An Introduction to Computational Methods in Fluids by Biringen S., Chow C.-Y.

By Biringen S., Chow C.-Y.

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A wind blowing in the direction of the body motion carries the body with it. To aim the projectile higher increases the contact time with air and therefore increases the range. On the other hand, in an adverse wind, the optimum angle should be lower than that in a quiet atmosphere in order to reduce the retarding effect of the wind. The computed results are in agreement with the experiences of a golfer. The optimum angles are not always below 45◦ , however, if the size of the projectile is changed.

1 Two-dimensional motion of a body through a fluid. 1) where x , y are the coordinates of the projectile and mf is the mass of fluid displaced by the body. 2) dy dv =v = F2 (x , y, u, v, t) dt dt The forms of the functions F1 and F2 vary in different problems. Suppose at an initial instant t0 the position (x0 , y0 ) and velocity (u0 , v0 ) are given, the trajectory and motion of the body for t > t0 are to be sought as functions of time. The initial-value problem can again be solved numerically by use of RungeKutta methods.

8) Because of its appearance on the right-hand side, it is called a central-difference formula for f . 3) and using the same technique just demonstrated. To approximate the second-order derivative of f , we show only a centraldifference formula . 9) h having an error O(h 2 fii v ). 5) to eliminate fi . 2). 1). 9).

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