SIMILITUDE and ship resistance
the ship resistance is generally predicted and studied with tests on scale models basins. To apply the results obtained, from model to prototype we must use similarity parameters.
the outcomes sought and are mainly: the ship resistance (hydrodynamic resistance)
In this case the resistance (Rh) is reduced for the operating facilitated, to a resistance factor named specific resistance. This cœfficient (Ch ) is the ratio of the resistance (Rh) on displacement (D)(equivalent weight of water immersed volume X water density kg/m3):Ch=Rh/D
Considering that the geometric shapes and the weight distribution of the model are identical to the actual ship (prototype) , the Rh determining parameters are:
- environement and fluid characteristics:
- the characteristics of the hull:
ship resistance Rh is a function of:
- Froude number (in the resistance component of the wave),
- Reynolds number and relative roughness K / L (in its component of friction).
at the transition from model to full-scale prototype, g Gravity, r water density, n kinematic viscosity of water, ra air density, na kinematic viscosity of air, t air water surface tension, Pa atmospheric pressure, Pv Vapor pressure of water, remain constant.
This implies that the L characteristic length (waterline length) and V speed advance, must change the model to the real world, keeping the Froude number and the Reynolds number constant, without changing the parameters g gravity, and n kinematic viscosity of water, which is impossible.
As we can not meet both the similarity of Reynolds (Re=V.L/n) and Froude(Fr= v/w(g.L) is performed for practical reasons, the Froude similarity, solving Frmodel= Frreal by adjusting the speed of the model.
With Ch specific resistance and Cv viscous component of resistance (See Froude):
Ch real = Ch model - (Cvmodel - Cvreal)
- (Cvmodel - Cv real) = frictional correction corresponds to the fact that we neglected in the similarity of Reynolds
the frictional correction is a negative value which is applied as a function of the Froude number: it can vary from -0.15 Ch model for fast vessels with high Fr (0.5 _ 0.6) to -0.25 Ch model for slow ships with low Fr (0.15 _ 0.2)