A three-dimensional theoretical model for calculating fireworks shell trajectory was built in the research work. A drag coefficient is assumed as a function of the Reynolds number in the theoretical model. The effects of wind direction, wind speed, air drag, and mortar tilt angle on the trajectory can be examined by the theoretical model. A numerical computing program was developed with the Microsoft Excel calculation. The input parameters and the graphs of calculated results can be shown on the PC screen at the same time, after several parameters such as initial velocity, drag coefficient are inputted. Therefore, the program is convenient and practically useful.
The optimal drag coefficient, wind speed and wind direction were easily determined with the Microsoft Excel calculation by fitting calculated trajectory to that of experiment. With the method, the drag coefficient of No. 3 shell was obtained.
本研究は空気抵抗係数をレイノルズ数の関数とした煙火玉の3次元筒外弾道の理論モデルを設け，風向，風速，発射角度等の要因を考慮し，煙火玉の筒外弾道の数値計算を行った。数値計算プログラムは従来のFORTRANプログラムではなく，Excelにより作成した。初速度や空気抵抗係数（レイノルズ数の関数）などの計算条件と図示した計算結果はパソコン（PC）の同一画面上で同時に表示され，実用且つ便利である。煙火玉の実測軌跡と合わせた計算結果から，レイノルズ数の関数とした3号煙火玉の空気抵抗係数を求めた。
Fireworks, Exterior ballistics, Drag coefficient, Numerical calculation