CG formula anyone ?

[supernova.surfer]

yup John ..will message you when i'm done getting rid of some bugs thx

[QAYS]

Hello,
In first time, my appologize for my poor english.
I am french And I search formula about % Mac.

i find this formula :

% MAC = 100* C*(LIZFW - K) /(ZFW*Chord) +
100*(Harm- Harm25%)/Chord

For A320 Aircraft:
C = 1000
K= 50
Chord=4,1935m
Harm=17,8015m
Harm25%=18,850m

But this formula is good in some case and false in other, some examples
AirCraftA320A330A320A320A320A320A320
Chord4,19357,274,19354,19354,19354,19354,1935
ZFI27,6112,828,1363,5530,6149,652,4
ZFW479301582635402956006553045462156870
K501005050505050
C1000250010001000100010001000
Harm17,801531,3417,801517,801517,801517,801517,8015
H2518,8533,1618,8518,8518,8518,8518,85%Mac Compute13,827,815,330,7716,6424,8226,00real
Value in loadsheet28,327,830,1730,7735,623235,6

Have you got an explication for this differences

Thank you
best regards

[john_tullamarine]

QAYS,

Good to have you on board .. don't worry about your English .. your English is far, far better than my long-forgotten schoolboy French.

You have posted an unusually complicated formula for %MAC. I think that we need some more information before we can make some sense of it. Can you advise what the following terms are (ie what do they mean in physical terms) ?

(a) C

(b) LIZFW

(c) K

(d) Chord (ie which particular chord ?)

(e) Harm (perhaps distance from OEM FS datum to CG location ?)

We could run some reverse engineering to relate it to the standard equation but, if you can provide the above information, it will save some time. Indeed, without the information, we can't even begin with a dimensional check of the equation.

regards,

John

[QAYS]

hello an thank you,

Sorry for this equation, in fact i found it on page 124 from airbus document "Getting_To_Grips_With_Weight_and_Balance", I will be back with more explanation

[QAYS]

hello I am back with more explanation :

Note : two different index formulae can be used depending on the unit of item H-arm : length (mor in) or %MAC.

Code:

Index = Weigth *( HarmItem-H25)/C + K = Weigth*(%Mac - 25)*C' +K
With C' = Length of RC/(100*C)

So,

Code:

Index = Weigth*(%Mac - 25)*Length of RC/(100*C) + K
%Mac = 100*C*(I-K)/Weigth*Length of RC + 25

In my first message I have given some information, here new value:

for A320

Chord :4,1935
ZFI on loadsheet: 27,6
ZFW on loadsheet: 47930
K :50
C :1000
Harm :17,8015
H25 :18,85
Mac by my equation : 13,85
Mac give by loadsheet : 28,3

For A330

Chord :7,27
ZFI on loadsheet :112,8
ZFWon loadsheet :158263
K :100
C :2500
Harm :31,34
H25 :33,16
Mac by my equation : 27,81
Mac give by loadsheet : 27,8

As you can see it for A330 my equation give a good result but for A320 give a wrong result, have you an explanation

I hope my new message in more comprehensible
Best regards

[QAYS]

hello, after hard work, I think found a good equation, I put it on paper and I submit to you

[QAYS]

I was wrong, my equation don't give a good result, worst when I submit the same data to another software which give %mac the result is not like in the loadsheet, I am lost!!!

If you have an idea
Here some equations :

Code:

     
            ( Harm - H25% ) * W
Index = ----------------------- + K
                          C
                 100*C*(Index - K)                  100* ( Harm - H25% )
% Mac = ------------------------------- + --------------------------
          Weigth * Length of Chord             Length of Chord

best regards

[john_tullamarine]

(a) I located the Airbus document via a Google search - it looks to be a quite useful pilot reference and one that Airbus pilots within the PPRuNe fraternity should review. Indeed, much of the general information would be of use to all the heavy iron pilot folk here. It is available on a number of sites - for instance, here.

(b) in respect of the weight and balance engineering section, the explanation is a bit convoluted and unnecessarily difficult to follow (and I'm a weights engineer, among other things) so I have some empathy with your confusion. However, the subject is very straightforward so I shall add some comments in this post .. as I work my way through the Airbus document .. to assist your understanding.

(c) p119. The standard Airbus trimsheet is a fairly stock standard sort of document. Points to notice are

(i) the %MAC grid line which is vertical tells you what the trim datum is - in this case, 25% MAC. (At the datum, the moment calculation is M = W * 0 = 0 (zero) for all weight values so you end up with a vertical line).

(ii) the general formula for such a trimsheet is

IU = [(CG - trim datum) * weight/constant A] + constant B

where

> CG is the horizontal distance ("arm" as the pilot fraternity likes to say) of a load from the OEM FS (fuselage station) datum to wherever the load is located.

> the trim datum is a location chosen to give an accurate trimsheet. In general, the trim datum should be somewhere within the CG envelope. Airbus has chosen 25% MAC (and that's fine - but 35% MAC for the A380 and that's fine, too) .. for other aircraft the designer would pick what he/she thinks will do the job best. So, for example, most light aircraft are best suited to a trim datum somewhere near the aftmost CG envelope limit. Be aware that, should you encounter a trim sheet for an Airbus designed other than by Airbus .. it might be quite different to the Airbus document. That is, just because Airbus design the document one way, doesn't mean that that is the only way it can be done.

> (CG - trim datum) is a calculation to change arms from being measured from the FS datum to being measured from the trim datum .. it just moves the tape measure along the side view of the aeroplane .. no more, no less. Using this analogy, the end of the tape measure is moved from the OEM FS datum to the trim datum. The significance is that ALL measurements MUST be made from ONE datum .. you MUST NOT mix and match measurements lest you end up with nonsense results in your calculations.

> weight is the weight (mass, strictly) of the load under consideration

> constant A is the typical moment to IU constant intended to make the numbers a bit more workable for us mere mortals. Typically, the constant A will be a nice round number like a thousand, a hundred thousand, or suchlike. If it is not a nice round number, that indicates that there are some conversion factors, etc., embedded within it or that a scaling factor was needed for some design reason.

> constant B. If we left constant B out of it, then the IU entry line for the trim sheet would have its zero at 25% MAC in the case of the Airbus document with minus numbers (IU values) to the left and positive IU to the right. That's a bit untidy so, if we put constant B to be a useful number, we can get rid of the minus IU values. Airbus, by observation, has chosen to put constant B = 100 in the trim sheet at p119.

.. and that's about all the hard stuff involved with a trim sheet so far as pilots are concerned ..

(d) p122-124. All that this says (in a round about sort of way) is that you do the calculations just like you did in your PPL weight and balance training ..

For calculating CG .. the usual table of weights, arms, and moments. Calculated final CGs (for ZFW and TOW) come from total moment/total weight.

Keep in mind, Airbus

> is now measuring their arms from 25% MAC (H25) rather than FS 0.0.

> approach here is to start with the empty aircraft and add non-fuel and fuel items as separate, aggregrated lumps .. still basically the same as the PPL table calculation.

IU = moment/constant. One word of warning .. the Airbus document makes reference to K (what I called constant B) in (a). This constant is ONLY used for working out the trim sheet entry IU value. For IU calculations at a particular trim line, the calculation is IU change (or "delta" as we often say) and the K is left out. This is not made clear in the Airbus notes. Their (b) relates to the delta calculation .. Δ is the Greek alphabet symbol for (upper case) delta .. δ is the lower case symbol, which is more likely to be encountered.

Another point to emphasise .. you can add (subtract) weights and moments (or IU) but NOT CG values. CG values are calculated from moments (IUs) and weights.

We'll come back to the MAC formula later on ... a great example of taking something which is very simple .. and making it very complicated.

(e) p127 These ΔIndex values per kg are presented in the AHM560, nevertheless on the manual balance chart it is not possible to take into account the ΔIndex of each individual row. The trim sheet is based on loading zones. For each seat row to be accounted separately, the sheet would require a separate trim line. Commonsense prevails and a sensible zone arrangement is found. This introduces errors which need to be addressed in the design error analysis .. correction for the error usually is by compressing the apparent CG envelope limits to account for the error magnitude.

(f) the equation initially queried was from p124 of the Airbus document -

for the FS calculation -

IU = W * (H - H25)/C + K

is the standard IU equation (albeit with a few subscripts to confuse the unwary).

with the %MAC equivalent being

IU = W * (%MAC - 25) * C' + K [where C' = length of RC/(100 * C)

Keeping in mind that RC is just another name for MAC in the Airbus document, the simplest way to show that the two equations are the same is to compare them and see what results.

For the FS version the arm (measured from the trim datum) is H - H25. This can be recast into a form using %MAC (which is just a different way to look at an arm). Keep in mind that the reference to "25" is to 25% which is 25/100 and which we might signify by H25 as an arm.

Let's start with the %MAC form and work back to the FS form -

= W * [(%MAC -25) * C'] + K

= W * [(%MAC - 25) *MAC / (100 * C)] + K

= W * [%MAC * MAC / (100 * C) - 25 * MAC / (100 * C)] + K

= W * [(H - LE) * 100 * MAC / (MAC * 100 * C) - (H25 - LE) * 100 * MAC / (MAC * 100 * C)] + K

= W * [(H - LE) / C - (H25 - LE) / C] + K

= W [(H - LE) / C] - W [(H25 - LE) / C] + K

= W H / C - W LE / C - W H25 / C + W LE / C +K

= W H / C - W H2 / C + K

= W * (H - H25) / C + K

which is the FS form so it all works out fine.



(g) Looking at QAYS' examples, we need to know just which trim sheets he is comparing his calculated examples with in post #3 ?

[QAYS]

Hello, I would like thank you for your help.

I' am working on this equation, I think I could compute Harm with DOW an DOI.in fact I noticed, for the same AirCraft A320 I can have DOI totaly different:

Exemple from LoadSheet :

A320 register XXXX
DOW 43780
DOI 45,5

A320 register YYYY
DOW 44128
DOI 27,1

index equation

DOW= 44218
DOI=27,1
Index = W*(Harm-H25)/C + K
With
H25 = 18,850 for A320
K= 50 for A320
C= 100 for A320

Harm = ((I - K)*C)/W + H25

Harm for register YYYY= 18,33 m
Harm for register YYYY= 18,74 m

in fact I suppose each company compute Harm of each aircraft, for me, it's the only reason which explain data difference between two A320

I continue the research

[john_tullamarine]

I think I could compute Harm with DOW an DOI

Of course you can -

IU = W(H-H25)/C +K

can be rearranged to give

H = C(IU-K)/W + H25


I noticed, for the same AirCraft A320 I can have DOI totaly different

Not at all unusual. This just reflects a range of empty weights and CGs across a similar fleet (presuming similar configuration and the same IU formula, of course). For the example you cite, CGs of 18.33m and 18.74m possibly are a little too far apart for comfort and need investigation.

It is important to realise that each aircraft is an individual machine and will have small differences from its apparently identical fleet colleagues.

Some operators use fleet average data for empty weight and IU. If this is your case, then part of the confusion may relate to having apparently identical data in the fleet average declared data .. it is important to keep in mind that the average comes from a small range of data which is used to calculate the average..

However, getting back to your original concerns, can you indicate the specific trimsheets from which you obtained your MAC values ? If the trimsheet is consistent with the Airbus calculation models then the reason for the apparent MAC difference should stand out.

[QAYS]

However, getting back to your original concerns, can you indicate the specific trimsheets from which you obtained your MAC values ? If the trimsheet is consistent with the Airbus calculation models then the reason for the apparent MAC difference should stand out.

In fact I obtain data (DOW and DOI) from Loadsheet gaetan , I Took It when I worked In Orly airport like Fligth dispacther.

So I prepared Two Fligth, one which have DOW = 44128 with DOI =27,1
and an other DOW =4378 and DOI=45,5

I noticed when I take paper trim sheet A320 from company alpha I can't use it for all A320, in fact for the first plane (DOI 27,1) le LITOW is out.

So I deduct each company have his owner trim sheet, but there must be an generic equation which give %Mac for all Airbus or aircraft.

I have a doubt about this equation % Mac =100*C*(I-K)/Weigth*Length of RC + 25 and I have a doubt about 25, I think this value is result of this equation :

100*(Harm -hH25)/Lenght of Chord

PS: I ma sorry if I repeat myself, but I'm very perplexed about determination % MAC,
I Continue the research
thank you

[john_tullamarine]

I obtain data (DOW and DOI) from Loadsheet gaetan

Question is whether the different loadsheets have the same design equation for IU. Keep in mind that the IU equation can vary from trimsheet to trimsheet .. ie I could design 10 A320 trimsheets which might look generally similar but have incompatible IU equations. So far as the pilot is concerned, the only obvious difference would be the IU value to start the trimsheet calculation.

Hence the need for us to know just which trimsheets you are using .. you may end up needing to post a scan of them so that we can reverse engineer the IU equation to check out just why you are getting apparently incompatible answers.

when I take paper trim sheet A320 from company alpha I can't use it for all A320, in fact for the first plane (DOI 27,1) le LITOW is out.

Exactly .. you MUST NOT use a trimsheet for another operator unless you have established that the document is compatible both for configuration and IU equation.

there must be an generic equation which give %Mac for all Airbus or aircraft.

No, not at all when it comes to trimsheets as you are plotting %MAC as a set of values of W by IU so, if the IU equation is different, then you need to take that into account when comparing things ... you MUST compare apples with apples for the numbers to make much sense.

The relationships are OK for basic calculations such as we have been using above. However, the IU equation is variable according to the views of the trimsheet designer ... so two different sheets may .. or may not ... be compatible when it comes to playing with the numbers.

It would be reasonable to presume that any trimsheet designed by Airbus will be as they describe in their document. Indeed, I would imagine that most airline Airbus operators would follow the Airbus model for convenience.

However, if I, or some other designer, were to design an Airbus trimsheet that trimsheet might be quite different in the detail when compared to the Airbus trimsheet. As I suggested earlier, just because Airbus chooses to design a trimsheet one way doesn't mean that that is the only way. Same thing applies with Boeing or any other OEM.

I have a doubt about this equation % Mac =100*C*(I-K)/Weigth*Length of RC + 25 and I have a doubt about 25,

You appear to have left out some brackets above. Just to clarify, the Airbus equation from p124 becomes -

%MAC = 25 + 100*C*(I-K)/(W*MAC)

(I've rearranged it a bit to emphasis what the brackets are doing .. RC is the same as MAC)

Nothing wrong with the Airbus equation. What do you see as the difficulty and we can discuss it to remove the concern ?

The "25" simply relates to the Airbus choice of trim datum to be 25%MAC and is 25%.

I'm sure that a few more exchanges and we will have your concerns put to rest.

Looking forward to your reply.

[QAYS]

Nothing wrong with the Airbus equation. What do you see as the difficulty and we can discuss it to remove the concern ?

I don't want to say Airbus equation is wrong, but i don't understand it.

I don't understand why, the same equation is able to compute %Mac correctly for one aircraft and isn't able to compute this %mac for an other.

The best way would be to meet pilot.

To explain the reason about my research, I created software which is able to compute the aircraft loading , like gaetan software.

I found Harm about Hold (in airbus doc) and to determine Index about Cabin I use trim sheet about aircraft, the first results is very good, My Index ZFW,TOW,and LDW are equal with values which are compute by gaetan (airfrance software), The only equation I don't have is equation %Mac,

So i search on Web, generic equation or not,which is able to compute %Mac for any aircraft, when I am able to compute Index value of ZFW,TOW,and LDW

thank you much for your understanding and for your help

[john_tullamarine]

but i don't understand it

I had to get out pencil and paper to work it through as well, so don't feel bad at all. The Airbus explanations are a bit (and unnecessarily) convoluted in my view .. but, nonetheless, correct. The aim, now, is to work out just where you are having problems and then fix those problems. Keep firmly in mind that this stuff is pretty straightforward but it requires meticulous housekeeping to avoid error.

the same equation is able to compute %Mac correctly for one aircraft and isn't able to compute this %mac for an other.

If the equation is correct, then there must be something different about the aircraft. That is what we need to find out.

The best way would be to meet pilot.

I suggest not .. the average pilot has a practical competence with the completion of trimsheets .. but generally a limited understanding of their design and construction.

The only equation I don't have is equation %Mac,

You will have to show us what data you are using .. ie trimsheet, software output, etc. Otherwise we cannot determine where the error occurs. My guess is that you either have

(a) an incorrect implementation of the equation, or

(b) different and incompatible trimsheet designs.

Until we can see and test we probably can't go much further.

If you don't want to post such documents by all means email a scan direct to me and I can sanitise the original for an explanatory post.

So i search on Web, generic equation or not,which is able to compute %Mac for any aircraft,

This is possibly a cause for your problem. The %MAC equations discussed in previous posts work just fine but only for the correct and applicable datum position. Because the IU equation for trimsheets can vary according to the preference of the trimsheet designer one requires a fairly complex equation to cover all the possibilities and then there remains the problem of reverse engineering an individual trimsheet to find equation constants.

[QAYS]

Hello, Goooooooooal (I think)


I found equation on AHM 560 of airlingus, in fact In this doc I found equation to compute Index and % Mac, I have explaination about almost constant.

as I thought it, each company for his each aircraft give LEMAC

Index =W*(Sta - Ref.Sta)/C + K
% MAC =( 100*C.(I-K) )/(MAC*W) + 100*(Ref.Sta - LEMAC)/(MAC)

W = Weight, actual
Sta. = Station, horizontal distance from station zero to the location
Ref.Sta. = Reference Station/axis. Selected station for calculation purpose
K = Constant used as a plus value to avoid negative index figures
C = Constant used as a denominator to convert moment values into
index values
I = Index value corresponding to respective weight
MAC = Length of Mean Aerodynamic Chord
LEMAC = Horizontal distance from the station zero to location of the
Leading Edge of the MAC

Now I nead found LEMAC for each aircraft which use in my software, because it's the only variable which move from aircraft to an onther aircraft

I made some test, and i ma on good way

PS: As i tell you in my previous posts, my english is poor and sometimes I don't understand all what you write, but I try to translate et I want thank you for all your help
See you later
Best regards

[john_tullamarine]

Index =W*(Sta - Ref.Sta)/C + K

Stock standard IU equation for a trimsheet as we have discussed before.

% MAC =( 100*C.(I-K) )/(MAC*W) + 100*(Ref.Sta - LEMAC)/(MAC)

This equation follows by some manipulation .... but it's a lot easier just to read the %MAC off the envelope overlay grid ie enter IU and W and read off %MAC. This %MAC equation is quite unnecessary and not even used for plotting the grid in the design phase of the trimsheet (although it certainly could be). As you will always work through a fuselage station for CG, it is a lot easier just to use the general basic equation -

%MAC = (CG - LEMAC)*100/MAC

What concerns me is that you are making something very simple into something a lot more complex ... but for no advantage to you.

as I thought it, each company for his each aircraft give LEMAC

I may be misunderstanding your intent here. The LEMAC is provided by the aircraft OEM (in the WBM, AFM, TCDS, etc). Not determined by the operator.

my english is poor and sometimes I don't understand all what you write

that's my fault .. not yours.

[QAYS]

I have impression I have diffilculties to make me understand.

In fact with this equation :
% MAC =( 100*C.(I-K) )/(MAC*W) + 100*(Ref.Sta - LEMAC)/(MAC)

C = 1000 for A320 / given by airbus nevertheless, for Airlingus C= 500
K = 50 for A320 / given by airbus
MAC = 4,1935m for A320 / given by airbus
Ref.Sta = 18,850m for A320 / given by airbus
I = Compute by loadsheet
W = Compute by loading Cabin and Hold

So I deduct the only data which is able to explain difference between two register is LEMAC, no

==>% MAC =( 100*C.(I-K) )/(MAC*W) + 100*(Ref.Sta - LEMAC)/(MAC)
==>LEMAC = %MAC*MAC/100 + C.(I-K) )/(W) + Ref.Sta

If I take my two A320
AirCraft 1 :
% MAC = 28,3%
IZW = 27,6
ZFW = 47930
Lemac = 19,5

AirCraft 1 :
MAC = 32
IZW = 49,6
ZFW = 54621
Lemac = 20,19

Perhaps I mix data which would not have like %MAC and other data !!
But I Don't desperate, I will find this equation

[john_tullamarine]

I have impression I have diffilculties to make me understand

Have no worry. One of the difficulties with any discussion involving folk without an idiomatic common language is making sure that what one is saying is what the other is hearing and comprehending and that applies for both people. Just means that we take a little bit longer to work through a discussion and that is fine.

nevertheless, for Airlingus C= 500

This suggests that the two trimsheets are not the same. I need to see the other trimsheet to check if that is the case or if, for instance, the 500 reference is in error.

So I deduct the only data which is able to explain difference between two register is LEMAC

LEMAC is a fixed position, defined by the OEM design. This cannot be the cause, I fear.

Your calculations are fine.

However, we don't have enough information to work out where the apparent error comes from. You will have to let me see both the trimsheets so that I can compare them. At this stage, the likely answer is that you are trying to treat two different designs as the same and that just won't work.

Can you scan both the trimsheets you are working with and email them to me ? That way there can be no confusion regarding just what data you are working with.

[QAYS]

Hello, I' m very sorry , I haven't got scan to send you trim sheet.

I Will try to explain it.

When I compute UI for Hold 1 with Airbus data:

Hold1 Harm = 12.283 m from Airbus Doc
Unit Index = W*(Sta - Ref.Sta)/C This equation compute Index for An item
With
Sta = Harm= 12,283 from Airbus Doc
Ref.Sta = 18,850 from Airbus Doc
C=1000 from Airbus Doc
So Unit Index = 0,0064 for Hold 1

The first come from AirFrance A320-100
Hold 1 ==>1000 kg = ~6,4UI i can deduct For Hold1 0,0064 UI/Kg
there are the same calc for all Hold

The second (Trim sheet) come from NouvelAir
Hold 1 ==>500 kg = ~3,2UI i can deduct For Hold1 0,0064 UI/Kg

The third (Trim sheet) come from XL AirWay
Hold 1 ==> 500kg = ~1,1 UI

I will try to scan the LOADSHEET and i will send it to you

In fact I didn't use trim sheet to make my calcul, but i used electronic Loadsheet create by gaetan (airfrance software) to control my result

the Unit Index are compute from My software with airbus data or with reading trim sheet when when I have one

In fact to create one aircraft on my software, I have two opportunity:

Case 1 : I have Doc Airbus ou AHM:
- For Hold I hava Airbus Data.
- For Cabin I use Trim sheet (because earch aircraft have onwer configuration)

Case 2 : I don't have Doc or AHM
- For Cabin and Hold I use trim sheet If I have one

That's why I can treat any aircraft when I have got trimsheet, I study It and I save all informations in my soft

according to you, I found Aircraft manual about Boeing with Arm of Hold, can I use the same equation to compute Unit Index?

best regards

[john_tullamarine]

I haven't got scan to send you trim sheet.

Oh, well, never mind ... let's work out a Plan B.

When I compute UI for Hold 1 with Airbus data: Hold1 Harm = 12.283 m from Airbus Doc

As the station is forward of the datum (Ref Stn), the ΔIU has to be negative. For interest, my calculation gives

ΔIU = -0.006567 / kg

The third (Trim sheet) come from XL AirWay Hold 1 ==> 500kg = ~1,1 UI

Ah, now this presents a problem. Most likely, the IU equation is different.

I will try to scan the LOADSHEET and i will send it to you

This is fairly important as, without the pictures of the various sheets, I can't figure out where the error is.

i used electronic Loadsheet create by gaetan (airfrance software) to control my result

That's fine but, if we sort out the trimsheets first, then we have somewhere to start and can look at the software.

I found Aircraft manual about Boeing with Arm of Hold, can I use the same equation to compute Unit Index?

You can only use the same IU equation if the two systems use the same equation. The problem is that there is no reason for different loading systems to use the same IU equation and, very often, the equations will be different. If is essential to make sure that sheets are compatible before you start running calculations other than using the sheet and the declared entry data.