Again Mass and Balance

[Olendirk]

Hi my friends!

Could you help me with this type of exercise and give me a formula?im not able to get the formula!

Grossmass: 41t
C.G. 663Sta
MAC LE: 625,6Sta
MAC TE: 760,1STa
Cargo CPT:360Sta

At which station is the C.g. located with 2500kg in the cargo compartment?

Thanks!

OD

[Keith.Williams.]

Although you have used the term "Sta" which appears to imply station numbers, the figures you quote are actually distances on the MRJT1 in the CAP 696.

You need to use two equations, Firstly to find the c of g position you need to use:

C of G positiuon = Total moment / total mass.

But first you need to find the total moment and total mass. You can do this by adding the cargo to the initial condition as shown below

Item Mass Moment Arm Moment = mass x Arm
Aircraft 41000 Kg +663 inches +27183000 Kg inches
Cargo 2500 Kg + 360 inches +900000 Kg inches
TOTALS 43500 Kg 28083000 Kg inches

Now using C of G = total maoment / total mass gives

C of g = +28083000 Kg inches / 43500 Kg = +645.59 inches


So the new C of G is 645.59 inches aft of datum


Now if you want to know the C of g positiona as a %MAC, you now need the second equation:

%MAC = 100% x (C of G - MAC Leading Edge) / MAC length

The MAC LE is at +625.6 and the MAC TE is at 760.1

So the MAC length is 760.1 - 625.6 = 134.5

Putting these figures into the equation:

%MAC = 100% x (C of G - MAC Leading Edge) / MAC length

Gives %MAC = 100% x (645.59 - 625.6) / 134.5 =14.86%

[Aim High]

Or alternatively

The first step is to calculate the length of MAC. Therefore:

Trailing edge - leading edge = MAC

760.1 - 625.6 = 134.5 (length of MAC)

The old centre of gravity was positioned at 663 aft of datum which needs to be calculated in relation to MAC.

The CG can be found in relation to the leading edge by the following method:

663 - 625.6 = 37.4 aft of the leading edge

To calculate this as a percentage (reference CATS Mass and Balance Book chapter 4)

%MAC = (100% / MAC) x Distance from leading edge

% MAC = (100 / 134.5) x 37.4 = 27.8% (old CG position)

If we are adding a mass into an aircraft we can use the following equation to calculate the new CG position:

CG distance from datum = total moment / total mass

The total mass is the old mass + the additional mass:
41000 kg + 2500 kg = 43500 kg

To calculate a moment use the equation:

moment = mass x arm

moment of the CG = 41000 kg x 663 = 27183000
moment of the cargo = 2500 kg x 360 = 900000

therefore the total moment = 28083000

Using the equation = 28083000 / 43500 = 645.59 aft of datum

We know that the leading edge is 625.6 aft of datum so therefore the CG is 19.986 aft of the leading edge.

19.986 aft of the leading edge can be calculated using the same equation

%MAC = (100% / MAC) x Distance from leading edge

% MAC = (100 / 134.5) x 19.986

% MAC = 14.86%

[Jinkster]

Passed M+B in February - havent looked at it since. Got 100% nearly fell of me perch.

Cant remember how to do these questions anymore. Will have to have a look as M+B is a useful subject :}

Jinkster

[paramac146]

I read this question quite diferently as he asked for the STN position of the new CG if 2500KG were to be added to the Aircraft in the cargo hold @ STN 360.

Wether or not it is within the % mac range is irrelevent to the question as he ONLY asked for the new position to be calculated which as Keith has done is 649.59. End of story I thought but then I am certainly not always right...