Three ways angle-based methods handle persistent summer twilight
North of about 48.6° latitude, the midsummer sun never sinks 18° below the horizon at local midnight (see our high-latitude prayer times data page). When a preset such as Muslim World League (18° Fajr / 17° Isha) or Karachi (18° / 18°) cannot find a direct solar depression crossing, astronomical prayer-time libraries apply one of three night-fraction approximations between sunset and sunrise, where N is the sunset-to-sunrise night duration:
- Middle of the Night (
middleofthenight): Caps Isha and Fajr at half the night (N / 2). In extreme cases both boundaries meet at the solar midnight midpoint. - One-Seventh of the Night (
seventhofthenight): Places Isha atsunset + N / 7and Fajr atsunrise − N / 7. Adhan'sHighLatitudeRule.recommended()selects this rule above 48° latitude. - Angle-Based Rule (
twilightangle): Scales the night fraction by the preset's depression angleα: Isha atsunset + (α_Isha / 60) × Nand Fajr atsunrise − (α_Fajr / 60) × N. For an 18° angle,18 / 60 = 0.30(30% of the night).
A fourth approach, used by Moonsighting Committee Worldwide (SalahTable's UK default), replaces raw angle crossings at high latitudes with latitude-interpolated seasonal curves.
Summer solstice comparison (21 June 2027): MWL (18°/17°) under each rule vs Moonsighting
In the table below, we hold the city, date (21 June 2027) and base angle preset (MWL: Fajr 18°, Isha 17°) constant across the first three columns, changing only the high-latitude rule, and compare the result with Moonsighting Committee in the final column.
| City / latitude | Middle of the Night (½) | One-Seventh (1/7) | Angle-Based (α/60) | Moonsighting Committee |
|---|---|---|---|---|
| London 51.5°N · United Kingdom | 1:02 AM / 1:02 AM | 3:40 AM / 10:25 PM | 2:31 AM / 11:27 PM | 2:43 AM / 10:42 PM |
| Birmingham 52.5°N · United Kingdom | 1:09 AM / 1:09 AM | 3:43 AM / 10:36 PM | 2:35 AM / 11:36 PM | 2:44 AM / 10:55 PM |
| Manchester 53.5°N · United Kingdom | 1:11 AM / 1:11 AM | 3:40 AM / 10:42 PM | 2:34 AM / 11:40 PM | 2:38 AM / 11:02 PM |
| Edinburgh 56.0°N · United Kingdom | 1:14 AM / 1:15 AM | 3:31 AM / 10:58 PM | 2:31 AM / 11:52 PM | 3:31 AM / 10:58 PM |
| Toronto 43.7°N · Canada | 3:13 AM / 11:15 PM | 4:23 AM / 10:16 PM | 3:13 AM / 11:15 PM | 3:43 AM / 10:23 PM |
| Vancouver 49.2°N · Canada | 1:14 AM / 12:44 AM | 4:00 AM / 10:28 PM | 2:47 AM / 11:34 PM | 3:09 AM / 10:42 PM |
Why the rules diverge in London, Edinburgh and Vancouver
- Above 48.6° N (London, Birmingham, Manchester, Edinburgh, Vancouver): On 21 June, an 18° depression is never reached. Under MWL, switching from One-Seventh to Angle-Based (
18 / 60) shifts Fajr earlier and Isha later because1/7 ≈ 14.3%of the night while18/60 = 30%of the night. - Below 45° N (Toronto, 43.7° N): On 21 June, the sun still reaches 18° below the horizon overnight in Toronto, so direct angle crossings succeed unless a tighter cap (such as Middle of the Night on very short nights) intervenes.
When two apps both say “Muslim World League (18°/17°)” in the UK or western Canada yet show June Fajr times that differ by more than an hour, they are using different high-latitude fallback rules. Read our UK mosque timetable comparison and methodology for how SalahTable configures its defaults.