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## Conversion for fuel calculation

• Posts: 56

### Dan created the topic: Conversion for fuel calculation

Hi Bob,

Just wondering which fuel calculation i should use for the Nav exam?. The ERSA fuel graph states 3.8 USG to litres, the table on the next page of the ERSA says 3.79 and the Bob Tait text book uses 3.78... Do you think if i use any of the three the CASA exam will consider the answer to be correct?...

Cheers, Dan.

• John.Heddles
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• ATPL/consulting aero engineer
• Posts: 345

### John.Heddles replied the topic: Conversion for fuel calculation

First, if the examiner, either in the exam or in an exam-related text on the CASA site, specifies a conversion factor, then that is the one to use, quite obviously. Bob will be able to comment on this for you.

Otherwise, with a non-legally defined conversion, you can use whatever number of decimals floats your boat. With this one, a more accurate conversion would be something like 1 USG = 3.7854 .. beyond this number of decimals and it gets a little silly for practical work.

Consider that,

(a) for 3.8, the error is around 0.4 percent, while
(b) for 3.78 or 3.79, the error is around 0.1 percent.

For practical aviation work, such error levels are fine so it doesn't really matter all that much which you use. Having said that, it isn't much harder to remember another decimal place so I would run (as a general rule here) with either 3.78 or 3.79. If you are a bit of a math purist, you would go with 3.79 as it is marginally closer to the conversion value but, all in all, it really doesn't matter.

Some conversions are defined exactly, eg 1 inch = 25.4 mm so that makes life easier. See, for instance, en.wikipedia.org/wiki/Inch .

Engineering specialist in aircraft performance and weight control.

• Posts: 56

### Dan replied the topic: Conversion for fuel calculation

In practice i would definitely go for 3.78 or 3.79 with my own flight planning. I hope the pexo exam allows for slight variances in the answer.

Thank you for your help mate, I appreciate it!.

Cheers, dan.

• Posts: 85

### Carello replied the topic: Conversion for fuel calculation

Hi Dan

All four conversion factors mentioned earlier (3.7854, 3.78, 3.79, 3.8) are "mathematically" correct. They only differ in the number of significant figures and the method of rounding - more on rounding below

As John stated earlier, 1 USG = 3.7854 lt - to 5 significant figures. This will round 3.8 to two sig. figures as shown in the ERSA conversion table balloon

Now, if rounding "3.7854" to three sig. figures (2 decimal places) things get a little confusing since the the 3rd decimal place is a "5". When rounding there are four option available
1) Round up - ie 3.7854 becomes 3.79
2) Round down - ie 3.7854 becomes 3.78
3) Round to the odd - ie 3.7854 becomes 3.79 (9 is odd)
4) Round to the even - ie 3.7854 becomes 3.78 (8 is even)

With the above in mind, the EASA has opted to round "up" or to the "odd' and Bob has opted to round "down" or the the "even" - I can't tell which from the limited data available. Mathematically all of the above are correct to 3 sig. figures.

For the purpose of the exam, stick with the oracle

• Posts: 1914

### bobtait replied the topic: Conversion for fuel calculation

Obviously, you would be best advised to use the ERSA figure since CASA can hardly dispute its own figures. However, as I often say to classes "show me a dip-stick calibrated to hundredths of litres and we'll continue with the conversation". Also, since a litre is a unit of volume, and the actual quantity of fuel depends on its weight, the coefficient of expansion of avgas would need to be considered to allow for the fact that a kg of fuel occupies different volumes at different temperatures. Let's get real here!

I note that the most used conversion in the CASA exams is litres to kg or gallons to kg.

• Posts: 85

### Carello replied the topic: Conversion for fuel calculation

However, as I often say to classes "show me a dip-stick calibrated to hundredths of litres and we'll continue with the conversation".... Let's get real here!

Thinking back to the high school science classroom, the subject of measurement (fuel dip stick) and arithmetic based on those measurements may come to mind. More specifically, there are rules for determining the number of significant figures in quantities calculated from measured quantities like fuel.

Within the scope of this original post, say we dip the tank and get a reading of 85 USG - this is a measurement to 2 sig. figs. Now if we wish to convert to litres we can use any of the conversion factors (3.7854, 3.78, 3.79, 3.8) discussed earlier and get the same answer to 2 sig. figs.

85x3.7854 = 321.759 = 320 to 2 sig. fig.
85x3.78 = 321.3 = 320 to 2 sig fig
85x3.79 = 322.15 = 320 to 2 sig fig
85x3.8 = 323 = 320 to 2 sig. fig.

(Note that the red 0 in 320 is not significant. If it were the answer would be 320. with a decimal point after the 0)

In summary, we can use as many decimal points in the conversion factor as we wish because the calculated answer will be limited by the number of sig. figs in the fuel measurement - ie the graduations on the dip stick

I don't know how CASA would deal with an answer like 320, but 320 lts is the mathematically correct conversion.

See Wikipedia for a more detailed discussion on significant figures

I have completely ignored the subject of the propagation of errors.