In version 26, the scaling of the periscopes underwent a significant change, a major step in the direction of historical authenticity. This change made it a bit more difficult to determine the distance to target ships, so it had a mixed reception among players, but with this change Wolfpack became one of the few submarine-themed games in which the scaling of the periscope matches the historically real one. This guide was created in order to bring as many players as possible one step closer to success in the game - sinking ships. Let's make it clear in advance, this guide is only about vertical distance determination, horizontal ranging, and the trigonometry involved in that will be the subject of another guide later.

Presumably, everyone is familiar with these terms: milliradian, centiradian. These terms refer to the hundredths, and the thousandths of a radian using metric prefixes, and represent the distance between the small lines visible in the periscope. The distance between two lines is one centiradian, or 10 milliradians.
One centiradian means 1 meter viewed from 100 meters distance. It was fairly simple to use and calculate as it was using the metric system and mostly full number, or maybe one decimal value.



In version 0.26 this is no longer valid!

In essence, the scale of one centiradian has been changed to one-sixteenth of a degree. Although the /16 mark in the periscope optics was already present in previous versions, the actual change has happened only in version 0.26. The change is about 10% different from a previously used centiradian, so players using the old formulas should still be able to sink ships, but with a significant decrease in accuracy. To understand the change in scaling, we need to examine the difference between degree and radian units.

The radian (symbol: rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. The radian is defined in the SI as being a dimensionless unit with 1 rad = 1.

A degree or arc degree (deg, symbol: ° ) is a measurement of a plane angle in which one full rotation is 360 degrees. It is not an SI unit (radian is) but it is an accepted unit listed in the SI Brochure.
Conversion between radian and degree looks like the following:
1° = (π/180) rad

In which:

1° = 0.01745 rad





Let's see how this all will look in terms of Wolfpack and our periscope. We previously stated that the scaling of the periscope changed to 1/16° in version 0.26.

1/16° = 0.0625°

Let’s convert this to radians.

0.0625° = 0.001090831 rad

Or if we use a prefix and some rounding:

1.0908 millirad


In practical terms this all means that we have to convert the degrees seen in the periscope into radians, which can be used to obtain distances expressed in SI meters, or with prefixes in hectometers or kilometers. We can perform the conversion within the formulas. Let's lay down the mathematical rule that multiplication can be easily converted into division by taking the reciprocal of one of the numbers. Whether we use multiplication or division usually depends on which way we can reach the solution more easily. Using this rule, convert the conversion number 1.0908 into a multiplier. The reciprocal of 1.0908 will be:

1 / 1.0908 = 0.9168


These two numbers will play a significant role in determining the distance, depending on which formula is easier to use for which player. In general, people use multiplication more often, but this is decided by individual preference.
The numbers are:

1.0908 0.9168

The 10% difference I mentioned earlier originates from these two numbers. So if you either multiply to old formula's result by 0.9167, or divide it by 1.0908, you'll get the same result. But we will get to the formulas in a bit.




The question may arise that if the distance between the small lines of the periscope changed from centiradian or milliradian to 1/16th of a degree, then what do we call them. Its official name: 1/16th of a degree. But it's too complicated, right? There were dozens of solutions for a simpler name, but there is no consensus. The subject of the Great Dispute. Lines, marks, ticks, bars, signs, as many players, as many names. What you call it is up to you, but the main factor is that the crew must understand what you’re talking about. And if you ever come across the name Günther Prien or Otto Kretchmer called it in some historical document, don't forget to share it with the Wolfpack community. In this guide I will use marks.

Later on, we will need data such as height and periscope marks. The height depends on which feature is used on the target. This can be the maximum mast height, which is indicated for each ship in the Recognition Manual, or we may use a part of the mast or the ship's funnel.




Any solution is suitable for the purpose, however, the higher feature we use, the more accurate our measurement will be. To find the number of markings, place the horizontal line of the periscope on the ship's waterline and count the number of vertical lines that are on the left side of the periscope. Alternatively, the horizontal line can be placed at the top of the feature, and the lines can be counted down to the waterline. The 5th line both down or upwards will tell you that it's 50.
If you use the distance of two marks as 10 (old milliradian way), you will get kilometers as the result. If you count it as 1 (old centiradian way), you will get hectometers.
Technically there's no difference between them, but make sure he proper value is put into the TDC.
It's using hectometers!

By using one of the two conversion numbers above, we can relatively easily compensate for the change in the periscope scale, but if it seems complicated at first, don't despair, we will simplify it completely in the end.
However, let's not forget one very important fact. The periscopes have 1.5x and 6x zoom levels. We must take these into account when using the formulas. The difference between the two zoom levels is 4 times, i.e. 1.5 x 4 = 6.

Let's get to new formulas with the conversion numbers included.


Or

In the first formula, the conversion number was used as a quotient, in the second formula as a multiplier. As we will see in the next example, from the point of view of the end result, it doesn't matter which version we use, the essence lies in the order of operations in the formula.

Let's assume the mast height is 30m, and the periscope marks are 22.

30 / (22 * 1.0908) = 1.25 km
Or
30 / 22 * 0.9168 = 1.25 km

Do not be alarmed if there is a minimal difference between the results you get, this is due to the fact that both conversion numbers are rounded values. The difference will be so insignificant that it will not affect the accuracy at all. If you want to get the final result not in kilometers, but in hectometers, which are needed for the TDC, you must use a decimal point in the number of periscope markings (2.2 instead of 22 in the example above).


Now let's see what the situation is in the case of 6x zoom. Since there is a 4 times difference between the two zoom levels, we must add a 4x multiplier to the formulas above.


Range = (height * 4) / (marks * 1.0908)
Or
Range = (height / marks) * 0.9168 * 4

Now let's take an example with the previously used data, height 30m, periscope marks 22.

(30 * 4) / (22 * 1.0908) = 5.0 km

(30 / 22) * 0.9168 * 4 = 5.0 km

Mathematics has a special property, i.e. a rule according to which if a multiplication or division consists of several terms, they can be multiplied or divided with each other, which will result in a constant number in our formula being modified, but with one less term.
With a very basic example if we have:
We can simplify to
by multiplying two numbers together. This is the concept we're going to use next.
In our case, the 4x multiplier and the conversion numbers 1.0908 and 0.9168 are also constant. Let's simplify our formulas.
In both cases we get the same number, which is:
Let's see how the formulas develop (still using the same example data) if we use these numbers as both quotients and multipliers.

30 * 3.667 / 22 = 5.0 km

30 / 22 * 3.667 = 5.0 km

As you can see, our formula for 6x zoom has been simplified to use height, periscope marks, and a new constant, the magic number of 3.667. Using this new constant the formulas will look like this:

Or

Simply put, the old 4x multiplier used for 6x zoom level needs to be changed to 3.667

To determine the distance without formulas, the Distance Table, or as a new addition in 0.26 the periscope overlay can be used. The Distance Table is available in the C menu, while the overlay can be brought up in the periscope using the set hotkey. In the overlay, you can change the desired height using the set hotkeys by 1 or by 10, while the zoom level is changed automatically using the mouse wheel. You can also switch between vertical and horizontal distances by using the appropriate hotkey. Both the Distance Table and the overlay have been updated to reflect the changes in version 0.26. The advantage of these is that they are immediately available and easy to use. However, their disadvantage is inaccuracy, i.e. they contain exact data for markings 20, 30, 40, etc., but if, for example, the number of periscope marks are 25 or 33, the intermediate value must be calculated or guessed by heart. This guide has been created precisely to eliminate this inaccuracy by calculating everything manually, thus we can get accurate impact times, which is important and necessary for the execution of coordinated attacks.

The author hopes that the guide will help with manual distance measurement, which only requires a basic calculator. With some practice, the calculations require a few seconds of action, which will not hinder the gameplay, but will increase the gaming experience due to its accuracy. I myself had a hard time understanding the change in version 0.26 at first, but with the help of some great minds I managed to understand it and gotten to the point where I can help others. I would like to thank both those who helped me out in these matters, and those who read this guide.


Happy hunting, sailor!


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