HM Nautical Almanac Office q-criterion (1997)
B.D. Yallop · NAO Technical Note No. 69Developed by B.D. Yallop at the HM Nautical Almanac Office in 1997, this method uses a statistical geometric model trained on historical crescent sighting records. It produces a single q-parameter derived from the Arc of Vision (ARCV) and the estimated crescent width (W'), and maps it to five classification zones.
The classification boundaries were derived empirically from records of successful and unsuccessful naked-eye and binocular sightings collected over many decades worldwide. It remains the most widely referenced standard for institutional crescent visibility prediction.
| Code | Meaning | q Parameter | Map Colour |
|---|---|---|---|
| A | Easily Visible with naked eye | q > 0.216 | ■ Dark Green |
| B | Visible under perfect conditions | −0.014 < q ≤ 0.216 | ■ Green |
| C | May require optical aid to find; naked-eye visible once found | −0.160 < q ≤ −0.014 | ■ Yellow |
| D | Probably not visible — optical aid needed | −0.232 < q ≤ −0.160 | ■ Orange |
| E | Impossible / Not visible even with optical aid | q ≤ −0.232 | ■ Red |
This platform provides astronomical modelling of crescent visibility based on the Yallop q-criterion. Results are probabilistic and for educational purposes only. Final religious decisions remain with local authorities.