The given data means that the aircraft empty CG is 3m aft of the datum at 25% MAC. Create a table:

 

Position

Weight

Arm

Moment

Basic Aircraft

1200 kg

3.00

3600 kgm

Front Seats

160 kg

2.50

400 kgm

Rear Seats

3.50

Rear Hold

4.50

Fuel Tanks

100 kg

3.00

300 kgm

Totals

1460 kg

4300 kgm

 

Now to convert to %MAC.

The CG position is moment ÷ mass = 4300 ÷ 1460 = 2.945m aft.

The BEM had a CG at 25%MAC on a 2m chord, and this was also 3m aft of the datum. 25% of 2m is 50cm or 0.5m so the leading edge of the MAC has to be 2.5m aft of the datum.

The CG position at take-off is 2.945 – 2.5 = 0.445m aft of the leading edge of the MAC.

The percentage MAC is therefore 0.445 ÷ 2 = 22.26% MAC.