Feb 16, 2019

[DevBlog] Direct firing gun accuracy for Eastern Front DLCs

Command Ops 2 Core Game - ioncore

As we have mentioned before, we will be posting regular devblogs about the progress of our Eastern Front DLC development. Here is the first one (and sorry: it's really big).

Disclaimer

Everything we mention or describe below is a work in progress. Any methods, numbers, figures and visuals posted in devblogs are not final and may change by the time DLC will be released officially.

Problem

Weapon accuracy is one of the challenges we are faced with the development of Khalkhin-Gol pack. As this will be our first Eastern Front DLC, the Estab will likely be used later as the base for other EF packs, so we should be very careful about decisions we make and steps we take.

New pack will bring two whole new nations into the game: Soviet Union and Japan. While some captured Soviet equipment was already introduced in previous packs and custom scenarios, this is nowhere near the introduction of the whole Japanese and Soviet arsenal.

At first we thought we could reuse the Soviet 1942/1943 Estab we have been developing during late 2000s (and which never resulted in official DLCs). However, as it quickly turned out, values there were coming from different people who were creating that Estab over several years, and those people had different ideas in mind, and also they have been using different sources. Names for weapons and vehicles were inconsistent sometimes, but, what's even worse, we have identified some very different approaches for defining weapon accuracies and penetration figures. So this was definitely not the way we wanted to go.

As we are not only going to add two new nations, but also later we would like to have added also Germany, Poland, Finland, Hungary, Romania, Czechoslovakia (and may be other nations of the Eastern European Theater), we have concluded that we need to develop completely new accuracy calculation system. The system that will be:
- consistent across all the weaponry of all the Eastern Front nations;
- transparent;
- based on a reasonable scientific methodology;
- simple and quick to use, so that it may be reused by any Eastern Front DLC developer without any special knowledge or skill.

Consistent would mean, that we need to create the generic approach to define weapons not only for this particular DLC, but also for all the other (future) Eastern Front DLC. That means, whenever we decide to add German Eastern Front weapons later, we will need to re-define their accuracies according to the new model (so they may be a bit different to what we have been using with old DLCs, but consistent with the rest of EF data).

Transparent would mean the methodology is well-defined, documented and is independent of any subjective opinions, "secret documents" or religious beliefs (which you could sometimes find in Internet battles between e.g. Wehrmacht and Red Army fanboys).

Scientific methodology means the following. There are different opinions about the hit probability: Thomas Jentz, for example, have described a probability to hit 2 m x 2.5 m target for German 88mm KwK 43 tank gun at 1000 m range as 0.85 (see here). But others may say that, e.g. 88mm Flak was able to score just one hit per eleven rounds fired (no source given, though, for this), etc.
So we definitely can not rely on these contradicting figures coming from different sources, comparing combat to non-combat conditions. Our approach should be based on math, theory of probabilities and ballistics.

Simple and quick to use would mean, that we prefer to have it implemented as a script or a tool, which could be run by anyone and calculate accuracies for any substantially large number of weapons.

We were able to meet all these goals, and results are presented below.

Sources

Our approach will be based upon works of Ballistic Research Laboratory (Aberdeen, MD). Namely, it is the article by E.C.Christman "The effect of system design characteristics on first round hitting probability of tank fired projectiles" published in February, 1959 (declassified).
This article establishes a mathematical model of hit probabilities under "quasi combat conditions" and provides a whole lot of nomograms connecting hit probabilities with firing conditions (firing range, muzzle velocity, drag characteristics defined through ballistic coefficients and G-shape models and targeting systems).

We are interested more in "follow-up hit probability", the definition of which can be found in "WORLD WAR II BALLISTICS: Armor and Gunnery" by L.R.Bird and R.D.Livingston, and is given as "...probability appears to be maximum obtainable accuracy after several shots at target, with errors in range estimation and target speed reduced to zero, mean jump and throw-off adjusted for". Command Ops 2 models continuous engagements rather than just first hit, so this is exactly the kind of probability we could use in our game.

Even though Christman's article deals with the "first round hit", we can still use their data. The fire control "System C" (which produces a standard error in range which remains constant for all ranges of interest) described there is something that could roughly represent "follow-up shot probability" we are interested in.

Model parameters

Same as Christman, we will be using several input parameters (factors listed below) that would affect our calculations.

Muzzle velocity is one of major factors, which determines the flight time and also projectile trajectory. The higher is velocity, the better are your chances.

Range also one of the most important factors, because it affects flight time and shell dispersion. Naturally, the larger is range, the worse are your chances.

Drag characterstics are defined by the projectile shape (described by one of G-model types) and ballistic coefficient. The former is rarely known for non-US projectiles, but may be roughly assumed from the shell's shape. Of course, for that we need to have a picture of a shell.
Below you can see a picture of Soviet BR-350A APHEBC shell used in various 76.2mm tank and field guns. Like with other ballistic-capped projectiles, we assume it to be of type G8 (secant-ogive flat-based projectiles).

Ballistic coefficient is calculated from the form-factor (which is also rarely known for any non-US projectiles, but can be either assumed using US projectiles of similar shape and purpose, or considered to be equal to 1.0), projectile diameter and projectile weight.

One may think all these ballistic nitpicks are of only minor importance (compared to the range and velocity), but actually they are very important. Drag characteristics are exactly the reason why low caliber high velocity guns (like 37mm or 57mm) may have accuracy similar to 75-90mm guns at ranges up to 500-800 m, but become less accurate beyond that range. So drag characteristics are very important things to consider if we ever want our weapons to behave realistically.

Last, but not least is round-to-round dispersion. This describes the variability of shell parameters (like variations in gunpowder amount, projectile surface and shape production quality etc). We consider this to be a rough representation of "weapon quality".
This is the only "subjective" parameter in our model, because it may not be derived from any kind of public data. For simplicity, we assume round-to-round dispersion to be low ("good") for countries known for using advanced industrial technologies, metalworking in particular (e.g. Germany, US, may be UK etc). Also we assume dispersion to be high ("bad") for countries known for their problems with the quality of their industrial production (e.g. USSR), as well as for any other country not fitting into the first category.
For the first category we assume round-to-round dispersion to be equal to 15 mil (low dispersion), and for the second category we assume dispersion equal to 60 mil (high one). Both USSR and Japan fall into the second category.

12-years-old boy operating milling cutter, USSR, 1943.

Implementation

We have manually digitized most of Christman's nomogramms; these have resulted in several thousands of data points for different ranges, muzzle velocities, ballistic coefficients and dispersions. It took us whole week just to enter all the data from the article, but now we have a huge array of multidimensional data to interpolate and extrapolate for nearly any possible combination of parameters. Some parts of this data array you can see on the screenshot below:

For interpolation within this multi-dimensional data we will be using free math package GNU Octave, there we have created a simple script using two-dimensional cubic spline interpolation to process CSV data, calculate ballistic coefficients from shell data and produce a list of hit probabilities for all the required ranges.
We will be using "standard" list of ranges for all the direct firing guns - 100 m, 500 m, 1000 m, 1500 m, 2000 m and 2500 m -

Now, all we need to do is to create CSV file with the list of Soviet and Japanese guns (and their shells' parameters) and pass it to the script.

Results and validation

Below you can find the diagram showing comparison of three kinds of accuracy data:
- solid lines - accuracies generated with our new approach that will be used in upcoming Eastern Front DLCs (and Khalkhin-Gol in particular);
- dashed lines - accuracies available in previous Command Ops 2 DLCs and also in previous iteration of CO2 Soviet Estab (deprecated);
- dotted lines - literature (Jentz and Bird).

Comparison is made for following systems:
- 45mm 19-K AT gun;
- 57mm QF 6-pdr AT gun;
- 76.2 QF 17-pdr AT gun;
- 8.8cm KwK 43 L/71 tank gun.

In all cases projectile type G8 was used for ballistic-capped shells (45mm BR-240 APHEBC shell, 6-pdr Mk.9 APCBC, 17-pdr Mk.8 APCBC and 8.8cm PzGr.39/43 APCBC), form-factor set to 1.0.

45mm gun:
- accuracy drops over distance with the new math more significantly than with old CO2 data;
- with the new math 45mm gun has significantly worse accuracy than 6-pdr beyond 500 m range, whereas with old CO2 data they would be nearly identical.

6-pdr gun:
- new math accuracies are much closer to historical references (Bird) than old CO2 accuracies.

17-pdr gun:
- new math accuracies are closer to historical references (Bird) than old CO2 accuracies.

88mm gun:
- new math accuracies are closer to historical references (Jentz) than old CO2 accuracies.

Conclusions

We have received a new powerful and scalable approach to calculate direct firing gun accuracies consistently. The approach is easy to use, integrated with spreadsheets import/export (CSV) and requires little manual work to prepare data.

New math produces values similar to old CO2 data, so you will not see any dramatic gameplay changes.

However, comparing new math to old CO2 data (especially comparing it to previous Soviet Estab developed in 2000s), our new model yields numbers closer to the historical references.
In some cases new math even feels more realistic. E.g. if we check accuracies for 45mm and 6-pdr guns, new math makes 6-pdr much better than 45mm starting at 500 m and beyond. Old CO2 Soviet estab would make them nearly identical in performance. And this is exactly what we would also expect, comparing 45mm and 6-pdr in real life.

We hope, that with our new math model we will deliver new content faster. We also hope, that the new model will better and more uniquely model particular guns, which will grant you better and more realistical battle experiences.