The cost of coins

Posted on 23rd January by Mr Reid

It used to be the case that coins used as currency had value because of the material from which they were made: a solid gold coin weighing one ounce had the same value as one ounce of gold. The intro­duc­tion of fiat cur­ren­cies, issued by central banks, that only have value because a gov­ern­ment decrees by law that they do, allowed gov­ern­ments to move away from this depend­ence on rare metals.

UK coins come in four “flavours”: the “copper” 1p and 2p coins, the “silver” 5p, 10p, 20p and 50p coins and the larger and heavier £1 and two-tone £2 coins. Before 1992 the “copper” 1p and 2p coins really did contain copper, being made from a bronze con­taining 97% copper, 2.5% zinc and 0.5% tin. With a mass of 3.56 and 7.12 grams respect­ively the pre-1992 coins con­tained 3.54 and 6.91 grams of copper; at the current bulk price and the current USD-GBP exchange rate this makes a 1p coin worth 1.66 pence and a 2p coin worth 3.23 pence (those links will take you to auto­mat­ic­ally cal­cu­lated values using current values for spot price and exchange rate).

If you were able to buy pre-1992 1p and 2p coins in bulk for their face value you could make a profit by melting them down and selling the res­ulting copper as scrap (though this is illegal under the 1971 Coinage Act). This increasing price of copper in the early lead to a change from bronze to copper-plated steel and this makes it very easy to dif­fer­en­tiate between the old and new 1p/2p coins: pre-1992 coins are not magnetic and post-1992 coins are.

The “silver” coins have pre­vi­ously been made from cupro-nickel, an alloy of copper and nickel in a 75:25 ratio. In terms of its raw metal, a 3.25 gram five pence coin, con­taining 2.44 grams of copper and 0.81 grams of nickel is cur­rently worth 3.08 pence (1.14p for the copper and 1.94p for the nickel). A 6½ gram ten pence coin is worth 6.16p, a five gram twenty pence coin is worth 4.74p and an eight gram fifty pence coin is worth 7.58p.

From January 2012 the “silver” coins will be made from nickel-plated steel (making them magnetic), a change driven probably by the rising cost of both copper and nickel. (In May 2007, when the price of nickel was at a peak, a five pence coin was worth more than six pence as scrap copper and nickel).

The high value of the £1 coin (current value), composed of 70% copper, 24.5% zinc, and 5.5% nickel and the £2 coin, with a cupro-nickel core sur­rounded by a ring of 76% copper, 20% zinc, and 4% nickel, makes them unlikely to ever approach a situ­ation in which they are worth more than their face value.

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Technetium-99m generators

Posted on 15th January by Mr Reid

Technetium-99m is a radio­active tracer that is used in twenty million medical dia­gnostic pro­ced­ures per year. At least 31 radio­phar­ma­ceut­icals based on Tc-99m are used for imaging and studying organs such as the brain, heart muscle, thyroid, lungs, liver, gall­bladder and kidneys, as well as the skeleton and blood and for the invest­ig­a­tion of tumours.

The ‘m’ in the name of technetium-99m indic­ates that it is meta­stable. Tc-99m is radio­active because one or more of the protons and neutrons in its nucleus is in an excited state. Tc-99m decays into Tc-99 with a half-life of six hours and this makes it par­tic­u­larly well suited to use in the body: after one day (four half-lives) only 6.3% of the initial Tc-99m remains. (It’s worth noting that the non-metastable technetium-99 is also radio­active, but with a half-life of 211000 years, it presents a very low risk.)

This short half-life also creates a problem: obtaining Tc-99m when required. Hos­pitals cannot run their own nuclear reactors and so they rely on tech­ne­tium gen­er­ators - machines that produce Tc-99m from the decay of its parent isotope molybdenum-99. Molybdenum-99 has a longer half-life (66 hours) and can there­fore be trans­ported to hos­pitals and still remain useful for up to a week.

Molybdenum-99 is produced in nuclear reactors by bom­barding a highly enriched uranium target with neutrons, causing it to fission, forming Mo-99 (and many other isotopes) as it does. The vast majority of Mo-99 is produced by five nuclear reactors around the world that are spe­cific­ally devoted to the pro­duc­tion of nuclear isotopes for medicine: NRU in Canada, BR2 in Belgium, SAFARI-1 in South Africa, HFR Petten in the Neth­er­lands and OSIRIS-1 in France.* Tem­porary shut­downs of NRU and HFR Petten in the 2000s led to a long-term shortage of Mo-99.

Once Mo-99 has been produced it is placed into a tech­ne­tium gen­er­ator and these gen­er­ators are trans­ported to hos­pitals. The tech­ne­tium gen­er­ators make use of the fact that molyb­denum likes to bond with alu­minium oxide (alumina) but tech­ne­tium does not. The gen­er­ators are “milked” by drawing a saline solution across an inner molybdenum/alumina capsule; during this elution process any tech­ne­tium that has formed will be drawn away with the saline and can then be used in tests.

A cutaway model of a tech­ne­tium generator.

The molybdenum/alumina sample is placed in the centre of the device, sur­rounded by shielding (painted red in this case). Saline is injected through one of the tubes at the top of the device and flows into a shielded con­tainer through the other tube, after having passed over the sample and “picked up” radio­active technetium-99m.

* Mo-99 is also produced in much smaller amounts from low-enriched uranium at the OPAL reactor in Aus­tralia and at other sites.

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Plug wiring colour scheme

Posted on 6th January by Mr Reid

UK plugs use brown insu­la­tion for the live wire, blue insu­la­tion for the neutral wire and green with yellow stripes insu­la­tion for the earth wire.

But why this par­tic­ular com­bin­a­tion of colours? The answer is decept­ively simple: there is no type of colour blind­ness that will result in these wires becoming confused.

Above: how a UK plug looks to someone who is red-green colourblind.

Above: how a UK plug looks to someone who is blue-yellow colourblind.

One of the lesser-known safety features of a UK plug is the extra distance that the neutral wire has to travel when compared to the live wire. If someone pulls on the mains cable the live wire will dis­con­nect first, making the plug safer.

Under the IEC 60446 standard only black, brown, red, orange, yellow, green, blue, violet, grey, white, pink and tur­quoise are accept­able colours for labelling wires. Coun­tries must choose an appro­priate selec­tion of colours that elim­in­ates the pos­sib­ility of confusion.

IEC 60446 colours. From top to bottom: normal vision, deu­ter­an­opic vision, trit­an­opic vision.

Continue reading →

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Night vision

Posted on 2nd January by Mr Reid

The vision of human beings is well-adapted to daylight; the human eye has evolved to see in the range of wavelengths that are brightest in the spectrum of light that the Sun emits.

The intensity of the light the Sun emits by wavelength, with the visible region highlighted.

But humans don’t see par­tic­u­larly well in the dark. The cones that are respons­ible for colour vision don’t function well at low light intens­ities, which is why night vision is almost entirely mono­chro­matic — in the dark humans see in black and white.

When moving from bright light into darkness the first thing that happens to the eye is that the pupil dilates to allow in more light. The iris dilator muscle causes the pupil to increase in diameter by a factor of five (from 2 mm to 10 mm), increasing the amount of light entering the eye by about twenty-five (52) times, but this isn’t enough for true night vision.

The chemical rhodopsin that is present in the rod (brightness-sensing) cells is respons­ible for night vision. When exposed to light, rhodopsin imme­di­ately (within 200 femto­seconds*) splits to form a chemical called pho­torhodopsin, and then soon after­wards (within a few pico­seconds) another chemical called bathorhodopsin.

The split­ting of rhodopsin is accom­panied by the form­a­tion of other chem­icals called retinals, and during this split­ting process a signal is sent down the optic nerve to the brain, regis­tering the detec­tion of light. (Retinal is created from vitamin A, and so people with a diet lacking in vitamin A fre­quently suffer from night blind­ness.)

A molecule of rhodopsin (rainbow-coloured) embedded in a lipid bilayer.
A (black) retinal molecule is bound within the rhodopsin.

Over time, and at a con­sistent rate, the opsins and retinals recom­bine to form rhodopsin. If the eye is exposed to bright light all the rhodopsin splits at once (a process called pho­tobleaching). When sub­sequently exposed to darkness there is there­fore no rhodopsin to split and the eye cannot detect light properly. The person in question must wait for the rhodopsin to nat­ur­ally recom­bine over time before proper vision can return, a process that takes between ten and thirty minutes to occur. When fully accus­tomed to the dark, the eye is between ten thousand and a million times more sens­itive to light than previously.

The rhodopsin in human eyes is less-sensitive to red light than to other colours and there­fore night vision is not par­tic­u­larly effected by red light. This is why red light is used in dark­rooms and in aircraft before night-time para­chute jumps.

Human eyes, unlike the eyes of many animals, do not have the tapetum lucidum which gives those animals superior night vision. The tapetum lucidum sits behind the retina and acts like a mirror, reflecting back photons of light that were not ini­tially absorbed by the retina, giving the retina a “second chance” to detect the light. This improves their night vision and is what gives rise to the phe­nomenon of “eyeshine” often seen when taking pho­to­graphs of animals.

The tapetum lucidum seen in a dis­sected calf’s eye.

“Eyeshine” is very obvious in this pho­to­graph of a raccoon.

* Inter­est­ingly, the split­ting of rhodopsin into pho­torhodopsin and retinal seems to be the fastest chemical reaction that has been directly studied.

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The most radioactive parts of the UK

Posted on 28th December by Mr Reid

The average radio­active back­ground dose in the UK is 2.7 mil­lis­iev­erts. Of this 2.7 mSv, 1.35 mSv comes from radio­active radon gas leaking out of the ground.

This radio­active radon (Rn-222) is produced by the decay of uranium-238, after a series of inter­me­diate non-gas stages that cannot escape from rocks.

Because radon has such a large effect on the annual radi­ation dose that someone receives, it is closely mon­itored. In the UK, this mon­it­oring is done by the Health Pro­tec­tion Agency (HPA). One of the things that the HPA does it produce radon maps, showing which areas of the UK have the highest presence of radon.

The map is graded by the per­centage of homes in that area which have a level of radon beyond the action level of 200 becquerels per cubic metre (200 radon decays per second per cubic metre).

There are a number of important radon hotspots in the UK. The most notice­able one is Cornwall in the south-west where the average UK back­ground dose is 7.8 mSv, nearly three times the national average. This is due to the presence of igneous granite, which nat­ur­ally contains more uranium (10 – 20 parts per million) than other rocks.

Radio­active areas tend to be hilly, where igneous rocks have been forced to the surface or left behind by the erosion of softer sed­i­mentary rocks (the Chiltern Hills are par­tic­u­larly radio­active, for example). The York­shire Dales sit on top of an under­ground deposit of pink granite called the Wens­ley­dale Granite that lies under­neath the Askrigg Block, and the Peak District features many granite outcroppings.

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Biosphere lungs

Posted on 27th December by Mr Reid

Some people refer to the rain­forests as “Earth’s lungs”. In reality this is quite far from the truth, as rain­forests actually con­tribute little (net) oxygen to Earth’s atmo­sphere; 70% of oxygen pro­duc­tion is done by water-bourne green algae and the cyanobac­teria present in every habitat on Earth.

Bio­sphere 2, a sealed eco­lo­gical system built in Arizona to study the inter­ac­tion between dif­ferent forms of life and as a test of the pos­sib­ility of using closed systems in space col­on­isa­tion, also had lungs.

Bio­sphere 2’s oxygen came from the facility’s six biomes: a 1900 square meter rain­forest, an 850 square meter “ocean”, a 450 square meter mangrove wetland, a 1300 square meter savannah grass­land, a 1400 square meter fog desert and a 2500 square meter agri­cul­tural system.

During the day the heat of the Arizona sun would cause the air inside the facility to expand. In order to avoid the large pressure dif­fer­ence that this would create (5000 Pa, or 5% of standard atmo­spheric pressure), Bio­sphere 2’s creators included two giant hemi­spher­ical “lungs”.

As the air inside the facility expanded it would flow through under­ground tunnels into the lungs. Each lung con­tained a large weight hanging from a rubber sheet; as the air expanded during the day the increased pressure would raise the weight into the air. In the evening, as the air cooled, the weight would pull the rubber sheet back down and push air back into the facility, thereby equal­ising any pressure dif­fer­ence as it appeared.

Source: lumierefl

William Dempster, “Bio­sphere 2 engin­eering design”, Eco­lo­gical Engin­eering 13 (1999): 31 – 42 doi:10.1016/S0925-8574(98)00090 – 1 (.PDF).

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Anscombe’s quartet

Posted on 21st December by Mr Reid

Anscombe’s quartet is four sets of data that are used to demon­strate the import­ance of graphing data.

Set 1 Set 2 Set 3 Set 4
x y x y x y x y
10 8.04 10 9.14 10 7.46 8 6.58
8 6.95 8 8.14 8 6.77 8 5.76
13 7.58 13 8.74 13 12.7 8 7.71
9 8.81 8 8.87 9 7.11 8 8.84
11 8.33 11 9.26 11 7.81 8 8.74
14 9.96 14 8.10 14 8.84 8 7.04
6 7.24 6 6.13 6 6.08 8 5.25
4 4.26 4 3.10 4 5.39 19 12.5
12 10.8 12 9.13 12 8.15 8 5.56
7 4.82 7 7.26 7 6.42 8 7.91
5 5.68 5 4.74 5 5.73 8 6.89
Mean 9 7.50 9 7.50 9 7.50 9 7.50
Variance 11 4.13 11 4.13 11 4.12 11 4.12
PMCC 0.82 0.82 0.82 0.82

Each set of data has near-identical stat­ist­ical prop­er­ties: the same average and variance (for both x and y), and the same product moment cor­rel­a­tion coef­fi­cient and linear regres­sion line. When plotted, however, they look entirely dif­ferent. (The scale of the last graph is dif­ferent from the others.)

You can download Anscombe’s quartet as an Excel spread­sheet.

Francis Anscombe, “Graphs in Stat­ist­ical Analysis”, American Stat­ist­i­cian 27(1) (1973): 17‑21. http://www.jstor.org/stable/2682899 (.PDF).

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Haversine formula

Posted on 20th December by Mr Reid

The hav­er­sine formula is used to cal­cu­late the distance between two points on the Earth’s surface spe­cified in lon­gitude and latitude.

d is the distance between two points with lon­gitude and latitude (ψ,φ) and r is the radius of the Earth.

As an example I have cal­cu­lated the distance between Fermilab in Illinois (41° 49′ 55″ N, 88° 15′ 26″ W) and CERN’s Meyrin campus in Switzer­land (46° 14′ 3″ N, 6° 3′ 10″ E). There’s a little too much maths for this site to handle so I have included a .PDF file of the working below.

The value cal­cu­lated is 7084 km, which isn’t quite correct. This is because the formula assumes that the Earth is a perfect sphere when in fact it is an oblate spheroid. To com­pensate for this Vincenty’s Formulae must be used; these are much more com­plic­ated but give a more accurate value of 7103 km.

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Patterns in birthdays

Posted on 17th December by Mr Reid

If births were evenly dis­trib­uted throughout the year (i.e. a 1 in 365 chance of being born on any given day) then the graph of number of births against birth month would look like the one below:

You’re least likely to be born in February, because it only has 28 days, and then slightly more likely to be born in the 31-day months of January, March, May, July, August, October and December than in the 30-day months of April, June, September and November.

I took the data from nearly a thousand pupils and looked at how their dates of birth compared with the expected values. (Included with the data are error bars of one standard deviation.)

The results for April, September and December (par­tic­u­larly December) show birth rates above what would be expected if births are random, and the results for July and August show depressed birth rates.

Con­sid­ering the months where births are more likely than they should be and working back­wards we find the most likely “sex months” to be March, July and December. These seem fairly sensible as all of these months coincide with major holiday periods: Easter, the long Summer Holiday and Christmas/New Year. People are more likely to be “cel­eb­rating” and to have more free time during these periods, and March and December have long, cold and dark nights when people are more likely to stay indoors in the evening than go out.

The “sex months” for the lowest birth rates are more puzzling: October and November. I suspect that it has to do with Seasonal Affective Disorder (SAD) and that the gen­er­al­ised depres­sion that comes with SAD includes reduced sex drive; this is combated come December by the general presence of good cheer and plenty of alcohol to lower inhib­i­tions. It is also possible that parents are delib­er­ately choosing when to conceive in order to avoid their child being the youngest in the school year, some­thing that has been shown* to have a negative effect.

Update: Thanks to @S3ym5n I’ve now included national data for 2010.

In the national data it is September and October that show birth rates above what is expected, making December and January the most popular sex months. April appears to be the only month with a sig­ni­fic­antly lower birth rate, making July, when people are out and about in the nice weather rather than stuck indoors, the least popular sex month.

Continue reading →

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Curiosity’s nuclear battery

Posted on 14th December by Mr Reid

The Curi­osity rover that is the main part of the Mars Science Labor­atory mission is very dif­ferent from its pre­de­cessors Sojourner and the twin rovers Spirit & Oppor­tunity.

L-R: Spirit/Oppor­tunity, Sojourner and Curi­osity.

L-R: The wheels of Sojourner, Spirit/Oppor­tunity and Curi­osity.

Curi­osity is nearly twice as long as Spirit/Oppor­tunity and has more than five times the mass; at 2.1 metres in height it is taller than most of the people that built it.

For me, the most inter­esting dif­fer­ence between Curi­osity and the other Mars rovers is its power source. Both Sojourner and Spirit/Oppor­tunity were powered by solar cells but Curi­osity is powered by a radioiso­tope ther­mo­elec­tric gen­er­ator (RTG), in par­tic­ular the Multi-Mission Radioiso­tope Ther­mo­elec­tric Gen­er­ator (MMRTG) built by Pratt & Whitney’s Rock­et­dyne division.

Curi­osity’s RTG is the large unit attached to the rover’s rear.

The main problem with using solar cells for power is that the cells only work during daylight hours and don’t function well at high lat­it­udes where there is less sunlight; Spirit/Oppor­tunity’s cells only worked at full strength for about four hours per day, pro­du­cing about 900 watt hours (about 3.2 mega­joules) per day at best. Mars is covered in fine dust and dust covering solar panels was a problem for the Spirit and Oppor­tunity rovers, though this dust was occa­sion­ally blown away by high winds.

Spirit’s solar panels before and after a “cleaning event”.

RTGs work via the Seebeck effect, where a dif­fer­ence in tem­per­ature between between the two junc­tions of a ther­mo­couple cause an electric current to be produced. The heat source in an RTG is the decay of a radio­active isotope; in the case of most RTGs this isotope is plutonium-238 in the form of plutonium dioxide. Pu-238 is a nearly pure alpha emitter and there­fore requires only minimal shielding.

A pellet of 238PuO2 glows red hot from internal radio­active decay.

The MMRTG uses 32 marshmallow-sized plutonium pellets and will ini­tially produce about 125 watts of elec­trical power (from 2000 watts of thermal power), but this will drop off over time as the plutonium decays. The MMRTG will con­sist­ently produce about 2500 watt hours of elec­tri­city per day compared with Spirit/Oppor­tunity’s average of 600 Wh and this will enable Curi­osity to operate in all seasons and at all times of day.

Curiosity’s MMRTG before installation.

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You’ve already experienced the earliest Easter you’ll ever know

Posted on 12th December by Mr Reid

You may have noticed that the date of Easter Sunday changes every year:

The date of Easter Sunday is cal­cu­lated using a calendar that is based both on the Sun and the Moon* and takes place “on the first Sunday after the Paschal Full Moon”. Because the Gregorian calendar is based on the Sun only, the date of Easter changes from year to year.

The Paschal Full Moon is based not on an actual astro­nom­ical event but on his­tor­ical tables estab­lished by a bunch of reli­gious guys in 325AD, and its date can be up to ± 2 days from the actual astro­nom­ical Full Moon. The Paschal Full Moon is selected as the first of the Full Moons recorded in these tables to follow the March Equinox (also known as the vernal equinox as it is the day on which the night and day are the same length when heading into Spring in the northern hemi­sphere and coming from the Latin ver for spring).

When a line con­necting adjacent dates is drawn a pattern becomes obvious, espe­cially when the scale is compressed.

The earliest Easter can possibly fall is March 22nd, though this is very rare, occur­ring most recently in 1818 and next in 2285. The next earliest date is March 23rd, as it was in 2008 and this will not happen again until 2160, by which time you will be dead.

The latest date Easter can occur is April 25th, which last occurred in 1943 and will next occur in 2038. The cycle for Easter dates repeats every 5 700 000 years exactly, and the most common date within that cycle is April 19th, occur­ring in 3.9% of cases. Easter moving around to the extent explained above is a real pain and in my opinion we should all just agree that from now on Easter Sunday is always the nearest Sunday to April 19th.

* Luni­solar cal­en­dars like this are used by many Jews, Buddhists, and some Hindus as well as those in Burma, China, Korea, Mongolia, Tibet and Vietnam.

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Logarithmic scales

Posted on 6th December by Mr Reid

Some of the quant­ities measured in physics cover a very large range of values and this can make dis­playing meas­ure­ments of their value dif­fi­cult or confusing.

pH, tra­di­tion­ally thought of as a meas­ure­ment of acidity, but actually a meas­ure­ment of the con­cen­tra­tion of hydrogen ions,* is one such quantity. Stomach acid has a con­cen­tra­tion of hydrogen ions of 0.1 per mole; bleach has a con­cen­tra­tion of hydrogen ions of 0.0000000000001 per mole.

In order to have a sensible scale by which to judge acidity a log­ar­ithmic scale is used: pH is the negative of the log­ar­ithm of the con­cen­tra­tion of hydrogen ions, so for stomach acid pH = −log(0.1) = 1.0 and for bleach pH = −log(0.0000000000001) = 13.

As can be seen from the graph above, it becomes very dif­fi­cult to tell the dif­fer­ence between H+ con­cen­tra­tion beyond pH 2 or 3. But on a log­ar­ithmic scale the dif­fer­ence is clearly visible:

There has been some fuss on various blogs about a chart from the Min­nesota Dental Asso­ci­ation (58kB, .PDF) listing the acidity of various sweets. One sweet, WarHeads Sour Spray is listed as having a pH of 1.6, which when compared with battery acid at pH 1.0 sounds very alarming. But when the log­ar­ithmic scale is taken into account an increase of 0.6 on the pH scale is equi­valent to a four-fold decrease in acidity — Sour Spray is only one-quarter as acidic as battery acid (that’s still pretty acidic, by the way, and not terribly good for your teeth).

The moment mag­nitude scale used to measure the strength of earth­quakes is another log­ar­ithmic scale. Earth­quakes vary in size (i.e. in the energy they release) from the giant MW 9.5 earth­quake in Chile in 1960 to tiny tremors caused by large vehicles going past and so a log­ar­ithmic scale is required. Because of the way that the moment mag­nitude scale is cal­cu­lated an increase in moment mag­nitude of 1.0 indic­ates a 31.6-fold (101.5) increase in the amount of energy released (an increase in moment mag­nitude of two is equi­valent to a 1000-fold (103) increase).

* For the sake of sim­pli­city I’m ignoring the effect of the activity factor, the tendency of hydrogen ions to interact, on pH.

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The Milky Way is shaped like a CD

Posted on 1st December by Mr Reid

The Earth orbits just one of the 200 – 400 billion stars that make up the Milky Way. This star, the Sun, orbits at a distance of about 27000 light years from the Galactic Centre, trav­el­ling at 220 km/s (one mile every seven thou­sandths of a second).

The Milky Way is about 100000 light years across, but only about 1000 light years in height, making it about one hundred times wider than it is tall. To scale, viewed from side on, it would look like the line below:

With a thick­ness of 1.2 mil­li­metres and a diameter of 120 mil­li­metres a standard CD or DVD has exactly the same thickness:width ratio as the Milky Way; you could cor­rectly describe our galaxy as “CD-shaped”.

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The speed of jet lag

Posted on 28th November by Mr Reid

Jet lag (ICD-10: G47.2) occurs when the body’s internal clock (its cir­ca­dian rhythm) gets out of sync with the time of day.

Example: London to Los Angeles

Leaving London at 1200 you will arrive in Los Angeles ten hours later and your body will feel like the time is 2200. The actual time will be 1400 and so your body expects it to be late night, but it’s actually the middle of the day: an offset of eight hours. Trav­el­ling back, leaving Los Angeles at 1200 you will arrive in London ten hours later and again feel like the time is 2200, but it will actually be 0600 the next day; your body expects late evening but gets early morning: an offset of sixteen hours. The dif­fer­ence in these offsets is what gives rise to the fact that trav­el­ling west to east causes worse jet lag than trav­el­ling in the opposite direction.

Jet lag only occurs when travel causes a dif­fer­ence between the internal and real clocks. If you take anything more than one hour to travel a time dif­fer­ence of one hour then jet lag does not occur. Also, flying north to south doesn’t cross any time zones and there­fore jet lag does not occur; flying from Cape Town to Stock­holm, for example, is safe for your body clock.

The Earth rotates once per day and there­fore contains twenty-four time zones, spaced evenly apart. Turning through 360° in twenty-four hours is equi­valent to 15° per hour. At the equator, fifteen degrees of lon­gitude is equi­valent to 1670 kilo­metres so an aero­plane flying along the equator would have to travel at a speed of at least 1670 kilo­metres per hour (over 1000 mph) for jet lag to occur. At a latitude of 45° (north or south) this 15° is only 1180 kilo­metres, reducing the speed of jet lag to 734 mph.

Both of the situ­ations above assume that plane fly directly along lines of latitude, but this never happens. In reality planes fly “great circle” paths (see the previous post about geodesics) and trav­el­ling along great circle paths, espe­cially those that fly close to or over the poles where time zones are “thinner”, lowers the speed of jet lag to below the 500 – 600 mph speed of an aeroplane.

The nar­rowing of time zones at northern lat­it­udes is obvious in this map of Western Europe.

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Types of Desert

Posted on 24th November by Mr Reid

A desert is defined as an area that receives a very small amount of pre­cip­it­a­tion: these areas come in three main forms.

The most recog­nis­able type of desert is the sub­trop­ical desert, typified by the Saharan and Arabian deserts. They are the hottest deserts and any rain that does fall often evap­or­ates before it hits the ground.

The Sahara Desert in North Africa.

The Earth has two polar deserts, the Arctic and the Ant­arctic. At 13.9 million square kilo­metres the Ant­arctic Desert is by far Earth’s largest, more than one and a half times the size of the next largest desert, the Sahara.

The Ant­arctic Desert at the South Pole

Cold winter deserts, like the Gobi Desert in China and Mongolia, are often created by the rain shadow effect in which a tall mountain range causes warm moist air to rise and cool. As the air cools water vapour con­denses out and falls as rain or snow, leaving the air dry and creating a desert on the lee (upwind) side of the mountain. For example, the Gobi Desert is created by the Himalaya Moun­tains; the Patago­nian Desert in South America by the Andes; and the Great Basin Desert in the western United States by the Sierra Nevada.

The Gobi Desert, north-east of the Himalaya Mountains.

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UK electricity import and export

Posted on 20th November by Mr Reid

The UK doesn’t have enough electricity.

The amount of elec­tri­city that the UK produces (from various sources) is not enough to meet demand, and the UK relies heavily* on imports from France and the Neth­er­lands in order to meet its needs. This energy gap is due to the closure of coal-fired power stations that cannot meet emission stand­ards and the shutdown of aging nuclear power stations.

The import and export of elec­tricty uses sub­marine high voltage direct current (HVDC) cables. HVDC cables waste less elec­tri­city than AC cables (about 3% per 1000km) and are simpler to con­struct and operate. A 73 km cable connects Bonningues-lès-Calais in France to Sellindge in Kent; a 55 km cable connects Auchen­crosh in Scotland and Bal­ly­cronan More in Ireland; and a 260 km cable connects Maas­vlakte in the Neth­er­lands to Grain in Kent.

The graph below shows elec­tri­city import and export (in GWh) for the eight months since February†, when the Britned Inter­con­nector began oper­ating. When the value is positive (when the line is above the origin) the UK is importing elec­tri­city and when it is negative elec­tri­city is being exported.

One of the most inter­esting features of the graph is the change in the import/export to Ireland via the Moyle Inter­con­nector. On 26th June at 0417 one of the 250 megawatt cables failed, halving the cable’s capacity, and at 1409 on 24th August the cable failed entirely and has not trans­ferred any elec­tri­city since.

The cause of the failure is unknown and the MV North Sea Giant, the world’s longest offshore con­struc­tion vessel, is cur­rently moored in the Irish Sea invest­ig­ating the fault. The cable has been dug out of the seabed 200m below the surface, cut in half, and both ends raised to the surface so the cause of the fault can be invest­ig­ated. The fault is expected to take up to six months to fix and were a similar fate to befall the Cross-Channel or Britned inter­con­nector the UK would have a very serious energy problem.

If it is to close the growing energy gap the UK must accel­erate the pace of con­struc­tion of energy infra­struc­ture, in par­tic­ular the con­struc­tion of safe, zero-carbon nuclear power stations.

* The UK is the world’s sixth largest importer of elec­tri­city despite being eleventh in terms of elec­tri­city pro­duc­tion and twenty-second in terms of population.

† The graph shows a seven day moving average of import/export values. For half-hourly data you can download the full dataset as an Excel spread­sheet.

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The Moses Bridge

Posted on 14th November by Mr Reid

The Moses Bridge, designed by Ro & Ad Archi­tects in the Neth­er­lands is my new favourite water crossing (taking over from the Mag­de­burg Water Bridge). The bridge allows visitors to cross the West Bra­bantse Water­line to reach Fort de Roovere.

 

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Why does metal feel cold?

Posted on 8th November by Mr Reid

One adjective commonly used to describe metals, along with the adject­ives like “shiny” and “silvery”, is “cold”.

But this doesn’t makes any sense when you take the Zeroth Law of Ther­mo­dy­namics into account. Over a long enough period, everything in the same location will tend* to the same tem­per­ature, so any metal must be at the same tem­per­ature as its surroundings.

So why does metal feel cold?

Metals feel cold because they are very good con­ductors. Both the metal blade and wooden handle of a shovel left out in the Sun will be at the same tem­per­ature but the blade will feel colder because the metal is a good con­ductor: it “sucks” the heat out of your fingers and this heat leaving your fingers is what makes them feel cold.


Fifteen minute timelapse of melting ice cubes.

In the video above identical ice cubes placed on a wooden board and a metal heatsink removed from a broken laptop computer melt at vastly dif­ferent rates. The wood is a poor con­ductor and so the ice cube takes a long time to melt; the opposite is true for the metal heatsink.

* I’m using “tend” in the physics sense of “to approach” rather than the general public sense of “to occur fre­quently” or “to look after”.

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Star traveller etymology

Posted on 2nd November by Mr Reid

The term astro­naut comes from the two Greek words: ástron (star) and nautes (trav­eller), making an astro­naut a “star trav­eller”. In Russia astro­nauts have always been known as cos­mo­nauts, an angli­cised version of the Russian word kos­monavt (ori­gin­ally from the Greek kosmos meaning “universe”) and the dif­fer­ence between the two terms used seems to have encour­aged other nations.

Offi­cially the Chinese use “astro­naut” when writing in English and “cos­mo­naut” when writing in Russian but the term taiko­naut (from the Chinese taikong for “space”) has often been used by non-Chinese media.  The French have used spa­tio­naut, from the Latin word for space spatium and some have sug­gested that the Indian space program should use anthanaut from the Hindi anthariksh, also meaning “space”.

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Looking at constellations from a different angle

Posted on 30th October by Mr Reid

You are probably familiar with the con­stel­la­tion of Orion (The Hunter), in par­tic­ular with the asterism that makes up Orion’s Belt.

Because of the way the right ascen­sion data is plotted the images shown here are how they would appear to a distant observer looking at Orion towards Earth.

Because stars are so far away we tend to think of them as being painted onto a surface at a fixed distance — “like a huge picture painted on the sphere of the sky”. But if you look at the stars in three dimen­sions then Orion looks very different.

From above it’s dif­fi­cult to recog­nise Orion’s shape as the lines con­necting the two right­most stars (Betel­geuse and Saiph) to the right­most star of Orion’s belt (Alnitak) overlap:

From the side the shape is more obvious. Alnilam, the middle star of Orion’s belt is by far the furthest star, more than 1300 light years away from Earth:

This post was inspired by an arXiv paper* by Dr Daniel Brown from the School of Science and Tech­no­logy at Not­tingham Trent Uni­ver­sity. You can download the data I used as an Excel spread­sheet (.XLS, 29 kB).

* Daniel Brown (2011) “The Orion con­stel­la­tion becomes install­a­tion: An innov­ative three dimen­sional teaching and learning envir­on­ment”, arXiv:1110.3469v1 [physics.ed-ph].

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