Mass – Adding & Substracting

With this sort of Mass & Balance calculation we are either trying to move the CG to a specific position or we want to find out where the new CG is. In the case of calculating the amount of mass to add or subtract we can use the same formula as the moving mass situation with a single subtle difference. When trying to find the new CG position it is easier to use a Mass/Arm/Movement table to obtain the required information. 

 Let us examine the situation where we are going to change the mass of the aeroplane to obtain the required CG position. To use the moving mass formula of: 

M x cc = m x D 

 Where M is the total original mass of the aeroplane, cc is the change in centre of gravity, m is the mass to be added or subtracted and D is normally the distance between the holds or rows etc. In the case of an adding or subtracting mass distance D is the distance from the new CG to the point the mass is being added or subtracted. 

 Let us examine an example question:

Given that the Total Mass of an aeroplane is 112 000 kg with a centre of gravity position at 22.62 m aft of the datum. The centre of gravity limits are between 18 m and 22 m. How much mass must be removed from the rear hold (30 m aft of the datum) to move the centre of gravity to the middle of the limits:  

The first thing to do is identify the items we know, so M = 112,000 kilograms, cc is the difference from the current CG of 22.62 metres and the desired CG of 20 metres, a distance of 2.62 metres. Distance D is the difference between the new CG position of 20 metres and the aft hold at 30 metres a distance of 10 metres. We populate the formula.  

                                                            112000 x 2.62
       112000 x 2.62 = 10 x M =                 10                  = 29344 kilograms.

In the second case where we need to find the new CG position when adding or subtracting mass then we need to use a basic Mass/Arm/Movement table.

Let us examine another example question: 

An aeroplane has 2 cargo holds: 

Hold 1 at 6 m forward of the datum, 

 Hold 2 at 7 m aft of the datum. 

 The Take-off Mass of the aircraft is 60 000 kg and the CG is located at 2 m aft of datum. Just prior to take-off, 1 250 kg of cargo is removed from cargo hold 1. What will be the new CG for take-off?   

The original mass is 60000 kilogrammes with an original arm of 2 metres aft. We are subtracting 1250 kilograms, which is a negative from the forward hold, which is 6 metres forward of the datum, a negative arm. 

The two negatives give a positive result, so the CG moves rearwards by 0.17 metres.  

 This is the simplest method to calculate for adding or subtracting masses without having to try and remember whether we are using the original mass or the new mass the original CG or the new one.