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Mathematical Model to Predict Drivers’ Reaction Speeds

Mental distractions and physical impairments can increase the risk of accidents by affecting a driver’s ability to control the vehicle. In this article, we developed a linear mathematical model that can be used to quantitatively predict drivers’ performance over a variety of possible driving conditions. Predictions were not limited only to conditions tested, but also included linear combinations of these tests conditions. Two groups of 12 participants were evaluated using a custom drivers’ reaction speed testing device to evaluate the effect of cell phone talking, texting, and a fixed knee brace on the components of drivers’ reaction speed. Cognitive reaction time was found to increase by 24% for cell phone talking and 74% for texting. The fixed knee brace increased musculoskeletal reaction time by 24%. These experimental data were used to develop a mathematical model to predict reaction speed for an untested condition, talking on a cell phone with a fixed knee brace. The model was verified by comparing the predicted reaction speed to measured experimental values from an independent test. The model predicted full braking time within 3% of the measured value. Although only a few influential conditions were evaluated, we present a general approach that can be expanded to include other types of distractions, impairments, and environmental conditions.

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A Mathematical Model to Examine Issues Associated With Using Portable Force-Measurement Technologies to Collect Infant Postural Data

modifications increase the vertical offset between the force plate reference system and the support surface, which will attenuate the measured postural excursions. In this paper, we used a mathematical model to characterize CoP errors that emerge during infant sitting and standing by manipulating various

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Validation of a Mathematical Model for Road Cycling Power

This investigation sought to determine if cycling power could be accurately modeled. A mathematical model of cycling power was derived, and values for each model parameter were determined. A bicycle-mounted power measurement system was validated by comparison with a laboratory ergometer. Power was measured during road cycling, and the measured values were compared with the values predicted by the model. The measured values for power were highly correlated (R 2 = .97) with, and were not different than, the modeled values. The standard error between the modeled and measured power (2.7 W) was very small. The model was also used to estimate the effects of changes in several model parameters on cycling velocity. Over the range of parameter values evaluated, velocity varied linearly (R 2 > .99). The results demonstrated that cycling power can be accurately predicted by a mathematical model.

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Mathematical Model of the Takeoff Phase in the Pole Vault

A mathematical model is presented of the takeoff phase in the pole vault for an athlete vaulting with a rigid pole. An expression is derived that gives the maximum height that the vaulter may grip on the pole in terms of the takeoff velocity, the takeoff angle, the athlete's vertical reach, and the depth of the takeoff box. Including the dependence of the vaulter's takeoff velocity on the takeoff angle reveals that there is an optimum takeoff angle that maximizes the vaulter's grip height. It is also shown that taller and faster vaulters are able to grip higher on the pole. The results of the investigation compare favorably with data for vaulters using bamboo and steel poles.

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A Mathematical Model of Competitive Swimming in Pools with Currents

Swimmers may be placed at a disadvantage when water in a pool is actively circulated during competition. This circulation may produce currents in specific lanes which add to a swimmer’s speed in one direction and subtract from it in the other direction. This article presents a mathematical model of swimming in a lane with a current. It predicts that even small currents can add significantly to a swimmer’s race time. The effects of the current will not equal out over an even number of lengths swum because the swimmer always loses more time swimming against the current than he or she gains from swimming with the current. Mathematical simulations of races of various distances show that the losses in time can range from 100ths of a second in a 100-m sprint to several seconds in the longer distances. Since circulating water may create currents only in specific lanes, some swimmers may be placed at a disadvantage compared to others. A simple solution to the problem of currents is suggested.

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A Mathematical Model for the Trajectory of a Spiked Volleyball and its Coaching Application

A wind tunnel test was conducted to empirically determine the relationship between the Magnus force (M), spin rate (ω), and linear velocity (V) of a spiked volleyball. This relationship was applied in a two-dimensional mathematical model for the trajectory of the spiked volleyball. After being validated mathematically and empirically, the model was used to analyze three facets of play that a coach must address: the importance of topspin, possibility of overblock spiking, and optimum spiking points. It was found that topspin can increase the spiking effectiveness dramatically in many ways. It was also found that a shot spiked from about 2 m behind the net has the least possibility of being blocked.

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Using Mathematical Modeling in Training Planning

This report aims to discuss the strengths and weaknesses of the application of systems modeling to analyze the effects of training on performance. The simplifications inherent to the modeling approach are outlined to question the relevance of the models to predict athletes’ responses to training. These simplifications include the selection of the variables assigned to the system’s input and output, the specification of model structure, the collection of data to estimate the model parameters, and the use of identified models and parameters to predict responses. Despite the gain in insight to understand the effects of an intensification or reduction of training, the existing models would not be accurate enough to make predictions for a particular athlete in order to monitor his or her training.

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A Computer Model to Simulate the Swing Phase of a Transfemoral Prosthesis

For amputees to perform an everyday task, or to participate in physical exercise, it is crucial that they have an appropriately designed and functional prosthesis. Past studies of transfemoral amputee gait have identified several limitations in the performance of amputees and in their prosthesis when compared with able-bodied walking, such as asymmetrical gait, slower walking speed, and higher energy demands. In particular the different inertial characteristics of the prosthesis relative to the sound limb results in a longer swing time for the prosthesis. The aim of this study was to determine whether this longer swing time could be addressed by modifying the alignment of the prosthesis. The following hypothesis was tested: Can the inertial characteristics of the prosthesis be improved by lowering the prosthetic knee joint, thereby producing a faster swing time? To test this hypothesis, a simple 2-D mathematical model was developed to simulate the swing-phase motion of the prosthetic leg. The model applies forward dynamics to the measured hip moment of the amputee in conjunction with the inertial characteristics of prosthetic components to predict the swing-phase motion. To evaluate the model and measure any change in prosthetic function, we conducted a kinematic analysis on four Paralympic runners as they ran. When evaluated, there was no significant difference (p > 0.05) between predicted and measured swing time. Of particular interest was how swing time was affected by changes in the position of the prosthetic knee axis. The model suggested that lowering the axis of the prosthetic knee could reduce the longer swing time. This hypothesis was confirmed when tested on the amputee runners.

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Normal and ACL-Deficient in Situ Measurement of Patellofemoral Joint Contact

Abnormal joinl coniact mechanics in the knee joint due to loss of anterior cruciate ligament (ACL) are often speculated to play an important role in the development of osteoarthritis. In this study, a technique was developed so that contact of the patellofemoral (PF) joint could be estimated in situ using a mathematical contact model. The model inputs were PF joint kinematics measured in situ and the PF joint surface topology. Due to the small size of the joint, techniques for measuring joinl kinematics and surface topology with sufficient precision were paramount so that reasonable estimates of joint contact could be obtained. The sensitivity of the model to measurement errors was examined. Differences in joint contact between ACL-intacl and ACL-deficient conditions were analyzed. Statistically significant differences in contact areas were detected between the intact and ACL-deficient knee joint, and different coniact areas and locations as a function of joint angle and quadriceps muscular stimulation.

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Systematic, Unintended Drifts in the Cyclic Force Produced with the Fingertips

result, we expected a smaller relative increase in A F with an increase in f TASK (Hypothesis 3). This exploration is intended to help in our plans to develop a mathematical model of the processes involved in unintentional force changes. Methods Subjects Fourteen adults participated in this study