Mass and Balance

[Olendirk]

Hi!

I have again a question:

Exercise:
Given: TOM=70 tons
C.G.=10%
MAC LE= Station 800
MAC TE= Station 1000

How much load has to be loaded from Sta 400 to sta 1200 to obtain a C.G. of 25%?

I know how to get the actual station with 10%,shoulkd be around Sta 780 but what do i do then? Do you guys have formulas which could hep me to handle the whole Mass and balance with all the shifts and c.g. calculations?

Thanks!

OL

[pa28biggles]

The first thing to do is to work out the actual c of g positions.
The length of the MAC is 200, TE - LE, 1000 - 800.
10% of 200 is 20.
So the original c of g is 20 rearward of the MAC LE.
Therefore the actual position is 20+800 = 820.

25% of 200 is 50, so the position of the new c of g is 850, using the same method.

The way that I work out such calculations is to use the following method. It is not what is tought where I am studying, but it is more logical to me because I am not learning a formula, I am actually understanding what is going on.

(New moment of c of g) = (Old moment of c of g) - (moment of where mass is being taken) + (moment of where mass is being added)

Mass moved is unknown.

(Mass X new c of g) = (Mass X old c of g) - (Mass moved X arm of position mass to be taken out of) + (Mass moved X arm of position mass to be added to)

(70000 X 850) = (70000 X 820) - (Mass moved X 400) + (Mass moved X 1200)

59500000 = 57400000 - (400 X Mass moved) + (1200 X Mass moved)

2100000 = 800 X Mass moved
Mass moved = 2625kg
Edited since I forgot to include the mass unit kg.
Hope this helps,
PA28.

[Field In Sight]

It's a little early to be testing my brain, but here goes:

Convert Mac % to stations:

10% MAC = (1000 - 800) * 10 % + 800 = 820 This is the CofG at the start.

25% MAC = (1000-800) * 25% + 800 = 850 This is the CofG that you want.


NB. TOM doesn't change and the weight must be moved from 400 to 1200 i.e. 800

Remember that:
New Overall Moment = Old Overall Moment + Change of Moment.
70 tons x 850 = 70 tons x 820 + (Mass to Move x 800)

This gives

59500 = 57400 + (800 x Mass to Move)

Mass To Move = (59500 - 57400) / 800 = 2.625 tons.

Hope that helps/is correct

FIS.

Edited to say:Sending PPrune messages are like RT transmissions, wait for a minute to see if anyone is responding and then as soon as you do, you get stepped on:

[no sponsor]

Use the formula:

(mass change / total mass of aircraft) = (change of c of g / distance moved)

re-arranging the above equation you get

mass change = (change of c of g / distance moved) * total mass of aircraft

Numbers are:

mass change = (30/800)*70

= 2.625

[Dillydally]

Hi there

By looking at the LE and TE you can see that MAC is 200 long. 10% of 200 is 20, therefore the old CG position was 20 aft of the LE and 820 aft of the datum. Now the CG needs to be repositioned at 25% which is one quarter of 200, thus being 50 aft of the LE and 850 aft of the datum.

To summarise, the CG was at 820 and needs to be moved to 850

With me so far?

If the question is how much mass needs to be transferred from 400 to 1200 then use the following equation:

Mass to move distance between cargo holds = aircraft mass x distance to move the CG

M x D = M x cc

M x (400-1200) = 70000 x (850 – 820)

M x 800 = 70000 x 30

M x 800 = 2100000

M = 2100000 / 800

M = 2625 kg

If the question is asking how much needs to be loaded into a hold positioned at 1200 then use the following equation:

Mass to move x distance between cargo hold and new CG position = aircraft mass x distance to move the CG

M x GD = M x cc

M x 350 = 70000 x 30

M x 350 = 2100000

M = 2100000 / 350

M = 6000 kg

The correct answer all depends on the way the question is worded.

Did a mass and balance brush up Cranfield Aviation Training School. It was worth every penny an more.

Hope this helps