For the arc length of Archimedes's spiral, we use the classical formula (Wolfram|Alpha)
where is the gap.
The thermometer is by default calibrated for the Mg/Fe bimetal. Other bimetal settings need to be calibrated individually. To do this, we insert a linear factor cal60, computed with Mathematica's built-in function FindRoot, to give a deflection of at 60 °C.
Snapshot 1: a very sensitive bimetal Mg/Ti with thermal expansion coefficients of 26/8.6
Snapshot 2: a less sensitive bimetal Cu/Ni with thermal expansion coefficients of 17/13
Snapshot 3: the uncalibrated version of Snapshot 2