Moments

A basic skill required in Mass and Balance is to use Mass, Arm and Moments to calculate the position of the Centre of Gravity of an aeroplane or a beam.  

To work out the pivot point or the CG we need a way of calculating the effect of the beam weight and the two additional weights on the beam. The way we do this is to pick a fixed point, which in aviation this is known as the datum. In the above diagram we could pick any one of 4 points, the left or right hand end of the beam, or the position of the beam mass or the 5 kilogram mass.  

I am going to use the position of the Beam mass as my datum point because this covers how we deal with items forward and aft of the datum. Everything forward of the datum has a negative moment arm and everything aft of the datum has a positive arm.  

To do the calculation we need to produce a Mass, Arm and Moment table like the one below. 

The beam mass does not have an arm because it is on the datum and creates a zero moment, the left mass produces a negative moment and the right mass a positive. We then add all the masses together and then all the moments. To find the pivot point or the CG we need to divide the total moments by the total mass, this gives 

30/17 = 1.76 metres to the right of the beam mass.  

Does it make any difference if the datum is in a different position, no it doesn’t as the table below shows if we use the left end we end up with. 

If we carry out the same maths the distance the CG is from the left hand end of the beam is  

115/17 = 6.76 metres, which is 1.76 metres from the beam weight, so exactly the same.