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If we start with $Total\ Weight = 2,850\ lbs$ and $CG = 101.67\ in$, then add $400\ lbs\ @\ 97.8 in$, then how much would the Center of Gravity move?

How can you calculate this?

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    $\begingroup$ I assume 97.8 is in ... inches? Same for CG? An important part about calculating things like this is to be clear on what units you are using. $\endgroup$
    – Jamiec
    Commented Nov 30, 2018 at 15:16
  • $\begingroup$ i do not know but i know the answer is -0.47 how its calculate? thanks $\endgroup$ Commented Nov 30, 2018 at 15:23

1 Answer 1

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The basic equation is $Weight \cdot Arm = Moment$, which also means that $Arm = \frac{Moment}{Weight}$.
That is all you need to work through these problems.

Calculate your starting moment:
$2,850\ lbs \cdot 101.67\ in = 289,759.50\ lbs/in$

After you add 400 lbs, the new Moment is:
$(2,850 \cdot 101.67) + (400 \cdot 97.8) = 328,879.50\ lbs/in$

And the new total weight is:
$ 2,850 + 400 = 3,250\ lbs $

This produces a new CG of:
$\frac{328,879.50}{3,250} = 101.193\ in$

The difference in CG is:
$101.193 - 101.67 = -0.477\ in$

Or, doing this all in one big equation: $$ \frac{(2850 \cdot 101.67) + (400 \cdot 97.8)}{(2850 + 400)} - 101.67\ in = -0.477\ in $$

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  • $\begingroup$ What is the calculation is telling us? What is the meaning of 400lbs @97.8 in? And what is the meaning of that -0.477 in? $\endgroup$ Commented Dec 15, 2018 at 1:06
  • $\begingroup$ @AirCraftLover: Information on Weight, Arm, Moment, CG, Weight&Balance calculations are readily available from multiple sources and are a basic part of pre-flight planning. I cannot possibly summarize it in a comment response. $\endgroup$
    – abelenky
    Commented Dec 15, 2018 at 3:55

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