1 Gas Mixer

The stationeers gas mixer ratio is skewed by temperature differences. If you set the mixer ratio to $r$ and the temperatures of the two inputs are not identical, you get a different ratio in the output.

\begin{array}{l} r^{'} & = \frac{\frac{r}{T_{a}}}{\frac{r}{T_{a}} + \frac{1 - r}{T_{b}}} \\ Δ m_{a} & = r^{'} Q \\ Δ m_{b} & = (1 - r^{'}) Q \\ m_{a}^{'} & = m_{a} + Δ m_{a} \\ m_{b}^{'} & = m_{b} + Δ m_{b} \end{array}

The quantity of gas transferred appears to be based on the volume $V$ of the output pipe network ( each pipe segment is 100L of volume).

\begin{array}{l} V 12.2 & = T_{a} Δ m_{a} + T_{b} Δ m_{b} \\ = T_{a} r^{'} Q + T_{b} (1 - r^{'}) Q \\ = (T_{a} r^{'} + T_{b} (1 - r^{'})) Q \\ \frac{V 12.2}{T_{a} r^{'} + T_{b} (1 - r^{'})} & = Q \end{array}

If you want to avoid hard-coding the volume of the pipe segment in your MIPS code, you can calculate it using the values you collect from a pipe analyzer.

V = \frac{nRT}{P}

I told you that story so I could tell you this one. If you have a pipe system with some gas already in it ( $m_{a}$ , $m_{b}$ ) and you want to add some to achieve a specific target ratio ( $r^{″}$ ).

\begin{array}{l} m_{a}^{'} & = r^{″} (m_{a}^{'} + m_{b}^{'}) \\ m_{a}^{'} - r^{″} m_{a}^{'} & = r^{″} m_{b}^{'} \\ (1 - r^{″}) m_{a}^{'} & = r^{″} m_{b}^{'} \\ (1 - r^{″}) (m_{a} + Δ m_{a}) & = r^{″} (m_{b} + Δ m_{b}) \\ (1 - r^{″}) (m_{a} + r^{'} Q) & = r^{″} (m_{b} + (1 - r^{'}) Q) \\ (1 - r^{″}) m_{a} + (1 - r^{″}) r^{'} Q & = r^{″} m_{b} + r^{″} (1 - r^{'}) Q \\ (1 - r^{″}) m_{a} + r^{'} Q - r^{″} r^{'} Q & = r^{″} m_{b} + r^{″} Q - r^{″} r^{'} Q \\ (1 - r^{″}) m_{a} - r^{″} m_{b} & = r^{″} Q - r^{″} r^{'} Q - r^{'} Q + r^{″} r^{'} Q \\ β = (1 - r^{″}) m_{a} - r^{″} m_{b} & = (1 - r^{″}) m_{a} - r^{″} m_{b} \\ β & = (r^{″} - r^{″} r^{'} - r^{'} + r^{″} r^{'}) Q \\ β & = (r^{″} - r^{'}) Q \\ β & = (r^{″} - r^{'}) \frac{V 12.2}{T_{a} r^{'} + T_{b} (1 - r^{'})} \\ β (T_{a} r^{'} + T_{b} (1 - r^{'})) & = (r^{″} - r^{'}) V 12.2 \\ β T_{a} r^{'} + β T_{b} (1 - r^{'}) & = r^{″} V 12.2 - r^{'} V 12.2 \\ β T_{a} r^{'} + β T_{b} - β T_{b} r^{'} & = r^{″} V 12.2 - r^{'} V 12.2 \\ β T_{b} - r^{″} V 12.2 & = β T_{b} r^{'} - r^{'} V 12.2 - β T_{a} r^{'} \\ β T_{b} - r^{″} V 12.2 & = (β (T_{b} - T_{a}) - V 12.2) r^{'} \\ \frac{β T_{b} - r^{″} V 12.2}{β (T_{b} - T_{a}) - V 12.2} & = r^{'} \end{array}

In order to turn $r^{'}$ into the $r$ we need to set on the gas mixer

\begin{array}{l} r^{'} & = \frac{\frac{r}{T_{a}}}{\frac{r}{T_{a}} + \frac{1 - r}{T_{b}}} \\ r^{'} (\frac{r}{T_{a}} + \frac{1 - r}{T_{b}}) & = \frac{r}{T_{a}} \\ r^{'} (\frac{1}{T_{a}} r + \frac{1}{T_{b}} - \frac{1}{T_{b}} r) & = \frac{r}{T_{a}} \\ r^{'} (\frac{1}{T_{b}} + (\frac{1}{T_{a}} - \frac{1}{T_{b}}) r) & = \frac{r}{T_{a}} \\ \frac{r^{'}}{T_{b}} + r^{'} (\frac{1}{T_{a}} - \frac{1}{T_{b}}) r & = \frac{1}{T_{a}} r \\ \frac{r^{'}}{T_{b}} & = \frac{1}{T_{a}} r - r^{'} (\frac{1}{T_{a}} - \frac{1}{T_{b}}) r \\ \frac{r^{'}}{T_{b}} & = (\frac{1}{T_{a}} - r^{'} (\frac{1}{T_{a}} - \frac{1}{T_{b}})) r \\ \frac{r^{'}}{T_{b} (\frac{1}{T_{a}} - r^{'} (\frac{1}{T_{a}} - \frac{1}{T_{b}}))} & = r \\ \frac{r^{'}}{\frac{T_{b}}{T_{a}} - r^{'} (\frac{T_{b}}{T_{a}} - \frac{T_{b}}{T_{b}}))} & = r \\ \frac{r^{'} T_{a}}{T_{b} - r^{'} (T_{b} - T_{a})} & = r \\ \frac{r^{'} T_{a}}{(1 - r^{'}) T_{b} + r^{'} T_{a}} & = r \end{array}

I wonder how many lines of MIPS that will turn into...