Single Observation Firing Solution Procedure
 

Season's Greetings Fellow Kaleuns!

First, an introduction. I am a short time lurker, and first time poster. Although I've been a flight simmer for almost half a decade, I started playing SH3 less than two weeks ago, and I've become quite addicted. What drew me into the submarine simulation genre was the mathematics involved in operating a submarine. My first exposure to submarines was the film "The Hunt for Red October". The scene that made the deepest impression on my young mind was when Captain Marko Ramius ordered his navigator to compute the timing of a critical course change:

"Navigator, recompute for 20 knots!"
"Yes sir! ...Turn on my mark... 3... 2... 1..."

The fact that abstract mathematical concepts were used to direct the operation of a physical, although fictional, submarine was more impressive than any of the spectacular action scenes that followed.

It should come as no suprise that I play on full realism, fully embracing the hands-on mathematics that are involved in a successful submarine mission. While initially frustrating, I've learned quickly, and I'm currently sinkng commerce with the best of them. To this end, I've received my virtual submariners education through several community members' contributions; namely Wazoo's Manual Targetting Tutorial, and an intercept tutorial written by a community member whose name I sadly forgot. I'd also like to thank the numerous other members of this forum, whose questions and answers helped me to perceive the subtle complexities of this simulation. Now I'd like to return the favor, and share a little something I worked up myself.

SINGLE OBSERVATION FIRING SOLUTION PROCEDURE

Objective
Using a single periscope observation of a target ship, compute all the variables necessary for an accurate torpedoe firing solution: Range, Speed, and AOB (Angle on the Bow)

Introduction
A target ship's position and behavior can be described using four elements: Bearing, Range, Course, and Velocity. Bearing and Range fix the target's location, and Course and Velocity predict it's future movements. These four elements are required to calculate an accurate torpedo firing solution.

The easiest way to gather this information is to take two successive bearing and range readings at a known time interval. This will create two points on a two-dimensional grid. A line connecting the points reveals course, and the distance between the points can be divided by the time interval to produce speed. This is the method used in Wazoo's Manual Targetting Tutorial.

While simple and effective, this method has two significant drawbacks. First, it is very time consuming. By its nature, this procedure requires the captain to wait some time interval between his readings. In a time critical situation, such as when engaging a target that's rapidly moving out of his optimal firing spot, a captain might not have the time needed to wait the minute or so between plots. Second, this method is very susceptible to user error. In order to get an accurate course and speed, one must acquire at least two accurate bearing and range readings. A single inaccuracy will result in an erroneous range and speed. This effect can of course be mitigated by taking many readings, and averaging the results. However, this also takes up valuable time. In the life of a submariner, the difference between victory and death is often measured in seconds.

This paper will detail a procedure by which a captain can obtain all the necessary information needed for a firing solution with just one target sighting. Since this only depends on one accurate sighting, rather than two, the potential of error is greatly reduced, and the time required to achieve a firing solution is reduced from minutes to seconds.

SINGLE OBSERVATION FIRING SOLUTION PROCEDURE

Since almost everyone is familiar with determining target range using the stadimeter tool, that will not be covered. Instead, I will focus on the two remaining variables: AOB and Speed.

Part I: AOB

Theory: A ship at 90 degrees AOB will appear to be as long as it's reported literature length. As the AOB increases or decreases from 90 degrees, the ship will appear narrower. This length contraction is directly related to the deviation from 90 degrees AOB. Therefore, if we can measure the apparent length of the ship, and read off it's actual length from the Target Recognition Handbook, then the target's deviation from 90 degrees AOB can be calculated. By adding or subtracting this deviation amount from 90 degrees, the target's true AOB can be determined.

Workup
http://img85.imageshack.us/img85/8761/aobuy0.gif

Knowing the range from stadimeter readings, as well as the angular size of the ship, measured using the periscope, the apparent target length can be calculated as:

(1) Apparent Length == Range * tangent[Angular Length]

Using the calculated Apparent Length, the deviation from 90 AOB can be calculated:

(2) Cosine[Deviation from 90 AOB] == Apparent Length / Actual Length
(3) Deviation from 90 AOB == Inverse Cosine[Apparent Length / Actual Length]

Putting equations (1) and (3) together...

(4) Deviation from 90 AOB == Inverse Cosine[(Range / Actual Length) * Tangent[Angular Length]]

Execution:

Suggested Method: Calculation

1) Identify Target Ship visually using Ship Recognition Handbook
2) Note down Target Ship Length (L)
3) Resolve Target Range (R) using Stadimeter Tool
4) Point periscope at Target Bow, note bearing.
5) Point periscope at Target Stern, note bearing.
6) Subtract 4 and 5 to resolve Target Angular Length (A)

7) Calculate deviation from 90 AOB using formula:

Deviation == Inverse Cosine[(R/L)*Tangent[A]]

8a) If target ship is heading towards you, subtract that deviation from 90 AOB. e.g. if Deviation == 20 degrees, target AOB is 70 degrees.
8b) If target ship is heading away from you, add that deviation to 90 AOB. e.g. if Deviation == 20 degrees, target AOB is 110 degrees.

Result: Target AOB is known.

Alternative Method: Graphical

1) Replicate the image shown, using ruler and protractor tools to draw the real lengths and angles.
2) Instead of drawing in target actual length with the ruler, use a compass with the radius set to the target's length, with center placed on the non-vertical arm.
3) Measure the angle from the horizontal to where the compass circle intersects the vertical line. That is your deviation.
4) Proceed using steps 8a or 8b as outlined above.

Note: This method takes longer, and is more susceptible to error than the calculation method. If you believe that it is "unrealistic" that a WW2 captain would be able to calculate tangents and inverse cosines, keep in mind that the stadimeter tool, which did not exist in real life, does exactly that. This does not depart from realism any more than using the stadimeter.

Welcome aboard kaleun :arrgh!:
Your next posting is the naval academy :know:

Welcome! :up:

How can you calculate speed from a single observation?

For speeds that are less than infinite, calculating speed from a single observation by definition its impossible.

Speed is distance/time. You need to observe distance and time to get speed.

In order to observe time you need two observations: One at the start of the time frame and one at the end.

In order to observe distance you need two observations: One at the start of the distance and one at the end.

The only way you could observe speed in a single observation is by either:
Observing a cause of speed (i.e. the settings in the ships control room)
or:
Observing a product of speed (i.e. the size of the bow wave)

but I'm not aware of anyway this is possible with any accuracy.


I'm gonna be very impressed if you have found a way! It's got me thinking. :hmm:

I think that it's impossible to get target speed without two observations ...even if you use the Carnot theoreme (that avoid you to wait 3 minutes or 1,5minuetes) you need two observations .
Anyway i'm curious to know your theory :up:

Didn't sub skippers (and others too if they could observe) estimate speed by observing the bow wave? In fact some ships had false bow waves painted to confuse subs.

You can estimate the speed, but you can't get more accurate than "slow medium or fast". That's no where near good enough to get a torpedo fireing solution unless you have homing torpedoes.

It was one single PERISCOPE observation......

nail the speed with hydrophone.

First you spot it in the scope.

Plot the range and AOB and make an extended course line.

Now take hydrophone bearings with 3.15 min seperation = speed (IF he continues his course...)

You are para-phrasing too much.



Useing hydrophones to "nail the speed" is not useing a "Single periscope observation... [to] compute all the variables".

Part 1 detailing how to solve for AOB has been uploaded. Expect Part 2: Speed to come with 24 hours.

For those of you guessing at how I'm going to calculate target speed, it's purely based off a single visual contact. It has nothing to do with the hydrophones, or waiting several minutes, or guessing it based on bow wake. It's honestly quite simple once you think about it. Feel free to keep guessing though!

Get on the radio and ask the nice enemy captain how fast he's sailing?

Beats me, I don't think you'd be able to get an accurate enough speed estimate just based on one scope sighting. But I've been wrong before. :D

The size of the bow wave. Some of you with sailing experience have probably heard the term "She has a bone in her teeth"...which refers to a vessel making good headway, thus a bigger bow wave. A slow moving vessel produces very little foam.

In real life you can make a rough guess as to speed based on the size of the bow wave. In a simulation or at night...that could be a bit tough!

Put crosshair on the bow and see how long it takes for the ship to sail through? Measures distance travelled (length of ship) in seconds and math it out for range to target?

Sorry I have no idea what I'm talking about.:doh: LOL

Why not just take one look with the periscope and mesure distance+ mark your position on the map. Than change course and use the hidrophones to track the bearing to target+ mark your new position.
If you do this a couple of times (more is better) you can calculate speed, AOB and distance from the map (it can even be done without any periscope observation at all) in other words just good old TMA fiddling

Of course because this IS WW2 I personaly just take a couple of periscope readings and use the 3:15 rule to get solutions because a few priscope peaks never gave me away so far- and if it works why bother complicate things