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A review of the analysis of wind-influenced projectile motion in the presence of linear and nonlinear drag force

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Abstract

The analysis of wind-influenced projectile motion in the case of linear and nonlinear (quadratic or nonquadratic) drag force is reviewed. For quadratic or more general nonlinear drag force, the results can be obtained only numerically, because the governing coupled differential equations of motion do not allow an analytical solution, although there is a closed-form relationship between the velocity and an appropriately defined angle parameter in the case of quadratic drag. For linear drag force, the entire solution, including the expressions for the time-variation of velocity components and the shape of the trajectory, can be derived in closed form. Forward-to-backward transition of the direction of motion of a projectile launched against horizontal wind is analyzed. If during different phases of motion different types of drag apply, the extents of these phases are not known in advance and the general expression for the drag force that encompasses the entire range of the Reynolds number must be used throughout the motion, in conjunction with the numerical solution of the governing differential equations. The transition from nonquadratic to quadratic drag is discussed. Illustrative examples of wind-influenced projectile motion considered in this review include the motion of golf balls, respiratory droplets, powder particles, and flea beetles.

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  1. Department of Mechanical and Aerospace Engineering, UC San Diego, La Jolla, CA 92093-0411, USA

    Marko V. Lubarda

  2. Department of NanoEngineering, UC San Diego, La, Jolla, CA 92093-0448, USA

    Vlado A. Lubarda

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Lubarda, M.V., Lubarda, V.A. A review of the analysis of wind-influenced projectile motion in the presence of linear and nonlinear drag force. Arch Appl Mech 92, 1997–2017 (2022). https://doi.org/10.1007/s00419-022-02173-7

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