Flight Paths & Great Circles

Ever wondered why a flight from New York to Singapore might cross Canada? Singapore sits just above the equator, yet the ideal airport-to-airport route leaves JFK at a bearing of 3.3 degrees, almost directly north.

The line passes over approximately 2,644 kilometres of Canadian land, climbs to 87.5 degrees north, about 279 kilometres from the North Pole, and then turns back toward Southeast Asia. On a flat map, that looks like an enormous detour. On a globe, it is the shortest route across the Earth's surface.

The explanation starts with a geometric idea called a great circle.

What is a great circle?

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 equator is one example. A meridian joined to the opposite meridian is another.

Choose two points on that circle, and there are usually two ways to travel between them. The shorter section, called the minor arc, is the shortest path across the sphere's surface. The longer section goes the other way around. When the points are exact opposites, both directions tie.

That shortest surface path is a geodesic. On a perfect sphere, its length is simply the planet's radius multiplied by the angle between the two locations, measured from the center in radians.

There is one complication: the Earth is not a perfect sphere. Its equatorial radius is approximately 6,378 kilometres, compared with 6,357 kilometres at the poles. Rotation contributes to that slight equatorial bulge, so a flattened shape called an ellipsoid is a better approximation.

For these routes, I used WGS84, the reference ellipsoid behind GPS, to calculate precise geodesics. Another model, the geoid, follows gravity and mean sea level. It matters for measuring heights, not for explaining why these paths curve.

How airlines use the curve

On a familiar Mercator map, a route that maintains the same compass bearing appears straight. That route is called a rhumb line, and it is usually not the shortest way around the planet. Mercator preserves local direction, not global distance. A geodesic usually changes its heading along the way, so flattening it onto a rectangular map makes it look as though it bends.

The difference is not subtle. Between Boston and Hong Kong, the constant-bearing route would be roughly 3,642 kilometres longer than the corresponding shortest path on the same spherical model.

To compare how geography changes the shortest path, I mapped 30 nonstop routes listed by airlines. They are selected examples, not a representative sample of global air traffic, and each line shows a calculated route rather than an aircraft's actual track.

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 has not 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.

Actual airline routes do not have to follow any of these ideal curves. Aircraft move through air, not across a stationary surface: a tailwind pushes them forward and increases their ground speed, while a headwind slows them down. A slightly longer route can therefore be faster if it catches a favorable wind or avoids one blowing against it. Dispatchers also consider weather, airspace restrictions, air-traffic control, diversion airports, fuel, and aircraft performance.

To see what that looks like, I sampled a NOAA upper-air analysis from August 6, 2026 along two calculated routes. Across 11 sampled points, the Toronto-to-Hong Kong line averaged approximately 39 kilometres per hour of tailwind. The New York-to-Singapore line averaged only 3 kilometres per hour of tailwind across nine points; at four sampled points at or north of 60 degrees, the wind reversed into approximately 28 kilometres per hour of headwind.

Those are single-day model samples, not onboard measurements or a comparison of real flight alternatives. They do show why dispatchers care about more than the shortest line on a map.

Why Canada keeps showing up

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. After looking at the geometry, that no longer seemed strange.

I calculated the ideal San Francisco-to-Heathrow route separately. It begins at a bearing of 32.8 degrees, heading northeast, covers approximately 8,638 kilometres, and reaches 64.6 degrees north before dropping toward London. By the time it arrives, its forward bearing has changed to 136.5 degrees. That is a high-latitude North Atlantic route, not a polar one: the FAA's polar region begins at 78 degrees north.

The modeled line itself intersects approximately 859 kilometres of Hudson Bay and another 382 kilometres of Hudson Strait. That does not establish the exact track my flight followed, but it does show that what I noticed from the window was entirely consistent with the underlying geography.

Of the 30 airline routes I mapped, 16 cross Canadian land, including 11 that neither start nor end in Canada. Even after excluding crossings shorter than 100 kilometres, 14 routes remain, ten of which neither start nor end in Canada. Only five enter the FAA's polar region.

Toronto-to-Hong Kong cuts north too, while transatlantic routes pass over eastern Canada before continuing toward Europe. These are intersections with simplified land boundaries, not sovereign airspace or records of where actual aircraft flew.

Canada's position is the explanation. It occupies a large part of the northern land between major North American cities, Europe, and Asia. Routes do not need to reach the pole for their shortest geographic paths to pass through that part of the world.

What changes above the atmosphere

Airliners stay close to the Earth's surface. A rocket could leave it, follow a much higher arc, and trade fuel and engineering difficulty for speed.

In 2017, SpaceX proposed using the vehicle that eventually became Starship for Earth-to-Earth travel at approximately 27,000 kilometres per hour. Its presentation suggested most long-distance trips could take less than 30 minutes. That was a proposal, not an operating passenger service or a demonstrated city-to-city timetable.

The idea would not require a complete orbit. An orbital spacecraft moves fast enough in the right direction to keep circling Earth. A suborbital trip follows a high ballistic arc and returns before completing one revolution. It could approach orbital speeds, but its destination would still be on the same curved planet.

Covering the 8,638-kilometre San Francisco-to-London surface distance in 30 minutes would require an average of approximately 17,276 kilometres per hour, even before accounting for ascent and descent. During that half hour, Earth would rotate about 7.5 degrees, so the vehicle would need to aim for where its destination will be, not where it was at launch.

Then it has to get back down. Atmospheric reentry, sonic booms, launch safety, environmental review, passenger regulation, and the distance between cities and launch sites do not disappear into a shorter flight time. No such commercial passenger network currently exists.

Whether a journey stays near the surface or briefly leaves it, the shape and rotation of the Earth still govern the route. Hudson Bay only looked like a detour because I was reading a round planet on a flat map.