dark matter halo using Equations \[eqn:halor\] and \[eqn:haloz\], where we calculate the gradients numerically, and use the mid-plane approximation $v^2=-RF$ [@Kuijken1989A].

Both tracers operate in drastically different numerical regimes. The total observed rotation curve is often near 100km/s, while the observed vertical force gradient has a value of -0.004 km$^2$ s$^{-2}$ pc$^{-2}$. As these numbers are so drastically different, the combined $\chi^2$ would be dominated by the rotation curve decomposition. We therefore normalise the data of each force by its maximum value in that range, such that the total $\chi^2$ error is calculated as $$\begin{aligned}
\chi^2 &=& \chi^2_R + \chi^2_z\,\label{eqn:halochi}\, ,\\
\chi^2_R &=& \sum_{R_i} \frac{v_\textrm{total}^2 - v_{  \relax
  \ifmmode
    \textrm{\textsc{HI}}
  \else
    \textsc{H{\smaller}I}
  \fi
}^2 - v_\textrm{stellar}^2 - v_\textrm{halo}^2}{\max({v_\textrm{total})^2}}\,\,,\label{eqn:halochi1}\\
\chi^2_z &=& \sum_{R_i} \frac{\left(  dF_{z,\textrm{diff}}/dz   \right)^2}{\min(dF_{z,\textrm{total}}/dz)^2}\,\,,\label{eqn:halochi2}\\
\frac{dF_{z,\textrm{diff}}}{dz} &=& \frac{dF_{z,\textrm{total}}}{dz} \nonumber \\
&-& \frac{dF_{z,\textrm{gas}}}{dz}+\frac{dF_{z,\textrm{stellar}}}{dz}+\frac{dF_{z,\textrm{halo}}}{dz}\,\,,\end{aligned}$$ where the $R_i$ values are all data points within the respective fitting ranges used for the vertical and radial directions. We have tested many variations of Equations \[eqn:halochi1\] and \[eqn:halochi2\], including converting and integrating both the tracers back into forces so that they could compared more directly. The overall problem however remained, as the two forces were too different in strength and the errors in the radial component would 