Apple Shape and Rolling Orientation

Theoretical Analysis of Stability of Axially Symmetric Rotating Objects with Regard to Orienting Apples

“…Similarly, numerous model parameter sets yield the same length and diameter but result in vastly different shapes. Whitelock et al (2006) developed a more restrictive measurement set by including a measure of the diameter (d) of apples in the plane perpendicular to the stem/calyx axis and 1.3 cm from the calyx end. Model parameter sets were developed using this measurement system with one caveat.…”

“…If φ is allowed to vary, then the optimization routine almost always returns the minimum value of φ allowed. Table 1 reproduces the table of apple cultivars and measurements in Whitelock et al (2006) and adds parameters for the corresponding optimal apple model.…”

“…Thus, the stem/ calyx axis corresponds to the axially symmetric z-axis of the ellipsoid, and the length-to-diameter ratio (LE/D) of the Stout et al (1971). [b] Data taken from Whitelock et al (2006). apple corresponds to the a/b ratio of the ellipsoid.…”

“…From table 2, it can be seen that the LE/D ratio for selected cultivars of apples have ranges of 0.7 to 1.1, while the average mass ranges from 140 to 215 g. For this study, the a/b ratios of ellipsoids were varied to simulate the range of LE/D ratios. A density of 0.856 g m -3 (Whitelock et al, 2006) and a mass of 189 g were used for a standard ellipsoid model. The masses of ellipsoids were varied as a percentage of this standard mass to encompass the range of values exhibited by apple cultivars.…”

Technical Note: Algorithms for Parameterization of Dynamics of Inertia-Based Apple Orientation

“…There is a long history of attempts to orient apples (Stout et al, 1971;Carlson, 1987;Throop et al, 2005;Whitelock et al, 2006). Unfortunately, the commercial impact of orientation systems continues to be limited due to mechanical complexity, cost, error, or some combination thereof.…”