Ballistics formula

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?

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

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.

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 ;)

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!

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?)

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

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.

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).

There are some interesting leads here.

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