# Closest Point of Approach (CPA) mathematical formula in ship radar

• April 5th, 2013, 03:59 AM
syamilsynz
Closest Point of Approach (CPA) mathematical formula in ship radar
Hello guys,

I recently searching for mathematical formula to find closest point of approach (CPA) between own ship and other ship to be applied to my radar ship program and I can't find the correct ways to calculates it.

anybody know what are the correct formula besides plotting in manually?

any mathematical formula or coding?

thank you very much for anyone that help me. :o sorry for my bad english.
• April 5th, 2013, 04:15 AM
pbrockway2
Re: Closest Point of Approach (CPA) mathematical formula in ship radar
Wikipedia has an article on the distance from a point to a line.
• April 5th, 2013, 04:58 AM
syamilsynz
Re: Closest Point of Approach (CPA) mathematical formula in ship radar
Quote:

Originally Posted by pbrockway2
Wikipedia has an article on the distance from a point to a line.

Thanks for the quick reply, but to calculate closest point of approach (CPA) in radar ship, we will needs speed, time, course and other things (maybe), and I don't know what are the correct formula. :(
• April 5th, 2013, 12:30 PM
syamilsynz
Re: Closest Point of Approach (CPA) mathematical formula in ship radar
Thanks pbrockway2 for the replies. :)

Anyway, that's not what I want to solve. Closest Point of Approach (CPA) involves speed, course, time and others (maybe) to get the answers. the problem is I don't know what the correct FORMULA to get the answer right. :(
• April 5th, 2013, 12:44 PM
Norm
Re: Closest Point of Approach (CPA) mathematical formula in ship radar
When I studied navigation, we didn't have a formula for solving that problem. The solution was found by some sort of vector addition(???) using a special drawing pad, parallel rulers, compass and dividers. This was pre-PC.
Problem: Given the positions of two ships, their courses and speeds, find the CPA. I can't remember any details on how to find the solution.
• April 7th, 2013, 12:18 PM
syamilsynz
Re: Closest Point of Approach (CPA) mathematical formula in ship radar
later if you remember the details, maybe you can share with us. we will appreciate it..:)
• April 7th, 2013, 12:23 PM
Norm
Re: Closest Point of Approach (CPA) mathematical formula in ship radar
Quote:

if you remember the details
The details are long gone.
I googled the topic and found a pdf that describes the technique as I vaguely remember it.
There was no formula used. The solution was found with manual vector manipulation.
• April 7th, 2013, 05:27 PM
pbrockway2
Re: Closest Point of Approach (CPA) mathematical formula in ship radar
Quote:

The solution was found with manual vector manipulation
If you subtract one ship's position from another (to find the vector displacement) the problem becomes one of minimising this displacement. But the displacements plotted at various times form a line and the dynamic problem of finding the CPA reduces to the purely geometric one of finding the distance between this line and the origin (the point of zero displacement). That's the relevance of the Wikipedia link.