Ballistics formula

[wossname]

I'm trying to find the formula that the military used in World War 2 to calculate artillery trajectories.

Particularly the ones that the early computers like Colossus and Edsac were using to do such calculations.

Does anyone have this info or know where I can get hold of a formula or two?

[dw85745]

Just a shot, don't even know if they have a web site, but try looking for:

Rock Island Arsenal
Red River Arsenal
Pentagon

I know Rock Island has a military museum and the curator there may assist you.

David

[Guv]

Almost any elementary physics text would have a discussion of this problem, assuming that the earth is a plane and ignoring atmospheric effects.

The assumption that the earth is a plane introduces no significant error, but atmospheric effects would be noticeable.

I think the following would be valid for a plane surface and no atmosphere.

• HorizontalDistance = Velocity*Time*cos(Angle)
• VerticalDistance = Velocity*Time*sin(Angle) - GravityAcceleration*Time²/2

Distances measured from end of the cylindrical hole in the cannon barrel. Correct units must be used.

I think the GravityAcceleration is 32.16 feet/seconds²

In metric it might be about 980 cm/seconds²

I would not advise using any of the above information without verifying from some reliable source.

I do not know how to calculate the effects due to the atmosphere. For golf balls, the direction of the wind is very significant, but I am not sure that direction is significant for artillery projectiles. I am pretty sure that density and composition of the atmosphere of the air is significant. I think the amount of water vapor in the air would have an effect.

[jemidiah]

If, like previously said, you exclude atmosphere (including friction due to it) and curvature of the earth, you should be able to use a simple y = ax[super]2[/super] function to find it, a being the power behind the shell. To include the previously excluded would require quite a bit more work (and, with wind, most likely a three dimensional graph instead). Just my 2.718 cents

[wossname]

Thanks for the suggestions chaps -

I already have a simple C++ class describing the path of a shell with parametric equations similar to Guv's suggestion. I was hoping to write a derived class that extends its capabilities to wind compensation.

I'll check out those links, although probably not the Pentagon one!

[jemidiah]

You know what? I just thought that you could probably use a three dimensional parametric equation to add in the wind. T_z = T_x * 90 / WindDeg * WindSpeed.

WindDeg = 90 when it is perpendicular to the projectile's windless trajectory. You could, of course, always use radians (deg * pi / 180 = rad). You'll probably have to tweak this to your needs, if it works at all (Speaking of which, would anyone be able to recommend a good 3d parametric grapher?)

[kedaman]

http://www.eskimo.com/~jbm/ballistics/cdkd.html

[Guv]

PSI-Plot has wonderful plotting capabilities, the 3D plots are z = Function(x, y).

See www.polysoftware.com

The above is an excellent application, and not expensive.

I also have Graphmatica, which was recommended by a friend who likes it. It might do parametric plots. I have never used it because I have PSI-Plot and did not want to learn a new interface. This can be downloaded

Try www.pair.com/ksoft/

I am not sure of the above URL. I found it in a Readme file from my Graphmatica directory. Post if it does not work and I will try to find the site.

MathCad & Mathematica have graphing capabilities, but are expensive. These applications are over kill for plotting, and not as good as PSI-Plot.

[jemidiah]

Thanks for those, although none (of the free/ones with trials, that is ) could do three dimensional parametric equations. Oh well, thanks again (and doubly for the Mathmatica reference).

[wossname]

There are some interesting leads here.

Thanks guys, I'll let you know how I get on.