematite? No, I don’t think so because hematite is practically opaque mineral which does not allow light to penetrate into it. But is it still caused by some intrinsic property that is specific to hematite?

This is also not likely. I have seen very similar effect in other minerals and rocks and I even remember some comic books which I read when I was much younger. It was about Native Americans that always had pitch black shiny hair with bluish glare. I doubt that they really have hair like that but maybe some tribes with very dark hair in some conditions? Somehow artists had to get the idea.

Morion
Smoky quartz is a silicate mineral that also reflects bluish light.
Obsidian
Obsidian is a glassy volcanic rock with occasional bluish reflections.

Smoky quartz is a silicate mineral, obsidian is a volcanic glass, and hematite is an oxide of iron. They are all very different materials. We can therefore almost certainly rule out the possibility that the bluish color has anything to do with the internal structure of these materials.

However, the surfaces of these samples have something in common — they all reflect light well and they are very dark-colored, almost black.

This in probably the key to understand this phenomenon. Blue color may be a weak reflection which looks bluish because it comes from a very dark surface. This is my guess. I have not found any confirmation to this. I would be interested to hear your opinions if you have an alternative explanation.

Speckled mystery rock

Do you know what causes these speckles in a mafic lava rock? These rock samples are from La Palma (Canary Islands) and appear to be basanite or olivine-phyric basalt. This is no quiz question. I don’t know the answer but hopefully someone with more experience has seen such rocks before.

Basanite
Width of sample: 30 cm.
Basanite
Basanite

Back from Tenerife

I am now back home in Estonia. I am very satisfied with my trip to Tenerife. It was not purely geological trip. We (I was there with my wife) also visited zoo, took a sea trip to spot dolphins and spent a whole day in a water park.

I have visited three islands in the Canary archipelago now and can say that they are all quite different. Gran Canaria is more eroded and noticeably older. La Palma looks and is very young with abundant examples of fresh volcanism but Tenerife is the most versatile. If I have to pick one which is the best of the three then I would be in trouble.

La Palma and Tenerife are both very interesting. I don’t know which one is the best. I probably have to go there again and take another look 🙂 Gran Canaria is probably somewhat behind the two but I also spent less time there.

Don’t hesitate to contact me if you plan to go to Tenerife to enjoy geology. I have many nice locations with coordinates recorded in my field notebook.

Tenerife-lizard-Gallotia-galloti
Tenerife Lizards or Western Canaries Lizards (Gallotia galloti) are common reptiles in Tenerife. I saw them in several places. They are usually very quick but this female lizard agreed to pose for a photo.

Beautiful dike in Tenerife

Today I took a very scenic hike in the NW part of Tenerife. This part of Tenerife is geologically known as Teno. It is one of the three original basaltic islands that were later joined into one bigger island.

I was hiking about 800 meters down along the Barranco de Masca and later up again. It took a little less than 6 hours and was physically quite demanding. This barranco is a deep and very narrow canyon. Maybe 200 meters deep in the lower part and 60 meters wide. I do not know the exact numbers at the moment. This is just a guess.

Volcanic islands are cut by lots of dikes that once fed the volcanoes higher up. They are easily noticeable in a vertical wall of canyon. Today I am showing you one which I took just before entering the canyon. Most of the photos I took later are unfortunately not that good because I did not want to hike with a tripod but there was not enough light at the bottom of the canyon to take good handheld shots.

http://picasaweb.google.com/107509377372007544953/Tenerife#5833805433454016130
This dike stands out as dikes often do because they tend to be more resistant to weathering than the surrounding volcanic material.

First glimpse of Tenerife

I am in Tenerife. Today was very long day in the field. I am too tired to write a lengthy post. But I would like to share at least one picture with you.

Sequence of pyroclastic rocks in Tenerife. Pumice layer is a product of violent plinian eruption farther away. Scoriaceous mafic dark-colored lapilli were ejected from nearby vents (Strombolian eruptions). Width of view is 12 meters.
This is pyroclastic sequence which is composed of dark layers of scoria and light-colored layer of phonolitic pumice fall deposit between them. Pumice layer is a product of violent plinian eruption farther away. Scoriaceous mafic dark-colored lapilli were ejected from nearby vents (strombolian eruptions). You can also see a minor fault running through the outcrop.

Here are the coordinates of the outcrop: 28° 20′ 02″ N 16° 27′ 50″ W. Altitude 1970 meters.

I am going to Tenerife

One month ago I came from the Canary Islands (La Palma and Gran Canaria). Now I am going there again. But this time my destination is Tenerife.

I have been in Tenerife once (in 2009). It was a memorable trip. I know several nice outcrops there but this time I hope to see and understand much more. I just took a review of my photos I took there. I am really amazed how poor is the quality of these snapshots. There is really nothing I would like to use here now. Tenerife is a beautiful and magnificent island (second largest island volcano in the world after Hawaii). It deserves better equipment than my point-and-shoot I used then and better photographer also. I have a better camera and lens now but I am not sure about the photographer. It is still only me.

This time my trip will be quite civilized. I will stay at a hotel. Who knows, maybe I will even have internet access there. I am not very optimistic though. People there have somewhat different lifestyle. It seems that internet is not a necessity for them. Sometimes they advertise that their hotel has internet access but in reality this means that there is a computer in the lobby into which you can insert a coin to access internet for 5 minutes. It would be laughable if it were not so sad.

If there is internet access, then I will try to post something once in a while.

Teide from plane window
I took this photo a month ago when I was flying from La Palma to Gran Canaria (Tenerife is right between these islands). Quality of the photo is terrible because it was taken with a phone but phonolitic cone of Mount Teide, the highest peak of Tenerife (3718 meters) and the rim of the caldera surrounding it are clearly recognizable.

Building stone gallery

Rock fences are interesting to take a look at. They usually reflect local geology remarkably well because it is expensive to transport such a heavy material which is readily available in most places. Here I present a collection of images of rock fences and walls I have taken so far.

Unfortunately my collection is very small but this post in its current state is just a start. I plan to update it as I take new photos. Now I have a reason to hunt these walls and a place where to upload the photos.

Ignimbrite wall
Ignimbrite (welded tuff). Gran Canaria, Canary Islands, Spain.
Turbidite mudstone wall
Mudstone (turbidite). Cliffs of Moher, Ireland.
Andesite stone wall
Andesite or basaltic andesite. Red blocks are weathered. Santorini, Greece.
Quartzite as building stone
Quartzite. Connemara, Ireland.
Basanite stone wall
Basanite stone wall. La Palma, Canary Islands, Spain.
Ignimbrite stone wall
Tuff (ignimbrite). Gran Canaria, Canary Islands, Spain.
Quartzite in wall
Quartzite. Santorini, Greece.
Ignimbrite wall
Ignimbrite wall
Ignimbrite bricks
These rocks may look like man-made bricks but they have entirely natural composition. This is the same Tenerife ignimbrite shown in the previous picture.
pumice lapillistone stone wall
Pumiceous lapillistone (pumice fall deposit known as Granadilla pumice), Tenerife, Canary Islands, Spain.
Gneiss wall
Wall made of gneiss blocks in Sweden. Even the rocks that do not seem to have a banded appearance do have it when looked from a different direction.