#### wooslehunter

##### Active member

Given I have the current position, course and speed of two vessels, anyone got some equations I can use?

I did derive some but they are huge and complex. There has to be a simpler way. Any ideas?

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- Thread starter wooslehunter
- Start date

Given I have the current position, course and speed of two vessels, anyone got some equations I can use?

I did derive some but they are huge and complex. There has to be a simpler way. Any ideas?

The closest point of approach between a fired projectile and a target is taken to be at the instant the projectile velocity vector (6) is orthogonal to the position error vector (13) between the projectile and target in accordance with the relationship: V.sub.p.cndot.(P.sub.P -P.sub.F)=0 where V.sub.p is the projectile velocity vector, P.sub.P is the projectile trajectory or position vector, P.sub.F is the target future position vector, .cndot. is the vector dot product and (P.sub.P -P.sub.F) is the position error vector.

/forums/images/graemlins/grin.gif

(PS> Seriously what is the environment of the problem pls ? Nautical, aeronautical, deep space....)

First thing you need to do is to convert the positions from circular(lat,lon) to grid (Eastings & Northings). Given that both vessels will be within close proximity and that you are only really interested in relative positions, you can take some short cuts to simplify the maths

Once you have grid co-ords you can generate vectors from cog and sog. Don't have time to go into too much dtail but sure I can dig out the formulae later if yo're still stuck

Optimal Intercept Course of Vessels to a Nonzero Range

SIAM Review archive

Volume 38 , Issue 4 (December 1996)

Pages: 647 - 649

Year of Publication: 1996

ISSN:0036-1445

Authors

B. U. Nguyen

D. Nguyen

Publisher

Society for Industrial and Applied Mathematics Philadelphia, PA, USA

ABSTRACT

An exact solution, based on minimum intercept time, is proposed for the optimal course of one ship approaching another to a nonzero range.

If you need a copy and can't get it from a library PM me and I will make arrangements.

This is for a nautical environment and close range so only need linear 2D trig rather than circular or 3D.

Go to http://www.patentstorm.us/patents/6249241-description.html

and search for:

and there is the formula.

No wonder that patent agents charge so much !

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