To create a proper torpedo solution, you need two main pieces of information from the target: its course and its speed.

This is true only if you're attempting to have the torpedoes impact at ~90 degrees to the target's hull. This is generally ideal for three reasons. Firstly, most torpedo warheads historically had vastly increased malfunction chances when impacting at oblique angles. Secondly, and most importantly to us, is that errors that cause inaccuracy are more mitigated when using a perpendicular attack. Lastly, it makes any math needed to be done simpler.

If for some reason that a situation occurs that you're forced into an angled shot, you will also need the target's range, so that the torpedo's gyroangle is set correctly. In UBOAT, as most subsims that I've played, the gyroangle is calculated and set by the game once the needed information is inputted. Also, certain methods to find course and/or speed may require getting range at certain times.

So, you've hunted or stumbled upon a ship and it's elevated a little too far above the sea floor for your tastes.



In most situations, this will form a triangle defined by the lines that consist of the target's course, your course and the target's bearing.



All triangles contain 3 angles that add up to 180°. The encounter triangle consists the three angles: the bearing angle, the angle on bow (AOB), and (what I refer to as) the angle of impact (AOI).

The bearing angle is defined as the angle formed by the lines of your course and the target's bearing.



Given that you are aware of a target, this is your only known value at the beginning of an encounter.

A target's Angle on Bow (AOB) is defined as the angle formed by the lines of target's course and the target's bearing.



By finding the target's AOB, you find its course since you know the bearing angle at which it was observed. Please note that a target's AOB will change as it, or you, travel. This does not indicate that the target's course has changed.

A target's AOI is defined as the angle formed by the lines of target's course and your course. It is commonly calculated as 180 - (BA + AOB).



This will be a static number if both you and the target keep your respective courses. As suggested by the name the AOI is the angle of impact for a torpedo with 0 gyroangle, so ideally this should be 90° before committing to a torpedo attack.

As of B128H4, this is also the number entered into the in-game course finding tool.

The in-game tool is modeled after an AOB course finder, one that is similar to other subsims.



However, it is programmed (as of B128H4) in UBOAT counter intuitively. Instead of an AOB course finder, it behaves like an AOI course finder, requiring a few more steps to use. Visually, it works like this:



And placed over the encounter triangle, it looks like this:



Practically, calculate the AOB. Enter that value with the sign (+/-) based on the side that the target is showing, based on the tool. Red (negative) for the port (left) side of the target or green (positive) for the starboard (right) side.

AOI = 180 - (BA + AOB)

This method is one of the easiest methods to use and one that many a captain uses. In more realistic difficulties, either in a game or self-imposed, this method may be unavailable due to it's reliance on the satellite like imagery information gained from most map modes.

To use it, plot at least 2 points on the map, with the points made over the target. These are preferably made over the same position on the target and for as long of a time period as you feel comfortable. Feel free to pause the game if it makes it easier.



Make a line using the first point and passing it through later ones as far as needed. This line is the target's course. I would recommend observing the target, watching if it follows this line and adjust the line if the target strays. It's not uncommon to have to adjust the line slightly after a few minutes to improve accuracy.



To find a vessel's numerical course from the map, extend the course line to pass through a given longitudinal (north-south) line. Measure the angle from a southern part of the longitudinal line, to the intersection between that and its course, to the farthest point of the course line in the direction the vessel is travelling.



If the vessel is travelling more east, subtract that angle from 180, the result is the vessel's course. If instead the vessel is travelling west, add that angle to 180, that is the vessel's course.

Course = 180 ± Angle

Course = 180 - 134
Course = 46

If you have the Compass Navigation mod installed, as it is in these screenshots, the azimuths of any given line is displayed, allowing you to skip this measuring step.

While an experienced captain can visually estimate a given target's AOB, it can also be calculated via the target's apparent aspect ratio. To do this you need to identify the target, so you can look up the ship's mast height and length. In addition, having a properly calibrated sight is helpful to use.

For ease later, first calculate the aspect ratio of the target's length over it's height.



AR = Length / Mast Height
AR (C3) = 143.67 m / 35.85 m
AR (C3) ≈ 4.0075

Next, you must determine the optical height (OH) of the target's mast. Typically, this is in milliradians (mrad). You can also use the stadimeter, if one is available.



Convert the optical height into the units for the optical length, if needed. This is generally in degrees.

OH ≈ 82 mrad
OH = 82 mrad / 10 (magnification level)
OH = 8.2 mrad
OH = 8.2 mrad / 17.45 (mrad / degree)
OH ≈ 0.47 degrees



Multiply the AR by the optical height (OH), this is our expected optical length (EOL).

EOL = AR * OH
EOL = 4.0075 * 0.47
EOL ≈ 1.884

Divide the optical length (OL) by the expected optical length, then either find the inverse sine or consult a sine table to find the AOB.



OL ≈ 15.75 degrees
OL = 15.75 degrees / 10 (magnification level)
OL = 1.575 degrees

AOB = asin (OL/EOL)
AOB = asin (1.575 / 1.884)
AOB = asin (~0.8359)
AOB ≈ 56.7 degrees

Sample sine table

This three bearing method is part of the larger four bearing method, which can be found via a quick google search. While the webpage where the pdf is located isn't malicious, it is also not secure so I will not link to it. Instead I will describe some variants of the larger method in the document which you can go to find more details.

In this more basic form, your boat must be stationary, while more advanced versions allow for maneuvering.

In a stationary boat, take three bearing readings and record the time intervals. Typically the intervals should be from 5 to 10 minutes; longer intervals provide better accuracy for the calculations. The method resolves more easily if the time between readings are the same. I recommend using the stopwatch from the TDC mod, though you could use the stock speed tool's stopwatch as well.



BEARING 1 = 307
BEARING 2 = 323.2
BEARING 3 = 334.8
TIME 1 = 10 m = 600s
TIME 2 = 15 m = 900s - TIME 1 = 300s

Plot the bearing lines.



Place 2 points whose distances are a ratio of the times between the bearing readings along the middle bearing line. If the time interval is the same, use a single point. I recommend using 10 meters per second measured or use some other value that you feel comfortable with.

POINT 1 = TIME 1 x 10 m = 6000 m



POINT 2 = TIME 2 x 10 m = 3000 m



Follow down the outer bearing line which has the largest measured time, measure the angle between that bearing line and the middle bearing line. Then go up the middle bearing line to the closest point of the ones you just made. Make a line at the angle you just measured that would be parallel to the outer bearing line that you first went down. If using the Compass Navigation mod you can use the reciprocal bearing instead.



Repeat for the other bearing line, except use the farther point on the middle bearing. If both time intervals were equal, use the same point. If you have the compass mod, you can use the azimuths it gives instead of bearing readings for more accuracy (10ths of a degree vs whole degrees).



Create a line going through the intersection points on the first and third bearings. This is the target's course line if you had adjusted for your heading. For simplicity, I'll use the in-game course finder. To do that measure the angle between the first bearing and the course line.



In this case, the target's AOB at the first bearing is measured at 41 degrees. The bearing it was at was 307, which is a bearing angle of 53 degrees.

AOB = 41
BA = 53

AOI = 180 - (BA + AOB)
AOI = 180 - (41 + 53)
AOI = 180 - 94
AOI = 86 degrees

Which, incidentally, is the 'course' of the target we calculated. Entering this into the course finder tool will calculate the target's course based on your current heading. It's important to enter the value before maneuvering, otherwise it will be inaccurate.

This is the same as the graphical variant, just using math. Hypothetically, this could have been used historically, as it only needs a 3 decimal place accuracy to yield viable results, which is doable with the slide rules and trig tables available in the period. Practically, to do so in the middle of combat is questionable.

First, gather and record the bearing readings and time intervals.

BEARING 1 = 307
BEARING 2 = 323.2
BEARING 3 = 334.8
TIME 1 = 10 m = 600s
TIME 2 = 15 m = 900s - TIME 1 = 300s

Measure or calculate the angles in the direction the target is traveling, negative for anticlockwise and positive otherwise.

A1 = 16.2 deg
A2 = 11.6 deg
t1 = 600 s
t2 = 300 s

Find the ratio of the time intervals.

Z = t1 / t2
Z = 600 / 300
Z = 2

Find the ratio of the sine of 2nd angle over the the sin of the sum of the angles.

Y = sin (A2) / sin (A1 + A2)
Y = sin (11.6 deg) / sin (11.6 deg + 16.2 deg)
Y = sin (11.6 deg) / sin (27.8 deg)
Y = 0.201 / 0.466
Y = 0.431

Then we find the first bearing's length relative to the center bearing.

b1 = (1 + Z) * Y
b1 = (1 + 2) * 0.431
b1 = 3 * 0.467
b1 = 1.293

Use the Law of Cosines to find the length of the target's track relative to the center bearing.

a1 = sqrt (b1 ^ 2 - 2 * b1 * cos(A1) + 1)
a1 = sqrt (1.293 ^ 2 - 2 *1.293 * cos(16.2 deg) + 1)
a1 = sqrt (1.671 - 2.586 * 0.960 + 1)
a1 = sqrt (1.671 - 2.482 + 1)
a1 = sqrt (0.189)
a1 = 0.434

Use the Law of Sines to find what the AOB at the first bearing was.

AOB @ b1 = asin (sin (A1) / a1)
AOB @ b1 = asin (sin (16.2 deg) / 0.434)
AOB @ b1 = asin (0.278 / 0.434)
AOB @ b1 = asin (0.641)
AOB @ b1 = 40 deg

Finally, figure out the course. As with the graphical variant, the easiest way is to use the in game tool. With the value given by the bearing angle at the first bearing, adding the AOB and subtracting the sum from 180.

Bearing Angle @ Bearing 1 = 360 - 307 = 53 deg
AOB @ Bearing 1 = 40 deg

AOI = 180 - (BA + AOB)
AOI = 180 - (40 + 53)
AOI = 180 - 93
AOI = 87 degrees

Entering this into the course finder tool will calculate the target's course based on your current heading. It's important to enter the value before maneuvering, otherwise it will be inaccurate.

To find an object's speed you need to find the distance it traveled and divide it by the time it took to travel it. So you need two pieces of information, distance and time.

One of the easier ways to do so is to time is takes a target to pass it's own length.

First you need to identify the target to determine it's length.




Then while stationary, measure the time it takes to pass front to back through the vertical line on a stationary periscope.

[Insert Images]


Finally convert to your unit of choice. The in-game tool will do this automatically.

As a word of caution, as noted on in the identification book, the Empire classes of ships have variable measurements. The chronograph tool will use the ships length based off the one listed in the book, instead of its true length. This makes this tool very unreliable for measuring those classes of ship.

Another thing to note, this chronograph's minute hand is 10 times faster than it should be (as of b129p3). This seems to be a visual bug, but needs to be kept in mind if you use it for anything other than the speed tool. It seems to be accurate when this oddity is accounted for.

This method is pretty straightforward.

Make a mark on the map where the target is and wait some time.



Then make another mark. Measure the length traveled, divide by the time passed and convert to the units you need.



1 knot = ~0.51444 m/s = ~0.5626 yd/s
1 km/h = ~0.27778 m/s

SPEED = (Distance / Time) / Mult
SPEED = (750 m / 194 s) / 0.51444 (m/s / kt)
SPEED = 3.8659 m/s / 0.51444 (m/s / kt)
SPEED = 7.51 kts

If you wait a specific amount of time, the conversion simplifies so that you'll only need to divide the length traveled by 100 and that will give the speed in the units you're using, depending on the unit set you're using.

Imperial should use 2 minutes 58 seconds. Usually this is simplified to 3 minutes.
Mixed should use 3 minutes 14 seconds. Usually this is simplified to 3 minutes 15 seconds.
Metric should use 6 minutes.

Time = 3 m 14s = 194 s
SPEED (kt) = Distance / 100
SPEED (kt) = 750 / 100
SPEED (kt) = 7.5 kts

To be clear, historically the Type VIIc did not have a stadimeter. However, I consider it to be equivalent to measuring the marks on the periscope and calculating from those.

To find the distance of an ship on the sea using the stadimeter, just follow the instructions on the tool. It should look similar to this:

To find the distance to a ship using the map tools, just use ruler tool. Drag the endpoints until the snap unto your boat and the target ship.

To use this method you need a calibrated periscope sight.

First, identify the target to find it's mast height.



Mast Height = 35.85 m

Then determine the optical height (OH) of the target in the periscope, generally this will be in mrad.


OH ≈ 82 mrad

RANGE (km) = Mast Height / OH * Magnification
RANGE (km) = 35.85 / 82 * 10
RANGE (km) = 35.85 / 82 * 10
RANGE (km) ≈ 0.437 * 10
RANGE (km) ≈ 4.37 km

Knowledge of the target's course is required. It is recommended to be submerged to improve the accuracy of your bearing readings.

First you need to record two bearing readings of the target, as well as your position when you make the readings. Additionally, you need to record the time interval between those readings.


Then predict your position, as well as the target's bearing from that position after an indeterminate time.


Finally, take the target's bearing after that amount of time has passed. You must have a different position than one on the predicted bearing line.


The point at where the predicted bearing and the actual bearing cross is the target's position.

It is VITAL to get an accurate speed reading. Your aim will be off ~20 to 25 m per km range per knot of error when launching @ 90 degrees. Assuming a larger ship at 150 m and aiming at the center, the maximum range in which to get a possible hit with a single knot of error is about 3 km. I believe this to be the source of the common advice of approaching to within 2 km of the target. While any inaccuracy is bad, it is slightly better to overestimate the target's speed than underestimate it, especially considering most ships speed up when a torpedo is sighted.

As for AOB/AOI, it's less important to be precisely accurate, unless doing some long range shooting. However, it is almost always better to err on the side of underestimating AOB than overestimating. For example, given a slower ship @ 7 kts and a torpedo speed of 40 kt, a 30 degree error of AOB underestimate has an offset of ~11 m per km of range, while an overestimate of 30 degree has an offset of ~33 m per km of range. AOB accuracy gets more important the slower your torpedo is and the faster the target is.

Still, it takes a 30 kt torpedo fired at a 13 kt target to make a 30 degree AOB underestimate contribute more of an error than 1 kt of target speed inaccuracy.

https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=2283105437
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=2282199115
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=2471078847
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=2096952547

These are tables of precalculated angles at which a target should be at to able to launch a torpedo at a 90 degree AOI.