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 (**C**h ) is the ratio of the resistance (**Rh**) on displacement (**D**)(equivalent weight of water immersed volume X water density kg/m3):**C**h**=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:
**g**Gravity**r**mass per unit volume of water**n**kinematic viscosity of water**ra**masse volumique de l'air**na**kinematic viscosity of air**t**air water surface tension**Pa**atmospheric pressure**Pv**saturation vapor pressure of water

- the characteristics of the hull:
**L**Characteristic length (waterline length)**V**Forward speed**K**hull roughness (represented by a coefficient of average roughness)

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 **Fr**model= **Fr**real by adjusting the speed of the model.

With ** C**h specific resistance and **C**v viscous component of resistance (See Froude):

** C**h real **= C**h model** - ** (Cvmodel - **C**vreal)

** - **(Cvmodel - **C**v 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** C**h model for fast vessels with high ** Fr ** (0.5 _ 0.6) to -0.25** C**h model for slow ships with low** Fr **(0.15 _ 0.2)