Looking for an online navigation calculator for plotting intercepts (or a formula)

Factual Questions
1

Ok, I admit it, this is for a game so I can get to an enemy fustest with the mostest.

I’m playing a game where I can (sometimes) get a reasonably exact distance and bearing between two game pieces, as well as the speed of each and the course of each. And from that I can pretty well ballpark in an interception, but I’d like to be able to do it more accurately and not have to futz with a new eyeball estimate so frequently.

The ranges of values will mostly be less than a thousand miles between the two pieces, but not always. The speeds will vary more, from pieces traveling at 5 mph (cargo ships) to 1500 mph (high performance fighters).

I may be able to determine lat. and long. on a world map, but that’s already something of a hassle. I would prefer it that the calculations be done more simply in reference to each other.

Also, let’s go with the concept of a flat earth, so we don’t have to worry about Great Circle courses.

Here is a typical situation. I am HERE (wherever I happen to be). There is a target w miles away at a bearing of x degrees from me, traveling at speed y on course z.

There are two questions to answer, and one introduces more variables.

  1. What speed and course to I need to travel to intercept the target?

  2. What speed and course do I need to arrive at location A, which is B miles ahead of my enemy, along the course my enemy is traveling? This is to lie in wait and ruthless ambush my opponent.

There are a few other considerations. For instance, difference game pieces have different maximum speeds, so in a number of cases (like a faster unit moving away from a slower one) an intercept will not be possible.

I have looked around and failed to find such a calculator online, but perhaps your Google foo is better than mine. Alternately, if any of you math whizzes can whip up a formula, odds are I can work it into a spreadsheet.

2

I can’t help with the formula but the game sounds interesting, what is it called?

3

The game is the ancient and revered Harpoon, created more than 20 years ago and upgraded constantly since. It became the basis for tactical simulator training at the US Naval Institution at some point. It’s latest incarnation is Harpoon Ultimate Edition, which collects several versions of the game into one “box” . The most recent is called “Advanced Naval Warfare”, but I prefer Harpoon “Classic”. Here’s a review of it.

This game started as the buggiest game in human history, but it had so much potential I stuck with it (on and off) since it was first release

4

I’ve downloaded it. Any suggestions where I should start?

5

P.S. I’ve been googling for something to do what you want but can’t really find anything. I can visualise it easily enough using paper, pencil, and dividers, but am too weak on maths to be able to translate it into a formula.

6

Check out MoBo. It’s a maneuvering board simulator that should work well with Harpoon.

7

I’ve influenced your purchasing decision? I am a god!! Not THE God, of course, but a lesser non-capitalized god.

I can only give you advice on Ultimate Commander’s Edition. My computer has issues running Advanced Naval Warfare (the mouse doesn’t work, and it’s a very mouse-intensive game), so I’ve never messed with it much.

When you open the game, your first choice will be to select a “battleset”. You can see by their titles that they’re actually sets of sets – as the game was upgraded through the years, the newer versions released revised battlesets. The oldest battlesets (GIUK thru IOPG) are at the top – the newest go to the bottom. Each set of sets contains a separate weapons database, and a map of a portion of the world. GIUK, for example, is a map of Greenland, Iceland and the UK, and was designed to study scenarios where the Soviet Northern Fleet would attempt to “break out” into the Atlantic through the gaps between the land masses.

The most important rule is to remain stealthy. Leave your ships’ radars off unless you are certain the enemy knows your location anyway. Your radar emission can be seen 3 or 4 times further away than they can actually see. Send up an AEW plane, and send it a couple of hundred miles away from your group, and use it’s radar. Because it’s radar will draw the attention of the enemy. Send fighters along to protect it, as enemy planes will start gunning for it.

The other most important rule is to conserve weapons that have a limit. Use plane weapons rather than ship weapons. Planes have a limited capacity for each mission, but when the land to rearm, their weapons warehouses are apparently bottomless. Ships, however, have only so many weapons that they can fire, and no way to replenish them.

And use your best. There are a lot of older airplanes in the scenarios with poor sensors and short-ranged weapons that are nothing but cannon fodder, because they will be slaughtered by the enemy before they are even aware of them, or before they can get in range to fire.

I would start with GIUK. You’ll see the first mission is a tutorial to show you hoe to use your sonars, radars, and weapons.

8

Hmmm… this looks very promising.

9

Here’s a method to solve the problem. To make it easy to understand, let’s choose a scenario where you start at the origin (0,0), with your target initially at (x,y) moving eastward with speed v (i.e., velocity (v,0)). That is, it is traveling along a path which has closest-approach distance to you of y, and it is a distance x from the point of closest approach.

Now draw a right triangle with vertices (0,0) (your initial position), (0,y) (the target’s position at closest approach to the origin), and (x+vt,y) (the target’s position at time t). The hypotenuse of this triangle has length h=sqrt((x+vt)[sup]2[/sup]+y[sup]2[/sup]), so you can reach this point at time t only if your speed is h/t.

Or, maybe a little more intuitively, if your speed is u, then you can reach this point at time t only if the hypotenuse has length ut:
(ut)[sup]2[/sup] = h[sup]2[/sup] = (x+vt)[sup]2[/sup] + y[sup]2[/sup] .
This is a quadratic in t; solve to find the intercept time. (There may be two, one, or zero distinct real roots; if there are no real roots, you can’t catch him.) Then (x+vt,y) is the position of the intercept; set that course.

If you instead want to lie in wait by reaching a point a distance z ahead of him, then you just replace x+vt with x+vt+z.

To do this in general, you can start by computing x and y from the parameters you specify: y=wsin(x-z) and x=wcos(x-z). Then compute t as above, use it to figure out your destination, and off you go.