Sometimes your enemy is faster than you. Sometimes your enemy has a headstart on you. This does not mean you cannot kill him, when you are on an intercept course with your enemy you do not move until he does. A side effect of this is that interception courses can be calculated using trigonometry. This way you can know in advance if you can successfully intercept your enemy next turn and make your decisions based on this knowledge. Lets look at a specific situation to see how this can be done.
Here is a real-game example of when I used trigonometry to make a decision on whether to try intercepting an enemy.
Here you can see that Zoot’s ship is moving past my fleet. Can I intercept? To give you the groundwork Zoot’s ship has a speed of 41.7 while my intercepting fleet has a speed of 35.0. This places me at a distinct disadvantage in terms of speed but since Zoot is going past me I do have a slight lead on him. In this situation I cannot say just by eyeballing the positions of the ships if I will succeed in intercepting. This is where trigonometry comes in. Now relax, you do not have to understand trig to make this work. This is the information age! There are plenty of online calculators that will do the work for you. First lets draw a 2 triangle overlay so you can see what we are working with. The points in the first triangle are Zoot’s origin point, Zoot’s current position, and my current position. The first two points in the second triangle are shared with the first, namely Zoot’s current position, and my current position. The third point is Zoot’s projected position.
Lets go ahead and seperate the triangles from the background and label them to form an easy to work with diagram. We will designate all the points in the two triangles with a letter designation for ease of reference.
Hopefully you can see we are trying to solve the length of line segment DC. If DC is less than 35 than the interception will be successful. So we need to start figuring out what we do know. We know that the speed of Zoot’s ship is 41.7(as previously mentioned). So the length of AB is 41.7. We also know that Zoot’s cruiser started at Oenone 5(well I know that it did, so now you know to). So if we measure the distance between Oenone 5(the Point of Origin) and Oenone 1(My Position) we find the length of line segment AD is 51.1 units. To find the length of line segment BD we simple measure off the distance between Zoot’s current position and Oenone 1 which turns out to be 11.2 units. So now our diagram looks like this:
The basic rule for trig is you need three values, which we now have. So now we need to plug these values into a trig calculator. If you just do a search they are easy to find but for the search impaired, here is a link.
If you have a spreadsheet they are also quite capable of doing the calculation. This will require a bit more understanding on your part but I am confident you can handle it.
Once you use the calculator(or spreadsheet, or whatever) you should end up with the angles of the first triangle. Lets go ahead and plug those in.
Now the question becomes, how do you apply these values to get your solution? The easy solution is to just make it all one big triangle. Eliminate line segment BD and you end up with this:
This still leaves us incomplete since we do not have the full measure of line segment AC. Since we already know the speed of Zoot’s ship we can actually figure this out.Since Zoot’s cruiser is traveling in a straight line for two turns we know that the length of line segment AC will be 41.7*2=83.4. So we now have 3 values. Lets plug that in.
Put these values into the trig calculator and you end up with a distance for line segment DC of 33.4 units. So I will be able to successfully intercept Zoot’s Ship. This is a technique that you will not have to use very often but when you really need to know you will be grateful you know how.
Disclaimer: The enemy ship/fleet can change direction or be moving towards a moving target so these two things can cause this method to be inaccurate. Additionally, since distances are calculated from the surface of planets this will also cause some slight inconsistencies so take care if the result is really close. In this instance the actual distance ended up being 31.8 which was smaller than my calculated distance of 33.4 so this worked in my favor. I am not a trig expert but it would not surprise me if sometimes it can work against you. Of course, maybe not. If anyone who is versed in trig is out there please clarify.
As stated the 3d nature of planets and suns can cause some issues with precision. Fortunately the size of these objects is known. Planets are split into two classes, Gaseous and Rocky. Gaseous planets have a radius of 1.8 to 2.0 units. Rocky planets have a radius of 1.1 to 1.6 units. Hopefully you can tell the difference between the two by appearance. Suns have a radius of 3.0 to 4.0 units. Adding these radii to your calculations will increase your precision, used wisely you should be able to reach an accuracy of a few tenths of units. If your really anal you could even use trig to measure the radii of objects in the galaxy.
Trigonometry can also be used to frustrate pursuers. If you know an enemy is chasing your fleet you can use this knowledge to move them to a specific point in space using trig. You can evade, dodge, set traps, and frustrate your enemy in a wide variety of ways. Not only that but it is fun to have your enemy miss you by 0.1 units.
This guide has been created by uncountednose. See the forum contact information.
