Michael wrote:
The question was asked in another forum: why doesn't the aircraft have
sensors in the landing gear so that it knows it's exact weight? It
would also be able to calculate it's centre of gravity if such sensors
were installed.

Honeywell has such a system for big aircraft:

http://www.honeywell.com/sites/aero/...431B6C7F21.htm

Honeywell advert on this link (contains embedded PDF):
http://www.flightglobal.com/pdfarchi...0-%200862.html

Definitely worthy of investigation by enterprising homebuilt
experimentalists. Strain gauges are not that expensive, but do require
careful attention to physical attachment and interface electronics.