# The speed of jet lag

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.

# What’s the time?

(This post was prompted by Samoa’s decision to jump forward a day by moving the international date line.)

“What’s the time?” seems like a simple question, but it’s not. There are many different ways of measuring time.

Universal Time is based on the rotation of the Earth, measured using observations by the International Earth Rotation and Reference Systems Service (IERS); it replaced Greenwich Mean Time (GMT) in 1928. The IERS uses a network of stations across the globe to perform Very Long Baseline Interferometry (VLBI) of 212 distant objects (mainly quasars) outside our Milky Way galaxy. During VLBI simultaneous readings from stations a long distance apart are compared and the differences between them used to calculate the distance to, and position of these extra-galactic objects. By combining the VLBI readings with lunar ranging and GPS satellite orbit data the principal form of Universal Time, UT1 is calculated.

Coordinated Universal Time (UTC) is the world’s time standard; if you want to know what the current time is, you want to know what UTC is. It is based on International Atomic Time (TAI) and is always kept to within ± 0.9 seconds of UT1. If it ever falls outside of this range a leap second is introduced by IERS to correct the difference. The difference between the two arises because TAI assumes that a day is a perfect 86400 seconds long (24×60×60) whereas in reality the Earth’s rotation is irregular, overall slowing by about 1.7 milliseconds every century.*

The last ten years’ of data is shown above; a sharp vertical line indicates the introduction of a leap second. The last leap second was at the end of 2008, taking the difference between UTC and UT1 from -0.591 to +0.409 seconds. Since 1999 there have been far fewer leap seconds (two in the ten year afterwards, eight in the ten years before). The Earth’s rotational speed increased in 1999 for some unknown reason, though there may be some link with earthquakes.

TAI is the average time from more than two hundred caesium atomic clocks at about seventy laboratories across the world; every month the data from these clocks is gathered by the International Bureau of Weights and Measures Bureau (BIPM) and published to participating organisations (e.g. May’s data). TAI and UTC were synchronised in 1958 but since TAI never includes leap seconds it is gradually moving away from universal time and is currently 34 seconds ahead of UTC.

Each GPS satellite contains four caesium atomic clocks that were synchronised with UTC in 1980. Leap second corrections are never applied to GPS clocks so GPS time is now 19 seconds behind TAI, putting it 15 seconds ahead of UTC. This offset is included in the GPS time signal and receivers usually apply the correction automatically.

* The pull of the Moon increases the length of the day by 2.3 ms/century but the increase in the height of land due to the melting of glaciers decreases it by 0.6 ms/cy.

# Why change the clocks?

Because the Earth is tilted on its axis, the length of the day (i.e. the time between sunrise and sunset) changes throughout the year. During summer in the northern hemisphere the North Pole is tilted towards the Sun and days are longer and warmer, and during winter the North Pole is tilted away from the Sun and the days are shorter and colder.

The change in the length of the day depends on latitude; the further north or south you go, the greater the variation.

For London, in 2011, the length of the day will change as shown below:

When British Summer Time is taken into account the pattern changes:

BST enables us to make better use of the available daylight by shifting hours of sunlight from the morning to the evening; it takes hours of daylight from the morning whilst most people are asleep and “moves” them to the evening when most people are awake. The term used in the US – “daylight saving time” – makes this more obvious.

Having more hours of daylight in the late evening reduces the use of electrical lighting. The environmental campaigners 10:10 (the same group that made that awful video) and others have been pushing for the permanent adoption of BST, with an extra increase of an hour during the summer, a system called Single/Double Summer Time (SDST).

The Royal Society for the Prevention of Accidents has suggested that moving to SDST would reduce accidents, benefit tourism and leisure and help prevent crime. Conservative MP Rebecca Harris has submitted a Private Member’s Bill that is currently before Parliament asking the Secretary of State to consider making this change.

# Decimalising time redux

If you’re arriving here via Ignite London, this is the post that sparked off my thoughts about decimalising time.

# Decimalising time

This is part of a work in progress…

To make teaching significant figures easier I’d like to decimalise time.

Basics

One 24-hour day would become 1 unit of time, six in the morning would be 0.25, midday would be 0.5 and six in the evening would be 0.75. Astronomers already do this with the concept of fractional days and the Julian calendar.

Accuracy

If you told someone to meet you at “0.5” (midday) then this could be any time between 0.45 (10:48) and 0.55 (13:12). If you asked to meet at “0.50” then this would be more specific, between 0.495 (11:52:48) and 0.505 (12:07:12). To be really specific (to within an “old minute”) you could specify “0.500” which would reduce the window to 0.4995 (11:59:16.8) and 0.5005 (12:00:43.2). The advantage of this is that any time during the day can now be specified to within any desired margin of error:
1 decimal point ± 2 hours 24 minutes
2 decimal points ± 14 minutes 24 seconds
3 decimal points ± 1 minute 26.4 seconds
4 decimal points ± 8.64 seconds

Calculations

Decimalising time would also make calculations involving time a great deal simpler: no more need for modular arithmetic, just simple plus and minus. There would be no more worrying about AM and PM and no more need for the 24-hour clock.

The accuracy implied by using two significant figures means that a percentage value would probably be accurate enough for most usages. Guest for a dinner party could be told “81 percent for 83 percent” which would be (approximately) equivalent to “seven-thirty for eight” (more accurately 19:26 for 19:55, though with the accuracy considerations above taken into account it could be any time between 19:19 and 20:02*).

Because the new unit of time would be a normal unit like any other, the standard (sub)multiple prefixes could be used: one centiunit would be about quarter of an hour and one milliunit would be about a minute and a half. For real accuracy microunits, equivalent to 0.0864s, could be used.

Clocks

The simplest change would be to replace the 12-segment clock with a 10-segment one. The two-hands-twice-around movement would be replaced with a one-hand-once-around movement.

I’d prefer a complete redesign: I favour a progress bar style arrangement.

Progress bar clocks could be set up to gradually reveal a picture throughout the day; alarms are marked with a simple line (the alarm below is set for 20:30).

Your entire day would be visible at a glance the clock below shows the average 9-5 workday: sleep from midnight to six, work from 9 to 5 and then sleep from ten at night onwards.

Other variations on the progress bar idea are possible:

* This was the point at which I realised I had been thinking about this far too much. [Back]