Hi,

Thanks for your time and the service you provide.

I am just a little stumped with Q15 on the first performance exam.

Answer says 190kg but when checked mathematically this lands infront of the forward limit? The only one that did not when checked was 100kg? would just really appreciate some some clarity on this before I sit the exam.

May I suggest that you post the question so that we know we are all singing to the same Prayer Book ?

An Echo aeroplane is loaded with the main tanks full and the auxiliary tanks empty.

If the gross weight and moment index are 2655 kg and 666 index units respectively, the maximum fuel that may now be added to the auxiliary tanks is -
Select one:
215 kg
190 kg
100 kg
295 kg

I answered 100, the answer says 190, but that would lead to weight 2845 arm 2527.94 index 719.2

2845 - 2360 x 0.271 + 2400 would give a forward limit of 2531.44?

Thank you in advance for any light you can shed on this.

All's well.

First off, did the question ask as you have posted or did it ask for the answer "closest to the correct answer", or something similar ?

You've run the question (I presume) on your handy spreadsheet and obtained an answer (what answer did you come up with ?) which commits you to selecting 100 kg as the "answer". Your answer is correct so far as the selection from the available answers is concerned - they could have been a bit better chosen. You might like to post your solution for our comments as it is more important to make sure that whatever you are doing is OK ?

The published solution pretty obviously ran the question on the chart (which is a bit rough and ready) and got an answer ... which is a little bit different to yours ... not a great deal different, but sufficient to cause you concern. 190, also, is a tad off the answer but probably OK for a graphical solution (I haven't bothered to run a graphical solution at this stage).

Suggest that you now run the question on the chart and see what you come up with for an answer. It may not be exactly the same as the published solution but let's see, shall we ?

The two solutions will always have a bit in the way of discrepancy simply due to the fact that one is numerically precise (although not necessarily that precise in pragmatic reality) while the other is a tad rough and ready. Providing that some care is exercised in obtaining the graphical solution and you take care not to be overtly non-conservative, the end discrepancy should be acceptable.

Please do let us know how you go with a graphical solution ....

If, indeed, you did do the question graphically, rather than numerically, then perhaps you can post your graphical solution for comment ?

It's very difficult to get anything like a precise answer using the envelope in this case. The lines cross at such a shallow angle that it's very difficult to be accurate within a margin of 20 or even 30kg.

However, if you try 175kg you get an new CofG of 2526.5mm and a new forward limit of 2526.9mm. That looks like a reasonable answer within about half a mm. But surely nobody expects you to do a tedious trial and error exercise to zero in on an accurate answer.

You can only hope that such a question would be multi-choice with a phrase like "is closest to" so that you could try each answer and see which one fits. Unless you want to resort to a simultaneous equation.

If I may add a comment or two to Bob's.

It's very difficult to get anything like a precise answer using the envelope in this case

I would go so far as to suggest impossible.

However, if you try 175kg

I'd go along with that. The "correct" answer is 170 kg but, as Bob suggests, that is not required. Keep in mind that the certification establishment of CG limits, itself, is fairly rubbery. The important thing, out in the field, is to make sure that you are a bit conservative so that, should you find yourself in an argument either with CASA or the legal system, you can maintain a squeaky clean position.

One of the important things which goes hand in hand with command is keeping the operator, the operation, and the crew on the nice side of the legal limits with a view always to having a defensible position to argue.