In order to pursue Harman index, etc, calculations, the first step is to extrapolate the viscosity data to 150°C. But there have been warnings that the formula cannot be relied upon.
First some background.
Extrapolation is usually done with the help of online calculators and Apps for your phone or tablet. E.g. Widman.
The "standard" calculation of the variation of oil viscosity is based on the ASTM-Walther formula.
log(log(KV+0.7)) = A+B log T
KV is the kinematic viscosity
T is the temp in Kelvin and A & B are constants unique to each oil.
This is the formula behind online calculators and the straight line graphs of log log data.
The advantage of this formula is that it only has two constants and therefore we only need two sets of data to solve for the constants A & B, usually the 40 and 100°C points. When you enter data into the calculator the first thing it does is solve for A& B and it then calculates for any other temperature.
The ASTM version with the 0.7 figure is said to be a good fit for light crudes and base stocks, however we are now interested in finished multigrades, PAO's, GTL's, etc.
So I have gone back to the fuller version of the formula which has another variable C instead of the 0.7.
This formula which I refer to as the Walther 3 formula is now
log(log(KV+C)) = A+B log T . To solve for A,B,C, 3 sets of data are now required.
So how do different C constants affect the extrapolation to 150 degs?https://i.postimg.cc/1RHfdP4Y/Variable-C-Constants.png
The chart shows how an oil will deviate from the "standard" C=0.7 calc, when it's viscosity is calculated with different C constants.
Considerable deviations from standard are apparent at low and high temps. Percentage differences are shown because at full scale the deviation at high temperature would not be visible.
As can be seen at high temperatures negative deviations up to -10% can be expected for oils with high C const such as PAO oils, meaning the KV150 is 10% less than the standard calculation.
GTLs, and ANs are close to standard with less than ±4% difference. Oils with different viscosities will have different deviations from standard.
Other oils have been investigated and as an example this chart shows the variation of the C const in a range of oils from the Shear Thinning paper by Hugh Spikes et al. https://i.postimg.cc/Qdwnp23f/1-to-17b-C-constants.png
Oils #1-#10 are simple base + VM
Oils #11-#17 are fully finished
Oils #1-11b-#17b are base oils + detergent inhibitor but no VM
It can be seen from these figures is that the effect of VM's is to lower the C constant while the "purer" oils have higher figures. The base oils without VM's are between 0.95 and 1.59 Oils #2 and #10 have extreme figures, presumably the effects of large amounts of VM's.
Finally, it would seem that there can be both positive and negative differences in extrapolation depending on the oil type, but if you are dealing with a finished oil and you don't know the C const, which is normally the case, as a rule of thumb calculate the KV150 as standard and add 10%.