SME
Aircraft Design · Problem type
CG shift when weight moves
Use this for “In a 5000 kg airplane, 200 kg of baggage moves 3 m aft. How far does the CG move?”
This is an example. Type your own values to start a new problem.
Δxcg (m)
=
w (kg)
×
d (m)
m (kg)
Formulas
Δxcg
=
w
×
d
m
+0.12
=
200
×
3
5,000
Assumptions
•
The total mass m does not change, only where the mass w sits.
•
Distances are + aft of the datum, so a forward move gives a negative shift.
•
Burned fuel is not a move: rerun the CG with the smaller fuel mass.
Step-by-step
WE KNOW
m = 5,000 kg, w = 200 kg, d = +3 m
FIND
CG shift (Δxcg)
Step 1 · Find CG shift (Δxcg)
Use Δxcg = w × d ÷ m
The moved mass’s change in moment, wd, spread over the whole mass.
Δxcg
=
200
×
3
5,000
Δxcg
=
600
5,000
Δxcg = +0.12 m
Check
Put the numbers back in. Both sides should match.
+0.12
=
200
×
3
5,000
✓
Topic check
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