TW202234090A - System and method for using weather applied metrics for predicting the flight of a ball - Google Patents

Abstract

A system and method for using weather applied metrics for determining the impact of weather conditions on the flight of a ball at an outdoor sports venue. Historical and current data for weather parameters, including wind, air pressure, humidity, temperature, and precipitation, are obtained to calculate the influence of each parameter on the flight of a ball. The influences of each of the parameters are summed to model the flight of the ball based on the current weather conditions. Weather instruments, such as weather sensors, anemometers, LiDAR and SODAR devices, weather consoles, data routing devices, and processors can be included in a system for using weather applied metrics to predict the flight of a ball based on current weather conditions.

Description

System and method for predicting the flight of a ball using metrics for weather applications

The present invention generally relates to weather factors in sports. More specifically, the present invention relates to a system and method for predicting the flight of a ball based on weather conditions at a particular location.

Weather has a major impact on many sports, such as baseball, American football, golf, and more. Numerous reliable studies explain how weather affects balls used in all major sports in outdoor venues. Considering that weather affects ball flight, it would be desirable to have a system that can predict ball flight in sports at a given location based on current and future weather conditions.

According to one embodiment, a computer-implemented method is provided for determining the effect of weather parameters on ball flight in an outdoor playground. A digital model of the outdoor playground is provided to the processor. At the processor, real-time data for at least one weather parameter at or near the outdoor playground is obtained. The at least one weather parameter is wind, and obtaining real-time data includes receiving real-time data from a wireless communication network, wherein the wireless communication network collects real-time data obtained from cellular transmission signals including signal attenuation information. At the processor, the current data obtained for at least one weather parameter is input into a computational fluid dynamics (CFD) model. At the processor, the CFD model is used using the input current data and the digital model of the outdoor playground to generate three-dimensional wind vectors at grid points in the digital model of the outdoor playground. At the processor, a ball trajectory is calculated at the outdoor playground using the three-dimensional wind vector based on current data obtained for the at least one weather parameter, wherein the calculated ball trajectory accounts for the impact of the at least one weather parameter. The calculated trajectory of the ball or a calculation based on the calculated trajectory of the ball is displayed on the screen.

According to another embodiment, a system is provided. The system includes a data store containing wind model data for an outdoor playground; at least one processor, a machine-readable medium containing instructions stored therein and for outputting in real time the calculated trajectory of the ball or based on the calculated ball A monitor for the calculation of the trajectory. At least one processor contains a digital model of an outdoor sports field. When executed by the at least one processor, the machine-readable medium causes the at least one processor to perform operations in real-time. The operations include obtaining current weather data including wind data at the server, wherein obtaining current weather data includes receiving current weather data from a wireless communication network. Wireless communication networks collect real-time data from cellular transmissions containing signal attenuation information. At the server, using the wind model data and the current weather data, and considering the influence of the current weather conditions on the movement of the outdoor playground ball, the trajectory of the outdoor playground ball is calculated according to the obtained current weather data of the current weather parameters.

According to yet another embodiment, a system is provided. The system includes: a data store containing wind model data for an outdoor playground; one or more processors; a machine-readable medium containing instructions stored therein; and a display for outputting the calculated ball trajectory in real time Or a calculation based on the calculated trajectory of the ball. The one or more processors contain a digital model of an outdoor sports field. When the machine-readable medium is executed by the one or more processors, the one or more processors perform the operations in real-time. The operations include obtaining, at a server, current weather data including wind data, wherein obtaining current weather data includes receiving current weather data from at least one wind sensor located at or near the outdoor playground. If the server stops receiving current weather data from any wind sensors located at or near the outdoor playground, the current weather data is obtained from the wireless communication network. Wireless communication networks collect real-time data from cellular transmissions containing signal attenuation information. At the server, using the wind model data and the current weather data, and considering the influence of the current weather conditions on the movement of the outdoor playground ball, the trajectory of the outdoor playground ball is calculated according to the obtained current weather data of the current weather parameters.

The present invention generally relates to a system and method for quantifying the effect of weather on ball flight in an outdoor field. For example, the embodiments described herein can be used to predict the flight of a ball at a given location based on weather conditions. Embodiments herein describe a system and method for collecting weather data at a location and using the data to predict the flight of a ball at that location based on weather conditions. The embodiments described herein can be used for any outdoor sport to model the effect of weather parameters on ball flight. It should be noted that the impact of weather on sporting events can be predicted in advance. In some cases, predictions can be made four to five days before the event.

1-4, embodiments of the system will be described. The system collects weather data and can use historical and current weather data for a given location to determine the impact of current weather on ball flight at that location. The five most important weather parameters in the flight of a ball (eg, baseball) are wind (horizontal and vertical), humidity, temperature, atmospheric pressure, and precipitation. According to one embodiment, the model used to predict the effect of these weather parameters on the flight of the ball is based on the weighted contribution of each of the following parameters: wind, humidity, temperature, atmospheric pressure and precipitation. The relative contributions of these parameters vary depending on the given conditions. For example, if the wind is not blowing, the effect of the wind is zero; if it is blowing at 50 mph, the effect of the wind can be almost 100%. It will be appreciated that all five weather parameters need not be included in the calculations to determine the effect of weather conditions on the flight of the ball. For example, in some embodiments, it may be sufficient to consider only wind and humidity. In other embodiments, one or more of wind and humidity and other weather parameters may be considered.

Temperature is positively correlated with the flight of the ball. That is, the higher the temperature, the farther the ball will travel. Relative humidity, on the other hand, is inversely related to the flight of the ball, because at a given impact velocity, a wet ball is less elastic than a dry ball and, therefore, leaves the point of impact more slowly than a dry ball. That is, the lower the relative humidity, the farther the ball will travel. Pressure is also negatively correlated with the flight of the ball. That is, the lower the pressure, the farther the ball will travel.

1A and 1B illustrate a conceptual schematic design of an embodiment of a system 100 described herein for predicting the flight of a ball based on wind, temperature, relative humidity, precipitation, and air pressure. In the embodiment shown in FIG. 1A , system 100 includes weather sensor 110 , wind measuring device 115 , weather console 140 , and server or processor 160 . The wind measuring device 115 includes an anemometer, a Light Detection and Ranging (LiDAR) device, a Sonic Detection and Ranging (SODAR) device, a radar device, and other instruments capable of measuring wind. Unlike anemometers, LiDAR, SODAR and RADAR devices measure wind remotely. According to one embodiment, at least three wind measuring devices 115 are positioned at or near the outdoor sports field to measure wind. As will be explained in more detail below, the vertical component of the wind can have a significant effect on the flight of the ball.

Another embodiment of the system 100 shown in FIG. 1B includes a weather sensor 110 , a LiDAR device 120 , a SODAR device 130 , a weather console 140 , a data routing device 150 and a server or processor 160 . Data routing device 150 sends the collected data to server or processor 160 . It will be appreciated that in some embodiments, anemometric instruments, such as anemometers, may be used instead of LiDAR and SODAR devices. In other embodiments, LiDAR and/or SODAR devices are used to measure wind. Thus, the system 100 typically includes one or more wind measuring devices 115 . In some embodiments, the weather sensor 110 may include a wind measuring device and a separate wind measuring device 115 is not required.

The weather sensor 110 in the embodiments described herein includes a sensor including at least one of: a thermometer for measuring temperature, a humidity sensor for measuring humidity, a sensor for measuring wind speed anemometers, barometers for measuring air pressure, and meters for measuring precipitation. A weather sensor 110 that may be used in the system 100 is shown in FIG. 2 . Commercially available weather sensors that may be used in system 100 include Campbell Scientific, Inc. of Logan, Utah Scientific, Inc), and Davis Instruments of Hayward, California Corporation) weather sensor. It will be appreciated that other weather sensors including thermometers and humidity sensors may also be used in the system. It should also be understood that in other embodiments, the system 100 may be any number of thermometers, anemometers, and humidity sensors, barometers for measuring air pressure, and meters for measuring precipitation, as well as any number of LiDAR devices and SODARs device and any number of data routing devices and weather consoles. It should be noted that commercially available Meteobridge devices are only one method of data transfer using a router connected to the network. Figure 4 shows an embodiment of a commercially available Meteobridge device that may be used in the system shown in Figure IB. Other data transmission systems include cellular modems or radio transmissions.

A weather sensor 110 that may be used in the system 100 is shown in FIG. 2 . Weather sensors 110 may include thermometers, humidity sensors, and anemometers. According to another embodiment, a weather sensor available from Campbell Scientific, Inc. contains two to ten pods arranged around the perimeter of the baseball field, and each pod contains an anemometer and a Instruments for measuring precipitation. In this embodiment, at least two of the pods further include a thermometer, a barometer and a humidity sensor.

In most cases, the wind has the most influence on the flight of the ball. Therefore, in most cases it is very important to obtain accurate wind speed measurements. In small stadiums with few obstructions (eg, minor league or high school baseball fields), wind direction measurements from standard anemometers (as described above) can be around the outside of the field to adequately represent the horizontal wind direction on the field. However, in larger sports fields, where there are obvious obstacles, the wind flow on the field is much more complicated. An example of this complexity is when wind flows over a large wall, the wall can cause the downwind airflow to become very turbulent. When water flows over a large rock, the flow is similar to that of a jet stream. Therefore, simply measuring the wind around the outside of a large stadium (with obstructions) using an anemometer does not provide enough useful information.

On larger sports fields, LiDAR and, to a lesser extent, SODAR devices can be used to measure wind on the field. What makes LiDAR and SODAR devices most useful is that they can measure wind remotely. That is, unlike standard anemometers that only measure wind at a given location, LiDAR and SODAR devices measure wind at many distances (horizontal and vertical) from the location of the device. With the help of LiDAR and SODAR devices, the wind on the sports field can be measured at many different heights and distances while the game is being played. Another benefit of using LiDAR and SODAR devices is that they can provide direct measurements of vertical winds. And, in cases where direct measurements of vertical wind are not available, horizontal wind measurements measured using LiDAR and SODAR devices can be used to calculate vertical wind. The LiDAR device 120 uses light to measure wind, while the SODAR device uses sound to measure wind conditions. SODAR systems measure wind primarily by emitting sound waves vertically. This limits the ability of SODAR systems to measure wind in real time across the playing field. However, LiDAR systems emit light waves both vertically and horizontally, allowing for better coverage of wind measurements across the playing field. According to one embodiment, the LiDAR device 120 is installed in a stadium somewhere outside the stadium, where it continuously scans the stadium to obtain wind measurements. Instruments containing commercially available Halo Doppler LiDAR, Zephir LiDAR and/or other LiDAR instruments can be set up around the stadium to collect wind data. In a particular embodiment, the LiDAR device 120 in the system 100 is a commercially available air duct (WindSube® 100S) manufactured by Leosphere and distributed in North America by NRG Systems. The above embodiments use only LiDAR and SODAR devices, as they are currently the most cost-effective means of obtaining useful wind measurements. But RADAR devices may also be suitable in the future.

Weather sensor 110, LiDAR device 120, and SODAR device 130 can be placed anywhere within the stadium to collect weather data. According to one embodiment, the weather sensor 110, LiDAR device 120, and SODAR device 130 are positioned along the roof of a building or along the perimeter of a stadium, as these locations are typically unobstructed. In the particular embodiment of the baseball field, the weather sensor 110, LiDAR device 120, and SODAR device 130 are positioned approximately 40 feet from the midfield fence, but they could also be positioned behind home plate, or along the On the right field line or the left field line in the stadium. In some embodiments, the weather measurement devices 110, 120, 130 may be solar powered or battery powered.

Weather data collected by weather sensor 110 , LiDAR device 120 and SODAR device 130 is preferably transmitted wirelessly to weather console 140 . It will be appreciated that the weather data can be transmitted to the weather console, either wired or wireless. According to one embodiment, existing Wi-Fi in the stadium can be used for wireless transmission. FIG. 3 shows an embodiment of a weather console 140 that may be used in the system 100 . Davis Weather Instruments and Campbell Scientific Scientific) has a commercially available weather console. As shown in FIG. 2 , a radio transmitter 112 is provided on each weather sensor 110 to transmit weather data collected by the sensor to a weather console 140 . Radio transmitters may also be provided on LiDAR device 120 and SODAR device 130 to transmit data to weather console 140 .

The weather console 140 then transmits the collected weather data to the data routing device 150 . The transmission from the weather console 140 to the data routing device 150 may be wired or wireless. The data routing device 150 then sends the collected weather data to a server or processor 160, which then performs calculations based on the model to predict the effect of weather conditions on ball flight. Different embodiments of the model for predicting the flight of the ball are described in more detail below. The data routing device 150 allows the collected microclimate weather data to be sent to a server or processor 160, which can use both historical and current weather data to calculate the effect of weather on ball flight. In other embodiments, other devices, such as a computer, may be used to connect weather console 140 to server or processor 160 instead of a data routing device. It will be appreciated that in some embodiments, weather sensor 110, LiDAR device 120 and SODAR device 130 send weather data directly to server or processor 160 without the need for data routing means.

It will be appreciated that temperature, relative humidity and barometric pressure are relatively static compared to wind, so weather sensors for measuring temperature, relative humidity and barometric pressure may be placed in and near the sports field. Alternatively, weather model data for temperature, relative humidity, and atmospheric pressure obtained from other sources such as the National Oceanic and Atmospheric Administration (NOAA) and other servers may be used. It will be noted, however, that three-dimensional wind fields within outdoor sports fields affecting ball flight are relatively difficult to measure directly using currently available techniques such as LiDAR, RADAR, SODAR, and the like. Therefore, the method using computational fluid dynamics (CFD) described in the examples below can be used to determine a three-dimensional wind field in an outdoor sports field. However, it should be noted that actual weather sensors are more accurate than weather data obtained from public and commercial sources, especially for wind data. Furthermore, wind measurements using anemometers, LiDAR, RADAR, SONAR, etc. are more accurate than 3D wind fields determined using CFD models. However, CFD modeling may be a more economical approach.

According to this embodiment, a computer-aided design (CAD) model is generated or otherwise obtained for the outdoor sports field. According to one embodiment, a CAD model is generated for an outdoor sports field and its surroundings containing a radius approximately 10 times the length or diameter of the field (depending on the shape of the field). In other embodiments, a CAD model is generated for an outdoor sports field and its surroundings containing a radius of about 2-20 times the field length or diameter (depending on the shape of the field).

As described in more detail below, using CAD models, CFD modeling was used to generate three-dimensional wind vectors at different grid points in the digital model of the outdoor sports field. The CFD model collects historical wind data upstream of the sports field to produce a set of 3D wind cases, which are then archived and retained for future use. Archived historical weather data can be used in conjunction with real-time or forecast weather data to produce real-time or predicted 3D wind fields in sports fields. An archived set of historical 3D wind cases should contain at least 10 different wind cases for a specific field on a given day. It will be appreciated that fields in locations with fairly consistent winds require fewer archived wind cases. If the wind varies more at a location, more archived wind cases are required in order to more accurately calculate the real-time 3D wind field.

Then, the wind upstream of the outdoor sports field can be measured. The most common way to measure wind is to use a standard anemometer located upstream of the field. However, wind may also be measured using other techniques (eg, LiDAR, RADAR, SODAR, etc.). Alternatively, as described above, other weather model data (eg, public or commercial sources) may be used instead of real-time estimated or forecast winds.

After the upstream wind data is obtained, the upstream wind data is matched or interpolated to the nearest surrounding archived historical CFD case to determine the 3D wind field in the sports field in real time (or forecast).

Then, use the real-time 3D wind field (along with temperature, relative humidity and atmospheric pressure) to calculate how weather affects the flight of a particular ball or how weather affects the flight of an average ball in general. These calculations are explained in more detail below. Likewise, weather forecast data can be used to determine how the weather will affect the flight of the ball in the future.

According to an alternative embodiment of the system 200, rather than collecting weather data from weather sensors located at or near the outdoor playground, the wireless communication network 215 is used to collect cellular transmission signals to generate real-time weather data. As shown in FIG. 5A , the real-time weather data is preferably transmitted wirelessly from the wireless communication network 215 to the server or processor 260 . In one embodiment, the real-time weather data from the wireless communication network 215 is obtained from a commercial entity such as ClimaCell that provides weather data obtained from the wireless communication network. Weather data is generated by analyzing the quality of cellular transmissions at the location. The collected weather data can then be used to calculate how weather affects the flight of a particular ball or how weather affects the flight of an average ball in general. As mentioned above, CFD modeling can be used for such calculations.

According to one embodiment, microwave link data containing signal attenuation information is obtained from cellular transmission signals at or near an outdoor sports field. A microwave link is a wireless signal connection between two separate antennas at frequencies above 1.8 GHz.

Microwave link data from different data points are aggregated and then processed using data transformations to produce weather data. The processing involves analyzing the signal quality from various devices such as cell phones, tablets, laptops, street light cameras, connected vehicles and other IoT devices to generate weather data. The analysis is based on the knowledge of what the cellular transmission signal should look like without any weather interference (signal quality), and that different weather phenomena (eg precipitation, wind, temperature, etc.) can affect the signal. By analyzing the signal quality, weather phenomena can be identified to generate weather data. With hundreds of millions of data points based on cellular transmissions at any given time, weather data can be extremely localized (for example, to a sports field, or even a specific location within a sports field), and weather data can be updated frequently - such as every five minutes Often once, maybe once every few seconds. For example, precipitation is known to attenuate microwave signals with frequencies above 5 GHz. Therefore, the attenuation of the microwave signal can be analyzed to determine whether the attenuation is due to precipitation, and also to determine the intensity of the precipitation. Similar analyses can be performed for other weather phenomena such as wind, temperature, humidity, etc.

As described in detail below, calculations may be made to determine the trajectory of the ball affected by the weather. Server 260 may send the calculated trajectory of the ball to display screen 270, as shown in the exemplary screen shot display of Figure 6A. As shown in Figure 6A, the solid line shows the trajectory of the actual ball flight affected by the weather, while the dashed line shows the trajectory of the ball (unaffected by the wind). The displayed track can be an animation of that track. FIG. 6B is an example of another display where the current or predicted wind will have an impact on a baseball from a home run. The arrows in Figure 6B show the wind direction and the direction the wind is pushing or will push the ball. The display shows how much the wind shortens or lengthens the ball's flight, and how much the wind pushes the ball to the left or right. The number next to the arrow is the magnitude of the deviation calculated from the effect of the wind on the baseball. The direction of the wind and the magnitude of the deviation can be updated and displayed every few seconds.

Alternatively, weather data can be obtained from public sources, such as NOAA, Weather Underground, and Davis Instruments, which have their own weather sensors for collecting weather data. In some embodiments, a combination of weather data measured by a weather sensor and weather data collected from a wireless communication network is used. According to the embodiment of the system 300 shown in FIG. 5B , the system 300 may include collecting weather data from both the weather sensor 310 and the wireless communication network 315 as shown in FIG. 5B . In this embodiment of the system 300, the weather data collected from the weather sensors 315 may be collected from sensors operated by NOAA, Weather Underground, etc., or from outdoor sports fields such as stadiums, golf courses, or other types of sports fields Weather sensors such as weather sensor 110 , LiDAR device 120 , and SODAR device 130 at or nearby are collected. In this embodiment, the weather data from the weather sensors and from the wireless communication network is preferably transmitted wirelessly to the server or processor 360 . According to one embodiment, weather data from all sources may be used by the server or processor 360 to calculate the effect of weather parameters on ball flight, as will be described in more detail below.

As described in detail below, calculations may be made to determine the trajectory of the ball affected by the weather. Server 360 may send the calculated trajectory of the ball to display screen 370, as shown in the exemplary screen shot display of Figure 6A. The displayed track can be an animation of that track. As shown in Figure 6A, the solid line shows the trajectory of the actual ball flight affected by the weather, while the dashed line shows the trajectory of the ball (unaffected by the wind). FIG. 6B is an example of another display where the current or predicted wind will have an impact on a baseball from a home run. The arrows in Figure 6B show the wind direction and the direction the wind is pushing or will push the ball. The display shows how much the wind shortens or lengthens the ball's flight, and how much the wind pushes the ball to the left or right. The number next to the arrow is the magnitude of the deviation calculated from the effect of the wind on the baseball. The direction of the wind and the magnitude of the deviation can be updated and displayed every few seconds.

According to another embodiment, the server or processor uses weather data from weather measurement devices 110, 120, 130 located at or near the playing field to calculate the trajectory of the weather-affected ball, and the weather obtained from the wireless communication network The data are used as backup weather data in the event that the weather measurement devices 110, 120, 130 fail or become inoperable. Thus, if the server or processor determines that weather data is no longer being received from the weather measurement devices 110, 120, 130, the server or processor will begin receiving weather data from the wireless communication network. Similarly, in another embodiment, weather data obtained from weather measurement devices 110, 120, 130 located at or near the sports field is used as backup weather data in the event that weather data obtained from the wireless communication network is not available . Thus, if the server or processor determines that weather data is no longer received from the wireless communication network, the server or processor will begin receiving weather data from the weather measurement devices 110, 120, 130.

According to an embodiment, the systems 100, 200, 300 use wind, temperature, relative humidity, air pressure, and precipitation to calculate how much the average ball being hit to the baseball field's outfield fence has added or subtracted from the flight to the average distance foot. These weather factors can also be used to calculate how many feet the ball is thrown from the outfielder to home plate and the flight of the pitcher's pitch is increased or decreased. These weather factors can also be used to calculate how much slower or faster a ball thrown from outfield to home plate is moving. It will be appreciated that although much of the description herein applies to baseball, the models described herein can be applied to other sports, including American football, golf, cricket, tennis, soccer, archery, rowing, cycling, racing, etc. Wait.

According to an embodiment, a model for predicting the flight of a ball at a given stadium is created by first analyzing long-term weather data sets, such as those generated by nearby weather sensors 110, LiDAR devices 120, and SODAR Device collected data 130 or a set of weather data specific to a site originating from a wireless communication network. From historical weather data collected at the site, determine the "mean day". That is, when each weather parameter (excluding wind and precipitation) is at its long-term average at the start of a baseball game, the sum of the effects of these parameters on the ball must equal zero. When there is absolutely no wind, the effect of the wind on the ball can only be zero. Otherwise, the wind affects the ball positive or negative, left or right, and up or down. The effect of precipitation on the flight of the ball is only negative, because the heavier the precipitation, the more adverse the effect on the flight of the ball. The model works by taking each parameter (except wind and precipitation) and adding (or subtracting) to the average day when the weather parameter enhances (or decreases) the ball flies. It should be understood that no two baseball fields (or any other type of field) will have exactly the same model, although they are often similar.

As mentioned above, there are five weather parameters that affect the flight of the ball: temperature, relative humidity, atmospheric pressure, precipitation, and wind. The model used in the particular example described herein is based on the game of baseball and the flight of the baseball, which has a flight distance of 375 feet, which is the average distance from the outfield wall to the home plate. It will be appreciated that this number will vary for each stadium since the average distance from the outfield wall is different for each stadium. The effects of different weather parameters are calculated to predict the flight of the ball, according to a model that will be explained in more detail below.

For the most part, a brief overview of the effects of weather on the flight of a baseball (or any type of ball) goes something like this. For every 10-degree increase in temperature, the ball's flight distance increases by about three feet. For every 10 percent increase in humidity, humidity reduces distance by about six feet. For every 1 inch of mercury increase in pressure, the pressure increases by about 7 feet. The effect of wind on the distance a ball travels is much more complex. The headwind hinders the flight of the ball more than the added impediment to the flight of the ball equally facing the wind. Downward winds adversely affect ball flight, while upward winds enhance ball flight. The effect of weather parameters on ball flight is discussed in more detail below.

Examples will be described below to illustrate the calculations performed by the system 100 . The mean value of each parameter (except wind and precipitation) was used as the basis for the calculation. It will be appreciated that these averages are exemplary and based on specific locations. For illustration purposes, in this particular example, the following conditions are assumed: an average temperature of 81°F, an average humidity of 59%, and an average pressure of 29.92 inches of mercury. The server or processor 160 calculates how many feet to add to the index values for left field, midfield and right field. The data is collected on-site and transmitted to the server. The software sifts through the data for accuracy, then feeds the data into a model that calculates the number of feet the weather adds or subtracts from a flyball hitting an average 375 feet. The calculations in this example are based on the flight of the ideal or average hit ball to the warning orbit, which is assumed to be approximately 375 feet from home plate. In other embodiments, where actual flight data is available, the specific effect of weather on that given ball can be calculated. According to one embodiment, the calculations are displayed on the screen. According to one embodiment, the calculations are uploaded to the website and may be updated frequently (eg, every 2-3 seconds).

It will be appreciated that since different weather parameters are measured in different units, each parameter must be multiplied by a certain predetermined factor in order to scale each parameter so that it has an appropriate contribution to the flight of the ball. Illustrated here are average simplified estimates of the impact of each weather parameter. As will be explained in more detail below, in a particular embodiment, there are 90 different configurations of coefficients. This is because many calculations of drag coefficient, lift coefficient, and spin rate decay are published in the scientific literature. In the model used for the calculation in this embodiment, the coefficients of each parameter are as follows: Temperature Coefficient = -0.3 Humidity coefficient = 0.6 pressure=7 Wind = Varies depending on the speed and direction of the wind and the spin of the ball Precipitation = Varies depending on how hard it is to drop in precipitation

Temperature is positively related to the flight of the ball. That is, the higher the temperature, the farther the ball will travel. This relationship is represented by mathematical equation (1) to determine the contribution of temperature to the effect of weather on ball flight: (1) Temperature = temperature coefficient * (average temperature - actual temperature)

Relative humidity, on the other hand, is negatively related to the flight of the ball, because at a given impact velocity, a wet ball is less elastic than a dry ball, and therefore leaves the point of impact slower than a dry ball. That is, the lower the relative humidity, the farther the ball will travel. This correlation is represented by the following equation to determine the contribution of humidity to the effect of weather on ball flight: (2) Humidity = humidity coefficient 0.6*(average humidity - actual humidity)

Pressure is also negatively related to the flight of the ball. That is, the lower the pressure, the farther the ball will travel. This relationship is represented by equation (3) to determine the contribution of air pressure to the effect of weather on ball flight: (3) Pressure = pressure coefficient * (average pressure - actual pressure)

Horizontal winds are considered forward and backward. The forward direction is downwind, which increases the flight of the ball. Backward is against the wind, which reduces the flight of the ball. Any wind that is not directly forward or backward will be broken down into its component parts so that forward or backward wind can be used. For vertical winds, it is positive up and negative down. In some embodiments, the vertical wind is assumed to be zero. Typically, for large stadiums, vertical winds will not be assumed to be zero.

Home runs take an average of 4-4.5 seconds from hit to ball landing. The average home run hits a maximum height of about 80 feet. The average home run ball takes about 3 seconds above 50 feet and below 100 feet. Therefore, the winds that most affect the flight of the ball are between 50 and 100 feet in elevation.

Obviously, the effect of the wind on the ball is not constant along its trajectory. In one embodiment, average wind speeds from 50 to 100 feet elevation are used in the model. In large stadium systems where LiDAR (or SODAR) can be used, actual measured wind speeds (rather than average wind speeds) are used in the model. Wind is represented mathematically as described below.

Horizontal wind is measured and then decomposed into component parts on the XY axis, where the X axis extends from the home plate in the direction the ball originally left the bat, and the Y axis is shifted to the left in that direction. So an initial hit from second base will increase the X-axis toward center field along the line from first to third base, and the Y-axis to third base.

Calculate the X component of the wind using equation (4): (4) X component of wind = wind speed * cosine (baseball field orientation + ball angle - wind direction) Where Ball Park Orientation is the direction (in degrees (360 degrees north, 180 degrees south) of the line from home plate to straight center field), and for a ball initially hitting center field, the ball The Ball Angle is 0 degrees. The ball initially hits right/left field at +/-45 degrees. For a 360-degree baseball field orientation, the home plate should be north of the straight-line center field. Calculate the Y component of the wind using equation (5): (5) Y component of wind = wind speed * cosine (baseball field orientation + ball angle + 90 - wind direction)

A headwind will shorten the ball's flight, while a tailwind will lengthen the ball's flight. The effect of wind on the flight of the ball is non-linear and includes drag, lift and gravity.

Precipitation only damages the flight of the baseball. When the ball becomes wet, the ball becomes heavier, which causes the ball to travel a shorter distance than when it is dry. Also, a wet ball is more like a sponge, which causes the ball to leave the bat with a lower initial velocity than a dry ball. Calculate the effect of precipitation using Table 1 below. It will be appreciated that Table 1 is only an example of a quantification of the impact of precipitation.

The contribution of each parameter (for example, temperature, humidity, pressure, wind, and precipitation) is calculated and then added together to obtain the net effect on ball flight.

In a particular embodiment, the model used to predict the effect of weather parameters on the flight of the ball resides in an application such as a spreadsheet that can receive various inputs and calculate the flight of the ball according to weather conditions. The various pages of the spreadsheet of this embodiment are shown in FIGS. 8-9 . The models shown in Figures 8 to 9 are for baseball. It will be appreciated, however, that the model can be modified to determine the effect of weather on the flight of balls in other sports including American football, golf, cricket and volleyball.

As the specific models shown in Figures 8 and 9 are based on a baseball, the forces affecting the flight of the baseball will be discussed below. In baseball flight, there are three vectors (forces) that act on the baseball. These vectors are gravity, drag, and lift or Magnus force. At each instant, the ball's velocity is moving in a specific direction, and the angle between that direction and the ground is the ball's current orientation angle. Resistance always acts in the opposite direction of the velocity vector. The lift or Magnus force acts perpendicular to the ball's axis of rotation and is generally directed towards the ground (assuming the ball is hit by backspin). Gravity always pulls the ball directly from its center of mass to the ground, so the direction of gravity has nothing to do with the ball's orientation.

Gravity is the natural force that pulls all objects (including balls) toward the Earth. Gravity is fairly simple and can be easily determined by multiplying the constant gravitational acceleration g by the mass of the ball M. So the gravity on the baseball is M*g.

Calculating resistance is much more complicated. Drag is the air resistance that slows the ball down. Physically speaking, drag is equal to 0.5 times the density of the air (rho), times the cross-sectional area and drag coefficient of the ball, and finally the ball's wind speed squared. Therefore, resistance = 0.5 * rho * _A * Cd * Va ² . Rho or air density is a measure of how tightly packed the air is. An increase in temperature or a decrease in pressure results in a decrease in air density. There are three different ways to calculate the density of air, the most common equation is as follows: rho = P/(RdT).

According to this embodiment, a spreadsheet (such as the one shown in Figure 8) is used to enter initial parameters for ball flight, such as ball launch velocity, launch angle, spin rate (in all directions), and spin rate decay. As shown in Figure 8, these initial parameters can be entered into a spreadsheet in place, manually entered by the user, or received from a source. Each initial parameter will be discussed below.

Launch velocity (mph), launch angle (degrees), and rotational speed (rpm) were routinely measured by all major league baseball teams by all teams (minor and major leagues). According to an embodiment used in real time, the application (spreadsheet) receives as input the average value of each of the launch speed, launch angle and rotational speed. Weather parameters (horizontal wind speed, wind direction, temperature, relative humidity, station pressure and precipitation) are measured by meteorological instruments such as those described above. A server or other processor may receive input of weather parameters from a weather instrument. As mentioned above, in some embodiments, the stadium elevation is also entered as it is sometimes important for adjustment calculations involving station pressure.

X-Z rotation is the rotation of the ball around the Y axis. This spin is counter-clockwise or clockwise from the right field view of the ball's flight, with the Z direction extending vertically from the ground into the air and the X direction extending from the home plate along the initial horizontal direction where the ball leaves the bat. Thus, when viewed from home plate, the Y-axis extends in a direction perpendicular to and to the horizontal plane to the left of the X-direction. This rotation results in an upward or downward movement, which will cause a change in the coefficient of lift and is therefore used in some embodiments of the models described herein. X-Z rotation is typically tracked by Doppler radar, and these statistics are provided by Major League Baseball teams.

X-Y rotation is the component of the ball's rotation around the Z axis. From a bird's-eye view of the ball's flight, the rotation would be in a counter-clockwise or clockwise direction, where the X and Y directions are as defined above. Typically a baseball hitting the center area will have very little spin along that axis, while a baseball hitting the left area will have positive (counterclockwise) spin and a baseball hitting the right area will have negative (clockwise) spin, but any spin will lead to a change in the lift coefficient.

Y-Z rotation is the rotation of the ball around the X axis. This rotation will be counter-clockwise or clockwise from the midfield view of the ball flight, with the X, Y and Z directions as defined above. This rotation results in side-to-side motion as well as up and down motion, and can be calculated with angular rotations readily available from the team's library. However, it should be noted that Y-Z rotation is usually negligible.

According to some embodiments, the vertical wind speed is assumed to be zero, but the actual vertical wind speed may be measured or calculated using LiDAR or SODAR measurements in larger stadiums. The wind start height is the height at which the wind is assumed to start acting on the ball. That is, surface wind is zero and generally increases with height. To calculate the effect of the wind on the ball, the wind is assumed to be approximately half the actual wind speed below the "wind start height". In the embodiment shown, the wind activation height is assumed to be ground level, as shown in FIG. 8 .

Contact height is the height above the ground at which the ball is hit. For baseball, it is most often assumed that it is on average 3 feet from the ground. The angle of the ball to the center field (CF) is the angle of the shot relative to the center field and can also be tracked by Doppler RADAR. So if the ball is hit directly into center field, the value is zero. If the ball is hit to the left of the immediate center, the value will be between -45 and zero. If the ball is hit to the right of the immediate center, the value will be between zero and +45.

Backspin (topspin) is just a counterclockwise X-Z rotation (see above), where 1 is backspin and -1 is topspin. This is used to calculate the up or down movement of the ball when the ball with backspin goes up and the ball with topspin goes down. This is used to calculate the direction and the amount of rotation in each direction, which affects the lift coefficient (explained later).

In this embodiment, counter-clockwise (CCW) (clockwise) (clockwise; CW) is just a counter-clockwise X-Y rotation (see above), where 1 is a counter-clockwise (clockwise) rotation when viewed from above ball. This will cause the ball to track left (right). This is used to calculate the direction of rotation and the magnitude of rotation in each direction, which affects the lift coefficient (explained in further detail below).

According to this embodiment, CCW(CW) is just a Y-Z rotation in a counterclockwise direction (see above), where 1 is the ball spinning in a counterclockwise direction (clockwise) when viewed from home plate. This will cause the ball to track left (right). This is used to calculate the direction of rotation and the magnitude of rotation in each direction, which affects the lift coefficient (explained in further detail below). In this embodiment, for vertical wind direction, 1 means upwind and -1 means downwind.

A time step is the time interval in seconds at which the ball is tracked through its flight. So a value of 0.001 has a ball that is tracked every thousandth of a second. It can be changed to suit any desired interval. It should be noted that a device such as Doppler RADAR is used to track the direction of the shot and the spin characteristics of the ball.

In this embodiment, the resistance (no resistance) is simply a switch that turns the resistance coefficient on or off. This is useful for theoretical calculations in a vacuum when Drag is set to zero. The drag coefficient will be discussed in more detail below, but a quick summary is that it is the frictional force that the air exerts on the ball as it travels. In the scientific literature, the drag coefficient has eight different values. There are mathematical reasons for each of these. Since it is not clear which is the most accurate, the user can choose from one of eight possibilities, or take the average of the eight possibilities.

A baseball field orientation is the angle (expressed in 1 to 360 degrees) that the center of the line points, based on the line extending from home plate (beyond the second base bag) to the center field of the line.

Lift (no lift) is the switch that turns on the lift coefficient, where 1 turns on and 0 turns off. This is useful for theoretical calculations where the ball has no lift. The lift coefficient is related to Bernoulli's equation, which is essentially how the ball's counter-rotation helps the ball rise as it travels. In the scientific literature, the lift coefficient has five different values. There are mathematical reasons for each of these. Since it is not clear which is the most accurate, the user can choose from one of five possibilities, or take the average of the five possibilities.

After all the above inputs have been entered, the flight of the ball is then calculated and the important variables are output and displayed on the screen as shown in Figure 8. Displayed variables can include calculated fly ball length, maximum ball height, ball angle at landing, ball speed at landing, etc.

After performing the calculations, a visual diagram of the ball's flight can be displayed on the screen, as shown in Figure 9. In Figure 9, line 910 shows a view from right field. Line 920 shows a view of the ball starting from home plate (left) and ending in outfield (right) from above. Line 930 represents a view of the ball from a straight line in outfield according to the input received as shown in FIG. 8 .

* (r ²) m ²空氣常數(Rd)= 287 J/kg/K 重力(G)= 9.8 m/s ² It will be appreciated that the embodiments described above with reference to Figures 8-9 are applicable to baseball. It will be appreciated that the method can be adapted to different types of balls used in different sports (depending on ball size, mass, profile, material (drag coefficient), etc.). Therefore, the following constants are used in the calculations set forth below to provide the calculations and visualizations shown in Figure 9: Baseball Mass (m) = 0.145 kg Baseball Radius (r) = 36.4 mm Sectional Area of Baseball (A ) =

* (r ² ) m ² Air constant (Rd) = 287 J/kg/K Gravity (G) = 9.8 m/s ²

As explained in more detail below, the current component position and current component acceleration can be determined by calculating the change in position (xy and z) in the direction of each component at each time step using the previous position and velocity components to determine the ball The current X component of the distance traveled from its trajectory's origin (origin). The current acceleration component is then used to determine the current velocity component. These calculations are repeated for each subsequent time step until the ball hits or is about to hit the ground.

其中x ₀是球在時間t = 0處(球被發射的位置)的起始點的初始X分量，Δx=u _i-1* Δt且u=x速度，i=時間步長，而Δt =時間變化(t _i- t _i-1)，同樣，v=y速度，w=z球的速度。 To determine the current X component of the distance traveled by the ball from the origin (initial position of the trajectory) from the given weather parameters, equation (6) is used:

where x ₀ is the initial X component of the ball's starting point at time t = 0 (where the ball was fired), Δx = u _i-1 * Δt and u = x velocity, i = time step, and Δt = Time variation (t _i - t _i-1 ), again, v=y velocity, w=z velocity of the ball.

其中abs( )是絕對值，FFFaᵢ是總的3維空速， 如果變量＞0，則符號(變量)=1；變量＜0時為-1；變量=0則為0。

uaᵢ=以x表示的空氣速度(uᵢ - uairᵢ) va _i=以y表示的空氣速度(v _i- vair _i) wa _i=以z表示的空氣速度(w _i- wair _i) uairᵢ=給定點風速的x分量(可以從CFD模型產生的3D風向量中進行測量或內插) vair _i=給定點風速的y分量(可以從CFD模型產生的3D風向量中進行測量或內插) wairᵢ=給定點風速的z分量(可以從CFD模型產生的3D風向量中進行測量或內插) T =攝氏溫度 P =空氣壓力，以毫米汞柱為單位 El =高程，以米為單位 Rh =相對濕度 SVP =飽和蒸氣壓

A =棒球的剖面面積 Cd =阻力係數=0.38 It will be understood that the subscript "i" refers to the ith time step, where i starts at zero when the ball is struck and continues for many time steps until z=0, i.e., the ball will be on the ground or will The home plate reaches the ground at the same height, where:

where abs( ) is the absolute value, FFFaᵢ is the total 3D airspeed, if variable > 0, sign (variable) = 1; if variable < 0, it is -1; if variable = 0, it is 0.

uaᵢ = air speed in x (uᵢ - uairᵢ) va _i = air speed in y (vi - vair _i ) wa _{i =} air speed in z ( _wi - wair _i ) uairᵢ = wind speed at a given point x component of (can be measured or interpolated from the 3D wind vector produced by the CFD model) vair _i = y component of the wind speed at a given point (can be measured or interpolated from the 3D wind vector produced by the CFD model) wairᵢ = given point The z-component of the wind speed (can be measured or interpolated from the 3D wind vector produced by the CFD model) T = temperature in degrees Celsius P = air pressure in mmHg El = elevation in meters Rh = relative humidity SVP = saturated vapor pressure

A = cross-sectional area of baseball Cd = drag coefficient = 0.38

其中，var＞ 0時sign(var)= 1，var ＜0時為-1，var=0時為0，其中Cl(升力係數)=0.225。在該實施例中，升力係數C1被假定為恆定的。在其他實施例中，C1可以變化。 In this embodiment, the drag coefficient Cd is assumed to be constant. In other embodiments, Cd may vary. The following equations (7) and (8) were also used in the calculations:

Among them, sign(var)=1 when var>0, -1 when var<0, 0 when var=0, and Cl (coefficient of lift)=0.225. In this embodiment, the lift coefficient C1 is assumed to be constant. In other embodiments, C1 may vary.

其中g=9.81 m/s ²。z方向的升力方程式如方程式(10)所示：

其中sign(var)=1 針對var＞0, -1針對var＜0, 並且0針對var=0。 In the other two dimensions, Y (oriented at a 90-degree angle to the forward direction of ball contact) and Z (upward, perpendicular to the ground), the equations of motion are the same as for x, when each corresponding term is changed to refer to the The equations are basically the same when dimensioned (e.g. each uᵢ will be replaced by a wᵢ when viewed in the z direction). Acceleration in the z direction must be treated differently because gravity must be accounted for using equation (9):

where g=9.81 m/s ² . The lift equation in the z direction is shown in equation (10):

where sign(var)=1 for var>0, -1 for var<0, and 0 for var=0.

7 is a flowchart of a method 700 of predicting the effect of current weather conditions on ball flight at a location. In step 710, a plurality of weather sensors 110 are provided at various locations near an outdoor field (eg, a sports field or stadium) to collect weather data. These locations are preferably accessible. In step 720, weather sensor 110 (and LiDAR device 120 and SODAR device 130, if present) collect weather data, which may include temperature, humidity, pressure, precipitation, and wind speed and direction. Then in step 730 , the weather sensor 110 (and the LiDAR device 120 and the SODAR device 130 , if applicable) send the data to the server or processor 160 . In some embodiments, the data transfer to the server or processor 160 may be performed wirelessly. In some embodiments, weather data is first sent to weather console 140 , which in turn sends the data to data routing device 150 , which then sends the data to server or processor 160 . The method 700 further includes step 740, wherein the server or processor calculates the flight of a ball according to the currently collected weather data and the historical weather data stored at the location, and considers the influence of current weather conditions on the flight of the ball in the field. In step 750, the calculated trajectory of the ball and the calculated deviation according to the weather may be displayed on the screen. Exemplary displays are shown in Figures 6A and 6B.

According to one embodiment, software on server 160 performs several functions. The weather data is screened for accuracy by comparing the weather data collected from the weather stations 110 with each other. Any material determined to be out of range based on certain benchmarks will be discarded. The data is then extracted into a model based on the model above, but in a form that facilitates fast computation, where a combination of computer-stylized languages is used to create the model output in less than a second, including C, Python and Perl. The model output gives in real-time the number of feet the baseball has flown that current weather conditions have added or subtracted. This information may be sent to and displayed on a website or screen, and may be updated frequently. According to one embodiment, the information is updated frequently (eg, approximately every 2-20 seconds). The server or processor 160 may also archive data and calculations performed.

According to another embodiment, computational fluid dynamics (CFD) modeling is employed. Created a computer-aided design (CAD) model of an outdoor sports field or sports field for use in CFD modeling. According to this embodiment, the wind is measured upstream of the stadium by a wind sensor, such as an anemometer, rather than placing the wind sensor in the stadium or outdoor sports field. Other suitable wind sensors include LiDAR and SODAR devices. Alternatively, upstream wind data can be obtained from commercial and/or public sources. In certain embodiments, the wind sensor is positioned approximately 1/8-1/4 mile upstream of the stadium so that wind measurements at approximately 1/8-1/4 mile upstream of the outer sports field can be used in the CFD model . In some stadiums (eg, stadiums with a consistent sea breeze), the wind is blowing continuously in a certain direction, and the wind sensor may be located upstream of the stadium in a certain direction. However, in other stadiums the wind direction may be less consistent and wind sensors will need to be placed in different directions in the vicinity around the stadium in order to be able to measure the wind upstream of the stadium on any given day. In other embodiments, the wind sensor may be positioned downstream of the stadium or at another convenient location near the stadium.

It will be appreciated that in this embodiment the wind sensor should be positioned far enough upstream from stadiums and other structures (eg billboards) so that no compression due to compression occurs in the location of the wind sensor. caused an increase in wind speed. Therefore, it will be appreciated that the distance from the wind sensor to the stadium is site specific. In most embodiments, the distance from the wind sensor to the stadium may be in the range of about 1/8-1/2 mile.

Wind measurements or wind data by wind sensors are used as input into a CFD model that generates 3D wind vectors at grid points above the field throughout the stadium. These 3D wind vectors are used as input into the trajectory model described above. As mentioned above, the trajectory model calculates the distance and direction a given ball will travel under current weather conditions. Linear interpolation can be used to determine the wind at the actual point of the ball.

As described below, according to one embodiment, even though wind data is collected outside the stadium, where x _s is zero at home plate and increases with the flagpole at the end of the right field sideline, y _s is zero at home plate and As the flagpole increases towards the end of the left field sideline, while z _s is only z, where z is equal to zero on the ground and increases vertically, the CFD model can be used to provide the wind component in the stadium coordinate system.

Using data from the CFD model, the wind component is then linearly interpolated to each position of the ball at each time step on the ball's trajectory. To calculate the ball's trajectory, the wind components along (tangential) and perpendicular (normal) to the horizontal component of the ball's original path are decomposed. Vertical wind does not require any transformation. This is a two-step process.

如上所定義，其中uair _s和vair _s分別是風在x _s和y _s方向上的水平分量，其中À=體育場定向角-225度，並且其中體育場定向角=從本壘板到直線中外野的羅盤方向+180度。 First, the interpolated winds in stadium coordinates are converted to winds blowing from the standard west-to-east (uair _g ) and south-to-north (vair _g ) components. This can be called a compass or a standard weather component. The equation for this conversion is as follows:

as defined above, where uair _s and vair _s are the horizontal components of the wind in the x _s and y _s directions, respectively, where À = stadium orientation angle - 225 degrees, and where stadium orientation angle = from home plate to straight midfield Compass direction +180 degrees.

其中dd =風所吹向的羅盤方向， 其中ff =水平風速。 Next, convert the compass or meteorological wind into tangential and normal wind components proportional to the horizontal components of the ball's original path. This conversion is done using the following equations (13) and (14):

where dd = compass direction the wind is blowing, where ff = horizontal wind speed.

其中ballangzero=體育場方向角+球角，球角=左外野邊線末端旗桿的-45度，零角至中外野的直線，而右外野邊線的下方45度，以及

Using equations (15) and (16), the tangential wind angle (tanwinang) and the normal wind angle (norwinang) are determined as follows:

where ballangzero = stadium direction angle + ball angle, ball angle = -45 degrees from the flagstick at the end of the left field sideline, the line from zero to center field, and 45 degrees below the right field sideline, and

One CFD model suitable for this embodiment is the ANSYS CFD software available from ANSYS of Canonsburg, Pennsylvania. The calculations in the CFD model can be done in real time. Other CFD models, such as OpenFOAM, SolidWorks, Star-CCM, COMSOL's CFD module, Altair's AcuSolve, can also be used to generate 3D wind direction vectors. In some embodiments, LiDAR can be used to measure wind within a stadium to validate the 3D wind vector produced by the CFD model. Other wind sensors, including drones, SODAR devices, and anemometers, can also be used to verify the 3D wind vectors produced by the CFD model. Therefore, in this particular embodiment, the LiDAR will not be used in real time, but the actual wind in the stadium can be measured using the LiDAR at different grid points to verify the 3D vectors produced by the CFD.

According to another embodiment, a number of pre-assigned CFD test cases are used to provide the trajectory model described above. In this embodiment, several wind inputs are calculated thoroughly in advance, and then real-time measurements are fitted to these calculations. In this setup, CFD modeling is not performed in real-time. Instead, a precomputed lookup table is used for the 3D vector grid points.

Besides CFD and direct measurements, there are other ways to estimate (parametric or approximate) wind in outdoor sports fields. These estimation methods are not well suited for large stadiums or outdoor sports fields with large, solid or high obstacles to wind entering the field, as they provide lower accuracy for such fields. That said, these types of obstacles typically result in very complex winds within the playing field. However, in sports fields with fewer obstacles and more openness, estimates (parametric or approximate) can be used and still provide useful results for wind flow.

One such estimation method is to use logarithmic wind profiles. In short, wind speed increases logarithmically with height. Therefore, according to another embodiment, log-wind profiling is used instead of CFD modeling. The log wind analysis method is described in more detail below for golf balls. However, it will be appreciated that the logarithmic wind profile can also be applied to other sports. golf

Embodiments for modeling golf ball hit trajectories in real time and in the future are described below. Typically, golf shots are made across the golf course, not just at the initial location. Therefore, all obstacles (such as tree canopies), height differences, the direction (or expected direction) of the lens, the distance (or expected distance) of the lens, and changes in weather conditions at different times and different locations should be considered at each golf course. Inside.

According to one embodiment, specific CFD modeling is performed for each golf course. In this embodiment, a CAD model of a particular golf course is created for use in CFD modeling. CAD models can be created using mesh material from Google Earth, which can then be used to create CAD models. The CAD model of the golf course provides a three-dimensional wind field across the golf course. As mentioned above, this 3D wind field is integrated into the trajectory model to calculate the effect of wind on ball flight.

According to another embodiment, generalized CFD modeling is used for all golf courses. Since CFD modeling is typically expensive and time-consuming, generalized CFD modeling allows the information learned from the full CFD modeling to be applied to a larger set of golf ball holes classified into types. There are many ways to classify golf holes. In one particular embodiment, golf holes are classified according to how they are surrounded by the canopy, i.e., all sides surrounded by crown, 3 sides surrounded by crown, 2 sides surrounded by crown, 1 side surrounded by crown , no side is surrounded by canopy.

Each golf hole contains a tee, fairway and green, each of which can be represented by a rectangle bounded by 4 sides: T=top, B=bottom, L=left, R=right, as in shown in Figure 10. Each of these rectangles can be connected to another rectangle at any angle, as shown in Figure 11. As shown in Figure 12, a straight golf hole is shown. Then, assign separate boundary conditions to each rectangular segment, where 0, 1, 2, 3, or 4 side bounds are as follows:

In this example, 864 CFD cases were run according to the following four assumptions. The first assumption is wind speeds of 12, 24, and 36 mph (that's three wind speeds). The second assumption is that the model runs in 20 degree increments (ie wind direction 0 degrees, 20 degrees, 0 degrees, etc.). Therefore, there are 18 cases for each wind speed. A third assumption is that the total number of CFD cases run in this example is as follows: (a) For each of the 16 different types of bounded tree canopies surrounding the hole segment, three wind speeds * 18 cases / wind speed = 54 wind cases; (b) 16 bounded roof combinations * 54 cases per segment = 864 CFD cases. The fourth assumption is: (a) a typical fairway length is 400 m; (b) a typical fairway width is 50 m; (c) the average height of the bounded canopy is 15 m; and 3D wind speeds between 18 wind directions are interpolated.

Using satellite data, Google Earth, maps, and any other method, classify each golf hole on the golf course into some combination of these 16 segment types and the angles connecting those hole segments. Each segment is also assigned a segment length factor. The configuration is then "stitched" together to obtain the final hole.

"Stitching" can be performed by mapping velocity components from the end of one region/rectangle to the start of the next region/rectangle. This procedure is also known as "submodeling" in the computing world. The process of mapping velocity components from one rectangle to another may be performed by a processor executing computer code that performs linear interpolation.

According to another embodiment, the wind profile of a golf course is modeled without using CFD modeling. In this embodiment, a logarithmic wind profile is used to determine the effect of wind on golf ball shots. To calculate the effect of wind on a shot, the ground elevation and canopy height for any location on the golf course need to be determined. In this embodiment, the first step is to overlay a high resolution grid (eg, 2 meters by 2 meters) on the golf course. The height of the actual canopy above the ground and the elevation of the ground at each grid point need to be determined. Canopy heights and ground elevations can be obtained from the following satellite datasets: (a) combined ground and actual canopy heights; (b) actual canopy heights above ground; (c) leaf density (varies with season). These datasets are available from third parties such as EcoAcumen )get. The combined ground and actual canopy elevations and the actual canopy height on the ground are interpolated into the golf course grid. Subtract the gridded actual canopy height from the gridded combined ground and actual canopy elevations to obtain the gridded ground elevation.

According to this embodiment for modeling wind profiles, the canopy effect on the wind is calculated at given points on the golf course (horizontal and vertical) to accurately model the trajectory of the ball. It will be noted that the effect of wind on the balls traveling close to the canopy is smaller than the effect on the wind on the balls farther away from the canopy.

The effective canopy height is defined as the elevation below which the wind will drop to zero in a vegetated area. The effective canopy height D for the entire golf course is determined from a score for average tree height that can be seasonally adjusted for the density of foliage. Then calculate the effective canopy height d for each grid point (instead of D for the entire golf course). Effective canopy height is used in the following calculations.

In this embodiment, each exposed ground grid point (grid point without a tree canopy, eg, fairway or teeing ground) has two weighting factors. The first weighting factor is inversely proportional to the square of the distance to the nearest canopy grid point. The second weighting factor is a weighted average of the actual canopy heights. This weighted average is obtained from all actual canopy heights within a given radius of this canopy grid point, weighted by the inverse square of their distance from the canopy grid point.

Each canopy grid point is weighted by the second factor only because it is an actual canopy. The sum of these two factors varies between 0.6 and 1.25 and is multiplied by the effective canopy height D for the entire grid or route to determine the effective canopy height d at each grid point.

The absolute value of the sine of the angle the wind makes with the golf ball strike angle times the effective canopy height d with a minimum value of 0.5 for each grid point for the wind The result is a gridded effective canopy between 1 and 0.5 Height, when the wind aligns with the golf ball, is less affected by the canopy next to the fairway because the wind hits the fairway up or down. A maximum value of 1 applies to winds that are perpendicular to the golf shot, as these winds blow across the fairway and are therefore more affected by the canopy next to the fairway.

According to this embodiment, three vertical layers are used to calculate the horizontal wind field during ball flight: (1) the log layer (on top of the tree), (2) the transition layer (upper third of the tree's height), and (3) the sub-canopy (the bottom two-thirds of the tree's height). The wind field is divided into three vertical layers because the wind acts differently at different heights above the ground. log level

In this particular embodiment, the log layer is the layer above 5/3 of the effective canopy height, the transition layer is the layer between the effective canopy height and 5/3 of the effective canopy height, and the sub-canopy layer is between the transition layer and the ground between (below effective canopy height).

The log layer is unconstrained at the top and defined by z _c = 5/3 z _d at the bottom. z _d is the effective height of the canopy, where canopy is defined as the average height of nearby tree tops. The effective height of the canopy is the height above the ground but below the top of the tree, within the canopy where the wind speed becomes zero. This happens because the tree absorbs wind very efficiently, thus minimizing it. It is estimated that somewhere between 0.5 and 0.8 of the canopy height, the wind speed inside the canopy drops to zero. Therefore, according to this embodiment, 5/3 of z _d is chosen based on the comparison with the measured wind.

其中U是風速，z _q是離地面的高度。 For a more accurate estimate of the wind in the logarithmic layer, the fluctuation of the terrain itself and the buoyant stability of the atmosphere (change in temperature with height) should be considered, resulting in the following logarithmic wind profile equation:

where U is the wind speed and z _q is the height above the ground.

According to this embodiment, wind data (substantially equal to _zc in height) are interpolated (wind data from wind sensors and/or from the wireless communication network) at grid points at height _zc , where _zc is Interpolated wind values at the bottom of the log layer. As mentioned above, z _c =(5/3)z _d , where z _q is the effective height of the canopy. The logarithmic wind profile equation (equation A1) is then used for all points above this point to calculate (for zq > _zc ) the horizontal air volume U( _z ) in the logarithmic layer. It will be understood that U(z _q ) is the horizontal wind speed as a function of the height z _q above the ground. U ₀ =U(z _c ), the wind speed at the bottom of the logarithmic layer. As mentioned above, _U0 is interpolated from nearby wind measurements or wind model inputs.

In equation A1, z ₀ = surface roughness, which is a parameterization of how much the underlying topography changes. For example, on a perfectly flat region, z ₀ =0. On the most extreme mountains and valleys, z ₀ =1. For most golf courses, _z0 is about 0.10.

Stability is important because if the atmosphere is unstable, where the temperature decreases rapidly with altitude, strong winds at high altitudes will easily mix down near the surface. Conversely, if the atmosphere is very stable, i.e. the temperature drops very slowly (or even increases) with altitude, then strong winds at high altitudes have a more difficult time blowing towards the ground and mixing downwards. It should be understood that stab = atmospheric static stability, and is a value between -1 (unstable) and 2.5 (fairly stable), which affects the likelihood of how easily the wind above mixes downward. transition layer

In the transition layer, tree blocking wind is taken into account in this embodiment. The transition layer is between the linear wind profile (bottom (sub-canopy) layer) and the unobstructed logarithmic wind profile (top (log) layer). The wind at the bottom of this transition layer must match the top wind at the top of the bottom (sub-canopy) layer (U _lo ). The wind at the top of this transition layer must match the wind at the bottom of the top (log) layer (U ₀ ).

其中z _lo是過渡層的底部(或樹冠高度的約2/3)，並由z _lo= z _d+z ₀e ^Vk表示，其中Vk是馮卡門(Von Karman)常數(0.41)。例行性地，在大氣建模中使用它來說明動量通量。此參數化了空氣由於邊界附近的紊流的垂直動量混合(摩擦參數化)。在該實施例中，邊界是地面。U _lo=U(z _lo)=U ₀/e ^Vk；z _n=ln((z _q-z _d)/z ₀)-stab。在方程式A2中，如上所述，藉由求解方程式A2，A和B是常數，使得U(z _lo)=U _lo並且U(z _c) =U ₀。 子樹冠 For transition layers, this is done logarithmically. Equation A2 is used to calculate the horizontal wind U(z) in the transition layer (for z _lo &lt; z _q &lt; z _c ).

where z _lo is the bottom of the transition layer (or about 2/3 of the crown height) and is represented by z _lo = z _d + z ₀ e ^Vk , where Vk is the Von Karman constant (0.41). Routinely, it is used in atmospheric modeling to illustrate momentum flux. This parameterizes the vertical momentum mixing of the air due to turbulence near the boundary (friction parameterization). In this embodiment, the boundary is the ground. U _lo =U(z _lo )=U ₀ /e ^Vk ; z _n =ln((z _q -z _d )/z ₀ )-stab. In Equation A2, as described above, by solving Equation A2, A and B are constants such that U(z _lo )=U _lo and U(z _c )=U ₀ . sub canopy

In the sub-canopy, the wind varies linearly from zero velocity at the ground to U _lo at the top of the sub-canopy. Equation A3 is used to calculate the horizontal wind U(z) in the sub-canopy (for 0 &lt; z _q &lt; z _lo ). (A3) U(z)=U _lo *z _q /z _lo where U(z) varies linearly with height and U(z)=0 at the surface.

For all of the above cases: specific CFD modeling for each course, generic CFD modeling for all courses, and Wind Profile without CFD modeling, the end point of the golf ball flight can be determined in a similar way. For the control case (no wind in average weather conditions), the control elevation change is the difference in the elevation of the exposed terrain surface between the start of the golf ball flight and the end of the golf ball flight, the case when the descending golf ball elevation is first less than or equal to Occurs when the elevation of bare ground terrain. For the weather-affected case, golf ball flight is terminated when the golf ball's elevation change is first greater than or equal to the absolute value of the descending golf ball's controlled elevation change. cricket

Embodiments may be used to model the trajectory of a cricket ball in real time and in the future. This embodiment is similar to the modeling described above for baseball. However, in this embodiment, as shown in Figure 13, the output is applied to 12 locations around the cricket pitch.

Figure 13 shows an example of real-time wind effects on the flight of an average fly ball in cricket to 12 different locations on the cricket pitch. As shown in the exemplary screen shot display of Figure 13, the larger numbers indicate that the wind is expanding or shortening (as shown by adjacent arrows) the flight of the ball and the magnitude of the impact. In the example of Figure 13, the large number "5" at the top of the center and "7" to the left of the center "5" indicate that the wind shortens the speed of the ball by 5 and 7 feet, respectively. In this example, all other larger numbers indicate that the wind is extending the ball's flight. The smaller numbers in Figure 13 show the deflection of the ball's flight caused by the wind, and the direction of the deflection is indicated by the adjacent arrows. In this particular example, the units are in feet. The large arrow in the center of the field indicates the direction of the prevailing wind.

Cricket is modeled similarly to baseball as described above. It should be noted that there are differences in cricket, which results in a slightly different shape compared to baseball. For example, cricket is slightly smaller and heavier than baseball. The discharge speed of a cricket ball is typically 85% of the discharge speed of a baseball. Also, cricket bats are essentially flat, which generally results in less spin on the ball when it is struck by the cricket bat. The spin speed of a cricket ball is about 60% of that of a baseball. Overall, these differences are not significant, and the ballistic equations vary the same as if only in coefficient values. football

According to one embodiment, modeling the trajectory of an American football can be both in real time and in the future. The modeling is similar to the baseball modeling described above, however, for American football, the output is applied to field goals from the 50-yard line (see Figure 14) and kicks from the 25-yard line in both directions (see Figure 15) .

Figure 14 shows an example of the effect of real-time wind on the flight of the average field goal played in American football. In this example, as shown on the left side of Fig. 14, the trajectory of playing the American football is extended by 3 yards and pushed by the wind by 2 yards to the left. As shown on the right side of Figure 14, in this example, the track was shortened by 5 yards by the wind and pushed 5 yards to the right by the wind.

Figure 15 shows an example of the effect of real-time wind on a fly average kick from the 25-yard line. In this example, the track is extended 2 yards and pushed 13 yards to the left.

According to one embodiment, specific field goals and kicks can be entered by clicking on capture locations and aiming points on the grid display. Specific weather conditions for wind direction, wind speed, temperature, relative humidity, and pressure/altitude can also be entered using the on-screen sliders on the on-screen display. The resulting trajectories in both field directions are then calculated, and similar to the examples shown in Figures 14 and 15, these trajectories are displayed along with the length deviation and directional deviation in yards from the average quiet condition.

It will be noted that in addition to field goals and kicks, the weather will also affect passing. According to one embodiment, to determine the effect of weather on passing, an American football field is divided into eight sections, as shown in FIG. 16 . The effect of wind for each of these eight sections was determined. It will be appreciated that in other embodiments, the American football field may be divided into more or fewer sections. The screen display shown in FIG. 16 shows how wind affects passing in each of these sections representing specific areas of the field.

There are other differences in American football, which result in a different shape compared to baseball. For example, the shape of an American football is significantly different from the shape of a baseball, and it travels through the air differently depending on whether the American football is thrown from the ground, kicked, or shot (kick-off or field goal). Therefore, different cross-sectional areas of an American football are used for different cases, depending on the wind direction relative to the ball. This requires the use of drag and lift coefficients that vary with wind direction and speed relative to the movement of the American football.

For field goals, the drag coefficient is 8/7 of the drag coefficient for kicks. For kicks and field goals, the drag coefficient of the motion component perpendicular to the original (tangential) motion of the ball, the drag coefficient is 1.5 times its tangential value, since the larger profile of an American football is always shown as vertical airflow.

Also, since American footballs are inflated with air, the inflation of the ball is adjusted according to the air temperature and atmospheric pressure. For example, for cooler temperatures (< about 65°F), the launch speed of an American football can be reduced by: launch speed = given launch speed + factor * (Tf-65), where Tf is the current temperature, factor is 0.104 mph/deg.

It is important to point out that American football has the same ballistic equation as baseball. The difference is due to the coefficient value of the ratio of the mass of the ball to the cross-sectional area. volleyball

According to one embodiment, the trajectory of the beach volleyball can be modeled both in real time and in the future. Figure 17 shows an example of real-time wind effects on average jump serve, float serve, pass and make trajectory from each side of the court. In this example, the numbers and arrows indicate the magnitude and direction of the wind's influence on the ball. In the embodiment shown, the magnitude of the impact is expressed in feet. As shown in Figure 17, depending on the location, the wind can shorten or lengthen the trajectory of the ball. Figure 17 also shows the deflection to the left or right due to the wind. In this embodiment, North is at the top of the pitch. Jump serve at every corner. The floating tee is in the middle of each finish line. Passing is the center of each half. Doing the ball is the number closest to the net. In this particular example, the average tee was extended by 5 feet and skewed by 0 feet when teeing off the north left side. When jumping from the right, the average serve is 4 feet longer and skewed 1 foot to the right. The average float tee was extended by 7 feet and skewed 2 feet to the right. The average passing distance is 4 feet longer and skewed 1 foot to the right. On average, the ball is pushed 2 feet closer to the net and 1 foot to the right. In Figure 17, the arrow in the center of the net represents the prevailing wind.

The modeling of an outdoor volleyball is similar to that of an American football, except that since the volleyball is spherical, the cross-sectional area does not change. Therefore, the coefficients do not change with the relative motion of the ball with respect to the wind. The drag coefficient increases to 1.5 times its baseball value, so the final velocity of the volleyball is appropriate.

Although only a few embodiments have been described in detail, it should be understood that the present invention may be embodied in many other forms without departing from the scope of the invention. In view of all the foregoing, it should be clear that the present embodiments are illustrative and not restrictive, and that the invention is not limited to the details given herein, but may be modified within the scope and equivalency of the appended claims .

100: System 200: System 300: System 110: Weather Sensor 115: Wind measuring device 120: LiDAR device 130: SODAR device 140: Weather Console 150: Data routing device 160: server or processor 215: Wireless Communication Network 260: server or processor 270: Display screen 300: System 310: Weather Sensor 315: Wireless Communication Network 360: Server 370: Display screen 700: Method 710: Steps 720: Steps 730: Steps 740: Steps 750: Steps 910: Line 920: Line 930: Line

The present invention and its further objects and advantages may be best understood by reference to the following description taken in conjunction with the drawings.

[FIG. 1A] is a conceptual diagram of a system for predicting the flight of a ball at a certain position, according to one embodiment.

[ FIG. 1B ] is a conceptual diagram of a system for predicting the flight of a ball at a certain position according to another embodiment.

[Fig. 2] shows an embodiment of a weather sensor that can be used in the system shown in Figs. 1A and 1B.

[Fig. 3] shows an embodiment of a weather console that can be used in the system shown in Figs. 1A and 1B.

[Fig. 4] shows an embodiment of a commercially available Meteobridge device that can be used in the system shown in Fig. IB.

[ FIGS. 5A and 5B ] are conceptual schematic diagrams of a system for predicting the flight of a ball at a certain location, according to various embodiments.

[FIGS. 6A and 6B] are exemplary outputs on a screen display showing the effect of weather on the trajectory of the ball.

[ FIG. 7 ] is a flowchart of a method of predicting current weather conditions when a ball flies at a certain location, according to one embodiment.

[FIGS. 8-9] are exemplary screen shots of a spreadsheet application for determining the effect of weather on baseball, according to one embodiment.

[Figures 10-12] are schematic rectangular representations of golf ball hole segments used in CFD modeling.

[FIG. 13] An example showing the effect of real-time wind on the flight of an average fly ball in cricket to different positions on the cricket pitch.

[Figures 14-16] show an example of the effect of real-time wind on the trajectory of an American football on a football field.

[ FIG. 17 ] An example showing the influence of real-time wind on the trajectory of a volleyball on an outdoor volleyball court.

Claims (26)

A computer-implemented method of determining the effect of a plurality of weather parameters on the flight of a ball in an outdoor playground, the method comprising: providing a digital model of the outdoor playground to the processor; at the processor, obtaining real-time data at or near the outdoor playground for at least one weather parameter, wherein the at least one weather parameter is wind, and wherein obtaining the real-time data comprises receiving the real-time data from a wireless communication network, the wireless communication network collects the real-time data from a plurality of cellular transmission signals including signal attenuation information; At the processor place, the current data obtained for the at least one weather parameter are input into a computational fluid dynamics (Computational fluid dynamics; CFD) model; at the processor, using the CFD model with the input current data and the digital model of the outdoor playground to generate a plurality of three-dimensional wind vectors at grid points in the digital model of the outdoor playground; At the processor, the three-dimensional wind vectors are used to calculate the trajectory of the ball at the outdoor playground based on the obtained current data for the at least one weather parameter, the calculated trajectory of the ball illustrating the at least one weather the effect of the parameter; and The calculated trajectory of the ball or a plurality of calculations based on the calculated trajectory of the ball is displayed on the screen. The method of claim 1, wherein obtaining the current data further comprises: receiving the current data from at least one weather sensor located at or near the outdoor playground. The method of claim 2, wherein the at least one weather sensor comprises at least one of a LiDAR device, a SODAR device, and an anemometer. The method of claim 3, wherein the at least one weather sensor comprises at least one weather sensor located approximately 1/8-1/2 mile upstream of the outdoor playground for obtaining wind data. The method of claim 1, wherein the at least one weather parameter further comprises humidity, atmospheric pressure and temperature. The method of claim 1, wherein the at least one weather parameter further comprises precipitation. The method of claim 1, wherein the digital model is a computer aided design (CAD) model. The method of claim 1, wherein the digital model of the outdoor playground includes a plurality of surroundings of the outdoor playground, wherein the surroundings comprise a radius of approximately 2-20 times the length or diameter of the field. The method of claim 1, wherein the outdoor sports field is a baseball field, an American football field, a golf course, a cricket field, or a volleyball field. A system that includes: Data storage, containing wind model data for outdoor sports fields; at least one processor, wherein at least one processor contains a digital model for the outdoor playground; and A machine-readable medium including a plurality of instructions stored therein that, when executed by the at least one processor, cause the at least one processor to perform a plurality of operations in real time, including: At the server, obtaining current weather data including wind data, wherein obtaining the current weather data includes receiving the current weather data from a wireless communication network collected from a plurality of cellular transmissions including signal attenuation information of such real-time information; At the server, using the wind model data and the current weather data, calculating the effect of the plurality of current weather conditions on the movement of the ball in the outdoor playground based on the obtained current weather data for the plurality of current weather parameters the trajectory of the ball at the outdoor playground; and A display for outputting the calculated trajectory of the ball or a plurality of calculations based on the calculated trajectory of the ball in real time. The system of claim 10, further comprising at least one wind sensor located at or near the outdoor playground, wherein obtaining current weather data further comprises receiving weather data from the at least one wind sensor. The system of claim 11, wherein the at least one wind sensor includes at least one of a LiDAR device, a SODAR device, and an anemometer. The system of claim 10, further comprising at least one temperature sensor and at least one of a humidity sensor and an atmospheric pressure sensor. The system of claim 10, wherein calculating the trajectory includes using a computational fluid dynamics model that generates a plurality of three-dimensional wind vectors within the outdoor playground. The system of claim 14, further comprising a wind sensor positioned at least 1/8 mile upstream of the outdoor playground. The system of claim 10, wherein calculating the trajectory includes using a logarithmic wind profile to generate a wind profile at the outdoor playground. The system of claim 10, wherein the outdoor sports field is a baseball field, an American football field, a golf course, a cricket field, or a volleyball field. The system of claim 10, wherein the system further comprises a data store containing historical wind data for locations at or near an outdoor playground, wherein a plurality of current weather conditions are determined for the movement of the ball at the outdoor playground Influence consists of determining the contribution of the current wind based on one of the actual measured wind speed and the historical average wind speed. A system that includes: Data storage, containing historical wind data for locations at or near outdoor sports fields; a data store containing wind model data for the outdoor playground; one or more processors, wherein the one or more processors contain a digital model of the outdoor playground; and A machine-readable medium including a plurality of instructions stored therein that, when executed by the one or more processors, cause the one or more processors to perform a plurality of operations in real time, including: At the server, obtaining current weather data including wind data, wherein obtaining the current weather data includes receiving the current weather data from at least one wind sensor located at or near the outdoor playground and if the server stops locating the current weather data from the outdoor playground any wind sensor at or near the stadium receives current weather data, obtains current weather data from a wireless communication network that collects such real-time data from a plurality of cellular transmissions including signal attenuation information; At the server, using the wind model data and the current weather data, calculating the effect of the plurality of current weather conditions on the movement of the ball in the outdoor playground based on the obtained current weather data for the plurality of current weather parameters the trajectory of the ball at the outdoor playground; and A display for outputting the calculated trajectory of the ball or a plurality of calculations based on the calculated trajectory of the ball in real time. The system of claim 19, wherein calculating the trajectory of the ball includes using a computational fluid dynamics model that generates a plurality of three-dimensional wind vectors within the outdoor playground. The system of claim 20, further comprising a wind sensor positioned at least 1/8 mile upstream of the outdoor playground. The system of claim 20, wherein the outdoor playground is a golf course and the digital model of the outdoor playground includes a plurality of rectangles, each rectangle representing a portion of a golf hole, and each rectangle is defined according to how the rectangle is bounded by a tree canopy Characterization, where the computational fluid dynamics model uses linear interpolation to map velocity components from the end of one rectangle to the start of the next rectangle. The system of claim 22, wherein for each golf hole, a first angle between the first rectangle and the second rectangle is determined, and a second angle between the second rectangle and the third rectangle is determined. The system of claim 19, wherein calculating the trajectory includes using a logarithmic wind profile to generate a wind profile at the outdoor playground. The system of claim 24, wherein the outdoor playground is a golf course or an outdoor volleyball court. The system of claim 19, wherein the display is capable of displaying the calculated trajectory of the ball as compared to the trajectory of the ball without the influence of weather.

Images