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Departure of longitudes at specified latitudes


dist = departure(long1,long2,lat)
dist = departure(long1,long2,lat,ellipsoid)
dist = departure(long1,long2,lat,units)
dist = departure(long1,long2,lat,geoid,units)


dist = departure(long1,long2,lat) computes the departure distance from long1 to long2 at the input latitude lat. Departure is the distance along a specific parallel between two meridians. The output dist is returned in degrees of arc length on a sphere.

dist = departure(long1,long2,lat,ellipsoid) computes the departure assuming that the input points lie on the ellipsoid defined by the input ellipsoid. ellipsoid is a referenceSphere, referenceEllipsoid, or oblateSpheroid object, or a vector of the form [semimajor_axis eccentricity].

dist = departure(long1,long2,lat,units) where units defines the angle units of the input and output data. In this form, the departure is returned as an arc length in the units specified by units. If units is omitted, 'degrees' is assumed.

dist = departure(long1,long2,lat,geoid,units) is a valid calling form. In this case, the departure is computed in the same units as the semimajor axes of the ellipsoid.


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On a spherical Earth, the departure distance is proportional to the cosine of the latitude. For example, calculate the departure distance for 0°.

distance = departure(0, 10, 0)
distance = 10

Now calculate the distance for 60°.

distance = departure(0, 10, 60)
distance = 5.0000

When you calculate the same departure distances on an ellipsoid, the result is more complicated. Again, calculate the departure distance for 0°.

distance = departure(0, 10, 0, referenceEllipsoid('earth', 'nm'))
distance = 601.0772

Now calculate the distance at 60°. You can see that the value is not exactly half the 0° value.

distance = departure(0, 10, 60, referenceEllipsoid('earth', 'nm'))
distance = 301.2959

More About

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Departure is the distance along a parallel between two points. Whereas a degree of latitude is always the same distance, a degree of longitude is different in length at different latitudes. In practice, this distance is usually given in nautical miles.

Version History

Introduced before R2006a

See Also