Sails' Surface Roughness: a relevant issue for HPS??

Happy New year Everybody,
Regarding High Performance Sailing(HPS), especially the foilers (Moth &A-Cat):
Sails have seen their apparent wind increasing significantly, at the same time, most of the addressable induced drag issue has been addressed with Deck Sweeping sails. So why not have a look at other components of sail's drag?

Assuming turbulent boundary layer on the sail, and using NIKURASE proxy formula for boundary layer thickness and surface roughness
(NIKURASE assumptions are Flate plate & constant Pressure)

It appears that with:
10 m/s to 15 m/s apparent wind velocity
at:
150mm to 300 mm from the leading edge
Maximum surface roughness :
h<= ( 0.0126 mm to 0.024 mm)

It seems much lower than any overlap of sail fabric especially for sails with radial cut,
Not to mention the impact of the mast/sail hinge at around 150 mm from the leading edge of an A-Cat rig for instance.

So the candide question which arises is :
How to compare drags for 2 sails one with h<=e/400
And the other one with h>= e/400 ?

Everything else equal of course.

Not sure it is a relevant question, just let me know.

Best regards

Erwan

 

I think the formula you are using probably only applies to the uniform roughness of the fabric itself, and not to the discontinuities at the panel edges or the mast/sail intersection.

For that type of roughness, Schlichting's book Boundary Layer Theory gives a formula Kadm <= 100 * Nu / V, which I suspect may be similar to the formula you used. In this formula, Kadm is the admissible roughness (i.e. - the value which can be tolerated without increasing the skin friction drag), Nu is the kinematic viscosity of the fluid, & V is the flow speed. Assuming Nu = 15.1e-06 m^2/s (a value corresponding to 20°C) & V = 15m/s, I get Kadm<=0.10mm.

That value is quite a bit larger than the values you quote. Can you post the formula that you used & also the value of Nu?

If my result is correct, I think the conclusion is that modern sailcloth is smooth enough that there is no extra drag due to surface roughness. Those other discontinuities may be another matter, though.

 

Thank you Doug for taking time to post, the topic is not that "sexy"

Here are the NIKURASE formulas for flat plate & Cste pressure:

With Rx the local Reynolds number @ x distance from the leading edge

1- Laminar boundary layer / BL Thickness e= (4.92/ Rx^0.5)*x
2- Turbulent boundary layer/ BL Thickness e= (0.37/ Rx^0.2)*x

Maximum acceptable roughness: h<= e/400

So for Turbulent BL with : x=150 mm V=15 m/s h<= 0.0126 mm
x=300 mm V= 10 m/s h<=0.0239 mm

Regarding your formula Nu/V = 1/Rx So Kadm<= 100/Rx

What I suspect is : higher surface roughness leads to thicker BL, which leads to earlier separation ( =lower max lift) and higher dissipation which increases drag as f(V^3).

Thanks and best regards

Erwan

 

For those who are inrested in the topic, please find attached an AIAA workpaper regarding wind turbines, which compares FLUENT/XFOIL/Experimental datas for both clean and rought surfaces airfoils.
This workpaper doesn't investigate only the effect of roughness on transition's location as it is usually the case, but it provides some interesting insights on other effects of surface roughness on wing section's performance.
While it is mostly about Leading Edge roughness, the change in L/D ratio is significant and the Reynolds numbers are not that far from what is observed in sailing, so it deserves some interest IMHO.

Cheers