Turn anticipation distance calculator

Enter the planned turn radius and the smaller course change, and it applies the standard tangent geometry for a fly-by waypoint. The result is expressed in the same distance unit as the radius, making the calculator useful with metres, nautical miles, feet, or any other consistent planning unit.

Understand the fly-by waypoint geometry

A fly-by turn starts before the waypoint because an aircraft cannot change heading instantaneously at the leg intersection. For two straight legs joined by a circular arc, the tangent points lie the same distance from the waypoint along each leg. A right triangle formed by the turn centre, waypoint, and tangent point gives the relationship distance = turn radius × tan(course change ÷ 2). This calculator evaluates that relationship directly. The course change is the smaller angle between the inbound and outbound courses, from zero degrees up to but not including 180 degrees. A zero-degree change produces zero anticipation because both legs continue in the same direction. As the change grows, the tangent point moves farther from the waypoint. An exact 180-degree reversal is rejected: the tangent becomes unbounded, and a single circular fly-by arc between the two collinear, opposite legs does not have a finite anticipation point under this model. The output includes the half-angle in radians and the formula used, making the numerical result straightforward to audit in a flight-planning worksheet or software test.

Choose a radius and course change consistently

Use the turn radius that belongs to the aircraft speed and planned bank angle for the relevant phase of flight. This capability does not derive radius from speed, bank, wind, or performance limits; it treats the supplied radius as the horizontal geometric radius of the intended ground-path arc. The anticipation distance inherits that radius unit. If the radius is 1.5 nautical miles, the result is in nautical miles; if it is 2,400 metres, the result is in metres. Supply the course change in degrees as a non-negative value smaller than 180. Determine it as the smaller angular difference between the inbound and outbound courses, accounting for the wrap through north. For example, a transition from 350 degrees to 020 degrees is a 30-degree course change, not 330 degrees. The calculation uses course change magnitude, so left and right turns with the same radius and angle have the same distance. Turn direction can be handled separately by navigation logic. Numeric strings are accepted for API convenience, while missing, infinite, negative-radius, out-of-range, and exact-reversal inputs return a clear invalid-input error.

Interpret the result and its operational limits

The returned anticipation distance is the along-leg distance from the theoretical waypoint back to the point where the constant-radius arc becomes tangent to the inbound leg. Under ideal planar geometry, beginning the turn there and maintaining the stated radius places the exit tangent on the outbound leg at the corresponding distance beyond the waypoint. Real navigation systems may add roll-in, roll-out, wind, groundspeed variation, containment, obstacle clearance, and guidance-law corrections. Those effects are intentionally outside this compact analytic calculation. Treat the result as a geometric planning value or a component inside a broader flight-management model, not as standalone operational authorization. Check that the selected radius is feasible for the aircraft, speed, bank limit, altitude, and environmental conditions, and follow approved procedures and certified avionics where required. The deterministic output is especially useful for validating route-design spreadsheets, producing reproducible software fixtures, or comparing a system’s nominal tangent geometry. Because no network, current weather, aircraft database, or random source is involved, identical inputs always produce identical values. Via the API, each calculation costs $0.002; the browser calculation can use the same pure solving logic.