ORIGINAL: 1Eye
I didn't see anybody mention the need to determine MAC (mean aerodynamic chord) yet. I've found the ''sweet spot'' for the pivot (and therefore balance) point is around 27% relative to the MAC.
ORIGINAL: HarryC
The ideal location of the pivot is at the aerodynamic centre.
The aerodynamic centre
is 25% of MAC, give or take a percent depending upon the section. Any point aft of that such as 27% is moving into instability.