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The target article by Dr. Prilutsky is based on three incorrectly derived mathematical rules concerning force-sharing among synergistic muscles associated with a cost function that minimizes the sum of the cubed muscle stresses. Since these derived rules govern all aspects of Dr. Prilutsky's discussion and conclusion and form the basis for his proposed theory of coordination between one-and two-joint muscles, most of what is said in the target article is confusing or misleading at best or factually wrong at worst. The aim of our commentary is to sort right from wrong in Dr. Prilutsky's article within space limitations that do not allow for detailed descriptions of mathematical proofs and explicit discussions of the relevant experimental literature.

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.

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.

The effect of an acute bout of physical activity on academic performance in school-based settings is under researched. The purpose of this study was to examine associations between a single, vigorous (70–85%) bout of physical activity completed during physical education on standardized mathematics test performance among 72, eighth grade students at a school in the Southwestern United States. Students received both a physical activity and nonactive condition, in a repeated measures design. Academic performance measures were collected at 30 and 45-minutes post condition. It was hypothesized that students would have greater gains in mathematics test scores post physical activity condition compared with post nonactive condition. Results reported students achieved 11–22% higher math scores at 30 minutes post physical activity condition compared with other time points (45 minutes post PA, 30 and 45 minutes post sedentary) (F(1, 68) = 14.42, p < .001, d = .90). Findings suggest that physical activity may facilitate academic performance in math.

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.

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.