Online Resistance calculator

Just image a plane perpendicular to mast. In that plane, sail area and profile do not change. So Cl Cd are constant. Now, do not heel the mast. Just heel the wind. The wind has now a in plane component , perpendicular to mast, reduced by cosine heel, and a mast direction component. The up component is just ignored. A sail has essentially no effect with wind in the mast direction.

And since apparent wind speed is reduced by cos heel, forces are reduced by (cos heel)² as mikko said.

Now, apparent wind is not exactly reduced by cos heel. (only beam wind). Front wind is not reduced by heel. Exact formula is (4) or (5) in the above document. And heel influence is in fact just a apparent wind change.

 

Thank you fcfc, well formulated.

One thing I'd like to add about VPPs: You should treat leeway angle as a independent variable in your model, otherwise your sail forces (amonst others) will be at err. You define apparent wind angle with reference to the boat centerline, but the boat is not moving in the direction of its centerline but leeway's amount away from it, in the direction of "drive". This means that the heeling force, defined by your sailforce equations and perpendicular to the centerline, also has a non-negligible component in the direction of drive.

To my knowlegde, the ORCi VPP does not take leeway into consideration, at least it does not appear in its equations.

 

Thanks fcfc, Mikko. I should make a 3d drawing to understand your concepts.
The leeway is clearly shown on figure 2 of the ORC document but can't find any mention on the formulae. Also, some of the acronyms used on the ORC are not explained so it's a little difficult to understand them.
ORC has many improvements and a much more detailed analysis over the Hazen model than the one in PYD 2nd ed.
Don't know when I will have the time to return to the VPP problem, it's a very interesting issue.

 

Is the resistance calculator valid for larger merchant vessels (for expl. vessels of 134m length)?

 

SailorSteve wrote:

I don't think so, Delft series involve typical sailboat's hulls. You should try Michlet or some thin ship theory. Anyway the calculator has a "warnings" window, there you can check if your values are into the expected margins.