# Parameter Study for the Ice Adhesion Centrifuge Test
## 2 Materials and Methods
Generally, the centrifuge test uses centripetal forces to apply shear stress to the ice and remove it from the test surface. The prepared sample was fixed in the centrifuge, in which the iced sample was spun at a constantly increasing rate until the ice was sheared off. Separation was detected by a piezoelectric cell (MTN/1185C Series, Monitran Ltd., Penn, UK) when the ice hit the centrifuge wall and was correlated to the rotational speed of the centrifuge rotor. This speed (angular velocity \(\omega\) in rad/s) was used to calculate the shear strength of ice to the substrate, according to the following equation:  
\[\tau=\frac{F}{A}=\frac{m_{ice}\,\omega^{2}\,r}{A} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multirow{2}{*}{**Static Ice**} & \multicolumn{3}{c}{**Impact Ice (Ice Wind Tunnel Velocity)**} \\ \cline{3-5}  & & **40 m/s** & **60 m/s** & **95 m/s** \\ \hline Temperature (\({}^{\circ}\)C) & \(-8\) (\(\pm 0.5\)) & \(-8\) (\(\pm 0.1\)) & \(-8\) (\(\pm 0.1\)) & \(-8\) (\(\pm 0.1\)) \\ Icing duration & 90 min & 55 s & 50 s & 50 s \\ Resulting ice mass (g) & 3.0 & 2.0 (\(\pm 0.1\)) & 2.2 (\(\pm 0.1\)) & 2.5 (\(\pm 0.1\)) \\ Ice area (cm\({}^{2}\)) & 9 & 9 & 9 & 9 \\ Liquid water content (g/m\({}^{3}\)) & n.a. & 1.2 & 1.0 & 0.6 \\ Median volume diameter (\(\mu\)m) & n.a. & 15 & 15 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Conditions for the ice formation processes. Figure 2: Test sample preparation with: (**a**) a silicone mold for static ice; (**b**) specimen holder for ice wind tunnel insertion for impact ice formation. where \(m_{icc}\) is the mass of ice (kg), \(r\) is the radius of the rotating beam at the mid-length ice position (m), and \(A\) is the surface area of the adherent interface (m\({}^{2}\)) [21]. The calculated values in this study express the adhesive strength of the ice. In addition to the ice types, the centrifuge acceleration speed varied from 100 rpm/s (10.472 rad/s\({}^{2}\)) and 200 rpm/s (20.944 rad/s\({}^{2}\)) to 300 rpm/s (31.416 rad/s\({}^{2}\)) for the static ice test samples. Figure 4a shows the device-specific force evolutions during the test runs with different acceleration speeds up to the maximum centrifuge rotational speed (10,000 rpm) for an ice mass of 3 g. For 300 rpm/s, the maximum speed was reached after 34 s, and for 100 rpm/s, after 100 s. Furthermore, the differences that occurred between the ice masses for impact ice (compared with Table 3) also have an effect on the strength evolution during the centrifuge test. Figure 4b depicts the correlations between the ice masses and adhesion strength for an acceleration speed of 200 rpm/s that was used for impact ice adhesion assessments in this study. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Static Ice** & **Impact ice: 40 m/s** & **Impact Ice: 60 m/s** & **Impact Ice: 95 m/s** \\ \hline glaze ice, compact, & glaze ice, brittle icing over & glaze ice, flat in center, icing & mixed ice, icing towards wind, \\ well-defined, sharp edges & the edges & over the edges & no ice on sides \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Ice types for ice adhesion tests. Figure 3: View inside the centrifuge test device with: (**a**) test sample with ice formation placed in the centrifuge; (**b**) test sample after fixation. Four to eight test samples per material type were available for the testing period and used randomly over the whole duration of this study with changing ice types and centrifuge acceleration speeds.