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I mean, the same aircraft, but empty or on MTOW. According to MAC, those limits are the same, but the indexes are different. So if I understand that correctly, the CG can be more forward when the aircraft is heavy.

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E.g., this Boeing 747 (and all 747s I have seen had an envelope like this), page 20, Report on the serious incident at Oslo airport Gardermoen on 21 September 2004 involving flight KAL520 Boeing 747-400F registered HL7467 operated by Korean Air.

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So if I understand that correctly the CG can be more forward when the aircarft is heavy.

Not really, although I guess you could say the index can move "forward" because of the way the form is drawn, but the index is not the CG. Indices are a composite number, namely the moment divided by a reduction factor.

The use of index numbers and a reduction factor greatly simplifies weight and balance calculations, especially for large aircraft. The index is a moment divided by a reduction factor and may be found by this formula:

Index = (Weight x Arm) / Reduction factor

(from http://avstop.com/ac/weightbalance/ch4.html)

While indices make manual calculations easier than using %MAC and weight (the way computerized systems typically do it), they do tend to obscure things in my opinion.

If you want to see a 747's weight and balance envelopes using %MAC and weight, go to 747.terryliittschwager.com and select any 747. The top one on the aircraft list will do, N402YY. When the aircraft comes up, scroll down to OPERATING ENVELOPES.

You can position your pointer over the vertices to see their values. Note that the forward limit for takeoff at 580000 lbs is 11.0 %MAC, staying at that limit up to 778000. Getting heavier from there moves the forward limit aft, not forward, and additional weight from there really sends it aft.

The forward limit for the zero fuel and landing envelopes stays constant throughout the weights of their range.

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    $\begingroup$ After I read the question, I thought 'unfortunately Terry doesn't contribute here anymore, he would love to answer this one'. But to my pleasant surprise, he did! @Terry, good to see you around here again! I missed your contributions. I hope you are doing well, captain. $\endgroup$
    – DeltaLima
    Dec 9 '20 at 19:19

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