A straight Mercator line is a constant course, not generally a spherical shortest path.
Precise claimOn a sphere, the shortest surface path is a great-circle arc; a straight line on a Mercator map represents a constant-bearing rhumb line and is generally longer.
Applies
New York and London city-center coordinates on a mean-radius sphere, comparing exact spherical great-circle and rhumb-line formulas.
Does not prove
The page does not model ellipsoidal geodesics, airways, winds, restricted airspace, operational routing or safety-critical navigation.
Portable rule
If distance is being judged from a flat map, then identify both the projection and the path rule before treating visual straightness as a shortest route.
Declare the discussion context, then copy a stable link. No account or personal data is attached.
projection-distortion puzzle
Great Circle or Rhumb Line: Which Is Shorter?
Choose between two fully visible New York–London paths, then hold coordinates and Earth model fixed while switching only the navigation rule.
Route A · visually straightRoute B · visually curved
The reveal · measure on the sphere
The curved map line is the shorter spherical arc.
You committed to: —
Flat projection · shape is not distance
Orthographic globe view · drag the sphere to inspect the same endpoints
Flat projection is the view you judged first.
Great circle5570 km
shortest spherical arc
Rhumb line5794 km
constant bearing
224 km difference
On a sphere, the shortest surface path is a great-circle arc; a straight line on a Mercator map represents a constant-bearing rhumb line and is generally longer.
The rhumb line is 4.02% longer than the great-circle route when the great-circle distance is the baseline; switching from rhumb to great circle removes 3.86% of the rhumb distance. Real routes can differ because this page excludes ellipsoidal refinements, winds, airways and restrictions.
The rebuilt model
You assumed:
The visually straight line between two map points must be the shortest route between the corresponding places.
The actual model:
A projection can make a useful navigation rule visually straight without preserving shortest surface distance. Great circles minimize spherical arc length; Mercator straight lines preserve bearing.
The variable that failed you:
Path rule — visual straightness selected constant bearing, while the distance question requires the shortest spherical arc.
Change one variable
Keep endpoints and Earth fixed. Switch only the path rule.
Reference mode opens the route switch without manufacturing a prediction.
Now explore another endpoint pairThe protected New York–London proof is complete. These local comparisons change endpoints without manufacturing another verdict.
Constant-bearing route is shown for New York → London. Choose Great circle to run the comparison.
If distance is being judged from a flat map, then identify both the projection and the path rule before treating visual straightness as a shortest route.
Flight-map review
A bowed route can be geometrically shorter even when the display makes it look like a detour.
Marine navigation
Distinguish the operational convenience of one constant course from minimum spherical distance.
Spatial analytics
Compute geodesic distance from coordinates instead of measuring projected screen pixels across large extents.