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You’re up there, looking down on the world at 7000ft, when your 120kg passenger (Bob) decides to move to a rearward seat for a better view. Will this affect how your aircraft flies, even though the total mass has not changed? The answer is most certainly yes, but let us see what happens, and how to make sure you don’t cause yourself any unexpected problems…

The number one concern here is that the centre of gravity (CG) has changed even though the total mass has not changed. As Bob has moved to a seat that is at the rear of the aircraft, this means that the CG will also move rearwards. The first noticeable feeling that will alert you that this has occurred, is that your controls suddenly feel very ‘light’, in other words, it takes little pressure to move or turn the aircraft. You may also find that your nose looks a little high, causing you to trim it back down to a more level position. This is not the most efficient way to fly, particularly as our range and endurance will be decreased, but the most significant threat that passenger Bob poses is to landing performance. If the CG has moved sufficiently rearwards, that it is beyond the aft limit (this is in your aircraft manual), then large elevator deflection will be required to balance the new tendency towards a nose up position. It will be difficult to maintain the flight path on the approach with already reduced stick authority. Essentially this could lead to a stall, as the forces will be too weak to keep the nose down and the aircraft flying at a safe speed.

So how do we check if it is safe for Bob to change seats, ‘on the fly’ in flight without the help of a calculator?

For example, let’s say that our aircraft total mass is 2000kg and the CG at take-off is at station 50. Bob is seated at station 20 and he moves to station 90. How do we calculate the new CG if Bob moves to station 90, and is this within the limits?

If you can remember this formula then do it this way:
Mass Moved / Total Mass = Change of CG / Total distance moved
Therefore:
Change of CG = Mass Moved x Total Distance Moved / Total Mass
= 120 x (90 – 20) / 2000
= 8400 / 2000
= 4.2 + 50 (add to original CG as Bob moves rearwards)
New CG = 54,2
If our aft limit is 52, then we will exceed the limit which means that Bob will have to stay put.

If you can’t remember that formula then try it this way:

Total Mass x Current CG = Moment Arm
2000 x 50 = 100 000
-120 x 20 (Remove Bob’s mass from his current seat) = -2400
120 x 90 (Add Bob’s mass to his desired seat) = 10 800
Now add all the moments 100 000 – 2400 + 10800 = 108 400
New CG = 108 400 / 2000
= 54,2

These methods can also be used in the case of a last minute addition of cargo. Bob’s Grandmother hands him a toolbox weighing 30kg that he left behind at the last moment, and this is added to a hold at station 200. How do we calculate the new CG with the addition of Bob’s toolbox to the total mass?

Change in CG = Mass added x (Difference between station and existing CG) / New Total Mass
= 30 x (200 – 50 = 150) / 2030
= 2,216 + 50 (Current CG)
New CG = 52,216
This is in excess of the aft CG limit, so Bob’s tool box will have to be moved to a station further forward.

So as you can see, whenever mass is moved in flight, or whenever mass is added or removed, it is necessary to check the change in centre of gravity. In case you are wondering what would happen in a passenger airliner if two thirds of the passengers all got up at the same time and moved to the rear of the aircraft, I am also wondering, but I guess it would depend on the size of the aircraft and the floor load capabilities. however, in the interests of safety, all having a drink at the same time is probably not the best idea!