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thegamefilmguruman

The Influence of Ship Length Upon Accuracy

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Occasionally when browsing threads, you come accross statements about how far apart a ship's turrets are spaced influences accuracy (particularly where it concerns Hood).  It got me wondering: How much does turret distance influence accuracy?  At what ranges is it relevant?  Keep reading, and we'll find out.  Be aware, there will be a fair bit of math involved.

To start out, it's important to state the obvious: Each shell from each gun in each turret has its own individually calculated trajectory using the dispersion formula WG uses.  This means that every shell from every gun on your ship has the same potential dispersion pattern centered on the same aim point, but the dispersion patterns don't fully overlap.  They are each at the angle of each gun relative to the target.  We'll illustrate this using this poor sketch (don't worry, I have better quality stuff later):
u7lPHA7.jpg
As we can see, the closer the angle of origin, the more overlap of the individual gun dispersion ellipses-ie, better dispersion/less are to disperse to.  You might also notice a few other things; 1. the drawing has a very close target, and 2. it also influences the angle a shell will hit an enemy at, which can determine a bounce or shatter.  This will be the focus of our little investigation.  We'll use 3 ships: Hood, Colorado, and Nelson for our case studies, as they represent 3 types of turret arrangement: Long, Stubby, and Clustered.  We'll start with Hood.

To determine the change in dispersion patterns and angle, we must first find that angle.  To do this, we must first determine what scale the ships and distances in WOWS are relative to each other.  We know the ships in WOWS are bigger so that they can be hit more realiably, but how much bigger?  We also know that the ships are relatively accurately modeled in relation to each other.  For this we need a top down view-an aircraft carrier.  I used Kaga:
FsB61ql.png
We know that distance is calculated from the center of a ship, so the distance to the planes (4.7km) is approximately 9.5 Kagas (possibly a little more at 9.7).  We know that Kaga is 782 ft, or around 238 m in length.  We divide 4700 m by 9.5 to find the length in game: 495m; by 9.7 we get 482m. This is roughly double the lenght of historical Kaga.  Therefore we can say Kaga is twice as big in game as in real life.  Let's now apply this to HMS Hood to find the distance between the foremost and aftmost turret:

UX35eyM.png

If you use the scale provided, we find this distance to be around 500 ft.  In game this becomes 1000 ft, or 300 m due to the ships being twice the size.  Now we can solve for the angles by using the quadratic equation and arcsin.  Let's select a target dead perpendicular to the ship perfectly centered between the fore and aft turrets.  We'll also only solve for the outside (relative to the center of the ship) gun of each turret; we're interested in maximum effect, after all.  Let's chose a target 4km away.  Now we have a triangle:
aeq8R5u.png

We need to solve for two things to determine our angle: h (the hypotenuse) and θ, our angle.  The total difference between the turrets will be 2*θ.  We find h using the quadratic equasion of a^2+b^2=c^2, where h=c and b=150m so that 4000^2+150^2=h^2.  Therefore h^2=16,022,500m^2 or h=4002.8m.  Now we solve for θ. sinθ = opposite/hypotenuse, or sinθ = 150/4002.8.  Therefore arcsin(150/4002.8)= θθ therefore is equal to approximately 2.15 degrees.  2*θ=4.29 degrees. We can use this same equasion for all ranges, so I plugged it into an spreadsheet:
8lJZqPS.png
Here we see that the angle is quite large at close range, but is around 2 degrees or below at ranges exceeding 8km.  How about Colorado and Nelson?  How does Hood stack up?  Colorado has a distance between turrets of about 330 ft, or 100 m; Nelson 50 m.  If we plug this into our spreadsheet, we get the following:
I2T0lg8.png
As can be seen, at close ranges, Nelson has a notable advantage in both dispersion and unified angles.  However, the difference between Colorado and Hood outside 7km is less than 1 degree, and outside 11km, the difference between Nelson and Hood is also less than 1 degree.  Besides bounce angles, what does this mean?  Well, I've compiled a chart of identical dispersion patterns offset by several of the degrees we came up with in our spreadsheet:
xlAUacW.png
As can be seen, anything below 2 degrees is practically meaningless, but it is noticable at greater than 5 degrees.  Our conclusion then is that outside of brawling ranges, there is no relevant difference, though one does exist.  How is this applicable in game?  Well, there are some tricks.  You remember how for the sake of simplicity, our ship was entirely broadside?  If you angle to 60 degrees (ie, bounce angles) to the enemy ship, this decreases the relative distance between your guns by half, and therefore that angle by half.  Simple trigonometry:
30-60-90-example-diagram.png
The other thing is that widely spaced guns can be an advantage or disadvantage in certain situations.  Yup, it's a mixed bag.  It can be the difference between a bounce or a penetration on an enemy ship.  Have two last terrible sketches to illustrate:
x9JRryY.jpg1o2Pscl.jpg
Increasing the angle may mean some guns pen that would otherwise bounce.  The inverse is also true.  This is not to say you should go broadside when brawling-unless you're on the enemy team.

TLDR: Distance between guns is irrelevant in most situations concerning bounce angles and dispersion, but when at close range, closely spaced guns offer a noticable advantage.  This advantage can be halved/doubled by simply angling to bounce angles.  At usual engagement ranges, however, it's a non issue, so stop arguing that Hood has a massive disadvantage in dispersion and bounce angles due to length.

Edited by thegamefilmguruman
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From my in-game observations, it does not appear that WG has provided any parallax corrections, which will also effect the spread, in addition to that shown in this excellent post.

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It's most relevant at brawling ranges, especially since your camera will center over one group of turrets, thus the other ones will aim at an angle to hit the target point.

crappy paint diagram as follows:

 

DkfOe47.png

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24 minutes ago, Tedster_ said:

It's most relevant at brawling ranges, especially since your camera will center over one group of turrets, thus the other ones will aim at an angle to hit the target point.

crappy paint diagram as follows:

 

DkfOe47.png

Yup, which is why when brawling it's important to zoom out a bit and try to center your aim a bit more.  Of course, at point blank (under 1km) this becomes more of an issue.  Outside of 1km, though, with a right angle from your front guns, the angle difference actually improves a bit.
lOemZiH.png
Gotta angle toward or away if possible to reduce the difference:
mHtfMbJ.png
Shameless edit of your pic.  Note, the sub 9degrees is for anything outside 1km.

Edited by thegamefilmguruman

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@thegamefilmguruman and I thought I was really into this game lol. Nice article but I'm still improving my aim based on whether I'm closing or opening the range as I'm shooting. After noticing it makes a difference in how you aim I'm scoring more hits...

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39 minutes ago, CaptnAndy said:

From my in-game observations, it does not appear that WG has provided any parallax corrections, which will also effect the spread, in addition to that shown in this excellent post.

The OP also makes the point that dispersion should be elliptical along the gun target line; as I understand it, WG uses moore circular patterns for dispersion.

Agree with you though...it doesn't appear that WG has accounted for parallax found in naval fire control systems.

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14 minutes ago, BBsquid said:

The OP also makes the point that dispersion should be elliptical along the gun target line; as I understand it, WG uses moore circular patterns for dispersion.

Agree with you though...it doesn't appear that WG has accounted for parallax found in naval fire control systems.

While the pattern itself is circular, that's on the plane perpendicular to the shells.  Since the shells have arc and don't land straight down at 90 degrees, it creates an ellipse when it intersects the plane of the water.  The higher the shell velocity at the point of impact, the longer the ellipse gets.  Hopefully this diagram is helpful.
ZN2BF4U.png

Edited by thegamefilmguruman
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6 minutes ago, thegamefilmguruman said:

While the pattern itself is circular, that's on the plane perpendicular to the shells.  Since the shells have arc and don't land straight down at 90 degrees, it creates an ellipse.  The higher the shell velocity at the point of impact, the longer the ellipse gets.  Hopefully this diagram is helpful.
2ePPDjz.png

True, but as modeled in game, if you spectate and watch the fall of shot around a target its more circular that elliptical, where as when we fired our guns you could actually visually see the elliptical pattern around the target on the PPI of the Mk 13 radar. The pattern in game should look more like this:

no31991-pic4.jpg.80bb9d6653cc8d5ee99ab3dd2cb1b026.jpg

Im not sure if its an ingame limitation due to artificial scale, or just something the engine cant model correctly.

Edited by BBsquid

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3 minutes ago, BBsquid said:

True, but as modeled in game, if you spectate and watch the fall of shot around a target its more circular that elliptical, where as when we fired our guns you could actually visually see the elliptical pattern around the target on the PPI of the Mk 13 radar. The pattern in game should look more like this:

no31991-pic4.jpg.80bb9d6653cc8d5ee99ab3dd2cb1b026.jpg

Not quite.  You see, if you run tests like Little White Mouse has in game, you'll find it looks like this instead.  Pretty clearly elliptical:
dispersion1.gif

Edited by thegamefilmguruman

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10 minutes ago, thegamefilmguruman said:

Not quite.  You see, if you run tests like Little White Mouse has in game, you'll find it looks like this instead.  Pretty clearly elliptical:
dispersion1.gif

where is the gun target line? Is the test conducted with the firing ship on the beam of the target, or crossing the 'T'. I can see the ellipse now, but depending on where the firing ship is, its backwards. If Mouse is firing from the beam of the target, the depeicted ellipse should be rotated about 90 degrees. The ellipse would be parallel to the gun target line/line of fire.

Likewise, WG's dispersion seems excessively loose depending on n umber of rounds fired. In the battle practice example I posted, I believe each ship was allotted 75 rounds for the test. 15km is 16,400 yards, so both 'tests' were conducted at *roughly* (cough, cough) the same range.

Edited by BBsquid

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The  big question I have is...from your study, does the game factor in, or attempt to, the parallax corrections made by the directors and the FCS?

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1 hour ago, BBsquid said:

where is the gun target line? Is the test conducted with the firing ship on the beam of the target, or crossing the 'T'. I can see the ellipse now, but depending on where the firing ship is, its backwards. If Mouse is firing from the beam of the target, the depeicted ellipse should be rotated about 90 degrees. The ellipse would be parallel to the gun target line/line of fire.

Likewise, WG's dispersion seems excessively loose depending on n umber of rounds fired. In the battle practice example I posted, I believe each ship was allotted 75 rounds for the test. 15km is 16,400 yards, so both 'tests' were conducted at *roughly* (cough, cough) the same range.

Mouse was firing from aft of the target, I believe, firing from right to left with the target point on the aft of the Nagato (the purple dot), for that test.  As for parallax, here's what I know: When you lock onto a ship in game, the FCS automatically makes ajustments to keep your guns tracking that target.  You're basically just adjusting the lead and elevation of the guns within a certain amount allowed by the game's FCS (example, when firing at a locked on target's deck you mostly hit said deck, were you to aim in the same spot while not locked on, your shells would go well over and behind).  As far as I'm aware, each gun is locked onto the target individually by the game, meaning it should account for that.  Otherwise when angled your rear shells would fall short-which we don't see in game.  In short, yes, the game engine accounts for parallax to the best of my knowledge.  Warthunder Naval Forces (for example) does not, which makes aiming more difficult.

Edited by thegamefilmguruman

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22 minutes ago, thegamefilmguruman said:

Mouse was firing from aft of the target, I believe, firing from right to left with the target point on the aft of the Nagato (the purple dot), for that test.  As for parallax, here's what I know: When you lock onto a ship in game, the FCS automatically makes ajustments to keep your guns tracking that target.  You're basically just adjusting the lead and elevation of the guns within a certain amount allowed by the game's FCS (example, when firing at a locked on target's deck you mostly hit said deck, were you to aim in the same spot while not locked on, your shells would go well over and behind).  As far as I'm aware, each gun is locked onto the target individually by the game, meaning it should account for that.  Otherwise when angled your rear shells would fall short-which we don't see in game.  In short, yes, the game engine accounts for parallax to the best of my knowledge.  Warthunder Naval Forces (for example) does not, which makes aiming more difficult.

cool...thanks, guruman. I can buy that. 

If Mouse was aft and perpendicular to the Nag target, the dispersion pattern looks *fairly* accurate too...although still maybe a little wide. Again, it also depends on how many rounds went downrange.

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13 minutes ago, TheCompGuy25 said:

Calling @LittleWhiteMouse.  Can you fill in the question related to your targeting?  Great discussion here.  +1, OP.

off topic, but love your tag. Yes, speed is most definitely life in SFB.

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1 minute ago, BBsquid said:

off topic, but love your tag. Yes, speed is most definitely life in SFB.

Glad you recognized it!  :cap_win:

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