Norrbin 



III. NON-DIMENSIONALIZING BY USE OF THE "BIS" SYSTEM 



The use of non-dimensloncul coefficients is accepted in all 

 branches of ship theory, and when motion studies are considered 

 even the variables of the equations are often normalized. 



Within the field of maneuvering a unit for time is usually the 

 time taken by a body to cover the distance of its own length, and the 

 unit for velocity then is most naturally given by the momentary 

 speed V = (u^ + v^)''^. If the body does not move forward this defi- 

 nition is less attractive. In the system just mentioned — which is 

 recommended by ITTC and which in most cases is fully adequate — 

 symbols for non-dimensional quantities usually are indicated by a 

 prime. 



The unit for length almost always is chosen equal to the length 

 L of the body, axid for the common surface ship more specified 

 L = Lpp« 



The unit for mass is mostly taken as the mass of a certain 

 volume of the liquid, defined in terms of the body or ship geometry. 

 In the "prime" systemt already referred to reference volumes are, 

 say, jL [8] or ^ L^T [9] , the latter one used with the reference 

 area L.T suggested by the wing analogy. 



In case of bodies , which are supported mainly by buoyancy 

 lift, the main hull contour displacement Vg is perhaps the most 

 natural reference volume: if body mass then is m = ji • p • Vq the 

 non-dimensional mass is equal to |j.. (When treating heavy aircraft 

 dynamics Glauert chose p.pV in place of pV for the mass unit, 

 [ 10]« ) In normal ship dynamics jj. = 1 , whereas for heavy torpedoes 

 \i - 1,3 - 1.5, say; the symbol fx will be rejected in certain appli- 

 cations* 



Here a consistent normalization of motion modes and forces 

 will be made in a new system, the "bis" system, where the unit for 

 mass is m = [ipVo» the unit for length is I_ and the unit for linear 

 acceleration is equal to g , the acceleration of gravity. From this 

 the unit for time is yjl./g, and it also follows the Table below: 



822 



