What is your TDC up to? the Law of Cos, the perfect torpedo shot

[starvingartist507]

You can download any of my guides from www.hoofinasia.net
Also @ hoofinasia, the working stopwatch program I detailed below

EDIT: added the link to the Math guide
EDIT: added guide to main page. Sorry the pictures suck so bad. I'm trying to get my file host back online, but for now, thats the best I can do.

Once you figure out whats going on, I promise that it only takes a minute to figure out this stuff using game data, so its not like you have to pause it for an hour (or at all) to get an accurate speed reading.

To nail down a ship, do 3 things:
1. Figure range
2. Figure speed
3. Figure AOB

When you look at a target, you note several critical pieces of information. The first, Bearing, the second Range. The third piece required for a good shot is Angle on Bow. At first, just estimate AOB, so that you can point your boat in the right direction. Once you are basically in position, knowledge of a perfect heading becomes more pressing. There are a couple ways to figure out AOB and Heading with a totally normal degree of accuracy detailed elsewhere in the forum. This small and poorly illustrated example makes no attempt to dethrone the current guides, but I am trying to provide a way to get exact measurements, which are especially helpful for long range, high speed, or submerged-only shots. This method can even be used to figure a “total forward movement” and “generic heading” for a zig-zagging target, given enough patience and observation time. I might not get into that just now, however.

Let’s start with your average situation. You managed to point your ship somewhere ahead of a hapless merchie, and are bearing down on their estimated course. For the sake of simplicity, we’ll say that you are submerged, and have a good visual contact under 2.5 NM (approx 5000 yds).

Now the method I use can be used to figure exact heading and speed information on the target, even while the sub is moving, but the math gets a lot more complicated. So until I become more adept at spatial reasoning, I usually bring my sub down to a negligible speed, preferably a dead stop. This happens 90% of the time when I am approaching a firing position anyway, since I don’t want the periscope to get noticed, I am moving silently to evade escorts, or I have a little time to kill before the target is in the kill zone. Basically, it is good sub-commanding to bring the ship into a firing position, and let the target drift its way into your sights, no matter what your solution calculating tactics.

So you have a target off to your port side. We’ll imagine that the relative bearing is 330, or 60 degrees left. The target is heading towards you, so the AOB is less than 90 and they are showing their starboard side. If you can accurately identify the target, do so asap. Once this is done, you have to do a few things at once (or as quickly as possible.) First, start the stopwatch, as soon as you do that, figure range. If it is easier for you to get range then click start, go ahead. Remember in all those sub movies you watched as a kid, when the Skipper would yell “Mark! Bearing such and such, range so and so!” Well that is what you are doing. Get a range, get a bearing, and start the timer. Now is a convenient time to “down scope” if you need to be stealthy. Keep that timer going, let some time pass, the more the merrier. I usually go for 2 mins or so a lot more if they are still very far away. Once you are happy with the amount of time that has passed, up-scope, and yell “Mark! Range such and such, bearing so and so!” Don’t piss off your neighbors. Jot down the second range, the second bearing, and the time that has passed. Pause if you want to now, since you are doing the work of 2 crew members and a machine. There’s no shame in working more slowly, but the information doesn’t necessarily get outdated unless your target veers off course or changes speed. So it could be ok to remain going at real time.

Ok, with the two bearing and range readings, you have all the information you need to figure range and speed, and with that, you can not only calc AOB to the degree, you can also predict the AOB on a certain bearing. I.E. when the target is at bearing 350 (or time to shoot) the AOB will be…

So the law of Cosine.
You knew there would be math. The law of cosine states that if you know the length of two sides a triangle, and the measure of one of the angles, you can solve for all lengths and angles. Find the difference of the two bearings. Using the above example, Bearing one was 330, and we’ll say bearing two was 345. The difference is 15 degrees. We’ll say for argument that Range 1 was 2200, and range 2 was 2000. Yarr!ds… or

a=2200
b=2000
c=distance traveled
C=bearing change
B=Angle on bow start
A= 180 - Angle on bow finish.

According to the trig law: The distance of the third leg (which is the distance that the ship traveled) is:


Distance Travled^2= First Distance^2 + Second Distance2^2 – 2*Distance1*Distance2*Cos(angle change)

Using our data:
1. add squares of both distances (8,840,000)
Distance 1 was 2200, squared to 4,840,000
Distance 2 was 2000 squared to 4,000,000
2. Figure the Cosine of the angle. (.9659 )
(Remember the difference of the two angles was 15 Degrees. The cosine of 15 is .9659)
3. Double this, multiply by both distances. (8500140)
(2 times .9659 times 2000 times 2200)
4. Subtract the first total (step 1) from the second total (step 3) 339,860
(8,840,000-8,500,140)
5. The square root of this, (582.9751) is the distance that our merchie traveled between the two marked times.
If I waited 2 minutes (120 seconds), this gives me a base speed of 4.852812 yards per second (582.9751 divided by time). From there,
6. multiply by 1.777 to get a base speed of 8.63288 knots.
Any yards/second times 1.777 = knots.

That’s what your stopwatch button is supposed to calculate, but it doesn’t. An exact speed is usually enough to make a perfect shot, with a roughly accurate AOB.

To figure an exact AOB using 2 ranges and 2 bearings:
You know the angle of one leg, 15 degrees, and the opposite distance (582.9751 from the above work, step 5)
You also know the distance of all sides of the triangle. Dusting off your trigonometry book again. Recall that:

So! Sin of bearing change, divided by distance travled, equals Sine of Angle on Bow, divided by the range at Mark 2. Or!

• Find the sin of the bearing change. Recall from above that the bearing change was 15 deg. (0.2588)
• Multiply by the second distance to target (which was 2000) (517.6380902)
• Divide by the distance traveled (found using the above method) (.889792)
• The angle on bow is the inverse sin of this number (so the angle on bow was 62.6136)

The greatest part about knowing the exact angle on bow at an exact bearing is that, all future AOB will be related to that. So when our mystery ship was on bearing 330, and had an AOB 62.61; I am absolutely positive that at Bearing 345, it will have an AOB of 77.61. Why? Because all these angles and ranges just graph out a big triangle and all the angles of a triangle have to add up to 180. So trust me:

If the target moves 5 degrees, and you don’t move at all, the angle on bow increases by that amount. Simple as that.

Don’t try to solve for the final AOB, since you are actually solving the “inside” angle of the triangle (see below)…
So if you pop up the scope and figure an AOB of 44 Deg at bearing 50, you can be darn sure that when that target is at bearing 10, that it will have an AOB of 84 Deg. In this way, if you get a sure range and speed, you can calculate and predict AOB with a fantastic amount of certainty. So now you can fix the AOB for any time, and find the target speed with pinpoint accuracy. Those fish should be hitting right on every time.

This can also be used to predict range at a future bearing. Just re-solve with new information, invent any old situation you want. But for the most part, the only thing you need to get a good shot is AOB, Speed, Range. And Range is easy enough to equate, and this will give you the rest, down to pinpoint accuracy.

Remember this method is reliant on accurate range findings, as the manual states. So use the sonar station to back up your calculations. If you use the Sonar to re-check your range, remember as of 1.2 sonar was still bugged, so go the station directly, don’t trust what the sonarman told you, because he’ll just say whatever you have entered on the TDC. Sit down, and ping the target yourself for best results.

To figure an exact heading, knowing their AOB and bearing
This is very easily estimated using the charts, but if you for some reason need to know. As I sometimes do, here’s how I figure it out. Its quick and dirty math.
I just remember, Port = negative, starboard = positive (with straight ahead being the origin), and the enemy ship is opposite.

Take the first AOB that you just calculated, and the first bearing that you noted at Mark 1.
1. Your heading minus their relative bearing if they are on the port side (left), or plus their relative bearing if they are on the starboard (right)
If from the above example, they were at bearing 330, this means 30 port. So take our heading (270) and subtract 30. 240 is the Absolute Bearing
2. 180 + absolute = (heading if AOB=0). So if AOB is 30 starboard, subtract 30 from this result. If 40 port, add 40.

From above, AOB was 62.61 at bearing 330. 330 = 30 to port side. So our heading (270) minus relative bearing since we are looking to port (30) = 240 Absolute bearing, or about WSW. Then take this absolute bearing and add 180, then add or subtract their AOB. So Absolute bearing of 240, plus 180 (420) minus their AOB (which was starboard 62.61) for an exact heading of 357.39. I apologize that the chart below doesn’t perfectly match the math. I was just throwing lines together to show how they relate. But you get the idea I hope!

Happy Hunting! If you actually use this with any measure of success let me know! It seems way to complicated once I write it down…

[MONOLITH]

Originally Posted by starvingartist507

Would anyone be interested in reading how to solve AOB, Target speed, heading, etc with two seperate range and bearing checks?

Yes, I would.

[XanderF]

Originally Posted by MONOLITH

Yes, I would.

This thread for you, then. More authentic to use a slide rule, too.

But that's what it gets you. Two separate range and bearing checks, doesn't even really matter how long apart (long enough for there to be some meaningful change in target position, anyway), and you have everything you need to shoot.

[starvingartist507]

anyway...
The point was, I'm not using a slide rule. I dont own one. Like I said, I admire the use of outside tools, I just don't have them. Authenticity is great, I was just thinking about the math involved. Just used pen, paper, and my scientific calc. I'm not too worried about the authenticity of it.

Thanks for the link. I'll see if I can't track down something like whats mentioned. However, I got this typed up if anyone wants to read what I did and I figure I'll just link it in case.

It'll get you exact numbers, and no reading of charts or anything extra to print, just write it down...

You can find my method @ www.hoofinasia.net/TDC.htm

[Swooth]

Even though I'm not good in math, I'll give it a whirl and see if I can understand it. Nevertheless, thanks for the info, greatly appreciated

[MONOLITH]

I just put a hand over one eye to reduce my depth perception and hit the fire key.

Works every time.


:rotfl:

[nattydread]

I only use them to determine distance from track. I determine AoB and speed by eye-balling it.

[Xelif]

Ahhh, you are my hero! I needed an explanation like this, finally a use for that trig I learned those years ago... Now, I haven't tested it myself, but I jotted down some notes and I would like to say your explanation so far is clear and seems perfectly workable! I've been using a different manual targeting method and this is a lot more flexible. I'll respond more after I've had time to wring it out in the ocean

(edit) This alone should be in bold in every sub sim manual:
If the target moves 5 degrees, and you don’t move at all, the angle on bow increases by that amount (or decreases if the target is moving away.) Simple as that.

Wow that'll make quickly changing my solutions easy!

(double ed) Your method for calculating AOB could use a little clearing up. Let me work through some of it tomorrow and I'll post again if I am still confused. Need to sleep...

[starvingartist507]

Its important to note my method only calculates the AOB for the first mark, as in the first time you grabbed range and bearing. Then add the number of degrees that the target has "tracked"

1. Sine of ( bearing change ) times Range at mark 2
2. This divided by distance merchant traveled
3. inverse sin of the result = AOB at first observation
4. if the merchie has moved 25 degrees since then, add 25 degrees to AOB
presto!

I noticed I had this wrong in the doc. Corrected it!
Hope this was a little more clear.
also added how to find exact heading, if you wanted to know... but not many people should need that.

[Xelif]

Grrrr I wrote an entire post, then reloaded the page by accident.

Ah, let me seek some clarification on your algebra for AOB calculations.

Initially, is this accurate?

1) c / sin C = a / sin A
Cross multiply out:
2) sin C * a = sin A * c
Isolate and solve for angle A (using inverse sin)
3) sin A = (sin C * a / c)

Now I have to dig my scientific calculator out!!

Assuming the above is right, can't you solve for final AoB by using the B portion of the formula?

c / sin C = b / sin B, etc etc solve for angle B?

[Xelif]

Your chart is remarkably similar to what I've got down in my notebook. I just sat down and tested everything. First I ran through your example numbers and got the same result as you (good!). I'm documenting everthing here in the hopes that another reader finds it useful... Starvingartist, you already -know- all this stuff but feel free to critique.

I realized I must be the only person who can't figure out how to switch SH4 from metric to imperial measurement... although I'm entirely used comfortable with metric (SI technically), despite being born in the United States.

Anyway, a quick lookup of meters/second to knots yields a conversion factor of 1.94384. That really helps in setting speed for your torps, using my math

Then I loaded up Ol' Faithful - the third sub school exercise, where you start with a not-quite perpendicular cruiser in the exact same place every time. I've trained with this scenario so much I know what the ranges, speed, and angles are, along with the proper torpedo settings. I use manual targeting but have map contacts on, so I can resort to the map for a quick range check / AoB check. This allows me to verify my solutions.

My previous method of calculating speed involved an observation period of 3 minutes 15 seconds, so I was very drawn to this method as it allows any two bearing/range checks to suffice - the further apart the better as it allows finer resolution. I immediately got range/bearing information, waited 1 minute 40 seconds (which works out to 100 seconds, making the math later a little easy... not neccessary but helpful) and took my second range/bearing information.

Relevent data (pretend it's in a sketched out table):
Range, Bearing, Time
1500 meters, 322 deg, 0 seconds
1200 meters, 337 deg, 100 seconds

Also sketched out is what I am going to call the triangle of torpedo love... see the above posts for starvingartists's images of the ABC triangle... I'm sure there's a technical name, so pardon me. Each side has the relevant data filled in, and the direction of travel is indicated just to make sure I don't forget. It helps to remember that the sub is at angle C, and if you view the triangle from that perspective (flip it upside down mentally or on paper), it becomes very clear which measurements are which.

I won't illustrate my math here, mostly because I can't represent exponents properly, but I ended up with the target's net distance travelled of 461 meters, at a net speed of 4.6 meters per second, or 8.964 knots, basically 9 knots... the speed I'd been using all along in this scenario. Yay! Angle on bow was calculating using the above formulas and resulted in 42 degrees, updated to 57 degrees at the time of second observation. This was exactly accurate according to the map (well, depending on where the line is drawn to your ship - it was perfect for my forward torpedo tubes.)

Torpedo solution was similar to every other solution I have used in that scenario... 3 torpedoes fired, 1 premature detonation, 2 hits, slightly aft of where I had been aiming. I did not enable the position keeper quickly enough, so the range solution was slightly too long, resulting in my torps hitting slightly aft - at least, that's what I believe happened. Overall, I was impressed with the accuracy. It took me a lot longer to calculate this by hand than is acceptable in a submarine environment, but the game has a pause key for a reason! I imagine I will get a lot faster with practice. Right now every step was written out so I could verify I didn't make any stupid math mistakes - a classic problem when I was in college

I'm going to start using this out on patrols now

[starvingartist507]

I think that when you click "fire" the target settings are fixed. I noticed a VERY substantial delay when ordering a second tube to fire. To compensate, I usually fire all torpedos just a bit ahead of predicted course, since there is no way to *AHEM* open all tubes at once, which would aleviate the problem of constant trailing shots for the second, third, etc tube.

...I think.

Glad it worked out for you. Once you get the steps laid out, it really is just a 1,2,3,4 type of operation, and its faster than plotting and estimating eventually. With a chronometer fix this will all just be academic, but its been a fun exercise, and finding an exact AOB is always useful, since the game never makes that real easy.

Oh well, I'll leave the guide up in the off chance that someone else likes it.

[Xelif]

This is unrelated to your solution calculating, but while we're on the topic of manual targeting... I've noticed very odd things with the manual targeting. For instance, I can't get a torpedo to aim where the optics are pointing, after I've entered in a solution. I have to aim at a new point, then click the range update button. At that point, the new heading is reflected in the torpedo panel to the left. It doesn't update as the periscope turns. I think I can get it to aim optically, but I can't remember offhand how.

Also, it doesn't do any kind of internal updating unless you activate the position keeper (the button on lower right that turns red).

In any case, I have best results by entering a valid firing solution, immediately activating the position keeper button, and firing using the following procedure:
1) Select tube 1
2) Open tube 1 with 'q', wait a few seconds
3) Fire tube 1
4) Select tube 2
5) Open tube 2 and wait a few seconds
6) Modify salvo angle setting on torpedo panel to 1 or 2 degrees right
7) Fire tube 2
8-9) Repeat 5-7 with tube 3, but 1 or 2 degrees left.

It fires a decent spread, and the solution is automatically updated as the target moves, with the position keeper active. The key is opening the torpedo tube, then WAITING five or more seconds (I can't remember offhand if there's a sound... there was in SHIII), then firing. It'll have a more accurate solution.

This is all in my experience of course, and I'm by no means a veteran. I recently got SHIV and have been practicing torpedo attacks almost endlessly, in order to get a feel for the system. If anyone disagrees, please respond I'm just trying to figure things out and listing my reasoning so anyone can point out where I'm wrong.

It all started with my torps hitting on the same area of the ship, despite my optics attempting to lead/lag the target. That made me question what the manual said about optical targeting. I finally hit upon the manual somewhat clumsy salvo procedure above. There's time lag between the torps, but as long as the solution is valid and the position keeper enabled, they will be accurate with regards to spread and each other. It's -almost- as good as firing a 3-torp salvo in SHIII, just on a longer timescale.

[MudMarine]

Can this method/math be used with a slide rule? If so how. Just learning to use one,a circular one at that.

[starvingartist507]

well, yeah, thats what a slide rule is for, but theres a thread about that somewhere else. I believe it is here:

http://www.subsim.com/radioroom/showthread.php?t=112765

I don't have one, and don't plan on getting one just yet
I'm more interested in applying that Trig I learned, exploring the math behind a good solution. Besides, I already labeled my old casio "TDC".

Also, its nice to use trig to set up a solution even when the sub is moving. No more coming to a dead stop for solutions. I'm not sure if a slide rule can do that, and if it can, thats dope. I just like my good old calc.