Thanks Paulo! That was a lot more than I was ever expecting. If I understand you...(to summarize):
1. wind speed is reflected by the concentric circles
2. boat speed is represented by the colored lines
3. radius lines = angle to wind
"We are talking about 40ft boats that have a hull displacement speed of about 8.5K."
I'm guessing the above statement is not information that can be garnered from looking at polar charts? I'm also guessing this has to do with an equation which incorporates displacement and perhaps LWL??
Therefore, am I correct in stating polar charts say nothing about a hull's theoretical planning speed? I was wondering if the shape of the arc's depicting boat speed allowed one to interpret planning speed. Sounds like that may not be the case.
Yes, that's about it.
The boat speed has only to do with LWL and can be calculated by a simple formula that you can find here:
You can find plenty calculators on line:
Displacement Hull Speed Calculator
Two boats with the same LWL have the same hull speed but that does not mean that the potential for speed on the two boats is equal. One can reach hull speed with much less wind than other, not to mention semi-planing speeds or planing speeds.
Regarding a "hull's theoretical planning speed" I am not sure what you mean. There are hulls that by design and weight of the boat will never go to planning speeds. Most cruising boats, specially old ones are displacement boats and most of the fast modern performance cruisers have a semi-displacement capability being very rares the ones that can reach planing speeds.
Planing speed is one that goes over hull speed with some margin.
The ones that can manage that need different wind forces to do that (as we have seen with the Elan and the Pogo). Some will went to planning speeds with less wind others with a lot more, some never will.
A boat designer using a VPP computer advanced program will know at what wind a given boat will plane (if it is design to do that). You only know when he prints the boat polars that have that data.
For a boat to have a planing potential it has to be very light and have a planing hull that means what the French call "tendue" and that I cannot express in English in any other way. That is not easy to have a cruising boat that light and there are not many around, most of them being cruiser racers. The Pogo is an exception in what regards not to be a cruiser racer but a performance cruiser.
In what regards planing potential the size of the boat is not significant, at least in a way LWL is for hull speed. You can have smaller boats that will go faster downwind and plan with less wind than bigger boats
Look at the polar of the Maestro 345 that I posted some posts back:
A smaller cruising boat that will be a lot faster than the Elan 400 downwind (I know the image is not good but the last line seems to be 20K wind).