# Trajectory / ballistics

I'm trying to calculate if a canon will be able to shoot over a height in the terrain.

lets saytThe canon have to be 15'000-18'000m from the target, and the impact degrees have to be over 30 degrees.

So the position of the target will be known, and the result i'm looking for are the areas where one can make the shot from. It would be fairly easy if one knew both the position of the target and the canon, but my trouble is that the canon is mobile and i do't know any efficient methods to calculate for all the possible positions...

I thought of making a spheroid or something and see how/where it would intersect with the elevation model, but i don't have the competence for it.

Tried to visualize me problem and desired output.

1 image: dilemma if the canon is to close to reach over the mountain

2 image: idea of result, red areas are areas where the shot can not be made from, while the green areas are ok

I'm using ArcGis for Desktop 10.3, also have 10.2 available, all extensions.

• I may be making this unnecessarily complicated, but I feel like you are overlooking a couple of critical variables here. Distance for a given load is dependent on the velocity and angle of launch. Essentially the amount of charge your canon has, and the angle of the muzzle. To simplify, given a fixed charge, or launch velocity, your load will travel farther horizontally at a lower launch angle. High launch angle clears taller obstacle, but has to be closer horizontally to target. How are you planning to control for those variables? – Get Spatial Apr 21 '15 at 20:02
• And then there's wind speed, which has a long time to act on a 25k arc. – Vince Apr 21 '15 at 23:45
• Plot the trajectory as a 3d stream of points, with all necessary variables accounted for or ignored, then convert to a elevation raster. Calculate trajectory raster height - surface height, if any points are less than 0 you've hit dirt. Basic ballistics says it should be an arc depending on the 'forward' component and 'upward' component of your starting vector - once you've solved your path using mathematics and physics the raster portion is the easy part. You will need to solve this for each cell in your focus area to get your intended result.. not hard but you will need to use arcpy. – Michael Stimson Apr 22 '15 at 2:54