Added mass (idea)

Added mass is a concept used in hydrodynamic engineering. It applies to objects accelerating through liquids, and is a direct link to how much the liquid resists the acceleration (the objects inertia).

To properly describe the concept, let us start with an example:

Say we have a box suspended in a crane. The box is hanging in the air, and has no additional restraints. If we now move the box, only air will resist its movement - creating some small drag, but no large visible forces.

Now we lower the box into the sea. To be able to move the box up and down, we now have to overcome both the water's friction along the sides of the box (drag - this is dependant on velocity), but we also need to move the water at the top and bottom of the box (added mass - dependant on acceleration). What happens in practical terms is that when we move the box down, a lump of water becomes part of the object and moves with it, while water flows around the box and this enclosed water. This enclosed water is called added mass, and it affects the inertia of the object. If an object has a large body of added mass one now needs to spend a much larger force to achieve the same acceleration:

	F1 = m1*a1    F2=(m1+m2)*a2   a1=a2   =>    F2 = F1(1+m2/m1)

The size of the added mass (the enclosed area) depends much on the geometry of the object. For example, a suction anchor will have a large added mass as it encloses much water inside it's bucket, while a streamlined object will have nearly zero added mass, because there is little for the water to hold on to:

           ____                ____
          |    |             /-|    |-\
          |    |            <  |    |  >
          |____|             \-|____|-/
   
          Object            Object with 
                            added mass

(the movement direction is horizontally across the screen)

A common misunderstanding with respect to added mass is that if you have 20 tonne enclosed water, you will need 20 tonne of additional lift rigging. This is wrong because the force experienced is proportional with the speed you plan to move the load with ( or more precisely - the acceleration you enforce on the load ).

If we say that the lift will only occur in waves less than 3 m, then the crane's maximum motion at this sea state is around 2 m/s² (a typical large North Sea construction vessel). This means that our additional mass of 20 tonne will now contribute 40000 newton to the load (20 tonnes * 2 m/s² = 40 kN). This makes us increase our shackles and wire rope capacity by 4 tonne. The required lift rigging is therefore very much dependant on the motion of the crane and therefore the weather window of the operation.