Hello hudla, excellent choice of thesis subject if you ask me!
What you want to get your hands on is a Weight & Balance manual. It will tell you what you need to know for the aircraft type it applies to. I wish I could supply you with one, but I'm not sure I'm able to. Try google and if you can't find one, get back to me and I'll see what I can do. I noticed a while ago that EADS have the POH for their TBM 700 Socata available online, including the weight and balance information. Perhaps that could be useful?
The first thing you have to consider is fuel burn. In a WBM, you will find the center of gravity of the fuel for various amounts of fuel (in the various tanks, if applicable). If you know the take-off weight (TOW) and center of gravity you will be able to calculate the center of gravity as the fuel burns off from these figures.
The other thing you have to consider are in-flight movements. That's the gear and flaps retracting, F/As and trolleys moving around, passengers and crew visiting the lavs and so on. You can never contain the case where all passengers pile up in one end of the cabin, so you have to assume reasonable worst-case scenarios for forward and aft in-flight movements.
The way this is usually handled in real life is through curtailing the center of gravity envelope. Curtailing the CoG envelope means moving the forward and aft limit of the take-off envelope in sufficiently to contain the aforementioned worst-case scenario for in-flight movements. That way you know that if you are OK (within the curtailed envelope) on take-off, you'll be OK in flight.
You can curtail the envelope for fuel burn as well, but as the fuel is located around the expected CoG for most aircraft, fuel burn tends to bring the CoG in towards the middle of the CoG envelope. Thus, if you are fine at zero fuel weight (ZFW, no fuel on board) you'll be fine when fueled. If you have e g a stabilizer tank, you might need to consider the effect of burning that fuel.
For flight testing, when we want to know the exact CoG for all phases of the flight and when we will often want the aircraft to be at the forward or aft extremes of the weight envelope, a fuel burn vector (a slight misnomer IMO) will be calculated to make sure that we are never actually outside of the envelope. This will be done both for extended and retracted gear, and for all the possible/expected in flight movements (although there typically aren't any during flight testing - you can simply tell people to stay put).
You might want to visit the Society of Allied Weight Engineers,
www.sawe.org, and browse through the papers available. You will probably find lots of good source material in there.
If you have any further questions, ask away.
Regard,
/Fred