calcGCdist function

Calculate Great-Circle Distance

Calculate the great-circle distance between geographic (LL) coordinates. Also calculate the initial bearing of the great-circle arc (at its starting point).

calcGCdist(lon1, lat1, lon2, lat2, R=6371.2)

Arguments

• lon1: numeric -- Longitude coordinate (degrees) of the start point.
• lat1: numeric -- Latitude coordinate(degrees) of the start point.
• lon2: numeric -- Longitude coordinate(degrees) of the end point.
• lat2: numeric -- Latitude coordinate(degrees) of the end point.
• R: numeric -- Mean radius (km) of the Earth.

Details

The great-circle distance is calculated between two points along a spherical surface using the shortest distance and disregarding topography.

Method 1: Haversine Formula

$$a = \sin^2((\phi_2 - \phi_1)/2) + \cos(\phi_1) \cos(\phi_2) \sin^2((\lambda_2 - \lambda_1)/2)$$ $$c = 2~\mathrm{atan2}(\sqrt{a}, \sqrt{1-a})$$ $$d = R cd = R * c$$

where

$phi$ = latitude (in radians),

$lambda$ = longitude (in radians),

$R$ = radius (km) of the Earth,

$a$ = square of half the chord length between the points,

$c$ = angular distance in radians,

$d$ = great-circle distance (km) between two points.

Method 2: Spherical Law of Cosines

$$d = \mathrm{acos}(\sin(\phi_1)\sin(\phi_2) + \cos(\phi_1)\cos(\phi_2)\cos(\lambda_2 - \lambda_1)) R$$

The initial bearing (aka forward azimuth) for the start point can be calculated using:

$$\theta = \mathrm{atan2}(\sin(\lambda_2-\lambda_1)\cos(\phi_2), \cos(\phi_1)\sin(\phi_2) - \sin(\phi_1)\cos(\phi_2)\cos(\lambda_2-\lambda_1))$$

Returns

A list obect containing:

a -- Haversine $a$ = square of half the chord length between the points,

c -- Haversine $c$ = angular distance in radians,

d -- Haversine $d$ = great-circle distance (km) between two points,

d2 -- Law of Cosines $d$ = great-circle distance (km) between two points,

theta -- Initial bearing $theta$ (degrees) for the start point.

References

Movable Type Scripts -- Calculate distance, bearing and more between Latitude/Longitude points

Author(s)

Rowan Haigh, Program Head -- Offshore Rockfish

Pacific Biological Station (PBS), Fisheries & Oceans Canada (DFO), Nanaimo BC

locus opus: Remote office, Vancouver BC

Last modified Rd: 2024-03-11

Note

If one uses the north geomagnetic pole as an end point, $theta$ crudely approximates the magnetic declination.

See Also

In package PBSmapping:

addCompass, calcArea, calcCentroid, calcLength

Examples

local(envir=.PBSmapEnv,expr={
  #-- Distance between southern BC waters and north geomagnetic pole
  print(calcGCdist(-126.5,48.6,-72.7,80.4))
})