Using a fictitious course to set TDC

[Rockin Robbins]

OK, what do you want to call progress? Let's just say that intuition doesn't always lead to the truth. I set up a situation in SH4 because other than MoBo, which I need to seriously do a refresher course on, SH4 has the most appropriate drawing tools for the situation. Inkscape just wasn't cutting it.

Now using the game to plot also gives me another advantage. I can kill all the trig tables, formulas, unclear hocus pocus altogether and let the TDC do the math for me. You can check my work at a glance and tell whether I've made any mistakes. I'm not here to make claims that you can't prove or disprove easily.

Here's the plot. I should annotate it, but I was pretty excited about what I found and wanted to get it posted quickly, especially since I've kept you waiting too long already.




We have a real target out there moving left to right on a course of 70º at 4.5 knots. But shhhhhhhh! We don't know that. Let's take a couple of sights and stick them on a fictitious course line 1000 yards away, running at right angles to our course. You can see the two courses actually cross and this should be an accurate setup if there is such a thing.

We take our first bearing at time 0:00 and find a bearing of 300º. There's the bearing line and our fictitious position is where the bearing line crosses the fictitious course line. The real position is where it passes the skewed real course line. Shhhhhhh! We aren't supposed to know anything about that.

Three minutes later we take our second bearing of 314º, plotting that on our fictitious bearing line. You can also see the real position where it crosses the real course line. Shhhhhhhh! Don't spill the beans...

With our compass we can measure the distance on our fictitious course line as 700 yards, which translates to 7 knots. We're going to fire when the target reaches the zero bearing so our angle on the bow for an attack 90º from our course will be 90 minus zero or just 90º starboard. We put a range of 1500 yards or so (doesn't matter for this application) into the TDC and with our four parameters entered we can check out our gyro angle.



Nice thing about the TDC is that you can verify that I have input the AoB at 90 starboard, speed 7 kt, range who cares. Gyro angle? 10º. Now let's enter the real numbers and see what we get.

You can see on the plot that his AoB is really 110º starboard, his speed 4.5 kt and his range 1500 yards exactly. Shhhhhhh! This is top secret information. We can enter this info into the TDC. If the gyro angle is the same, we have a hit! So with great anticipation and foaming at the mouth, Napolean (arcane reference to a badly botched attempt at a personal insult in another thread) enters the golden numbers. Hehehehehehehe!



Fail! 6º is the actual gyro angle for a hit. Set by our fictitious course data, our gyro angle was 10º so we're 4º ahead of MOT (standard US Navy for middle of target. I don't make up arcane abbreviations or use non-standard variables in my formulas) if that's what we're aiming for.

OK, how bad did we miss? What the hell, let's do some hocus pocus trigonometry. Well, at 1500 yards, .0175 (approx) is the sine of 1º. Multiplying that by the 1500 yard range yields an error of 26.25 yards per degree of error. We have four of those, so we're off by 105 yards. Figuring that our average merchie is about 130 yards (390') long, taking half of that (since we are firing at MOT) we have a 65 yard allowance for error, our shot misses by 45 yards ahead and we're dog meat.

Now we could get hits with a small enough range. For instance, at 500 yards 1º of error is only 8.75 yards. We'd hit four of those, 35 yards ahead of MOT for a big boom and be a hero! But I daresay at 500 yards you can just eyeball a lead with no calculation at all and hit just about anything, so our method is just a waste of time.

We could'a had a V-8!

Note: anybody catching on how to rigorously prove a method? I did make a small error in the hocus pocus section. Can anyone catch it and apply the correction? Play the Jeopardy waiting music!

[Rockin Robbins]

Now, what went wrong here. I think number one is the inappropriate use of a constant bearing technique. After all, the constant bearing techniques work at any range if you know the target speed. In other words, the solution is just the same at 1000 yards as it is at 2000 yards.

The same gyro setting hits both targets moving the same speed! However when we project bearings onto a fictitious course we end up changing the speed, according to whether the fictitious course is nearer or farther than the real target.

So though intuitively, it seems reasonable that this should work, it cannot. I will now investigate more conventional targeting methods.

I have had a bad stadimeter reading and set for a range over or under the real range. Using the attack screen I can adjust the speed to a wrong speed that is proportional to my error.

For example, suppose my input range is too large. I can input a speed higher than the target's real speed. If I get the right one, a line from my submarine through the impact point in the empty ocean intersects with the target position. That is a valid solution and I will get a hit.

The same thing applies to a range too short. By reducing the speed, I can make a situation where a line from the submarine through the impact poiint on the attack map intersects the real target. I'll hit that target with a bad range and speed.

In both instances the AoB/target course has to be nearly right.

So that's where I go next: to familiar ground and outside my normal preference for constant bearing techniques.