# How do I calculate this question? mass and balance

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?

• 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. – Jamiec Nov 30 '18 at 15:16
• i do not know but i know the answer is -0.47 how its calculate? thanks – Enki Sumerian Nov 30 '18 at 15:23

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.

$$2,850\ lbs \cdot 101.67\ in = 289,759.50\ lbs/in$$

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: $$\frac{(2850 \cdot 101.67) + (400 \cdot 97.8)}{(2850 + 400)} - 101.67\ in = -0.477\ in$$

• 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? – AirCraft Lover Dec 15 '18 at 1:06
• @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. – abelenky Dec 15 '18 at 3:55