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Mont Hubbard and LeRoy W. Alaways

Changes in the rules for construction of the men's javelin have dramatically altered the pitching moment profile as a function of angle of attack. Thus the optimal release conditions are different for the new javelin. Optimal release conditions are presented for nominal release velocities in the range 20 < vn < 35 m/s. Although the optimal release angle remains roughly constant near 30° over this speed range, the optimal angle of attack and pitching angular velocity change substantially with speed. The main effects of the rule change have been (a) to decrease the achievable range at a nominal velocity vn = 30 m/s by about 10% by making it impossible to take advantage of the javelin's potentially large aerodynamic lift forces, and (b) to make the flight much less sensitive to initial conditions.

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LeRoy W. Alaways, Sean P. Mish and Mont Hubbard

Pitched-baseball trajectories were measured in three dimensions during competitions at the 1996 Summer Olympic games using two high-speed video cameras and standard DLT techniques. A dynamic model of baseball flight including aerodynamic drag and Magnus lift forces was used to simulate trajectories. This simulation together with the measured trajectory position data constituted the components of an estimation scheme to determine 8 of the 9 release conditions (3 components each of velocity, position, and angular velocity) as well as the mean drag coefficient CD and terminal conditions at home plate. The average pitch loses 5% of its initial velocity during flight. The dependence of estimated drag coefficient on Reynolds number hints at the possibility of the drag crisis occurring in pitched baseballs. Such data may be used to quantify a pitcher’s performance (including fastball speed and amount of curve-ball break) and its improvement or degradation over time. It may also be used to understand the effects of release parameters on baseball trajectories.

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Scott O. Cloyd, Mont Hubbard and LeRoy W. Alaways

Feedback control of a human-powered single-track bicycle is investigated through the use of a linearized dynamical model in order to develop feedback gains that can be implemented by a human pilot in an actual vehicle. The object of the control scheme is to satisfy two goals: balance and tracking. The pilot should be able not only to keep the vehicle upright but also to direct the forward motion as desired. The two control inputs, steering angle and rider lean angle, are assumed to be determined by the rider as a product of feedback gains and “measured” values of the state variables: vehicle lean, lateral deviation from the desired trajectory, and their derivatives. Feedback gains are determined through linear quadratic regulator theory. This results in two control schemes, a “full” optimal feedback control and a less complicated technique that is more likely to be usable by an inexperienced pilot. Theoretical optimally controlled trajectories are compared with experimental trajectories in a lane change maneuver.