Do you remember from your pilot training why its important to have the center of gravity within acceptable limits? Its more than a theoretical physics question as your plane’s center of gravity will be impacted by the load (passenger or luggage) that you are carrying.
Hence, a recent post by Vincent on PlasticPilot is well worth reading as he goes into some detail about what would otherwise sound like a dry physics question. As Vincent explains, flying with passengers in the back seats of some aircraft will make quite a difference in the required control forces to keep the aircraft stable and hence, this is why tests of new aircraft designs will include a flight at maximum take-off mass.
I won’t repeat Vincent’s explanation for physics again; however, his last comments are well worth repeating again:
Nobody will check that you’re flying with a properly positioned center of gravity before you go flying. It’s one of the numerous duties of pilots to ensure the plane is loaded correctly, before and during each and every flight. As soon as you operate with a center of gravity outside the approved limits, you become a test pilot.
Insurance companies don’t like test pilots at all.
A very good point indeed!