Type a line (991 kg/m3 380 cSt 50 °C; density 0.985 viscosity 180 cSt; CCAI 860 at 380 cSt) or fill in the fields: the line and the fields stay in step.
Enter the density of a residual marine fuel at 15 °C and its kinematic viscosity with the temperature it was measured at, and the calculator gives the CCAI, the calculated carbon aromaticity index, by the equation of the ISO 8217 annex. Enter a CCAI and a viscosity, and it gives the density at 15 °C that matches them. The working is shown with your numbers, the value is marked on a CCAI scale, and the result comes as a line you can copy or add to a request.
The CCAI is an indicator of ignition quality: the higher the CCAI, the poorer the ignition quality. The limit for each residual grade is in the ISO 8217 table and the engine maker’s guidance governs, so the calculator sets no limit of its own, gives no view on whether a fuel suits an engine, does not correct a density to 15 °C and does not give the CII.
CCAI = density - 81 - 141 lg(lg(viscosity + 0.85)) - 483 lg((T + 273) / 323): the density at 15 °C in kg/m3, the kinematic viscosity in mm2/s at T °C, lg the logarithm to base 10. For 991 kg/m3 and 380 mm2/s at 50 °C: 991 - 81 - 58.0563 - 0 = 851.9.
The viscosity term, 141 lg(lg(viscosity + 0.85)), grows with the viscosity: 49.8566 at 180 mm2/s, 58.0563 at 380 mm2/s, 64.0391 at 700 mm2/s. The temperature term, 483 lg((T + 273) / 323), is zero at 50 °C and accounts for a viscosity measured at another temperature: 18.6304 at 80 °C, -6.5969 at 40 °C.
density = CCAI + 81 + 141 lg(lg(viscosity + 0.85)) + 483 lg((T + 273) / 323). A CCAI of 860 at 380 mm2/s and 50 °C matches a density at 15 °C of 999.1 kg/m3. At a given viscosity the CCAI follows the density one for one: 10 kg/m3 more is 10 more.
| Item | Equals | Note |
|---|---|---|
| Density term | density at 15 °C, kg/m3, less 81 | for 991 kg/m3: 991 - 81 = 910 |
| Viscosity term | 141 x lg(lg(viscosity + 0.85)) | viscosity in mm2/s (cSt); at 380 mm2/s, 58.0563 |
| Temperature term | 483 x lg((T + 273) / 323) | T in °C; zero at 50 °C |
| lg | logarithm to base 10 | lg 10 = 1, lg 100 = 2 |
| 1 g/ml = 1 kg/l = 1 g/cm3 | 1000 kg/m3 | density units |
| 1 cSt | 1 mm2/s | kinematic viscosity units |
| Kelvin | t in °C = T in K - 273.15 | a viscosity temperature in K |
The CCAI is a calculated figure, not a measurement: the density and the viscosity are measured, and the equation combines them.
The equation is the one in the informative annex of ISO 8217 on the ignition characteristics of residual marine fuels: CCAI = density - 81 - 141 lg(lg(viscosity + 0.85)) - 483 lg((T + 273) / 323), with the density at 15 °C in kg/m3, the kinematic viscosity in mm2/s, T the viscosity temperature in °C and lg the logarithm to base 10. The constants were checked against two independent published reproductions of the annex, and every step of the working is shown so that it can be checked: 960 kg/m3 and 180 mm2/s at 50 °C give 829.1. That a higher CCAI means a poorer ignition quality, and that the engine maker’s guidance governs the ignition quality an engine accepts, are each stated in at least two sources. 1 g/ml = 1 kg/l = 1000 kg/m3 and 1 cSt = 1 mm2/s by definition.
With the equation of the ISO 8217 annex on the ignition characteristics of residual fuels: CCAI = density - 81 - 141 lg(lg(viscosity + 0.85)) - 483 lg((T + 273) / 323), with the density at 15 °C in kg/m3, the kinematic viscosity in mm2/s (cSt) and T the temperature in °C at which the viscosity was measured; lg is the logarithm to base 10. For 991 kg/m3 and 380 mm2/s at 50 °C: lg(380 + 0.85) = 2.580754, lg 2.580754 = 0.411747, 141 x 0.411747 = 58.0563, the temperature term is zero at 50 °C, and the CCAI is 991 - 81 - 58.0563 = 851.9.
It is an indicator of the ignition quality of a residual fuel: the higher the CCAI, the poorer the ignition quality. ISO 8217 sets a CCAI maximum for each residual grade in its table, and the engine maker’s guidance governs the ignition quality an engine accepts. The calculator sets no limit of its own and gives no view on whether a fuel suits an engine.
The density at 15 °C in kg/m3, as on the fuel test report or the bunker delivery note; g/ml, g/cm3 and kg/l are multiplied by 1000. A density at another temperature is not corrected to 15 °C here: the calculator asks for the density at 15 °C instead. The kinematic viscosity in mm2/s, the same figure as in cSt, with the temperature it was measured at; with no temperature, 50 °C is taken, the temperature at which ISO 8217 states the viscosity of residual fuels. A grade such as RMG 380 is not a viscosity: it gives a maximum, not the fuel’s own figure.
The last term of the equation, 483 lg((T + 273) / 323), takes care of it: it is zero at 50 °C (323 = 50 + 273), above zero for a higher temperature and below zero for a lower one. For 991 kg/m3 and 100 mm2/s at 80 °C the term is 483 x lg(353 / 323) = 18.6304, the viscosity term 141 x lg(lg 100.85) = 42.5577, and the CCAI 991 - 81 - 42.5577 - 18.6304 = 848.8. The calculator does not convert the viscosity itself from one temperature to another.
Yes: density = CCAI + 81 + 141 lg(lg(viscosity + 0.85)) + 483 lg((T + 273) / 323). For a CCAI of 860 at 380 mm2/s and 50 °C the density at 15 °C is 860 + 81 + 58.0563 + 0 = 999.1 kg/m3; at that viscosity a denser fuel has a higher CCAI and a lighter one a lower CCAI. Type CCAI 860 at 380 cSt, or fill in the CCAI field.
Some print the equation with 140.7 and 80.6 in place of 141 and 81, and 483.5 in place of 483 in the temperature term; for 991 kg/m3 and 380 mm2/s at 50 °C that gives 852.5 instead of 851.9. Others leave out the temperature term, which matters only for a viscosity measured at another temperature than 50 °C. This calculator uses the constants of the ISO 8217 annex and shows every step, so the figures can be checked. It does not work out the CII, the calculated ignition index.
The calculator gives the CCAI only. When a fuel injection pump, an injector, a fuel filter element or a separator part is needed, send the line from the calculator with a photograph of the nameplate or the part, and Vessel Core checks the details before an offer goes back.
