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Study on modeling and production inaccuracies for artillery firing

Khalil Mostafa

Archive of Mechanical Engineering

2022

LXIX, nr 1

165--183

Production and assessment of artillery firing tables (FT) are the key tasks in solving ballistic problems through both standard and non-standard firing conditions. According to the literature, two different standard firing table formats were developed by the former-Soviet and the United States armies. This study proposes the main difference between these FT formats, as the standard meteorological conditions. An accuracy assessment has been proposed to justify different sources of errors through modeling and production of such tables, including applied meteorological message, aiming angles round-off, linear superposition principle, and Earth approximation. A~case study has been proposed for the 155M107 projectile to demonstrate the impact of the Coriolis effect as well as other ballistic and atmospheric non-standard conditions. As a part of the construction of artillery FT, a fitting process has to be made between available firing data and simulations. Therefore, a parametric study is implemented to study the number of test elevations per charge needed through the fitting process and its corresponding production error. Hence, based on the number of test elevations available, the genetic algorithm (GA) has been utilized to obtain the test elevations order needed with minimum FT production error. The results show a good agreement with the data stated in the literature.

Mathematical model of Coriolis effect

Sobczak E., Kasprzak J., Ringel T.

Inżynieria i Aparatura Chemiczna

2017

Nr 1

23--25

Mathematical model describing acceleration and the Coriolis force for an object moving along a longitude with a velocity v > 0 (northwards) or v < 0 (southwards) and at same time along a latitude with a velocity vs > 0 (eastwards) or vs < 0 (westwards) has been elaborated: ac = - ( ω + vs /r ) v sinϕ = - ωv sinϕ (1 + s/cosϕ). At a positive velocity along a latitude (vs > 0) an increase in the angular velocity of the Earth globe “cycle” (Δω = vs/r; r = R cosϕ and an increase in the absolute value of the acceleration lacl and the Coriolis force at a given object velocity along a longitude (v > 0 or v < 0) occur, while for a negative value of this velocity (vs < 0) a decrease by the similar value lacl appears. The acceleration and the Coriolis force are not observed when vs= - R ωcosϕ or ϕ= 0.

Opracowano matematyczny model opisujący przyśpieszenie Coriolisa dla obiektu poruszającego się jednocześnie wzdłuż południka z prędkością v > 0 (na północ) lub v < 0 (na południe) oraz wzdłuż równoleżnika z prędkością vs > 0 (na wschód) lub vs < 0 (na zachód): ac = - ( ω + vs /r ) v sinϕ = - ωv sinϕ (1 + s/cosϕ). Dla dodatniej prędkości wzdłuż równoleżnika (vs > 0) następuje wzrost prędkości kątowej obiegu obiektu wokół osi kuli ziemskiej (Δω = vs/r; r = R cosϕ oraz wzrost bezwzględnej wartości przyśpieszenia Coriolisa lacl przy danej prędkości obiektu wzdłuż południka (v > 0 lub v < 0), natomiast dla (vs < 0) następuje zmniejszenie lacl. Przyśpieszenie Coriolisa zanika dla vs= - R ωcosϕ lub ϕ= 0.