Ballistics of Firework Shells

Dr Takeo Shimizu


Heretofore we have had four important problems with calculations in this field, i.e., with the interior ballistics when using Black Powder as the propellant:

(1) to obtain a suitable form function of the propellant which consists of irregular grains,
(2) to obtain solutions when the burning rate ofthe propellant grains is proportional to Pα,

(where P is an internal pressure of the mortar barrel and α the pressure exponent)

(3) to obtain suitable solutions when the propellant gas escapes from the burning room through the clearance between the wall and the shell in the mortar, and with the exterior ballistics
(4) to obtain simply the drag coefficient for various shapes of shells.

For (1) a treatment to calculate the surface areas and volumes of grains assuming the propellant grains consist of a mixture of cubes and spheres is proposed. For (2) a method to solve a three order differential equation derived from three basic interior ballistic equations step by step with proper time intervals is proposed. For (3) the nozzle theory used for rocket engines is introduced. For (4) the fact that the maximum height of the projectile in the air is almost the same as that of vacuum when the flying times of the both are equal is applied. These methods are applied to 6-inch shells and examined if they are suitable in practice.


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