Trajectory Analysis

[rexford]

If a Stug IIIG fires on a target at 500m but sets the gun for 350m, and the shot has a constant velocity to any range, the physics equation of motion is:

tangent (0.2°) x distance - 0.5 x 9.8 x (flight time) squared = elevation above gun (assumed to equal target center of mass in this case to simplify math)

Above equation yields 0m from aim point at 350m, and -0.72m below aim point at 500m.

"My" trajectory equations predicts -0.8m below aim point.

So a hit still occurs with 350m aim and 500m target if there is no dispersion, which is due to relatively flat trajectory of round. One can be off by 30% in range estimate at 500m and still hit on most of shots, if not practically all if range estimation errors are the only errors that occur.

[rexford]

Original post assumed 700 m/s velocity to any range, so 0.5 second flight time to 350m and 0.71 seconds to 500m.

[rlh1138]

I'm not sure I understand all the parts of your equation. What is '= elevation above the gun'? You mean how much to elevate to hit the target. As I remember, if a barrel is level, the round starts dropping the instant it leave the barrel. (It drops at the acceleration due to gravity - 32 ft. per sec per sec, or something like that) Depending on target distance, you then need to elevate the barrel (now 'not level') so the round doesn't hit the ground before it gets to the target. The target elevation changes the equation, tho not much in 'real life', ie. hunting, combat. But, for example, if the target were directly overhead or directly below you, the elevation formula would go to zero. The things you're getting at, if I'm following this, are about 'how high do I have to hold at 200 yards?' type questions. Normally there are trajectory tables available, and I'm talking small arms here, that give the necessary 'rise' in a bullet's path to be sighted in at xxx yards. i.e. - A 220 Remington, 90 grain bullet, xxx grains powder, etc. rises 2.5 inches above line of sight at 200 yards - (fake data). So by sighting your rifle for 200 yards, you can shoot at anything up to that and hit within 2.5 inches. Is this what you're saying? I wonder if those type tables are available for the tanks/guns in question. I'd think they must be... but don't know where to look. I'm an ex-bench rest shooter, so know about this stuff for rifles - just assuming the army would have all that type data out there.