Sunday, May 3, 2015

The 'Cooke passage' : a new world's longest straight-line sail ?

David Cooke said he discovered
the longest land to land 'straight line' ocean route on Earth.
Over 2000 miles longer than the one from Kamchatka to Pakistan.
Really ?

Timothy Whitehead from Google Earth blog recently came across this post on Reddit.
It references to the above YouTube video from David Cooke, claiming to have discovered the longest straight line that can be sailed without going over land.
The video creator calls it the "Cooke Passage".
However, we have attempted to recreate it in Google Earth, and it appears that it is not actually a straight line.

GoogleMapsMania has in the past discussed what constitutes a straight line in Google Earth.
In this instance, we are interested in Great Circles, which is what Google Earth uses by default when drawing a path.
However, Google Earth always draws the shorter arc of a Great Circle, so to draw the longer section of a Great Circle it is necessary to include at least one more point and then adjust it with care.
You know you have got it right if you can draw another shorter path on any section of it and it still follows the same path.
Using the above techniques, and locations shown in the video, we have investigated the Cooke Passage and decided that it does not follow a great circle.

We also confirm this statement and in order to go further in analyzing this route, we propose a more accurate method for drawing the longer section of a Great Circle (orthodromic route) on Google Earth :

Note : Great-circle navigation is the practice of navigating a ship along a great circle (shortest route).
A great circle track is the shortest distance between two points on the surface of a sphere; the Earth isn't exactly spherical, but the formulas for a sphere are simpler and are often accurate enough for navigation.

1/ calculate the Great Circle route from the Start point to the End point :

    in this Cooke passage case :
. start : near Port Cartier, Quebec : 49°52'9" N / 67°0'0" W (49.86916667/-67 in decimal)
. end : Port Renfrew, Victoria BC : 48°35'34,34" N / 124°43'48" W (48.59287222/-124.73 in decimal)

Minor Arc Great circle on Google Maps (2,214.33 Nm GC / 2,269.52 Nm Rhumb Line)
initial bearing : 290.9° from East to West

As the long arc is higher than half of the Earth circumference at the Equator (so higher than 10,819 Nm, actually in this case about 19,401 Nm), the calculation will give the shorter arc of the Great Circle.
Effectively, points A and B split their great circle in two arcs of which (except for antipodal A and B) one is shorter than the other. The important bit is that the calculation of the shortest distance between two points on a sphere is done for the minor arc of a Great Circle.

Then how to calculate the major arc ?

2/ calculating at first the midpoint of this minor arc (the half-way point along a great circle path between the two points) using the ‘Haversine’ formula.

Cook passage (minor arc Great Circle) midpoint : 52.9425/-95.72694444
on Google Maps (Mercator projection)

3/ then calculating the antipodal of the midpoint for this minor arc which represents the midpoint of the major arc :
Given a point on a sphere with latitude and longitude, the antipodal point has latitude -Lat and longitude Lon+/-180 degrees (where the sign is taken so that the result is between -180 degrees and  +180 degrees).

Cook passage (minor arc) antipodal midpoint in the South of the Indian ocean
Map tunneling tool : -Lat/180+Lon so -52.9425/84.27305556
illustration : AntipodeMap

This point will be the necessary intermediate waypoint allowing to draw the major arc Great Circle with Google Earth : see the resulting kml file. and the Cooke passage Great Circle major Arc on Google Earth  showing the line crossing Australia, so not a new world longest GC straight-line sail :

video realized from GeoGarage kml file
- see another video created by Liam Nash -

By the way, to follow a great circle track, the navigator needs to adjust the ship's course continuously because the great circle track is a curve when plotted on a Mercator map (see illustration above).
Therefore, it is not really practicable to sail on an exact Great Circle route.
In order to take advantage of the shorter distance given by the Great Circle track, mariners usually divide a Great Circle track between the initial position and the destination into smaller segments (way points) corresponding to some sailing time and make course adjustments at each next waypoint.
The total distance is therefore the sum of the distances of those rhumb line segments (loxodromic with constant angle route) calculated by means of Napier rules for spherical triangles, allowing to calculate several individual waypoint's WGS84 Latitude and Longitude.

 In some previous GeoGarage posts regarding longest GC sailing :
  • Pakistan-Siberia: The longest straight line you can sail on Earth ?
  • Norway-Antarctica : Sail all the way around the world to Antarctica without touching land in a straight line ?

  • we can apply the above method -using the antipodal of the midpoint for this minor arc- and also calculate the Great Circle major Arc waypoints with other intermediates (for example a serie of waypoints at x Nm of distance)

     Pakistan-Siberia.kml route on Google Maps (straight on the Google Earth globe) :
    real Great Circle corrected by the GeoGarage team (about 32,105 km/17,335 Nm)
    not crossing Aldabra and Assumption island in the North West of Madagascar.
    & Pakistan-Siberia_WPTS.kmz built with 1731 intermediate waypoints every 10 Nm
    (note some difference with the above Pakistan-Siberia.kml route due to different GC calculations)

    GoogleMapsMania also came across another interesting, though shorter route that goes from Norway to Antarctica by way of the Bering Strait.

     GoogleMapsMania : Various routes (kml file)  
    including Norway-Antarctica route
    Using an intermediate waypoint as the antipodal of the midpoint for this minor arc between Norway and Antarctica, passing by the Bering straight, we get a different result comparing to the above kml file issued from GoogleMapsMania.

      &  Norway-Antarctica kmz built with 1178 intermediate waypoints every 10 Nm
    crossing Saint Lawrence island in the Bring Strait 

    But another factor to take into consideration is the location of the vertex,
    or the point of greatest latitude through which the circle passes.
    In this case, the route mainly crosses the North pole area.
    So this is not a realistic sailing route, by the way some Composite Great Circle
    with limited Latitude can't be used.
    Note : when using a Composite Great Circle track, a limiting Latitude is chosen,
    beyond which the vessel does no go.
    When the limiting latitude is reached the vessel then sails either due East or West on the limiting Latitude as in parallel sailing.
    In order to reach the limiting Latitude, the vessel follows an appropriate Great Circle track whose vertex lies on the limiting Latitude.

    Links :

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