Norihisa Fujii and Mont Hubbard
A simulation and optimization procedure was constructed to investigate the relationships between optimal movement and muscular strength for baseball pitching. Four segments (torso, upper arms, lower arms, hands) and six torque generators (shoulders, elbows, wrists) are modeled. The torque generators have torque-angle and torque-angular velocity characteristics of Hill-type muscle function. The optimization objective function includes release velocity and negative terms penalizing joint loading and inaccuracy. The weighting coefficient for joint loads has a strong influence on the results. As this coefficient increases, the motion becomes more similar to actual measured pitches. Combining active state patterns optimized for different weighting coefficients gives larger joint loads in the simulated motion. This supports the hypothesis that well-coordinated active states are important for controlling the relationships of the different torque generators in order to create a reasonable and effective pitching motion. The model proposed here is superior to previous simulations for throwing, from the viewpoint of modeling with characteristics of Hill-type muscle function, and can be used to explore realistic baseball pitching.
Mont Hubbard and Stephane Laporte
Javelin vibrations in flight are caused by large forces applied transversely to the javelin's long axis during its acceleration. These decay throughout the early portion of the flight but can have substantial effects on aerodynamic lift and drag forces. Vibration decay is due to two main factors: aerodynamic dissipation and material, or hysteretic, damping. The relative contributions of these two factors are identified using theoretical models and laboratory experiments. With models for vibration decay, flight simulations can include realistic, if hypothetical, vibrational effects on the achievable range.
Mont Hubbard and Christy D. Bergman
The theory of crossflow aerodynamics is used to estimate the effect of thrower-induced vibrations on javelin mean lift and drag. Vibrations of all modes increase both lift and drag from the vibration-free condition. Percentage in-creases in lift and drag are largest at small mean angles of attack, large vibrational amplitudes, and large relative wind speeds. Thus the consequences of vibration effects on aerodynamics may be most significant for elite throwers.
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.
Mont Hubbard, Michael Kallay and Payam Rowhani
We have developed a mathematical model and computer simulation of three-dimensional bobsled turning. It is based on accurate descriptions of existing or hypothetical tracks and on dynamic equations of motion including gravitational, normal, lift, drag, ice friction, and steering forces. The three-dimensional track surface model uses cubic spline geometric modeling and approximation techniques. The position of the sled on the track is specified by the two variables α and β in the along-track and cross-track directions, differential equations for which govern the possible motions of the sled. The model can be used for studies involving (a) track design, (b) calculation of optimal driver control strategies, and (c) as the basis for a real-time bobsled simulator. It can provide detailed quantitative information (e.g., splits for individual turns) that is not available in runs at actual tracks. The model also allows for comparison of driver performance with the numerically computed optimum performance, and for safe experimentation with risky driving strategies.
Mont Hubbard, Robin L. Hibbard, Maurice R. Yeadon and Andrzej Komor
This paper presents a planar, four-segment, dynamic model for the flight mechanics of a ski jumper. The model consists of skis, legs, torso and head, and arms. Inputs include net joint torques that are used to vary the relative body configurations of the jumper during flight. The model also relies on aerodynamic data from previous wind tunnel tests that incorporate the effects of varying body configuration and orientation on lift, drag, and pitching moment. A symbolic manipulation program, “Macsyma,” is used to derive the equations of motion automatically. Experimental body segment orientation data during the flight phase are presented for three ski jumpers which show how jumpers of varying ability differ in flight and demonstrate the need for a more complex analytical model than that previously presented in the literature. Simulations are presented that qualitatively match the measured trajectory for a good jumper. The model can be used as a basis for the study of optimal jumper behavior in flight which maximizes jump distance.
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.
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.