Abstract:
A method and an apparatus for estimating the weight of horses. To estimate the weight of a horse, a girth, a length, and a height of the horse are measured. The measurements can be taken with commercially available measurement tapes, for example. The weight of the horse is then estimated based on the girth, the length and the height of the horse. The present invention will be utilized in the care and management of horses thereby resulting in advanced equine health and nutrition, better training results, and improved overall health monitoring.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Not Applicable. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
     Not Applicable. 
     BACKGROUND OF THE INVENTION 
     There are many instances where determining an accurate weight of a horse is desirable, if not essential for proper medication, feeding, training and health monitoring requirements. Equine scales for weighing horses are available. Equine scales are large pieces of machinery which are typically expensive and unaccessible. For example, in many situations veterinary care must be administered in the field as opposed to a clinical setting. While the veterinarian may have an equine scale at her place of business, such scale may not be accessible when the veterinarian is working in the field. 
     For these reasons, methods have been developed for estimating the weight of the horse. One such method has been visual weight estimation, based only upon observation of the horse. This method has proven to be the least reliable and typically results in substantial estimation errors. Usually, such estimation errors result in a significant under estimation of weight. 
     Another method utilizes the girth measurement of a horse to estimate a weight. The practical application of this method involves the use of a girth weight tape which is stretched around the heart girth of a horse. Printed on the girth weight tape are weight estimates corresponding to the girth measurement. Where the tape overlaps after being wrapped around the girth, the indicated weight is read from the tape. The girth measurement calculation method is more accurate than the visual estimation method in predicting a horse&#39;s weight. 
     Yet another method utilizes both girth and length measurements of a horse to estimate a weight. The girth and length measurement method is more accurate than either the visual estimation method or the girth measurement calculation method. Although the girth and length measurement method is more accurate than either the visual weight estimation or the girth measurement method, substantial estimation errors are still made. 
     In light of the foregoing, the need exists for a more accurate weight estimation method which can be utilized in the care and management of horses thereby resulting in advanced equine health and nutrition, better training results and improved overall health monitoring. It is to such an improved method of estimating the weight of a horse that the present invention is directed. 
     SUMMARY OF THE INVENTION 
     The present invention relates to a method and apparatus for estimating the weight of horses. It is envisioned that the present invention will be utilized in the care and management of horses thereby resulting in advanced equine health and nutrition, better training results, and improved overall health monitoring. 
     Broadly, to estimate the weight of a horse, a girth, a length, and a height of the horse is measured. The measurement can be taken with commercially available measurement tapes, for example. The weight of the horse is then estimated based on the girth, the length and the height of the horse. 
     Utilizing the present invention, a more accurate estimate of the horse&#39;s weight has been made. For example, in one embodiment, weight estimates produced in accordance with the present invention produced an adjusted R 2  of 0.097559 compared to an adjusted R 2  of 0.095349 for the next most accurate prior art model, i.e., the girth and length measurement method discussed above. By using the present invention, the general health and welfare of horses can be improved significantly by eliminating under dosing or over dosing of medication, preventing improper nutritional decisions and enhancing training regimens while improving the overall health monitoring of horses. 
     In one aspect of the present invention, an apparatus for estimating the weight of a horse is provided. The apparatus includes an input unit, a storage unit, a computer unit, and an output unit. The input unit is adapted to receive a measured height, a measured girth, and a measured length of the horse. The storage unit stores weight estimation logic adapted to estimate the weight of the horse based on the measured height, the measured girth and the measured length of the horse. The computer unit receives the measured height, the measured girth and the measured length of the horse and executes the weight estimation logic to estimate the weight of the horse. The output unit outputs a signal indicative of the weight of the horse in a format perceivable by an individual. 
     The apparatus can be in the form of a handheld calculator, a desk top computer, or a laptop computer, for example. 
     In yet another aspect of the present invention, a software program capable of running on a computer for estimating the weight of a horse is provided. The software program can be stored on a storage unit, such as a hard disk, a CDROM, a memory or the like. The software program is provided with input logic, weight estimation logic, and output logic. The interface logic is adapted to receive a measured height, a measured girth, and a measured length of the horse. The weight estimation logic estimates the weight of the horse based on the measured height, the measured girth and the measured length of the horse. The output logic generates an estimated weight indicative of the weight of the horse. In one preferred embodiment of the present invention, the input logic and the output logic are implemented as a computer screen populated with appropriate fields to permit the measured height, the measured girth, the measured length, and the estimated weight to be entered and displayed. 
     Thus, it will be understood by those skilled in the art that the present invention provides more accurate weight estimates than methods currently available so that more accurate medication dosages, feed and nutrition considerations, training and racing performance and health monitoring requirements can be provided. 
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
     FIG. 1 is a top plan view of an apparatus, constructed in accordance with the present invention, for estimating the weight of a horse. 
     FIG. 2 is a side elevational view of a horse illustrating measurements of such horse being taken in accordance with the present invention. 
     FIG. 3 is a diagrammatic view of a software program, constructed in accordance with the present invention, for estimating the weight of a horse. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to the drawings, in particular to FIG. 1, shown therein and designated by the referenced numeral  10  is an apparatus, constructed in accordance with the present invention, for estimating the weight of a horse  12  (FIG.  2 ). In general, the apparatus  10  is provided with an input unit  14 , a storage unit  16 , a computer unit  18 , and an output unit  20 . 
     As best shown in FIG. 2, the horse  12  is standing on the ground  36 . As will be well understood by those skilled in the art, the horse  12  is provided with withers  40 , a shoulder  42  and a buttocks  44 . The shoulder  42  has a point  46 , and the buttocks  44  has a point  48 . The point  46  is typically at the outermost portion of the shoulder  42 . Likewise, the point  48  is an outermost portion of the buttocks  44 . 
     The measured height  30  is obtained by measuring the distance from the ground  36  to a top  50  of the withers  40  of the horse  12 . The measured girth  32  can be obtained by measuring about the heart girth  32  with a measuring tape snug against the horse  12  following respiratory expiration. For example, the measured girth  32  can be taken using a commercially available measuring tape. 
     The measured length  34  of the horse  12  can be obtained by measuring the distance from the point  46  of the shoulder  42  to the point  48  of the buttocks  44  in a straight line. In other words, the measured length equals the distance from the tuber ischium to the point  46  of the shoulder  42 . Once the measured height  30 , measured girth  32  and the measured length  34  of the horse  12  are determined, the input unit  14  is utilized to enter the measured height  30 , the measured girth  32  and the measured length  34  into the apparatus  10 . For example, as shown in FIG. 1, the input unit  14  can be a keyboard. However, it should be understood that the input unit  14  can be any type of input unit capable of entering in the measured height  30 , measured girth  32  and the measured length  34  into the apparatus  10 . For example, the input unit  14  can be a microphone and the measured height  30 , measured girth  32 , and the measured length  34  can be spoken into the microphone. 
     The storage unit  16  stores weight estimation logic adapted to determine an estimated weight of the horse  12  based on the measured height  30 , the measured girth  32  and the measured length  34  of the horse  12 . The storage unit  16  can be any type of medium which can be read by the computer unit  18 . For example, the storage unit can be an optical storage unit, a magnetic storage unit, or any other type of suitable storage unit such as an EEPROM, a ROM, or the like. The weight estimation logic will be discussed in more detail below. 
     The computer unit  18  receives the measured height  30 , the measured girth  32  and the measured length  34  of the horse  12  and executes the weight estimation logic so as to estimate the weight of the horse  12  based on the measured height  30 , the measured girth  32  and the measured length  34 . The computer unit  18  can be any type of computer capable of receiving the measured height  30 , the measured girth  32  and the measured length  34  of the horse  12  and executing the weight estimation logic so as to estimate the weight of the horse  12 . For example, the computer unit  18  can be a central processing unit, a digital signal processor or a logic control unit, each of which is well known in the relevant art. Thus, no further comments are deemed necessary to one skilled in the art how to make or use the computer unit  18 . 
     The output unit  20  outputs an estimated weight  54  indicative of the estimated weight of the horse  12  in a format perceivable by an individual. For example, the output unit  20  can output the estimated weight  54  in an audio format, a video format, or a combination thereof. As shown in FIG. 1, the estimated weight  54  can be provided as alphanumeric characters displayed on a display device, such as a LCD screen. 
     In a preferred embodiment shown in FIG. 1, the input unit  14  is provided with a girth button  56 , a height button  58  and a length button  60 . To estimate the weight of the horse  12  utilizing the apparatus  10 , an individual determines the measured height  30  as discussed above, and then enters the measured height  30  via the input unit  14  into the apparatus  10 . The individual then punches the height button  58 . The individual then determines the measured girth  32  as discussed above, and enters such measured girth  32  into the apparatus  10  via the interface unit  14 . The individual then punches the girth button  56  to store the measured girth  32  in the storage unit  16 . The individual then determines the measured length  34  as discussed above, and then enters the measured length  34  into the apparatus  10  utilizing the interface unit  14 . The individual then punches the length button  60  to store the measured length  34  in the storage unit  16 . The individual then punches a weight estimation button  62  to cause the computer unit  18  to execute the weight estimation logic stored in the storage unit  16  to determine the estimated weight  54  of the horse  12 . Once the weight estimation logic has executed, the estimated weight  54  is displayed or otherwise outputted in a format perceivable by the individual. 
     In the preferred embodiment shown in FIG. 1, the apparatus  10  is in the form of a handheld calculator. However, it should be understood that the apparatus  10  can be implemented in many other forms. For example, as will be discussed below, the apparatus  10  can be implemented as a desktop computer, a laptop computer, a palm computer or any other device, such as a cellular telephone, capable of executing the weight estimation logic as discussed herein. 
     Referring now to FIG. 3, shown therein and designated by a reference numeral  70 , is a software program, constructed in accordance with the present invention, for determining the estimated weight of the horse  12 . The software program  70  is adapted to be run on a computer, such as a desktop computer, a laptop computer, a notebook computer, a mainframe computer, a personal data assistant (PDA), a cellular telephone, a pre-programmed calculator or a user programmable calculator. In general, the software program  70  is provided with input logic  72 , weight estimation logic  74  and output logic  76 . The software program  70  is stored on any suitable type of storage unit. The storage unit for storing the software program  70  can be any device capable of storing data in a format readable by a computer. For example, the storage unit can be an optical disk suitable for reading by an optical drive, a magnetic disk (hard or floppy) suitable for reading a magnetic drive, a memory unit (RAM or ROM) or the like. 
     The software program  70  can be run on any suitable type of computer, such as a hand held calculator, a desktop computer, a laptop computer, a palm computer or any other device, such as a cellular telephone or a personal data assistant, capable of executing the weight estimation logic  74  as discussed herein. The software program  70  can be run on a remote computer, such as a website. In this case, the input logic  72  and the output logic  76  could gather and output data from any device having a browser program, such as a personal computer, a cellular telephone or personal data assistant. 
     The input logic  72  is adapted to receive the measured height  30 , the measured girth  32 , and the measured length  34  of the horse  12 . The weight estimation logic  74  determines an estimated weight  78  of the horse  12  based on the measured height  30 , the measured girth  32  and the measured length  34  of the horse  12 . The output logic  76  outputs the estimated weight  78 . 
     In a preferred embodiment of the software program  70 , the input logic  72 , and the output logic  76  are implemented as a computer screen  80  populated with a plurality of fields  82 ,  84 ,  86 , and  88  so as to permit the measured height  30 , measured girth  32 , the measured length  34 , and the estimated weight  78  to be entered and displayed. 
     More specifically, the field  82  receives the measured girth  32 . The field  84  receives the measured height  30 . The field  86  receives the measured length  34 . The estimated weight  78  is displayed in the field  88 . 
     The weight estimation logic  74  can be linked to the computer screen  80  via any suitable logic, such as a weight estimation button  90  disposed on the computer screen  80 . 
     To determine the estimated weight of the horse  12  utilizing the software program  70 , an individual determines the measured height  30  as discussed above, and then enters the measured height  30  into the field  84 . The individual then determines the measured girth  32  as discussed above, and enters such measured girth into the field  82 . The individual then determines the measured length  34  as discussed above, and then enters the measured length  34  into the field  86 . The individual then clicks on or otherwise actuates the weight estimation button  90  to cause the software program  70  to execute the weight estimation logic  74  to determine the estimated weight  78  of the horse  12 . Once the weight estimation logic  74  has been executed, the estimated weight  78  is displayed or otherwise outputted in a format perceivable by the individual. For example, the estimated weight  78  could be provided in an audio format, a video format, a printed format or a combination thereof. 
     As will be well understood by those skilled in the art, once the estimated weight  78  is provided, an owner, a veterinarian or other care provider of the horse  12  can then use the estimated weight  78  to provide care for the horse  12 . For example, the estimated weight  78  can be used to determine dosages of medications, such as anthelmintics (medications for parasites) or anesthesia. The estimated weight  78  can also be used to determine dosages of vitamins or nutrients for the horse  12 . 
     The weight estimation logic  74  utilized by the software program  70  and the apparatus  14  will now be described in more detail. In general, the weight estimation logic  74  was determined by taking measurements (i.e., the measured height  30 , the measured girth  32 , and the measured length  34 ) of a plurality of horses so as to develop a data base including the girth, height and length of a variety of horses. Through regression analysis, and using the variables girth, height and length, the following formula was developed by using the natural logarithm of actual weight as the dependent variable, and the natural logarithms of girth, height and length as independent variables in the following linear regression equation: 
     
       
         Weight Estimate= k   1 ×Girth x1 ×Height x2 ×Length x3   
       
     
     where k 1  is a constant, and x 1 , x 2  and x 3  are exponents. 
     In one preferred embodiment, k 1  is about 0.003591, x 1  is about 1.638339, x 2  is about 0.948065 and x 3  is about 0.397592. 
     The foregoing formula produces weight estimates to an accuracy having an adjusted R 2  of about 0.97559. It should be noted that the units used in each of the examples set forth herein for girth  32 , height  30  and length  34  are in inches. However, it should be understood that other units of measurement could also be used so long as the units of measurement are used consistently. The regression analysis can be performed by any type of analysis for fitting curves to a plurality of data points, such as multiple regression methods, linear regression methods, forward stepwise regression methods, and backward stepwise regression methods. 
     A second model was produced using similar methods as discussed above to estimate the weight of the horse  12  using the measured height  30 , measured girth  32  and the measured length  34 . The second model is based on the following mathematical formula: 
     
       
         Estimated Weight= k   2 ×(Girth× f   1 +Height× f   2 ×Length×f   3   ) x4   
       
     
     where k 2  is a constant, f 1 , f 2 , f 3  are factors, and x 4  is an exponent. 
     When the units used to determine the measured height  30 , measured girth  32  and the measured length  34  are inches, k 2  can be about 0.003633, f 1  can be about 0.056, f 2  can be about 0.031, f 3  can be about 0.13, and x 4  can be about 0.2978070. 
     Two additional models were produced using similar methods as discussed above to estimate the weight of the horse  12  using the measured girth  32  and the measured height  30 . The third model can be based on the following mathematical formula: 
     
       
         Estimated Weight= K   3 ×Girth x5 ×Height x6   
       
     
     where K 3  is a constant and x 5  and x 6  are exponents. 
     When the units used to determine the measured height  30 , measured girth  32  and the measured length  34  are inches, k 3  can be about 0.003538, x 5  can be about 1.989527, and x 6  can be about 1.004088. The third model produced weight estimates to an accuracy having an adjusted R 2  of about 0.97003. 
     The fourth model can be based on the following mathematical formula: 
     
       
         Estimated Weight= K   4 ×(Girth× f   4 +Height× f   5 ) x7   
       
     
     where K 4  is a constant, f 4  and f 5  are factors, and x 7  is an exponent. 
     When the units used to determine the measured height  30 , measured girth  32  and the measured length  34  are inches, k 4  can be about 0.003479, f 4  can be about 0.63, f 5  can be about 0.37 and x 7  can be about 2.999198. The fourth model produced weight estimates to an accuracy having an adjusted R 2  of about 0.97076. It should be understood that the foregoing values set forth in the formulas discussed above, are only examples of suitable constants, factors and exponents. Also, it should be understood that mathematical techniques other than regression analysis could be utilized to produced similar formulas or results. For example, numerical methods for fitting curves or lines to data, such as splines, polynomials, or factorials could be used. As more horses are measured, weighed and added to the data base, it is believed that such constants may be refined so as to give a more accurate estimate of the weight of the horse  12 . The term “about” as used in the claims is intended to cover all such refinements to the constants, factors and exponents so long as the models forming the weight estimation logic determine the estimated weight, as set forth herein. 
     Furthermore, it should be understood that the  224  horses provided in the data base were not placed in categories before determining the constants provided in the foregoing models. It is believed that the foregoing models can be made more accurate by categorizing the horses into predetermined different classes before utilizing the multiple regression analysis. For example, the horses could be categorized into specific groupings, such as miniature horses, ponies, light horses, draft horses, or even wild horses and feral horses, horses in show condition and those that are not, each of which is a category of horses well known in the art. By categorizing the horses in the data base into different specific groupings, it is believed that the constants, factors and exponents discussed herein would be refined to provide a more accurate estimated weight of the horses  12  in each category. 
     The apparatus  14  and the software program  70  can include a button, field or other suitable input device to permit selection of a predetermined class before the estimated weight of the horse  12  is determined. 
     Examples used for determining each of the models are set forth below. It should be understood that the examples set forth herein are illustrative and not limitative. 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Equine Weight Estimation Research Database 
               
             
          
           
               
                 ID 
                 ESTWT 
                 BREED 
                 GENDER 
                 ACTWT 
                 LENGTH 
                 GIRTH 
                 HEIGHT 
                 AGE 
               
               
                   
               
             
          
           
               
                 1 
                 1200 
                 2 
                 1 
                 1140 
                 64 
                 76 
                 68 
                 9.0 
               
               
                 2 
                 900 
                 2 
                 1 
                 1125 
                 67 
                 72 
                 61 
                 6.0 
               
               
                 3 
                 1100 
                 2 
                 1 
                 1150 
                 67 
                 73 
                 63 
                 14.0 
               
               
                 4 
                 1100 
                 2 
                 1 
                 1325 
                 71 
                 78 
                 66 
                 6.0 
               
               
                 5 
                 1200 
                 2 
                 1 
                 1225 
                 69 
                 75 
                 63 
                 12.0 
               
               
                 6 
                 1200 
                 2 
                 1 
                 1285 
                 74 
                 76 
                 64 
                 17.0 
               
               
                 7 
                 1200 
                 2 
                 1 
                 1380 
                 74 
                 78 
                 65 
                 7.0 
               
               
                 8 
                 1100 
                 2 
                 2 
                 1020 
                 71 
                 75 
                 60 
                 2.0 
               
               
                 9 
                 1050 
                 2 
                 2 
                 1025 
                 67 
                 71 
                 61 
                 2.0 
               
               
                 10 
                 950 
                 2 
                 1 
                 965 
                 70 
                 66 
                 60 
                 1.3 
               
               
                 11 
                 900 
                 2 
                 1 
                 875 
                 61 
                 66 
                 58 
                 1.3 
               
               
                 12 
                 925 
                 2 
                 1 
                 920 
                 65 
                 68 
                 60 
                 1.3 
               
               
                 13 
                 950 
                 2 
                 4 
                 1040 
                 68 
                 71 
                 62 
                 1.3 
               
               
                 14 
                 900 
                 2 
                 4 
                 925 
                 63 
                 68 
                 59 
                 1.3 
               
               
                 15 
                 975 
                 2 
                 1 
                 1065 
                 67 
                 71 
                 63 
                 1.3 
               
               
                 16 
                 950 
                 2 
                 1 
                 1002 
                 66 
                 69 
                 61 
                 1.3 
               
               
                 17 
                 900 
                 2 
                 4 
                 870 
                 64 
                 67 
                 58 
                 1.3 
               
               
                 18 
                 925 
                 2 
                 4 
                 960 
                 68 
                 69 
                 59 
                 1.3 
               
               
                 19 
                 975 
                 2 
                 1 
                 1005 
                 67 
                 69 
                 61 
                 1.5 
               
               
                 20 
                 850 
                 2 
                 4 
                 585 
                 55 
                 57 
                 53 
                 0.5 
               
               
                 21 
                 500 
                 2 
                 3 
                 470 
                 53 
                 51 
                 50 
                 0.5 
               
               
                 22 
                 525 
                 2 
                 3 
                 615 
                 56 
                 60 
                 52 
                 0.5 
               
               
                 23 
                 590 
                 2 
                 3 
                 555 
                 56 
                 55 
                 53 
                 0.5 
               
               
                 24 
                 500 
                 2 
                 4 
                 465 
                 51 
                 52 
                 48 
                 0.5 
               
               
                 25 
                 450 
                 2 
                 4 
                 485 
                 51 
                 53 
                 50 
                 0.5 
               
               
                 26 
                 1000 
                 2 
                 2 
                 1010 
                 70 
                 73 
                 60 
                 20.0 
               
               
                 27 
                 800 
                 2 
                 1 
                 774 
                 58 
                 65 
                 52 
                 4.0 
               
               
                 28 
                 1200 
                 2 
                 1 
                 1295 
                 70 
                 77 
                 66 
                 5.0 
               
               
                 29 
                 1200 
                 2 
                 2 
                 1265 
                 76 
                 75 
                 64 
                 3.0 
               
               
                 30 
                 1000 
                 2 
                 2 
                 1070 
                 63 
                 72 
                 60 
                 2.0 
               
               
                 31 
                 1000 
                 2 
                 2 
                 1165 
                 69 
                 71 
                 62 
                 3.0 
               
               
                 32 
                 1000 
                 2 
                 2 
                 970 
                 65 
                 69 
                 61 
                 3.0 
               
               
                 33 
                 1000 
                 2 
                 2 
                 968 
                 60 
                 70 
                 59 
                 2.0 
               
               
                 34 
                 1000 
                 2 
                 1 
                 1195 
                 69 
                 73 
                 63 
                 4.0 
               
               
                 35 
                 1200 
                 2 
                 1 
                 1140 
                 66 
                 73 
                 63 
                 3.0 
               
               
                 36 
                 1100 
                 2 
                 2 
                 1165 
                 73 
                 76 
                 62 
                 6.0 
               
               
                 37 
                 1000 
                 2 
                 1 
                 998 
                 63 
                 69 
                 63 
                 3.0 
               
               
                 38 
                 1000 
                 2 
                 2 
                 1012 
                 66 
                 69 
                 61 
                 3.0 
               
               
                 39 
                 950 
                 2 
                 2 
                 980 
                 63 
                 70 
                 62 
                 2.0 
               
               
                 40 
                 1100 
                 2 
                 1 
                 1235 
                 67 
                 74 
                 65 
                 3.0 
               
               
                 41 
                 1100 
                 2 
                 2 
                 1115 
                 67 
                 71 
                 64 
                 4.0 
               
               
                 42 
                 1200 
                 2 
                 1 
                 1052 
                 67 
                 70 
                 64 
                 3.0 
               
               
                 43 
                 1200 
                 2 
                 1 
                 1265 
                 70 
                 75 
                 68 
                 3.0 
               
               
                 44 
                 1100 
                 2 
                 1 
                 1046 
                 62 
                 69 
                 62 
                 6.0 
               
               
                 45 
                 1200 
                 2 
                 1 
                 1220 
                 70 
                 75 
                 67 
                 5.0 
               
               
                 46 
                 1000 
                 2 
                 2 
                 1050 
                 65 
                 70 
                 62 
                 2.0 
               
               
                 47 
                 900 
                 2 
                 2 
                 724 
                 58 
                 65 
                 51 
                 7.0 
               
               
                 48 
                 900 
                 2 
                 2 
                 988 
                 58 
                 71 
                 62 
                 4.0 
               
               
                 49 
                 1100 
                 2 
                 1 
                 1084 
                 66 
                 72 
                 63 
                 2.0 
               
               
                 50 
                 1000 
                 2 
                 1 
                 996 
                 65 
                 69 
                 63 
                 2.0 
               
               
                 51 
                 700 
                 2 
                 1 
                 684 
                 56 
                 60 
                 56 
                 1.0 
               
               
                 52 
                 700 
                 2 
                 5 
                 694 
                 60 
                 61 
                 56 
                 1.0 
               
               
                 53 
                 950 
                 2 
                 2 
                 998 
                 64 
                 69 
                 62 
                 2.0 
               
               
                 54 
                 900 
                 2 
                 2 
                 1096 
                 70 
                 72 
                 60 
                 3.0 
               
               
                 55 
                 1000 
                 2 
                 1 
                 974 
                 63 
                 69 
                 63 
                 2.0 
               
               
                 56 
                 1000 
                 2 
                 1 
                 1072 
                 64 
                 70 
                 63 
                 2.0 
               
               
                 57 
                 1500 
                 3 
                 2 
                 1690 
                 80 
                 84 
                 66 
                 2.0 
               
               
                 58 
                 1700 
                 3 
                 1 
                 1865 
                 80 
                 86 
                 72 
                 4.0 
               
               
                 59 
                 125 
                 1 
                 2 
                 135 
                 35 
                 36 
                 28 
                 1.0 
               
               
                 60 
                 130 
                 1 
                 4 
                 151 
                 40 
                 39 
                 32 
                 0.4 
               
               
                 61 
                 160 
                 1 
                 1 
                 215 
                 47 
                 42 
                 36 
                 2.0 
               
               
                 62 
                 150 
                 1 
                 5 
                 191 
                 41 
                 42 
                 35 
                 11.0 
               
               
                 63 
                 190 
                 1 
                 2 
                 207 
                 44 
                 42 
                 35 
                 2.0 
               
               
                 64 
                 185 
                 1 
                 5 
                 211 
                 43 
                 43 
                 35 
                 1.0 
               
               
                 65 
                 200 
                 1 
                 1 
                 232 
                 45 
                 46 
                 38 
                 4.0 
               
               
                 66 
                 325 
                 2 
                 4 
                 413 
                 57 
                 49 
                 51 
                 0.4 
               
               
                 67 
                 600 
                 2 
                 5 
                 410 
                 57 
                 51 
                 52 
                 0.4 
               
               
                 68 
                 950 
                 2 
                 2 
                 1012 
                 75 
                 53 
                 59 
                 12.0 
               
               
                 69 
                 870 
                 2 
                 5 
                 815 
                 74 
                 62 
                 61 
                 1.3 
               
               
                 70 
                 850 
                 2 
                 1 
                 890 
                 76 
                 66 
                 59 
                 5.0 
               
               
                 72 
                 1000 
                 2 
                 1 
                 998 
                 77 
                 67 
                 63 
                 2.0 
               
               
                 73 
                 975 
                 2 
                 1 
                 967 
                 77 
                 68 
                 63 
                 2.0 
               
               
                 74 
                 950 
                 2 
                 2 
                 986 
                 74 
                 68 
                 63 
                 3.0 
               
               
                 75 
                 1000 
                 2 
                 1 
                 890 
                 74 
                 68 
                 63 
                 7.0 
               
               
                 76 
                 940 
                 2 
                 5 
                 910 
                 71 
                 68 
                 63 
                 7.0 
               
               
                 78 
                 1150 
                 2 
                 1 
                 1021 
                 74 
                 69 
                 63 
                 5.0 
               
               
                 79 
                 1000 
                 2 
                 1 
                 935 
                 76 
                 69 
                 64 
                 9.0 
               
               
                 80 
                 977 
                 2 
                 1 
                 980 
                 75 
                 69 
                 63 
                 5.0 
               
               
                 81 
                 1350 
                 2 
                 1 
                 1309 
                 84 
                 76 
                 64 
                 10.0 
               
               
                 82 
                 1200 
                 2 
                 1 
                 1192 
                 79 
                 76 
                 65 
                 7.0 
               
               
                 83 
                 1400 
                 2 
                 1 
                 1375 
                 82 
                 76 
                 67 
                 13.0 
               
               
                 84 
                 1350 
                 2 
                 1 
                 1305 
                 81 
                 76 
                 67 
                 6.0 
               
               
                 85 
                 1100 
                 2 
                 1 
                 1060 
                 76 
                 70 
                 60 
                 1.0 
               
               
                 86 
                 1050 
                 2 
                 2 
                 985 
                 77 
                 70 
                 62 
                 10.0 
               
               
                 87 
                 850 
                 2 
                 1 
                 884 
                 72 
                 70 
                 62 
                 7.0 
               
               
                 88 
                 1290 
                 2 
                 2 
                 1210 
                 80 
                 72 
                 60 
                 10.0 
               
               
                 89 
                 1115 
                 2 
                 1 
                 1107 
                 78 
                 72 
                 62 
                 12.0 
               
               
                 90 
                 1050 
                 2 
                 1 
                 1100 
                 81 
                 72 
                 63 
                 5.0 
               
               
                 91 
                 1110 
                 2 
                 1 
                 1154 
                 80 
                 72 
                 60 
                 3.6 
               
               
                 92 
                 900 
                 2 
                 5 
                 1079 
                 79 
                 72 
                 58 
                 1.0 
               
               
                 93 
                 1050 
                 2 
                 2 
                 1015 
                 80 
                 72 
                 63 
                 5.0 
               
               
                 94 
                 950 
                 2 
                 2 
                 1035 
                 77 
                 72 
                 63 
                 13.0 
               
               
                 95 
                 1000 
                 2 
                 1 
                 1003 
                 76 
                 72 
                 63 
                 7.0 
               
               
                 96 
                 1200 
                 2 
                 1 
                 1023 
                 77 
                 72 
                 65 
                 15.0 
               
               
                 97 
                 1250 
                 3 
                 5 
                 1344 
                 82 
                 73 
                 67 
                 2.0 
               
               
                 98 
                 1300 
                 2 
                 1 
                 1143 
                 79 
                 73 
                 59 
                 18.0 
               
               
                 99 
                 1200 
                 2 
                 1 
                 1117 
                 80 
                 73 
                 62 
                 2.0 
               
               
                 100 
                 1200 
                 2 
                 2 
                 1126 
                 80 
                 73 
                 61 
                 12.0 
               
               
                 101 
                 1350 
                 2 
                 1 
                 1116 
                 77 
                 73 
                 65 
                 9.0 
               
               
                 102 
                 1215 
                 2 
                 1 
                 1171 
                 81 
                 73 
                 64 
                 3.0 
               
               
                 103 
                 1200 
                 2 
                 2 
                 1130 
                 80 
                 73 
                 64 
                 7.0 
               
               
                 104 
                 1250 
                 2 
                 1 
                 1204 
                 81 
                 73 
                 64 
                 3.0 
               
               
                 105 
                 1200 
                 2 
                 1 
                 1165 
                 78 
                 73 
                 64 
                 9.0 
               
               
                 106 
                 1000 
                 2 
                 1 
                 1175 
                 77 
                 73 
                 63 
                 19.0 
               
               
                 107 
                 1100 
                 2 
                 1 
                 1075 
                 74 
                 73 
                 64 
                 10.0 
               
               
                 109 
                 1310 
                 3 
                 2 
                 1306 
                 84 
                 74 
                 66 
                 1.0 
               
               
                 110 
                 1150 
                 2 
                 2 
                 1109 
                 78 
                 74 
                 59 
                 3.0 
               
               
                 111 
                 1225 
                 2 
                 2 
                 1225 
                 82 
                 74 
                 61 
                 15.0 
               
               
                 112 
                 1300 
                 2 
                 1 
                 1220 
                 82 
                 74 
                 64 
                 17.0 
               
               
                 113 
                 1100 
                 2 
                 2 
                 1196 
                 81 
                 74 
                 59 
                 5.0 
               
               
                 114 
                 1250 
                 2 
                 1 
                 1190 
                 80 
                 74 
                 63 
                 3.0 
               
               
                 115 
                 1275 
                 2 
                 1 
                 1182 
                 83 
                 74 
                 65 
                 7.0 
               
               
                 116 
                 1250 
                 2 
                 2 
                 1310 
                 84 
                 74 
                 62 
                 15.0 
               
               
                 117 
                 1200 
                 2 
                 1 
                 1280 
                 85 
                 74 
                 66 
                 14.0 
               
               
                 118 
                 1250 
                 2 
                 1 
                 1300 
                 82 
                 74 
                 65 
                 14.0 
               
               
                 119 
                 1300 
                 2 
                 1 
                 1253 
                 84 
                 74 
                 66 
                 25.0 
               
               
                 120 
                 1100 
                 2 
                 2 
                 1105 
                 80 
                 74 
                 64 
                 5.0 
               
               
                 122 
                 1275 
                 2 
                 2 
                 1187 
                 80 
                 75 
                 64 
                 6.0 
               
               
                 123 
                 1280 
                 2 
                 1 
                 1290 
                 86 
                 75 
                 65 
                 7.0 
               
               
                 124 
                 1300 
                 2 
                 2 
                 1215 
                 79 
                 75 
                 61 
                 7.0 
               
               
                 125 
                 1250 
                 2 
                 1 
                 1203 
                 80 
                 75 
                 63 
                 5.0 
               
               
                 126 
                 1250 
                 2 
                 1 
                 1250 
                 79 
                 75 
                 65 
                 9.0 
               
               
                 127 
                 1170 
                 2 
                 1 
                 1177 
                 79 
                 75 
                 65 
                 22.0 
               
               
                 128 
                 1250 
                 2 
                 1 
                 1188 
                 80 
                 75 
                 65 
                 10.0 
               
               
                 129 
                 1280 
                 2 
                 1 
                 1315 
                 81 
                 78 
                 67 
                 10.0 
               
               
                 130 
                 700 
                 3 
                 4 
                 745 
                 67 
                 63 
                 58 
                 0.5 
               
               
                 132 
                 1100 
                 2 
                 1 
                 1125 
                 77 
                 71 
                 61 
                 4.0 
               
               
                 133 
                 1150 
                 2 
                 1 
                 1120 
                 83 
                 71 
                 63 
                 5.0 
               
               
                 134 
                 1075 
                 2 
                 1 
                 1170 
                 82 
                 71 
                 62 
                 10.0 
               
               
                 135 
                 1150 
                 2 
                 1 
                 1055 
                 74 
                 71 
                 62 
                 5.0 
               
               
                 136 
                 1325 
                 2 
                 1 
                 1292 
                 84 
                 77 
                 65 
                 19.0 
               
               
                 137 
                 600 
                 3 
                 2 
                 655 
                 63 
                 59 
                 58 
                 0.4 
               
               
                 138 
                 1275 
                 2 
                 1 
                 1170 
                 78 
                 76 
                 62 
                 3.0 
               
               
                 139 
                 1175 
                 2 
                 2 
                 1190 
                 80 
                 76 
                 62 
                 4.0 
               
               
                 140 
                 1550 
                 3 
                 2 
                 1280 
                 86 
                 76 
                 67 
                 2.0 
               
               
                 141 
                 2225 
                 3 
                 1 
                 1952 
                 96 
                 85 
                 70 
                 7.0 
               
               
                 142 
                 1750 
                 3 
                 2 
                 2175 
                 96 
                 91 
                 70 
                 6.0 
               
               
                 143 
                 1500 
                 3 
                 2 
                 1626 
                 92 
                 82 
                 68 
                 5.0 
               
               
                 144 
                 1500 
                 3 
                 1 
                 1530 
                 85 
                 83 
                 65 
                 19.0 
               
               
                 145 
                 1400 
                 3 
                 1 
                 1460 
                 87 
                 81 
                 67 
                 19.0 
               
               
                 146 
                 1775 
                 3 
                 1 
                 1850 
                 91 
                 92 
                 75 
                 12.0 
               
               
                 147 
                 1875 
                 3 
                 1 
                 1900 
                 92 
                 92 
                 75 
                 5.0 
               
               
                 148 
                 1925 
                 3 
                 1 
                 2200 
                 93 
                 91 
                 75 
                 6.0 
               
               
                 149 
                 2000 
                 3 
                 1 
                 2100 
                 93 
                 87 
                 76 
                 6.0 
               
               
                 150 
                 1765 
                 3 
                 1 
                 1745 
                 91 
                 88 
                 75 
                 9.0 
               
               
                 151 
                 1775 
                 3 
                 1 
                 1732 
                 90 
                 83 
                 73 
                 8.0 
               
               
                 152 
                 1700 
                 3 
                 1 
                 1674 
                 88 
                 85 
                 72 
                 8.0 
               
               
                 153 
                 1600 
                 3 
                 1 
                 1595 
                 89 
                 84 
                 68 
                 8.0 
               
               
                 154 
                 1650 
                 3 
                 1 
                 1659 
                 84 
                 85 
                 72 
                 5.0 
               
               
                 155 
                 1700 
                 3 
                 1 
                 1682 
                 92 
                 84 
                 71 
                 12.0 
               
               
                 156 
                 755 
                 2 
                 2 
                 803 
                 71 
                 67 
                 52 
                 17.0 
               
               
                 157 
                 1000 
                 2 
                 2 
                 981 
                 76 
                 70 
                 57 
                 11.0 
               
               
                 158 
                 1100 
                 2 
                 1 
                 1040 
                 78 
                 70 
                 59 
                 5.0 
               
               
                 159 
                 950 
                 2 
                 2 
                 1013 
                 82 
                 70 
                 58 
                 8.0 
               
               
                 160 
                 900 
                 2 
                 4 
                 990 
                 72 
                 70 
                 56 
                 1.0 
               
               
                 161 
                 1175 
                 2 
                 2 
                 1035 
                 78 
                 70 
                 57 
                 13.0 
               
               
                 162 
                 1150 
                 2 
                 1 
                 1204 
                 81 
                 74 
                 63 
                 17.0 
               
               
                 163 
                 1275 
                 2 
                 1 
                 1180 
                 80 
                 74 
                 64 
                 8.0 
               
               
                 164 
                 1225 
                 2 
                 1 
                 1225 
                 80 
                 74 
                 62 
                 6.0 
               
               
                 165 
                 1245 
                 2 
                 1 
                 1230 
                 83 
                 74 
                 63 
                 4.0 
               
               
                 166 
                 1200 
                 2 
                 4 
                 1283 
                 81 
                 74 
                 63 
                 2.0 
               
               
                 167 
                 1200 
                 2 
                 2 
                 1180 
                 81 
                 74 
                 61 
                 7.0 
               
               
                 168 
                 1200 
                 2 
                 2 
                 1105 
                 78 
                 74 
                 60 
                 10.0 
               
               
                 169 
                 1175 
                 2 
                 1 
                 1140 
                 77 
                 74 
                 63 
                 4.0 
               
               
                 170 
                 1000 
                 2 
                 2 
                 930 
                 75 
                 68 
                 55 
                 6.0 
               
               
                 171 
                 950 
                 2 
                 1 
                 1013 
                 76 
                 68 
                 59 
                 3.0 
               
               
                 172 
                 950 
                 2 
                 5 
                 1030 
                 77 
                 68 
                 61 
                 1.0 
               
               
                 173 
                 1000 
                 2 
                 2 
                 920 
                 76 
                 68 
                 58 
                 18.0 
               
               
                 174 
                 965 
                 2 
                 2 
                 980 
                 75 
                 69 
                 57 
                 7.0 
               
               
                 175 
                 975 
                 2 
                 5 
                 1030 
                 77 
                 69 
                 57 
                 6.0 
               
               
                 176 
                 1200 
                 2 
                 1 
                 1240 
                 80 
                 75 
                 63 
                 4.0 
               
               
                 177 
                 1075 
                 2 
                 1 
                 1182 
                 81 
                 75 
                 65 
                 6.0 
               
               
                 178 
                 1150 
                 2 
                 1 
                 1162 
                 79 
                 75 
                 62 
                 10.0 
               
               
                 179 
                 1350 
                 2 
                 1 
                 1282 
                 81 
                 75 
                 62 
                 7.0 
               
               
                 180 
                 1230 
                 2 
                 1 
                 1255 
                 82 
                 75 
                 63 
                 8.0 
               
               
                 181 
                 1050 
                 2 
                 2 
                 1210 
                 80 
                 75 
                 62 
                 11.0 
               
               
                 182 
                 1275 
                 2 
                 1 
                 1386 
                 84 
                 76 
                 62 
                 11.0 
               
               
                 183 
                 1275 
                 2 
                 2 
                 1230 
                 83 
                 76 
                 61 
                 6.0 
               
               
                 184 
                 1280 
                 2 
                 1 
                 1246 
                 81 
                 76 
                 62 
                 17.0 
               
               
                 185 
                 1100 
                 2 
                 1 
                 1208 
                 80 
                 76 
                 60 
                 4.0 
               
               
                 186 
                 1250 
                 2 
                 2 
                 1206 
                 82 
                 76 
                 63 
                 17.0 
               
               
                 187 
                 1200 
                 2 
                 1 
                 1280 
                 84 
                 76 
                 64 
                 5.0 
               
               
                 188 
                 1175 
                 2 
                 1 
                 1250 
                 79 
                 77 
                 64 
                 11.0 
               
               
                 189 
                 1225 
                 2 
                 2 
                 1327 
                 83 
                 77 
                 63 
                 11.0 
               
               
                 190 
                 1000 
                 2 
                 5 
                 1165 
                 78 
                 77 
                 61 
                 1.0 
               
               
                 191 
                 1305 
                 2 
                 2 
                 1060 
                 78 
                 71 
                 57 
                 7.0 
               
               
                 192 
                 1090 
                 2 
                 1 
                 1045 
                 77 
                 71 
                 58 
                 1.0 
               
               
                 193 
                 975 
                 2 
                 1 
                 1072 
                 78 
                 71 
                 61 
                 7.0 
               
               
                 194 
                 1275 
                 2 
                 1 
                 1137 
                 81 
                 71 
                 65 
                 15.0 
               
               
                 195 
                 1100 
                 2 
                 2 
                 1075 
                 80 
                 71 
                 60 
                 10.0 
               
               
                 196 
                 1180 
                 2 
                 1 
                 1157 
                 79 
                 72 
                 61 
                 16.0 
               
               
                 197 
                 1100 
                 2 
                 1 
                 1194 
                 80 
                 72 
                 60 
                 9.0 
               
               
                 198 
                 1180 
                 2 
                 2 
                 1160 
                 81 
                 72 
                 59 
                 5.0 
               
               
                 199 
                 1100 
                 2 
                 1 
                 1165 
                 79 
                 72 
                 60 
                 4.0 
               
               
                 200 
                 1150 
                 2 
                 1 
                 1198 
                 83 
                 72 
                 63 
                 13.0 
               
               
                 201 
                 1050 
                 2 
                 1 
                 1209 
                 82 
                 72 
                 60 
                 11.0 
               
               
                 202 
                 1100 
                 2 
                 1 
                 1131 
                 80 
                 72 
                 64 
                 21.0 
               
               
                 203 
                 950 
                 2 
                 1 
                 1130 
                 79 
                 72 
                 61 
                 11.0 
               
               
                 204 
                 1150 
                 2 
                 2 
                 1090 
                 77 
                 72 
                 59 
                 1.5 
               
               
                 205 
                 1100 
                 2 
                 1 
                 995 
                 78 
                 72 
                 62 
                 16.0 
               
               
                 206 
                 1240 
                 2 
                 2 
                 1225 
                 83 
                 73 
                 60 
                 11.0 
               
               
                 207 
                 1300 
                 2 
                 1 
                 1295 
                 83 
                 73 
                 62 
                 8.0 
               
               
                 208 
                 1000 
                 2 
                 1 
                 1036 
                 75 
                 73 
                 57 
                 22.0 
               
               
                 209 
                 1275 
                 2 
                 1 
                 1200 
                 83 
                 73 
                 62 
                 4.0 
               
               
                 210 
                 1350 
                 2 
                 1 
                 1220 
                 82 
                 73 
                 64 
                 5.0 
               
               
                 211 
                 1075 
                 2 
                 1 
                 1190 
                 82 
                 73 
                 63 
                 9.0 
               
               
                 212 
                 1175 
                 2 
                 1 
                 1130 
                 78 
                 73 
                 63 
                 9.0 
               
               
                 213 
                 1350 
                 2 
                 1 
                 1393 
                 89 
                 78 
                 63 
                 9.0 
               
               
                 214 
                 1400 
                 2 
                 1 
                 1660 
                 88 
                 83 
                 67 
                 3.0 
               
               
                 215 
                 1325 
                 2 
                 4 
                 1490 
                 86 
                 82 
                 65 
                 3.0 
               
               
                 216 
                 375 
                 2 
                 4 
                 618 
                 65 
                 59 
                 52 
                 0.8 
               
               
                 217 
                 700 
                 2 
                 2 
                 730 
                 70 
                 63 
                 52 
                 7.0 
               
               
                 218 
                 750 
                 2 
                 2 
                 696 
                 69 
                 63 
                 51 
                 19.0 
               
               
                 219 
                 960 
                 2 
                 2 
                 826 
                 70 
                 66 
                 54 
                 15.0 
               
               
                 220 
                 850 
                 2 
                 2 
                 740 
                 68 
                 66 
                 52 
                 15.0 
               
               
                 221 
                 985 
                 2 
                 1 
                 921 
                 74 
                 66 
                 57 
                 7.0 
               
               
                 222 
                 800 
                 2 
                 5 
                 828 
                 69 
                 65 
                 53 
                 4.0 
               
               
                 223 
                 2 
                 2 
                 5 
                 682 
                 66 
                 60 
                 53 
                 0.6 
               
               
                 224 
                 250 
                 2 
                 5 
                 303 
                 49 
                 45 
                 43 
                 0.3 
               
               
                   
               
             
          
         
       
     
     The software program  70  and/or the weight estimation logic  74  can be implemented in any suitable programming language or format. For example, Visual Basic 6.0, or C++ can be utilized to implement the software program  70  and/or the weight estimation logic  74 . Set forth hereinafter is one embodiment of the software program  70 , which was written in Visual Basic 6.0. 
     From the above description it is clear that the present invention is well adapted to carry out the objects and to attain the advantages mentioned herein as well as those inherent in the invention. While presently preferred embodiments of the invention have been described for purposes of this disclosure, it will be understood that numerous changes may be made which will readily suggest themselves to those skilled in the art and which are accomplished within the spirit of the invention disclosed and as defined in the appended claims.