Physical problem: converting two independent functions into one

[Markovicz]

Hello,

I have a physical problem that calls out for the help of mathematicians. I would like to measure the state of charge (SOC) value of NiMH batteries. The SOC value is strongly dependent on the open circuit voltage (OCV) and the temperature. I can measure both, the OCV and the temperature and I have empirically determined graphs for SOC as a function of temperature and as a function of voltage. I would like to come up with an empirical formula for SOC(OCV,temperature). Please have a look at the attached graphs.

Best and thank you!
Marco

 

[Paul Belino]

Graph one will be exponential. Have a look at capacitor charging equations. Fitting to exponential functions can be tricky. You can do it in EXCEL.
Graph 2 looks cubic. Again you can fit to a cubic in EXCEL.
This then gives you two expressions. However there does not seem to be a common parameter with which to connect them since you seem to have 4 variables two of which are independent but not the same parameter.