G'day,

I gave myself an out of balance scenario with the C172 and made the ZFW further forward than the most forward limit to try and apply the weight to shift formula. Everything was going well and it did cause the ZFW arm to be exactly on the forward limit, however, my ToW arm was still too far forward. I used the ZFW because that arm was further forward than the ToW arm so I thought that if the ZFW is within limits then the ToW will also shift further inwards.

Just trying to determine what I did wrong, any help is always appreciated.

Cheers.

A bit hard to be precise without the numbers and envelope.

The 172's forward limit, like the majority of light aircraft, has a constant CG at low weights and then an aft-moving limit as the weight increases toward MTOW - usually there is little value to the OEM in trading off the extra load capability against performance and structural penalties.

I suspect you have been caught out by the CG limit's varying faster than the fuel CG change. If you are looking at a moment x GW envelope the effect should be apparent - one caveat is that the upper CG line is a curve (ie not a straight line) so if it is plotted as a straight line, as often is the case, that may confuse the issue a little more. Noticing the effect depends a lot on the datum chosen for plotting the envelope.

Perhaps some numbers and a note as to the particular 172 model and we can help a little more ? In all likelihood you have done nothing wrong, per se, perhaps just presumed the incorrect weight was limiting.