APPENDIX A 



Location of Impound Points and Relationship of 

 Radial Distance to Road Distance 



Location of Impound Points 



The impound point concept is a very convenient one for a study 

 of this type. On the average, all the poultry in a given supply hand is 

 assumed to be located at impound points on a circle which is a certain 

 distance inside that band. The research problem is to determine, under 

 all conditions of density and distances, the location of this circle on 

 which the impound points are located. Since the broilers are located 

 evenly over the surface of the supply band, the problem is to locate a 

 circle within the supply hand which divides the area of the band (and 

 the quantity of poultry) in half. This is found by the following equation: 



/ Q2 4- N^ 

 V 2 



Where: 



P = radial distance in miles from the processing plant at the center 

 to the circle of impound points 



N = radial distance in miles from the processing plant at the center 

 to the inner rim of the supply band 



Q = radial distance in miles from the processing plant at the center 

 to the outer rim of the supply band 



One use of this equation nuist be made for Supply Band I because 

 for that supply band the inner rim and the processing plant coincide 

 at a point, so N has a value of zero. Such a situation is shown in Figure 

 A-1 for Supply Band I, 5,000 pound per year density level. Solving by 

 the above equation results in the impound points being located on a 

 circle 11.5 radial miles from the processing plant at the center: 



/ 16.3^ + 02 _ 

 ^ — V 2 ~ 



The other use of this equation is for all other supply bands. For 

 these the inner rims are some distance from the center. Figure A-2 illus- 

 trates Supply Band II at the 5,000 pound density level where Q is 28.2 

 miles and N is 16.3 miles from the processing plant at the center. Solv- 

 ing by the above equation results in the impound points Ijeing located 

 on a circle 23 radial miles from the processing plant at the center. 



For a supply band where the inner rim and the processing plant 

 coincide at a point (Supply Band I) the impound points will always 

 be on a circle with a radial distance equal to 70.71 percent of the radius 

 of the band. This is the maximum distance that impound points can be 

 from the center of a circle or inner perimeter of a band. For supply 

 bands whose inner rims are some distance from the processing plant at 

 the center, the impound points will fall on a circle that ranges between 

 50 and 70.71 percent of the width of the band from the inner rim. This 



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