Abstract:
A tire pressure and temperature measurement system adapts a Y-block ( 30 ) to an existing valve stem ( 20 ). One branch ( 44 ) of the Y-block accepts a conventional valve core ( 42 ) and another branch ( 38 ) accepts a flexible tubular temperature sensor ( 36 ) that leads “down the throat” of the existing valve stem and into the interior of a tire ( 14, 18 ). A second embodiment is adapted for use on inside dual tires ( 18 ). Making a measurement entails attaching a pressure sensor ( 40 ) to the valve stem and attaching a hand-held processor ( 112 ) to the sensors. The hand-held processor reads the current tire pressure and temperature; executes a program (Eqs. 1-6) that accounts for measured and target temperatures, vapor pressures, and gas compressibility; aid indicates how much pressure to add or subtract to the tire to achieve an accurate final tire operating pressure. In third and fourth embodiments, respective spherical ( 70 ) and U-shaped channel ( 120 ) protective housings enclosing pressure and temperature sensors ( 72 ), a controller  76,  and a data transceiver ( 74 ) are loosely placed or attached by magnets ( 122 ) within the interior of a tire ( 126 ). A remote measurement system ( 80 ) receives at another data transceiver ( 108 ) pressure and temperature data transmitted from inside the tire while the vehicle is moving and conveys the data to a processor ( 112 ) for executing the above-described program.

Description:
RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. patent application Ser. No. 09/038,761, filed Mar. 11, 1998 for OFF-THE-ROAD TIRE TEMPERATURE AND PRESSURE MONITORING SYSTEM, now U.S. Pat. No. 6,025,777. 
    
    
     TECHNICAL FIELD 
     This invention relates to pressure and temperature measurements and more particularly to systems for measuring giant off-the-road tire temperatures and pressures under first sets of conditions and predicting inflation pressure changes required to achieve targeted operating pressures under second sets of conditions. 
     BACKGROUND OF THE INVENTION 
     Giant off-the-road tires, particularly those employed by earth moving and mining ore vehicles, are subjected to very heavy loads that make them susceptible to premature failure unless proper inflation pressures are maintained. For example, FIG. 1 shows a mining ore truck  10 , which can weigh up to 550 tons when loaded and carries its heavy loads on only two axles. A front axle  12  has two single tires  14  mounted thereon and a rear axle  16  has two dual tires  18  (only one “dual” shown) mounted thereon, resulting in loads of about 50 tons per tire. A typical tire is inflated through a conventional valve stem  20  (only two shown) to an operating pressure ranging from about 85 to 185 pounds per square inch of gauge pressure (“psig”) and, when operating, may have an operating temperature ranging from about 100 to 255 degrees Fahrenheit (“° F.”). If the tire pressure is too high, a worst case failure mode (explosion) may occur. However, if the tire pressure is too low, the excess heat generated may cause separation of some of the 18 to 22 tire layers after only 300 hours of operation, whereas such tires normally have at least a 1,000 hour operating life. Giant off-the-road tires cost about $25,000 to $30,000 each, and vehicle downtime costs at least about $500 per hour. Clearly, maintaining proper tire operating pressure is an economic imperative. 
     Unfortunately, conventional tire pressure measurement methods require allowing the tires to cool for about eight hours before an accurate tire pressure measurement and inflation pressure adjustment can be made. The resulting costly downtime often leads to infrequent tire pressure measurements. To make matters worse, air compressors often add water vapor and compression heating of the inflation air, causing errors between the measured and operating air pressures in the tires. Moreover, off-the-road vehicle operators often add fluids to tires to inhibit rim rust and scale that otherwise makes tire removal difficult. Also, new tires are stored outdoors where they can collect rainwater, some of which inevitably remains in the tire when it is installed on a vehicle. Unfortunately, such fluids have vapor pressures that contribute to pressure measurement errors. Tires operating under these conditions are referred to as “wet” tires. Finally, many off-the-road vehicles operate in cold climates but are maintained in heated facilities, further complicating the tire inflation pressure problem. Unfortunately, conventional gas law equations do not provide solutions to these problems. 
     There are previously known apparatus and methods for solving some of the above-described problems. In particular, U.S. Pat. No. 5,452,608 for PRESSURE AND TEMPERATURE MONITORING VEHICLE TIRE PROBE WITH RIM ANCHOR MOUNTING describes a tire rim mounted sensor probe and conductor terminal apparatus for sensing the air pressure and temperature inside a tire. When the vehicle stops, a conventional electronic measuring device is electrically connected to the conductor terminal to convert the sensor probe data into pressure and temperature measurements. Unfortunately, the sensor probe is separately mounted through a hole in the rim, a disadvantage that weakens the rim and requires a relatively expensive field retrofit to every rim. If a new rim is required, it similarly has to be retrofitted, adding to the downtime of vehicle. Of course, a tire cool down period may be required to obtain usable readings. 
     U.S. Pat. No. 5,335,540 for TIRE MONITORING APPARATUS AND METHOD describes a tire pressure and temperature sensing apparatus that employs radio telemetry to continuously monitor tire pressure and temperature while the vehicle is operating. However, as in the above-described patent, the pressure and temperature sensing probe is separately mounted to the rim, which has many of the above-described disadvantages. Moreover, every vehicle carries a telemeter receiver by which the vehicle driver monitors the tire operating pressures and temperatures. 
     There are many other patents describing tire pressure and temperature monitoring apparatuses and methods. Some describe sensors embedded in the tires, others describe wheel hub mounted slip rings for conducting sensor data to a vehicle data processor, and still others describe complex systems for inflating and deflating tires while the vehicle is operating. However, there is no known prior method or apparatus that accounts for pressure measurement errors caused by air compressors, water vapor pressure, and temperature changes. 
     What is needed, therefore, is an accurate tire pressure measuring system that does not require a cool down time, does not require expensive retrofitting or weakening of tire rims, accounts for sources of measurement errors, is readily transferred among tires and vehicles, and is usable on a wide variety of tire and wheel combinations. 
     SUMMARY OF THE INVENTION 
     An object of this invention is, therefore, to provide an apparatus and a method for measuring tire pressure and predicting inflation pressure changes that account for many sources of measurement errors without requiring a tire cool down period. 
     Another object of this invention is to provide an apparatus and a method for measuring tire pressure and temperature without resorting to expensive retrofitting or weakening of tire rims. 
     A further object of this invention is to provide a tire pressure and temperature measuring apparatus and a method that is readily transferable among tires and vehicles and is usable with a wide variety of tire and rim combinations. 
     A first embodiment of a tire pressure and temperature measurement system of this invention adapts a Y-block to an existing valve stem. One branch of the Y-block accepts a conventional valve core and the other branch of the Y-block accepts a flexible tubular temperature sensor that leads “down the throat” of the existing valve stem and into the interior of the tire. Making a measurement entails stopping the vehicle and, without a cool down period, attaching a pressure sensor to the conventional valve stem and attaching a hand-held processor to the pressure and temperature sensors. The hand-held processor reads the current tire pressure and temperature and executes a program that accounts for measured and target temperatures, vapor pressures, and gas compressibility and indicates how much pressure to add or subtract to the tire to achieve an accurate final tire operating pressure. 
     A second embodiment of the tire pressure and temperature measurement system employs a modified Y-block that adapts to an existing rim, angle adaptor, and extension hose of an inside dual tire. The modified Y-block receives an elongated temperature sensor with sufficient flexibility for feeding down the throat of the extension hose, bending around the corner of the angle adaptor, and protruding into the interior of the tire. Making a measurement is carried out as in the first embodiment. 
     A third embodiment of the tire pressure and temperature measurement system encloses pressure and temperature sensors and a battery powered telemetry transmitter inside a generally oblate protective housing, all of which is simply placed loosely within the interior of a tire when it is mounted to a rim. The telemetry transmitter battery capacity is sufficient for one year of continuous operation, which exceeds the expected tire life. In this embodiment, a telemetry receiver receives pressure and temperature data transmitted from inside the tire and conveys the data to a processor that executes the program described in the first embodiment. The telemetry receiver can be tuned to receive data from multiple tires while the vehicle is moving. Alternatively, the telemetry receiver can be adapted to receive data only from a closely adjacent tire. 
     A fourth embodiment of the tire pressure and temperature measurement system encloses the pressure and temperature sensors and the battery powered telemetry transmitter inside a protective U-shaped channel housing that is magnetically attached to the rim inside the tire. As in the third embodiment, the telemetry receiver receives pressure and temperature data transmitted from inside the tire and conveys the data to a processor that executes the program described in the first embodiment. The telemetry receiver can be tuned to receive data from multiple tires while the vehicle is moving. Alternatively, the telemetry receiver can be adapted to receive data only from a closely adjacent tire. 
     Additional objects and advantages of this invention will be apparent from the following detailed description of preferred embodiments thereof that proceed with reference to the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is an isometric pictorial view of an exemplary prior art ore truck suitable for employing this invention. 
     FIG. 2 is a sectional side elevation view of a first embodiment of a Y-block of this invention adapted to an existing rim and valve stem. 
     FIG. 3 is a sectional elevation view of a second embodiment of a Y-block of this invention adapted to an existing inside dual rim, valve stem, and extension hose. 
     FIG. 4 is a sectional elevation view of a third embodiment of this invention showing pressure and temperature sensors and a battery powered telemetry transmitter enclosed within a spherical protective housing. 
     FIG. 5 is an electrical block diagram of a tire pressure and temperature measuring system based on the third and fourth embodiments of this invention. 
     FIG. 6 is an isometric cutaway view of a fourth embodiment of this invention showing the pressure and temperature sensors and battery powered telemetry transmitter of FIG. 4 enclosed in a protective U-shaped channel housing that is magnetically attached to a tire rim. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 2 shows a first embodiment of this invention in which a Y-block  30  is threaded onto existing valve stem  20 , which is bolted in place on a wheel rim  32 . Single tire  14  is mounted to wheel rim  32 , which is attached to an axle hub  34  by multiple studs and nuts (not shown). The interior temperature of tire  18  is sensed by a temperature sensor  36 , such as a thermocouple or thermistor that is inserted through a first branch  38  of Y-block  30 , through existing valve stem  20 , and into the interior of tire  14 . A seal nut  39  that is threaded into first branch  38  secures temperature sensor  36  therein and prevents air from leaking out first branch  38 . 
     Tire pressure is measured by attaching a pressure sensor  40  to a valve core  42  that is threaded into a second branch  44  of Y-block  30 . Pressure sensor  40  is preferably an ECLIPSE model 9251702, manufactured by Data Instruments, Inc. of Acton, Mass. Conventional means are employed to connect, condition, and digitize the signals generated by temperature and pressure sensors  36  and  40 . The digitized signals are processed as described with reference to the EXAMPLE herein to compute how much air pressure to add to, or subtract from, tire  14 . 
     Preferably, temperature sensor  36 , pressure sensor  40 , and the associated connecting, signal conditioning, and digitizing circuitry are securely housed and mounted to rim  32 , and a portable computer (not shown) is plugged into an interface port on the housing to compute how much pressure to add to, or subtract from, tire  14 . 
     FIG. 3 shows a second embodiment in which a Y-block  50  is connected to an extension hose  52  that connects through an elbow  54  to existing valve stem  20  on inside dual tire  18 . This embodiment requires an elongated, flexible temperature sensor  56  to make a 90-degree bend before entering the tire. Preferably, a flexible thermocouple housed in a “speedometer cable-style” housing is sufficiently flexible to traverse such bends while surviving the harsh environments of off-the-road vehicle tires. 
     As in the first embodiment, Y-block  50  has first and second branches  58  and  60  and is coupled to associated connecting, signal conditioning, and digitizing circuitry that are securely housed and mounted to rim  32 . In this embodiment, however, inside dual tire  18  is mounted to an inside dual wheel rim  62 , which is bolted in place on an inside dual axle hub  64 . 
     FIG. 4 shows a third embodiment of this invention in which a generally oblate spherical housing  70  encloses a pressure and temperature sensor  72 , a data transceiver  74 , a controller  76 , and batteries  78 , all of which are simply inserted loosely inside the tire when it is installed on the vehicle. Pressure and temperature, sensor  72  s preferably a model PPT-R manufactured by Honeywell, Inc. of Plymouth, Minn. Pressure and temperature sensor  72  is housed within a 1.375 inch diameter, 3.65 inch long stainless steel cylinder having a data connector at one end and a ¼ inch NPT female pipe threaded sensor access hole at the other end. The model PPT-R includes signal conditioning, digitizing, and communicating electronics within its package. 
     Housing  70  may be shaped like a ball, a football, or any other suitable shape that will not damage the interior of the tire and protects the components inside housing  70 . In a developmental prototype, housing  70  was a 10 inch diameter polypropelene ball having about a 0.187 inch wall thickness and six 4.0 inch diameter holes evenly distributed about its surface. Such a ball is available from pet stores as a ferret toy named the “Jolly Ball,” which is manufactured by Jolly Pet, Inc. of Ravenna, Ohio. The holes are of a suitable size and distribution to allow assembly of the components inside housing  70 . Of course, other housing constructions are possible including mated hemispheres, cages, blunted cylinders, tauruses, dumb-bell shapes, and inflatable shapes. Testing revealed that a 20 inch diameter housing is preferred to keep the antenna associated with transceiver  74  at least 10 inches off the tire floor, thereby increasing transmission efficiency through the tire side wall. 
     Sensed pressure and temperature data are telemetered by transceiver  74  to a remote measurement system  80  while the vehicle is in operation. Tire life can be significantly improved by remotely measuring tire pressure and temperature at the end of each ore-transporting run, computing in remote measurement system  80  any pressure changes required, and adjusting the tire pressure accordingly before the nest run. The computing is carried out as described with reference to the EXAMPLE herein. 
     A two inch diameter, spherically faced first end cap  82  is attached by six screws  84  (only two shown) to the interior of housing  70 . The spherical face has a radius of curvature chosen to match the inside radius of housing  70 . The center of first end cap  82  is drilled and tapped with ¼ inch NPT female threads. A ¼ inch NPT male nipple  86  mechanically connects pressure and temperature sensor  72  and first end cap  82  and provides an opening between pressure and temperature sensor  72  and the air inside the tire. 
     A second end cap  90  having a similar spherical face is attached by six screws  92  (only two shown) to the side of housing  70  that is diametrically opposed to the first end cap mounting position. Second end cap  90  includes a cylindrical protrusion  94  that preferably has the same diameter as pressure and temperature sensor  72 . An aluminum center tube  96  having slotted ends and an inside diameter chosen to fit snugly over the diameters of protrusion  94  and pressure and temperature sensor  72  extends between and is secured thereto by clamps  98  fitted around the slotted ends. Thereby, center tube  96 , pressure and temperature sensor  72 , and male nipple  86  form a rigid axle extending through the center of housing  70  with first and second end caps  82  and  90  acting as axle hubs. Pressure and temperature sensor  72 , data transceiver  74 , controller  76 , and batteries  78  are all securely mounted to and interconnected through center tube  96 . 
     FIG. 5 shows the interconnections among electronic subassemblies implementing a preferred tire pressure and temperature measuring system  100  of this invention, which employs the third embodiment described above with reference to FIG.  4 . Housing  70  encloses pressure and temperature sensor  72 , data transceiver  74 , controller  76 , a battery pack  102 , and a voltage regulator  104 . 
     Controller  76  preferably includes a model MC68HC11 CMOS microprocessor that is manufactured by Motorola, Inc. located in Phoenix, Ariz. The microprocessor includes on chip random access memory and electrically erasable programmable read-only memory to support program memory and data transmission functions. Controller  76  intercommunicates with pressure and temperature sensor  72  through a model LT1180 differential logic driver/receiver (not shown), which is manufactured by Linear Technology Corporation of Milpitas, Calif. Pressure and temperature data received by controller  76  are transferred along with a data synchronization clock to data transceiver  74 , which may be a MICROSTAMP 20M remote intelligent communications unit model MSEML256X10SG manufactured by MICRON Technology, Inc. located in Boise, Id. Data transceiver  74  includes an on chip 256 bit data memory and employs direct sequence spread spectrum transmission at a 2.44175 GHz center frequency. Reception employs a differential phase shift keyed modulated backscatter in the 2.400 to 2.4835 GHz band on a 596 kHz subcarrier. A simple circuit board “patch” antenna  106  permits a pair of such data transceivers and antenna to have a line of sight range of about 15 meters. A range greater than about 3 meters is suitable for communicating with remote measurement system  80  of this invention. 
     Alternatively and preferably, data transceiver  74  is a conventional 900 MHz data transceiver, such as ones employed in wireless telephones, with a flexible quarter wavelength vertical antenna. 
     The above-described circuits receive 5.5 to 6.0 volt DC power from voltage regulator  104 , which is preferably a model LT1121 manufactured by Linear Technology Corporation of Milpitas, Calif. Voltage regulator  104  receives nominal 7.5 volt DC power from battery pack  102  that includes a group of six series connected batteries  78  (FIG.  4 ), which are preferably “super C” sized nickel-cadmium or lithium cells that are available from various manufacturers. Batteries  78  are evenly distributed around and clamped to center tube  96  near the end that is attached to second end cap  90 . Because it employs on-demand burst data transmission, tire pressure and temperature measuring system  100  has a very low standby power drain, resulting in a typical battery lifetime of about one year when lithium batteries are employed. 
     Remote measurement system  80  includes a data transceiver  108  and a patch antenna  110  that are similar to and intercommunicate with data transceiver  74  and patch antenna  106 . Data transceiver  108  intercommunicates with a processor  112 , such as a conventional laptop personal computer that includes a memory  114 . Because remote measurement system  80  is most suitably hand-held, processor  112  and memory  114  are preferably a model PC9000-A/D manufactured by DAP Technology Corporation of Tampa, Fla. Of course, a wide variety of PC types are usable including tower and desk top versions. 
     FIG. 6 shows a fourth embodiment of this invention in which a generally U-shaped channel  120  encloses and provides mounting points for pressure and temperature sensor  72  (not shown), data transceiver  74 , controller  76  (not shown), and batteries  78  (not shown). U-shaped channel  120  has at least one but preferably four magnets  122  attached to the terminal margins of its side flanges for magnetically clamping U-shaped channel  120  to a wheel  124  when a tire  126  is being installed on the vehicle. Magnets  122  may be selected from among various commercially available types, but preferably are those made from rare-earth and ceramic compositions and having pole pieces attached to each side that are shaped to mate to substantially flat surfaces. Field testing has shown that such magnets have sufficient flux density to firmly secure U-shaped channel  120  to wheel  124  under any acceleration loading condition experienced by the vehicle. Optimal magnetic coupling of magnets  122  to wheel  124  is preferably attained by orienting the long axis of U-shaped channel  120  substantially parallel to the rotational axis of wheel  124  as shown in FIG.  6 . Of course, U-shaped channel  120  is but one possible shape for implementing the invention. 
     Employing magnets  122  eliminates the need for drilling mounting holes in wheel  124  and, thereby, prevents weakening of wheel  124 . U-shaped channel  120  preferably extends about 3.5 inches (8.9 cm) above wheel  124 , including 0.75 inches (1.9 cm) for magnets  122 , and is about 4 inches (10.2 cm) wide by 6 inches long (15.25 cm), which is a sufficiently volume to enclose pressure and temperature sensor  72 , data transceiver  74 , controller  76 , and batteries  78  without touching interior side walls  128  of tire  126 . Tire  126  is typically mounted between a flange  130  and a rim  132  that both extend from wheel  124 . 
     The above-described magnetic mounting of U-shaped channel  120  to wheel  124  provides a sufficient separation of a flexible vertical antenna  134  from a floor  136  of tire  126  to provide adequate communications efficiency of data transceiver  74  through side walls  128  of tire  126 . Flexible vertical antenna  134  preferably extends perpendicularly from the center member of U-shaped channel  120 . 
     As in the third embodiment of this invention, sensed pressure and temperature data are telemetered by transceiver  74  to a remote measurement system  80  while the vehicle is in operation. 
     In operation, a vehicle, such as mining ore truck  10  (FIG.  1 ), has a tire pressure and temperature measuring system  100  installed in each of tires  14  and  18 . When ore mining truck  10  approaches remote measurement system  80 , an operator commands processor  112  to interrogate each tire pressure and temperature measuring system  100  regarding the current pressure and temperature inside each of tires  14  and  18 . Processor  112  conveys the command to data transceiver  108  that transmits in sequence an interrogation burst to each of data transceivers  74 , which each in turn exit standby mode, retrieve from the memory of associated controller  76  the current pressure and temperature data received from pressure and temperature sensor  72 , and transmit the retrieved data to remote measurement system  80 . 
     Processor  112  stores in memory  114  the current pressure and temperature data associated with each of tires  14  and  18  and follows the process described below and with reference to FIG. 6 to accurately predict the tire pressure reading that would result if the tires were allowed to cool down to a predetermined temperature. If the predicted pressure at the predetermined temperature is outside an optimal inflation pressure range, mining ore truck  10  is stopped and its tire pressures adjusted accordingly. 
     The calculation process followed by processor  112  is based on equation (1), which expresses the relationships among the current and final temperatures, pressures, vapor pressures of water, and compressibility factors of a gas confined in a fixed volume. 
     Initial and Final Pressure Relationships:                P   2     =           Z   2       Z   1            (       P   1     -     P   W1       )            T   2       T   1         +     P   W2               Eq.  (1)                                
     where: 
     P 2 =Final (predicted) pressure (atm), from Eq. (6) 
     P 1 =Current (measured) pressure (atm), from Eq. (6) 
     T 2 =Final (target) temperature in degrees Rankine (° R)*, from Eq. (7) 
     T 1 =Current (measured) temperature (° R), from Eq. (7) 
     P W2 =Water vapor pressure (atm) at temperature T 2 , from Eqs. (2) and (5) 
     P W1 =Water vapor pressure (atm) at temperature T 1 , from Eqs. (2) and (5) 
     Z 2 =Gas compressibility at pressure P 2 , from Eqs. (3) or (4) 
     Z 1 =Gas compressibility at pressure P 1 , from Eqs. (3) or (4) 
     *The Rankine scale is the Fahrenheit-based absolute temperature scale just as the Kelvin scale is the Centigrade-based absolute temperature scale. Therefore, 180° R separate the freezing and steam points of water, whereas 100° K separate the freezing and steam points of water. 
     Because vapor pressures and compressibility factors Z are used to correct for non-ideal conditions, equation (1) does not rely on well-known ideal gas law equations known as Boyle&#39;s law and Charles&#39; law. The vapor pressure relationships are described with reference to equation (2) and the compressibility factor relationships are described with reference to equations (3) and (4), which were statistically derived using nitrogen and air compressibility data published in Perry&#39;s Chemical Engineers&#39; Handbook, 4th and 6th editions. 
     Moreover, because the compressibility factors depend on the final pressure and temperature, equation (1) is used twice to calculate an accurate final pressure. Equation (1) is first used to calculate a trial final pressure assuming that Z 1  equals Z 2 . Then, using the trial final pressure, values for Z 1  and Z 2  are calculated. Then, equation (1) is used the second time to calculate an accurate final pressure value. An example calculation process is described later. 
     As mentioned above, equation (1) includes vapor pressure corrections P W1  and P W2  for wet tires. Equation (2) is used to calculate the vapor pressure of water at the current and final temperatures. Vapor pressure correction of equation (1) is necessary when a tire encloses sufficient water for saturation, which occurs if any liquid water is present at the warmer operating temperature; that is, not all of the water is vaporized. At the colder temperature, saturation occurs when the volume of liquid water is only about 0.5% of the total enclosed tire volume. 
     Vapor pressure of water:                P   W     =     e     11.113   -     6369.6     T   +   360                   (   2   )                                
     where: P W  is the partial pressure in (atm) of water and T is the tire interior air temperature in ° F. 
     Equation (2) was derived by employing statistical regression. Table 1 shows a comparison of measured and calculated (using equation 2) vapor pressures. 
     
       
         
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
             
             
               
                   
                   
               
               
                   
                 Temp 
                 Vapor Pressure 
                   
               
             
          
           
               
                   
                 ° F. 
                 psia 
                 Calc. 
                 % Error 
               
               
                   
                   
               
             
          
           
               
                   
                  20 
                 0.050 
                 0.052 
                 2.58 
               
               
                   
                  30 
                 0.081 
                 0.080 
                 −1.58 
               
               
                   
                  40 
                 0.122 
                 0.120 
                 −1.70 
               
               
                   
                  50 
                 0.178 
                 0.176 
                 −0.90 
               
               
                   
                  60 
                 0.256 
                 0.255 
                 −0.29 
               
               
                   
                  70 
                 0.363 
                 0.363 
                 0.15 
               
               
                   
                  80 
                 0.507 
                 0.509 
                 0.41 
               
               
                   
                  90 
                 0.698 
                 0.702 
                 0.55 
               
               
                   
                 100 
                 0.949 
                 0.955 
                 0.63 
               
               
                   
                 110 
                 1.274 
                 1.282 
                 0.61 
               
               
                   
                 120 
                 1.692 
                 1.700 
                 0.47 
               
               
                   
                 130 
                 2.221 
                 2.229 
                 0.35 
               
               
                   
                 140 
                 2.887 
                 2.890 
                 0.12 
               
               
                   
                 150 
                 3.716 
                 3.711 
                 −0.14 
               
               
                   
                 160 
                 4.739 
                 4.718 
                 −0.44 
               
               
                   
                 170 
                 5.99  
                 5.945 
                 −0.76 
               
               
                   
                   
               
             
          
         
       
     
     The maximum relative error is 2.58% at 20° F., which error is less than 0.002 psi (the percentage error multiplied by the vapor pressure of the water). The 0.002 psi error is very small compared to typical tire operating pressures over 100 psi. The maximum absolute error using equation (2) is 0.046 psi at 170° F., which is still less than 0.05% of the typical tire operating pressure. 
     As mentioned above, equation (1) employs compressibility factors Z to correct the pressure, volume, and temperature relationships of real gases. Equations (3) and (4) express the compressibility factors Z for air and nitrogen respectively and were statistically obtained from actual data, rather than using generalized charts. The resultant equations are: 
     Compressibility factor Z of air:              Z   =     0.99980   +     0.0025335   ×   P     -       1.5303   ×   P     T               (   3   )                                
     Compressibility factor Z of nitrogen:              Z   =     0.99979   +     0.0074727   ×   P     -       2.7270   ×   P     T     -       4.7453     -   6       ×   P   ×   T               (   4   )                                
     where: Z equals the compressibility factor for nitrogen or air, P equals the pressure in atmospheres (atm), and T equals the temperature in ° R. 
     The comparisons of measured and calculated data and the relative errors resulting from using equations (3) and (4) are shown below in respective Tables 2 and 3. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Air Compressibility 
               
             
          
           
               
                 Temp 
                 Pressure 
                   
                   
                 % 
               
               
                 ° F. 
                 psig 
                 Z 
                 Z 
                 Error 
               
               
                   
               
             
          
           
               
                 −10 
                  44 
                 0.9963 
                 0.9963 
                 −0.00 
               
               
                 −10 
                  58 
                 0.9957 
                 0.9955 
                 0.02 
               
               
                 −10 
                  88 
                 0.9935 
                 0.9937 
                 −0.02 
               
               
                 −10 
                 130 
                 0.9911 
                 0.9912 
                 −0.01 
               
               
                 −10 
                 132 
                 0.9908 
                 0.9911 
                 −0.03 
               
               
                 −10 
                 275 
                 0.9822 
                 0.9827 
                 −0.05 
               
               
                 80 
                  44 
                 0.9988 
                 0.9986 
                 0.02 
               
               
                 80 
                  58 
                 0.9987 
                 0.9983 
                 0.04 
               
               
                 80 
                  88 
                 0.9980 
                 0.9977 
                 0.03 
               
               
                 80 
                 130 
                 0.9974 
                 0.9968 
                 0.06 
               
               
                 80 
                 132 
                 0.9972 
                 0.9968 
                 0.04 
               
               
                 80 
                 275 
                 0.9950 
                 0.9939 
                 0.11 
               
               
                 170 
                  44 
                 1.0001 
                 1.0002 
                 −0.01 
               
               
                 170 
                  58 
                 1.0002 
                 1.0003 
                 −0.01 
               
               
                 170 
                  88 
                 1.0002 
                 1.0005 
                 −0.03 
               
               
                 170 
                 130 
                 1.0004 
                 1.0008 
                 −0.04 
               
               
                 170 
                 132 
                 1.0004 
                 1.0008 
                 −0.04 
               
               
                 170 
                 275 
                 1.0014 
                 1.0019 
                 −0.05 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Nitrogen Compressibility 
               
             
          
           
               
                 Temp 
                 Pressure 
                   
                   
                 % 
               
               
                 ° F. 
                 psig 
                 Z 
                 Z 
                 Error 
               
               
                   
               
             
          
           
               
                 −10 
                 −0 
                 0.9992 
                 0.9991 
                 −0.01 
               
               
                 −10 
                 58 
                 0.9960 
                 0.9962 
                 0.02 
               
               
                 −10 
                 130 
                 0.9924 
                 0.9927 
                 0.03 
               
               
                 −10 
                 275 
                 0.9857 
                 0.9855 
                 −0.02 
               
               
                 80 
                 −0 
                 0.9998 
                 0.9996 
                 −0.02 
               
               
                 80 
                 58 
                 0.9990 
                 0.9991 
                 0.01 
               
               
                 80 
                 130 
                 0.9983 
                 0.9984 
                 0.01 
               
               
                 80 
                 275 
                 0.9971 
                 0.997  
                 −0.01 
               
               
                 170 
                 −0 
                 1.0001 
                 0.9999 
                 −0.02 
               
               
                 170 
                 58 
                 1.0007 
                 1.0006 
                 −0.01 
               
               
                 170 
                 130 
                 1.0011 
                 1.0013 
                 0.02 
               
               
                 170 
                 275 
                 1.0029 
                 1.0028 
                 −0.01 
               
               
                   
               
             
          
         
       
     
     Tables 2 and 3 show that comparing the calculated compressibility values and actual data results in suitably low errors for both gases of less than 0.06%. 
     The following equations are used to convert between commonly used pressure and temperature units. 
     
       
         Pressure Unit Conversion: P(psig)=[P(atm)−1]×14.696  (5)                Pressure                 Unit                 Conversion        :                   P                   (   atmosphere   )       =       P                   (   psia   )       14.696             (   6   )                               Temperature Unit Conversion: T(° F.)=T(° R)−460  (7)
      
     
     As described in the following example, processor  112  employs equations (1) through (7) to accurately predict a tire pressure that would result were the tire allowed to cool from a current temperature to a final temperature. 
     EXAMPLE 
     Tire pressure and temperature measuring system  100  and remote measurement system  80  determine that an operating wet tire has a measured 140 psig current air pressure and a measured 125° F. current air temperature. A system operator needs to know what the tire pressure would be if it was allowed to cool to 40° F. The applicable steps and example calculations are set forth below with relevant variables underlined. 
     In a first step, processor  112  computes water vapor pressure at 125° F. and 40° F. using equation (2): 
     P W1 =e{circumflex over ( )}{11.113−6369/(125+360)}=0.13279 atm 
     P W2 =e{circumflex over ( )}{11.113−6369/(40+360)}=0.00815 atm 
     In a second step, processor  112  converts the current pressure measurement P 1  psig units to atm units using equation (5): 
     140 psig={P 1 (atm)−1}×14.696 
     Solving for P 1 (atm) yields: 
     P 1 (atm)=140/14.696+1=10.526 atm 
     In a third step, processor  112  converts ° F. units to ° R units using equation (7): 
     T 1 ° R=125° F.+460=585° R 
     T 2 ° R=40° F.+460=500° R 
     In a fourth step, processor  112  sets the ratio Z 2 /Z 1  equal to one and computes a trial pressure P 2  using equation (1): 
     Trial P 2 =(1/1)×(10.526−0.13279)×(500/585)+0.00815=8.8916 atm 
     In a fifth step, processor  112  computes Z 2  and Z 1  using equation (3) and the trial P 2 . Equation (4) would be used if the system operator specified that the tire was filled with nitrogen rather than air: 
     Z=0.99980+0.0025335×10.526−1.5303/585×10.526=0.99894 
     Z=0.99980+0.0025335×8.8916−1.5303/500×8.8916=0.99511 
     In a sixth step, processor  112  computes a final P 2 (atm) by recalculating equation (1) with the calculated values of Z 2  and Z 1 : 
     P 2 =(0.99511/0.99894)(10.526−0.13279)(500/585)+0.00815=8.8575 atm 
     In a seventh step, processor  112  converts final P 2  psi atmosphere units to P 2  psi gauge units using equation (5): 
     P 2 (psig)=(8.75−1)14.696=115.47 psig 
     End of EXAMPLE. 
     Because the temperature sensors of this invention sense the temperature of the air contained in a tire, the same general process may also be employed to determine temperature adjustments cause by compression heating, expansion cooling (as the compressed air enters the tire), tire casing temperature caused by outside storage, and hot wheel and drum resident heat. 
     For example, an ambient inflation adjustment (“AIA”) may be calculated for the original inflation of a newly installed tire or the reinstallation of a used tire. When using equation (1) to calculate the AIA, T 1  is the ambient outside air temperature (or the working environment temperature), and T 2  is the temperature of the compressed air used to inflate the tire (in this example, the temperature of a heated maintenance facility). Assume a 40.00×57 tire has a cold inflation pressure specification of 110 psig at 65° F. The tire is inflated inside a 65° F. maintenance facility, whereas its operating environment temperature will be 0° F. Using equations (1) through (7) reveals that the tire must be inflated to 128 psig at 65° F. if it is to achieve a 110 psig operating pressure after cooling to 0° F. 
     When using equation (1) as a prediction formula, T 1  is redefined as the original inflation air temperature inside the tire, T 2  is the currently measured air temperature inside the tire, and P 1  is the original inflation air pressure inside the tire. Equations (1) through (7) are used to calculate P 2 , the current air pressure inside the tire. P 2  is used as a baseline pressure that is compared with the currently measured pressure reading to determine whether to increase, decrease, or maintain the current pressure inside the tire. 
     Skilled workers will recognize that portions of this invention may be implemented differently from the implementations described above for a preferred embodiment. For example, processor  112  could employ lookup tables stored in memory  114  to fetch precalculated values usable in many of the steps set forth above. This would be particularly useful for rapidly retrieving values in the vapor pressure and unit conversion steps. It is also conceivable that some or all of the steps could be performed by the processor in controller  76  upon receipt of an interrogation command that included a final temperature value. 
     Of course, skilled workers will understand how to use a wide variety of programming languages and computer types to implement the invention. Likewise, the invention may be implemented with other than the sensors, batteries, and electronic and mechanical components described above. For example, the data transceivers may employ other frequencies and modulation types or may be deleted in favor of a device that employs inductive or capacitive coupling directly through the tire. In the latter alternative, the vehicle may need to be stopped and the device held against the tire. 
     Also, in addition to taking on a variety of shapes and constructions, housing  70  need not be loosely enclosed within a tire, but may be bonded or otherwise attached to the tire or wheel without weakening them, or slung from the wheel inside the tire interior to increase the height of patch antenna  106  off the tire floor. Range may also be increased by making patch antenna  110  a directional antenna with gain. Of course, many different antenna designs would be effective for either transceiver depending on the particular application. Likewise the invention can be adapted to work with many different tire shapes, sizes, and applications including automobile, aircraft, and truck tires. 
     It will be obvious to those having skill in the art that many changes may be made to the details of the above-described embodiments of this invention without departing from the underlying principles thereof. Accordingly, it will be appreciated that this invention is also applicable to pressure and temperature measuring and predicting applications other than those found in the inflation of heavy truck tires. The scope of the present invention should, therefore, be determined only by the following claims.