Lubricant viscosity vs temperature
Interpolates a lubricant's kinematic viscosity at any target temperature from two known reference points, using the Walther/ASTM D341 method -- explicitly not linear interpolation.
Formula
W(nu) = log10 log10(nu + 0.7), linear in log10 T[K]
Viscosity-temperature curves for mineral oils are strongly curved; nu falls by orders of magnitude over a wide temperature range. Walther found that the double-log transform log10 log10(nu+0.7) is approximately linear in the base-10 logarithm of absolute temperature. From two reference points (usually 40 C and 100 C) the slope and intercept of this line can be determined and viscosity back-calculated at any intermediate temperature.
What this model does not show
This method interpolates from two data points, it is not a substitute for measurement. It gives markedly different (typically lower) results than naive linear interpolation of nu over T -- the latter significantly underestimates the curve's curvature. Viscosity index (VI) is a separate, standardized figure for temperature behavior and is not computed here.
Worked example
An ISO VG 46 oil has nu1 = 46 mm2/s at T1 = 40 C and nu2 = 6.8 mm2/s at T2 = 100 C. Find nu at 70 C. In Kelvin: T1 = 313.15 K, T2 = 373.15 K. Walther values: W1 = log10 log10(46.7) ~ 0.1875, W2 = log10 log10(7.5) ~ -0.0691. Slope B = (W2-W1)/(log10 T2-log10 T1) ~ -3.49. At 70 C (343.15 K), W ~ 0.0424, back-transformed to nu ~ 15.6 mm2/s -- well below the naive linear average of (46+6.8)/2 = 26.4 mm2/s.
Common mistakes
- Linearly interpolating between nu1 and nu2 instead of using the Walther transform -- gives markedly too-high viscosity values at intermediate temperatures.
- Using Celsius instead of Kelvin in the line equation.
- Extrapolating far beyond T2 (e.g. to 150 C from 40/100 C references) and treating the result as reliable.
Frequently asked questions
Why is linear interpolation wrong here?
Viscosity-temperature curves fall in a roughly exponential shape, not linearly. Linear interpolation between two points overestimates viscosity at all intermediate temperatures, sometimes substantially, because it ignores the curve's actual curvature.
Is this the same as ASTM D341?
The underlying principle (the Walther equation, double-log transform) is the one described in ASTM D341. This calculator implements that mathematical relationship but does not claim to reproduce every detail of the full ASTM D341 standard (e.g. chart-paper constants, rounding rules) -- hence it is labeled a Walther interpolation.
What is viscosity index (VI) and is it computed here?
VI is a dimensionless figure (per ISO 2909) describing how strongly an oil's viscosity changes with temperature -- higher VI means less temperature dependence. It is computed from viscosities at 40 C and 100 C plus reference tables, and is not part of this calculator.
Can I interpolate outside 40-100 C?
Yes, with any two reference points. The further the target temperature is from both reference points (extrapolation), the less reliable the result becomes, because the Walther line is only a good local approximation.
Why do I need this for plain-bearing design?
The Sommerfeld number (calculator 58) needs dynamic viscosity at the actual operating film temperature, which usually differs from the datasheet reference temperature (40 C). This calculator gives the matching kinematic viscosity, which is then converted to dynamic viscosity via calculator 51.
Why is 0.7 added inside the Walther equation?
The term nu+0.7 is an empirical correction that keeps the Walther equation numerically well-behaved even for very low viscosities (close to that of water); without it, the double logarithm becomes unreliable at small nu values.