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From “Using Density 12MF.xls” :

“Why does this spreadsheet give different answers to other programs?”

When using this spreadsheet and comparing the results to the results obtained from other programs, some apparently significant differences may be noted.

These apparent errors will most usually be the result of particular industry’s standard operating procedures being implemented in the other programs while the spreadsheet is intended to be universal in application.

This apparent error situation will be encountered in the bunker industry where a number of free programs are available (e.g. from the oil companies and from some test houses) which are specifically designed for use in the bunker industry, but similar situations may be found in other industry sectors.

Background:

The historical method of determining the density is to measure the density at some temperature using a hydrometer.

The next step is to either use the tables to look up the base density or use a program.

Programs are often more convenient because they will calculate base densities and alternative densities, with or without hydrometer corrections.

The tables tabulate results with a 2.0kg/m3 increment but the user may interpolate and report the results to the nearest 0.1kg/m3.

However, in the bunker industry an accuracy of +/-0.5kg/m3 has long been considered “good enough”. Thus the programs designed for bunkering may produce results with some differences from the values given in the spreadsheet and found from tables.

Example:

The recorded hydrometer reading is      740.6 at 33°C.

A program gives the base density as    756.4   kg/m3.

The spreadsheet reports                      756.53 kg/m3.

Difference:                                             0.13 kg/m3

Which is right?

Tables give the base density as            756.5  kg/m3

This is consistent with the spreadsheet (its result should be rounded to one decimal place when used with hydrometers) but differing from the program result.

It is further found that any hydrometer reading  between 740.3 and 740.7 entered into the program will all give the result 756.4  kg/m3.

The program result can be re-created in the spreadsheet and in tables if the hydrometer reading is rounded to the nearest 0.5 value before being entered. Thus, when 740.6 is rounded to 740.5: the programs, the spreadsheet and the tables all then agree the base density is 756.4  kg/m3.

For a hydrometer reading of 740.7 the base density ought to be 756.6kg/m3 which is a bit more significant, a 0.26 kg/m3 difference.

When using the spreadsheet, once the rounding rules are understood for any particular operation, the spreadsheet will give the appropriate results if required.

However, the spreadsheet is the more accurate method and while the 0.5kg/m3 rounding rule may have been appropriate to help simplify calculations etc. when using tables, and has transitioned into the programs so that the program results are consistent with general practice, it is suggested the spreadsheet results should be taken as the more accurate.

If in doubt, or where different operators are working with different methods for the same fuel e.g. Fuel supplier and ship’s engineer are using different methods, it is suggested that the operator should enter both the recorded hydrometer reading and the rounded reading in successive lines and duplicate calculations so that the magnitude of the calculation differences can be always be appreciated and reconciled with program based solutions.

However, it should be noted that programs intended for use with hydrometers in the bunker industry should not , therefore, be used with digital density meters whether off line, inline, portable or fixed tank types because they all measure to two decimal place accuracy - the spreadsheet should be used.

For any questions or for other spreadsheet solutions please contact RMI (contact details below)