Establishment and optimization of the method for determining fruit firmness based on applied load and deflection distance in sweet cherry

【Objective】Firmness is a key quality attribute of sweet cherry fruit, directly affecting postharvest storage duration, transportation tolerance, and consumer acceptance. Fruits with insufficient firmness are prone to mechanical damage during logistics, leading to rapid decay and reduced market value. Therefore, it is crucial to standardize non-puncture detection of fruit firmness for quality evaluation and germplasm screening in sweet cherry breeding and production. However, the existing nonpuncture testing techniques suffer from high equipment costs, complex operation or limited applicability to specific fruit varieties. The objective of this study is to establish and optimize the non- puncture testing parameters for determining the fruit firmness based on the applied load and deflection distance. 【Methods】The Firmtech eleven soft fruit firmness non-puncture tester system was used throughout the experiment. The principle is measuring the force required to achieve a specific deformation or the deformation caused by a specific force. The firmness of 200 sweet cherry fruits was determined by a pressure threshold of 250 g. The mean of the firmness measurements of 200 fruits was set as the‘true value’, and the interval of ±5% standard deviation of the‘true value’was set as the confidence interval. The 200 firmness measurements were divided into three levels, and the sampling amounts of 100, 75, 50, 25, and 5 measurements were taken according to the stratified sampling method. Each sampling amount was repeated 1000 times. The mean value of the extracted samples was calculated as the virtual determination value of the sampling amount. The probability of the virtual determination value falling within the confidence interval was counted. Subsequently, the fruit firmness of four varieties was determined with different pressure thresholds (150, 200, 250, 300 and 350 g) and deflection threshold modes (0.5, 1.0, 1.5 and 2.0 mm). Correlation analysis was carried out between fruit firmness and applied load or deflection distance. Finally, the firmness of 14 sweet cherry varieties from four major production areas was measured using the optimized 200 g pressure threshold mode.【Results】As the sampling amount increased, the proportion of the fruit firmness determination of four varieties falling into the confidence interval gradually increased. When the sampling amount was 75, the proportion of the firmness determination values falling into the confidence interval was more than 99%. When the sampling amount was more than 75, the coefficient variation of the four varieties was less than 0.02. Thus, 75 fruits were determined to be the optimal sampling amount, balancing accuracy and operational efficiency. In the pressure threshold mode, the fruit firmness measurements showed a synchronous increase with the increasing applied load. Moreover, the correlation between fruit firmness and process applied load was stronger at low applied load, especially at 200 g. In the deflection threshold mode, the fruit firmness measurement was the highest when the deflection distance was 1.5 mm. Moreover, the 1.5 mm deflection threshold mode resulted in more stable firmness measurements and better correlation with deflection distance for sweet cherry fruits. The firmness of 14 varieties from four production areas based on the 200 g pressure mode showed that there were significant differences in firmness among different varieties in the same production area. Among the five varieties from Beijing, Brooks exhibited the lowest firmness (214.74 g·mm-1 ) and Lapins showed the highest firmness (310.15 g·mm-1 ). The firmness of Tieton, Linglongcui and Summit fruits from Hebei were 192.76, 220.03 and 257.77 g ·mm- 1 , respectively. Among the four varieties of sweet cherry from Sichuan, Hongdeng exhibited the highest firmness (137.17 g · mm-1 ) and Satonishiki exhibited the lowest firmness (84.42 g ·mm-1 ). The firmness of Tieton and Summit from Liaoning were 242.14 and 183.16 g·mm-1 , respectively. The fruit firmness from the same variety also varied across production areas. The firmness of Tieton from Liaoning was higher than Beijing and Hebei. The firmness of Summit from Hebei was higher than Beijing and Liaoning.【Conclusion】It is recommended to use 75 fruit consumption and combine with 200 g applied load or 1.5 mm deflection distance for detection. These parameters ensure high accuracy and stability of measurement results, as evidenced by the low coefficient of variation and strong correlation with relevant variables. The firmness of 14 sweet cherry varieties from four production areas showed that there were significant differences in firmness among different varieties from the same production area, and the magnitude of variation of the same cultivar across production areas was also significant. The results provide a technical reference for unifying sweet cherry firmness testing protocols in both academic research and industrial applications.