FAQ: Flight Paths

Q: How is a path specified?

A: A path consists of two more more locations, separated by dashes. For example, ORD-SFO specifies a path from ORD (Chicago O'Hare International Airport) to SFO (San Francisco International Airport).

Q: Can multiple paths be specified?

A: Independent paths can be placed on separate lines or separated by commas or semi-colons. A single path can consist of more than two locations for multi-hop routings. For example, LAX-JFK,LAX-TUS-FTW-BNA-LGA compares the contemporary non-stop flight from Los Angeles to New York to the 1941 vintage route of American Airlines' Flight 004, the "Limited Mercury," which was flown using a Douglas DC-3.

Q: Why do actual flight paths differ from what is shown on the maps?

A: Eastbound flights often fly a path that's closer to the equator (more southerly in the northern hemisphere) than the great circle path in order to hitch a ride on strong tailwinds. These tail winds result in a shorter flying time for the longer ground path.

Various other factors may also dictate a flight path that is longer than the great circle path. A track system is used across the North Atlantic to efficently and safely manage the larger number of flights, even though this may result in a less efficient path for a given flight. There may also be a need to avoid certain areas, including areas too far from a suitable landing point (see the ETOPS section of the FAQ) or over unfriendly countries.

Q: What does specifying the ground speed do?

A: If a ground speed is specified the distance table will include a time computed from the distance and speed. This assumes the entire trip will occur at the selected speed, ignoring acceleration and deceleration.

Q: How is Mach used to calculate trip time?

A: A Mach number is a fraction of the speed of sound. The speed of sound varies as a function of type of gas (dry air is different from humid air!), pressure, and temperature, so there isn't a straightforward conversion of Mach to distance/time.

The Great Circle Mapper assumes the speed of sound is 574 knots (about 660.5 miles per hour or 1063 kilometers per hour), which is a close approximation for the lower stratospheric altitudes from 36,000 feet to well above 65,000 feet where transport jets usually fly, assuming a temperature of -70°F. More information is available from the following resources:

• Speed of Sound (NASA)
• Earth Atmosphere Model (NASA)
• Speed of Sound & Standard Atmosphere (Aerospaceweb.org)

Q: Why are statute miles and miles/hour the default instead of nautical miles and knots?

A: The Great Circle Mapper serves a diverse community of users. Some are pilots and would prefer nautical miles and knots. Others large groups of users, frequent fliers being one example, are less likely to understand the distinction between nautical and statute miles and might be confused or annoyed if the default were different. Hence, the site uses defaults which are least likely to cause confusion.

Perhaps a better answer would be if you could choose your own default. That capability will appear eventually.

Q: What types of paths can be drawn?

A: The default is to draw geodesic paths, commonly known as great circles. Alternatives include rhumb lines, Bézier curves, spline paths, and longest paths.

Q: What is a geodesic path?

A: The default is to draw geodesic ("great circle") paths. A great circle path is the shortest path on the surface of a sphere between two points on that sphere. Since Earth is not a true sphere, the proper term is a geodesic path though great circle is commonly used.

Q: What is a rhumb line?

A: A rhumb line, also known as a loxodrome, is a path of constant heading. In almost all cases a rhumb line will be longer than a geodesic path, but it was far easier to navigate in a time when the primary tools were a magnetic compass, a sextant, and maybe a decent chronometer.

Q: What is a Bézier curve?

A: A Bézier curve is a parametric curve defined by its end points and one or more control points which tug the curve toward them. A good overview of these curves can be found at The Birth of Bézier Curves & How It Shaped Graphic Design.

The Great Circle Mapper offers Bézier curves for creating network diagrams and similar "maps" where geodesic paths don't do a good job of illustration. Cubic Bézier curves are used, with two control points per path segment, defined relative to the end points of the segment. The user should configure these points to generate a suitable curve. No single configuration works for all cases so some experimentation may be necessary.

Q: How are Bézier control points configured?

A: The Map Conf tab of map pages includes a Bézier Configuration field, which populates to PB parameter in a map URL. In its basic form, this option specifies a distance along the geodesic path (as a percentage) and an offset from the initial angle of the geodesic path. A simple example is

25%@-30°

This says that the first control point should be 25% along the geodesic path, 30 degrees to the left of the initial heading along the geodesic path. The second control point is formed the same way, working backwards from the end of the geodesic path, except the sign of the offset is flipped, so in this example the second control point would be 30 degrees to the right of the reverse path. Here's how they look for an SFO-ORD map:

The % and ° can be omitted: 25@-30.

Numbers are rounded to integers and the percentage is clamped to the range [-99% .. 99%].

A different configuration for the second control point can be specified if desired. This example specifies that the second point should be 45° to the right of the reverse geodesic path:

25@-30/25@45

If there are multiple paths form the same origin, it may be desirable to adjust the angular offset from starting point for each path. For example,

25@-30-10

places the control point for the first path 30° to the left of the geodesic path, then 40° to the left for the second path, etc. This is illustrated in the Featured Map for 24 March 2023.

Q: What are good choices for Bézier configuration values?

A: For the distance along the geodesic path 25% seems to be good, though for some cases 33% may be worth a try.

As for angles relative to the geodesic, both the magnitude and sign need to be considered. 30° or 45° seem like good starting value for the magnitude for most cases though angles of 90º or more can be interesting for special cases. Sign (negative is left, positive is right) depends on the path; there does not seem to be an easy rule.

Q: What is a spline path?

A: A spline path is a special case of a Bézier curve for paths with multiple segments. Bézier control points are calculated to produce a smooth curve through intermediate points along the path.

Q: What is a longest path?

A: A longest path is like a geodesic path except in reverse: the longest path starts 180 degrees opposite from the geodesic path and continues the long way. It's not really the longest since a zig-zag route with backtracks could be infinitely long but it's the longest route without a turn.

For paths that begin and end in the same location, there would be an infiinite number of paths if Earth were a sphere. The Great Circle Mapper models Earth as an oblate spheroid but for this corner case the longest path is collapsed into a null path.

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