Type a line (380 cSt at 50 °C and 35 cSt at 100 °C, target 13 cSt) or fill in the fields: the line and the fields stay in step.
Enter two measured points of the fuel, each the kinematic viscosity with the temperature it was measured at, for example from the quality certificate or the bunker delivery note at 50 °C and from a fuel analysis at 100 °C, and the calculator draws the ASTM D341 (Walther) line through them. It gives the fuel heating temperature at which a target viscosity is reached, such as the injection viscosity the engine maker specifies, the viscosity at any temperature, and a table and a chart over a range. It shows the working with your numbers and gives a line you can copy or add to a request.
The relation holds for liquid petroleum products from 2.0 mm2/s up: the calculator does not apply the extra terms ASTM D341 gives below 2.0 mm2/s, and names any viscosity below that as outside its range. It does not guess a slope from one point: with one viscosity only, it says that a second measured point is needed. It gives no injection viscosity and no heating temperature of its own: enter the injection viscosity the engine maker specifies.
log10(log10(v + 0.7)) = A - B log10(T), with v the kinematic viscosity in mm2/s (cSt) and T the temperature in kelvin (t + 273.15). On a chart with log10(log10(v + 0.7)) up and log10(T) across, each fuel is a straight line, so two points fix it.
At each point Z = log10(log10(v + 0.7)); B = (Z1 - Z2) / (log10 T2 - log10 T1) and A = Z1 + B log10 T1. For 380 mm2/s at 50 °C and 35 mm2/s at 100 °C: Z1 = 0.411718, Z2 = 0.191079, B = 3.5314, A = 9.2734.
log10 T = (A - log10(log10(v + 0.7))) / B. For 13 mm2/s on the same line: T = 407.6 K, that is 134.4 °C; at 120 °C the same line gives 18.85 mm2/s. Beyond the two points this extends the line; a measured viscosity nearer that temperature checks it.
| Quantity | Relation | Note |
|---|---|---|
| Relation | log10(log10(v + 0.7)) = A - B log10(T) | v in mm2/s (cSt), T in K; ASTM D341, plain form |
| Z at a point | Z = log10(log10(v + 0.7)) | the double logarithm of the viscosity plus 0.7 |
| Slope B | B = (Z1 - Z2) / (log10 T2 - log10 T1) | from the two points |
| Constant A | A = Z1 + B log10 T1 | either point gives the same A |
| Viscosity at t | v = 10^(10^(A - B log10 T)) - 0.7 | T = t + 273.15 |
| Temperature for v | T = 10^((A - Z) / B) | t = T - 273.15 |
| Range | 2.0 mm2/s and up | below 2.0 mm2/s ASTM D341 adds terms not applied here |
| Units | 1 mm2/s = 1 cSt; T/K = t/°C + 273.15 | t/°C = (t/°F - 32) / 1.8 |
The logarithms are to base 10 and the temperature in the relation is in kelvin. Both points belong to the same fuel or oil; the viscosity is the kinematic one, in mm2/s (cSt).
The relation log10(log10(v + 0.7)) = A - B log10(T), with the temperature in kelvin, and the working of A and B from two points are taken from two independent published descriptions of ASTM D341 (the Walther relation), and the calculator reproduces two published worked examples: 68 mm2/s at 40 °C and 8.6 mm2/s at 100 °C give 17.0 mm2/s at 75 °C, and 404 mm2/s at 40 °C and 28 mm2/s at 100 °C give 132.1 mm2/s at 60 °C. Both descriptions put the lower end of the plain form at about 2 mm2/s; below it ASTM D341 adds exponential terms, which the calculator does not apply. ASTM D341 is a practice for liquid petroleum and hydrocarbon products. That residual fuels are specified by their viscosity at 50 °C is taken from the ISO 8217 tables. 1 mm2/s = 1 cSt and T/K = t/°C + 273.15 by definition.
In three steps on the ASTM D341 relation, log10(log10(v + 0.7)) = A - B log10(T), with T in kelvin. First Z = log10(log10(v + 0.7)) at each of the two points. Then B = (Z1 - Z2) / (log10 T2 - log10 T1) and A = Z1 + B log10 T1. Last, for the target viscosity, log10 T = (A - Z) / B. For 380 mm2/s at 50 °C and 35 mm2/s at 100 °C: Z1 = 0.411718, Z2 = 0.191079, B = 3.5314 and A = 9.2734; a target of 13 mm2/s gives T = 407.6 K, that is 134.4 °C.
Because the line has two constants, A and B, and each fuel has its own slope B. One viscosity, such as 380 mm2/s at 50 °C, fixes a point but not the slope, and the calculator does not assume one: with one point only it says that a second measured viscosity at another temperature is needed, such as a viscosity at 100 °C from a fuel analysis report.
The injection viscosity the engine maker specifies for the engine. The calculator gives no injection viscosity and no heating temperature of its own: it gives the temperature at which the fuel, on the line through your two points, reaches the viscosity entered.
The line continues beyond them, and the calculator gives the figure, but it marks it as outside the two points: it is an extrapolation along the line, not a measurement. A measured viscosity nearer that temperature checks it. The table marks each row beyond the points in the same way.
The calculator uses the plain form, with 0.7 added to the viscosity, from 2.0 mm2/s up. Below about 2 mm2/s ASTM D341 adds exponential terms to that 0.7, and the calculator does not apply them: a point, a target or a table row below 2.0 mm2/s is named as outside its range instead of given.
Kinematic viscosities in mm2/s or cSt, which are the same, from 2.0 to 100 000 mm2/s; temperatures in °C, and also in K or °F, from -50 to 300 °C. Two points, each a viscosity with its temperature, and a target viscosity, a temperature to check or a table range. A dynamic viscosity in mPa s or cP, and Saybolt, Redwood or Engler figures, are not converted.
The calculator gives the temperature for a viscosity on the line through your two points. When parts for the fuel heater, the viscosity controller or the fuel module are needed, send the line from the calculator with the details and a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
