Low-speed high-torque applications, e.g. wind energy generation, favor high number of pole solutions. This usually results in a dominating leakage flux in traditionally radial or axial field machines while the output power remains constant. Within Transverse Flux Machines (TFM) an increase in output power proportional to the number of poles is achieved by traversing the flux direction. However, TFMs still suer from a relative large leakage reducing their application in present industries. In order to research this leakage, fast and relatively accurate 3-D models are essential. To date, Finite Element Models (FEM) is dominantly used to calculate these 3-D magnetic fields. However, FEM requires a large number of elements, hence is very time consuming (hours for a single solution). A fast and more accurate parameterized model is essential to maximize the power factor while maintaining a high torque density. In this paper the validity of a 3-D analytical magnetic charge model is used to investigate its applicability to model TFM topologies. As such, an automated parametric search has been undertaken to minimize machine volume, i.e. without considering power factor although with fixed constraints on magnetic flux density and slot leakage. Although this does not provide a global optimized minimum, it is surely interesting for the experienced machine designer that wants to further understand the physics of this machine. To illustrate the accuracy of the magnetic charge model, the error of the final result of such a parametric search is compared to a 3-D FE-model, which shows an error in force prediction of only 8.9%.