Abstract:
An airborne sonar collision avoidance system is disclosed. The system compensates for changes in temperature in real time to provide more accurate sonar detection. In addition, the sensors are arranged in a communications network that allows for the sensors to be programmed at run time, thus providing the ability to relocate the sensors without having to pre-program the sensors before the sensors are installed onto a different location.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is a continuation of application Ser. No. 10/630,214, filed Jul. 30, 2003, now U.S. Pat. No. 6,859,418 B2, and claims the benefit of U.S. Provisional Application No. 60/412,350, filed on Sep. 20, 2002, entitled “Sonar Object Detection System”, the contents of each of which are incorporated herein by reference. 

   TECHNICAL FIELD 
   The present invention relates to ultrasonic systems and more particularly to an airborne sonar detection system. 
   BACKGROUND 
   Ultrasonic ranging systems use airborne high frequency sound waves to detect target objects. In these systems, high frequency sound waves are generated and transmitted to an object. The transmitted sound waves then bounce off the object and return to their source as an echo. The distance from the source of the sound waves to the object can then be measured based on the speed of sound and the time it takes for the sound wave to travel to an object and return to the source. 
   Although ultrasonic sound with frequencies ranging from 20 to 200 kHz can be used for a wide variety of ranging and sensing applications, when designing an ultrasonic-based system, a great care must be taken to compensate for the many variables involved. An example of such variables includes dynamic temperature changes in the atmosphere. If atmospheric temperature is not properly compensated for, an erratic system operation will result. An uncompensated system could, for example, exhibit undesirable traits such as a range that varies, blind spots, moving blind spots, a target that is detected one time and not the next, unwanted target acquisitions, and false target acquisitions. 
   In addition, a reliable ultrasonic system needs to account for acoustic properties that are affected by the environmental dynamics. Such acoustic properties include variation in the speed and wavelength of sound in air over temperature; variation in sound attenuation based on frequency, temperature, and humidity and over distance; variation in the return echo, target strength, based on target distance, shape and composition; turbulence in the detection zone; effects of background noise; and sound radiating pattern, beam angle, of the selected ultrasonic transducer. 
   For example, speed of sound varies from 1041 feet/second (“ft/sec”) at −10 degrees Fahrenheit (“F”) to 1172 ft/sec at 110 F. This presents a change of 12.5% and would result in an apparent change in measurement of 2.5 ft over a 20 ft distance. Further, wavelength is defined as the speed of sound in inches/second (“in/sec”) divided by frequency, w1=c/f. Since the speed of sound, c, changes over temperature so does the wavelength. Solving for wavelength, it can be seen that a 40 kHz signal at −10 F has a wavelength of 0.3123 inch, while at +110 F, the wavelength is 0.3516 inch. For reflection to occur, the wavelength should be small compared to the dimension of the target because the larger the target in comparison to wavelength, the stronger the return. Thus it can be seen that as temperature goes up, wavelength goes up and the amount of reflection goes down. That is, the target strength diminishes. 
   Sound propagates through air by causing air molecules to collide with each other pushing the sound along like a wall of dominoes. As sound travels through air, these collisions result in friction loss, higher frequency means more collisions, hence greater loss. Complicating the issue is the fact that density and composition of the medium varies with temperature and humidity. Further, the medium behaves differently above 50 kHz. A useful approximation for figuring maximum attenuation up to 50 kHz and above 50 kHz may be used. While useful for approximating maximum ranges, however, the actual temperature humidity attenuation is highly non-linear. Accordingly, this attenuation also needs to be compensated for or target strength will vary radically over temperature causing erratic target acquisition. 
   As described above, because both sound and target objects have complex properties, many considerations need to be taken into account when building an ultrasonic system. Accordingly, there is a need for a properly designed ultrasonic system that compensates for the environmental factors such as dynamic temperature changes. 
   SUMMARY 
   There is provided a sonar detection system and method that compensates for dynamic temperature changes in real time. In one aspect, the method includes an object detection model residing in a sensor. The model compensates for atmospheric changes that result from environmental dynamics. For example, an air density model outputs air density depending on the temperature. From this air density output, a gain model computes amount of gain used for processing a received echo signal. A thermistor and resistor network is added to a feedback loop of a preamp and causes the preamp to automatically change gain with temperature according to the output of the air density and gain models. 
   In another aspect, the ultrasonic detection system includes a controller, and a plurality of sensors. The controller is connected to a data input of a first one of the plurality of sensors. A data output of the first one of the plurality of sensors is connected to a data input of a second one of the plurality of sensors, such that the subsequent sensors in the plurality are connected via data output of one to data input of another. The controller polls for addresses and configures them for the sensors in real time, thus allowing the addresses of the sensors to change. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram of an ultrasonic sensor in one embodiment of the present invention that compensates for atmospheric temperature in real time. 
       FIG. 2  is a flow diagram illustrating a method of detecting objects, compensating for temperature in real time, in one embodiment of the present invention. 
       FIG. 3  is an electrical schematic circuit diagram of a drive circuit in one embodiment of the present invention for controlling output sound pressure level in an ultrasonic transducer. 
       FIG. 4  is a flow diagram illustrating the method of controlling output sound pressure level in an ultrasonic transducer in one embodiment of the present invention. 
       FIG. 5  is a communications network diagram illustrating the sensor network in one embodiment of the present invention. 
       FIG. 6  is a graph illustrating plotted air density data output from an air density model. 
       FIG. 7  is a graph illustrating plotted gain data output from a gain model. 
       FIG. 8  is a schematic circuit diagram illustrating an intelligent sensor in one embodiment. 
       FIG. 9  is a schematic diagram illustrating an individual sensor shown in  FIG. 5 . 
   

   DETAILED DESCRIPTION 
     FIG. 1  is a block diagram of an ultrasonic sensor in one embodiment of the present invention that compensates for atmospheric temperature in real time. A sensor  102  is connected to a controller  104  by, for example, a bus  116 . The sensor  102  may also communicate to the controller wirelessly. The sensor  102  includes a transducer  106  that outputs sound waves as directed by the drive  108 . The sensor  102  also receives sound wave echoes from an object, that is, the sound waves that bounce back after hitting an object. The sensor  102  in one aspect may include separate transducers for transmitting and receiving sound waves. 
   A variable gain pre-amplifier  115  receives echo signals from the transducer  106 . The variable gain pre-amplifier provides real time compensating for environment dynamics such as the environment temperature. A filter  112  filters the amplified echo signals. The filtered echo signals are then input to an amp  114 . The amp  114  amplifies the signals and outputs the amplified signals to a microprocessor  110 . An object detection algorithm may reside in the sensor  102 , for example, in the microprocessor  110 . The microprocessor  110  computes distances of objects using the received echo signals and the time duration between the transmission of sound waves and receipt of echo signals. The microprocessor  110  may use an air density and gain models to determine how much gain is used on the received signal as a function of temperature. 
   The microprocessor  110  outputs the computed data such as distances, for example, via the data bus  116 , to a controller  104 . The controller then alerts a user, for example using a user interface such as displays and sound alerts, that objects are nearby. The controller  104 , for example, includes a microprocessor  120  for processing data received or to be transmitted to the sensor  102 , user interface functions, input/output (“I/O”) functions, etc. The controller  104  also may include a transmitter/receiver  122  for communicating data to the sensor  102 . The transmitter/receiver  122  may be a wired or wireless transceiver. The alert means  126  may include an alarm or a display interface for alerting or informing a user about the objects detected by the sensor  102 . The I/O  124  performs typical input/output functions. The controller  104  may include a bus interface  128  for communicating data or control signals among the microprocessor  120 , transceiver  122 , I/O  124 , and alert means  126 . The typical functions of microprocessor, transceiver, I/O, alarms, and user interfaces are generally known to those skilled in the art and therefore, will not be described in further detail here. The controller  104  generally controls how individual sensors  102  should operate. 
     FIG. 2  is a flow diagram illustrating a method of detecting objects, compensating for temperature in real time, in one embodiment of the present invention. At  202 , transformed sound waves are transmitted and echo signals are received. The echo signals are filtered and amplified at  204 . The signals are then input to a microprocessor that computes the distance of a detected object using the information about the echoed signals such as the time it took for the echoed signal to be reflected back to the transducer. 
   At  206 , using an air density and gain model that adjusts the gain on the received echo signals, the distance of an object is computed and thus object is detected. At  208 , the detected data is transmitted to a controller. At  210 , the controller generates an alert or otherwise informs a user of the detected object, for example, by a displaying the data on a user interface or other visual warnings or by audio warnings such as beeping alarm or voice activated alarm. 
   As described above, in one aspect, atmospheric and gain models are used to compensate the atmospheric changes, for example, temperature. Although the atmosphere is in constant motion and is inhomogeneous, useful approximations may be formed if the variations in the medium are small with respect to the wavelength. In one aspect, the ideal gas laws of Charles and Boyle are used to calculate air density, with a basic assumption that the atmosphere within the range of technology is stable during this very short time of flight of the sound waves. The ideal gas law takes the base form of PV=nRT, where P=pressure, V=volume, n=mole volume of gas, R=the gas constant, and T=temperature. The formula for density is derived as D=P/T*R. Gas constants are published in most chemistry texts. The value of R for dry air is 287. With pressure assumed to be constant, in this case barometric pressure at sea level, and temperature varied, the values shown in Table 1 result. 
   
     
       
             
           
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
               Atmospheric pressure data (at sea level) based 
             
             
               on temperature and humidity 
             
             
               Data is based on published values 
             
             
               of H 2 O saturation vapor pressure 
             
             
               Calculations are based on the law 
             
             
               of partial pressures and the ideal gas law 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
                 
               Temperature for this humidity data is 0 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.38249 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.38241 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.38233 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.38225 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.38218 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.3821 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.38202 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.38195 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.38187 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.38179 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.38171 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 5 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.36761 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.36751 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.36742 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.36732 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.36722 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.36713 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.36703 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.36693 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.36684 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.36674 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.36664 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 10 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.35305 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.35293 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.35281 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.35269 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.35257 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.35245 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.35232 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.3522 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.35208 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.35196 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.35184 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 15 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.3388 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.33865 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.3385 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.33835 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.3382 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.33805 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.3379 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.33775 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.3376 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.33745 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.3373 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 20 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.32484 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.32466 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.32448 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.32429 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.32411 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.32393 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.32375 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.32356 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.32338 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.3232 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.32301 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 25 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.31118 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.31095 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.31073 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.3105 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.31028 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.31005 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.30983 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.3096 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.30938 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.30915 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.30893 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 30 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.29779 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.29752 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.29725 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.29697 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.2967 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.29643 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.29616 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.29589 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.29562 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.29535 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.29508 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 35 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.28467 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.28434 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.28401 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.28368 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.28335 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.28302 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.28269 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.28235 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.28202 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.28169 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.28136 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 40 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.27181 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.27142 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.27102 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.27062 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.27022 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.26982 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.26942 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.26902 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.26863 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.26823 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.26783 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 45 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.25921 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.25874 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.25826 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.25778 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.2573 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.25682 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.25634 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.25586 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.25538 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.2549 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.25442 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 50 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.24686 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.24629 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.24572 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.24514 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.24457 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.244 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.24343 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.24286 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.24228 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.24171 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.24114 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 55 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.23475 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.23407 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.23338 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.2327 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.23202 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.23134 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.23066 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.22997 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.22929 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.22861 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.22793 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 60 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.22287 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.22206 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.22125 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.22044 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.21964 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.21883 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.21802 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.21721 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.21641 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.2156 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.21479 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 65 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.21121 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.21027 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.20932 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.20837 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.20742 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.20647 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.20552 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.20457 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.20362 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.20267 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.20172 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 70 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.19978 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.19866 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.19754 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.19642 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.1953 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.19418 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.19306 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.19195 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.19083 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.18971 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.18859 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 75 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.18856 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.18725 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.18594 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.18462 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.18331 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.182 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.18068 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.17937 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.17806 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.17675 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.17543 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 80 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.17755 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.17601 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.17447 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.17293 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.1714 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.16986 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.16832 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.16678 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.16524 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.16371 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.16217 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 85 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.16674 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.16495 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.16317 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.16138 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.1596 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.15781 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.15603 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.15424 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.15246 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.15067 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.14889 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 90 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.15613 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.15405 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.15198 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.1499 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.14783 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.14575 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.14367 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.1416 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.13952 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.13745 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.13537 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 95 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.1457 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.1433 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.1409 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.1385 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.13609 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.13369 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.13129 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.12888 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.12648 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.12408 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.12168 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 100 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.13547 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.13269 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.12991 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.12713 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.12435 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.12157 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.11879 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.11601 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.11323 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.11045 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.10767 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 105 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.12541 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.12221 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.11901 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.11581 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.11261 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.10941 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.10621 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.10301 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.09981 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.09661 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.09341 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 110 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.11554 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.11188 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.10823 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.10457 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.10092 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.09726 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.09361 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.08995 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.0863 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.08264 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.07899 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 115 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.10583 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.10165 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.09746 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.09328 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.08909 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.08491 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.08072 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.07654 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.07236 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.06817 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.06399 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 120 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.09629 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.09151 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.08674 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.08196 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.07718 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.0724 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.06762 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.06284 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.05807 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.05329 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.04851 kg/m{circumflex over ( )}3 
             
             
                 
               Temperature for this humidity data is 125 degrees f. 
             
             
                 
               At a relative humidity of 0 percent, the air density at sea 
             
             
                 
               level is 1.08692 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 10 percent, the air density at sea 
             
             
                 
               level is 1.08147 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 20 percent, the air density at sea 
             
             
                 
               level is 1.07603 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 30 percent, the air density at sea 
             
             
                 
               level is 1.07059 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 40 percent, the air density at sea 
             
             
                 
               level is 1.06514 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 50 percent, the air density at sea 
             
             
                 
               level is 1.0597 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 60 percent, the air density at sea 
             
             
                 
               level is 1.05426 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 70 percent, the air density at sea 
             
             
                 
               level is 1.04881 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 80 percent, the air density at sea 
             
             
                 
               level is 1.04337 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 90 percent, the air density at sea 
             
             
                 
               level is 1.03793 kg/m{circumflex over ( )}3 
             
             
                 
               At a relative humidity of 100 percent, the air density at sea 
             
             
                 
               level is 1.03248 kg/m{circumflex over ( )}3 
             
             
                 
                 
             
           
        
       
     
   
   From a plot of this data, slope of the curve at any point may be calculated and a matching preamp gain curve generated. In this case, the standard gain formula of the ideal non-inverting op-amp, E(o)/E(in)=R(in)+R(f)/R(in), is used. R(in) in this equation has the temperature compensation network substituted for it. Referring to the sensor schematic of  FIG. 8 , E(o)/E(in) is calculated according to the following equation:
 
 E ( o )/ E ( in )=((( R 16 +TR 1)*( R 16 +TR 1))/(( R 16 +TR 1)+( R 16 +TR 1)))+( R 18)/((( R 16 +TR 1)*( R 16 +TR 1))/(( R 16 +TR 1)+( R 16 +TR 1)))
 
Where TR1 changes with temperature. When calculated over temperature the values in Table 2 result.  FIG. 6  represents the plotted data of Table 1, and  FIG. 7  represents the plotted data of Table 2.
 
   
     
       
             
           
         
             
               TABLE 2 
             
             
                 
             
           
           
             
               At −40 deg. c. with trim = 1000 thrm = 1752 fb1 = 2000 fb2 = 33000 gain = 28.54018 
             
             
               At −35 deg. c. with trim = 1000 thrm = 1392 fb1 = 2000 fb2 = 33000 gain = 30.22285 
             
             
               At −30 deg. c. with trim = 1000 thrm = 1115 fb1 = 2000 fb2 = 33000 gain = 31.90042 
             
             
               At −25 deg. c. with trim = 1000 thrm = 900 fb1 = 2000 fb2 = 33000 gain = 33.53286 
             
             
               At −20 deg. c. with trim = 1000 thrm = 732 fb1 = 2000 fb2 = 33000 gain = 35.08427 
             
             
               At −15 deg. c. with trim = 1000 thrm = 599 fb1 = 2000 fb2 = 33000 gain = 36.53813 
             
             
               At −10 deg. c. with trim = 1000 thrm = 494 fb1 = 2000 fb2 = 33000 gain = 37.86408 
             
             
               At −5 deg. c. with trim = 1000 thrm = 409 fb1 = 2000 fb2 = 33000 gain = 39.0783 
             
             
               At 0 deg. c. with trim = 1000 thrm = 341 fb1 = 2000 fb2 = 33000 gain = 40.15735 
             
             
               At 5 deg. c. with trim = 1000 thrm = 286 fb1 = 2000 fb2 = 33000 gain = 41.11112 
             
             
               At 10 deg. c. with trim = 1000 thrm = 241 fb1 = 2000 fb2 = 33000 gain = 41.95243 
             
             
               At 15 deg. c. with trim = 1000 thrm = 205 fb1 = 2000 fb2 = 33000 gain = 42.66929 
             
             
               At 20 deg. c. with trim = 1000 thrm = 175 fb1 = 2000 fb2 = 33000 gain = 43.29915 
             
             
               At 25 deg. c. with trim = 1000 thrm = 150 fb1 = 2000 fb2 = 33000 gain = 43.84831 
             
             
               At 30 deg. c. with trim = 1000 thrm = 129 fb1 = 2000 fb2 = 33000 gain = 44.32777 
             
             
               At 35 deg. c. with trim = 1000 thrm = 112 fb1 = 2000 fb2 = 33000 gain = 44.72871 
             
             
               At 40 deg. c. with trim = 1000 thrm = 97 fb1 = 2000 fb2 = 33000 gain = 45.09245 
             
             
               At 45 deg. c. with trim = 1000 thrm = 85 fb1 = 2000 fb2 = 33000 gain = 45.39042 
             
             
               At 50 deg. c. with trim = 1000 thrm = 75 fb1 = 2000 fb2 = 33000 gain = 45.64364 
             
             
               At 55 deg. c. with trim = 1000 thrm = 66 fb1 = 2000 fb2 = 33000 gain = 45.87546 
             
             
               At 60 deg. c. with trim = 1000 thrm = 58 fb1 = 2000 fb2 = 33000 gain = 46.08471 
             
             
               At 65 deg. c. with trim = 1000 thrm = 52 fb1 = 2000 fb2 = 33000 gain = 46.24365 
             
             
               At 70 deg. c. with trim = 1000 thrm = 46 fb1 = 2000 fb2 = 33000 gain = 46.40436 
             
             
               At 75 deg. c. with trim = 1000 thrm = 41 fb1 = 2000 fb2 = 33000 gain = 46.53966 
             
             
               At 80 deg. c. with trim = 1000 thrm = 37 fb1 = 2000 fb2 = 33000 gain = 46.64879 
             
             
               At 85 deg. c. with trim = 1000 thrm = 33 fb1 = 2000 fb2 = 33000 gain = 46.75873 
             
             
                 
             
           
        
       
     
   
   The uncompensated gain is 17.17647 at trim=1000, fb1=2000, and fb2=33000. The air density and gain models compensate for changes in temperature by first modeling air density as a function of temperature. Sound travels better when air density is high, that is, air molecules are closer together allowing for better medium for sound to travel. Accordingly, as air density goes up, gain is adjusted to be decreased. 
     FIG. 3  is an electrical schematic circuit diagram of a drive circuit in one embodiment of the present invention. The drive circuit  108  shown in  FIG. 1 , for example, may be implemented according to this circuit diagram. This drive circuit controls output sound pressure level (“SPL”) in an ultrasonic transducer such that the sound pressure levels may be reduced at extremely low temperatures where sound travels best. That is, when the temperature is lower, air density is high, and since sound travels better in the denser air, lower SPL may be needed. 
   The ultrasonic transducer is an electromechanical device. When a voltage is applied, a ceramic element is displaced to move air. The shape, mass, and applied voltage determine the displacement. Thus, sound is generated by flexing a piezo electric element. The more voltage applied the more the element is flexed. The more it is flexed the higher the output sound pressure level. Maximum applied voltage is 140 VPP at 40 kHz. This voltage level generates a minimum 108 db SPL. Any voltage less than 140 VPP generates less output. 
   The drive circuit  300  in one aspect includes a logic level field effect transistor (FET)  306  to pulse a primary of a step up transformer. Transformer T 1   302  is a step-up transformer that steps 8.75 V up to 140 V. When Q 5  has 5V applied to the gate of the transistor  306 , PING_HI 140 V is applied to the transducer element  304 . When Q 5  has 3V applied to the gate of the transistor  306 , PING_LO 80V is applied to the transducer element  304 . This provides two different maximum drive levels. 
   The secondary of T 1   302  and the inherent capacitance of the transducer  304  form a tank circuit with a Q&gt;50 without R 11   308  in place. The Q of the tank circuit determines how fast the transducer ramps up to full sound pressure level. R 11   308  programs the final Q of the circuit. In general, R 11   308  determines how much energy is lost between excitation pulses and programs the transducer ramp. 
   Before the first excitation pulse, the transducer element  304  is a mass at rest. A mass at rest tends to remain at rest. As such, the first excitation pulse does not yield maximum deflection of the transducer element. Depending on how much energy R 11   308  is lost between pulses, and the mass of the element, maximum deflection/voltage may never be reached or it may be reached from 2 to 8 pulses. Using two different maximum voltages with a known ramp up allows for the generation of any output SPL up to the maximum. The FET  306  may be controlled by a micro-controller, which includes software that controls the pulsing of the transducer, thus controls output sound pressure levels with software. 
     FIG. 4  is a flow diagram illustrating the method of controlling output sound pressure level in an ultrasonic transducer in one embodiment of the present invention. At  402 , micro-controller controlled FET is used to pulse a primary step up transformer. For example, a step-up transformer steps 8.75 volts up to 140 volts. Depending on the voltage applied to the FET, up to 140 volts may be applied to the transducer. Thus, for example, having 3 volts applied at the gate of the FET will apply 140 volts to the transducer; having 5 volts applied at the gate of the FET will apply 80 volts to the transducer, providing two different maximum drive levels. At  404 , a resistor determines how much energy is lost between excitation pulses to determine the number of pulses needed for the transducer to reach maximum voltage, and ultimately deflection. Accordingly, at  406 , using two different maximum voltages with a known ramp up, a desired output sound pressure level up to the maximum is generated. 
     FIG. 5  is a communications system network diagram illustrating the sensor network in one embodiment of the present invention. The communications system allows the sensors  504   a  to  504   n  in the network  500  to be programmed at run time.  FIG. 9  is a schematic diagram illustrating an individual sensor shown in  FIG. 5 . Referring to  FIGS. 5 and 9 , a first sensor  504   a  in the network has its data input  506   a  tied, or electrically connected, to a controller  502 . The first sensor&#39;s data output  508   a , the drain of MOSFET Q 1 , is tied to the second sensor&#39;s data input  506   b . The second sensor&#39;s data output  508   b  is tied to the third sensor&#39;s data input  506   c . All sensors  504   a  to  504   n  in the network  500  are tied this way up to for example, 128 sensors in a daisy chain fashion. 
   Since diode D 1  of Q 1  is reversed biased, Q 1  can operate as a high power analog switch. This switch can provide the serially connected sensors to operate serially without complex readdressing wiring or algorithms if the sensors are relocated. 
   Initially, all sensors  504   a  to  504   n  in the network are turned off and their addresses are set to “$ff.” At power-up, only sensor  1504   a , for example, is electrically connected to the controller  502 . All subsequent sensors  504   b  . . .  504   n  are isolated from the controller  502  and still turned off. The connection with the controller  502  from these sensors  504   b  . . .  504   n  are through the previous sensors. At power-up, the controller  502  directs the first sensor  504   a  to turn itself on and assigns the first sensor  504   a  an address. Using the address, the controller  502  then directs the first sensor  504   a  to direct the second sensor  502   b  to turn itself on and assigns the second sensor  502   b  its address. In this daisy chain fashion, the controller  502  turns on all the sensors and assigns them addresses. 
   After power-up, the controller  502  polls the sensors  504   a  . . .  504   n  for their addresses. If an address of $ff is returned to the controller  502  from any one of the sensors  504   a  . . .  504   n , the controller  502  assigns a valid address. The controller  502  then turns on Q 1  for the addressed sensors. 
   In one aspect, the returned addresses from the sensors when polled by the controller  502  may be accumulated in a sensor array. The controller  502  then addresses each element in the sensor array, and for each $ff address encountered in the sensor array, the controller assigns a valid address to the sensor and turns on Q 1  for the addressed sensor. This unique scheme of assigning addresses at runtime allows all sensors to be interchangeable with one another. This is advantageous, for example, when a sensor installed in front of a vehicle needs to be moved to the back. The sensor being moved need not be individually reprogrammed before being installed at its new location. 
   In one aspect, each sensor&#39;s dimension is typically less than or equal to 55 mm (L)×25 mm (W)×20 mm (H). Active board area is about 9. square centimeters. These dimensions, however, may be altered. Sensors are typically mounted about 30 inches above the ground, with appropriate spacing to cover the width of the surface. A single sensor may cover an area of 1.5 meters by 3 meters. 
   Sensor response is unsolicited. Sensors respond to the host if a sensor error occurred as a result of the last command or if a target was detected. If a sensor times out without finding a valid target it does not report so as not to burden the communications channel. Responses are sent to the controller in a form of designated bit patterns. Examples of responses from the sensors include: 
   $4c8014e0 Address zone  1  unit  4  found a target at 11 ft. 6 in., checksum is $e0. 
   $00016364 Address zone  6  unit  3  suffered a transducer error, checksum is $64. 
   The above described invention can compensate for the attenuation changes by adjusting for changes in air temperature and changes in air density. Then the microcontroller can adjust for the speed of sound to calculate the distance to an object. 
   While the invention has been described with reference to several embodiments, it will be understood by those skilled in the art that the invention is not limited to the specific forms shown and described. Thus, various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.