Abstract: A golf club having a sensor that is releasably connected is disclosed, where the sensor comprises a plurality of inertial measurement units. Each inertial measurement unit is able to measure linear accelerations along three orthogonal axes and angular rates of rotation along the same three orthogonal axes. Each inertial measurement unit is positioned such that at least two of the axes of each inertial measurement unit are oriented differently. Additionally, a process may be implemented by a processor to expand the measurement range of the sensor.

Abstract: A golf club having a sensor that is removably connected at one or more positions of the golf club where the sensor comprises an inertial measurement unit including an accelerometer capable of measuring linear accelerations in three orthogonal axes and a gyroscope capable of measuring an angular rate of rotation around the same axes. The sensor may further comprise a processor which may perform instructions to detect the impact of the golf club with a golf ball and determine the start of the golf swing without any additional input from the user. The sensor may further have a power management system to extend the life of the power source.

Abstract: A golf club having a sensor that is removably connected at one or more positions of the golf club where the sensor comprises an inertial measurement unit including an accelerometer capable of measuring linear accelerations in three orthogonal axes and a gyroscope capable of measuring an angular rate of rotation around the same axes. The sensor may further comprise a processor which may perform instructions to detect the impact of the golf club with a golf ball and determine the start of the golf swing without any additional input from the user. The sensor may further have a power management system to extend the life of the power source.

Abstract: Golf performance and equipment characteristics may be determined by analyzing the impact between a golf ball and an impacting surface. In some examples, the impacting surface may be a golf club face. The impact between the golf ball and the surface may be measured based on sound and/or motion sensors (e.g., gyroscopes, accelerometers, etc.). Based on motion and/or sound data, various equipment-related information including golf ball compression, club head speed and impact location may be derived. Such information and/or other types of data may be conveyed to a user to help improve performance, aid in selecting golf equipment and/or to insure quality of golfing products.

Abstract: A golf club head having accelerometer and gyroscope sensors measuring swing motion acceleration and angular rate values. Inputs of force and torque to the golf club head during the swing motion may be unknown, such that a system of motion equations may be used to calculate functions for the unknown input force and torque, as well as roll angle and pitch angle for the golf club head, and compensate for gyroscope bias, without using static leveling processes.

Abstract: A golf club head having accelerometer and gyroscope sensors measuring swing motion acceleration and angular rate values. Inputs of force and torque to the golf club head during the swing motion may be unknown, such that a system of motion equations may be used to calculate functions for the unknown input force and torque, as well as roll angle and pitch angle for the golf club head, and compensate for gyroscope bias, without using static leveling processes.

Abstract: Golf performance and equipment characteristics may be determined by analyzing the impact between a golf ball and an impacting surface. In some examples, the impacting surface may be a golf club face. The impact between the golf ball and the surface may be measured based on sound and/or motion sensors (e.g., gyroscopes, accelerometers, etc.). Based on motion and/or sound data, various equipment-related information including golf ball compression, club head speed and impact location may be derived. Such information and/or other types of data may be conveyed to a user to help improve performance, aid in selecting golf equipment and/or to insure quality of golfing products.

Abstract: Golf club heads having sensors configured to measure one or more swing parameters are provided. The golf club head may include several gyroscopes and accelerometers. In one embodiment, the club head contains three gyroscopes that measure angular rate data along different orthogonal axes. At least one gyroscope may an analog gyroscope. Accelerometers may provide data regarding the three orthogonal axes associated with the gyroscopes. The club head may further include software and/or hardware that perform computer-executed methods for determining one or more swing parameters. Exemplary club heads may include a display device for displaying an output of the swing parameter(s). Further aspects of the invention relate to novel methods and algorithms for calculating measurements relating to the swing parameters.

Abstract: Golf club heads having sensors configured to measure one or more swing parameters are provided. The golf club head may include several gyroscopes and accelerometers. In one embodiment, the club head contains three gyroscopes that measure angular rate data along different orthogonal axes. At least one gyroscope may an analog gyroscope. Accelerometers may provide data regarding the three orthogonal axes associated with the gyroscopes. The club head may further include software and/or hardware that perform computer-executed methods for determining one or more swing parameters. Exemplary club heads may include a display device for displaying an output of the swing parameter(s). Further aspects of the invention relate to novel methods and algorithms for calculating measurements relating to the swing parameters.

Abstract: A water heater that includes a cylindrical storage tank, at least one heating element, and at least one temperature sensor is modeled using a one-dimensional model that includes: a vertical stack of disks representing the water volume in the cylindrical storage tank, and a stack of annular segments surrounding the vertical stack of disks. The stack of annular segments represents the cylindrical wall of the cylindrical storage tank. The one-dimensional model may be used by a condition-based maintenance system comprising an electronic data processing device configured to detect a failure mode present in the water heater based on an output of the water heating model component. Some illustrative failure modes include insulation disturbance, heating element failure, excessive sediment buildup, or a drip tube rupture.

Abstract: An aggregation comprises: loads that draw electricity, and a hierarchy including a root dispatch engine at the top of the hierarchy, downstream dispatch engines each servicing downstream points comprising further downstream dispatch engines or loads, and the loads at the bottom of the hierarchy. Each downstream dispatch engine sends draw dispatches to its downstream points such that the total draw computed by summing the draw dispatches equals a draw dispatch received by the downstream dispatch engine from the dispatch engine above it in the hierarchy. The sent draw dispatches also satisfy downstream point draw constraints communicated to the downstream dispatch engine from its downstream points. In a method, a baseline long-term draw dispatch is determined for the aggregation, and the baseline long-term draw dispatch is modulated over a shorter time interval based on a short-term draw requirement to determine a draw dispatch for the aggregation.

Abstract: Golf club heads having sensors configured to measure one or more swing parameters are provided. The golf club head may include several gyroscopes and accelerometers. In one embodiment, the club head contains three gyroscopes that measure angular rate data along different orthogonal axes. At least one gyroscope may an analog gyroscope. Accelerometers may provide data regarding the three orthogonal axes associated with the gyroscopes. The club head may further include software and/or hardware that perform computer-executed methods for determining one or more swing parameters. Exemplary club heads may include a display device for displaying an output of the swing parameter(s). Further aspects of the invention relate to novel methods and algorithms for calculating measurements relating to the swing parameters.

Abstract: Golf performance and equipment characteristics may be determined by analyzing the impact between a golf ball and an impacting surface. In some examples, the impacting surface may be a golf club face. The impact between the golf ball and the surface may be measured based on sound and/or motion sensors (e.g., gyroscopes, accelerometers, etc.). Based on motion and/or sound data, various equipment-related information including golf ball compression, club head speed and impact location may be derived. Such information and/or other types of data may be conveyed to a user to help improve performance, aid in selecting golf equipment and/or to insure quality of golfing products.

Abstract: Golf club heads having sensors configured to measure one or more swing parameters are provided. The golf club head may include several gyroscopes and accelerometers. In one embodiment, the club head contains three gyroscopes that measure angular rate data along different orthogonal axes. At least one gyroscope may an analog gyroscope. Accelerometers may provide data regarding the three orthogonal axes associated with the gyroscopes. The club head may further include software and/or hardware that perform computer-executed methods for determining one or more swing parameters. Exemplary club heads may include a display device for displaying an output of the swing parameter(s). Further aspects of the invention relate to novel methods and algorithms for calculating measurements relating to the swing parameters.

Abstract: Golf club heads having sensors configured to measure one or more swing parameters are provided. The golf club head may include several gyroscopes and accelerometers. In one embodiment, the club head contains three gyroscopes that measure angular rate data along different orthogonal axes. At least one gyroscope may an analog gyroscope. Accelerometers may provide data regarding the three orthogonal axes associated with the gyroscopes. The club head may further include software and/or hardware that perform computer-executed methods for determining one or more swing parameters. Exemplary club heads may include a display device for displaying an output of the swing parameter(s). Further aspects of the invention relate to novel methods and algorithms for calculating measurements relating to the swing parameters.

Abstract: A method of optimizing a waveform of an electrical current applied to an electrode of an electrochemical device that consists of at least two electrodes separaged by an electrolyte that includes the steps of: applying an electrical current to an electrode of a device; determining a waveform of the voltage or the current of the electrical current; representing the waveform by a mathematical expression or numbers taking measurements of output voltage, current or power of the device associated with the application of the electrical current; and varying the shape and frequency of the waveform to optimize the output voltage, current or power of the device and thereby determine an optimized waveform of the electrical current to be applied to the electrode of the device.

Abstract: A method of optimizing a waveform of an electrical current applied to an electrode includes the steps of: applying an electrical current to an electrode of a device; determining a waveform of the voltage or the current of the electrical current; representing the waveform by a mathematical description such as a number of points or an analytical function characterized by a number of unknown coefficients and a fixed number of known functions; measuring a function of the device associated with the application of the electrical current; feeding the waveform description and the measurements to an algorithm, which may be in a computer program or other calculating device including manual calculations, including an optimization routine which uses the points or coefficients as independent variables for optimizing the function of the device; and performing the calculations to determine values of the points or coefficients which optimize the function of the device, and thereby determine an optimized waveform of the elect

Abstract: A method of optimizing a waveform of an electrical current applied to an electrode of an elecetrochemical device that includes at least two electrodes separated by an electrolyte, includes the steps of: applying an electrical current to an electrode of a device; determining a waveform of the voltage or the current of the electrical current; representing the waveform by a mathematical expressions or numbers; taking measurements of output voltage, current or power of the device associated with the application of the electrical current; and varying the shape and frequency of the wave form to optimize the output voltage, current or power of the device and thereby determine an optimized waveform of the electrical current to be applied to the electrode of the device.

Abstract: This invention relates to a method of operating an electrochemical device. The method includes controlling the mass flow of fuel to the device so that the mass flow varies during the operation of the device. In combination with the mass flow control, the method also includes controlling an electrical parameter of the device so that the electrical parameter varies during the operation of the device. Another embodiment includes a method of operating a fuel cell using a flow of fuel or oxidant that contains a contaminant, and using a controller to control the flow and an electrical parameter of the fuel cell. A further embodiment includes a method of operating an electrochemical device using reactants that include a reactant causing an undesired electrochemical reaction, and using a controller to control the flow of reactants and an electrical parameter of the device.