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Analyzing an athlete's “technique,” sport scientists often focus on preselected variables that quantify important aspects of movement. In contrast, coaches and practitioners typically describe movements in terms of basic postures and movement components using subjective and qualitative features. A challenge for sport scientists is finding an appropriate quantitative methodology that incorporates the holistic perspective of human observers. Using alpine ski racing as an example, this study explores principal component analysis (PCA) as a mathematical method to decompose a complex movement pattern into its main movement components. Ski racing movements were recorded by determining the three-dimensional coordinates of 26 points on each skier which were subsequently interpreted as a 78-dimensional posture vector at each time point. PCA was then used to determine the mean posture and principal movements (PMk) carried out by the athletes. The first four PMk contained 95.5 ± 0.5% of the variance in the posture vectors which quantified changes in body inclination, vertical or fore-aft movement of the trunk, and distance between skis. In summary, calculating PMk offered a data-driven, quantitative, and objective method of analyzing human movement that is similar to how human observers such as coaches or ski instructors would describe the movement.

Carbon dioxide and hydrogen will react over iron at 800° to 1 000°K and 1 bar pressure yielding water, carbon monoxide, methane, and carbon. In addition, iron oxides and carbides form during reaction. Phase diagrams are used to analyze this complex reaction system. Data are presented which suggest that the formation of magnetite (Fe3O4) or wustite (FexO) inhibits carbon formation. The water yield thus observed is limited by the time dependent iron-iron oxide-gas equilibrium. Preliminary data also suggest that the formation of carbides has little effect on water yield.

Currently available group-contribution methods for Tc, Pc, and Vc were evaluated using the Ambrose (1980) critical property data compilation. The Ambrose estimation methods were found to be the most accurate. Linear regression methods were also employed to develop alternate estimation methods which were found to have an accuracy comparable to those of Ambrose.

Criteria are derived to specify the limit of stability for pure material and multicomponent thermodynamic systems. Through the use of Legendre transforms, the criteria may be expressed in a very simple form that only involves the determination of positiveness of a single second-order partial derivative of a potential function. Alternate and equivalent criteria are shown to result from a simple reordering of the independent variables in the Fundamental Equation of Gibbs. Certain criteria that are often stated as necessary conditions of stability (for example, Cv > 0) are shown to be insufficient for specifying the limit of stability; that is, a system will always become unstable for other reasons before Cb can attain a negative value.

Legendre transform theory is: (1) developed to show the relationships among the common thermodynamic potential functions (that is, energy, enthalpy, and free energy); (2) extended to introduce other potential functions which are particularly convenient in certain applications (for example, stability and critical point phenomena of multicomponent systems). General derivative operators are employed to allow partial derivatives of a given potential functions to be transformed to derivatives of other potential functions.

Legendre transform theory is used to develop two general critical point criteria for a classical thermodynamic system. The problem of indeterminacy is discussed, as is the option of employing mole fractions (rather than mole numbers).

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1985.

An experimental and analytical study is reported of transient natural convection in a vertical cylinder. For the experiments a cylinder was partially filled with liquid and subjected to a uniform heat flux at the walls. Thermocouples were used to measure the unsteady temperature field within the liquid; dye tracers were used to study flow patterns. Parameters that were varied included the test liquid (water-glycerin mixtures), the liquid depth, and the wall heat flux. A range of Prandtl number from 2 to 8,000, L/D ratio from 1 to 3, and Grashof number from 103 to 1011 were studied, encompassing both laminar and turbulent flow regimes. An analytical model was developed by dividing the system into three regions: a thin boundary layer rising along the heated walls, a mixing region at the top where the boundary layer discharges and mixes with the upper core fluid, and a main core region which slowly falls in plug flow. The temperature of the core fluid was assumed to vary in the vertical direction but not in the horizontal direction. Natural convection boundary-layer equations were modified to allow for a temperature variation at the outer edge of the boundary layer. The model may be used with a step-by-step computational procedure to predict the temperature distribution in the fluid as a function of time for an arbitrary set of conditions. Results computed by using the model were in good agreement with the experimental data.

An experimental study was undertaken of simultaneous heat transfer and frost deposition inside a liquid nitrogen-cooled tube for a range of humidities and Reynolds numbers. The data indicate that diffusion of water vapor within the frost layer caused the frost density and thermal conductivity to increase with time. The increase was so great that the heat transfer rate became constant even while frost continued to accumulate. In a separate study the thermal conductivities of frosts formed on a cryogenic surface were measured and found to be lower than values near the freezing point of water.

Heat transfer coefficients were measured for the dissociating system 2 NO2 ⇋ NO + O2 in turbulent flow. Heat transfer rates to this reacting gas are limited by the kinetics of the decomposition and recombination reactions. Experimental results agree to within 10% with a film-theory solution for heat transfer accompanied by a nonequilibrium chemical reaction.

Experimental data and theory both support the contention that there is a maximum solubility in solid-fluid equilibria. An example system, naphthalene-ethylene, at temperatures between the upper and lower critical end points and at pressures from 1 to 1000 bar is considered. There is also a solubility minimum in this system.