ATPL Moving Mass problem

[rpetersson]

"An aircraft has a loaded mass of 5500 lb. The CG is 22 in. aft of the datum. A passanger, mass 150lb, moves aft from row 1 to row 3 a distance of 70 in. What will be the new position of the CG.(All dim. aft of the datum)"


Heres how i failed, i took 5500lb*X / 70in =150 lb, X= 2.1

So i expected to get new CG at 2.1in+22in = 24.1

Book says it should be 23.9.

What have i done wrong? Any ideas?

[hippo123]

Heres how i failed, i took 5500lb*X / 70in =150 lb, X= 2.1

I get x = 1.90 from the above:

(5500*x) / 70 = 150

=> 5500*x = 150 * 70

=> x = (150 * 70) / 5500 = 1.90

(and 1.90 + 22 = 23.9)

[rpetersson]

I yea i got the same as you now with the same equation, dont know what the F*** i did to get 2.1.

Many thanks tho!

[keith williams]

For load shifts (but not load additions or removals) use the following.

MS = ms

Where

M is the total mass (big M = big mass)
m is the mass moved (little m = little mass)
S is the distance that the CG shifted (Big S = big mass shift)
s is the distance that the mass is moved (little s = little mass shift)

In this case we have

M = 5500 lbs
m = 150 lbs
s = +70

MS = ms

Rearranging this gives

CG Shift = S = (ms) / M = (150 x 70) / 5500 = +1.909

Adding this to the original CG gives + 22 + 1.909 = 23.909