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## Rounding

• Posts: 4

### oznickaviation created the topic: Rounding

Hi all, I know it says it in the introduction but I just wanted to clarify a few things.
When calculating minimum fuel required, you round UP? In some practise questions, it seems Bob rounds up “early”. For example, Ex4.15 (page 102), question 1... I did 69/60x28x1.1 + 18= 53.42 + 16.3=69.72gal which rounds UP to 70. Then I look at the answer page 132 and the answer is 71.3, which, rounded up, would be 72?? I found it confusing that in the work out you can see Bob is already rounding the trip fuel to 33 instead of leaving it to 32.2...
So my question is, in the exam would CASA want you to round on the safest side (ie up or down depending on whether you’re talking about max cargo to be carried, or minimum ballast fuel etc...) only at the very end of your calculation?

Another example, if you’re calculating MAXIMUM cargo that CAN be carried in the rear compartment before your ZFW/TOW CG is out of balance, if you get an answer of say, “62.8 kg”, then you would enter 62kg in the box?
Kind regards,
Nick

• John.Heddles
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• ATPL/consulting aero engineer
• Posts: 555

### John.Heddles replied the topic: Rounding

Several considerations -

(a) for routine calculations, round off should be in accordance with normal math protocols - x.5 though (x+1).499 repeated rounds to (x+1) so, for example, 4.6 rounds to 5 while 4.4 rounds to 4, presuming you require precision to an integer value.

(b) where there is a need for conservatism, this might, appropriately, be varied to maintain the conservative margin. So, for fuel required, round up to the next unit of required precision. So, if you calculate that you need 209.1 litres, this would be rounded to 210, rather than 209, litres. Alternatively, if the CG limit is 1234 mm and you are adding ballast of, say, 22.7 kg to achieve a cg at the limit (from inside the envelope), then you would restrict the ballast round off to 22 kg to keep the cg within the envelope. Alternatively, coming from outside, you would round to 23 kg.

It just takes a little bit of thought to keep things on an even keel. Be careful in exam questions to read the examiner's intent. He may well use words which infer a modified round off protocol.

(c) as to consecutive calculations, you should be running at your machine's level of precision until the final answer, at which stage you round appropriately. So, for example, if you are running the sums on your electronic calculator, just let the machine do its tricks to whatever its level of floating point precision might be and then, at the end, round off the ridiculous answer of 23,918456383981 to the appropriate precision required for the answer. So, for example, were you requiring an answer precise to 3 decimals, the answer would be 23.918 while, for an integer, 24 and so on. Clearly, you need to modify this approach if you are running the sums longhand or, say, on the slide rule but the principle remains valid.

Engineering specialist in aircraft performance and weight control.

• Posts: 4

### oznickaviation replied the topic: Rounding

Thanks for clarifying that... makes sense, and I’m glad that’s what I’ve been doing during my preparation..... all the best, Nick

• Posts: 11

### jkatz098 replied the topic: Rounding

What about in a question like this

I ended up with a final answer of 116.1 and since its fuel I rounded up to the next highest number.

I assume if CASA are looking for logical answers with fuel they will have options like 116 and 117 so you could round up

Otherwise should we just round to the closest?
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• John.Heddles
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• Posts: 555

### John.Heddles replied the topic: Rounding

Re-read my earlier comment - Be careful in exam questions to read the examiner's intent. He may well use words which infer a modified round off protocol.

Now read the question, this time carefully, and read what is written rather than what you might think should be written ....

Engineering specialist in aircraft performance and weight control.

• Posts: 4

### oznickaviation replied the topic: Rounding

Hi John and Jkatz, I got 116.2 gals, which, normally, would be rounded up to 117. However I think the key word here is “IS CLOSEST TO”?
Cheers

• John.Heddles
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• Posts: 555

### John.Heddles replied the topic: Rounding

Exactly.

The question doesn't ask "what fuel would you take", for which you would answer 122.

Engineering specialist in aircraft performance and weight control.

• Posts: 9

### JamesScot replied the topic: Rounding

Sorry to belabor the issue, but I'm not confident I still understand how to round. Here are a number of questions, and my calculations, how should I round? I've written my thoughts behind my rounding, are they reasonable?

If the question was:

1. How much usable fuel, in litres, will be left after 14 minutes of flight?
If I calculated 190.62 litres, do I write 190 or 191?
I would ROUND DOWN to 190 because relying on 191 would see fuel exhaustion.

2. To the nearest litre/hour, what was the fuel consumption during this period?
If I calculated 56.25 litres/hour, do I write 56 or 57?
I would ROUND DOWN to 56, because of the wording of the question, but ROUND UP to 57, if I was relying on the figure for further calculations.

3. What is the remaining endurance (including reserves) at time 1200 UTC?
If I calculated 254.5 minutes, do I write 254 or 255?
I would ROUND DOWN to 254 because fuel would be exhausted before 255 minutes.

4. To the nearest litre, the MINIMUM fuel required at start up for this flight is -
If I calculated 273.043 litres, do I write 273 or 274?
I would ROUND UP to 274 because the key word here is 'required'. If I had 273, that would be less than required.

5. To the nearest litre/hour, what is the average fuel consumption?
If I calculated 65.25 litres, do I write 65 or 66?
I would ROUND DOWN to 65 because of the wording of the question, unless I was using it for future fuel calculations in which case I'd ROUND UP to 66.

• John.Heddles
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• Posts: 555

### John.Heddles replied the topic: Rounding

As before, the mantra is -

(a) if the examiner indicates he wants something specific in the question, do it

(b) otherwise, round conservatively, where appropriate - especially for fuel and weight and balance

(c) otherwise, follow the usual maths rules.

Your approach looks pretty good -

1. How much usable fuel, in litres, will be left after 14 minutes of flight?
If I calculated 190.62 litres, do I write 190 or 191?
I would ROUND DOWN to 190 because relying on 191 would see fuel exhaustion.

Perhaps not exhaustion, but it's non-conservative. Keep in mind that, for many aircraft, there will be fuel left below usable, which is usable in some circumstances but not planned-to-be-usable. This arises due to the way unusable fuel is established in flight test work.

2. To the nearest litre/hour, what was the fuel consumption during this period?
If I calculated 56.25 litres/hour, do I write 56 or 57?
I would ROUND DOWN to 56, because of the wording of the question, but ROUND UP to 57, if I was relying on the figure for further calculations.

I would suggest that you keep the extra precision for any successive calculations, rounding off at the end. However, were the cited example the final calculation, then you have nailed it nicely.

3. What is the remaining endurance (including reserves) at time 1200 UTC?
If I calculated 254.5 minutes, do I write 254 or 255?
I would ROUND DOWN to 254 because fuel would be exhausted before 255 minutes.

Good man

4. To the nearest litre, the MINIMUM fuel required at start up for this flight is -
If I calculated 273.043 litres, do I write 273 or 274?
I would ROUND UP to 274 because the key word here is 'required'. If I had 273, that would be less than required.

Possibly, the examiner would be looking for 273, as the question imposes the "nearest" criterion. Operationally, though, you have it nailed.

5. To the nearest litre/hour, what is the average fuel consumption?
If I calculated 65.25 litres, do I write 65 or 66?
I would ROUND DOWN to 65 because of the wording of the question, unless I was using it for future fuel calculations in which case I'd ROUND UP to 66.

As per Q2.

Engineering specialist in aircraft performance and weight control.
The following user(s) said Thank You: JamesScot