TY - JOUR

T1 - Nondestructive determination of fruit surface area using archimedean buoyancy

AU - Hurtado, Grecia

AU - Lüdeke, Patrick

AU - Knoche, Moritz

N1 - Funding information: Received for publication 17 June 2020. Accepted for publication 3 Aug. 2020. Published online 10 September 2020. This research was funded in part by grants from the Deutsche Forschungsgemeinschaft. The publication of this article was funded by the Open Access Fund of Leibniz Universit€at Hannover. We thank Andreas Meyer and Ulrich Hering for building the displacement apparatus, Heike and Karl Walter Bruggenwirth and Bendix Meyer for the gift of fruit, and Alexander Lang and Andreas Winkler for helpful comments on an earlier version of this manuscript. M.K. is the corresponding author. E-mail: moritz. knoche@obst.uni-hannover.de. This is an open access article distributed under the CC BY-NC-ND license (https://creativecommons. org/licenses/by-nc-nd/4.0/).

PY - 2020/10

Y1 - 2020/10

N2 - Estimates of fruit surface area are often required in physiological and technological studies. The objective was to establish a procedure to accurately quantify the fruit surface area based on Archimedean buoyancy measurements. The setup comprised a fixed, linear stepper motor mounted with its spindle vertical and aligned directly above the pan of an electronic balance. A fruit was clamped to the motor spindle and a beaker of water rested on the balance pan. When the motor was activated, the fruit was progressively immersed, stepwise, in the water. Each vertical displacement step increased the buoyant upthrust on the fruit, which was opposed by a corresponding increase in the downthrust on the balance. Pairs of the step displacement length (mm) and corresponding buoyancy increment (g) values were recorded in an MS Excel (Microsoft, Redmond, WA) spreadsheet using Arduino components. Each displacement step immersed another ‘‘virtual slice’’ of the fruit in the water. From each pair of known displacement–buoyancy measurements, the volume (mL) of that slice could be calculated with high precision based on the known density of the liquid (g·mLL1). With the fruit orientated so that its morphological ‘‘long’’ axis was vertical, for most fruitcrop species, the slice can be assumed to have a circular cross-section. Hence, the slice can be analyzed geometrically as a truncated cone of known height (mm) and known volume (mL). Therefore, the surface area of its outer face is calculable. The surface area of the whole fruit was calculated as the cumulative total of the surface areas of all steps (virtual slices). The procedure was evaluated and calibrated using stainless-steel spheres in place of the fruit. However, the measured surface area was slightly greater than that calculated for a sphere. The calculated and measured areas did not differ by more than 1.7%. The surface area determinations were highly reproducible (CV = 0.95%). The magnitude of the displacement steps affected the variability of the surface area measurements. Increasing the step displacements decreased the measurement variability, but there were no significant effects on the surface area measurements of the surface tension of the liquid or of the wettability of the surface of the fruit or the stainless-steel subject. Using stainless-steel spheres (diameter, 5–60 mm) or rubber truncated cones (mean diameter, 8–45 mm) revealed an excellent agreement between the measured and calculated surface areas. Using tomatoes, grapes, blueberries, and strawberries, the measured surface areas were in excellent agreement with those calculated from the fruit dimensions and appropriate geometrical assumptions. The results demonstrate that the surface areas of fruit with approximately circular cross-sections normal to their morphological axes can be determined with high accuracy and reproducibility using Archimedean buoyancy.

AB - Estimates of fruit surface area are often required in physiological and technological studies. The objective was to establish a procedure to accurately quantify the fruit surface area based on Archimedean buoyancy measurements. The setup comprised a fixed, linear stepper motor mounted with its spindle vertical and aligned directly above the pan of an electronic balance. A fruit was clamped to the motor spindle and a beaker of water rested on the balance pan. When the motor was activated, the fruit was progressively immersed, stepwise, in the water. Each vertical displacement step increased the buoyant upthrust on the fruit, which was opposed by a corresponding increase in the downthrust on the balance. Pairs of the step displacement length (mm) and corresponding buoyancy increment (g) values were recorded in an MS Excel (Microsoft, Redmond, WA) spreadsheet using Arduino components. Each displacement step immersed another ‘‘virtual slice’’ of the fruit in the water. From each pair of known displacement–buoyancy measurements, the volume (mL) of that slice could be calculated with high precision based on the known density of the liquid (g·mLL1). With the fruit orientated so that its morphological ‘‘long’’ axis was vertical, for most fruitcrop species, the slice can be assumed to have a circular cross-section. Hence, the slice can be analyzed geometrically as a truncated cone of known height (mm) and known volume (mL). Therefore, the surface area of its outer face is calculable. The surface area of the whole fruit was calculated as the cumulative total of the surface areas of all steps (virtual slices). The procedure was evaluated and calibrated using stainless-steel spheres in place of the fruit. However, the measured surface area was slightly greater than that calculated for a sphere. The calculated and measured areas did not differ by more than 1.7%. The surface area determinations were highly reproducible (CV = 0.95%). The magnitude of the displacement steps affected the variability of the surface area measurements. Increasing the step displacements decreased the measurement variability, but there were no significant effects on the surface area measurements of the surface tension of the liquid or of the wettability of the surface of the fruit or the stainless-steel subject. Using stainless-steel spheres (diameter, 5–60 mm) or rubber truncated cones (mean diameter, 8–45 mm) revealed an excellent agreement between the measured and calculated surface areas. Using tomatoes, grapes, blueberries, and strawberries, the measured surface areas were in excellent agreement with those calculated from the fruit dimensions and appropriate geometrical assumptions. The results demonstrate that the surface areas of fruit with approximately circular cross-sections normal to their morphological axes can be determined with high accuracy and reproducibility using Archimedean buoyancy.

KW - Archimedes

KW - Buoyancy

KW - Fruit surface area

KW - Surface area

KW - Water displacement

UR - http://www.scopus.com/inward/record.url?scp=85092383585&partnerID=8YFLogxK

U2 - 10.21273/HORTSCI15240-20

DO - 10.21273/HORTSCI15240-20

M3 - Article

AN - SCOPUS:85092383585

VL - 55

SP - 1647

EP - 1653

JO - HortScience

JF - HortScience

SN - 0018-5345

IS - 10

ER -