Many operators use a similar system when using a 'free seating' arrangement; CofG calculation by bay split, and manual loadsheet.
The pax will board, and take their seats as they wish. While this is going on, the numeric part of the manual loadsheet (eg FIT/TOW/TOF/TIF/LDW etc) will have been completed. The flightcrew know where the bags are, because there will either be a 'standard loading' for a particular airline, or the despatcher will have told them for example 'all in hold 4'.
When the pax are on the No.1 will do a count relating to sections of the aircraft. Each section is a 'bay' and the number of seats in each bay, indeed how many bays, is specific to each aircraft type. For example, for aircraft X (fictional) :
BAY A : Rows 1-10.
BAY B : Rows 11-20.
BAY C : Rows 21-30.
There will be a small form which the No.1 has which will have the bays written on it - he or she will then write in how many are in each bay, and present it to the Captain/F.O. as appropriate. Not only does this give them the final load information, but also it acts as a crosscheck on the headcount too. Some airlines have a complete load chit which also confirms the position of bags/cargo/AOG spares etc.
The loadsheet will, on the trim chart / drop boxes, have a seperate scale for each bay. The person doing the loadsheet will finish the dropline quickly using the bay split, determining whether the CG at TOW and ZFW remains inside the envelope.
Should the aircraft be out of trim, due to where the pax have sat...the crew will be informed and told to move them as directed.
The process really does not take long at all, and should the flight be full, then the manual loadsheet should state how many can be sat in each bay, therefore no count is needed.
On the B737-300/400 putting all of the bags towards the back usually keeps things right...on the 800 I have seen several rules of thumb for example 1/3 in hold 4, 2/3 in hold 3, rest in hold 2. Unless the pax all decide to sit as close to one end as possible, which they are not likely to do, trim should be good.
This is the system which several carriers use, however variations are likely depending on individual airline and airport systems.
Cheers,
starship
[ 15 December 2001: Message edited by: starship ]