Converting arc into time
Earth completes one rotation in 24 hours. Longitude can therefore be converted directly into a time difference.
The conversion chain
| Arc | Time | Reason |
|---|---|---|
| 360 degrees | 24 hours | One mean solar rotation |
| 15 degrees | 1 hour | 360 divided by 24 |
| 1 degree | 4 minutes | 60 minutes divided by 15 |
| 15 minutes of arc | 1 minute of time | One quarter of a degree |
| 15 seconds of arc | 1 second of time | The same ratio at the next unit |
Direct calculation
Divide an angular arc in degrees by 15 to obtain decimal hours. Convert the decimal part into minutes by multiplying by 60. If the arc includes minutes, either convert them separately at 15 minutes of arc per minute of time or first turn the whole angle into decimal degrees.
Worked examples
For 137 degrees 36 minutes, 137 degrees gives 9 hours 08 minutes, and 36 minutes of arc gives 2 minutes 24 seconds. The total is 9 hours 10 minutes 24 seconds, or 9 hours 10 minutes to the nearest minute. For 127 degrees, 127 divided by 15 is 8.4667 hours. The decimal 0.4667 multiplied by 60 gives 28 minutes, so the result is 8 hours 28 minutes.
For 96 degrees 17 minutes, 17 divided by 60 gives 0.283 degree. Then 96.283 divided by 15 gives 6.4189 hours. The decimal part multiplied by 60 gives about 25 minutes, so the result is 6 hours 25 minutes.
Local Mean Time and UTC
Local Mean Time follows the mean Sun at one meridian. UTC supplies the single world datum used by aviation.
Local Mean Time
When the mean Sun crosses a meridian, every place on that meridian has 1200 LMT. When it crosses the opposite meridian, the local time is 0000 at the start of the new day, equivalent to 2400 at the end of the old day. Latitude is irrelevant to a basic LMT calculation.
Coordinated Universal Time
UTC changes at a constant rate and is regulated using atomic time. Small corrections keep it aligned with Earth's rotation. For practical navigation calculations, UTC is treated as equal to GMT, which is Local Mean Time at the Greenwich meridian. UTC is the common time datum everywhere.
East and west longitude
At an easterly longitude, LMT is later than UTC. At a westerly longitude, LMT is earlier. Oxford's mnemonic is longitude east, UTC least; longitude west, UTC best. Algebraically, add east longitude converted to time to UTC, or subtract west longitude converted to time.
| Known value | Longitude | Operation |
|---|---|---|
| UTC, find LMT | East | Add arc time |
| UTC, find LMT | West | Subtract arc time |
| LMT, find UTC | East | Subtract arc time |
| LMT, find UTC | West | Add arc time |
Worked LMT and UTC problems
A reliable layout keeps the longitude correction, clock time and date on separate lines. Work through UTC when comparing two places.
From LMT to UTC
If Cairo at 030 degrees east has 0900 LMT, the longitude equals 2 hours. East means UTC is less advanced, so 0900 minus 0200 gives 0700 UTC. If Madrid at 004 degrees west has 0400 LMT, 4 degrees equals 16 minutes. West means UTC is more advanced, so 0400 plus 0016 gives 0416 UTC.
From UTC to LMT
If UTC is 1345, Berlin at 013 degrees east is 52 minutes ahead, giving 1437 LMT. If UTC is 2115, San Francisco at 122 degrees west is 8 hours 08 minutes behind, giving 1307 LMT.
Two places through UTC
At A, 137 degrees 50 minutes west, it is 1812 LMT on 18 August. The longitude correction is 9 hours 11 minutes, added to LMT because A is west. This gives 0323 UTC on 19 August. At B, 121 degrees 12 minutes east, add 8 hours 05 minutes to UTC, giving 1128 LMT on 19 August.
| Step | Time and date | Reason |
|---|---|---|
| LMT at A | 1812, 18 August | Given at 137 degrees 50 minutes west |
| Add 9 hours 11 minutes | 0323 UTC, 19 August | West longitude, UTC is ahead |
| Add 8 hours 05 minutes | 1128 LMT, 19 August | B is 121 degrees 12 minutes east |
Theoretical Zone Time
Zone Time replaces continuously changing LMT with bands that keep one clock value across a useful area.
Zone geometry
The theoretical system uses 15 degree bands because the Sun appears to move 15 degrees in one hour. Zone Z is centred on Greenwich and extends from 7.5 degrees west to 7.5 degrees east. Each following full zone extends 7.5 degrees either side of its central meridian. The conventional system contains 25 zone designators, including Z and the two semi zones beside the 180 degree meridian.
Zone number convention
Divide longitude by 15 and round to the nearest whole number, with 0.5 rounded upward. Under Oxford's algebraic zone number convention, east longitude gives a negative zone number and west longitude gives a positive number. Latitude does not enter the calculation.
At 137 degrees east, 137 divided by 15 is 9.13, so the zone number is minus 9. At 097 degrees 30 minutes west, 97.5 divided by 15 is 6.5, rounded upward to zone number plus 7.
Converting Zone Time
The governing equation is UTC = Zone Time + Zone Number. To find Zone Time from UTC, subtract the Zone Number from UTC. An east zone has a negative number, so subtracting it makes local Zone Time later than UTC.
Standard Time and Indian Standard Time
Civil authorities select Standard Time for practical use. Its boundaries need not follow the theoretical Zone Time meridians.
Why Standard Time is practical
Local Mean Time changes with every longitude, which is unsuitable for a countrywide clock. A theoretical zone boundary may cut through a city or administrative region. Standard Time therefore follows legal and administrative decisions. It normally keeps noon near the middle of the daylight period, but it may use a whole hour, half hour or another notified offset from UTC.
Standard Time, Zone Time and LMT
| System | Basis | Boundary |
|---|---|---|
| LMT | Mean Sun at the exact meridian | Changes continuously with longitude |
| ZT | Theoretical 15 degree bands | Usually 7.5 degrees from a central meridian |
| ST | National or regional legal choice | Political and administrative |
| UTC | Worldwide atomic time datum | Same instant worldwide |
Daylight saving
Some states advance clocks seasonally. Never assume that daylight saving is active from longitude or season alone. Use current official information and apply any stated correction after identifying the underlying Standard Time.
The 180 degree meridian and the Date Line
At 180 degrees east and west the clock time agrees, but the calendar dates differ by one day. The date line resolves that difference.
The theoretical rule
LMT and theoretical Zone Time change date at the 180 degree meridian. Travelling westward across it, add one day. Travelling eastward across it, subtract one day. The clock reading stays continuous while the calendar is corrected.
The International Date Line
The practical International Date Line generally follows the 180 degree meridian but bends east or west to keep island groups and political territories on the same civil date. Standard Time changes at the legal line, not necessarily at the exact geographic meridian.
Why the line bends
Oxford uses Chatham Island and the Tonga group to show the administrative problem. Although their geographic longitudes place them on the western side of 180 degrees, their legal time arrangements keep them on the same civil day as nearby communities to the west of the line. The International Date Line is therefore displaced around the territories.
Worked date line flights
Work through UTC, add the flight time, then convert to the arrival longitude or Standard Time. This prevents the date correction being applied twice.
Westbound from 164 west to 173 east
An aircraft departs longitude 164 degrees west at 2200 LMT on 3 May and flies westbound for 6 hours. Convert departure LMT to UTC by adding 10 hours 56 minutes, giving 0856 UTC on 4 May. Add 6 hours to reach 1456 UTC on 4 May. Longitude 173 degrees east is 11 hours 32 minutes ahead of UTC, giving 0228 LMT on 5 May.
Eastbound from 175 east to 150 west
An aircraft departs 175 degrees east at 0100 LMT on 18 November and flies eastbound for 4 hours. Subtract 11 hours 40 minutes to get 1320 UTC on 17 November. Add 4 hours to get 1720 UTC. At 150 degrees west, subtract 10 hours to obtain 0720 LMT on 17 November.
| Flight | Departure in UTC | Arrival in UTC | Arrival LMT |
|---|---|---|---|
| 164 west to 173 east, 6 h | 0856, 4 May | 1456, 4 May | 0228, 5 May |
| 175 east to 150 west, 4 h | 1320, 17 Nov | 1720, 17 Nov | 0720, 17 Nov |
A reliable method for every time problem
The safest habit is to identify each time system, pass through UTC, and carry the date beside every clock value.
The standard sequence
| Step | Action | Check |
|---|---|---|
| 1 | Name the given time system and date | LMT, UTC, ZT, ST or daylight time |
| 2 | Convert any longitude into arc time | 15 degrees per hour |
| 3 | Convert the departure value to UTC | East LMT subtracts, west LMT adds |
| 4 | Add or subtract elapsed time | Carry through midnight immediately |
| 5 | Convert UTC to the requested arrival system | Apply the notified legal offset |
| 6 | Sense check direction and daylight | East is usually later, west usually earlier |
Integrated India example
At 1830 IST, subtract 5 hours 30 minutes to obtain 1300 UTC. At longitude 105 degrees east, add 7 hours of longitude time to UTC, giving 2000 LMT. These are simultaneous instants expressed in three systems.
Zone and date example
At longitude 130 degrees east, the theoretical zone number is minus 9. If Zone Time is 0600 on 1 January, apply UTC = Zone Time + Zone Number. The answer is 2100 UTC on 31 December.
Common errors
Do not use latitude in a basic time conversion. Do not confuse the east positive Standard Time offset with Oxford's east negative zone number. Do not assume a political Standard Time from longitude. Do not change date at Greenwich. Finally, do not apply a date line correction separately after a complete UTC calculation has already produced the correct date.