Abstract
The exact trajectory of the direct fire gun results from the standard differential equations given in (1, 2, 3, 4). Under the condition that the elevation firing angle has a very small angle, the standard differential equations may be changed into the solvable differential equations. We compare two trajectories from the exact and the solvable differential equations. For a range distance of 570m, the error between the exact and approximate trajectory is 0.0055m if there is neither crosswind nor range wind. Under the condition of existence of the range and cross-range, their error is 0.2016m for a range distance of 570m. It turns out that the derived new trajectory has a very small discrepancy compared to the exact trajectory derived from the standard differential equations.
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