The Mathematics of Calculating Prayer Times at 35,000 Feet
Calculating prayer times on the ground is a solved problem of static trigonometry. Calculating prayer times in the air, however, is a dynamic problem involving spherical geometry, altitude adjustments, and relative velocity. This document outlines the three core variables our algorithm processes to deliver accurate results.
1. The Dip of the Horizon (Altitude Adjustment)
The most critical factor in aviation prayer times is altitude. On the ground, the horizon is effectively at eye level (0 degrees). However, as an aircraft ascends to cruising altitude (approx. 35,000–40,000 ft), the observer can see much further over the curvature of the Earth.
This creates a phenomenon known as the Dip of the Horizon. Practically, this means the sun sets later and rises earlier than it does for a person on the ground directly below the plane.
Where θ is the dip angle in degrees and h is altitude in meters.
Our calculator dynamically adjusts the standard Maghrib (Sunset) and Fajr (Sunrise) angles based on the flight's projected altitude curve, ensuring you do not break your fast prematurely.
2. Geodesic Paths (Great Circles)
A common misconception is that planes fly in straight lines on a map. In reality, aircraft follow Geodesic paths (Great Circles), which appear as curved arcs on 2D projections. This is the shortest distance between two points on a sphere.
Because of this, a flight from New York to Dubai flies far North over Europe, not in a straight line across the Atlantic. Our algorithm maps the flight coordinates along this arc to determine the exact latitude and longitude of the aircraft at every minute of the journey.
3. Relative Velocity Calculation
Finally, the speed of the aircraft affects the length of the "day." If you are flying West (chasing the sun), you are effectively extending the daylight hours. If the plane flies fast enough, it can "freeze" the time of Maghrib.
Conversely, flying East (towards the sunrise) compresses the night significantly. Our tool calculates the Time at Position by interpolating the aircraft's velocity against the rotation of the Earth, providing a precise window for when prayer times enter and exit.