Mapping Toolbox

reckon

Determine new position from starting point, azimuth, and range

Syntax

• [newlat,newlon] = reckon(lat,lon,rng,az)
  [newlat,newlon] = reckon(lat,lon,rng,az,units)
  [newlat,newlon] = reckon(lat,lon,rng,az,geoid)
  [newlat,newlon] = reckon(lat,lon,rng,az,geoid,units)
  [newlat,newlon] = reckon(track,lat,...)
  

Description

[newlat,newlon] = reckon(lat,lon,rng,az) returns a new geographic position in newlat and newlon at a given range rng and azimuth az from starting points in lat and lon. There must be a one-for-one correspondence between the elements of all four inputs.

[newlat,newlon] = reckon(lat,lon,rng,az,units) specifies the angular units of the inputs and outputs, where units is any valid angle units string. The default value is 'degrees'. Note that the range input, rng, must be in these angular units as well.

[newlat,newlon] = reckon(lat,lon,rng,az,geoid,units) specifies an elliptical definition of the Earth, where geoid is a two-element geoid vector. The default geoid is a spherical Earth, which is sufficient for most applications. If a geoid vector is input, the range input, rng, is in the units of the semimajor axis, that is, the first element of geoid.

[newlat,newlon] = reckon(track,lat,...) specifies the sense of the reckoning. If the string track is 'gc' (the default), the new positions are reckoned by following great circle paths. Alternatively, track can be the string 'rh', in which case the new positions are reckoned by following rhumb lines.

Examples

What are the coordinates of the point 600 nautical miles northwest of London, UK (51.5ºN,0º), in a great circle sense?

• dist = nm2deg(600)  % convert nm distance to degrees
  dist =
      9.9932
  
  reckon(51.5,0,dist,315)  % northwest is 315 degrees
  pt1 =
     57.8999  -13.3507
  

Now, where would a plane taking off from London and traveling on a constant northwesterly course for 600 nautical miles end up?

• reckon('rh',51.5,0,dist,315)
  pt2 =
     58.5663  -12.3699
  

How far apart are these points (distance in great circle sense)?

• separation = distance('gc',pt1,pt2)
  separation =
      0.8430
  
  nmsep = deg2nm(separation)  % convert answer to nautical miles
  nmsep =
     50.6152  
  

Over 50 nautical miles separate the two points.

See Also

azimuth	Azimuth between two points on the globe
distdim, distance	Distance between two points on the globe
km2deg	Convert distance units
dreckon	Navigational dead reckoning
track track1 track2	Tracing paths on the globe

rec2geod

reducem