Gerritsma and Beukelman 



ANALYSIS OF THE RESULTS 



The experimental values for the hydrodynamic forces and moments on the 

 oscillating shipmodel will now be analysed by using the strip theory, taking into 

 account the effect of forward speed. For a detailed description of the strip the- 

 ory the reader is referred to [1], [2] and [3]. For convenience a short descrip- 

 tion of the strip theory is given here. The theoretical estimation of the hydro- 

 dynamic forces on a cross-section of unit length is of particular interest with 

 regard to the measured distributions of the various coefficients along the lei^th 

 of the shipmodel. 



Strip Theory 



A right hand coordinate system x^y^z^ is fixed in space. The z^ -axis is 

 vertically upwards, the x^-axis is in the direction of the forward speed of the 

 vessel and the origin lies in the undisturbed water surface. A second right hand 

 system of axis xyz is fixed to the ship. The origin is in the centre of gravity. 

 In the mean position of the ship the body axis have the same directions as the 

 fixed axis. 



Consider first a ship performing a pure harmonic heaving motion of small 

 amplitude in still water. The ship is piercing a thin sheet of water, normal to 

 the forward speed of the ship, at a fixed distance x^ from the origin. 



At the time t a strip of the ship at a distance x from the centre of gravity 

 is situated in the sheet of water. From x^ = vt + x it follows that x = -V, where 

 V is the speed of the ship. 



The vertical velocity of the strip with regard to the water is z^, the heav- 

 ing velocity. The oscillatory part of the hydromechanical force on the strip of 

 unit length will be 



^H " ~ dt ^""'^o^ ~ ^'^o ~ 2pgyz„ , 



where m' is the added mass and N' is the damping coefficient for a strip of unit 

 length and y is the half width of the strip at the waterline. Because 



dm' _ dm' ^ • 

 dt " dx "" ' 



it follows that 



F^ = -m-i^-{N' - V^) z„-2pgyz„. (5) 



For the whole ship we find, because 



r dm_' 

 J dx 



L 



dx = 0: 



238 



