## 2 Cable Model and Effective Length in 3D Twisted Conductors
### Introducing Twisting: Lay Length Definition
#### 2.2.2 Range of Lay Lengths Studied  
To capture a broad range of twisting scenarios, \(\lambda\) is swept from 0.1 m (very tight twist) up to 5.0 m (nearly parallel). The total extruded length of each model is equal to \(\lambda\). To achieve exactly one full turn over length \(\lambda\), the model is parameterized such that \(z\) runs from 0 to \(\lambda\), and the segment centroid is rotated 360\({}^{\circ}\) about the \(z\)-axis over these interval steps. This is a complex geometry design which was achieved by changing the software's Global Coordinate System to cylindrical when extruding the 2D areas into three-dimensional volumes alongside the z-axis and offsetting its angle by a certain degree on every step of the extrusion.  
The 2D cross-sectional areas for one-fifth of the cable (Figure 4a) are first imported in IGES format. Then, by adjusting the lay length parameter in the APDL batch script (LayLength), the same 2D model is extruded and replicated at varying pitches to produce different twisted geometries. Below is an excerpt of the APDL code to create the volumes:  
Figure 3: A schematic representation of the five-segment cable twisted around the \(z\)-axis.  
!----------------------------------------------------------------------Define Parameters. LayLength = 1 NumberOfDivisions = 16 OffSetAng = 360/NumberOfDivisions OffSetZ = LayLength/NumberOfDivisions!-------------------------------------------------------------------Making the 1/5 slice volume twisted.!-------------------------------------------------------------------Change Active CS to Cylindrical. CSYS,1!-------------------------------------------------------------------Do Loop - Modeling one twisted volume at a time. /prep7 *D0,i,3,88,1 ASEL,S,,i VEXT,ALL,,0,OffSetAng,OffSetZ,,, VGEN,NumberOfDivisions,1,,,OffSetAng,OffSetZ,,0 VSEL,S,,1,NumberOfDivisions, VADD,ALL!-------------------------------------------------------------------Partitioning all the conductors and the air. ALLSEL,ALL VPTN,ALL!-------------------------------------------------------------------Copy the 1/5 slice section five times. VGEN,5,ALL,,0,72,0,0,0 ```  
In this macro:  
* LayLength sets the total helical pitch (0.1-5 m), while NumberOfDivisions controls how many increments (VEXT and VGEN) will be used to create the continuous twist;  
Figure 4: Developing the 3D twisted geometry process staring from the 2D 1/5 slice model (**a**), 3D 1/5 slice conductor (**b**), 3D 1/5 slice conductor with air (**c**) and the full model volume (**d**).  
* The variables OffSetAng and OffSetZ are computed, ensuring a uniform and perisse helical extrusion in cylindrical coordinates;
* A DO loop (from lines *DO,i,3,88,1) selects each 2D area in turn (ASEL), then extrudes (VEXT) and replicates (VGEN) the geometry with the appropriate angular and \(z\)-axis offset (Figure 4b,c);
* Once the single-fifth twist is complete, it is repeated five times (VGEN,5,ALL) to form the full 360\({}^{\circ}\) cross-section (Figure 4d).  
By simply changing LayLength in this script (for instance, from 0.1 m to 5 m), the same input 2D areas yield different 3D twisted models. Subsequent steps--such as meshing, material property assignments, and boundary conditions--are identical for each geometry, enabling a systematic investigation of how the lay length affects AC and DC resistive losses.