Lost Marbles

Not the angle of repose I was looking for

I lost several hours this morning when I fell down a rabbit hole of interesting facts. I was looking for something specific about what is called an ‘angle of repose.’ No it isn’t the angle of my lawn chair - although I did stumble upon a blog called ‘My Angle of Repose’ and a 1971 novel titled ‘Angle of Repose’.

The angle of repose I’m interested in is the maximum angle a pile of something (i.e. a granular material) could reach before tumbling down. A google scholar search found scientists piling a plethora of items from mustard seeds to firewood.

Not surprisingly, the shape of what you are piling matters. In a 1966 paper, piles of tiny spheres and angular crushed quartzite were examined. For diameters of 0.5 mm, the angle of repose for the spheres was 38 degrees while for the quartzite it was a steeper 57 degrees. Meaning flatish, irregular things pile better than round things.

But, diameters of 0.5 mm are tiny, what about something bigger? For bigger things, the angle of repose decreases. The tiny spheres above would form a pile while attempting to pile marbles would only lead to escaped marbles - and an excuse to say: “help, I’ve lost my marbles.”

Adding water changes things - and this is where I really got sucked in. A 1997 paper titled ‘What keeps sandcastles standing’ was irresistible to me and completely unrelated to what I was looking for, so I read it.

If you are going to build a fancy sandcastle, you’ll quickly discover that dry sand won’t work, only wet sand will do. That’s because the properties of wet and dry sand are different. They did a lab experiment to prove it by modeling wet sand with spherical polystyrene beads ‘wetted’ with corn and vacuum-pump oil.

As a tangent - a completely different study used rice piles to model avalanches. What you use likely comes down to what you can get to work in the lab. My experience with lab experiments I designed myself clearly demonstrated that it isn’t easy to come up with something that works.

They found that by only slightly coating the beads (coating of less than 50 nm) dramatically increases the angle of repose. This means that by adding water to sand, the liquid introduces attractive forces that act to bind the particles. At first clumps form, which grow as more liquid is added until what you are working with (sand, polystyrene beads, etc) holds together.

The angle of repose is an important factor when studying slope stability and landslide prediction. How gravity influences the angle has also been studied, so what we know here can be transferred to exotic locals such as Mars. A point to ponder if you have to trek across scree in your local mountains or on Mars.

It might be hard, but...

The result of blowing bubbles in my backyard

While reading a textbook* aimed at first year science students, deep in a chapter, I came across this passage:

 “... because a mathematical description of the coriolis deflection involves vector equations and, hence, is difficult to grasp, we will rely on a more general and somewhat inaccurate explanation of the concept.” 

Now, the author did put the technical stuff in an appendix, which began with: “Although few understand the coriolis effect...” 

The author's right, vector calculus can be hard, but, that’s beside the point. All sorts of things are ‘difficult to grasp’ yet we do them anyway. This textbook is for students in a first year science course. We should be inspiring them to go on and study more science, not scare them off because of perceived difficulty. Why even mention concepts are ‘difficult’ or that ‘few understand’?

Reminds me of an old article in the Onion about how science is hard (here).

We are doing ourselves a disservice when we set up things as hard - if you are interested, hard things are doable and should be tackled. I don’t think people aim to be a professional dancer or lawyer thinking they are on an easy path. Science is the same. The fact that there is so much complexity in the world around us is fascinating and we’ll never run out of new things to learn.

Why not present information in a science textbook without judgement on how difficult the concepts are? I’ve never come across another textbook that did. Unfortunately, there was more:

“Unfortunately, the concept of vorticity is difficult to grasp without a background in physics and mathematics ...” 

And that was the end of the discussion of vorticity.

On a tangent... some time ago, I rushed into the living room to catch a science story on the news about how a particle was clocked traveling faster than light (which has since been shown not to be the case). At the end, the anchor (Peter Mansbridge) questioned why we should care about this result and the science correspondent (Bob McDonald) gave a good answer. Then the next story was about the auction of Elizabeth Taylor’s jewels and no one ever questioned why we should care. Interesting...

*the textbook is Invitation to Oceanography by P.R. Pinet. Over all, it reads well, has nice figures and is easy to follow.

Floating Trees

A tree in the forest near my home

Years ago I read C.S. Lewis’s Space Trilogy since I had enjoyed his The Lion, The Witch and The Wardrobe series as a kid. The Space Trilogy books were too weird for me and I can’t remember if I finished all three. What does stick in my memory is one of the settings (on Venus I think, but I could be wrong). The main character ran across surreal floating islands coated in trees and surrounded by water. The movie ‘Avatar’ also brought us tree covered floating islands (this time floating in the air due to a ‘flux vortex’), but the strangest trees I’ve come across are floating on glaciers and they’re real.

A while back, I went to a talk by Hig about his trek with his wife, toddler and baby across Malaspina Glacier (find their blog here). They lived in the wild for two months. Clearly they are somewhat crazy - in a fantastic way, I wish more people took their kids into nature that way. From the video and photos clearly the kids had an awesome time.

Malaspina Glacier sits by the ocean on the southern reaches of Alaska reaching 600m thick in places and covering an area of 3,900 square km. Like many glaciers, this one is shrinking however the most striking feature to my mind is that in places trees grow on it. Trees growing on top of ice - how fabulous is that! Even assuming there is some sort of soil layer buffering the roots from the ice.

Are there other glaciers out there with trees growing on them?

How deep is it?

Once a lead line was the only way to figure out how much water was beneath your ship. Now, there are all sorts of options for determining ocean depths from echosounders to satellite images. I suppose one could even venture out with reel of line and a weight, but not me as spooling in kilometres of line is quite tiring.

I wrote about how our technology evolved for determining ocean depths here.

on a snowy day ...

Snow is falling on my island in the Pacific - and more snow is threatening to dump on us. The lyrics from Paul Simon's 'Slip Sliding Away' come to mind when I think about venturing out onto a snowy road. If I don't have to go anywhere, I don't mind the snow and enjoy the change to the landscape it brings. From my window or backyard, watching snow falling is fascinating. There's something about the silence when snow falls that I find quite compelling. If you have ever wondered about a snowflake's shape and how it relates to the temperature outside, check out this.

Ageing maple leaves

a maple leaf in the sun

Yesterday, in the parking lot at work, a maple leaf rested on the pavement. The golden-hued morning light caught the leaf highlighting the red-tending-to-maroon tones. The leaf sharply contrasted the cold grey of the pavement, its vividness catching my eye. What if I picked up the leaf and saved it? Could archeologists in the far future figure out when the leaf fell from the tree?

Currently, we can estimate how old plant-based objects are using radiocarbon dating - often just called carbon dating. In 1949, Willard Libby and his team accurately estimated the age of the wood in an ancient Egyptian barge – a barge with a recorded age. This process works through knowing the ratio of carbon-12 (the ordinary stuff) to carbon-14 (a radioactive isotope) in the atmosphere.

Carbon-14 isn't particularly stable and decays quickly. It has a half-life of about 5,730 years - only a moment of time compared to the approximately 4.5 billion year half-life of uranium-238 (which is roughly the age of Earth). Continuously formed in the atmosphere by cosmic rays, carbon-14 reacts with oxygen becoming carbon dioxide. Plants take up some of this carbon dioxide along with carbon dioxide formed from the more abundant carbon-12. When the plant dies, no more carbon dioxide is taken in and the existing carbon-14 begins to decay.

If we assume the carbon-12 to carbon-14 ratio was the same when the plant died to now, using the decay rate of carbon-14 will give us the item's age (back to about 60,000 years). But, we know this ratio has fluctuated over time. To compensate, the age results are calibrated to something known like written records or tree rings. The biggest change to the carbon-12 to carbon-14 ratio has occurred in modern times through nuclear testing. Carbon-14 levels in the atmosphere were boosted around 1950 and peaked in the 1960's (at which time, testing bans were agreed to).

So, could a future archeologist figure out the are of my leaf using carbon dating? Probably not accurately because we've messed with the carbon-12 to carbon-14 ratio in our atmosphere. It would be more accurate for that archeologist to look at the date of this article.

As a tangent: At the end of the day when I returned to my car, the leaf was still there. Without the sunlight shining on it, the leaf looked brown and uninteresting.

Sunny paradoxes – part 2

A hazy sun

Since the solar system's beginning, the sun has increased its energy output by about 25 percent. What has that meant for earth? From ancient rocks, we can tell that a younger earth had surface liquid which can be taken to mean that earth has remained roughly the same temperature as we still have liquid water. If the sun was cooler back then, why wasn't the earth cooler? This is known as the 'faint young sun paradox'. A number of mechanisms may have been responsible for keeping a relatively constant surface temperature. Probably a combination of things are involved, but no one knows for sure. Here are some possibilities:

The Earth was warmer despite less incoming solar energy because of a larger greenhouse effect. For this to work, the greenhouse effect responsible would have tapered off as the sun grew brighter. The greenhouse effect is caused by an atmosphere rich in 'stuff' that prevents radiation from escaping. Two of the better culprits are water vapour and carbon dioxide (methane is a good at this too, as is nitrous oxide i.e., laughing gas). Assuming carbon dioxide played a big role, where would extra carbon dioxide come from? Way back, a more geologically active earth spewed more carbon dioxide from volcanoes. This excess carbon dioxide eventually was sunk into places like our oceans thereby reducing this greenhouse gas over time (only in the last 200 years have people begun spewing out our own contribution of this gas). So, when the sun was cooler the extra carbon dioxide created a greenhouse effect that has decreased at a similar rate as the sun heating up. Other processes probably put more of the other greenhouse gases into our atmosphere long ago and removed them slowly over time as well.

A recent thought based on big assumptions is that the early atmosphere also had more nitrogen. Nitrogen all on its own isn't a greenhouse gas on Earth (on Saturn's moon Titan, some funky stuff happens to the nitrogen, so there it acts a greenhouse gas), however extra nitrogen bounces around and hits the greenhouse gases which gives the greenhouse gases extra energy and makes them unstable or wobbly. This molecular wobble spreads out absorption lines (the range where a particular molecule absorbs energy) resulting in a wider band to absorb the radiation – thus more radiation is absorbed. On the flip side, extra nitrogen could also increase Rayleigh scattering, thus reflecting more of the incoming radiation away. So knowing which process dominated would be important.

As for why early earth wasn't colder with a cooler sun, we have good some ideas, but we really don't know for sure.

Refs:

Walker, C.G., P.B. Hays and J.F. Kasting, 1981: A negative feedback mechanism for the long-term stabilization of Earth's surface temperature. Journal of Geophysical Research, 86, 9776-9782

Goldblatt, C., M.W. Claire, T.M. Lenton, A.J. Matthews, A.J. Watson and K.J. Zahnle, 2009: Nitrogen-enhanced greenhouse warming on early Earth. Nature Geoscience, 2, 891-896.

Sunny paradoxes – part 1

A sunset over Cumberland Sound

The sun continuously shines on Earth, but how much sunlight reaches us varies through the year. Since the Earth's orbit is elliptical, we are closest to the sun around 3 January and farthest around 4 July. Every illustration of the elliptical orbit of Earth that I've seen shows a hugely skewed orbit, which could lead one to think Earth would have its hottest global temperature in January.

However, the elipticalness of our orbit doesn't have much of an impact. From Wikipedia: Earth's farthest point is 152,098,232 km and the closest 147,098,290 km – a difference of 4,999,942 km, which is a small fraction of the orbit's radius (yeah, it's still a huge number, but everything in space is huge). Another way to look at this is to consider the eccentricity of Earth's orbit. Eccentricity is a measure of how circular an orbit is, zero is a perfect circle and one isn't a closed orbit (like a slingshot). Earth's eccentricity is about 0.02 – really close to a circle.

For those of us in the northern hemisphere, we are closest to the sun in the middle of winter – not the hottest time of year. Instead, it's the Earth's tilt that creates the seasons – we are tipped 23.5 degrees from the plane of Earth's orbit. When the pole closest to us is tipped away from the sun, we get winter. At the pole itself there is complete darkness (good for vampires).

The tilt of the Earth's rotation plays a greater role in our temperatures than the elipticalness of Earth's orbit. Either way, we still get a free trip of 150 million kilometres each year.