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.

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

Wikipedia has an article on the distance from a point to a line.

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. :(

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.

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..:)

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.

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.