Fuel Rounding and General Rounding Considerations


For almost any fuel based question there are a variety of valid methods of calculation and application of rounding procedures

Any CASA exam question would have been carefully validated to ensure the tolerance applied to the final answer is acceptable for any valid method of calculation and rounding procedures

Our RQG system takes into account as best we can variations in the final answer due to rounding off, but because our system can literally produce millions of possible question combinations, in some rare cases you might find the answer you submitted falls outside our computer generated tolerance when your answer is legitimate

To show how this occasionally happens, here is an example of legitimate rounding methods diverging

-------------------------------------------------------------------------------------------------

Refer to CASR Part 133 MOS chapter 6 - Chapter 6.05(2)(i) and 6.04(2)

A Day VFR flight as a CASR Part 133 Passenger Air Transport operation in a 4 seat piston powered rotorcraft is being conducted

The rotorcraft arrives overhead waypoint GUBBI (GUBBI LST = UTC+10) at 1714 LST with 40 kilograms of useable fuel on board. GUBBI is NOT a suitable place for a landing

An in-flight replanning is specified for arrival at GUBBI

The mission is to do survey work overhead GUBBI and then depending on the clients needs, plan a sector to a suitable HLS for a landing and refueling

HLS GIDGEE (GIDGEE LST = UTC+10) appears to be a suitable HLS to re-plan to for a landing

A decision is made to hold overhead HLS GUBBI as long as possible before flying to HLS GIDGEE

Flight planning data for all holding and the flight sector to HLS GIDGEE -

TAS ..... 118 kt
Total Distance GUBBI to HLS GIDGEE ..... 74 nm
Outbound Track GUBBI to HLS GIDGEE ..... 093 M
GPWT Wind (all crz levels) ..... 304M/22
Cruise/Range Fuel Flow ..... 37 litres per hour
Fuel Specific Gravity ..... 0.72
Holding Fuel Flow ..... 29 litres per hour

HLS GIDGEE has an NOTAM 15 minute holding fuel requirement

Entered as a four figure group, what is the latest possible ETD you can plan at GUBBI for the sector to HLS GIDGEE in LST?

-------------------------------------------------------------------------------------------------

We have shown below just the important numbers in the final fuel calculation, without showing all steps along the way

The generally accepted rounding procedure is "if the number you are rounding is less than half way between whole numbers round DOWN and if it's halfway or more round UP"

It is also important to remember that there is really no such thing as always rounding to the side of 'safety', because if you always plan to burn the highest amount of fuel you can calculate at the fuel plan stage, then later during the weight calculations if you burn less than planned you may find you are overweight on landing. What was 'safe' for one calculation is not 'safe' for another part of the flight

And have you ever used a fuel tank dipstick that accurately displays fuel contents to tenths of a litre? No? A good reason to not think too hard about which way to go with rounding
 
Minimal Rounding (two decimal places) Progressive Rounding (to whole units)
74 nm/136 kt x 37 lt/hr = 20.13 lt trip fuel 20 lt trip fuel
+ 5/60 x 29 lt/hr = 2.4 lt Contingency Fuel (5 min is greater than 10%) + 2 lt Contingency Fuel
+ 20/60 x 37 lt/hr = 12.34 lt Final Reserve + 12 lt Final Reserve
+ 15/60 x 29 lt/hr = 7.25 lt Holding + 7 lt Holding
= 42.1 lt Minimum Fuel Required = 41 lt Minimum Fuel Required
Total fuel on board = 40 kg /.72 = 55.55 lt Total fuel on board = 56 lt
55.55 lt - 42.1 lt = 13.45 lt Fuel for holding 56 lt - 41 lt = 15 lt Fuel for holding
13.45 lt / 29 lt/hr x 60 = 27.8 minutes max holding 15 lt / 29 lt/hr x 60 = 31 minutes max holding
 
You can see by comparing the data that at the Minimum Fuel Required stage the Minimal Rounding total of 42.1 lt is only 1.1 lt higher than the rounded off total of 41 lt

So the difference at that point is very small and the rounded version requires less total fuel

At the next step where the total fuel on board is converted from kilograms to litres the difference is .45 lt with the rounded version giving more fuel available, so when the fuel available to hold is finally calculated the minimal rounded version has 13.45 lt available, while the rounded version has 15 lt available

The difference in fuel available to hold is just 1.55 lt between calculations after all of that work

BUT.. with a very low Holding Fuel Flow of just 29 lt/hr, each litre gives about 2 minutes holding time, so 1.55 lt difference is about 3 minutes total holding and outside the usual +/- 2 minutes allowed

That's why for examples with low fuel flows we have increased the tolerance to +/- 3 minutes and even that can be on the edge when a groundspeed is a few knots different

So as an overview of this example, by absolute chance all of the rounding to the nearest whole unit in the fuel required calculation ended up rounding DOWN, while the single conversion of the fuel available on board rounded UP. That is true random chance

Follow the process as carefully as you can, without stressing over a single litre, pound, knot or minute. The correct process is the key to success


Please Click Here to return to the CFPH login page or use the 'Back' button to return to the previous page.