Examples on model testing

1)  A ship has a length of 200 m and is designed to operate at 12.5 m/s. A model is made to a length of 7 m and is to be tested in a towing tank. When towed at the corresponding speed for wave-making the total resistance to motion is 82.5 N.

 

The skin drag of the model is given by  and for the ship by  where the resistances are in pound force and  is in square feet and  is in knots.

 

Calculate the corresponding speed and the resistance to motion of the ship if it has a wetted area of 5,000 m².

 

2) A ship has a length of 100 metres and a wetted surface area of 2,600 square metres. It is to be driven at 0.55 of its critical speed. A model is to be tested and the chosen scale ratio is 25. The total resistance to motion when tested under dynamically similar conditions is  28.5 N

 

Calculate the speed of the model, the resistance to motion of the ship at its design speed and the power needed to drive it..

 

For the model use skin drag  N ;  for the ship skin drag  N where  is in square metres and  in metres/second.

 

 

Solutions

1) 1 knot = 0.515 m/s. Therefore speed of ship  knot.

 square feet.  lbf  kN.

 and then

We need . .          knot

Therefore  lbf  N

 

And  N

 and from this  kN.

Total resistance = 980 + 663 =1,643 kN.  Power needed = 20.5 MW

 

2) Critical speed . So speed of ship:-

                      knots.

 Then

 and  N

 N   from which  N.

Resistance to motion of the ship is  N.

Power to drive ship