I have a data from experimental system concerning temperature of molten lead. In this system, temperature is increased in one place and then is measured when this increase of temperature travels to a different place by natural convection.
Data are pairs time vs. measured temperature. The time have steps of one second (sometimes two, due to the measuring system) and temperatures have steps of 0.1 degree of Celsius.
I would like to find when temperature crossed a certain temperature threshold. Let´s say I have something like:
- Time [s] - Temperature [°C]
- 1 - 440.8
- 2 - 440.9
- 3 - 441.1
- 4 - 441.2
I tried linear fit on two points (right below and right above threshold e.g. 441.0) but I would like to try something more "advanced". I know that Excel can do fitting quite well and it is possible to find root by Wolfram Alpha, but it is not an option since I have to evaluate several experiments done each day (thus I have prepared program for it in C# programming language).
Thus I would like to know if there is some plan like saying "take 2 points below threshold and two above, do [something] and you will get time when temperature crossed your chosen threshold". It can use of course more data points. I am not interested in the fitting equation itself, just its root(s).
Thank you for your hints and ideas! Michal
EDIT: My data are somewhat noisy at constant temperature, but when rise of temperature takes place, it is not a problem.