Closest Point of Approach

This form calculates the Closest Point of Approach or CPA of two vessels. Vessel 1 is the reference vessel (you). The range and bearing are measured from Vessel 1. If the resulting CPA is zero, that means a collision will occur. T1 and T2 are the two times that observations are made to determine the speed and position of the tracks.

The first version is based upon two range/bearing measurements made from Vessel 1. Each measurement includes the range in nautical miles and the true bearing in decimal degrees of Vessel 2 as measured from Vessel 1.

        Range at T1 (nmi): 

  Bearing at T1 (degrees): 

        Time T1 (minutes): 

        Range at T2 (nmi): 

  Bearing at T2 (degrees): 

        Time T2 (minutes): 





                CPA Range: 

              CPA Bearing: 

           Relative Speed:

This second version is computed using vectors and needs as input the speeds and courses of the two vessels.


           Speed1 (knots): 

Course1 (decimal degrees): 

           Speed2 (knots): 

Course2 (decimal degrees): 

   Range (nautical miles): 

Bearing (decimal degrees): 





Closest Point of Approach:

Note that these are 2D approximate solutions to a 3D problem. At long distances these solutions becomes inaccurate.
The full general 3D solution should take into account the spherical nature of the earth.

View the source code to this page to see the underlying formulas used.

Back to Dan's Home Page

Created:  15 Aug 2000  
Modified: 12 Aug 2011