Ballistics Calculations/Charts

[aidenpryde]

Hello,

I'm new to these forums but hope to be here awhile to gather information about various aspects of weapon performance. I'll let you know right now I'm not really good at math, which is why I'm looking for a solution, or how to set up a solution, so that I can just input variables and get the proper result.

I am a indie game developer and am currently working on getting the naval side of our game together. In addition to modeling (currently working on the Type 34A German Destroyer) I am also responsible for writing the game design document, which means that I need accurate stats for different types of artillery.

I've been looking around the internet and have been able to find several excel spreadsheets that have the calculations set up in different fields already. But these spreadsheets really only pertain to small arms and not to the larger caliber weapons (such as the 15cm main guns on the Type 34A). Indeed the spreadsheets seem to freak out and break down when I try to input the types of ranges that you would see in game (20km, etc). They also do not display the velocity of the shell as it moves downrange.

This is important because our game needs to know the velocity of a shell at a given range in order to (at least with Armor Piercing ordinance) calculate how much energy it directs at the target. An important consideration when determining whether or not a shell will penetrate a given thickness of armor (angle of impact, angle of armor, thickness of armor, and size of the shell will be a different calculation).

So basically I am looking for an excel sheet that will allow me to input things like muzzle velocity and then generate fields that will break down how fast the shell is moving at different ranges.

I found one that will tell me how far the shell will travel (inputs are: angle of the gun at firing, height of gun, and muzzle velocity, and gravity) but it doesn't break down the velocity at different ranges.

Any help or workarounds would be appreciated.

 

[zgozvrm]

Do you need to take air resistance (drag) into account?
If so, that complicates things quite a bit, especially when dealing with differently-shaped projectiles.

Otherwise, I see no reason that a spreadsheet would "break down" when large ranges are entered.

 

[Bob S]

If you want some information on long-range siege guns like the one the Germans used to bombard Paris during WW I, look up

http://en.wikipedia.org/wiki/Paris_Gun

It had a maximum range of about 81 [STRIKE]km[/STRIKE] miles.

The flight time was about 3 minutes, which might be excessive for a computer game.

Bob S

 

[K^2]

aidenpryde, I have quite a bit of experience with projectile computations for games. Ballistic charts aren't going to be terribly useful for what you are doing. You'll need to run your own simulation.

First of all, how many simultaneous projectiles are you looking at? Second, am I correct in assuming that you'll need an AI that aims these projectiles?

The main point here is that this is a game, which means you don't need simulations to be perfect. You need them to be fast, you need them to be close enough to real to look right, and that's a LOT easier. And you need to make sure that your AI can handle whatever model you choose.

Your best bet is a model with simple quadratic drag. That's a one parameter model (excluding external parameters, like air density and wind velocity) that let's you get incredibly close to real data with reasonable time steps. (Personally, I've ran comparisons against real ballistics charts and have been able to get to within about 5% of that with minimum of assumptions.)

This, however, means that you don't have a formula that immediately gives you range and velocity. You'll be simulating the entire trajectory. That's going to require some CPU time, and this is why I'm asking about number of projectiles. If we are only talking about a few hundred projectiles, this shouldn't be an issue at all. If there are more, we need to start talking shortcuts and optimization.

 

[aidenpryde]

aidenpryde, I have quite a bit of experience with projectile computations for games. Ballistic charts aren't going to be terribly useful for what you are doing. You'll need to run your own simulation.

First of all, how many simultaneous projectiles are you looking at? Second, am I correct in assuming that you'll need an AI that aims these projectiles?

The main point here is that this is a game, which means you don't need simulations to be perfect. You need them to be fast, you need them to be close enough to real to look right, and that's a LOT easier. And you need to make sure that your AI can handle whatever model you choose.

Your best bet is a model with simple quadratic drag. That's a one parameter model (excluding external parameters, like air density and wind velocity) that let's you get incredibly close to real data with reasonable time steps. (Personally, I've ran comparisons against real ballistics charts and have been able to get to within about 5% of that with minimum of assumptions.)

This, however, means that you don't have a formula that immediately gives you range and velocity. You'll be simulating the entire trajectory. That's going to require some CPU time, and this is why I'm asking about number of projectiles. If we are only talking about a few hundred projectiles, this shouldn't be an issue at all. If there are more, we need to start talking shortcuts and optimization.

Thank you for your responses.

Yes, we won't be considering things like air density and wind direction/velocity (though we will have changing weather effects that will be graphical in nature). In terms of the number of projectiles there could be thousands in a given battle. It is a MMO that includes land sea and air (though most naval battles will be instanced while the rest is open world - thus the large amounts of bullets flying around) so there could be hundreds of players within a relatively small area. As far as the naval battles are concerned however I wouldn't expect more than a few hundred in the air at anyone time.

At the moment however I am just compiling stats, how these will be used by our programmers is not yet clear. I am aware of the concepts of steps and how the projectiles won't be tracked in real time. But I am not a programmer, just a designer. I expect they will take the stats and then decide upon the best way to implement them.

So at this point I am just finding information about the weight of shells, the muzzle velocity, possible angles of firing, etc and compiling them into Excel documents for easy editing and reference. But I need something that will allow me to input these base stats and then return things like the velocity at say 100m to 20,000m.

 

[Bob S]

Here is information on the 16" guns on the battleship Iowa.

They fired projectiles weighing from 1,900 to 2,700 pounds (850 to 1,200 kg) at a maximum speed of 2,690 feet per second (820 m/s) with a range of up to 24 miles (39 km). At maximum range the projectile spent almost 1½ minutes in flight.

from http://en.wikipedia.org/wiki/16"/50_caliber_Mark_7_gun

I simulated this using quadratic drag, and determined that a drag coefficient of 0.25 matches the above trajectory fairly well. How will you manage a flight time of about 90 seconds in a computer game?

Bob S

 

[aidenpryde]

Here is information on the 16" guns on the battleship Iowa.

They fired projectiles weighing from 1,900 to 2,700 pounds (850 to 1,200 kg) at a maximum speed of 2,690 feet per second (820 m/s) with a range of up to 24 miles (39 km). At maximum range the projectile spent almost 1½ minutes in flight.

from http://en.wikipedia.org/wiki/16"/50_caliber_Mark_7_gun

I simulated this using quadratic drag, and determined that a drag coefficient of 0.25 matches the above trajectory fairly well. How will you manage a flight time of about 90 seconds in a computer game?

Bob S

Well each shell fired is a "physicalized" object. Meaning that our physics engine can impart certain effects onto the shell. We can simulate the effect that gravity has on the object. Once we determine how fast the shell moves once it leaves the barrel (muzzle velocity), and the ballistic coefficient (drag), and the angle and height at which it was fired, the shell then moves basically like it normally would in real life.

If it impacts an object, say an angled piece of armor on another ship, the game then calculates the angle of impact and then takes the speed it was traveling at the point of impact to determine if there was penetration. The stats of the shell, such as HE filler, type of cap, etc then come into play and determine what sort of damage is done.

As far as how we will render 20+ kilometers in game (that 90 second flight time you mentioned) it's really a matter of adjusting the view distance. Any modern engine is capable of simulating such extended views, its just that most games don't because their designs don't need them to.

I found a nice program that will export into excel, and it appears to have much of this stuff already built in. It has all the different armor types used from 1890-1945, most of the weapons types from that time period as well. It will give me a chart of how much a shell will penetrate (we probably will have a generic type of armor for all ships or just a couple types in the game - as the program has 20+ different types and that would be too much to simulate and the player probably won't know the difference), and at different ranges how fast the shell is moving.

The only problem is that it doesn't have some of the 12.7cm German torpedoboat guns. The program allows you to input your own stats into it, and I know the muzzle velocity, and the weight of the shell, but don't currently know how to calculate the ballistic coefficient.