For loading problem involving a forward limit, with aircraft weight BELOW 2360 kg (i.e. the forward limit does NOT change with weight), does it mean the flow chart method can be used instead of the graphical method?

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<< The following question has been resolved >>

For Ex. 5.13 - No. 6 & 7 (p.190), the answer (p.219) states that the CG envelope graph is to be used to work out the answer.
I wonder if the flow chart method could be used? If yes, the answer seems to be quite different from the one in the textbook, why?




P. 190, Ex. 5.13 #6

Present Weight	Present CG	Shift in CG	Weight to be added/ removed
2400	2458.33	31.78	118 kg
590	2426.55	1780	(Answer in the book: 90kg)
Present Moment	Required CG	CG of Weight to be changed
		Difference in arms: 646.55

P. 190, Ex. 5.13 #7

Present Weight	Present CG	Shift in CG	Weight to be added/ removed
2392	2391.3	17.15	15.83 kg
572	2408.45	5000	(Answer in the book: 20kg)
Present Moment	Required CG	CG of Weight to be changed
		Difference in arms: 2591.55

Edit: Answering my own question
When FORWARD weight limit is involved for weights between 2360 and 2950 kg, the flow chart method CANNOT be used. A graphical method should be used instead!
Book p.185 (sorry for the stupid question... I should have RTFB and memorised it well...)

For loading problem involving a forward limit, with aircraft weight BELOW 2360 kg (i.e. the forward limit does NOT change with weight), does it mean the flow chart method can be used instead of the graphical method?

Yes, as for the (fixed) aft limit. All you need is for the CG limits involved to stay stationary.

The problem with the upper forward limit is that the goalposts keep moving every time you change the gross weight. You can't use a simple calculation to find the final target CG. You can work it out algebraically but the work required is not really appropriate for pilot stuff and involves the solution of simultaneous equations.

The easiest way to tackle the problem is by plotting. You won't get super accurate answers but, with a modicum of care, the answers will be fit for purpose. Alternatively, you can run an iterative normal moment calculation and home in on the final answer to whatever level of precision might float your boat.

Do keep in mind that most light aircraft will have an envelope generally similar in shape to that for the Echo.

Update 2:
I thought I have understood the concept, but then another similar question pops up (please see questions in red).
Below is my working to the Question 10 on p.234 (Review Question Set 2) - or see attachment, please tell me where went wrong... :

Current CG is 2480.92,
[ which is within the Forward limit for 2620kg is ( 2620 - 2360 ) x 0.27 + 2400 = 2470.2 ]
(the answer said it is just outside the forward limit...)
But regardless of where the forward limit is, since this is an aft limit problem (because CG of aux tanks 2800 are behind the aft limit of the aircraft 2680), the flow chart method CAN be used, no?

Also, I tried using the graphical method, but the answer I get is 30kg (see orange line in the attached)... what went wrong?

This type of questions appear to be really easy and straight-forward, I don't know what's wrong with me...

since this is an aft limit problem (because CG of aux tanks 2800 are behind the aft limit of the aircraft 2680)

Careful, I think that you have missed an important point here. A reference to "forward limit problem" or "aft limit problem" just means that we have a problem with loading the aircraft to remain within either the forward or aft limit CG respectively. The terms have nothing to do with whether a particular loading station is forward or aft of either limit.

You can solve any of these problems graphically. The difficulty is that, very often, the accuracy of the answer you might achieve often leaves something to be desired. For practical problems out flying on the line, we run the sums graphically as that is the practical way available to us. For the exams, though, the examiner seeks a bit better precision in the answers so we resort to unrealistic techniques to keep the examiner happy.

Thanks for the reply, John.

Yet, I still don't know why my answer (using the graphical method) is wrong.
I got 30 kg but the answer key says 70 kg.
I attached my working for the graphical method above, I hope someone can point out what has gone wrong.

Also, can I use the flow chart method for the question in the post "Update 2" above? Why or why not?

I got 30 kg but the answer key says 70 kg.

It's not a case of your being wrong. Because the two lines are of very similar slope, the plotting and reading bits become critical. The answer is pretty close to 70 kg (within a kilo or two). If you replot with increased care you will get an answer quite a bit closer to 70kg.

Also, can I use the flow chart method for the question in the post "Update 2" above? Why or why not?

Once you get into the region where the CG limit is varying with weight, you only have the option of the graphical approach or running simultaneous equations. The former is easy but rough and ready, the latter mathematically much more accurate but not appropriate for pilot work. You need to keep the goal posts stationary while you are trying to kick a goal.