NUMERICAL TECHNIQUES FOR ESTIMATING THE SURFACE-AREAS OF ELLIPSOIDS REPRESENTING FOOD MATERIALS

Food materials (seeds, grains, fruits and vegetables) resembling the s hape of a general ellipsoid were modelled for accurate determination o f surface area from measurements of their three principal dimensions. The process of surface area estimation involved partitioning the ellip soid into an appropriate number of elliptical discs, determination of the surface areas of the edges of the discs and summing them to obtain the total surface area. Two types of perimeters were used to determin e the edge surface areas: (1) the average perimeter; and (2) the root mean square perimeter. For edge length, three measures were considered : (1) parallel to the axis; (2) inclined to the axis; and (3) length o f the elliptical are. Six different surface area models were developed by combining the two perimeters with the three edge lengths and these were validated against exact analytical solutions for a sphere, prola te spheroid and oblate spheroid. The models with parallel edge length always produced the greatest underestimate of surface area and they ca nnot, in fact, give accurate results, even if a large number of discs is used. The models with inclined and elliptic are edge length perform ed well in the entire range of width/length of prolate spheroids and t hickness/length of oblate spheroids. For practical computations involv ing the general ellipsoid, a minimum of 100 discs was found to be suff icient, as it produced a maximum deviation of less than +/- 0.1% from 1000 discs for all the models and geometries considered. The performan ces of two approximate formulae for the surface area of the general el lipsoid were also studied for comparison but they were suitable only i n the near-spherical range. Predictions were made and compared with th e reported surface areas for a few paddy varieties, which were experim entally determined by previous researchers, and were found to deviate within + 7.0 to + 30.0%. (C) 1998 Silsoe Research Institute.