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Height Of Center Of Gravity (KG)



A vessel displacing 29,500 long tons has a KG of 60 feet. A weight of 500 long tons is added at a VCG of 150 feet. What is the change in KG?

Given:

            Vessel’s displacement = 29,500 tons
                       Weight of load = 500 tons                                      
                                     VCG = 150 ft
                                       KG = 60 ft

What is asked?

           The change in KG

Solution:

Step 1. We have to solve for the moment. It is done by multiplying weight and distance.
            
             Weight   x   Distance   =   Moment
            
                  29,500 tons x 60 ft = 1,770,000 ft/tons  
                     500 tons x 150 ft = 75,000 ft/tons

Step 2. We have to add all weights and all moments because the problem tells that we are loading. But if unloading of cargoes, we have to subtract weights and also subtract the moments.

                Weight   x   Distance   =   Moment
            
                     29,500 tons x 60 ft = 1,770,000 ft/tons  
                   +   500 tons x 150 ft = +  75,000 ft/tons
Total Weight = 30,000 tons           1,845,000 ft/tons = Total Moment

Step 3. Solving for the new KG. We are going to divide total moment by total weight.

              New KG = TM ÷ TW
                           = 1,845,000 ft/tons ÷ 30,000 tons  
                           = 61.5 ft is the new KG

Step 4. Solving for the change in KG:

              Change in KG = New KG – Old KG
                                   = 61.5 ft – 60 ft
                                   = 1.5 ft upward - is the final answer

*** The change in KG is upward because it is going higher from 60 ft to 61.5 ft.

Height of Center of Gravity


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