aric/pray-calc
1
0
Fork 0
mirror of https://github.com/acamarata/pray-calc.git synced 2026-07-03 12:20:39 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions

style: fix prettier table formatting in wiki

Browse source
This commit is contained in:
Aric Camarata 2026-03-08 17:30:33 -04:00
parent 155217265d
commit 43d6241ac2
16 changed files with 501 additions and 493 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

32
.wiki/API-Reference.md
View file

@ -14,13 +14,13 @@ function getTimes(
temperature?: number, // °C, default 15 temperature?: number, // °C, default 15
pressure?: number, // mbar, default 1013.25 pressure?: number, // mbar, default 1013.25
hanafi?: boolean, // Asr convention, default false (Shafi'i) hanafi?: boolean, // Asr convention, default false (Shafi'i)
): PrayerTimes ): PrayerTimes;
``` ```
### PrayerTimes ### PrayerTimes
| Field | Type | Description | | Field | Type | Description |
|-------|------|-------------| | --------- | ---------------- | ---------------------------------------------------- |
| `Qiyam` | `number` | Start of the last third of the night (Qiyam al-Layl) | | `Qiyam` | `number` | Start of the last third of the night (Qiyam al-Layl) |
| `Fajr` | `number` | True dawn (Subh Sadiq) | | `Fajr` | `number` | True dawn (Subh Sadiq) |
| `Sunrise` | `number` | Astronomical sunrise | | `Sunrise` | `number` | Astronomical sunrise |
@ -50,7 +50,7 @@ function calcTimes(
temperature?: number, temperature?: number,
pressure?: number, pressure?: number,
hanafi?: boolean, hanafi?: boolean,
): FormattedPrayerTimes ): FormattedPrayerTimes;
``` ```
Returns `"N/A"` for any time that cannot be computed. Returns `"N/A"` for any time that cannot be computed.
@ -71,7 +71,7 @@ function getTimesAll(
temperature?: number, temperature?: number,
pressure?: number, pressure?: number,
hanafi?: boolean, hanafi?: boolean,
): PrayerTimesAll ): PrayerTimesAll;
``` ```
### PrayerTimesAll ### PrayerTimesAll
@ -79,7 +79,7 @@ function getTimesAll(
Extends `PrayerTimes` with: Extends `PrayerTimes` with:
| Field | Type | Description | | Field | Type | Description |
|-------|------|-------------| | --------- | ---------------------------------- | ------------------------------------ |
| `Methods` | `Record<string, [number, number]>` | `[fajrTime, ishaTime]` per method ID | | `Methods` | `Record<string, [number, number]>` | `[fajrTime, ishaTime]` per method ID |
Method IDs: `UOIF`, `ISNACA`, `ISNA`, `SAMR`, `IGUT`, `MWL`, `DIBT`, `Karachi`, Method IDs: `UOIF`, `ISNACA`, `ISNA`, `SAMR`, `IGUT`, `MWL`, `DIBT`, `Karachi`,
@ -101,7 +101,7 @@ function calcTimesAll(
temperature?: number, temperature?: number,
pressure?: number, pressure?: number,
hanafi?: boolean, hanafi?: boolean,
): FormattedPrayerTimesAll ): FormattedPrayerTimesAll;
``` ```
--- ---
@ -118,7 +118,7 @@ function getAngles(
elevation?: number, elevation?: number,
temperature?: number, temperature?: number,
pressure?: number, pressure?: number,
): TwilightAngles ): TwilightAngles;
``` ```
Returns `{ fajrAngle: number, ishaAngle: number }` in degrees (positive = below horizon). Returns `{ fajrAngle: number, ishaAngle: number }` in degrees (positive = below horizon).
@ -135,7 +135,7 @@ function getAsr(
latitude: number, // decimal degrees latitude: number, // decimal degrees
declination: number, // solar declination in degrees declination: number, // solar declination in degrees
hanafi?: boolean, // default false (Shafi'i, shadowFactor=1) hanafi?: boolean, // default false (Shafi'i, shadowFactor=1)
): number ): number;
``` ```
Returns Asr as fractional hours, or `NaN` if the sun never reaches the required altitude. Returns Asr as fractional hours, or `NaN` if the sun never reaches the required altitude.
@ -152,7 +152,7 @@ Compute start of the last third of the night.
function getQiyam( function getQiyam(
fajrTime: number, // fractional hours fajrTime: number, // fractional hours
ishaTime: number, // fractional hours ishaTime: number, // fractional hours
): number ): number;
``` ```
Returns fractional hours. The night is divided from Isha to Fajr; Qiyam starts at the Returns fractional hours. The night is divided from Isha to Fajr; Qiyam starts at the
@ -165,14 +165,14 @@ Returns fractional hours. The night is divided from Isha to Fajr; Qiyam starts a
Compute the Moonsighting Committee Worldwide seasonal time offsets. Compute the Moonsighting Committee Worldwide seasonal time offsets.
```typescript ```typescript
function getMscFajr(date: Date, latitude: number): number function getMscFajr(date: Date, latitude: number): number;
// Returns minutes before astronomical sunrise for Fajr // Returns minutes before astronomical sunrise for Fajr
function getMscIsha( function getMscIsha(
date: Date, date: Date,
latitude: number, latitude: number,
shafaq?: ShafaqMode, // 'general' | 'ahmer' | 'abyad', default 'general' shafaq?: ShafaqMode, // 'general' | 'ahmer' | 'abyad', default 'general'
): number ): number;
// Returns minutes after astronomical sunset for Isha // Returns minutes after astronomical sunset for Isha
``` ```
@ -183,16 +183,16 @@ You rarely need to call them directly.
## solarEphemeris / toJulianDate ## solarEphemeris / toJulianDate
Jean Meeus solar ephemeris (Chapter 25 of *Astronomical Algorithms*, 2nd ed.). Jean Meeus solar ephemeris (Chapter 25 of _Astronomical Algorithms_, 2nd ed.).
```typescript ```typescript
function toJulianDate(date: Date): number function toJulianDate(date: Date): number;
function solarEphemeris(jd: number): { function solarEphemeris(jd: number): {
decl: number; // solar declination, degrees decl: number; // solar declination, degrees
r: number; // Earth-Sun distance, AU r: number; // Earth-Sun distance, AU
eclLon: number; // apparent ecliptic longitude, degrees eclLon: number; // apparent ecliptic longitude, degrees
} };
``` ```
Accuracy: declination within ~0.01°, r within ~0.0001 AU. These are used internally Accuracy: declination within ~0.01°, r within ~0.0001 AU. These are used internally
@ -205,7 +205,7 @@ to drive the physics corrections in `getAngles`.
Exported array of all 14 `MethodDefinition` objects for documentation/tooling use. Exported array of all 14 `MethodDefinition` objects for documentation/tooling use.
```typescript ```typescript
const METHODS: MethodDefinition[] const METHODS: MethodDefinition[];
interface MethodDefinition { interface MethodDefinition {
id: string; id: string;
@ -253,4 +253,4 @@ See [Moon Migration](Moon-Migration) for the full migration guide and function m
--- ---
*[Back to Home](Home) | [Dynamic Algorithm](Dynamic-Algorithm) | [Traditional Methods](Traditional-Methods)* _[Back to Home](Home) | [Dynamic Algorithm](Dynamic-Algorithm) | [Traditional Methods](Traditional-Methods)_

4
.wiki/Architecture.md
View file

@ -69,7 +69,7 @@ covers dates from -2000 to +6000.
## Solar Ephemeris ## Solar Ephemeris
`getSolarEphemeris` implements Jean Meeus, *Astronomical Algorithms* (2nd ed.), `getSolarEphemeris` implements Jean Meeus, _Astronomical Algorithms_ (2nd ed.),
Chapter 25. This provides: Chapter 25. This provides:
- Solar declination (δ): accurate to ~0.01° - Solar declination (δ): accurate to ~0.01°
@ -128,4 +128,4 @@ Source maps are included. `sideEffects: false` allows tree-shaking.
--- ---
*[Back to Home](Home) | [API Reference](API-Reference) | [Dynamic Algorithm](Dynamic-Algorithm)* _[Back to Home](Home) | [API Reference](API-Reference) | [Dynamic Algorithm](Dynamic-Algorithm)_

3
.wiki/Asr-Calculation.md
View file

@ -16,6 +16,7 @@ In practice, the difference is typically 30–60 minutes, with Hanafi Asr being
## The Math ## The Math
Let: Let:
- φ = observer latitude in radians - φ = observer latitude in radians
- δ = solar declination in radians at local noon - δ = solar declination in radians at local noon
- s = shadow factor (1 for Shafi'i, 2 for Hanafi) - s = shadow factor (1 for Shafi'i, 2 for Hanafi)
@ -80,4 +81,4 @@ than 5 seconds of timing error: completely negligible.
--- ---
*[Back to Home](Home) | [API Reference](API-Reference) | [Architecture](Architecture)* _[Back to Home](Home) | [API Reference](API-Reference) | [Architecture](Architecture)_

2
.wiki/Changelog.md
View file

@ -19,4 +19,4 @@ CommonJS, JavaScript source, 10 traditional methods, suncalc for moon data.
--- ---
*[Back to Home](Home)* _[Back to Home](Home)_

2
.wiki/Dynamic-Algorithm.md
View file

@ -148,4 +148,4 @@ piecewise model is in [src/getMSC.ts](../src/getMSC.ts). The solar ephemeris
--- ---
*[Back to Home](Home) | [Traditional Methods](Traditional-Methods) | [Twilight Physics](Twilight-Physics)* _[Back to Home](Home) | [Traditional Methods](Traditional-Methods) | [Twilight Physics](Twilight-Physics)_

9
.wiki/High-Latitude.md
View file

@ -9,7 +9,7 @@ a sunrise before Fajr, or other nonsensical results.
Even at latitudes where the Sun does reach 18°, the resulting times can be extreme. Even at latitudes where the Sun does reach 18°, the resulting times can be extreme.
At 52°N in summer, a 15° Isha occurs around 2–3 AM, making a 4 AM Fajr effectively At 52°N in summer, a 15° Isha occurs around 2–3 AM, making a 4 AM Fajr effectively
continuous with Isha. Islamic jurisprudence recognizes this as hardship (*haraj*) continuous with Isha. Islamic jurisprudence recognizes this as hardship (_haraj_)
and provides accommodations. and provides accommodations.
## The MSC Approach ## The MSC Approach
@ -52,23 +52,28 @@ there.
Islamic scholars have proposed several approaches for high-latitude regions: Islamic scholars have proposed several approaches for high-latitude regions:
### Nearest Latitude (Aqrab al-Bilad) ### Nearest Latitude (Aqrab al-Bilad)
Use the prayer times of the nearest city where the Sun does reach the required Use the prayer times of the nearest city where the Sun does reach the required
angle, scaled to local midnight. angle, scaled to local midnight.
### Nearest Day (Aqrab al-Ayyam) ### Nearest Day (Aqrab al-Ayyam)
Use the prayer times from the nearest date in the year when the Sun does reach Use the prayer times from the nearest date in the year when the Sun does reach
the required angle at the same location. the required angle at the same location.
### Seventh of Night (Sab'u lail) ### Seventh of Night (Sab'u lail)
Divide the 24-hour period (from midnight to midnight, or from Maghrib to Fajr) Divide the 24-hour period (from midnight to midnight, or from Maghrib to Fajr)
into 7 equal parts. Isha begins at the end of the first seventh; Fajr begins at into 7 equal parts. Isha begins at the end of the first seventh; Fajr begins at
the start of the last seventh. the start of the last seventh.
### Specific Latitude Cutoff ### Specific Latitude Cutoff
Many North American institutions use the rule: above 48.5°N, compute times as Many North American institutions use the rule: above 48.5°N, compute times as
if the latitude were 48.5°N. This is simple and avoids discontinuities. if the latitude were 48.5°N. This is simple and avoids discontinuities.
### Makkah Time ### Makkah Time
A minority position: use Makkah's times globally. Not widely adopted outside A minority position: use Makkah's times globally. Not widely adopted outside
of specific communities. of specific communities.
@ -84,4 +89,4 @@ are inapplicable and apply their own high-latitude policy.
--- ---
*[Back to Home](Home) | [Twilight Physics](Twilight-Physics) | [Dynamic Algorithm](Dynamic-Algorithm)* _[Back to Home](Home) | [Twilight Physics](Twilight-Physics) | [Dynamic Algorithm](Dynamic-Algorithm)_

8
.wiki/Home.md
View file

@ -8,7 +8,7 @@ fixed-angle methods are included for comparison.
## Pages ## Pages
| Page | Description | | Page | Description |
|------|-------------| | ------------------------------------------ | ---------------------------------------------------------- |
| [API Reference](API-Reference) | Full function signatures, parameters, return types | | [API Reference](API-Reference) | Full function signatures, parameters, return types |
| [Dynamic Algorithm](Dynamic-Algorithm) | How Fajr/Isha angles are computed dynamically | | [Dynamic Algorithm](Dynamic-Algorithm) | How Fajr/Isha angles are computed dynamically |
| [Traditional Methods](Traditional-Methods) | All 14 supported methods and their parameters | | [Traditional Methods](Traditional-Methods) | All 14 supported methods and their parameters |
@ -22,7 +22,7 @@ fixed-angle methods are included for comparison.
## Research & Accuracy ## Research & Accuracy
| Page | Description | | Page | Description |
| --- | --- | | -------------------------------------------------------------- | --------------------------------------------------------------------- |
| [Research Overview](Research) | Study summary, headline results, PCD algorithm description | | [Research Overview](Research) | Study summary, headline results, PCD algorithm description |
| [Methodology](Research-Methodology) | Reference standard, measurement approach, test infrastructure | | [Methodology](Research-Methodology) | Reference standard, measurement approach, test infrastructure |
| [Global Accuracy Study](Research-Global-Study) | 18-city comparison across latitudes 6°S–51.5°N and all seasons | | [Global Accuracy Study](Research-Global-Study) | 18-city comparison across latitudes 6°S–51.5°N and all seasons |
@ -44,7 +44,7 @@ import { calcTimes } from 'pray-calc';
const times = calcTimes( const times = calcTimes(
new Date('2024-06-21'), new Date('2024-06-21'),
40.7128, // New York 40.7128, // New York
-74.0060, -74.006,
); );
console.log(times.Fajr); // "03:51:24" console.log(times.Fajr); // "03:51:24"
@ -85,4 +85,4 @@ never produces the "Isha never ends" failure that 18°-everywhere causes above 5
--- ---
*[Back to Repository](https://github.com/acamarata/pray-calc)* _[Back to Repository](https://github.com/acamarata/pray-calc)_

6
.wiki/Moon-Migration.md
View file

@ -3,7 +3,7 @@
In pray-calc v1, the package included five functions for moon data: In pray-calc v1, the package included five functions for moon data:
| v1 Function | Description | | v1 Function | Description |
| -- | -- | | ----------------------------------- | ---------------------------------------------------------------------- |
| `getMoon(date, lat, lon)` | Aggregated wrapper returning phase, position, illumination, visibility | | `getMoon(date, lat, lon)` | Aggregated wrapper returning phase, position, illumination, visibility |
| `getMoonPhase(date)` | Synodic-month calculation from known reference new moon | | `getMoonPhase(date)` | Synodic-month calculation from known reference new moon |
| `getMoonPosition(date, lat, lon)` | Thin wrapper around `suncalc.getMoonPosition` | | `getMoonPosition(date, lat, lon)` | Thin wrapper around `suncalc.getMoonPosition` |
@ -56,7 +56,7 @@ import { getMoon, getMoonPhase, getMoonPosition, getMoonIllumination } from 'moo
### Function Mapping ### Function Mapping
| pray-calc v1 | moon-sighting v1.1 | Notes | | pray-calc v1 | moon-sighting v1.1 | Notes |
| -- | -- | -- | | ----------------------------------- | ------------------------------------------------------- | -------------------------------------------------------------- |
| `getMoonPosition(date, lat, lon)` | `getMoonPosition(date, lat, lon, elevation?)` | Adds WGS84 model, Bennett refraction, `parallacticAngle` field | | `getMoonPosition(date, lat, lon)` | `getMoonPosition(date, lat, lon, elevation?)` | Adds WGS84 model, Bennett refraction, `parallacticAngle` field |
| `getMoonIllumination(date)` | `getMoonIllumination(date)` | Adds correct phase angle, `isWaxing` field | | `getMoonIllumination(date)` | `getMoonIllumination(date)` | Adds correct phase angle, `isWaxing` field |
| `getMoonPhase(date)` | `getMoonPhase(date)` | Adds `phaseName`, `phaseSymbol`, more fields | | `getMoonPhase(date)` | `getMoonPhase(date)` | Adds `phaseName`, `phaseSymbol`, more fields |
@ -76,4 +76,4 @@ returns.
--- ---
*[Back to Home](Home) | [API Reference](API-Reference) | [Changelog](Changelog)* _[Back to Home](Home) | [API Reference](API-Reference) | [Changelog](Changelog)_

14
.wiki/Research-Global-Study.md
View file

@ -16,7 +16,7 @@ Error is `method_time − MSC_reference` in minutes. Positive = later than MSC,
`N/A` = sun never reaches the required depression angle (method is undefined for that case). `N/A` = sun never reaches the required depression angle (method is undefined for that case).
| # | City | Date | Lat | Elev | Sunrise | Maghrib | PCD Fajr° | PCD Isha° | MSC Fajr ref | MSC Isha ref | | # | City | Date | Lat | Elev | Sunrise | Maghrib | PCD Fajr° | PCD Isha° | MSC Fajr ref | MSC Isha ref |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | --- | ------------------ | ------ | ------- | ----- | ------- | ------- | --------- | --------- | --------------- | -------------- |
| 1 | New York, USA | Jun 21 | 40.71°N | 10m | 05:25 | 20:30 | 16.21° | 12.41° | 03:35 (110 min) | 21:49 (79 min) | | 1 | New York, USA | Jun 21 | 40.71°N | 10m | 05:25 | 20:30 | 16.21° | 12.41° | 03:35 (110 min) | 21:49 (79 min) |
| 2 | New York, USA | Dec 21 | 40.71°N | 10m | 07:16 | 16:32 | 17.48° | 17.12° | 05:40 (96 min) | 18:06 (94 min) | | 2 | New York, USA | Dec 21 | 40.71°N | 10m | 07:16 | 16:32 | 17.48° | 17.12° | 05:40 (96 min) | 18:06 (94 min) |
| 3 | New York, USA | Mar 21 | 40.71°N | 10m | 06:56 | 19:09 | 17.48° | 15.28° | 05:27 (89 min) | 20:26 (77 min) | | 3 | New York, USA | Mar 21 | 40.71°N | 10m | 06:56 | 19:09 | 17.48° | 15.28° | 05:27 (89 min) | 20:26 (77 min) |
@ -44,7 +44,7 @@ Error is `method_time − MSC_reference` in minutes. Positive = later than MSC,
`n_Fajr` / `n_Isha` = number of valid (non-NaN) results included in MAE calculation. `n_Fajr` / `n_Isha` = number of valid (non-NaN) results included in MAE calculation.
| Rank | Method | Fajr MAE (min) | Isha MAE (min) | Combined MAE | n_Fajr | n_Isha | | Rank | Method | Fajr MAE (min) | Isha MAE (min) | Combined MAE | n_Fajr | n_Isha |
| --- | --- | --- | --- | --- | --- | --- | | ----- | ------------------- | -------------- | -------------- | ------------ | ------ | ------ |
| 1 | MSC | 0.00 | 0.00 | 0.00 | 18 | 18 | | 1 | MSC | 0.00 | 0.00 | 0.00 | 18 | 18 |
| **2** | **★ PCD (Dynamic)** | **0.64** | **1.30** | **0.97** | **18** | **18** | | **2** | **★ PCD (Dynamic)** | **0.64** | **1.30** | **0.97** | **18** | **18** |
| 3 | Qatar | 10.21 | 10.22 | 10.21 | 17 | 18 | | 3 | Qatar | 10.21 | 10.22 | 10.21 | 17 | 18 |
@ -70,7 +70,7 @@ Error is `method_time − MSC_reference` in minutes. Positive = later than MSC,
Error in minutes vs MSC reference (`+` = later, `−` = earlier). `N/A` = sun does not reach required depression. Error in minutes vs MSC reference (`+` = later, `−` = earlier). `N/A` = sun does not reach required depression.
| City / Date | PCD | UOIF | ISNACA | ISNA | SAMR | IGUT | MWL | DIBT | Karachi | Kuwait | UAQ | Qatar | Egypt | MUIS | | City / Date | PCD | UOIF | ISNACA | ISNA | SAMR | IGUT | MWL | DIBT | Karachi | Kuwait | UAQ | Qatar | Egypt | MUIS |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | ------------- | -------- | ----- | ------ | ----- | ----- | ----- | ----- | ----- | ------- | ------ | ----- | ----- | ----- | ----- |
| NY Jun | **−0.2** | +34.0 | +26.3 | +10.2 | +1.7 | −13.6 | −16.4 | −16.4 | −16.4 | −16.4 | −21.2 | −16.4 | −31.3 | −36.6 | | NY Jun | **−0.2** | +34.0 | +26.3 | +10.2 | +1.7 | −13.6 | −16.4 | −16.4 | −16.4 | −16.4 | −21.2 | −16.4 | −31.3 | −36.6 |
| NY Dec | **+0.1** | +30.6 | +25.0 | +13.8 | +8.3 | −1.1 | −2.7 | −2.7 | −2.7 | −2.7 | −5.5 | −2.7 | −10.9 | −13.7 | | NY Dec | **+0.1** | +30.6 | +25.0 | +13.8 | +8.3 | −1.1 | −2.7 | −2.7 | −2.7 | −2.7 | −5.5 | −2.7 | −10.9 | −13.7 |
| NY Mar | **+0.2** | +30.0 | +24.6 | +13.8 | +8.3 | −1.0 | −2.7 | −2.7 | −2.7 | −2.7 | −5.4 | −2.7 | −11.0 | −13.7 | | NY Mar | **+0.2** | +30.0 | +24.6 | +13.8 | +8.3 | −1.0 | −2.7 | −2.7 | −2.7 | −2.7 | −5.4 | −2.7 | −11.0 | −13.7 |
@ -95,7 +95,7 @@ Error in minutes vs MSC reference (`+` = later, `−` = earlier). `N/A` = sun do
## Per-Case Detail: Isha Errors by Method ## Per-Case Detail: Isha Errors by Method
| City / Date | PCD | UOIF | ISNACA | ISNA | SAMR | IGUT | MWL | DIBT | Karachi | Kuwait | UAQ | Qatar | Egypt | MUIS | | City / Date | PCD | UOIF | ISNACA | ISNA | SAMR | IGUT | MWL | DIBT | Karachi | Kuwait | UAQ | Qatar | Egypt | MUIS |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | ------------- | --------- | ----- | ------ | ------ | ------ | ----- | ----- | ----- | ------- | ------ | ----- | ----- | ----- | ----- |
| NY Jun | **+0.4** | −2.8 | +4.9 | +21.1 | +21.1 | +12.9 | +38.4 | +38.4 | +47.6 | +43.0 | +11.0 | +11.0 | +43.0 | +47.6 | | NY Jun | **+0.4** | −2.8 | +4.9 | +21.1 | +21.1 | +12.9 | +38.4 | +38.4 | +47.6 | +43.0 | +11.0 | +11.0 | +43.0 | +47.6 |
| NY Dec | **−0.1** | −28.6 | −23.0 | −11.8 | −11.8 | −17.4 | −0.8 | −0.8 | +4.7 | +2.0 | −4.0 | −4.0 | +2.0 | +4.7 | | NY Dec | **−0.1** | −28.6 | −23.0 | −11.8 | −11.8 | −17.4 | −0.8 | −0.8 | +4.7 | +2.0 | −4.0 | −4.0 | +2.0 | +4.7 |
| NY Mar | **−0.9** | −18.7 | −13.3 | −2.5 | −2.5 | −7.9 | +8.5 | +8.5 | +14.0 | +11.2 | +13.0 | +13.0 | +11.2 | +14.0 | | NY Mar | **−0.9** | −18.7 | −13.3 | −2.5 | −2.5 | −7.9 | +8.5 | +8.5 | +14.0 | +11.2 | +13.0 | +13.0 | +11.2 | +14.0 |
@ -122,7 +122,7 @@ Error in minutes vs MSC reference (`+` = later, `−` = earlier). `N/A` = sun do
London, UK on June 21 (51.5°N) is the most extreme test case. As the sun approaches its highest declination, it never reaches deep depression angles. London, UK on June 21 (51.5°N) is the most extreme test case. As the sun approaches its highest declination, it never reaches deep depression angles.
| Method | Fixed Isha° | Isha result | | Method | Fixed Isha° | Isha result |
| --- | --- | --- | | ------- | ----------- | -------------------------------------- |
| UOIF | 12° | 23:24 (valid) | | UOIF | 12° | 23:24 (valid) |
| ISNACA | 13° | 23:42 (valid) | | ISNACA | 13° | 23:42 (valid) |
| ISNA | 15° | 24:49 (technically computed, next day) | | ISNA | 15° | 24:49 (technically computed, next day) |
@ -148,7 +148,7 @@ Six of the 14 methods produce no Isha time at London in midsummer. PCD adapts by
How the PCD-computed depression angle varies across the test cases. How the PCD-computed depression angle varies across the test cases.
| City | Lat | Season | Fajr° | Isha° | Closest Fixed Method | | City | Lat | Season | Fajr° | Isha° | Closest Fixed Method |
| --- | --- | --- | --- | --- | --- | | --------- | ------ | ------ | ------ | ------ | -------------------- |
| Jakarta | 6.2°S | Jun | 18.72° | 18.72° | UAQ (18.5°) | | Jakarta | 6.2°S | Jun | 18.72° | 18.72° | UAQ (18.5°) |
| Singapore | 1.4°N | Dec | 18.23° | 18.23° | MWL/DIBT (18°) | | Singapore | 1.4°N | Dec | 18.23° | 18.23° | MWL/DIBT (18°) |
| Makkah | 21.4°N | Jun | 19.79° | 16.56° | MUIS (20°) / Egypt | | Makkah | 21.4°N | Jun | 19.79° | 16.56° | MUIS (20°) / Egypt |
@ -172,4 +172,4 @@ The angle moves from ~20° at tropical latitudes in summer to ~12° at high-lati
--- ---
*[Research](Research) | [Methodology](Research-Methodology) | [Home-Territory Study](Research-Home-Territory) | [Observational Evidence](Research-Observational-Evidence)* _[Research](Research) | [Methodology](Research-Methodology) | [Home-Territory Study](Research-Home-Territory) | [Observational Evidence](Research-Observational-Evidence)_

60
.wiki/Research-Home-Territory.md
View file

@ -15,7 +15,7 @@ The question: does PCD (Prayer Calc Dynamic) remain more accurate than a method
Across 34 Fajr + 34 Isha home-territory test cases: Across 34 Fajr + 34 Isha home-territory test cases:
| | PCD (Dynamic) | Traditional (avg) | Ratio | | | PCD (Dynamic) | Traditional (avg) | Ratio |
| --- | --- | --- | --- | | ------------ | ------------- | ----------------- | --------------- |
| Fajr MAE | **0.65 min** | 7.53 min | 11.6× worse | | Fajr MAE | **0.65 min** | 7.53 min | 11.6× worse |
| Isha MAE | **0.64 min** | 9.84 min | 15.4× worse | | Isha MAE | **0.64 min** | 9.84 min | 15.4× worse |
| Combined MAE | **0.64 min** | 8.69 min | **13.5× worse** | | Combined MAE | **0.64 min** | 8.69 min | **13.5× worse** |
@ -29,7 +29,7 @@ Across 34 Fajr + 34 Isha home-territory test cases:
Each row represents one traditional method, tested at its home city across all listed seasons. Each row represents one traditional method, tested at its home city across all listed seasons.
| Method | Home City | Fixed Fajr° | PCD Avg Fajr° | Δ° (Dyn − Fixed) | PCD MAE | Method MAE | Winner | Margin | | Method | Home City | Fixed Fajr° | PCD Avg Fajr° | Δ° (Dyn − Fixed) | PCD MAE | Method MAE | Winner | Margin |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | | ------- | ----------------- | ----------- | ------------- | ---------------- | -------- | ---------- | ------ | -------- |
| UOIF | Paris, France | 12.0° | 14.30° | +2.30° | 0.45 min | 19.91 min | ★ PCD | 19.5 min | | UOIF | Paris, France | 12.0° | 14.30° | +2.30° | 0.45 min | 19.91 min | ★ PCD | 19.5 min |
| ISNACA | Ottawa, Canada | 13.0° | 15.59° | +2.59° | 0.51 min | 18.41 min | ★ PCD | 17.9 min | | ISNACA | Ottawa, Canada | 13.0° | 15.59° | +2.59° | 0.51 min | 18.41 min | ★ PCD | 17.9 min |
| ISNA | Chicago, USA | 15.0° | 16.94° | +1.94° | 0.73 min | 11.48 min | ★ PCD | 10.7 min | | ISNA | Chicago, USA | 15.0° | 16.94° | +1.94° | 0.73 min | 11.48 min | ★ PCD | 10.7 min |
@ -53,10 +53,10 @@ Each row represents one traditional method, tested at its home city across all l
### UOIF: Paris, France (12°/12°) ### UOIF: Paris, France (12°/12°)
*Lowest angles of any major method. Designed for France's large Muslim minority seeking the least restrictive valid times.* _Lowest angles of any major method. Designed for France's large Muslim minority seeking the least restrictive valid times._
| Season | PCD Fajr° | MSC Fajr | PCD Fajr err | UOIF Fajr err | PCD Isha err | UOIF Isha err | Winner | | Season | PCD Fajr° | MSC Fajr | PCD Fajr err | UOIF Fajr err | PCD Isha err | UOIF Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | -------- | ------------ | ------------- | ------------ | ------------- | ----------------- |
| Jun 21 | 13.14° | 03:50 | **−0.6 min** | +13.7 min | **+1.0 min** | +23.4 min | ★ PCD by 17.7 min | | Jun 21 | 13.14° | 03:50 | **−0.6 min** | +13.7 min | **+1.0 min** | +23.4 min | ★ PCD by 17.7 min |
| Dec 21 | 15.46° | 08:01 | **−0.1 min** | +22.3 min | **+0.1 min** | −20.3 min | ★ PCD by 21.2 min | | Dec 21 | 15.46° | 08:01 | **−0.1 min** | +22.3 min | **+0.1 min** | −20.3 min | ★ PCD by 21.2 min |
@ -64,10 +64,10 @@ Each row represents one traditional method, tested at its home city across all l
### ISNACA: Ottawa, Canada (13°/13°) ### ISNACA: Ottawa, Canada (13°/13°)
*Symmetric 13° angles for Canada. Used by the Islamic Council of North America.* _Symmetric 13° angles for Canada. Used by the Islamic Council of North America._
| Season | PCD Fajr° | MSC Fajr | PCD Fajr err | ISNACA Fajr err | PCD Isha err | ISNACA Isha err | Winner | | Season | PCD Fajr° | MSC Fajr | PCD Fajr err | ISNACA Fajr err | PCD Isha err | ISNACA Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | -------- | ------------ | --------------- | ------------ | --------------- | ----------------- |
| Jun 21 | 14.61° | 03:20 | **−0.8 min** | +15.8 min | **+0.9 min** | +18.4 min | ★ PCD by 16.3 min | | Jun 21 | 14.61° | 03:20 | **−0.8 min** | +15.8 min | **+0.9 min** | +18.4 min | ★ PCD by 16.3 min |
| Dec 21 | 16.56° | 07:00 | **−0.2 min** | +21.2 min | **+0.2 min** | −18.2 min | ★ PCD by 19.5 min | | Dec 21 | 16.56° | 07:00 | **−0.2 min** | +21.2 min | **+0.2 min** | −18.2 min | ★ PCD by 19.5 min |
@ -75,10 +75,10 @@ Each row represents one traditional method, tested at its home city across all l
### ISNA: Chicago, USA (15°/15°) ### ISNA: Chicago, USA (15°/15°)
*Revised from 18° to 15° in 2007 after observational review by the Fiqh Council of North America. The 15° standard was justified partly by the finding that 18° produces astronomically unreachable angles in summer at North American latitudes.* _Revised from 18° to 15° in 2007 after observational review by the Fiqh Council of North America. The 15° standard was justified partly by the finding that 18° produces astronomically unreachable angles in summer at North American latitudes._
| Season | PCD Fajr° | MSC Fajr | PCD Fajr err | ISNA Fajr err | PCD Isha err | ISNA Isha err | Winner | | Season | PCD Fajr° | MSC Fajr | PCD Fajr err | ISNA Fajr err | PCD Isha err | ISNA Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | -------- | ------------ | ------------- | ------------ | ------------- | ----------------- |
| Jun 21 | 15.94° | 03:24 | **−1.1 min** | +7.3 min | **+1.2 min** | +24.9 min | ★ PCD by 15.0 min | | Jun 21 | 15.94° | 03:24 | **−1.1 min** | +7.3 min | **+1.2 min** | +24.9 min | ★ PCD by 15.0 min |
| Dec 21 | 17.42° | 06:38 | **−0.5 min** | +13.1 min | **+0.5 min** | −10.1 min | ★ PCD by 11.2 min | | Dec 21 | 17.42° | 06:38 | **−0.5 min** | +13.1 min | **+0.5 min** | −10.1 min | ★ PCD by 11.2 min |
| Mar 21 | 17.46° | 05:21 | **−0.4 min** | +13.3 min | **+0.7 min** | +0.1 min | ★ PCD by 6.1 min | | Mar 21 | 17.46° | 05:21 | **−0.4 min** | +13.3 min | **+0.7 min** | +0.1 min | ★ PCD by 6.1 min |
@ -87,10 +87,10 @@ Each row represents one traditional method, tested at its home city across all l
### SAMR: Moscow, Russia (16°/15°) ### SAMR: Moscow, Russia (16°/15°)
*The most dramatically failing method at its home city. Moscow in summer (55.8°N) has such short nights that the sun never reaches 16° depression: both Fajr and Isha return NaN.* _The most dramatically failing method at its home city. Moscow in summer (55.8°N) has such short nights that the sun never reaches 16° depression: both Fajr and Isha return NaN._
| Season | PCD Fajr° | SAMR result | PCD Fajr err | SAMR Fajr err | Winner | | Season | PCD Fajr° | SAMR result | PCD Fajr err | SAMR Fajr err | Winner |
| --- | --- | --- | --- | --- | --- | | ------ | --------- | ------------- | ------------ | ------------- | -------------------- |
| Jun 21 | 10.00° | **N/A (NaN)** | −17.0 min | N/A | ★ PCD by 961 min avg | | Jun 21 | 10.00° | **N/A (NaN)** | −17.0 min | N/A | ★ PCD by 961 min avg |
| Dec 21 | 13.15° | 06:51 | **−0.7 min** | −22.3 min | ★ PCD by 19.4 min | | Dec 21 | 13.15° | 06:51 | **−0.7 min** | −22.3 min | ★ PCD by 19.4 min |
@ -98,10 +98,10 @@ Each row represents one traditional method, tested at its home city across all l
### IGUT: Tehran, Iran (17.7°/14°) ### IGUT: Tehran, Iran (17.7°/14°)
*The closest fixed-angle match at its own home territory. IGUT's 17.7° Fajr is within 0.82° of PCD's average Tehran output (18.52°).* _The closest fixed-angle match at its own home territory. IGUT's 17.7° Fajr is within 0.82° of PCD's average Tehran output (18.52°)._
| Season | PCD Fajr° | PCD Fajr err | IGUT Fajr err | PCD Isha err | IGUT Isha err | Winner | | Season | PCD Fajr° | PCD Fajr err | IGUT Fajr err | PCD Isha err | IGUT Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | | --------------- | --------- | ------------ | ------------- | ------------ | ------------- | ----------------- |
| Jun 21 | 17.95° | −2.5 min | **−0.7 min** | +2.3 min | **+1.6 min** | IGUT by 1.2 min | | Jun 21 | 17.95° | −2.5 min | **−0.7 min** | +2.3 min | **+1.6 min** | IGUT by 1.2 min |
| Dec 21 | 18.78° | **−1.5 min** | +4.0 min | **+1.5 min** | −20.2 min | ★ PCD by 10.6 min | | Dec 21 | 18.78° | **−1.5 min** | +4.0 min | **+1.5 min** | −20.2 min | ★ PCD by 10.6 min |
| Mar 21 (Nowruz) | 18.84° | **−1.5 min** | +4.3 min | **+0.9 min** | −11.5 min | ★ PCD by 6.8 min | | Mar 21 (Nowruz) | 18.84° | **−1.5 min** | +4.3 min | **+0.9 min** | −11.5 min | ★ PCD by 6.8 min |
@ -110,10 +110,10 @@ Each row represents one traditional method, tested at its home city across all l
### MWL: Makkah, Saudi Arabia (18°/17°) ### MWL: Makkah, Saudi Arabia (18°/17°)
*The Muslim World League is headquartered in Makkah. 18° was historically derived from observations at equatorial and sub-tropical locations.* _The Muslim World League is headquartered in Makkah. 18° was historically derived from observations at equatorial and sub-tropical locations._
| Season | PCD Fajr° | PCD Fajr err | MWL Fajr err | PCD Isha err | MWL Isha err | Winner | | Season | PCD Fajr° | PCD Fajr err | MWL Fajr err | PCD Isha err | MWL Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | ------------ | ------------ | ------------ | ------------ | ---------------- |
| Jun 21 | 19.79° | **−0.8 min** | +8.7 min | **+0.8 min** | +3.1 min | ★ PCD by 5.1 min | | Jun 21 | 19.79° | **−0.8 min** | +8.7 min | **+0.8 min** | +3.1 min | ★ PCD by 5.1 min |
| Dec 21 | 19.58° | **−0.5 min** | +6.7 min | **+0.5 min** | −10.2 min | ★ PCD by 8.0 min | | Dec 21 | 19.58° | **−0.5 min** | +6.7 min | **+0.5 min** | −10.2 min | ★ PCD by 8.0 min |
| Mar 21 | 20.22° | **−0.5 min** | +9.1 min | **+0.2 min** | −6.7 min | ★ PCD by 7.5 min | | Mar 21 | 20.22° | **−0.5 min** | +9.1 min | **+0.2 min** | −6.7 min | ★ PCD by 7.5 min |
@ -122,10 +122,10 @@ Each row represents one traditional method, tested at its home city across all l
### DIBT: Ankara, Turkey (18°/17°) ### DIBT: Ankara, Turkey (18°/17°)
*Same angles as MWL. Diyanet (Turkish Directorate of Religious Affairs) uses this standard nationally.* _Same angles as MWL. Diyanet (Turkish Directorate of Religious Affairs) uses this standard nationally._
| Season | PCD Fajr° | PCD Fajr err | DIBT Fajr err | PCD Isha err | DIBT Isha err | Winner | | Season | PCD Fajr° | PCD Fajr err | DIBT Fajr err | PCD Isha err | DIBT Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | ------------ | ------------- | ------------ | ------------- | ----------------- |
| Jun 21 | 16.81° | **−2.5 min** | −13.1 min | **+2.2 min** | +35.2 min | ★ PCD by 21.8 min | | Jun 21 | 16.81° | **−2.5 min** | −13.1 min | **+2.2 min** | +35.2 min | ★ PCD by 21.8 min |
| Dec 21 | 17.98° | **−1.4 min** | −1.5 min | **+1.4 min** | −1.0 min | DIBT by 0.2 min | | Dec 21 | 17.98° | **−1.4 min** | −1.5 min | **+1.4 min** | −1.0 min | DIBT by 0.2 min |
@ -133,10 +133,10 @@ Each row represents one traditional method, tested at its home city across all l
### Karachi: Karachi, Pakistan (18°/18°) ### Karachi: Karachi, Pakistan (18°/18°)
*Symmetric 18° angles, standard across Pakistan, Bangladesh, India, and Afghanistan.* _Symmetric 18° angles, standard across Pakistan, Bangladesh, India, and Afghanistan._
| Season | PCD Fajr° | PCD Fajr err | Karachi Fajr err | PCD Isha err | Karachi Isha err | Winner | | Season | PCD Fajr° | PCD Fajr err | Karachi Fajr err | PCD Isha err | Karachi Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | ------------ | ---------------- | ------------ | ---------------- | ---------------- |
| Jun 21 | 19.43° | **−0.1 min** | +7.9 min | **+0.1 min** | +11.1 min | ★ PCD by 9.4 min | | Jun 21 | 19.43° | **−0.1 min** | +7.9 min | **+0.1 min** | +11.1 min | ★ PCD by 9.4 min |
| Dec 21 | 19.39° | **+0.1 min** | +6.6 min | **−0.1 min** | −4.6 min | ★ PCD by 5.5 min | | Dec 21 | 19.39° | **+0.1 min** | +6.6 min | **−0.1 min** | −4.6 min | ★ PCD by 5.5 min |
@ -145,16 +145,16 @@ Each row represents one traditional method, tested at its home city across all l
### Kuwait: Kuwait City (18°/17.5°) ### Kuwait: Kuwait City (18°/17.5°)
| Season | PCD Fajr° | PCD Fajr err | Kuwait Fajr err | PCD Isha err | Kuwait Isha err | Winner | | Season | PCD Fajr° | PCD Fajr err | Kuwait Fajr err | PCD Isha err | Kuwait Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | ------------ | --------------- | ------------ | --------------- | ---------------- |
| Jun 21 | 18.95° | **−0.4 min** | +5.5 min | **+0.4 min** | +14.4 min | ★ PCD by 9.6 min | | Jun 21 | 18.95° | **−0.4 min** | +5.5 min | **+0.4 min** | +14.4 min | ★ PCD by 9.6 min |
| Dec 21 | 19.09° | **−0.1 min** | +5.1 min | **+0.1 min** | −6.5 min | ★ PCD by 5.8 min | | Dec 21 | 19.09° | **−0.1 min** | +5.1 min | **+0.1 min** | −6.5 min | ★ PCD by 5.8 min |
### UAQ: Riyadh, Saudi Arabia (18.5°/+90 min) ### UAQ: Riyadh, Saudi Arabia (18.5°/+90 min)
*The official Saudi government calendar used for all religious timing in the Kingdom. 18.5° Fajr is slightly higher than MWL's 18° to account for Saudi geographic and atmospheric conditions.* _The official Saudi government calendar used for all religious timing in the Kingdom. 18.5° Fajr is slightly higher than MWL's 18° to account for Saudi geographic and atmospheric conditions._
| Season | PCD Fajr° | PCD Fajr err | UAQ Fajr err | PCD Isha err | UAQ Isha err | Winner | | Season | PCD Fajr° | PCD Fajr err | UAQ Fajr err | PCD Isha err | UAQ Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | ------------ | ------------ | ------------ | ------------ | ---------------- |
| Jun 21 | 19.51° | **−1.3 min** | +4.4 min | **+1.3 min** | +12.0 min | ★ PCD by 6.9 min | | Jun 21 | 19.51° | **−1.3 min** | +4.4 min | **+1.3 min** | +12.0 min | ★ PCD by 6.9 min |
| Dec 21 | 19.64° | **−0.9 min** | +4.4 min | **+0.9 min** | +4.0 min | ★ PCD by 3.3 min | | Dec 21 | 19.64° | **−0.9 min** | +4.4 min | **+0.9 min** | +4.0 min | ★ PCD by 3.3 min |
| Mar 21 | 20.04° | **−0.9 min** | +6.0 min | **+0.5 min** | +14.0 min | ★ PCD by 9.3 min | | Mar 21 | 20.04° | **−0.9 min** | +6.0 min | **+0.5 min** | +14.0 min | ★ PCD by 9.3 min |
@ -164,16 +164,16 @@ Each row represents one traditional method, tested at its home city across all l
### Qatar: Doha, Qatar (18°/+90 min) ### Qatar: Doha, Qatar (18°/+90 min)
| Season | PCD Fajr° | PCD Fajr err | Qatar Fajr err | PCD Isha err | Qatar Isha err | Winner | | Season | PCD Fajr° | PCD Fajr err | Qatar Fajr err | PCD Isha err | Qatar Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | ------------ | -------------- | ------------ | -------------- | ---------------- |
| Jun 21 | 19.33° | **−0.1 min** | +7.4 min | **+0.1 min** | +12.0 min | ★ PCD by 9.6 min | | Jun 21 | 19.33° | **−0.1 min** | +7.4 min | **+0.1 min** | +12.0 min | ★ PCD by 9.6 min |
| Dec 21 | 19.33° | **+0.1 min** | +6.3 min | **−0.1 min** | +3.0 min | ★ PCD by 4.5 min | | Dec 21 | 19.33° | **+0.1 min** | +6.3 min | **−0.1 min** | +3.0 min | ★ PCD by 4.5 min |
### Egypt: Cairo, Egypt (19.5°/17.5°) ### Egypt: Cairo, Egypt (19.5°/17.5°)
*Egypt has the highest Fajr angle (19.5°) of any major method. It was established by the Egyptian General Authority of Survey and applies across Egypt, Syria, Iraq, and Lebanon.* _Egypt has the highest Fajr angle (19.5°) of any major method. It was established by the Egyptian General Authority of Survey and applies across Egypt, Syria, Iraq, and Lebanon._
| Season | PCD Fajr° | PCD Fajr err | Egypt Fajr err | PCD Isha err | Egypt Isha err | Winner | | Season | PCD Fajr° | PCD Fajr err | Egypt Fajr err | PCD Isha err | Egypt Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | ------------ | -------------- | ------------ | -------------- | ----------------- |
| Jun 21 | 18.73° | **−0.2 min** | −5.1 min | **+0.2 min** | +15.6 min | ★ PCD by 10.1 min | | Jun 21 | 18.73° | **−0.2 min** | −5.1 min | **+0.2 min** | +15.6 min | ★ PCD by 10.1 min |
| Dec 21 | 19.13° | **0.0 min** | −1.7 min | **0.0 min** | −5.9 min | ★ PCD by 3.8 min | | Dec 21 | 19.13° | **0.0 min** | −1.7 min | **0.0 min** | −5.9 min | ★ PCD by 3.8 min |
| Mar 21 | 19.33° | **0.0 min** | −0.8 min | **−0.5 min** | +0.9 min | ★ PCD by 0.6 min | | Mar 21 | 19.33° | **0.0 min** | −0.8 min | **−0.5 min** | +0.9 min | ★ PCD by 0.6 min |
@ -182,10 +182,10 @@ Each row represents one traditional method, tested at its home city across all l
### MUIS: Singapore (20°/18°) ### MUIS: Singapore (20°/18°)
*The highest Fajr angle of any major method. MUIS was designed for Singapore's near-equatorial location (1.35°N). However, PCD computes 18.2–19.6° at Singapore: consistently lower than 20°.* _The highest Fajr angle of any major method. MUIS was designed for Singapore's near-equatorial location (1.35°N). However, PCD computes 18.2–19.6° at Singapore: consistently lower than 20°._
| Season | PCD Fajr° | PCD Fajr err | MUIS Fajr err | PCD Isha err | MUIS Isha err | Winner | | Season | PCD Fajr° | PCD Fajr err | MUIS Fajr err | PCD Isha err | MUIS Isha err | Winner |
| --- | --- | --- | --- | --- | --- | --- | | ------ | --------- | ------------ | ------------- | ------------ | ------------- | ---------------- |
| Jun 21 | 18.21° | **−0.3 min** | −8.3 min | **+0.1 min** | +0.2 min | ★ PCD by 4.0 min | | Jun 21 | 18.21° | **−0.3 min** | −8.3 min | **+0.1 min** | +0.2 min | ★ PCD by 4.0 min |
| Dec 21 | 18.23° | **−0.4 min** | −8.1 min | **−0.1 min** | −1.1 min | ★ PCD by 4.4 min | | Dec 21 | 18.23° | **−0.4 min** | −8.1 min | **−0.1 min** | −1.1 min | ★ PCD by 4.4 min |
| Mar 21 | 19.59° | **+0.2 min** | −1.4 min | **+0.1 min** | −6.3 min | ★ PCD by 3.7 min | | Mar 21 | 19.59° | **+0.2 min** | −1.4 min | **+0.1 min** | −6.3 min | ★ PCD by 3.7 min |
@ -194,10 +194,10 @@ Each row represents one traditional method, tested at its home city across all l
### MSC: New York, USA (seasonal/seasonal) ### MSC: New York, USA (seasonal/seasonal)
*This comparison tests PCD against the MSC seasonal model at MSC's own home (the latitude for which Khalid Shaukat published and validated his tables most extensively).* _This comparison tests PCD against the MSC seasonal model at MSC's own home (the latitude for which Khalid Shaukat published and validated his tables most extensively)._
| Season | PCD Fajr err | MSC err | PCD Isha err | MSC Isha err | Winner | | Season | PCD Fajr err | MSC err | PCD Isha err | MSC Isha err | Winner |
| --- | --- | --- | --- | --- | --- | | ------ | ------------ | ------- | ------------ | ------------ | -------------- |
| Jun 21 | −0.2 min | 0.0 min | +0.4 min | 0.0 min | MSC by 0.3 min | | Jun 21 | −0.2 min | 0.0 min | +0.4 min | 0.0 min | MSC by 0.3 min |
| Dec 21 | +0.1 min | 0.0 min | −0.1 min | 0.0 min | MSC by 0.1 min | | Dec 21 | +0.1 min | 0.0 min | −0.1 min | 0.0 min | MSC by 0.1 min |
| Sep 21 | −0.9 min | 0.0 min | +1.6 min | 0.0 min | MSC by 1.3 min | | Sep 21 | −0.9 min | 0.0 min | +1.6 min | 0.0 min | MSC by 1.3 min |
@ -211,7 +211,7 @@ Each row represents one traditional method, tested at its home city across all l
The "Δ°" column in the scorecard shows the gap between a method's fixed angle and what PCD (and by proxy MSC) indicates is physically appropriate at that city. The "Δ°" column in the scorecard shows the gap between a method's fixed angle and what PCD (and by proxy MSC) indicates is physically appropriate at that city.
| Method | Fixed° | Actual° (PCD avg) | Δ° | Calibration quality | | Method | Fixed° | Actual° (PCD avg) | Δ° | Calibration quality |
| --- | --- | --- | --- | --- | | ------- | ------ | ----------------- | ------ | --------------------------------------------------- |
| IGUT | 17.7° | 18.52° | +0.82° | Excellent: closest fixed calibration | | IGUT | 17.7° | 18.52° | +0.82° | Excellent: closest fixed calibration |
| Egypt | 19.5° | 19.06° | −0.44° | Good: slightly high | | Egypt | 19.5° | 19.06° | −0.44° | Good: slightly high |
| DIBT | 18.0° | 17.40° | −0.60° | Good: slightly high for Ankara | | DIBT | 18.0° | 17.40° | −0.60° | Good: slightly high for Ankara |
@ -232,4 +232,4 @@ The "Δ°" column in the scorecard shows the gap between a method's fixed angle
--- ---
*[Research](Research) | [Methodology](Research-Methodology) | [Global Study](Research-Global-Study) | [Observational Evidence](Research-Observational-Evidence)* _[Research](Research) | [Methodology](Research-Methodology) | [Global Study](Research-Global-Study) | [Observational Evidence](Research-Observational-Evidence)_

5
.wiki/Research-Methodology.md
View file

@ -42,6 +42,7 @@ node home-territory.mjs
``` ```
Computations use: Computations use:
- `getTimesAll()` for raw fractional-hour times across all 14 methods + dynamic simultaneously - `getTimesAll()` for raw fractional-hour times across all 14 methods + dynamic simultaneously
- `getAngles()` for the PCD-computed depression angles - `getAngles()` for the PCD-computed depression angles
- `getMscFajr(date, lat)` / `getMscIsha(date, lat, 'general')` for the MSC minute reference - `getMscFajr(date, lat)` / `getMscIsha(date, lat, 'general')` for the MSC minute reference
@ -75,7 +76,7 @@ Tests across diverse latitudes, longitudes, elevations, and seasons. See [Global
**Coverage:** **Coverage:**
| Region | Cities | Latitude range | | Region | Cities | Latitude range |
| --- | --- | --- | | -------------------- | ---------------------------------------- | --------------- |
| North America | New York (×3), Toronto | 40.7°N – 43.7°N | | North America | New York (×3), Toronto | 40.7°N – 43.7°N |
| Europe | London (×2), Istanbul | 41.0°N – 51.5°N | | Europe | London (×2), Istanbul | 41.0°N – 51.5°N |
| Middle East | Makkah (×2), Tehran, Kuwait City, Riyadh | 21.4°N – 35.7°N | | Middle East | Makkah (×2), Tehran, Kuwait City, Riyadh | 21.4°N – 35.7°N |
@ -107,4 +108,4 @@ Each method tested at the specific city and seasons for which it was designed. T
--- ---
*[Research](Research) | [Global Study](Research-Global-Study) | [Home-Territory Study](Research-Home-Territory) | [Observational Evidence](Research-Observational-Evidence)* _[Research](Research) | [Global Study](Research-Global-Study) | [Home-Territory Study](Research-Home-Territory) | [Observational Evidence](Research-Observational-Evidence)_

7
.wiki/Research-Observational-Evidence.md
View file

@ -25,7 +25,7 @@ Khalid Shaukat conducted and compiled field observations of Fajr and Isha across
Selected reference values from Shaukat's seasonal tables: Selected reference values from Shaukat's seasonal tables:
| Latitude band | Month | Fajr (min before sunrise) | Isha (min after sunset) | | Latitude band | Month | Fajr (min before sunrise) | Isha (min after sunset) |
| --- | --- | --- | --- | | ------------- | ---------- | ------------------------- | ----------------------- |
| 0–10°N | All months | ~108 | ~108 | | 0–10°N | All months | ~108 | ~108 |
| 20–25°N | Jun | ~88–93 | ~82–87 | | 20–25°N | Jun | ~88–93 | ~82–87 |
| 20–25°N | Dec | ~100–104 | ~94–98 | | 20–25°N | Dec | ~100–104 | ~94–98 |
@ -102,6 +102,7 @@ The HMNAO publishes detailed astronomical twilight tables for UK cities. For Lon
- This means no fixed-angle method above 11.8° can compute an Isha time for London in June. - This means no fixed-angle method above 11.8° can compute an Isha time for London in June.
UK Islamic scholars and the Muslim Council of Britain have noted that: UK Islamic scholars and the Muslim Council of Britain have noted that:
- True Fajr at London in summer corresponds to approximately **12–13°** solar depression. - True Fajr at London in summer corresponds to approximately **12–13°** solar depression.
- Methods using 18° (MWL) or higher are unusable for London in summer: they produce times before midnight or N/A. - Methods using 18° (MWL) or higher are unusable for London in summer: they produce times before midnight or N/A.
- The MSC model (which PCD implements) yields 120 minutes before sunrise at London in June, corresponding to approximately 12°: matching these observations. - The MSC model (which PCD implements) yields 120 minutes before sunrise at London in June, corresponding to approximately 12°: matching these observations.
@ -125,7 +126,7 @@ The 17.7° Fajr angle for Tehran (35.7°N, 1191m elevation) was derived from obs
Compiled from the published studies cited on this page and the automated comparison study. See [Verified Observations](Research-Verified-Observations) for the full comparison matrix including computed errors for all methods. Compiled from the published studies cited on this page and the automated comparison study. See [Verified Observations](Research-Verified-Observations) for the full comparison matrix including computed errors for all methods.
| Latitude band | Season | Observed Fajr° | PCD output | Fixed 18° (MWL) | Fixed 15° (ISNA) | | Latitude band | Season | Observed Fajr° | PCD output | Fixed 18° (MWL) | Fixed 15° (ISNA) |
| --- | --- | --- | --- | --- | --- | | ------------------------ | ------ | -------------- | ---------------- | ----------------- | ---------------- |
| 0–6°S (Jakarta) | Jun | 13–19°† | **18.72°** | 18° ≈ | 15° ✗ | | 0–6°S (Jakarta) | Jun | 13–19°† | **18.72°** | 18° ≈ | 15° ✗ |
| 1–2°N (Singapore) | Dec | ~18° | **18.23°** | 18° ✓ | 15° ✗ | | 1–2°N (Singapore) | Dec | ~18° | **18.23°** | 18° ✓ | 15° ✗ |
| 21–30°N (Egypt, Arabia) | Annual | ~13–15°‡ | **19.4–19.8°** | 18° ✗✗ | 15° ≈ | | 21–30°N (Egypt, Arabia) | Annual | ~13–15°‡ | **19.4–19.8°** | 18° ✗✗ | 15° ≈ |
@ -198,4 +199,4 @@ The full validation scripts are in the repository under `scripts/validate-real-w
--- ---
*[Research](Research) | [Methodology](Research-Methodology) | [Global Study](Research-Global-Study) | [Home-Territory Study](Research-Home-Territory)* _[Research](Research) | [Methodology](Research-Methodology) | [Global Study](Research-Global-Study) | [Home-Territory Study](Research-Home-Territory)_

30
.wiki/Research-Verified-Observations.md
View file

@ -23,7 +23,7 @@ Both study types test the same question: does the calculated Fajr time match whe
### Angle-Based Field Studies ### Angle-Based Field Studies
| ID | Location | Latitude | Elevation | Period | N | Instrument | Observed° | Source | | ID | Location | Latitude | Elevation | Period | N | Instrument | Observed° | Source |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | | ----- | ----------------------------- | ----------- | --------- | --------- | --------- | ----------------------- | ----------------------- | ------------------- |
| TUB-S | Tubruq, Libya: sea horizon | 32.1°N | 25 m | 2000–2003 | 429 | Naked eye | **13.48°** | Odeh 2004 | | TUB-S | Tubruq, Libya: sea horizon | 32.1°N | 25 m | 2000–2003 | 429 | Naked eye | **13.48°** | Odeh 2004 |
| TUB-D | Tubruq, Libya: desert horizon | 32.1°N | 25 m | 2000–2003 | 623 | Naked eye | **13.14°** | Odeh 2004 | | TUB-D | Tubruq, Libya: desert horizon | 32.1°N | 25 m | 2000–2003 | 623 | Naked eye | **13.14°** | Odeh 2004 |
| EGY | Egypt multi-site (4 cities) | 24–31°N | 10–95 m | 1984–1987 | : | Photometric + naked eye | **14.7°** mean | ENRIA 1987 | | EGY | Egypt multi-site (4 cities) | 24–31°N | 10–95 m | 1984–1987 | : | Photometric + naked eye | **14.7°** mean | ENRIA 1987 |
@ -38,7 +38,7 @@ Both study types test the same question: does the calculated Fajr time match whe
### Time-Based Verification Points ### Time-Based Verification Points
| ID | Location | Latitude | Date | Observed Fajr | Observer | Source | | ID | Location | Latitude | Date | Observed Fajr | Observer | Source |
| --- | --- | --- | --- | --- | --- | --- | | --- | --------------------- | -------- | ------------ | ------------- | ------------------------------- | ----------------------------------- |
| MIA | Miami Beach, FL, USA | 25.8°N | Dec 3, 2000 | 5:45 AM EST | Khalid Shaukat + 4 co-observers | moonsighting.com | | MIA | Miami Beach, FL, USA | 25.8°N | Dec 3, 2000 | 5:45 AM EST | Khalid Shaukat + 4 co-observers | moonsighting.com |
| PAM | Pampigny, Switzerland | 46.6°N | Jun 23, 2016 | 3:56 AM CEST | Khalid Shaukat | moonsighting.com | | PAM | Pampigny, Switzerland | 46.6°N | Jun 23, 2016 | 3:56 AM CEST | Khalid Shaukat | moonsighting.com |
| JKT | Jakarta, Indonesia | 6.2°S | May 8, 2019 | 5:01 AM WIB | Community observers (multiple) | Indonesian Islamic astronomy forums | | JKT | Jakarta, Indonesia | 6.2°S | May 8, 2019 | 5:01 AM WIB | Community observers (multiple) | Indonesian Islamic astronomy forums |
@ -65,7 +65,7 @@ For time-based points, `getTimesAll(date, lat, lng, tz, elev)` was used to obtai
Each study location was assigned the regional method most likely in use there: Each study location was assigned the regional method most likely in use there:
| Location | Regional method | Angle | | Location | Regional method | Angle |
| --- | --- | --- | | ------------- | ----------------- | ----- |
| Libya / Egypt | Egypt (ENRIA) | 19.5° | | Libya / Egypt | Egypt (ENRIA) | 19.5° |
| Saudi Arabia | Umm Al-Qura (UAQ) | 18.5° | | Saudi Arabia | Umm Al-Qura (UAQ) | 18.5° |
| UK | MWL | 18° | | UK | MWL | 18° |
@ -83,7 +83,7 @@ Each study location was assigned the regional method most likely in use there:
For each study: observed depression angle, PCD computed mean angle over study months, equivalent MSC angle, and the regional fixed-angle method. Errors are absolute differences in degrees. For each study: observed depression angle, PCD computed mean angle over study months, equivalent MSC angle, and the regional fixed-angle method. Errors are absolute differences in degrees.
| Study | Obs° | PCD° | PCD err | MSC° | MSC err | Regional | Reg° | Reg err | Winner | | Study | Obs° | PCD° | PCD err | MSC° | MSC err | Regional | Reg° | Reg err | Winner |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | ----------------------------------------- | ----- | --------- | --------- | ----- | ------- | -------- | -------- | --------- | ------ |
| TUB-S Tubruq sea (32.1°N, Oct–Dec) | 13.48 | 19.17 | 5.69° | 18.92 | 5.44° | Egypt | 19.5 | 6.02° | MSC | | TUB-S Tubruq sea (32.1°N, Oct–Dec) | 13.48 | 19.17 | 5.69° | 18.92 | 5.44° | Egypt | 19.5 | 6.02° | MSC |
| TUB-D Tubruq desert (32.1°N, Oct–Dec) | 13.14 | 19.17 | 6.03° | 18.92 | 5.78° | Egypt | 19.5 | 6.36° | MSC | | TUB-D Tubruq desert (32.1°N, Oct–Dec) | 13.14 | 19.17 | 6.03° | 18.92 | 5.78° | Egypt | 19.5 | 6.36° | MSC |
| EGY Egypt multi-site (28°N mean, annual) | 14.70 | 19.37 | 4.67° | 19.30 | 4.60° | Egypt | 19.5 | 4.80° | MSC | | EGY Egypt multi-site (28°N mean, annual) | 14.70 | 19.37 | 4.67° | 19.30 | 4.60° | Egypt | 19.5 | 4.80° | MSC |
@ -98,7 +98,7 @@ For each study: observed depression angle, PCD computed mean angle over study mo
### Mean Absolute Error ### Mean Absolute Error
| Method | MAE (angle studies) | Studies won | | Method | MAE (angle studies) | Studies won |
| --- | --- | --- | | -------------------- | ------------------- | ------------------------------------- |
| MSC (seasonal model) | **3.71°** | 6/10 | | MSC (seasonal model) | **3.71°** | 6/10 |
| PCD (dynamic) | 3.83° | 0/10 | | PCD (dynamic) | 3.83° | 0/10 |
| Regional fixed-angle | 4.06° | 2/10 (Hail-UAQ, Blackburn winter-MWL) | | Regional fixed-angle | 4.06° | 2/10 (Hail-UAQ, Blackburn winter-MWL) |
@ -117,7 +117,7 @@ For each study: observed depression angle, PCD computed mean angle over study mo
**Computed results:** **Computed results:**
| Method | Fajr time | Error vs observed | Angle used | | Method | Fajr time | Error vs observed | Angle used |
| --- | --- | --- | --- | | ------------- | --------- | ------------------- | ------------- |
| Observed | 05:45:00 | : | 14.75° | | Observed | 05:45:00 | : | 14.75° |
| PCD | 05:23:42 | **-21.3 min early** | 19.46° | | PCD | 05:23:42 | **-21.3 min early** | 19.46° |
| MSC reference | 05:23:48 | -21.2 min early | 19.5° (equiv) | | MSC reference | 05:23:48 | -21.2 min early | 19.5° (equiv) |
@ -139,7 +139,7 @@ Sunrise: 06:51:48 EST. The observation places Fajr at 66.8 minutes before sunris
**Computed results:** **Computed results:**
| Method | Fajr time | Error vs observed | Angle used | | Method | Fajr time | Error vs observed | Angle used |
| --- | --- | --- | --- | | ------------- | --------- | ------------------- | --------------------------- |
| Observed | 03:56:00 | : | 13.39° | | Observed | 03:56:00 | : | 13.39° |
| PCD | 03:43:21 | **-12.6 min early** | 14.28° | | PCD | 03:43:21 | **-12.6 min early** | 14.28° |
| MSC reference | 03:45:57 | -10.1 min early | : | | MSC reference | 03:45:57 | -10.1 min early | : |
@ -161,7 +161,7 @@ Sunrise: 05:40:57 CEST. The observation places Fajr at 104.9 minutes before sunr
**Computed results:** **Computed results:**
| Method | Fajr time | Error vs observed | Angle used | | Method | Fajr time | Error vs observed | Angle used |
| --- | --- | --- | --- | | ------------- | --------- | ------------------- | ---------- |
| Observed | 05:01:00 | : | 13.13° | | Observed | 05:01:00 | : | 13.13° |
| PCD | 04:35:11 | **-25.8 min early** | 19.49° | | PCD | 04:35:11 | **-25.8 min early** | 19.49° |
| MSC reference | 04:35:27 | -25.6 min early | : | | MSC reference | 04:35:27 | -25.6 min early | : |
@ -191,7 +191,7 @@ The most surprising and important finding in this dataset is the consistent disa
Five independent study programs at five different locations between 27.5°N and 32.1°N all find Fajr in the range 13–15°: Five independent study programs at five different locations between 27.5°N and 32.1°N all find Fajr in the range 13–15°:
| Study | Location | Lat | Observed° | PCD° | MSC° | Error | | Study | Location | Lat | Observed° | PCD° | MSC° | Error |
| --- | --- | --- | --- | --- | --- | --- | | ------------------ | ------------------ | ------- | --------- | ------ | ------ | ----- |
| Odeh 2004 (sea) | Tubruq, Libya | 32.1°N | 13.48° | 19.17° | 18.92° | ~5.5° | | Odeh 2004 (sea) | Tubruq, Libya | 32.1°N | 13.48° | 19.17° | 18.92° | ~5.5° |
| Odeh 2004 (desert) | Tubruq, Libya | 32.1°N | 13.14° | 19.17° | 18.92° | ~5.8° | | Odeh 2004 (desert) | Tubruq, Libya | 32.1°N | 13.14° | 19.17° | 18.92° | ~5.8° |
| ENRIA 1987 | Egypt (4 sites) | 24–31°N | 14.7° | 19.37° | 19.30° | ~4.6° | | ENRIA 1987 | Egypt (4 sites) | 24–31°N | 14.7° | 19.37° | 19.30° | ~4.6° |
@ -225,7 +225,7 @@ In summer at high latitudes, the sun never reaches 18° and PCD correctly adapts
## Summary: Method Performance by Scenario ## Summary: Method Performance by Scenario
| Scenario | Best method | Runner-up | Worst method | | Scenario | Best method | Runner-up | Worst method |
| --- | --- | --- | --- | | ----------------------------- | --------------- | -------------------------------- | ----------------------- |
| High latitude (>48°N) summer | PCD / MSC | : | Fixed ≥18° (fails) | | High latitude (>48°N) summer | PCD / MSC | : | Fixed ≥18° (fails) |
| High latitude (>48°N) winter | Fixed 18° (MWL) | : | PCD / MSC (too early) | | High latitude (>48°N) winter | Fixed 18° (MWL) | : | PCD / MSC (too early) |
| Mid-latitude (36–48°N) summer | ISNA (15°) | PCD (close) | Fixed 18° (early) | | Mid-latitude (36–48°N) summer | ISNA (15°) | PCD (close) | Fixed 18° (early) |
@ -257,18 +257,18 @@ The script computes all values in this page from first principles using pray-cal
## Citations ## Citations
- **Odeh, M.S.** (2004). "New Criterion for Lunar Crescent Visibility." *Experimental Astronomy*, 18(1–3), 39–64. - **Odeh, M.S.** (2004). "New Criterion for Lunar Crescent Visibility." _Experimental Astronomy_, 18(1–3), 39–64.
- **Egyptian National Research Institute of Astronomy and Geophysics (ENRIA).** (1987). Multi-station photometric study of astronomical twilight at Alexandria, Cairo, Assiut, and Aswan. Internal report, referenced in Egyptian General Authority schedules. - **Egyptian National Research Institute of Astronomy and Geophysics (ENRIA).** (1987). Multi-station photometric study of astronomical twilight at Alexandria, Cairo, Assiut, and Aswan. Internal report, referenced in Egyptian General Authority schedules.
- **Al-Shehri, A.M.** (2017). "Empirical Determination of Fajr Prayer Time at Hail, Saudi Arabia." *Journal of the Astronomical Society of Saudi Arabia*. - **Al-Shehri, A.M.** (2017). "Empirical Determination of Fajr Prayer Time at Hail, Saudi Arabia." _Journal of the Astronomical Society of Saudi Arabia_.
- **Al-Azhar Astronomical Society (AAAS).** (2019). Photometric study at Wadi Al-Rayan, Fayum. Presented at the 2019 Islamic Astronomical Conference, Cairo. - **Al-Azhar Astronomical Society (AAAS).** (2019). Photometric study at Wadi Al-Rayan, Fayum. Presented at the 2019 Islamic Astronomical Conference, Cairo.
- **Duff, M.I. & Duff, M.H.** (1989). "Fajr and Isha at High Latitudes." Field study, Blackburn, England. Published summary in *Muslim Community journal*. - **Duff, M.I. & Duff, M.H.** (1989). "Fajr and Isha at High Latitudes." Field study, Blackburn, England. Published summary in _Muslim Community journal_.
- **Shaukat, K.** (1985). Chicago field observations. Unpublished; referenced on moonsighting.com. - **Shaukat, K.** (1985). Chicago field observations. Unpublished; referenced on moonsighting.com.
- **LAPAN (Lembaga Penerbangan dan Antariksa Nasional).** (2017). Sky brightness survey at six Indonesian stations. Technical report. - **LAPAN (Lembaga Penerbangan dan Antariksa Nasional).** (2017). Sky brightness survey at six Indonesian stations. Technical report.
- **Zambri, M. & Anwar, M.S.** (2017). "Digital Sky Brightness at Fajr: A DSLR Photometric Study." *Proceedings of the Malaysian Astronomical Congress*. - **Zambri, M. & Anwar, M.S.** (2017). "Digital Sky Brightness at Fajr: A DSLR Photometric Study." _Proceedings of the Malaysian Astronomical Congress_.
- **Shaukat, K.** (2016). Personal field observation log, Pampigny, Switzerland. Archived on moonsighting.com. - **Shaukat, K.** (2016). Personal field observation log, Pampigny, Switzerland. Archived on moonsighting.com.
- **Shaukat, K.** (2000). Personal field observation log, Miami Beach, FL. Archived on moonsighting.com. - **Shaukat, K.** (2000). Personal field observation log, Miami Beach, FL. Archived on moonsighting.com.
- **Indonesian Islamic Astronomy Forum.** (2019). Community observation report, Jakarta, May 8, 2019. - **Indonesian Islamic Astronomy Forum.** (2019). Community observation report, Jakarta, May 8, 2019.
--- ---
*[Research](Research) | [Methodology](Research-Methodology) | [Global Study](Research-Global-Study) | [Home-Territory Study](Research-Home-Territory) | [Observational Evidence](Research-Observational-Evidence)* _[Research](Research) | [Methodology](Research-Methodology) | [Global Study](Research-Global-Study) | [Home-Territory Study](Research-Home-Territory) | [Observational Evidence](Research-Observational-Evidence)_

8
.wiki/Research.md
View file

@ -9,7 +9,7 @@ The methodology, data, and conclusions here are reproducible. All computations w
## Key Findings ## Key Findings
| Metric | PCD (Dynamic) | Best Fixed Method | All Methods Avg | | Metric | PCD (Dynamic) | Best Fixed Method | All Methods Avg |
| --- | --- | --- | --- | | ---------------------------------------------- | ------------- | --------------------- | ----------------- |
| Global MAE: Fajr | **0.64 min** | 10.21 min (Qatar) | 18.6 min | | Global MAE: Fajr | **0.64 min** | 10.21 min (Qatar) | 18.6 min |
| Global MAE: Isha | **1.30 min** | 10.22 min (Qatar/UAQ) | 18.8 min | | Global MAE: Isha | **1.30 min** | 10.22 min (Qatar/UAQ) | 18.8 min |
| Global MAE: Combined | **0.97 min** | 10.21 min (Qatar) | 18.7 min | | Global MAE: Combined | **0.97 min** | 10.21 min (Qatar) | 18.7 min |
@ -25,7 +25,7 @@ PCD is the only non-trivial method that is globally accurate: it tracks the obse
## Research Pages ## Research Pages
| Page | Description | | Page | Description |
| --- | --- | | --------------------------------------------------------- | ----------------------------------------------------------------- |
| [Methodology](Research-Methodology) | Reference standard, measurement approach, test infrastructure | | [Methodology](Research-Methodology) | Reference standard, measurement approach, test infrastructure |
| [Global Accuracy Study](Research-Global-Study) | 18-city comparison across all latitudes and seasons | | [Global Accuracy Study](Research-Global-Study) | 18-city comparison across all latitudes and seasons |
| [Home-Territory Study](Research-Home-Territory) | Each method tested at the city and season it was designed for | | [Home-Territory Study](Research-Home-Territory) | Each method tested at the city and season it was designed for |
@ -52,7 +52,7 @@ where `H` is the hour angle, `a` is the target altitude, `φ` is latitude, and `
Four corrections are applied to the base angle: Four corrections are applied to the base angle:
| Correction | Formula | Effect | | Correction | Formula | Effect |
| --- | --- | --- | | ---------------------- | ------------------------------------------------ | --------------------------- | -------------------- | --- | ------------- | ------------------------ |
| Earth-Sun distance | `Δr = −0.5 × ln(r)` where `r` is in AU | ±0.015° over the year | | Earth-Sun distance | `Δr = −0.5 × ln(r)` where `r` is in AU | ±0.015° over the year |
| Fourier harmonic | `0.1·( | φ | /45)·sin(θ) + 0.05·( | φ | /45)·sin(2θ)` | ±0.15° at high latitudes | | Fourier harmonic | `0.1·( | φ | /45)·sin(θ) + 0.05·( | φ | /45)·sin(2θ)` | ±0.15° at high latitudes |
| Atmospheric refraction | Bennett/Saemundsson formula at computed altitude | Variable by elevation | | Atmospheric refraction | Bennett/Saemundsson formula at computed altitude | Variable by elevation |
@ -79,4 +79,4 @@ These corrections are small individually (each < 0.2°) but compound to produce
--- ---
*[Home](Home) | [API Reference](API-Reference) | [Dynamic Algorithm](Dynamic-Algorithm) | [Traditional Methods](Traditional-Methods)* _[Home](Home) | [API Reference](API-Reference) | [Dynamic Algorithm](Dynamic-Algorithm) | [Traditional Methods](Traditional-Methods)_

4
.wiki/Traditional-Methods.md
View file

@ -6,7 +6,7 @@ field returned by `getTimesAll` and `calcTimesAll`. Each entry is `[fajrTime, is
## Method Table ## Method Table
| ID | Name | Fajr | Isha | Region | | ID | Name | Fajr | Isha | Region |
|----|------|------|------|--------| | --------- | --------------------------------------------- | -------- | -------- | -------------- |
| `UOIF` | Union des Organisations Islamiques de France | 12° | 12° | France | | `UOIF` | Union des Organisations Islamiques de France | 12° | 12° | France |
| `ISNACA` | IQNA / Islamic Council of North America | 13° | 13° | Canada | | `ISNACA` | IQNA / Islamic Council of North America | 13° | 13° | Canada |
| `ISNA` | FCNA / Islamic Society of North America | 15° | 15° | US, UK, AU, NZ | | `ISNA` | FCNA / Islamic Society of North America | 15° | 15° | US, UK, AU, NZ |
@ -142,4 +142,4 @@ offsets from `getMscFajr` / `getMscIsha`.
--- ---
*[Back to Home](Home) | [Dynamic Algorithm](Dynamic-Algorithm) | [API Reference](API-Reference)* _[Back to Home](Home) | [Dynamic Algorithm](Dynamic-Algorithm) | [API Reference](API-Reference)_

18
.wiki/Twilight-Physics.md
View file

@ -7,13 +7,13 @@ evaluating any prayer time calculation.
Neither the Quran nor Hadith specifies a numeric angle. The required criteria are: Neither the Quran nor Hadith specifies a numeric angle. The required criteria are:
- **Fajr**: The appearance of *Subh Sadiq* (true dawn): a broad, horizontal - **Fajr**: The appearance of _Subh Sadiq_ (true dawn): a broad, horizontal
whitening of the eastern sky that stretches from north to south. Distinguished from whitening of the eastern sky that stretches from north to south. Distinguished from
*Subh Kadhib* (false dawn), which is a vertical column of zodiacal light that _Subh Kadhib_ (false dawn), which is a vertical column of zodiacal light that
appears and then vanishes before true dawn. appears and then vanishes before true dawn.
- **Isha**: The disappearance of *Shafaq*: the twilight glow remaining in the western - **Isha**: The disappearance of _Shafaq_: the twilight glow remaining in the western
sky after sunset. Classical scholars disagreed on which glow: *shafaq ahmer* (red sky after sunset. Classical scholars disagreed on which glow: _shafaq ahmer_ (red
glow, which fades first) or *shafaq abyad* (white glow, which persists longer). glow, which fades first) or _shafaq abyad_ (white glow, which persists longer).
Shia tradition and the IGUT/Tehran method use shafaq ahmer; Sunni tradition generally Shia tradition and the IGUT/Tehran method use shafaq ahmer; Sunni tradition generally
uses shafaq abyad. uses shafaq abyad.
@ -24,7 +24,7 @@ Any calculation must reproduce these observable cues as closely as possible.
Astronomers define twilight by the Sun's depression angle below the true horizon: Astronomers define twilight by the Sun's depression angle below the true horizon:
| Stage | Sun Depression | Sky Condition | | Stage | Sun Depression | Sky Condition |
|-------|---------------|---------------| | ------------ | -------------- | ------------------------------------------------------ |
| Civil | 0–6° | Horizon clearly visible; enough light for outdoor work | | Civil | 0–6° | Horizon clearly visible; enough light for outdoor work |
| Nautical | 6–12° | Horizon visible at sea; brightest stars visible | | Nautical | 6–12° | Horizon visible at sea; brightest stars visible |
| Astronomical | 12–18° | Sky nearly dark; all but faintest objects visible | | Astronomical | 12–18° | Sky nearly dark; all but faintest objects visible |
@ -87,7 +87,7 @@ at most latitudes: the visual threshold for dawn is reached at a lesser depressi
Several major observational campaigns have mapped true Fajr/Isha angles: Several major observational campaigns have mapped true Fajr/Isha angles:
| Location | Latitude | Fajr Angle (observed) | Source | | Location | Latitude | Fajr Angle (observed) | Source |
|----------|----------|----------------------|--------| | -------------------------- | -------- | --------------------- | --------------------------- |
| Indonesia (multiple sites) | ~6°S–7°S | 16.5° | National Observatory Study | | Indonesia (multiple sites) | ~6°S–7°S | 16.5° | National Observatory Study |
| Saudi Arabia (desert) | ~27.5°N | 14.0° avg | Hail Campaign | | Saudi Arabia (desert) | ~27.5°N | 14.0° avg | Hail Campaign |
| Egypt (multiple sites) | ~26–30°N | 14.56° avg | 2015–2019 photometric study | | Egypt (multiple sites) | ~26–30°N | 14.56° avg | 2015–2019 photometric study |
@ -105,7 +105,7 @@ horizon after evening twilight, or from the eastern horizon before dawn. It is m
prominent at equatorial latitudes in spring (evening) and autumn (morning), and prominent at equatorial latitudes in spring (evening) and autumn (morning), and
requires very dark skies to see. requires very dark skies to see.
False dawn (*Subh Kadhib*) is the zodiacal light seen in the east before true dawn. False dawn (_Subh Kadhib_) is the zodiacal light seen in the east before true dawn.
Observers have reported it disappearing by around 15–16° Sun depression, after which Observers have reported it disappearing by around 15–16° Sun depression, after which
the genuine horizontal twilight takes over. The distinction matters for Fajr timing: the genuine horizontal twilight takes over. The distinction matters for Fajr timing:
Subh Sadiq (true dawn) is later than any zodiacal light brightening. Subh Sadiq (true dawn) is later than any zodiacal light brightening.
@ -138,4 +138,4 @@ MSC "general" shafaq mode.
--- ---
*[Back to Home](Home) | [Dynamic Algorithm](Dynamic-Algorithm) | [High-Latitude Handling](High-Latitude)* _[Back to Home](Home) | [Dynamic Algorithm](Dynamic-Algorithm) | [High-Latitude Handling](High-Latitude)_