Abstract: A method of modeling a tire includes providing a tire having a first tire design, rotating the tire under a vertical load, and measuring a plurality of forces at a plurality of selected conditions. The method further includes using a computer to plot the plurality of forces against the plurality of conditions, using the computer to plot a plurality of moments against the plurality of conditions, and using the computer to fit a first force curve to the plurality of plotted forces at the plurality of conditions, such that the first force curve is asymmetric. The method also includes using the computer to fit a first moment curve to the plurality of plotted moments at the plurality of conditions, evaluating the first force curve and the first moment curve, and making a second tire design based on the evaluation of the first force curve and the first moment curve.

Abstract: An apparatus and method are disclosed for modeling at least a portion of a rolling tire (200). A finite element model of at least a portion of a tire (200) rolling against a tire contacting surface (202, 506, 602) is input into a finite element analysis system (100). The system executed instructions that result in the application of a constant force to the model tire (200) or portion thereof by the tire contacting surface (202, 506, 602). The application of force control boundary conditions, as opposed to displacement control, provides significant benefit in terms of computational time of the finite element analysis solution. A finite element analysis simulation of the model against the tire contacting surface (202, 506, 602) is performed while maintaining the force on the model tire (200). Alternatively, a camber (?) is also applied to the tire and maintained throughout the simulation.

Abstract: A method of modeling a tire includes providing a tire having a first tire design, rotating the tire under a vertical load, and measuring a plurality of forces at a plurality of selected conditions. The method further includes using a computer to plot the plurality of forces against the plurality of conditions, using the computer to plot a plurality of moments against the plurality of conditions, and using the computer to fit a first force curve to the plurality of plotted forces at the plurality of conditions, such that the first force curve is asymmetric. The method also includes using the computer to fit a first moment curve to the plurality of plotted moments at the plurality of conditions, evaluating the first force curve and the first moment curve, and making a second tire design based on the evaluation of the first force curve and the first moment curve.

Abstract: A system and method for modeling a distribution of a tire footprint boundary (202) include inputting a finite element model of a tire rolling against a road surface described by discrete road surface coordinates into a finite element analysis system (100). A finite element analysis simulation of tire model rolling against the road surface for a plurality of time increments is performed. A plurality of tire footprint boundary (202) data are generated, each having road surface coordinates on which a footprint boundary (202) overlaps during a unique one of a second plurality of time increments. The number of second plurality of time increments during which the footprint boundary (202) overlaps the each of the discrete road surface coordinates is determined for each of the time increments of the simulation. For each coordinate, the number of the second plurality of time increments may be associated with a color scale or grayscale (510).

Abstract: A system and method for modeling a distribution of a tire footprint boundary (202) include inputting a finite element model of a tire rolling against a road surface described by discrete road surface coordinates into a finite element analysis system (100). A finite element analysis simulation of tire model rolling against the road surface for a plurality of time increments is performed. A plurality of tire footprint boundary (202) data are generated, each having road surface coordinates on which a footprint boundary (202) overlaps during a unique one of a second plurality of time increments. The number of second plurality of time increments during which the footprint boundary (202) overlaps the each of the discrete road surface coordinates is determined for each of the time increments of the simulation. For each coordinate, the number of the second plurality of time increments may be associated with a color scale or grayscale (510).

Abstract: An apparatus and method are disclosed for modeling at least a portion of a rolling tire (200). A finite element model of at least a portion of a tire (200) rolling against a tire contacting surface (202, 506, 602) is input into a finite element analysis system (100). The system executed instructions that result in the application of a constant force to the model tire (200) or portion thereof by the tire contacting surface (202, 506, 602). The application of force control boundary conditions, as opposed to displacement control, provides significant benefit in terms of computational time of the finite element analysis solution. A finite element analysis simulation of the model against the tire contacting surface (202, 506, 602) is performed while maintaining the force on the model tire (200). Alternatively, a camber (?) is also applied to the tire and maintained throughout the simulation.

Abstract: A therapeutic sleep device worn about an individual's torso and intended to discourage an individual from sleeping in a supine position includes a body securing member and a sleep fin. The body securing member has an interior side and a posterior side. The sleep fin includes a supine-suppression fin providing a right convex surface and a left convex surface tapering from a wider base region to a narrower peak region at which the right and left convex surfaces join at an apex. The apex and at least a portion of the right and left convex surfaces extend beyond said posterior side of the body securing member. A spine indentation formed in the sleep device can help to increase the comfort and improve the securing of the device to a individual.