Increase Length, decrease skin friction?

Dears,

I was studying about resistance in this material found online:

https://www.usna.edu/NAOE/_files/documents/Courses/en400/TEXT%20-%202011/12-Chapter%207%20Text%202011.pdf

and there is an affirmation saying that "Note from the above equations that for a given speed, as ship length increases the skin friction (tangential) component of viscous resistance decreases."

The "above equations" are the Reynolds number formula and the friction resistance formula. Taking for example the ITTC 1957 formula for Cf, the reynolds number's log is used, which for me seems to be almost insensitive to length variations of the hull, in the order of a couple of meters. Plus, if we think about the dimensional skin friction resistance

Rf=Cf*0.5*rho*v^2*wetted surface area

if we increase the length, the wetted surface area increases and so does the resistance. So coming back to the affirmation, what does it mean when relating increase of L to decrease of Rf?

 

I think better get clear idea of friction resistance,viscous resistance and prohaska theorem.

You can get some insight in this online calculator.

http://www.mermaid-consultants.com/resistance-prediction-holtrop-menon-method.html

 

As length increases, the Reynolds number also increases.
As the Reynolds number increases, the coefficient of friction decreases.

The result is that, for a given area, resistance will be less for a longer surface.

However, if making the surface longer increases the area, the increased area can* equal or outweigh the reduction in coefficient of friction. In that case, the frictional resistance will increase, but it will not increase in direct proportion to the increase in area.

*Often does.

 

It is probably also important to understand the main resistance component for different ranges of froude number(low, medium, high).

For instance, increasing length for high froude numbers increases the frictional resistance, but overall resistance decreases due to a reduction in wave-making resistance. (How much depends on hull form)

 

Actually what it said was the "component" of Rv (viscous resistance) caused by Cf decreases. It did not say the absolute Rv decreases. The entire quote is

What this says is as the ship becomes longer while keeping the same beam and draft, then the proportion of Rv caused by Cf decreases. It says nothing about absolute Rv.

 

Thanks a lot for your informative posts. They helped me too.