The Hitchhiker's Revolutionary* Manufacturer's Guide to the Galaxy Temperature Dependent Resistance Curves
* and Game Changer and Prodigious and Visionary . Very.
STEP 2: Plotting a curve
For illustration purpose we will use Ni200 as it’s TCR is definitely nonlinear. Titanium would be too easy.
Specialmetals’
datasheet is perfect, so we just load the temperature and resistance values into a
Google sheet. (SI for now, Imperial on demand)
Now, we can derive our factors, relative to 20C (room temperature) and insert a chart to see how big the trouble is. (Resistance factor is divided by 10 for demonstration) So far, we can agree that Ni200’s resistance change is indeed far from linear even within the 20-300C vaping range.
To do the magic we need to import(copy/paste) our input data into a highly sophisticated mathematical software called
Geogebra which happens to be open source and available on several platforms. (we will import temperature and resistance data only)
Then we create a polyline from the spreadsheet data and add two lines representing our temp limits and we get this:
Then pick the points from our range with +1 from above and below and play a bit with the FitPoly command to find the polynomial which suits us.
This quintic function looks pretty promising. (any polynomials of lower degree didn’t work to well).
1.0358E-14 x^5-1.752E-11 x^4+7.0109E-9 x^3+3.8532E-8*x^2+0.00031974x+0.09037
Of course, it is way off beyond our range, but we don't care.
Our sole purpose is to gain an equation we can use to compute all the missing factors with acceptable accuracy . And this lusty curve will do this job. Ok, an inflection point around 300C would be even better but that’s what we can get for free.
So we open a new tab in our sheet, copy the known values into it and includes the missing temperature steps. (known data: normal, calculated: italic)
Now we derive the factors and we are actually ready. Even though we had no initial data for all the temp options now we can allocate a surprisingly accurate resistance value to all.
TCR calculation (Column ‘D’) is just a bonus feature for those who happen to own a mod with TCR settings option.
Thank you for reading
Happy tinkering
P.S.
I have used this datasheet because of its immense data. However this particular Ni seems a bit lazier than others with smaller resistance changes and TCRs (e.g. its R300~=2.71*R20. I generally use
Kanthal's Nickel DH as reference and it has 2.97*R20@300C)
But like I said, values depend on the circumstances
It is not my fault