(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 ?