Solving What Course To Steer To Intercept A Vessel

You are enroute to assist vessel A. Vessel A is underway at 5.5 knots on course 033° T and bears 248° T at 64 miles from you. What is the course to steer at 13 knots to intercept vessel A?

Given:

    Target Course = 033° T
     Target Speed = 5.5 knots
   Target Bearing = 248° T
  Target Distance = 64 miles
Own Ship Speed = 13 knots

What is asked?

Course to steer to intercept  vessel A.

Solution:

Step 1. Solving for bearing of own ship from target.

          Bearing of own ship from target = (Target Bearing + 180°) - 360°
                                                            = (248° + 180°) - 360°
                                                            = 428° - 360°
                                                            = 068°

Step 2. Solving ∠A. Angle A is a difference between the target vessel's true course and the true bearing of your vessel from the target vessel.

           ∠A = Bearing of own ship from target - Target Course
                 = 68° - 33°
                 =  35°

Step 3. Solving for Angle C.

     Sin ∠C = Target Speed × Sin ∠A 
                        Own Ship Speed
     Sin ∠C = 5.5 kts × Sin 35°
                           13 kts
     Sin ∠C = 0.24267
           ∠C = inv Sin 0.24267
           ∠C = 14°

Step 4. Solving for True course to steer.

          True course to steer = Target Bearing ± ∠C
                                           = 248° + 14°
                                           = 262°

   

Course to steer to intercept a vessel

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