CG formula anyone ?

[supernova.surfer]

Does anyone know if there is a generic formula to calculate an aircrafts CG ? this is with reference to 3 weights i.e. Take off CG , ZeroFuel CG and Landing CG with the CG's expressed in terms of % of MAC

[Wizofoz]

I'm not sure what you mean by a formula. It's pretty simple. It's just a matter of mass times distance.

The aircraft has a Dry Operating Weight and a Dry Operating Index reference to a fixed datum. Each item loaded then has a moment which is its mass times its distance from the datum.

After everything is loaded you have a total mass and a total moment. Divide the moment by the mass and you have the CG expressed as a distance from the datum. Find out where that is, divide it's distance from the mean leading edge by the mean chord and you have a % MAC

To determine MAC ZFW, simply leave the fuel out of the equation, and for landing use takeoff fuel- trip fuel.

Simple!!

('Course, all I do is sign the Computer Load-sheet!!)

[supernova.surfer]

cg

Wiz thanks for the nice explanatory reply , its making more sense to me now , actually i'm in the process of writing some code for a loadsheet as a personal project (amateur programmer).I have the moments in the form of indices and the total effect as an index , i have all the weights too,what i dont have is the mean leading edge and chord . I'll try and get that info now

quote "Find out where that is, divide it's distance from the mean leading edge by the mean chord and you have a % MAC" unquote

i have the distance effect in terms of indices , i suppose....i need to get the mean leading edge now ? can you explain what you said ( quotes) ? that would be great

edit : what parameters do i need besides the ones i have

[Wizofoz]

Super,

I'll try!!

As you say, you have a series of indicies. These are reference a particular datum. By dividing your total index (sum of all indicies, which will be in the form of KGM, Foot-pounds or whatever system you are using) by your all up weight, you end up with a distance. This is the CG as a distance from the datum. You therefore meed to know where the datum is (it is typically, but not exclusivley, the nose of the aircraft.). This will almost certainly (no, make that CERTAINLY for any conventional aircraft) fall somewhere on the wing.

MAC is simply the avegage chord. For a constant chord wing, it IS the chord. For a constant taper wing, it is simply the average of the root and the tip chord. Sweep back makes it a little challenging, but draw a couple of wings and a graphical solution will become obvious.

If the CG you've just established falls 1/3rd of the way back from the front of this mean chord, your %MAC is 33%. If it's half way, it's 50% and so fourth.

Typical ball-park figures for a jet transport would be 10-40% MAC.

So, the parameters you need are Zero Fuel Weight, Zero Fuel index, index for each loading zone, index for fuel, and position of the leading and trailing edge of the MAC reference the Datum.

Hope that helps!!

[supernova.surfer]

excellent info thanks again Wiz , yes i'll have to get the chord details , i have my script giving me the ZFW and LIZFW , TOW and Index and LAW and index , i've just applied a script to do what the manual loadsheet does, its for an Airbus A310F ,i have the DOW and DOI etc in a database and the deadload is calculated by the script , when i decided to depict the graph is when i came to this hurdle , about the datum ..yes in this case it is 6.3825 meters forward of the nose and there is a reference point to get the +ve and -ve moments,i'll look to get the chord info now....thanks for your help..will post again to follow up this thread

[john_tullamarine]

I have the moments in the form of indices

Why bother ? .. if you are doing the sums on a PC, stay in moment .. using IU just adds calculations for the sake of adding calculations and certainly gives no benefit along the way. I've not done any load work on Airbus but I can't imagine that they would do things differently .. then again .. ?


By dividing your total index (sum of all indicies, which will be in the form of KGM, Foot-pounds or whatever system you are using) by your all up weight, you end up with a distance.

Suggest that either

CG = total moment/total weight, or

CG = (total index * index constant)/total weight


You therefore meed to know where the datum is

Very true. Generally the FS datum is near, or forward of, the nose .. such a bore .. negative numbers. For graphical loading system work, it is more usual to see the (trim) datum somewhere inside the CG envelope.


MAC is simply the average chord

Not quite .. MAC gives a theoretical wing with similar aerodynamic properties

[Wizofoz]

Thanks John!

Super, you'll find that when recieving contrary information, "Listen to John Tullamarine" is a pretty safe bet!

[supernova.surfer]

Thanks for the replies

Why bother ? .. if you are doing the sums on a PC, stay in moment

its not really a bother (thats the form i have the data in) , to clarify.....i am taking this info from a physical manual loadsheet , thats why i have the indices which is infact better for me since i have to show index units on the loadsheet anyway , however i do know that the reduction factor (index constant) is 1000 , the datum is 6.3825 meters forward of the nose and Kgs/in is what is being used...i have the CG bit so far..and i understand that in this case it would be in inches ..which again brings me to MAC ?? .......

here's some data from a computer loadsheet for the same aircraft type

LIZFW -4.59 MACZFW 24.21 ZFW = 100278 KGS
LITOW -31.60 MACTOW 21.16 TOW = 141278 KGS
LILAW 4.47 MACLAW 25.68 LAW = 112578 KGS

given the above data , and the mentioned datum and index constant
to get any MAC = ??

[john_tullamarine]

i am taking this info from a physical manual loadsheet

suggest that you get a copy of the TCDS, the AFM and reverse engineer the trimsheet to figure out the actual numbers .. quite easy to do once you get into it .. and then set up a normal calculation for the PC. Trying to make a trimsheet directly into something else is a recipe for ulcers and frustration.

the datum is 6.3825 meters forward of the nose

if you have such a datum for the trimsheet, forget the exercise ... the trimsheet will be a dog's breakfast so far as (in)accuracy is concerned. More likely, the basic OEM FS datum is forward of the nose .. but the trimsheet uses a more appropriate trim datum (located somewhere in the envelope) .. you can tell if this is the case by the shape of the envelope on the trimsheet .. if it's long and skinny and slopes from lower left to upper right .. then the datum is somewhere out the front (and whoever designed the trimsheet really doesn't know what he was doing) ... if it's sort of squarish and boxy .. the (trim) datum is in the envelope. I've not played with Airbus but I could not imagine that anyone in his/her right mind would have designed a trimsheet using the FS datum.

MAC overlay

the only reason for you to worry about MAC is if your operator prefers to use MAC to describe CG and (as would be the case) the loaded CG/flap defines stab setting for takeoff. If the present trimsheet has a CG (or MAC) overlay, you can reverse engineer this in a doddle as part of the larger exercise.

Why don't you scan and email a copy of your trimsheet or post it somewhere and we can offer specific advice ?


(Logarithms don't come into it at any stage ...)

[supernova.surfer]

That is the datum given to us in our manual and there is a reference point as i mentioned earlier , the trimsheet looks like any other trimsheet i have prepared for many airlines with a slight difference in that this has indices for the deadload instead of the scales to trim the deadloads , i will definitely scan the trim chart since i dont have the knowledge to ellaborate further

as far as the exercise is concerned it is definitely no waste of time or dogs breakfast as you put it since it is only a script which actually greatly simplfies (so far) with 100% accuracy that which is being done manually and seems to be working , all the airlines i've dealt with so far have used MAC on their loadsheets and MAC to determine the T/O stab trim settings so i wouldnt know the difference,but i'll do the scan first

[john_tullamarine]

We look forward to seeing the picture ....

That is the datum given to us in our manual

Invariably, manuals give the OEM FS datum ... if the OEM suggests a trim datum (as most of the larger crowds do) generally it is hidden away in a Weight and Balance Manual somewhere. Nevertheless, the appearance (shape) of the envelope on the trimsheet gives the secret away in a glance ...

indices for the deadload instead of the scales to trim the deadloads

Presumably, this means that you don't have a "normal" trimsheet presentation .. and that the IU sums are done by tabulation and the answers transferred to the envelope ? .. a bit like a GAMA loading system calculation ?

definitely no waste of time or dogs breakfast

.. some elaboration .. my comment related only to extracting the base data from the trimsheet by reverse engineering the picture .. if the datum is the FS datum, then the sheet will be very coarse in its accuracy and the said extraction of underlying numbers becomes a tad more problematic .. if a sensible trim datum is used, the numbers usually fall out with a few minutes "back of a fag packet" calculations.

a script which actually greatly simplfies (so far) with 100% accuracy

Many of us who practise in the weight control arena avoid PC simulations like the plague due to the need for a LOT of error checking routines, etc. .. do be careful with your work ...

MAC to determine the T/O stab trim settings

Very conventional practice.

When you post the picture, we can help with the reverse engineering .. my interest is to help you get the thing correct .. far too many folk play with trim sheets and end up with all sorts of strange results ...

[rubik101]

sorry! Opened the wrong window.

[gr8shandini]

I'm confused. How does changing the datum affect accuracy? It's just a reference point.

[john_tullamarine]

How does changing the datum affect accuracy?

Therein lies a (pretty obvious, if you think about it) secret of good trimsheet (in fact, any graphical system) design.

For a longhand (or PC) calculation, for all reasonable purposes, datum position doesn't matter an iota. However, that is not the case when it comes to drawing pictures ...

Consider the datum position -

(a) if a long way forward of the envelope, the envelope graph will be long and thin and stretch from lower left to upper right - typical GAMA POH style which, in turn, is based on an ICAO sampler

(b) if somewhere inside (or near) the envelope, the envelope will be squarish and boxy in shape

(c) if a long way aft of the envelope, it will be like (a) but sloping from lower right to upper left - can't imagine that anyone would bother doing this

Now ..

(d) if you are not convinced that this is the case, take your favourite aircraft's AFM and rework the CG envelope (weight by moment) for such datum positions ... then plot the co-ordinates.

(e) without running any sort of error analysis, consider the way one can scale the envelope variations ... and the resulting physical chart dimensions.

(f) in case (a) one might have, say, 10 inches of CG travel (forward to aft limit ... represented as moment) drawn with a dimension of, say, half inch, between forward and aft limits ... simply because you have to fit in the sloping characteristic on the page

(g) in case (b) the slopey bit goes out of consideration and you can stretch the envelope laterally so that, say, the 10 inches might be scaled to fit on, say, 5 inches of paper

(h) when completing a trimsheet, which of (a) and (b) would you reckon might give you the more accurate answer ? (where "more accurate" = "lesser error")

(i) re (b), the designer ends up having to be careful that he/she doesn't go overboard and make the scale too generous.


As this thread develops we may end up doing a critique on whatever sheet the originator has in mind .. and all will become patently clear.

[gr8shandini]

Hmm. Still not quite getting it, but I'm unfamiliar with a trimsheet. I'm not an operator, just an engineer working for the OEMs, so I've always been happy with our "slopey" charts. I'd like to see an example if you have one.

[john_tullamarine]

If you have slopey charts, then your folk may need to have a beer and reconsider what they are trying to do. If the envelope is not boxy then the sheet is not as good as it could be ...

In general, the slopey charts are the province of the GAMA fraternity (largely because the GAMA standard format follows the ICAO recommended practice .. ie both are a bit silly when it comes to loading systems). The heavy metal brigade generally use a more suitable trim datum for trimsheet design. There's naught difficult or fancy about this stuff .. all quite straightforward once you get the hang of it.

Quite happy to send you a sample sheet (for my sins I have done more than a lot of these little joys) ... do email me and we can discuss offline ... engineer to engineer ...

[supernova.surfer]

graph

OK i've uploaded the chart http://losheet.bravehost.com/losheet.jpg
clicking on the link directly wont work , please copy and paste the URL

the reference point i've mentioned earlier is 26.67 metres from the Datum which is 6.3825 metres forward of the nose ( added that info in case needed by you)

[john_tullamarine]

Thanks for the scan ... now we're cooking with gas ...

(a) bit late in the evening to do much tonight but will have a look in more detail tomorrow during the odd coffee break at work

(b) presuming that the A310F has a US TC the TCDS will give me most of the info I need .. any other stuff I will post for you to provide

(c) now clear that you are working not with a trimsheet but a (presumably) tabular system for doing the loading sums (which is all the normal trimsheet trimlines do) and then you transfer the total moments (IU) and weights to the envelope to check if the loading is OK

(d) the loading system envelope appears to be well designed. Notice that, with a bit of imagination, you can describe the envelope as being sort of squarish and boxy ... rather than being like the typical envelope one sees in a GAMA style light aircraft POH.

(e) your "reference point" is almost certainly the loading system datum (which is most usually referred to as a "trim datum" .. doesn't matter what you call it, of course)

(f) the loading system datum is 25% MAC which you can tell by a quick look at the envelope .. how ? .. that CG line is vertical ... at the datum the arm is zero so any weight x arm calculation must give a zero moment (and, in this case, IU)..

(g) the designer appears to have done a conventional error analysis for the load calculations


Now, I presume that what you are looking to end up with is the IU equation for this loading system ? (If not, do describe your goal in a bit more detail).

The IU equation, for just about any system, has the general form

IU = A + ((FS - trim datum) * weight)/B

(you might have some unit conversion constants stuck here and there as well but the form doesn't change ...)

where

IU = index units

A = a constant IU to get rid of the minus numbers on the IU scale. For your system, A=0. If you wanted to get rid of the negatives, you might put A=80 (depending on how long a scale you want to draw ... you only need to make it cover the likely range of entry IU values). If you used 80, then -80 on the scale would become 0, -70 would become 10 and so on.

FS = the (fuselage) station of interest (typically where a load is positioned). In your case, FS will be measured from the main datum (6.3825 m fwd of the nose).

trim datum = a convenient and useful FS value which gives you a suitably shaped CG envelope when drawn wt x IU. It appears that, in your case, this value is 26.67

Note that (FS-trim datum) gives you a revised arm measured from the trim datum rather than from the main FS datum .. no more, no less.

weight = is the weight located at the FS of interest

B = the non-dimensionalising constant moment used to convert the basic moment (=wt*arm) to an IU. You suggested that this value is 1000 .. we can check this out in due course as part of the reverse engineering exercise

Note that, if we put A=0 and don't use a trim datum (put trim datum = 0 .. ie the trim datum is at the FS datum) then the general equation becomes

IU = (FS * wt)/constant

which is the usual

IU = moment/constant

basic formula with which we are all familiar.

[cwatters]

Free online calculator (not tried it myself but it looks funky)...

http://adamone.rchomepage.com/cg_calc.htm

http://www.geistware.com/rcmodeling/cg_super_calc.htm

[supernova.surfer]

great explanation thanks , (ooh) the ball is back in my court ,hmm lemme see hope i get racket to ball at least ... here goes.......

(c) now clear that you are working not with a trimsheet but a (presumably) tabular system for doing the loading sums (which is all the normal trimsheet trimlines do) and then you transfer the total moments (IU) and weights to the envelope to check if the loading is OK

yes thats it , i have all the index units in tabular form on the manual loadsheet itself for each ULD(unit load device) position ,i.e. in effect the station . Had been instructed that the reference point(or trim datum which you explain it is) was created to enable/create -ve & +ve moments for easier calculations instead of -ve moments alone . The IU's i already have in tabular form like you had mentioned , my script only adds them up after given the weights(form inputs by user) for all the ULD positions(stations) . At the end of processing , i have my ZFW/TOW/LAW weights and their respective indices ready for use

Now, I presume that what you are looking to end up with is the IU equation for this loading system ? (If not, do describe your goal in a bit more detail).

yes so the goal is to transfer the weights and IU's i already have(automated) , transfered to the envelope ...so thats what i need ...a method to generate the CG Given the weights and IU's

i could graphically attempt to depict the graph provided i have a method to calculate the CG's by the script .....hope i'm clear