Flight Paths & Great Circles
On a recent flight from San Francisco to London, I looked down and noticed we were passing over Hudson Bay. London was east, yet the journey had taken us deep into Canada.
I calculated the shortest San Francisco-to-Heathrow route. It covers approximately 8,638 kilometres, reaches 64.6 degrees north, and crosses about 859 kilometres of Hudson Bay along the way. It's a modeled line, not a record of where my plane flew.
The shortest path from San Francisco to London crosses Hudson Bay
The view from above the North Pole makes the route easier to follow. Canada lies between the endpoints; the trip doesn't need to stay near the latitude of either city.
A great circle is the largest circle you can draw on a sphere. Imagine slicing the Earth with a flat plane that passes through its center: the circle around that cut is a great circle. The shorter arc between two points on it is the shortest path across the sphere's surface.
The shorter arc of a great circle
One circle, two possible arcs
On a Mercator map, a route that maintains the same compass bearing appears straight. That's a rhumb line, and it usually isn't the shortest way around the planet. The shortest path usually changes its heading along the way, so flattening it onto a rectangular map makes it look as though it bends.
New York-to-Singapore is the more extreme version. Singapore sits just above the equator, yet the shortest airport-to-airport route leaves JFK at a bearing of 3.3 degrees, almost directly north.
New York to Singapore on a flat world map
The line crosses approximately 2,644 kilometres of Canadian land and climbs to 87.5 degrees north, about 279 kilometres from the North Pole, before heading back toward Southeast Asia.
To compare how geography changes the shortest path, I mapped 30 nonstop routes listed by airlines. They're selected examples, separate from San Francisco-London, and each line shows a calculated route rather than an aircraft's actual track.
Thirty modeled airline routes across both hemispheres
Keep Singapore as the destination but depart from Vancouver, and the route only reaches 58 degrees north. Leave from Los Angeles, and it stays near 46 degrees north. The destination hasn't changed; the shortest path has moved because its starting point did.
Across the Atlantic, routes bend north more gently. Auckland-to-New York crosses the equator. Farther south, Sydney-to-Santiago reaches almost 62 degrees south, reversing the pattern seen above Canada.
For a real flight, a slightly longer route can be faster if it catches a favorable wind or avoids a headwind. Dispatchers also consider weather, airspace restrictions, air-traffic control, diversion airports, fuel, and aircraft performance.
Why Canada keeps showing up
Of those 30 calculated routes, 16 cross Canadian land, including 11 that neither start nor end in Canada. That's a count of the examples I chose, not an estimate of how often aircraft fly over Canada.
Canada's position is the explanation. It occupies a large part of the northern land between major North American cities, Europe, and Asia. Routes don't need to reach the pole for their shortest geographic paths to pass through that part of the world.
Hudson Bay only looked like a detour because I was reading a round planet on a flat map.
How the routes were mappedThirty selected airline-listed routes, a separate San Francisco-London calculation, and public airport and cartographic data.
The sample contains 30 nonstop city pairs listed by airlines across six route categories, verified August 7, 2026. These routes illustrate different geographic patterns; they are not a representative sample of global airline traffic. Coordinates for the 23 airports come from the public-domain, community-maintained OurAirports registry. Published airline service shows that a route was offered, not that a particular flight operated.
On a perfect sphere, a great-circle arc's length is the planet's radius multiplied by the angle between the two locations, measured from the center in radians. When the endpoints are exact opposites, both semicircles have the same length. Earth is slightly flattened: the WGS84 reference ellipsoid has an equatorial radius of approximately 6,378 kilometres and a polar radius of 6,357 kilometres.
Each atlas line is an independently verified airport-to-airport geodesic on the WGS84 ellipsoid. "Great circle" is shorthand: an ellipsoidal geodesic is the more precise real-Earth equivalent of the shortest arc on a perfect sphere. The 30 mapped routes contain 62,216 points with no segment longer than five kilometres; their 17 crossings of the map's 180-degree longitude boundary are split before projection to avoid false lines across the map.
The separate San Francisco-London route uses the same saved OurAirports coordinates, the GeographicLib WGS84 geodesic calculation, and 241 sampled points. Its maximum latitude is calculated along the complete route rather than selected from the display samples. Intersections with Natural Earth's generalized 1:10m marine boundaries total 858.613 kilometres for Hudson Bay and 382.018 kilometres for Hudson Strait; two separate Hudson Bay intervals result from an unnamed generalized land feature. It is separate from the 30 airline routes used for the Canada-wide comparisons and is not a recorded aircraft track. The author's actual Hudson Bay observation and the modeled route are distinct evidence.
The six route categories include six high-latitude examples with no Canadian endpoint, three Canadian-origin examples, four North Atlantic routes, six North Pacific routes, six equator-crossing examples, and five Southern Hemisphere routes.
Canadian-land comparisons use Natural Earth's public-domain 1:50m Admin-0 Countries version 5.1.1. Sixteen calculated lines touch generalized Canadian land, including 11 with neither endpoint in Canada. Excluding intersections under 100 kilometres leaves 14 lines, including ten without a Canadian endpoint. These are cartographic land overlaps, not sovereign airspace, flight-information regions, legal boundaries, or observed aircraft crossings.
Only five of the 30 calculated lines enter the FAA's North Polar Area, defined as north of 78 degrees latitude. San Francisco-London reaches 64.6 degrees north, so it is a high-latitude North Atlantic route, not a polar one under that definition.
The New York-Singapore and global atlas maps use a simple longitude-latitude projection, not Mercator. The Mercator example in the text explains why a straight-looking, constant-bearing rhumb line is a different object from a shortest surface path; it is not a distance comparison measured from either map.
Sources
- OurAirports. Open airport data
Public-domain airport registry; coordinates for 23 airports selected from the August 2026 release.
- NASA. Great circles and Earth's geometry
Why paths across a curved planet look different on a flat map.
- NOAA VDatum. WGS84 reference ellipsoid dimensions
Published equatorial and polar semi-axes for the WGS84 reference model.
- PROJ. Geodesic calculations
Independently verified WGS84 ellipsoidal route calculations.
- NOAA / International Hydrographic Organization. Geodesic and constant-bearing lines
Great-circle, ellipsoidal, and loxodrome geometry.
- NOAA Office of Coast Survey. Nautical cartography and the Mercator projection
Why constant-bearing rhumb lines plot straight on Mercator charts while surface-shortest paths usually do not.
- Natural Earth. Public-domain land and Admin-0 country vectors
Public-domain cartographic land and generalized Canadian country polygons; not aviation or legal-boundary data.
- Natural Earth. 1:10m named marine and physical vectors
Generalized Hudson Bay and Hudson Strait polygons used for the separate San Francisco-London water-intersection comparison.
- Singapore Airlines. Flights from New York to Singapore
Airline-published New York-Singapore service information.
- San Francisco International Airport. Nonstop flights to Europe and the Middle East
Airport-published confirmation of nonstop San Francisco-London Heathrow service.
- Federal Aviation Administration. Extended operations and polar operations
Official definition of the North Polar Area as north of 78 degrees latitude.
- British Airways. Summer 2026 North American network
Airline-published London-Heathrow routes, including New York and St. Louis.
- Japan Airlines. FY2026 international network schedule
Airline-published Los Angeles and San Francisco service to Tokyo Haneda.
- Air New Zealand. Nonstop destinations from Auckland
Airline-published Auckland routes across the equator and the Southern Hemisphere.
- Qantas. South America and Sydney's nonstop Santiago service
Airline-published confirmation of the Sydney-Santiago nonstop route.