Studies of fruit physiology and agricultural and food technology often require information regarding the fruit surface area. Typical examples are measurements of water uptake or transpiration (Beyer et al., 2005) or of gas exchange (e.g., O2, CO2, C2H4) through fruit surfaces (Cameron and Yang, 1982; Knee, 1991). These processes are often described using Fick’s law of diffusion, for which knowledge of fruit surface area is a prerequisite for calculation of the permeability of the fruit skin (Cameron and Yang, 1982; Knee, 1991). Moreover, in studies of agrichemical spray application, the dose of the active ingredient retained per fruit depends (among other factors) on the fruit size or, more precisely, fruit surface area (Schlegel and Schönherr, 2002). In food technology, the estimation of the fruit surface area is central to calculations of fruit mass and heat transfer, which are important for shelf life determination, drying and freezing technologies, designing storage facilities, and applications of postharvest treatments (coatings, heat treatments, and designing minimally processed products) (Moreda et al., 2009).
Commonly, fruit surface areas are estimated by approximating the fruit shape using simple three-dimensional (3D) geometrical models. The surface area is then calculated from the major fruit dimensions. For closely spherical fruit, such as cherry tomatoes (Solanum lycopersicum L.) or (less so) apples [Malus domestica (Suckow) Borkh.], the surface area may be calculated from the mean of the three orthogonal diameters of the fruit. This assumes that the fruit resembles a sphere or ellipsoid (Baten and Marshall, 1943; Clayton et al., 1995). The sphere and ellipsoid models may underestimate the actual surface area of fruit by as much as 15 to 18% for some apple cultivars. This is because their shape significantly departs from ellipsoidal (the stylar and stem cavities), thereby compromising the underlying assumption (Clayton et al., 1995). Similar 3D geometry approaches have been used to estimate surface areas of plum (Prunus domestica L. subsp. domestica) (Baten and Marshall, 1943), pear (Pyrus communis L.) (Baten and Marshall, 1943; Scharwies et al., 2014), and pepper (Capsicum annuum L. var. annuum) (Marcelis and Baan Hofman-Eijer, 1995). Moreover, different cultivars, even of the same species, differ markedly in shape. Additionally, the shapes of some common fruitcrops, such as strawberry (Fragaria ×ananassa Duchesne ex Rozier), are so far removed from being ellipsoidal that they require more sophisticated and complex 3D geometrical models with measurements of multiple dimensions, not just the three orthogonal ones.
Several alternative methods have been used for the direct determination of the fruit surface area. These include measuring the area of the fruit skin after peeling (destructive) or measuring the area of a film applied to the fruit as a coating that is subsequently peeled off (Clayton et al., 1995). Other methods that have been used to quantify the fruit surface area are image processing (Sabliov et al., 2002), structured light systems (Sakai and Yonekawa, 1992), atomic force microscopy (Hershko et al., 1998), and 3D scanners (Eifert et al., 2006). All these methods are laborious, and some require specific and/or costly equipment. To our knowledge, the Archimedes principle has not been used to quantify the fruit surface area. According to this principle, the buoyancy experienced by a body submerged in water equals the weight of the displaced water. Because the density of water is close to 1 g·cm−3, the weight of the displaced water (g) can be considered numerically equal to the volume (cm−3) of the submerged body. The Archimedes principle has been used to quantify fruit volume (Baumann and Henze, 1983; Clayton et al., 1995; Drazeta et al., 2004; Mohsenin, 1970; Sabliov et al., 2002).
The objective of our study was to investigate whether Archimedean buoyancy measurements could be used to quantify the surface areas of fruit with a circular cross-section (perpendicular to their morphological long axis). Setups for measuring fruit volume and fruit density are available in many horticultural laboratories and may be converted to surface area meters using the procedure described here.
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