# Freeze-Thaw Pre-Treatment of Cassava Tubers to Improve Efficiency of Mechanical Peeling
## 3 Results and Discussion  
### Characteristics of Cassava Tubers  
The characterization of cassava tubers in this study is presented in Table 2. The mass proportion of the peels in the cassava tubers ranged from 13.3 to 15.6%, which is in accordance to the results (8.5 to 17%) reported by [PERSON] [13]. The observed thickness of the peels ranged from 2.7 to 3.3 mm in this study. A wider thickness range for peels of 1.2 to 4.1 mm was reported by [PERSON] et al. [11]. The range of diameter and length of cassava tubers varied from 53.1 to 90.9 mm and from 194 to 320 mm, respectively. The force necessary to penetrate the cassava tuber peels and cassava tuber flesh varied from 4.4 to 5.6 (N/mm\({}^{2}\)) and from 2.8 to 3.8 (N/mm\({}^{2}\)), respectively. Similarly, a peel penetration force of 3.3 to 5.47 (N/mm\({}^{2}\)) for cassava tubers was reported by [PERSON] et al. [11]. Other characteristic parameters including the weight of the tuber, the dry matter of the peel, and the dry matter of tuber in this study are similar to previous studies with slight differences [11; 24]. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multirow{2}{*}{**Unit**} & \multirow{2}{*}{**Coded Factors**} & \multicolumn{5}{c}{**Levels**} \\ \cline{3-8}  & & & \(-\)**2** & \(-\)**1** & **0** & **1** & **2** \\ \hline Rotational speed of brushes & rpm & X\({}_{1}\) & 550 & 700 & 850 & 1000 & 1150 \\ Peeling time & min & X\({}_{2}\) & 1 & 2 & 3 & 4 & 5 \\ Thawing temperature & \({}^{\circ}\)C & X\({}_{3}\) & 50 & 60 & 70 & 80 & 90 \\ Incubation time & s & X\({}_{4}\) & 0 & 30 & 60 & 90 & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Independent variables and limit levels for response surface study. A weight range of about 900 g (415-1287 g) was observed in the sample, associated with the mean \(\pm\) SD of \(733.4\pm 254.7\). Sorting of the agricultural products prior to packaging or processing is a routine in post-harvest operations. Therefore, based on the properties of the normal distribution and after checking for normality, the weight range of the tubers was limited to 500-900 g, which as approximation of \"mean \(\pm\) 1 \(\times\) SD\" should cover more than two- thirds of the population. Effect of the Rotational Speed of the Brushes, the Peeling Time, and FTP on the Peeling Process for Cassava Tubers  
The RSM design matrix for the rotational speed of the brushes, the peeling time, and FTP are presented in Table 3 together with the peeled surface area and the peel loss. The peeled surface area and peel loss ranged from 14.9 to 97.9% and 4.2 to 37.5%, respectively, by variation of condition parameters (rotational speed of brushes, peeling time, thawing temperature, and incubation time). The average peeled surface area and peel loss of cassava tubers was 64.1 and 18.7%, respectively. The mathematical equation obtained from RSM for the peeled surface area (PSA) of cassava tubers is as follows:  
\[ \begin{split} PSA=-148.87408+0.135258\cdot v-14.11093\cdot t_{p} +2.4693\cdot T-3.72594\cdot t_{t}\ +0.135243\\ \cdot v\cdot t_{p}+0.005847\cdot v\cdot t_{t}\ -0.76666\cdot t_{p} \cdot T+1.61357\cdot t_{p}\cdot t_{t}\ -0.000283\cdot v^{2}\\ -6.01193\cdot t_{p}^{2}-0.006776\cdot t_{t}^{2}-0.001856\cdot v \cdot t_{p}\cdot t_{t}\end{split}  \tag{3}\]  
where \(PSA\) is the peeled surface area after FTP and the peeling process (%), \(v\) is the rotational speed of the brushes (rpm), \(t_{p}\) is the peeling time (min), \(T\) is the thawing temperature (\({}^{\circ}\)C), and \(t_{t}\) is the incubation time (s). It was observed that increasing the rotational speed of the brushes, the peeling time, thawing temperature, and incubation time had a positive effect on the peeled surface area. The effects of individual variables and their interaction on the peeled surface area are shown in Table 4. The accuracy of the model was indicated by \(R^{2}\) and adjusted \(R^{2}\) of 0.890 and 0.813, respectively. The _MAPE_ was 13.8%.