The standard measure of hull roughness that has been adopted in the marine industry is (Rt50). This is a measure of the maximum peak-to-valley height over a 50 mm lengths of the hull surface.
When undertaking a survey of a hull, several values of (Rt50) will be determined in a particular location on the hull and these are combined to give a Mean Hull Roughness (MHR) at that location defined by:
Where h are the individual (Rt50) values measured at that location.
The Average Hull Roughness (AHR) is an attempt to combine the individual MHR values into a single parameter defining the hull conditions at a particular time. Typically the vessel may have been divided up into a number of equal sections, perhaps 100 – 120, and a MHR determined for each section. These MHR values are then combined in the same way as the equation in the formula above to give the AHR for the vessel:
Where Wj is a weight function depending on the location of the patch on the hull surface. For many purposes Wj is put equal to unity for all j values; however, by defining the relation in the general way some flexibility is given to providing a means of weighting important areas of the hull with respect to hull roughness. Most notable here are the regions in the fore part of the vessel. Townsin* suggest that if a full hull roughness survey is made, the AHR will be statistically correct using Wj = 1 in the equation above. However, should some sections be left out for reasons of access, etc., then the AHR can be obtained in the following way:
AHR for vessel = ( MHR of sides )
x fraction of the sides covered
+ (MHR of flats)
x fraction of the flats covered
+ (MHR of boot topping)
x fraction of the boot topping covered