NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Closest point of approach.
From: Peter Hakel
Date: 2011 Dec 28, 00:25 0800
From: Gary LaPook <garylapook@pacbell.net>
To: NavList@fer3.com
Sent: Tuesday, December 27, 2011 1:11 AM
Subject: [NavList] Re: Closest point of approach.
From: Peter Hakel
Date: 2011 Dec 28, 00:25 0800
I attach a spreadsheet with Gary's example.
Peter Hakel
From: Gary LaPook <garylapook@pacbell.net>
To: NavList@fer3.com
Sent: Tuesday, December 27, 2011 1:11 AM
Subject: [NavList] Re: Closest point of approach.
Sure, it's easy. I have attached several photos of a sample plot to show how the calculation proceeds. At 0120 the vessel bears 060° relative, distance 4.0 NM. At 0126 the vessel now bears 043° R, 2.2 NM. The difference in bearings is 017°. With this information we use the law of cosines to find the length of the third side which is 2.0022 NM. With the lengths of all three sides we use the law of sines to find the angle between the relative bearing to the second position and the direction of relative movement which is 35.7°. At the point of closest approach the angle between the realative bearing and the direction of relative movement is 90° the sine of which is 1. Now using the law of sines again we compute the distance at the point of closest approach which is 1.28 NM. Using the law on sines again we compute the distance the other vessel moves from the second position to the point of closest approach which is 1.78 NM. Next we divide this distance by the distance traveled between the first two positions and then multiply by the time between the first two positions to find the time to the point of closest approach which is 5 minutes and 21 seconds. gl  On Mon, 12/26/11, Amrin Shahziya <ammushaz@gmail.com> wrote:

File: 117671.cpa.xls