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.