Edit: Answering my own (rather stupid) questions... The takeaway is try not to study when you are too tired (but it's hard for some of us with a full time job including myself).
The two questions in the replies below are still unresolved though!

I am trying to find the relationship among formulae to get a better understanding:-

p.173-174 says weight shifting formula is:
( Present weight x shift in CG ) / difference in arms = weight to be shifted

Answer to Exercise 5.13 - p.190 #5 (answer on p.219) says Alternative formula for finding weight shift is:
Change in MOMENT / difference in arms = weight to be shifted

(Please see attachment below)

Does it mean:
Present weight x shift in CG = Change in MOMENT?

Answer: Yes, reason below.
Given ( weight x arm = moment ). [Note: arm and CG position are used interchangeably here, and will be shortened as "CG"]

Change in moment
= new moment - present moment
= new weight x new CG - present weight x present CG
= Present weight x (new CG - present CG) [ONLY if new weight = present weight]
= Present weight x shift in CG

---

On the other hand, I am not quite sure how the flow chart for calculating weight to be shifted/ added/ removed is deduced from ( weight x arm = moment ). Or is it more complicated than that?
I suppose I can get by by just memorise the flow chart, but I would like to know how it is being deduced, so that I can truly understand the topic.

Answer:
For weight shifting, given ( weight x arm = moment ). A small weight is to be removed from Original CG arm and added to New CG arm.

Present Weight x Present CG - Weight to be shifted x Original CG arm + Weight to be shifted x New CG arm = New moment
Present Weight x Present CG + Weight to be shifted x ( New CG arm - Original CG arm ) = New moment
Present Weight x Present CG + Weight to be shifted x ( difference in arm ) = New moment
Present Weight x Present CG + Weight to be shifted x ( difference in arm ) = ( New Weight x New CG )
Weight to be shifted x ( difference in arm ) = ( New Weight x New CG ) - ( Present Weight x Present CG )
Weight to be shifted x ( difference in arm ) = Present Weight x ( New CG - Present CG )
[Because weight is only shifted, not added or removed. So the Present weight and the New weight are the same**]
Weight to be shifted x ( difference in arm ) = Present Weight x ( Shift in CG )
Weight to be shifted = Present Weight x ( Shift in CG ) / ( difference in arm )
-- which is the same as the flow chart method in the book.

**Note: but then this formula is used in scenarios where weights are added/ subtracted too...
So for weight adding, see deductions below.

Change in moment = Present moment - Moment added because of the added weight (let's just call it "Moment added", and the CG where the additional weight is added to "CG added")
Present moment - Moment added = (Present weight - Weight added ) x CG required
( Present weight x Present CG ) - ( Weight added x CG added ) = ( Present weight x CG required ) - ( Weight added x CG required )
Re-arranging the items in the equation, we have:
( Present weight x Present CG ) - ( Present weight x CG required ) = ( Weight added x CG added ) - ( Weight added x CG required )
Present weight x ( Present CG - CG required ) = Weight added x ( CG added - CG required )
Present Weight x ( Shift in CG ) / ( difference in arm ) = Weight added
Weight added = Present Weight x ( Shift in CG ) / ( difference in arm )
-- which is the same as the flow chart method in the book.
For weight to be subtracted, the deduction will be exactly the same.




Thanks a lot!

Please don't continually rewrite your posts. It makes following the thrust of the thread near impossible for the reader. If you see the need to make a major change to what you have already written, leave the original post(s) and then write a new post with whatever it is you wish to say. That way we can follow your thought processes.

This thread has become an absolute nightmare to follow.

Thanks for the reply, John.
I was initially worried about copyright issue, but on second thought it does make more sense to attach relevant pages.
I guess I will attach the pages first and take it down if a copyright issue does arise. Cheers!

There are provisions for limited citing of text within the copyright rules so I wouldn't fuss too much.

[Edit: Resolved. Reason: RTFQ. Note: thanks John!!]

For forward limit problems, the CG envelope graph should be used.
For aft limit problems, the flow chart method (shown above) should be used.

Can I use the CG envelope method for aft limit problems regardless?
I tried it on Question 12 of CPL Final Test (p.237), but it doesn't work.
The answer I have from the CG envelope method (orange line) is around 100kg, but the answer in the book is around 20kg.
I wonder where the CG envelop concept went wrong.

I have yet another similar question for Final Test Q33 (p.240).
I tried using a flow chart method to put the CG to the aft limit (because the question asks for the max fuel that can be stored in the auxiliary tanks, meaning it will shift the CG aft) but I end up getting a ridiculously large figure. (Present CG: 2508.5, Req'd CG: 2680, that's why)

Because the figure is ridiculous, I reckon I was wrong. So instead, I substitute one of the answer options to find whether it will go out of CG limits (in particular the aft limit). I started working with Option (b) - 215kg.

Weight	Arm	Index
2655		666
215	1780	38.27
2630		704.27

The CG is 2677.8, which is within the aft limit of 2680. But this answer is wrong.

The questions I have is:
1. I know how to use the graphical method, but I don't know WHEN to use it. Esp in questions where it is not as obvious to me whether it is a forward limit problem.
2. I don't know WHY using other methods are wrong, because mathematically they seem right?


I am thinking I have misinterpret some concepts, and am trying to identify where the knowledge gap is...
I would be grateful if someone could give me an answer!

Possibly our video lectures might help you get the concepts clear in your head.

online.bobtait.com.au/course/index.php?categoryid=29

They are all categorized by topics, very affordable and you have access to them for 3 months.

Have a look they might really help you get a sound understanding.

Thanks for the reply, Stuart. I think what I struggle with the most is when to use CG envelope graph and when to use mathematical method for CG balance questions, and why can't the CG envelope graph be used in all scenarios.
I will summarise my biggest questions below and go see the videos if they are still unresolved, although I think I will still need pointers after watching the video because I cannot seem to recognise the main point - even after reading relevant sections of the book multiple times.

1. For forward limit problems, the CG envelope graph should be used. For aft limit problems, the flow chart method (shown above) should be used.
Can I use the CG envelope method for aft limit problems regardless? Why or Why not?

2. For loading problems, do I use the CG envelope graph AND calculate the CG to see if it's a forward or aft limit problem first, then decide whether to use graphical method or CG calculation to tackle the problem?

3. Why does the aft CG limit moves aft for the CG envelope but remains 2680mm in Performance Supplement p.18?

Similar question/ example can be found in the reply section of:
www.bobtait.com.au/forum/performance/731...7-new-review-q-set-2

For forward limit problems, the CG envelope graph should be used.
For aft limit problems, the flow chart method (shown above) should be used.

It is convenient to use the graphing method if you are working in a region where the CG envelope data has the CG changing with gross weight.

Can I use the CG envelope method for aft limit problems regardless?

You can use the graphing method for any problems. Just be aware that the accuracy achievable might not be all that precise for the exam requirements. With a bit of conservatism applied, though, it is fine for real world work out flying the line.

but I end up getting a ridiculously large figure.

I suspect you are trying to do things which just don't work. When I get some spare time I will have a look at the sums and give you some more detailed guidance.

I think what I struggle with the most is when to use CG envelope graph and when to use mathematical method for CG balance questions,

You can use the graphical method for ALL AND ANY problems - it doesn't matter whether we are playing with the forward limit or the aft limit. However, for some problems (eg OTHER than the upper forward limit area) we CHOOSE to do the sums to obtain a more precise answer for the exam.

For loading problems, do I use the CG envelope graph AND calculate the CG to see if it's a forward or aft limit problem first

You need to figure out, first, whether you have a problem with the forward limit OR the aft limit before you can figure out how to go about tackling the problem. Just a quick plot of the starting point weight and CG/moment/IU will give you that information.

Why does the aft CG limit moves aft for the CG envelope

I think you had best show us where you see this problem as it doesn't make much sense to me at the moment ?

OK, let's have a look at what your posts say at the moment. Please don't change the posts - if you want to do that, leave the original post(s) and write a new post with whatever the current story might be. Otherwise we have no idea what you are talking about .....

Does it mean: Present weight x shift in CG = Change in MOMENT?

Of course it does. If we move some stuff from FS A to FS B,

Original moment = gross weight x A
New moment = gross weight x B
Difference (or change) in moment = gross weight x B - gross weight x A
= gross weight (B - A)
= gross weight x distance we move the load

(Please don't talk FS and CG interchangeably or else you will get yourself into the most dreadful confused places ....)

Bob's technique is just a play on the basic equation w x arm = moment and running adjustment calculations to try and give the folk without any algebraic background a basis for understanding the story. It doesn't matter how you think about it or process it - things don't get any more complex than what I have suggested above.

I tried it on Question 12 of CPL Final Test (p.237), but it doesn't work.
The answer I have from the CG envelope method (orange line) is around 100kg, but the answer in the book is around 20kg.
I wonder where the CG envelop concept went wrong.

Actually, the concept didn't do anything wrong. What you have done is answer another question altogether. Your process finds the load you can add to the rear seats to end up at the aft limit. The question asked, having added two extra passengers, which puts you outside the rear limit, how much rear cargo do you have to offload to get back to the aft limit. Suggest you revisit the question in some more detail this time around ? It never helps if you don't answer the problem at hand. While your process might be all fine, you end up with something different to what you wanted.

I have yet another similar question for Final Test Q33 (p.240).
I tried using a flow chart method to put the CG to the aft limit (because the question asks for the max fuel that can be stored in the auxiliary tanks, meaning it will shift the CG aft) but I end up getting a ridiculously large figure.

The problem is that you are missing the whole point of the question.

(a) the starting CG puts you a little inside the forward limit.

(b) as you add fuel into the aux tank the CG of the progressive load does, indeed, move aft. However the forward CG limit moves aft faster than the changing aircraft does. End result is that you end up going out of the forward limit which then put a stop on how much fuel you can add. You will never get to the aft limit - this is your problem. You are thinking that you are trying to get to the aft limit and that is just not a feasible option. Your point of misunderstanding is I tried using a flow chart method to put the CG to the aft limit and you just can't achieve that.

1. For forward limit problems, the CG envelope graph should be used. For aft limit problems, the flow chart method (shown above) should be used. Can I use the CG envelope method for aft limit problems regardless? Why or Why not?

That should read "for upper forward limit problems". You can do it other ways but they involve mathematics stuff which is not appropriate for this work in pilot talk. You can use the graphical approach for ANY problem. However, you get better precision in the answers by using the equations. This is for the exams. In real life, most folk would just use a graphical approach with an appropriate level of conservatism to make sure you end up inside the envelope. Can I use the CG envelope method for aft limit problems regardless? Sure you can, you can use a graphical approach for any problem but that might not be the best approach.

Why does the aft CG limit moves aft for the CG envelope but remains 2680mm in Performance Supplement p.18?

We have talked about this before. Can you post some detail to amplify your thoughts as what you have said just doesn't make any sense to this engineer.