ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT AZOJETE September 2021. Vol. 17(3):415-428 Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818 www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 415 ORIGINAL RESEARCH ARTICLE PREDICTION OF MASS AND VOLUME OF TACCA INVOLUCRATA TUBERS USING PHYSICAL CHARACTERISTICS A. O. Raji and B. O. Oyefeso* Department of Agricultural and Environmental Engineering, Faculty of Technology, University of Ibadan, Ibadan, Nigeria *Corresponding author’s email address: oyefesobabatunde@gmail.com 1.0 Introduction Tacca (Tacca involucrata, Schum. and Thonn.) is an important member of the root and tuber crops which serve as staple foods in many parts of the tropics. Although the crop is grown at subsistent level in the Eastern part of Nigeria, it is yet to be domesticated in many regions of Africa where it is still found predominantly in the wild and reproduces asexually on its own at a later period (Raji and Ahemen, 2011). It is noteworthy that some parts of the plant are useful for various purposes while the tuber is well known for its starch which has almost zero percentage fat content and therefore, suitable for industrial uses especially in the ARTICLE INFORMATION ABSTRACT Knowledge of physical properties of crops is necessary for the development of processing machines. Relationships between the various physical properties of crops could also be useful in ensuring proper handling and more efficient design of processing machineries. This study was therefore, aimed at developing mathematical models for predicting the mass and volume of Tacca involucrata tubers using some physical characteristics of the crop. Physical characteristics of Tacca tubers at average moisture content of 73.3% (wet basis) namely axial dimensions, Arithmetic Mean Diameter (AMD), Geometric Mean Diameter (GMD), projected areas along the three mutually- perpendicular axes, criterion area (Ac), mass and volume were determined. Out of 240 samples used in the study, data from 120 samples were used for development of the prediction models while the remaining were used for validation of the developed models. Data analysis tool in Microsoft Excel (2013 version) was used to carry out regression analysis and develop the predictive models. Statistical parameters namely correlation coefficient, coefficient of determination, root mean square error and mean bias error were used to determine the goodness of fit of the predictive models. The mass and volume models were divided into three classifications namely: single and multiple variable regression models based on axial dimensions; single and multiple variable regression models based on the projected areas; single variable regression model based on volume (for mass prediction only). Average length, width, thickness, AMD and GMD of the tubers were 71.88, 57.22, 46.71, 58.60 and 57.57 mm respectively while average criterion area, longitudinal, cross-sectional and transversal projected areas were 2614.24, 2580.61, 2097.04 and 3165.07 mm2 respectively. Average mass and volume of the tubers were 129.30 g and 111.55 cm3 respectively. All the developed models performed well in predicting the mass and volume of Tacca tubers (R2 ≥ 0. 905) except for those based on the axial dimensions as single independent variables (R2 ≤ 0.890). The predicted mass and volume of Tacca tubers were not significantly different (p ≤ 0.05) from the experimentally observed values for all the classifications considered. Mass and volume modelling based on a single variable of any of the projected areas was the most convenient modelling for Tacca tubers since it involves the use of a single image capturing device and the whole measurement could therefore, be automated. The developed models would be useful for automated sorting and packaging of Tacca tubers. © 2021 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved. Submitted 16 March, 2021 Revised 14 June, 2021 Accepted 16 June , 2021 Keywords: Tacca tubers physical properties geometrical attributes mass and volume modelling Raji and Oyefeso.: Prediction of mass and volume of Tacca involucrata tubers using physical characteristics. AZOJETE, 17(3):415-428. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 416 pharmaceutical industries (Omojola, 2013; Raji and Ahemen, 2011). Its tuber and starch are traditionally used for treatment of diarrhoea and bleeding (internal and external). Its stems are also useful for making mats while the leaves are used for treatment of nausea and vomiting (Ofoefule et al., 2004). Tacca tuber processing involves a lot of unit operations which are largely carried out manually in the developing countries where the crop is available for use. The increasing global demand for its starch necessitates commercialisation of its production which inevitably requires mechanization of its processing and handling operations (Ahemen and Raji, 2017). Knowledge of the engineering properties of the tubers is therefore, needed as they constitute essential data for the design of machineries for processing and handling operations (Mohsenin, 1986). Sizing by weighing mechanism is recommended for the irregular-shaped products (Stroshine and Hamann, 1994) which is typical of most agricultural products. Determining the relationships among mass, axial dimensions and projected areas may also be useful and applicable in the automation of sorting processes for agricultural products (Stroshine and Hamann, 1994; Pathak et al., 2020). Though these relationships or models may be cumbersome to establish, once established, they can easily be used to quickly predict the unknown parameters in the relationships. Axial dimensions, projected areas, mass and volume of agricultural products are important parameters in sorting and grading machines (Naderiboldaji et al., 2009). Crops are often graded on the basis of size and the projected area, although it may be more economical to develop a machine which would grade by mass or volume of the product. Therefore, this will necessitate establishing relationships between mass or volume and other physical attributes of the crops (Khanali et al., 2007; Jahromi et al., 2007a). Mathematical modelling helps to develop functional relationships between different crop variables and thereby, make it easy to predict the values of the dependent (unknown) variables based on the different values of the independent (known or measured) variable(s). The development of models that could be used to predict the mass and volume of agricultural products based on the dimensions and the projected areas will give a good description of the size and shape of the products and this will be of tremendous help in the design of processing machines as well as sorting and handling equipment for the products. Several researches have been carried out to predict some physical properties of interest using developed regression models based on the geometrical attributes of the crops. Some of these studies include development of mass models for kiwi fruit (Lorestani and Tabatabaeefar, 2006), date fruit (Jahromi et al., 2007a), pomegranate fruit (Khoshnam et al., 2007), apple (Meisami-asl et al., 2009), fava beans (Lorestani and Ghari, 2012), potato (Berberoglu et al., 2014), Sohiong fruit (Vivek et al., 2017), persimmon fruits (Subbarao and Vivek, 2017), apricot fruit (Rashidi et al., 2018), Belleric myrobalan fruit (Pathak et al., 2020), Indian coffee plum (Barbhuiya et al., 2020) and pepper berries (Azman et al., 2021). Mass and volume prediction models were developed for tangerine fruit (Khanali et al., 2007), citrus fruits (Omid et al., 2010), sweet cherry (Khadivi-Khub and Naderiboldaji, 2013), and Nigeria-grown sweet and Irish potatoes Arid Zone Journal of Engineering, Technology and Environment, September, 2021; Vol. 17(3):415-428. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 417 (Oyefeso and Raji, 2018). Mass and surface area of bergamot fruits were also predicted based on axial dimensions, projected areas and volume (Jahromi et al., 2007b). All these studies were carried out for prediction of various properties such as mass, volume, surface area etc with varying degrees of success in the development of their predictive models. However, there appears to be scarcity of information on prediction models for Tacca tuber which are useful in its automated sorting and handling. This study therefore, aimed at developing mathematical models for predicting mass and volume of Tacca tuber which are grown in Nigeria using some of their physical characteristics. This is with the ultimate aim of generating data which could serve as a quick guide in the design of sorting and handling equipment for the tubers. 2. Materials and Methods 2.1 Sample preparation Some Tacca tubers were randomly selected and purchased from a pit storage stock harvested within a period of one month from Tse-Ikyor and Tse-Adawa villages, Benue State, Nigeria. The study was conducted on 240 tubers which were sorted into different fractions based on their weights and labelled to enable proper identification and documentation of data from the samples. 2.2 Moisture content determination Moisture content of the tuber was determined according to ASABE (2003) standard method which involved drying the samples in an oven maintained at temperature of 103 ± 2°C until constant weight was attained (Ahemen and Raji, 2017). 2.3 Determination of geometrical attributes The physical characteristics determined include mass, volume, length (L), width (W), thickness (T), Arithmetic Mean Diameter (AMD), Geometric Mean Diameter (GMD), projected areas along the three mutually-perpendicular axes (PAL, PAW and PAT) and the Criterion Area (AC). The individual mass of each of the Tacca tubers was measured using an electronic weighing balance (A&D Co. LTD, AND EK-6100i model, Japan) with an accuracy of 0.1g. Volume of each of the tubers was obtained using the water displacement method (Mohsenin, 1986; Khanali et al., 2007; Jahromi et al., 2007). The axial dimensions (L, W and T) were measured with the aid of a digital Vernier calliper (Carrera Precision model CP8812-T 12-Inch, United States) having an accuracy of 0.01 mm. The three mutually-perpendicular axes were determined by allowing each tuber crop to drop freely under gravity and then rest on its natural axis. At this natural resting position, the axial dimensions along the three mutually-perpendicular axes were obtained as length (the longest dimension), width (the axial dimension perpendicular to the length) and thickness (the axial dimension which is perpendicular to both length and width) (Tabatabaeefar, 2002; Raji and Ahemen, 2011; Ahemen and Raji, 2017). The three mutually perpendicular axes of the tubers are illustrated in Figure 1. Raji and Oyefeso.: Prediction of mass and volume of Tacca involucrata tubers using physical characteristics. AZOJETE, 17(3):415-428. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 418 Figure 1: Major axial dimensions and projected areas of Tacca tubers AMD and GMD were calculated from the measured axial dimensions according to Equations 1 and 2 respectively (Pathak et al., 2020). (1) ( ) (2) where: AMD = Arithmetic Mean Diameter (mm); GMD = Geometric Mean Diameter (mm); L = length or longest diameter of the tuber (mm); W = width or the axial dimension perpendicular to the length (mm); T = thickness or diameter which is perpendicular to both length and width (mm). Forty samples were selected at random for developing mass and volume models based on the projected areas. The projected areas along the three mutually-perpendicular axes PAL (along the longitudinal plane), PAC (along the cross-sectional plane) and PAT (along the transverse plane) were obtained by image processing (Khanali et al, 2007; Jahromi et al., 2007). The image processing technique involved the acquisition of the images of the tubers using a digital camera and the projected areas were then obtained by reading the images in portable pixel map (ppm) format as input into an algorithm developed in Fortran 95 programming language. An image acquisition lighting box (Figure 2) was constructed to flood the samples with light and ensure proper capturing of the images by preventing shadow-casting. The algorithm extracted the total number of pixels making up the acquired image enclosed in a rectangle of known area and the number of pixels making up the projection of Tacca tuber in the image. The projected area was calculated within the algorithm according to Equation 3. L T w PAC PAL PAT W L T Arid Zone Journal of Engineering, Technology and Environment, September, 2021; Vol. 17(3):415-428. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 419 Figure 2: The image acquisition lighting box (3) where: PA = Projected area of the tuber (mm2); NPP = Number of pixels of tuber projection; NTP = Total number of pixels making up the enclosing rectangle; AR = Area of the smallest enclosing rectangle (mm2). Table 1 shows the areas of the smallest enclosing rectangle for the acquired images along the longitudinal, cross-sectional and transverse orientations. Table 1: Areas of the smallest circumscribing rectangles for the acquired images S/N Orientation Projected Area (mm2) Area of Circumscribing Rectangle (mm2) 1 Longitudinal PAL 2 Cross-sectional PAC 3 Transverse PAT The Criterion Area (Ac) of the tubers was calculated according to Equation 4 (Tabatabaeefar, 2002). (4) where: Ac = Criterion Area (mm2); PAL = projected area along the longitudinal plane (mm2); PAC = projected area along the cross-sectional plane (mm2) and PAT = projected area along the transverse plane (mm2). 2.4 Development of the prediction models Out of the 240 tubers used in this study, data from 120 samples were used for actual development of the prediction models while the remaining 120 samples were used for validation of the developed models. All the data were averaged over three replications. Mathematical models for predicting the mass and volume of Tacca tubers were developed by regression analysis using the Data analysis tool in Microsoft Excel (2013 version). The regression analysis involved estimating the likely relationship between the dependent variables (mass and volume) and one or more physical properties of the tubers as independent variable(s). The base The translucent screens Raji and Oyefeso.: Prediction of mass and volume of Tacca involucrata tubers using physical characteristics. AZOJETE, 17(3):415-428. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 420 Different regression models that were suggested in analysing the data obtained include linear ( ), exponential ( ), logarithmic ( ), power ( ) and polynomials of order 2 to 6 ( ). However, the regression models that best describe the relationships that exist between the dependent and independent variables are the only ones presented in the study. Suitability and adequacy of fit of the developed mass and volume models were determined on the basis of highest coefficients of determination (R2) and lowest error estimates. The mass and volume models were divided into three classifications based on the independent variables as follows: i. single and multiple variable regression models based on axial dimensions namely length (L), width (W), thickness (T), AMD and GMD of the tubers for the first classification; ii. single and multiple variable regression models based on the projected areas ( ) for the second classification; iii. single variable regression model based on volume (for mass prediction only) for the third classification. The mass of the tuber was predicted using the measured volume and a simple linear regression obtained is of the form shown in Equation 5. (5) Where: M = mass of Tacca tubers (g); V = volume of Tacca tubers (cm3); k = intercept on the M-axis; = slope or gradient of the equation. Model validation involved using the developed models to estimate the mass and volume of the tubers and then determining the closeness of the predicted values to the experimental or observed values. Highest coefficient of determination (R2) and lowest error estimates namely mean bias error (MBE) and root mean square error (RMSE) were used as the basis for determining the goodness of fit of the developed models. Values of R2, MBE and RMSE for the data were calculated using Equations 6, 7 and 8 respectively. ∑ ( ( ) ( )) (∑ ( ( )) ) (∑ ( ( )) ) (6) ∑ ( ( ) ( )) (7) ∑ ( ( ) ( )) (8) where: Y(exp,i) is the ith experimentally observed value; Y(pre,i) is the ith predicted value; N is the number of observations. 3. Results and Discussion The minimum and maximum values of the measured physical properties of Tacca tubers at average moisture content of 73.3 ± 1.2% (wet basis) are as presented in Table 2. These physical properties include the axial dimensions (length, width, thickness, AMD and GMD), projected areas, criterion area, mass and volume of the tubers. These data are of significance in the design of processing machines and handling equipment for the tubers. Accurate packaging of the tubers based on mass or volume could also be ensured based on these physical characteristics. Arid Zone Journal of Engineering, Technology and Environment, September, 2021; Vol. 17(3):415-428. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 421 Table 2: Some physical properties of Tacca tubers Physical Characteristics Number of Samples Range L (mm) 240 34.81 – 114.24 W (mm) 240 20.05 – 94.58 T (mm) 240 24.22 – 70.70 AMD (mm) 240 29.72 – 97.92 GMD (mm) 240 28.82 – 97.36 PAL (mm2) 40 602.77 – 5,277.89 PAC (mm2) 40 588.94 – 4,283.63 PAT (mm2) 40 840.44 – 6,792.78 AC (mm2) 40 677.38 – 5451.43 M (g) 240 14.80 – 566.40 V (cm3) 240 13.00 – 460.00 3.1 Mass and volume prediction models Mass and volume prediction models developed based on the three classifications are as presented in Tables 3 and 4 respectively. Statistical parameters (R, R2, RMSE and MBE) for validation of the mass and volume models are presented in Tables 5 and 6 respectively. There were no significant differences (p ≤ 0.05) between the predicted and experimentally observed values of mass and volume of Tacca tubers. Table 3: Mass models for Tacca tubers based on the selected geometrical attributes Model No. Classification Independent variable Relation R2 1 First L (mm) 0.890 2 W (mm) 0.854 3 T (mm) 0.762 4 L, W, T (mm) 0.930 5 AMD (mm) ( ) ( ) 0.987 6 GMD (mm) ( ) ( ) 0.980 7 Second PAL (mm2) ( ) 0.986 8 PAC (mm2) ( ) 0.982 9 PAT (mm2) ( ) 0.985 10 PAL, PAc, PAT (mm2) ( ) ( ) ( ) 0.982 11 Ac (mm2) ( ) 0.996 12 Third V (cm3) 0.965 Raji and Oyefeso.: Prediction of mass and volume of Tacca involucrata tubers using physical characteristics. AZOJETE, 17(3):415-428. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 422 Table 4: Volume models for Tacca tubers based on the selected geometrical attributes Model No. Classification Independent variable Relation R2 1 First L (mm) 0.881 2 W (mm) 0.840 3 T (mm) 0.738 4 L, W, T (mm) 0.905 5 AMD (mm) ( ) ( ) 0.955 6 GMD (mm) ( ) ( ) 0.949 7 Second PAL (mm2) ( ) 0.984 8 PAC (mm2) ( ) 0.982 9 PAT (mm2) ( ) 0.978 10 PAL, PAc, PAT (mm2) ( ) ( ) ( ) 0.979 11 Ac (mm2) ( ) 0.992 Table 5: Comparison of predicted and observed mass of Tacca tubers Model No. Model type Independent variable R R2 MBE RMSE 1 Power L (mm) 0.959 0.920 -1.517 18.354 2 Quadratic W (mm) 0.906 0.822 1.669 26.727 3 Power T (mm) 0.861 0.742 -2.848 32.229 4 Linear (multiple) L, W, T (mm) 0.972 0.945 4.273 15.789 5 Quadratic AMD (mm) 0.993 0.985 0.353 7.700 6 Quadratic GMD (mm) 0.990 0.980 0.512 8.921 7 Power PAL (mm2) 0.992 0.984 0.274 9.860 8 Power PAC (mm2) 0.990 0.980 -0.143 11.004 9 Power PAT (mm2) 0.992 0.983 -0.183 9.975 10 Linear (multiple) PAL, PAc, PAT (mm2) 0.991 0.982 0.018 10.385 11 Power Ac (mm2) 0.997 0.994 0.076 6.074 12 Linear V (cm3) 0.979 0.959 -1.457 12.911 Arid Zone Journal of Engineering, Technology and Environment, September, 2021; Vol. 17(3):415-428. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 423 Table 6: Comparison of predicted and observed volume of Tacca tubers Model No. Model type Independent variable R R2 MBE RMSE 1 Power L (mm) 0.940 0.883 -3.097 19.647 2 Quadratic W (mm) 0.907 0.822 2.711 23.547 3 Power T (mm) 0.834 0.695 -2.025 30.679 4 Linear L, W, T (mm) 0.957 0.916 1.926 16.529 5 Quadratic AMD (mm) 0.975 0.950 1.701 12.484 6 Quadratic GMD (mm) 0.971 0.943 1.809 13.372 7 Power PAL (mm2) 0.988 0.977 -0.201 9.642 8 Power PAC (mm2) 0.987 0.975 -0.102 10.116 9 Power PAT (mm2) 0.988 0.976 -0.249 9.879 10 Linear (multiple) PAL, PAc, PAT (mm2) 0.989 0.979 -0.011 9.173 11 Power Ac (mm2) 0.994 0.987 0.056 7.266 3.1.1 First classification models (axial dimensions, AMD and GMD) Mass and volume models based on axial dimensions as single independent variable numbered 1, 2 and 3 in Tables 3 and 4 had low fitness with low R2 and higher MBE and RMSE. This thereby indicates that no single axial dimension can be reliably used to predict mass and volume of Tacca tubers. However, mass and volume models based on length gave better results than the ones based on width and thickness. Mass and volume models based on multiple regression of the three axial dimensions (L, W and T) had relatively good fitness with R2 of 0.930 and 0.905 respectively. Models on the basis of AMD and GMD as independent variables gave consistently high R2 (≥ 0.958). This clearly indicates that these models can consistently predict the mass and volume of the tubers with high level of accuracy. However, the models are multi-variate, relying on all the three axial dimensions in their computations and are therefore, more complex than those that are univariate. Although mass and volume of the tubers may not be effectively predicted on the basis of any of the axial dimensions individually due to low R2, it can be suggested that the models having length as the independent variable can still be adopted. These models (based on length) are preferred to the models that consider all the three mutually-perpendicular axial dimensions despite their lower R2 values, because it is more practicable, less cumbersome and faster to handle and compute. Variations in mass and volume of the tubers against length as the independent variable are presented in Figures 3 and 4 respectively. Figure 3: Mass model of Tacca tubers on length at average moisture content of 73.3% (wet basis) M = 0.003L2.484 R² = 0.890 0 100 200 300 400 20 40 60 80 100 120 M as s o f T ac ca t u b er s (g ) Length of Tacca tubers (mm) Raji and Oyefeso.: Prediction of mass and volume of Tacca involucrata tubers using physical characteristics. AZOJETE, 17(3):415-428. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 424 Figure 4: Volume model of Tacca tubers on length at average moisture content of 73.3% (wet basis) 3.1.2 Second classification models (projected and criterion areas) Mass and volume models developed based on second classification involving the projected and criterion areas are presented in Tables 3 and 4, as models numbered 7 to 11. These models gave very consistent and relatively higher R2 and could therefore, be suggested as the best models to be adopted for the estimation of mass and volume of Tacca tubers. Models based on the Criterion Area (Ac) also had consistently high R2, indicating their suitability for accurately predicting the mass and volume of Tacca tubers. However, the models rely on all the three projected areas along mutually-perpendicular axes which makes them more cumbersome to compute. Best predictive mass and volume models (with highest R2) in the second classification for the tubers were those on the basis of PAL as the independent variable and their plots are presented in Figures 5 and 6 respectively. Figure 5: Mass model of Tacca tubers on PAL at average moisture content of 73.3% (wet basis) V = 0.002L2.499 R² = 0.881 0 100 200 300 400 20 40 60 80 100 120 V o lu m e o f T ac ca t u b er s (c m 3 ) Length of Tacca tubers (mm) M = 0.0008(PAL)1.506 R² = 0.986 0 100 200 300 400 0 1,000 2,000 3,000 4,000 5,000 6,000 M as s o f T ac ca t u b er ( g ) PAL (mm2) Arid Zone Journal of Engineering, Technology and Environment, September, 2021; Vol. 17(3):415-428. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 425 Figure 6: Volume model of Tacca tubers on PAc at average moisture content of 73.3% (wet basis) 3.1.3 Third classification Models (Volume) This classification was considered only for predicting the mass of the tubers with volume as the independent variable. The mass models based on volume is numbered 12 on Table 3. Variations in mass against the volume of the tubers are presented in Figure 7. For the third classification, the mass model had R2 of 0.961 which indicates a high level of accuracy in its prediction and could therefore, be recommended for adoption in predicting the mass of the tubers. Figure 7: Mass model of Tacca tubers on volume at average moisture content of 73.3% (wet basis) V = 0.0011(PAL)1.446 R² = 0.984 0 50 100 150 200 250 300 0 1,000 2,000 3,000 4,000 5,000 6,000 V o lu m e o f T ac ca t u b er ( cm 3 ) PAL (mm2) M = 1.121V + 3.045 R² = 0.965 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 M as s o f th e T ac ca t u b er ( g ) Volume of the Tacca tubers (cm3) Raji and Oyefeso.: Prediction of mass and volume of Tacca involucrata tubers using physical characteristics. AZOJETE, 17(3):415-428. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 426 4. Conclusions Selected physical properties of Tacca tubers were determined in this study and predictive models were determined based on these physical characteristics to estimate the mass and volume of the tubers. Length, width, thickness, arithmetic mean diameter (AMD) and geometric mean diameter (GMD) ranged from 34.81 to 114.24, 20.05 to 94.58, 24.22 to 70.70, 29.72 to 97.92 and 28.82 to 97.36 mm respectively. Longitudinal, cross-sectional, transversal and criteria projected area of the tubers ranged from 602.77 to 5277.89 mm2, 588.94 to 4283.63, 840.44 to 6792.78 and 677.38 to 5451.43 mm2 respectively. Mass and volume of the tubers ranged from 14.80 to 566.40 g and 13.00 to 460.00 cm3 respectively. Mass and volume models developed based on the length and projected area along the longitudinal plane (PAL) were the best models on the basis of a single variable of axial dimension and projected area respectively. The predictive models based on AMD, GMD and criterion area had consistently high correlation and error estimates, although they are more cumbersome to compute since they depend on multiple attributes in their computations. There existed a very good correlation between mass and volume of the tubers, thereby indicating that mass of the tubers can be reliably predicted with the volume. Mass and volume modelling based on a single variable of any of the projected areas can be considered as the most reliable and convenient modelling for Tacca tubers since it involves the use of a single image capturing device and the whole measurement could therefore, be automated. The models developed in this study will be useful for automated sorting and packaging of Tacca tubers. References Ahemen, SA. and Raji, AO. 2017. Moisture-dependent physical properties of Tacca involucrata tubers. Journal of Food Process Engineering, 40(5): e12541. https://doi.org/10.1111/jfpe.12541 Azman, PNMA., Shamsudin, R., Che-Man, H. and Ya’acob, ME. 2021. Mass modelling of pepper berries (Piper nigrum L.) with some physical properties. Food Research, 5 (Suppl. 1): 80-84. https://doi.org/10.26656/fr.2017.5(S1).047 Barbhuiya, RI., Nath, D., Singh, SK., and Dwivedi, M. 2020. Mass modeling of Indian coffee plum (Flacourtia jangomas) fruit with its physicochemical properties. International Journal of Fruit Science, 20(Suppl. 3): S1110-S1133. doi:10.1080/15538362.2020. 1775161 Berberoglu, E., Altuntas, E. and Dulger, E. 2014. Development of adequate mathematical models to predict the mass of potato varieties from their physical attributes. Journal of Agricultural Faculty of Gaziosmanpasa University, 31(3): 1-9. Jahromi, MK., Jafari, A., Rafiee, S., Keyhani, AR., Mirasheh, R. And SS. Mohtasebi 2007a. Some physical properties of date fruit (cv. Lasht). Agricultural Engineering International: the CIGR E- journal, Manuscript FP 07 019, Volume IX. Jahromi, MK., Rafiee, S., Mirasheh, R., Jafari, A., Mohtasebi, SS. and Varnamkhasti, MG. 2007b. Mass and surface area modelling of bergamot (Citrus medica) fruit with some physical attributes. Agricultural Engineering International: the CIGR E-journal, Manuscript FP 07 029, Volume IX. Khadivi-Khub, A. and Naderiboldaji, M. 2013. Predicting models for mass and volume of the sweet cherry (Prunus avium L.) fruits based on some physical traits. Canadian Journal of Plant Science, 93: 831-838. https://doi.org/10.1111/jfpe.12541 https://doi.org/10.26656/fr.2017.5(S1).047 Arid Zone Journal of Engineering, Technology and Environment, September, 2021; Vol. 17(3):415-428. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 427 Khanali, M., Varnamkhasti, MG., Tabatabaeefar, A. and Mobli, H. 2007. Mass and volume modelling of tangerine (Citrus reticulate) fruit with some physical attributes. International Agrophysics, 21(1): 329-334. Khoshnam, F., Tabatabaeefar, A., Varnamkhasti, MG. and Borghei, A. 2007. Mass modelling of pomegranate (Punica granatum L.) fruit with some physical characteristics. Scientia Horticulturae, 114(1): 21-26. Lorestani, AN. and Tabatabaeefar, A. 2006. Modelling the mass of kiwi fruit by geometrical attributes. International Agrophysics, 20(1): 135-139. Lorestani, AN. and Ghari, M. 2012. Mass modelling of fava beans (Vicia faba L.) with some physical characteristics. Scientia Horticulturae, 133(1): 6-9. Meisami-asl, E., Rafiee, S., Keyhani, A. and Tabatabaeefar, A. 2009. some physical properties of apple cv. ‘Golab’. Agricultural Engineering International: the CIGR E-journal, Manuscript 1124, Volume XI. Mohsenin, NN. 1986. Physical properties of plant and animal materials. Gordon and Breach Science Publishers, New York., pp. 20-89. Naderiboldaji, M., Jannatizadeh, A., Tabatabaeefar, A. and R. Fatahi 2009. Development of 11 mass models for Iranian Apricot fruits based on some physical attributes (cv. Shahroud-8 and Gheysi-2). Journal of Agricultural Technology, 4(1): 65-76. Ofoefule, SI., Osuji, AC., and Okorie, O. 2004. Effects of physical and chemical modifications on the disintegrant and dissolution properties of T. involucrata starch. Bio-Research, 2(1): 97-102. Omid, M., Khojastehnazhand, M. and Tabatabaeefar, A. 2010. Estimating volume and mass of citrus fruits by image processing technique. Journal of Food Engineering, 100(2): 315-321. Omojola MO. 2013. Tacca starch: a review of its production, physicochemical properties, modification and industrial uses. African Journal of Food, Agriculture, Nutrition and Development, 13(4): 7972-7985. Oyefeso, BO. and Raji, AO. 2018 Estimating mass and volume of Nigerian grown sweet and Irish potato tubers using their geometrical attributes. Adeleke University Journal of Engineering and Technology, 1(1): 123–130. Pathak, SS., Pradhan, RC., and Mishra, S. 2020. Mass modeling of Belleric myrobalan and its physical characterization in relation to post-harvest processing and machine designing. Journal of Food Science and Technology, 57(4): 1290-1300. https://doi:10.1007/s13197-019-04162-1 Raji, AO. and Ahemen, SA. 2011. Engineering properties of Tacca involucrata tubers. Journal of Food Process Engineering, 34(1): 267-280. Rashidi, M., Beheshty-Asl, H. and Behboodi, S. 2018. Apricot mass modeling based on geometrical attributes. Agricultural Engineering Research Journal, 18(1): 1-5. Stroshine R. and Hamann DD. 1994. Physical Properties of Agricultural Materials and Food Products. Course Manual, Purdue Univ. Press, USA. http://www.aginternetwork.net/whalecomwww.sciencedirect.com/whalecom0/science?_ob=PublicationURL&_tockey=%23TOC%235159%232007%23998859998%23666146%23FLA%23&_cdi=5159&_pubType=J&view=c&_auth=y&_acct=C000056118&_version=1&_urlVersion=0&_userid=2789858&md5=0ce8257602ae10b749b8380f2e59db20 Raji and Oyefeso.: Prediction of mass and volume of Tacca involucrata tubers using physical characteristics. AZOJETE, 17(3):415-428. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: oyefesobabatunde@gmail.com 428 Subbarao, KV. and Vivek, K. 2017. Models for predicting the mass of persimmon (diospyros kaki) fruits by some physical properties. International Food Research Journal, 24(6): 2353-2359. Tabatabaeefar, A. 2002. Size and shape of potato tubers. International Agrophysics, 16(1): 301- 305. Vivek, K., Mishra, S., and Pradhan, RC. 2017. Physicochemical characterization and mass modelling of sohiong (Prunus nepalensis L.) fruit. Journal of Food Measurement and Characterization, 12(2): 923-936. doi:10.1007/s11694-017-9708-x