Cannon Penetration Overhaul

[Kiithnaras]

I've been working on and mathing over a subject that's been bothering me for quite a while - Cannon Penetration. Specifically, Carronades and how their penetration drops off to 0 at extreme ranges, so it got me thinking. Could one really stop a 42-pound iron ball that's been flying through the air for 1000m by...holding up a piece of paper? Noooo, that's silly. Therefore, I'd like to introduce a concept I like to call Minimum Penetration. Min Pen should be identical for shots of identical size, no matter what sort of gun they're fired from. Min Pen is based on the terminal velocity of an iron sphere of a specific mass in free-fall for an indefinite period of time.

As I was pondering this subject, I said to myself, "You know, I'm sure the devs have a formula in the background that they tweak for this sort of thing, but it isn't readily apparent and carronades don't seem to follow a simple mathematical model." So, I devised a plan. Two alternate models for cannon penetration, easily adjustable based on the minimum (infinite-range) penetration, maximum (gun barrel againt hull) penetration, and the distance at which the devs want the weapon to have a pen value halfway between min and max.

Edit/Update: After far too many hours than is healthy, I've updated things. I dropped the previous "Falloff" model as it was a little silly and had zero chance of being adopted. Instead, I have done extensive research on the internal and external ballistics of cannons and cannon balls for a "Historical" model that should more closely fit a realism-based scenario.

The Epic Spreadsheet of Epic

The above sheet shows current values, Exponential Decay, and "Historical" models as well as data on relative penetration based on kinetic energy divided by projected area. I arbitrarily set 4 pdrs to pen through 5cm of wood in a free fall, which seems reasonable to me, but this is easily adjustable with the data present After lots of research, I finally was able to simply calculate the hypothetical oak penetration, at terminal velocity, of the various weights of cannon rounds. The key is that minimum penetration is solely dependent upon the mass of the iron ball - 42pd carronades and 42pd long guns will have the same minimum penetration at hypothetical infinite range. I have two models here. The first is a gamey, Exponential model that has, as Gamelabs does, all guns of the same type lose energy at the same rate, and has Carronades' initial penetration equal to Long guns of half their caliber. The second is a "Historical" model that attempts to more accurately model internal and external ballistics.

In the Exponential Model, I attempted to adhere to the theme of Gamelabs design - long guns maintaining energy over long ranges, Carronades dropping off quickly, and medium guns somewhere in between. Here, Medium cannons have 5% less 0m-Pen compared to Long guns of the same caliber, and Carronades have the same 0m-pen as a Long cannon half its caliber. The horizontal lines are for reference, from top down, Victory mast thickness, Connie mast thickness, Actual physical diameter of the HMS Victory's lower mainmast, and the current thickness of the Victory's hull. It's clear that even using this model that, while any gun is capable of damaging a 1st-rate's hull if the ship is close enough (Privateer swarm ftw), being able to deal effective damage to the masts of a 1st-rate is nigh-impossible; ONLY 42-pounders at close range (and 68pd Carros at sneezing distance) are able to pen through the thickness of those masts.

The advantage of this model is that it keeps carronades short-ranged in all regards and clearly defines roles for guns. The disadvantage is that it can make using carronades, and even medium guns in some cases, frustrating at anything more than a stone's throw from an enemy ships.

The Historical model attempts to more accurately simulate both external and internal ballistics. With this model, Long guns are 20 calibers in length and use a 1/4 charge-to-shot ratio. Medium guns (historically termed Short cannons) are 16 calibers in length and use a 1/5 charge-to-shot ratio and have a 10% lower muzzle velocity than Longs. Carronades are only 8 calibers in length and use a 1/12 charge-to-shot ratio but have much tighter windage that results in a higher-than-expected muzzle velocity for such a lower charge. This winds up with Carros having about a 30% lower muzzle velocity than long guns of the same caliber, but curiously about the same muzzle energy as a long gun of half their caliber (even though it's a little less penetrating potential since the same energy is being distributed over a larger projected area). Here, Carronades are slightly less effective at point-blank range, but it treats, externally, all shot of the same size the in the same manner - a 42 pound ball will lose energy flying through the air at the same rate (as a proportion of its velocity) as any other 42-pound ball. However, larger shot maintains its energy better over distance (since the shot's mass increases as a cube of radius, while its projected area only increases as a square of radius) and thus will lose penetrating potential slower than smaller long guns. It can be readily seen that guns of the same caliber, regardless of type, decay to the same minimum penetration value at extreme range.

With this model, accuracy becomes much more important; long guns are the kings of this, while medium guns have a little more dispersion and slightly reduced muzzle velocity and carronades are not very accurate at all. Carronades, while having the potential to reach the same range as a long gun (due to the capacity for higher gun elevation), it will not only strike with less force, but a higher impact angle (which significantly reduces the effective impact energy). Large carronades fired at range, if aimed well with decent accuracy mods, might be acceptable for chaining sails or raining grape onto weather decks, but little else.

The Comparison chart shows existing 42pdrs in red, Exponential model guns in green, and Historical model guns in blue. Obviously, no concrete data is available for shots beyond 1km with the current values.

Personally, I am a fan of the Historical model that I've concocted here. It makes Carronades much more of a skill weapon - high damage potential with very low accuracy. A skilled captain could, potentially, out-damage a similar ship at medium range with carronades.

While this treatise does not address cannon damage, my initial thoughts are that damage and reload should be adjusted so that cannons of the same caliber do the same damage, but different types of cannons have faster reload times. E.g. 50 damage for 42-pound shot, 72 seconds for a 42-Long, 64 seconds for a 42-Short, and 48 seconds for a 42-Carro. Edit: It is this way mostly, already, just some minor tweaks and fine-tuning.

The other issue at hand is mast thickness. Hull thickness is more or less acceptable (a few outliers, like the Constitution), but Masts are far and away far too thick to avoid "demasting at range". A general rule of thumb to go by is that the lower main mast should be no thicker than 4/3rds the hull thickness. By this logic, the thickest that a Victory's main mast should be is 100cm. This means that, even with the Historical model, all but 42-pd carronades will have trouble demasting a Vic, while Long 12s and Medium 24s should be up to the task, albeit at very close range. However, that doesn't mean they should be necessarily easy to demast. Lower mast sections were quite tough. While this thickness should be dropped to less than 100cm, the mast HP should be buffed easily 50% for lower mast sections, and 25% for mid-sections with the lower mast thickness.

One amusing side effect of the Historical model is that the 68pd-smashers would actually retain more penetrating potential outside 1200m - but good luck hitting anything, let alone hitting it square enough to do significant damage.

Edited February 17, 2017 by Kiithnaras

[Kiithnaras]

I suppose there's also some subtext that ship masts are waaaay too thick >_>

[Kiithnaras]

Updated the main post with the new Historical model. Take a look!

[Farrago]

Thank you for using your expertise and research to improve the game. 

[Ned Loe]

Very good work here. 

[balticsailor]

I just saw your post in the combat mechanic feedback thread and remembered some older threat about this topic and just tough i put the link to some here.

First a very good and detail one:

and here some other relevat once:

 

[Tonnerre de Brest]

On 1/9/2017 at 4:40 PM, Kiithnaras said:

I suppose there's also some subtext that ship masts are waaaay too thick >_>

Not thick but really hard to hit intentionally while shooter and target are both in motion (and rolling as well) .

Not being a programmer I don't know how this is modeled but the target to hit while aiming at the mast for guide from a distance is the base of the shrouds.

It is a wider target than the mast, especially on a large ship, and easier to hit and also it is a much softer target that can get significant damage from even small ordinance like a 6 pounders. Once damaged it is hard to balance the huge pressure from the sails and the ship must be handle gently. If one side of the shrouds lets go, the rig falls from the pressure of shrouds on the other side of the boat where full tension is still pulling.

I think that loosing a rig was happening more often than not because of that and not from direct hit(s) on the mast itself.

[Kiithnaras]

Well, no, they are modeled as being too thick. a 1st-rate's masts are listed around 119cm. In reality, the HMS Victory's masts are about 94cm in diameter. From a gameplay mechanics perspective, the masts should be reduced to this range (some ratio like 1 and some small fraction of an inch per foot of beam at the mast) and simply receive an HP buff to compensate, simulating off-angle shots. I think right now the masts are simple hitboxes without any physical form, meaning that a shot on a mast is treated as "dead on", as if you were shooting the hull of a ship directly perpendicular. The devs have indicated that they don't want to complicate ship models much more than they already are, though we should see ship Structure appearing in a patch sometime Soon™.

While it would be nice to have rigging and shrouds more accurately modeled, doing so would really load down the game engine, and things get pretty chuggy with 50 ships in a battle already. AFAIK, only sails and masts are modeled, and taking out a mast section, even one of the upper mast sections, can really be painful in disabling a ship.

[Tonnerre de Brest]

I can see how it makes sense, more data to crunch in real time equal more lag for slower connections or nodes that are far away.  

Still I'm impressed at how well it play even with all the shortcomings that people complain about. Even playing on EU server from the USA is fine. (I'm on fiber though that might help a bit too)

[Kiithnaras]

On 3/18/2017 at 4:28 AM, Tonnerre de Brest said:

more data to crunch in real time

Except it really isn't. Most of the data on the spreadsheet is used to calculate the minimum and maximum pen values as well as assign relative half-pen distances for each caliber. All of that data is exposed for the Devs to make use of and tweak and adjust on their own.

In terms of gameplay, all it's doing is plugging in the distance of impact into the Pen vs Distance formula, much like happens now on the live servers, so there would be zero performance impact of adopting this model. Balance, however...well, that's the whole point of my arguments here : )