After a thread on the forums about aimtime and how it works. I decided I wanted to figure it out exactly. All we know for now is that aim time is the time it take to reduce the aimcircle to 40% its size, dispersion is something that say show much the circle gets bigger and accuracy is the size of the aimingcircle when fully aimed. However, we do not know the exact relations between these 2 and how exactly they influence the size of the aiming circle at all times.

So thats what I set out to do, finding a mathmatical description of the size of the aimingcircle. The method is simple: measure the size of the aimingcircle for different tanks and speeds in a trainingroom. Thanks for uglycousin for giving me a second person to set up the trainingroom.

To measure the size of the circle, first I did the test driving in the room. Then I watched the replays and paused at certain moments. I then took a screenshot of my whole screen, makign sure I was always in 8x zoom. Then I took those screenshots into paint and measured the circle diameter in pixels.

I will now describe the process and results of my investigation. But if you dont want to read that, scroll down tot he conclusion on the bottom.

Disclaimer: the following formulas are NOT what WG uses, I made a linear model that describes the size of the aimingcircle as close as possible.

**Aiming circle bloom**

I assumed there where 3 variables that had an influence on bloom: speed, dispersion and accuray. I tried to do test in which I held 2 variables constant to see the influence of 1.

I started with gathering data of 2 different dispersion numbers for which I picked 4 tanks with different accuracy and measured the size at each speedincrease of 10 untill 50 kph.

These are the raw results:

From that I made a graph of the dispersion in function of speed , and calculated the gradient of the graph assuming linear increase. Then obviously the aiming circle size = C*v+accuracy.

With V=speed and C being the gradient, which consist of unknown factors. To check the linear approach was decent I plotted the model and experiment:

As you can see the linear approach to the speed factor isnt perfect but not massivly different, only in the middle it differs. I am happy enough with this.

Now we need to determine what the C factor consist off. Since there are only 2 variables left, it has to consist dispersion or/and accuracy components.

As you can see in the data, with the same dispersion numbers, the aiming circle fort he same speed is bigger when the accuracy is bigger. So there has to be an accuracy factor in C, which is proportional to accuracy.

Here you can see accuracy vs circle size:

As you can see, the increase isnt marginal. We can now rewrite our formula as:

Size=Acc(D*v+1)

With D an unknown factor containing dispersion in some form. As we can see, size of aiming circle is directly proportional to accuracy. So an increase in accuracy of 25% will results in 25% better gun handling. This is why the E50/E50M have such amazing gun handling , their dispersion isnt great , but good, but due to the very good accuracy their gun handling is much better than at first glance. The WZ-132-1 has the exact same dispersion values, so you would think the gun handling would bet he same, but no, since it has 33% worse accuracy is will have 33% worse gun handling, which is massive! Thats more than a vstab!

Next task is determining the factor D. The only variable left is dispersion, so I tested different tanks with differnt dispersion at the same speed, their accuracy was different, but thats fine, sicne we can normalise for that. These numbers showed that the factor D was proportional to the dispersion values, so D=c*dispersion, with c an unknow constant.

Now the formula looks like this:

S=Acc(c*d*v+1)

Determining c was done by plottign the experminetal result and trying some numbers until the model best fits the experiment. I took c=0.68.

The influence of dispersion can be see in this graph:

Spoiler

Now we have a formula that gives a perfect description of aiming circle size in function of all variables. Next up is determing a the time it takes fort he circle to shrink, or the actuall aiming time for the tank.

**Aiming time:**

We know aiming time is the time it takes fort he circle to shrink by 60% its startign size.

So we can write:

S1=S2*(4/10)^(t/T) with T=aiming time, S1 size after time t, S2= starting size.

Solving this for t we get: t=T*(log(S1/S2)/log(4/10)).

We can now determine the time it take from any speed to reach any size we want.

To determe the time it takes to fully aim, jsut replace S1 by the accuracy of the gun. Note this time is independant of accuracy! ( which is logical, since it needs to go to a smaller circle but also does it faster, these 2 cancel out)

Plotting this for 3 different tank in fucntion of time comming to a stop from a speed of 50 (40 for conway) we get:

**Influence of equipment/skills etc.**

Now that we have every formula we need we can quantify the influence of equipment/skills/directives/modules. To do so simply multiply the variable that gets influenced by (1-0,01*improvement in %). Dispersion values only get influenced by vstabs and the smooth ride skill.Other equipment only influences the accuracy value.

Note that the same improvement to acc or dispersion results in a bigger improvement in size for what improves acc than what improves dispersion. Vstabs for example do not make the size of the circle shrink by 20%, they make the increase in size less by 20%.

Lets take a look at a common dillema:vstabs vs gun laying drive, lets try this on 2 different tanks:

We can clearly see what the difference in vstab and gld is, vstab makes the circle smaller, so you start smaller but the decrease is still the same, gld starts at a bigger size but then starts to decrease faster, catching up tot the vstabs. In the BCs case, the time to fully aim is actually lower when equiping gld than when equiping vstabs.

Matmaticly, gld decrease the total time to aim by 10%, whereas vstabs decrease the total time to aim by subtracting 20% *initial size. To know wether vstabs or gld is better depends on the tank and how much you want to aim, you can determine this by pluggin in the numbers and plotting it for each vehicle, sicne i twill be different for each.

As general rules however, these apply:

- Bad dispersion + bad aimtime

Vstab better, unless you fully aim from full speed.

- Bad dispersion + good aimtime

Vstab better, unless at high speed when fully aiming.

- Good dispersion + bad aimtime

Vstabs always superior

- Good aimtime + good dispersion

Vstabs always superior

**Conclusion and TLDR:**

- Accuracy has a massive influence on aiming circle size on the move, they are proportional.
- Aiming circle size is proportional to speed/dispersion.
- To determine what gun has better actual gun handling: multply accuracy with dispersion, the lower the numbers the better the gun handling.
- Size of aiming circle= Acc(0.68*d*v+1)
- Time to fully aim = Aiming time*(-log(0.68*d*v+1)/log(4/10))
- Vstabs is superior to gld in most situations.
- Influencing accuracy gives a better boost than influencing dispersion values.

**Whats next?**

Next up I need to investigate how turning the turret and hull effect dipsersion and work with the above formulas.

I wil also try to combine this with my previous thread where I determined shot distribution in the aiming circle, then I can plot change to hit a target vs time and determine the optimal time to shoot.

I hope you enjoyed the read and that i twill help you determinign how a tank will perform. I hope that youtubers do become aware that accuracy has a massive influence over dispersion, as currently reviews are misleading since they dont know what actually effects gun handling. Spread the word!