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CG changes with removal of weight

Asked by: 2586 views Aircraft Systems, General Aviation

Can someone please help me understand how they got the answer here? When I add, subtract, divide or do anything I cannot come up with the answer. Maybe somone can break it down a bit further. 


Aircraft Total Weight

 6,860 lb

CG Station



Determine the location of the CG if 140 pounds of baggage is added to station 150.



Added Weight/ New Total Weight


ΔCG/ Distance between weight and old CG

140/(6,860 + 140)



140/ 7,000





1.4 in aft


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1 Answers

  1. John D. Collins on Dec 12, 2011

    Doing it the long way, the total weight and CG station are the weight and CG location before adding the 140 pound baggage load at station 150.  Multiply the weight of the additional load times its station to obtain the moment or the baggage (140 x 150 = 21,000). Convert the original weight and CG location to a moment by the same process (6860 x 80 = 548,800).  Add the two weights and the two moments. The new total weight is (6860+140) 7000 pounds.  The new total moment is (21,000 + 588,800) 569,800 inch-pounds. Divide the total moment by the total weight (569,800/7000) to get the adjusted CG of 81.4 inches. The difference is 1.4 inches aft.


    The method you are using is similar.  As long as one is consistent, the location of the datum is arbitrary. In effect, the equation works because the datum is being redefined to be at the current CG location before the baggage is added. Assuming D1 is the original CG location, D2 is the location of the baggage, and D3 is the new CG location. Also assume W1 is the original weight and W2 is the baggage. The basic equation for the CG location is:


    D3 = [(W1 x D1) + (W2 x D2)]/(W1+W2) .


    If we redefine the moment arm to be at the location of D1, then the equation becomes


    D3-D1 = [(W1 x (D1 – D1)) + (W2 x (D2 – D1))] / (W1+W2)


    The first term on the numerator of the right side of the equation becomes zero, so the equation can be rewritten as:


    D3-D1 = W2 x (D2 – D1) / (W1+W2)


    Divide both sides by the term (D2 – D1), yeilds the form of the equation you started with:


    (D3-D1) / (D2 – D1) = W2 / (W1+W2), where D3 – D1 is the delta CG location.

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