How to convert straight lines to great circles
You can use the
ST_Segmentize PostGIS function to emulate flight routes or great circles.
SELECT ST_Transform( ST_Segmentize( the_geom::geography, 10000 )::geometry, 3785 ) as the_geom_webmercator, cartodb_id FROM table_name
Notice that when any of these routes crosses the dateline, some horizontal lines will appear. To solve this issue, you can check this blog post and apply it’s workaround.