Manually plotting an intercept course

[aatyler]

Hello every one. This is my first time posting on the forums but I've been perusing them here and there for several years now. I have been playing silent hunter since its debut with Silent Hunter 1.

I'm a big fan of realism and I enjoy doing things by hand. I've seen several posts on calculating intercept courses by using the protractor but with little mathematics. Being that I am an engineering student I enjoy math and wrote the attached document on how to calculate the intercept course.

It's based on the law of sines and requires a basic understanding of units (what a kilometer is, what a knot is, how units work in an equation, etc) and a little trigonometry. I hope it isn't to "mathy."

In any case, it shows a way to calculate the course to intercept a target with a basic scientific calculator. Of course, it requires two things:

1) a guess of the targets speed and course
2) your own speed

Once you make a calculation, it will yield a course that will ideally have you and your target arriving at the same time. To adjust for this, calculate the course at a speed slightly slower than the speed your actually going to travel, thus, you will arrive slightly before the target.

Now, this formula, in theory, could be used to calculate the manual solution to the torpedoes, but, there would be some corrections from courses to gyro angles and such, but I didn't write this guide with that in mind and honestly, in reality, a captain would not calculate that himself.

If anyone has any questions feel free to PM me or reply to this post and I'll make any corrections or further explanations as best as I can.

Happy hunting everyone!

Here is the link to the document: EDIT (Version 1.1 uploaded to make some clarifying additions)
https://drive.google.com/file/d/0B4O...it?usp=sharing

[Laufen zum Ziel]

Very interesting.

LzZ

[aatyler]

Hello again, everyone:

After some testing, after my previous post, there are some problems with the formulas such as when heading towards the target (IE the speeds combine to create a faster closing speed), I will work on this over the next few weeks and post an update as soon as possible.

thanks!

[aatyler]

Thank you. As I just posted, I need to make a few corrections to account for various things. But I am glad that it is interesting.

Regards

[aatyler]

Hello all,

I rechecked the calculations and the calculations for the time to intercept was wrong. It should all work now.

It is valid for where you can intercept (if you can't, the math *may* still work out) and for when you are in a position that the angle on the bow is less than 90 degrees. Again, if you are in a position, relative to the target that this isn't the case, the math on a calculator will work out, but, it will be in error.

For those of you interested in why, it has to due with the domain on the arcsin function. It is restricted to [-pi/2, pi/2]. I will spend more time trying to define this and explain it better in the documentation, but for now, in most cases it works as a good rough estimate for an intercept course, especially once you've closed to visual range and you need an exact course to travel to intercept the target.

Regards,

[Pisces]

Your document with formulas seem entirely correct. I just found a spot where you are cutting corners a bit in explaining why the numbers are as you state. Bottom of page 4, just after the ATI calculation in the example. Otherwise, nice job.

And since our initial course is not directly to the target, we find the course to the target as 21◦

It's true, but you do not show how that is found based on the data given in the example. Likely you will be losing a lot of people here. As the earlier used drawing of the intercept triangle does not match this setup. The drawing assumes the submarine is pointed to the target directly. Only when the situation drawing is recreated based on the given information can the reader determine that it is not in this example. Which I would suggest to readers to do anyway anyhow!!!

... You can find this by using the protractor on the map (if playing Silent Hunter) or by adding the bearing to target to your current course and subtracting 360◦ if the result is greater than 360◦.

Again true, but only on the assumption that you actually mean the relative bearing to the target. As given by the periscope dial or crew reports. (I suppose it can be considered obvious, as the true bearing is the one that we are trying to figure out here) But that one (relative bearing) isn't given in the initial data. Also, as intercepts are usually starting from beyond visual range, the AOB also cannot be determined visually. So using AOB and relative bearings is bit of an inappropriate example to explain the most frequent beyond-visual-range cases.

To solve this anyway, work your way back from the target course, via the AOB, from the target point of view, to the submarine point of view:

The relevant data given is your current course, targets current course and AOB. To calculate the course(true bearing) to target the starboard AOB needs to be added to the target course (port-side deducted). That gives the course/bearing to you from the target's point of view. To get the course from you to the target you add or subtract 180 degrees. (whichever one keeps you between 0 and 360)

target course + stb. AOB, or target course - port AOB; then +/- 180 degrees:

90+111=201 degrees (you are at 201 degrees from the target's position)

201-180= 21 degrees (course to target from your position)

I rechecked the calculations and the calculations for the time to intercept was wrong. It should all work now.

It is valid for where you can intercept (if you can't, the math *may* still work out) and for when you are in a position that the angle on the bow is less than 90 degrees. Again, if you are in a position, relative to the target that this isn't the case, the math on a calculator will work out, but, it will be in error.

For those of you interested in why, it has to due with the domain on the arcsin function. It is restricted to [-pi/2, pi/2]. I will spend more time trying to define this and explain it better in the documentation, but for now, in most cases it works as a good rough estimate for an intercept course, especially once you've closed to visual range and you need an exact course to travel to intercept the target.

I wouldn't worry about the sin function doing funky business if angles out side of 0-90 degrees are entered. Angles up to 180 degrees would still give positive values. ATI can only be negative if the AOB is given as a negative angle between 0 and -180. Which theoretically can indicate port vs starboard, but is never done in the context of the game(s). Nor have I ever seen AOB be reported as negative.

The intercept cannot happen when the submarine speed is less than target speed*sin(AOB). You might come closer if he is approaching (AOB < 90), but never enough to 'ram'. In order to gain in on a target that is moving away (AOB=90 to 180) the submarine must be going faster than the target speed. No other way around that. That is important to know to even consider the intercept.

[aatyler]

Piesces, thank you very much for your comments. I see your points and added some more diagrams and explanation within my example. I initially made my calculations assuming that my course would be directly to the target to simplify my calculations. I then made up the example in the manner that I new would be more common, I think that I have adequately explained the methods used to get the course.

I see your point about the AOB never being reported as negative, I present the mathematical domain of asin simply because I have that sort of thinking drilled into my brain from school.

Again, thank you very much for the feedback.

Happy hunting!

[Zosimus]

Is this better than the other method that's been floating around involving drawing a similar triangle whose interior angle is the same and whose sides are proportional? If so, how exactly is it better?

[Pisces]

It all comes down to the same formulas. One is done graphically. The other is done punching numbers and functions on a calculator. But no difference really.

[Zosimus]

Then I'll stick to my drawing tools. No offense.

[aatyler]

Why, none taken. So long as your method works for you, then that's all that matters. For whatever reason, my brain works better with formulas than graphics.

Regards,

[desirableroasted]

Originally Posted by aatyler

Why, none taken. So long as your method works for you, then that's all that matters. For whatever reason, my brain works better with formulas than graphics.

Regards,

I think you have done a fine job. Bringing brains to this game never hurts.

[Pisces]

Originally Posted by Zosimus

Then I'll stick to my drawing tools. No offense.

Well, there are sliderulers if you want to be historically correct. Like with a recreation of a Kriegsmarine Angriff Scheibe, or the US based Submarine Attack Course Finder. But I'm sure ebay or whatever has real linear sliderules for sale that your (grand)father used in his school days. If you want to stay authentic to the timeline. You aren't restricted to use modern scientific calculators made of silicon. But it does require a bit more thinking on your part in where the decimal point shifts to. As these things can't do that for you. Well, they would end up being yards or meters in length. Not very useful to handle.