## 2 Materials
### Basilisk
The combined conservation equations that govern both the fluid and the solid (if there is motion) are written as follows:  
* Continuity equation: \[\
abla\cdot\mathbf{u}^{*}=0,\quad\text{over}\ \Omega.\] (11)
* Combined momentum equations: \[\left(\frac{\partial\mathbf{u}^{*}}{\partial t^{*}}+\mathbf{u}^{*}\cdot\
abla\mathbf{u}^{ *}\right)=-\
abla p^{*}+\frac{1}{\mathcal{R}e_{t}^{*}}\
abla^{2}\mathbf{u}^{*}- \mathbf{\lambda}^{*}\quad\text{over}\ \Omega,\] (12)  
\[(\rho_{r}^{*}-1)V_{b}^{*}\left(\frac{d\mathbf{v}_{b}^{*}}{dt}- \mathcal{F}r^{*}\frac{\mathbf{g}}{g}\right)-\int_{B(t)}\mathbf{\lambda}^{*}d\mathbf{x}^{*} =\mathbf{0},\quad\text{over}\ B(t), \tag{13}\] \[I_{b}^{*}\frac{d\mathbf{\omega}^{*}}{dt^{*}}+\mathbf{\omega}^{*}\times I _{b}^{*}\cdot\mathbf{\omega}^{*}+\sum_{j}\left(F_{c}\right)_{j}^{*}\times\mathbf{R}_{ j}^{*}+\int_{B(t)}\left(\mathbf{\lambda}^{*}\times\mathbf{r}^{*}\right)\cdot d\mathbf{x}^{*} =\mathbf{0},\quad\text{over}\ B(t), \tag{14}\]  
\[\mathbf{u}^{*}-(\mathbf{v}_{b}^{*}+\mathbf{\omega}^{*}\times\mathbf{r}^{*})=\mathbf{0},\quad\text {over}\ B(t), \tag{15}\]  
where \(\mathbf{u}^{*}\) stands for the fluid velocity vector, \(p^{*}\) the pressure, \(\mathbf{\lambda}^{*}\) the distributed Lagrange multiplier vector, \(\mathbf{r}^{*}\) the position vector with respect to body gravity center, \(I_{b}^{*}\) the body inertia tensor, \(\mathbf{R}^{*}\) the vector between the body gravity center and the contact point for eventual contact (but not the case in this study), \(V_{b}^{*}\) the body volume, \(M^{*}\) the body mass, \(\mathbf{g}^{*}\) the gravity acceleration, \(\rho_{r}^{*}=\rho_{b}/\rho_{f}\) the density ratio, and \(g^{*}\) the gravity acceleration magnitude. The twine Reynolds number \(\mathcal{R}e_{t}\) is defined as \(\mathcal{R}e_{t}^{*}=\frac{\rho_{f}u_{\text{stw}}d_{t}}{\mu_{f}}\), and the Froude number \(\mathcal{F}r^{*}\) is defined as \(\mathcal{F}r^{*}=\frac{gd_{t}}{u_{\text{stw}}^{2}}\). The full details of this method are reported in [PERSON] et al. [40], [PERSON] [45], [PERSON] et al. [46]. Using the aforementioned method, the hydrodynamic force about the \(i\)th body center of mass can be computed as:  
\[\mathbf{f}_{i}^{*}=\int_{B_{i}(t)}\mathbf{\sigma}^{*}\cdot\mathbf{n}dS^{*} \tag{16}\]  
where, \(\mathbf{\sigma}^{*}\) and \(\mathbf{n}\) are, respectively, the stress tensor, which is the summation of the Lagrange multipliers of the rigid body, and the outward-oriented unit normal vector to \(\partial B_{i}\). Hence, the total force acting on all the twines is \(\sum\limits_{i}^{N_{t}^{*}}\mathbf{f}_{i}^{*}\). In this study, the main focus was the drag force (therefore, the drag coefficient). As the total force is the summation of the individual forces acting on each twine, it is legitimate to consider the twine's projected area for the calculation of the drag coefficients. For each twine, the dimensional drag force is written as:  
\[\mathbf{f}_{D,\text{CFD}}^{i}=\frac{1}{2}\rho_{f}C_{D,\text{CFD}}^{i*}A^{i}|\mathbf{u} _{\text{stw}}|\mathbf{u}_{\text{stw}}, \tag{17}\]then the average drag coefficients of the net can be defined as:  
\[\widehat{C^{*}_{D,\text{CFD}}}=\frac{2\sum\limits_{i=0}^{N_{t}^{*}}f_{D,\text{ CFD}}^{i}}{\rho_{f}Au_{\text{stw}}^{2}} \tag{18}\]  
where \(A^{i}\) is the cross-sectional area of the \(i\)th twine. Since \(A^{i}\) remains constant for all twines, we can write \(A=\sum\limits_{i=0}^{N_{t}^{*}}A^{i}\). In this study, the drag coefficients were projected onto the net intrinsic reference frame (Section 3.5 ). Its axes' unit vectors are defined as normal and axial (respectively, \(\mathbf{n}\) and \(\mathbf{a}\)). Figure 6:0