The Wool Sock’s Carbon Footprint

Four years ago, I blogged about the cognitive disconnect between the ecological perceptions of wearing wool and eating beef.  However, I did not actually calculate out exactly what the carbon footprint of a wool sock is.  Here it goes:

According to Wikipedia’s wool bale article, a bale contains about 60 fleeces, and weights 150 ± 50 kg.  This gives a fleece weight of about 2.5 kg.

This wool sock weighs about 100g, meaning that you can get about 25 socks per fleece.  A sheep produces one fleece per year.

A ballpark estimate from the NSW department of primary industries suggests that a medium sized (45 kg) adult sheep in warm weather needs about 500g of dry feed per day to survive.  If this feed is mostly cellulose, it will metabolize to produce about 800g of CO₂ per day, or 297 kg/ year. Assuming 25 socks per year, that gives about 12 kg of respired CO₂ per sock.

However, in addition to respiration, sheep also produce a fair amount of methane, which is generally considered to be 25 times more potent a greenhouse gas than carbon dioxide.   This paper estimates a methane yield of about 20 grams / day/ sheep, or about 7.3 kg of methane per year.  Using the 25 times multiplier, we get a CO₂ equivalence for that methane of about 180 kg / sheep/ year, which is a bit over half the direct respiration emissions.  Dividing by 25 socks/sheep gives is a CO₂ equivalent of 7.3 kg per sock (300 grams methane).  In total, our CO₂ equivalent emissions from the sheep are about 19 kg of CO₂ per wool sock- 12 from respiration, and 7 from methane.  This figure only includes the CO₂ footprint for growing the wool.  It does not include additional emissions from shearing, transporting the wool, spinning it into yard, and manufacturing the sock.  This is the same amount of CO₂ released by burning about 8 liters of gasoline (which is enough to drive a mid-size car 100 km), or one sixth the emissions of a top fuel drag race (with 2 cars in it).  So a hackey sack game with more than three pairs of new socks in it is worse for the atmosphere than this.

In contrast, a 50 gram synthetic sock (synthetics weigh less than wool) probably has a carbon footprint of 10-25 grams*.  It production is one THOUSAND times less carbon intensive than a wool sock.  So the next time some green evangelists starts looking down their noses at your car or your plate, check out their feet.

* In both the case of the plastic sock and the wool sock, the carbon in the sock itself is sequestered in the sock drawer for the lifetime of the sock, and in a landfill for several decades afterwards.  Unless you burn your old socks, which smells, or recycle your used synthetic socks into drink bottles, which is disgusting.

Why deflecting asteroids is a really bad idea

In the aftermath of the Chelyabinsk fireball last month, there have been increasing calls to identify asteroids on a collision course with Earth and develop technologies to deflect them.  This would be a very stupid thing to do.

The reason for this can be seen in figure 1, below.  In part A, this figure shows the minimum deflection necessary to make an asteroid on a collision course with  Earth to miss.  The deflection angle depends on how far from Earth this deflection occurs; the farther away, the smaller the angle.  In practice, very small angles from very far away would be used. 

The green line shows the minimum translational distance an asteroid must be deflected in order to miss the Earth.

Figure 1. An illustration for how the deflection needed to make an asteroid miss can be used to make many more hit.

The problem with such a system is shown in part B of the figure.  Here, an identical deflection is applied to a harmless asteroid that never would have hit Earth.  However, by deflecting it towards the Earth, this harmless rock ends up exploding in the atmosphere.  For a rock the size of the Chelyabinsk bolide, this is similar in force to a large nuclear weapon.

The area of the red circle- the smallest radius necessary to protect the earth- is three times the cross section of the earth.  So for every rock you deflect, there will be at least three harmless rocks that can be turned into weapons of mass destruction.  By definition, a “planetary defense system” turns every rock that passes close to the Earth into a potential weapon of mass destruction. 

Who would actually crash a space rock into a populated area of the Earth?  The same people who crash airplanes into skyscrapers of course.  And while only a few rouge countries can launch satellites, any spacecraft in radio contact with Earth can potentially be hijacked by a hacker on Earth with enough chicken wire to erect a makeshift dish in a desert.  Amateurs already pick up signals from our most distant space probes; an asteroid deflection mission would be a magnet for every doomsday cult, terrorist fanatic, delusional hacker, and other misanthropes whose imagination had previously been limited to shooting up schools.  Obviously nobody is going to design a space deflector to be hackable, but then the drone the Iranians hijacked wasn’t supposed to be vulnerable to those sorts of attacks either. 

The threat of an asteroid impact is miniscule.  More people were killed in floods this week than were killed by impacts in the known history of the human race.  A quick glance at the morphology of our planet will explain why.    Even the giant extinction-causing impacts are less common than large flood basalt eruptions of similar ecological lethality.  But developing the technology to deflect asteroids potentially gives all the wrong people access to a weapon the size of a large hydrogen bomb for a fraction of the development cost.  This is not a smart thing to do.

High mass resolution mass spectrometry

Mass spectrometry is the dark art of separating objects by mass.  The name comes from the alchemal days of photographic plate detectors; just like a prism separates white light into a spectrum of colors, a magnet can separate a beam of ions into their component masses, which will then form an image on a plate.

These days, electronic counting systems have replaced chemical emulsion ion detectors, but the name lives on.  In the case of atomic and molecular charged particles, the masses are not continuously distributed, like the energy distribution of white light.  Rather, different ions have discrete masses.  To a first approximation, the nominal mass of an atom (or an atomic ion, if the atom is charged) is simply the sum of its protons and neutrons.  Thus, an atom with 26 protons and 30 neutrons (Iron fifty-six, abbreviated by scientists as “⁵⁶Fe”) has a nominal mass of 56. 

The whole point of mass spectrometry is to separate things with different masses.  So, for example, most mass spectrometers can separate ⁵⁶Fe, with 26 protons 30 neutrons, from ⁵⁴Fe, which also has 26 protons, but only has 28 neutrons. The ability to distinguish atoms of the same element with different mass- isotopes- is one of the main uses of mass spectrometers.  In this case, separating ⁵⁴Fe from ⁵⁶Fe requires a mass resolution of 1 part in 28.  The mass resolution, defined by IUPAC as M/ΔM = 56/2 = 28.  This is quite low. It is about nine times worse than what is needed to separate ²⁴⁰Pu from ²³⁹Pu, for example. And even then, a mass resolution of 240 is still generally considered low.  There is no formal definition of high and low mass resolution.  However, as a general rule, mass spectrometers which can only measure the nominal masses of inorganic ions are generally known as low mass resolution instruments.

Note the use of the word ‘nominal’ when describing ionic masses so far.  As it turns out, exact masses are not the same was nominal masses.  For one thing, protons and neutrons do not have the same mass; their mass differs by about one part in a thousand.  More importantly, combining them into nuclei changes some of their mass into energy via Einstein’s famous equation, E=mc².  This ‘binding energy’ makes the nucleus lighter than its component protons and neutrons, and different nuclei have different binding energies, and therefore different exact masses.  So, for example, the mass resolution required to resolve a molecule of hydrogen, ¹H₂, from deuterium (²H) atom (a hydrogen atom with a neutron in its nucleus) is about 1350.  As a good working definition, high mass resolution is mass resolution high enough to resolve ions with the same nominal mass (called “isobaric interferences” by mass spectrometrists) as a result of the small differences in real mass caused by their binding energy.

The trouble with this definition, of course, is that the mass resolution required to separate isobaric interferences, depends on what they are. For example, see the isobaric interferences in figure 1.

Figure 1. SHRIMP mass spectrum of atomic and molecular peaks at mass 56 in San Carlos Olivine (Mg₂SiO₄ with Fe and Ca substituting for Mg). Green and purple: nominal M/dM = 5000; orange and blue: nominal M/DM = 15000; green and orange: Faraday cup; blue and purple, electron multiplier.

This figure contains mass scans taken on both high (~5000) and higher (~15000) mass resolution.  The mass resolution required depends on the interference.  For example, the resolution required to resolve ²⁸Si₂ from ⁴⁰Ca¹⁶O is more than ten times higher (~15000) than the mass resolution required to resolve ⁵⁶Fe from ²⁴Mg¹⁶O₂ (~1500). Note that increasing mass resolution also decreases signal intensity.

The easiest way to avoid interferences is to not create them in the first place.  This can be done by chemists who purify the element whose isotopes they wish to measure, or by material scientists who make pure compounds without trace elements (such as Ca in the above figure).

Another technique is to use an ionization source that doesn’t produce many molecular ions.  So high mass resolution is most useful when a compositionally complex material is ionized using a method that creates all sorts of complex species.

This is why high mass resolution mass spectrometry is popular in geological SIMS analyses.  Minerals generally contain a wide variety of minor and trace elements, and the SIMS ionization produces all sorts of molecular fragments.  So being able to resolve species based on their mass defects is extremely useful.

Do you really need a Nobel prize to know...

that heat is most easily lost from the head on cold January mornings...

Putting the Russian meteorite in perspective

Friday morning, a large meteor entered the atmosphere over the southern Ural area of Russia, detonating with enough force to shatter windows in nearby towns and injure over 1000 people.  Preliminary estimates suggest an impactor traveling at 15 to 20 km/s, and weighing 8000 to 10,000 tons, exploding at an altitude of 20-30 km with the force of a nuclear weapon.

These are hard numbers to wrap one’s head around.

Let’s start with the size. There are numerous reports around on the bolide being “bus sized.”  But buses are not made of solid rock, so this is deceptive. In this situation, mass is more important than dimensions. A bus weighs about 15-20 tons. That’s a lot less than 8000-10,000.  For example, 8000-10,000 tons is the approximate size of the naval destroyer USS Cole, which was famously attacked by Al Qaeda in Yemen in 2000. It’s a lot bigger than a bus. Of course, that ship doesn't fly in space.  Rather, it sails in the ocean at about 50 km/ hour, thousands of times slower than 20 km/ second. The International Space Station is about 450 tons.

Orbital velocity for a low earth orbit is about 8 km/second, and reentry speeds returning from low earth orbit are similar.  So this meteor was traveling at about twice orbital speed when it hit the atmosphere.  This is substantially faster than the 11 km/s reentry of the Apollo missions returning from the moon, and about twice as fast as the space shuttles (and other low earth orbit spacecraft) re-enter.  It is about 50 times faster than a handgun bullet.

The total energy released, between a quarter and a half a megaton, was similar to a modern H-bomb.  However, it was more dispersed, and released high in the atmosphere. Because the impactor was traveling at twice orbital speed, the energy would be equivalent to an orbital object of four times the mass re-entering.  32,000 to 40,000 tons is about the size of the Titanic, or a WWII battleship. 

Something similar to this has been imagined.  Below is a model of CV-6, the famous 20,000 ton WWII aircraft carrier Enterprise.

Compare that to the fictional NCC 1701 spaceship enterprise, at the same scale.

The internet gives a spaceship mass of 10 times the aircraft carrier, which seems way to heavy to be sensible. 

If we say the spaceship is twice the mass of the aircraft carrier (it is bigger, after all, even if it is also probably made from a lighter & stronger material than steel), then it would have about the same energy on re-entry as the Chelyabinsk bolide.

We can compare the videos:

Star Trek III

Chelyabinsk Friday morning:

Reality is still far more gripping than imagination. 

Finally, here is what the Earth looked like from the asteroid’s point of view an hour before impact.  A few things to note:

First, the Earth is almost full.  As a result, the side of Earth facing the asteroid was in day, so it would have been hard to spot, as the sun was behind it.  However, the US space junk tracking radars in Hawaii should have been able to pick it up.  I wonder if they did, if they passed any sort of a warning on, or even are they allowed to?  It would be a shame if the 1200 injuries that occurred were preventable, but for American government red tape.

I build huge cans of learning named after a small pink water animal with lots of legs.

I build huge cans of learning named after a small pink water animal with lots of legs. The can of learning fires the tiniest bits of air, hurried up by a field, at rocks to break them into the tiniest bits of matter. We suck all of the air out of the box, leaving only empty space. That way the bits of the rock don't hit bits of air that are in the way.

Another field sucks these bits off of the face of the rock, and into a big box filled with empty space and more fields.  The fields in the box sort the bits by exactly how heavy they are. The force that holds the bits together makes them a little bit lighter, so knowing exactly how heavy they are lets us tell tiny bits holding on to each other from single other tiny bits that are slightly lighter or heavier.
The very heavy bits are actually too big to hold themselves together. So they fall into pieces over time.  We look at how many pieces there are. This tells us the age of the rock.
People wonder how old rocks are.  My business builds cans of learning to tell them.

Brief: Explain your technical job using only the 1000 most common words #upgoerfive

Thanks to Anne and Chris for the brief.

The world has ended, but this blog rambles on.

In this timezone, it’s the 21^st of December already, and the world has been destroyed.

Sorry guys, but the Mayans were right.  At 12:01 am, Eastern Australian Daylight time, this section of the world was destroyed.  The planet is disintegrating along the time-zone lines like the segments of an orange getting peeled off and tossed into a juicer.  Sorry folks, it’s all over.  And they didn’t even use my method for destroying the planet.

Fortunately, the super expensive Australian National Broadband Network is extensive and robust enough to survive this catastrophe, so I am still able to blog from the cosmic void.  It is getting cold and hard to breathe out here, but there are some benefits.  For example, without a globe there is no global warming.  And, in space, no-one can hear your neighbor throw up in the front lawn after a big night out.  And the big night will last forever.  Unfortunately, the nearest place to grab a drink is now the Saturnian moon Titan.  No word from the Mayans yet on when that baby is due to go.

Odd-shaped lakes in Google Earth

I was goofing around in Google Earth this evening, performing an activity that started out as meaningful and quickly degenerated into a Game of "Ooh what's that", when I came across the following:
Note the very strange shoreline on this lake, with numerous straight line borders. The first time I saw this, I thought I was looking at some dams I didn't know about, but I quickly realized that such an interpretation made no sense.

 Instead, what I believe this image is showing is a mosaic from pictures acquired several years apart. One of those years was a wet year, while another must have been after a period of extended drought. As a result, the lake is ~90% full in some of the images, but almost empty in others. And the straight-line lakeshores are just the tile borders, which Google's new color autocorrect makes less obvious.

 I have no idea where WoGE is up to these days, but I left the co-ordinates off in case anyone wants to chase up the Reservoir.