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18-01-2025, 17:36
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#1
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Registered User
Join Date: Jul 2014
Location: Southeast US
Posts: 467
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SA/Displ Ratio that Factors in Wind Speed?
Is there a modification of the SA/displ ratio formula that incorporates wind speed? In other words, is there a formula that uses sail area, displacement, and wind speed to calculate a value that equates to the power produced by the combination of sails and wind to move the boat along without be under powered (or over powered)? Perhaps such a formula can be called "power ratio"?
For example, if a SA/Displ ratio for a given boat is 16, this indicates that a boat will move along reasonably well in light winds; whereas, a boat with a SA/Displ of 12 would be slow, in light winds. I understand that there are other variables that affect a boat's sailing ability (wetted surface, waterline length, prop drag, underwater profiles when heeled, etc...), but I'd like to start by being as simple as possible.
As the wind increases, the SA/Displ becomes a less usable metric because there is more wind; however, if we reduce the sail area too much for a given wind, then the boat will be too slow in that wind speed.
If we want to maintain the equivalent of a SA/Displ ratio of 16 at a given wind speed for a given sail reduction amount, can the SA/Displ formula be modified to take the reduced sail area and wind speed?
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18-01-2025, 20:25
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#2
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Moderator
Join Date: Sep 2014
Location: Channel Islands, CA
Boat: 1962 Columbia 29 MK 1 #37
Posts: 15,328
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Re: SA/Displ Ratio that Factors in Wind Speed?
The SA/D isn't really a formula for power, it is just a ratio. It sounds like what you are saying is how can we quantify the optimal sail area for a given wind speed, on a given hull/ballast/center of gravity; is that right? I think that is more art than science since it will depend on your experience with the boat, i.e. at what wind speeds and apparent wind angle should you reef? What heeling angle of the particular boat is ideal? etc. to maintain the optimal speed and upwind performance. The other thing is, you can have a high SA/D on any boat but it is more work for crew because you'll need to reef sooner and more often if you are trying to maximize performance or power. Reefing doesn't reduce the power or speed necessarily, it optimizes the rig for the given wind speed. If you are going too slow then you may have reefed too much. Or if you want to just put a taller mast on a boat and get better light air performance, that's fine, but then you'll have greater weight aloft which may negatively affect performance. Many boats over the years have offered "tall rigs."
Not sure if I answered your query though...
As the wind pipes up you will necessarily be reducing the SA/D ratio on any boat to maintain optimal performance. You cannot maintain that ratio as the wind speed increases. A boat with a low SA/D will probably not perform well in light air as you say, but it won't need to reef as soon.
__________________
DL
Pythagoras
1962 Columbia 29 MKI #37
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18-01-2025, 20:42
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#3
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Moderator
Join Date: Sep 2014
Location: Channel Islands, CA
Boat: 1962 Columbia 29 MK 1 #37
Posts: 15,328
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Re: SA/Displ Ratio that Factors in Wind Speed?
I was pondering this when the discussion of Kelly-Peterson 44 and its low SA/D came up recently. With a boat with a higher SA/D, you'll get better light air performance, but then you'll have to reef. And reefed sails, especially roller furled, don't usually have the shape to perform optimally. The lower SA/D cruising boat will have un-reefed sails with better shape (and power) when the wind picks up.
__________________
DL
Pythagoras
1962 Columbia 29 MKI #37
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18-01-2025, 22:11
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#4
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Registered User
Join Date: Jul 2014
Location: Southeast US
Posts: 467
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Re: SA/Displ Ratio that Factors in Wind Speed?
Thanks Don,
I understand everything you wrote and am in process of replacing all my sails when my brain went down this rabbit hole looking for an equation that might be used to output a value that can, as you correctly interpreted, "quantify the optimal sail area for a given wind speed, on a given hull/ballast/center of gravity". Not sure if it even exists or if it does, whether or not it has any value.
This started when I made a spreadsheet. . . The SS outputs the sail area at the different reef levels and calculates sheet loads and winch loads (pounds to input on the winch handle to sheet in the sail) at specified wind velocities. The initial objective of the was to calculate the sheet loads so I can select the correct hardware for the loads at different reef combinations and wind speeds and to ensure my winches are big enough.
Then the rabbit appeared. "Wouldn't it be cool if you had an equation that calculated the "power" needed keep the boat moving easily as I changed reef levels and wind speed?" Apparently, not so simple!
At least now I have an idea of sheet loads involved so I can get the correctly-sized hardware and that my winches are more than adequate (Lewmar 48 and 54)
One time, someone asked me what my favorite computer game: Excel
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18-01-2025, 23:07
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#5
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Registered User
Join Date: Aug 2010
Location: Arctic Ocean
Boat: Under construction 35' ketch (and +3 smaller)
Posts: 3,006
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Re: SA/Displ Ratio that Factors in Wind Speed?
Wouldn't the polars tell you the sail areas, anyways for some boats?
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19-01-2025, 00:22
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#6
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Moderator
Join Date: Feb 2010
Location: La Ciudad de la Misión Didacus de Alcalá en Alta California, Virreinato de Nueva España
Boat: Cal 20
Posts: 21,625
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Re: SA/Displ Ratio that Factors in Wind Speed?
SA/D is actually a good indicator of light air performance. Better would be SA/WA (Wetted Area) but that info is not as available and SA/D is a good proxy.
In heavy winds LWL is usually the governing factor. Soars that can surf or plan will perform somewhat above expectations. If you are cruising you won’t be trying to surf let alone plane.
Remember cruising is a shorthanded endurance sport not a fully crewed sprint.
When you replace you sails your sail maker may be able to provide you with polars for your boat in varying conditions with varying sails and reefs.
One thing about SA/D is that although it measures 100% fore-triangle and a triangular main it’s a good indicator of the maximum sail area you are likely to be able to hoist. It starts to not predict so well when the boat is a fractional rig or if it has a short boom.
If you want to estimate average speed over a long time period Evans Starzinger gave a formula on his website:
Daily Ave. Mileage = 24*(2.62 + 0.066*SA/D + 0.051*LWL)
__________________
Num Me Vexo?
For all of your celestial navigation questions: https://navlist.net/
A house is but a boat so poorly built and so firmly run aground no one would think to try and refloat it.
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19-01-2025, 01:06
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#7
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registered user
Join Date: Dec 2012
Location: back in West Australia
Boat: plastic production boat, suitable for deep blue water ;)
Posts: 1,194
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Re: SA/Displ Ratio that Factors in Wind Speed?
Quote:
Originally Posted by Adelie
If you want to estimate average speed over a long time period Evans Starzinger gave a formula on his website:
Daily Ave. Mileage = 24*(2.62 + 0.066*SA/D + 0.051*LWL)
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I too play with Excel, and plugged the above into a spreadsheet. The number it gives me for my boat is nearly 2 knots under the average I am doing. I use the proper manufacturer's data.
Note, the actual displacement is always much more than the manufacturer number, just add a few tonnes in cruising mode
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19-01-2025, 10:15
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#8
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Moderator
Join Date: Feb 2010
Location: La Ciudad de la Misión Didacus de Alcalá en Alta California, Virreinato de Nueva España
Boat: Cal 20
Posts: 21,625
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Re: SA/Displ Ratio that Factors in Wind Speed?
Quote:
Originally Posted by HankOnthewater
I too play with Excel, and plugged the above into a spreadsheet. The number it gives me for my boat is nearly 2 knots under the average I am doing. I use the proper manufacturer's data.
Note, the actual displacement is always much more than the manufacturer number, just add a few tonnes in cruising mode 
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Do you mean 2knots (nm/hr) or do you mean 2nm/d faster?
I have a giant database of boat data. The Starzinger formula corelates very well with PHRF ratings.
The PHRF ratings gives a higher daily speed which matches with the fact that when racing you are probably fully crewed and races are abandoned in very high or very low winds so data from those conditions do not become part of the ratings.
What's your boat?
__________________
Num Me Vexo?
For all of your celestial navigation questions: https://navlist.net/
A house is but a boat so poorly built and so firmly run aground no one would think to try and refloat it.
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19-01-2025, 11:56
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#9
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Registered User
Join Date: Dec 2022
Location: Surrey, BC, Canada
Boat: TES 246 Versus
Posts: 145
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Re: SA/Displ Ratio that Factors in Wind Speed?
I'm not sure if this is what you're looking for but let's consider the situation where you want to adapt to changing wind speed by reefing, to keep a constant boat speed. (Slightly below hull speed, for example.)
Sail force will be the product of sail area and sail load factor (lbf/ft^2). Sail load factor varies with the square of apparent wind speed. So, to maintain constant sail thrust you need to decrease sail area by a factor of 4 for each doubling of the apparent wind speed.
I.e., SA2/SA1 = AWS1^2/AWS2^2.
Since your sails are (probably) basically triangles, and the area of a triangle is base*height/2, and since furling or reefing the sail decreases the base and height roughly proportionally, reefing the main to half its height (or furling the jib to half its extension) will give you approximately 1/4 the sail area, which will give you the same "power ratio" at twice the apparent wind speed.
Proof reading the above I feel like it's needlessly complicated when I try to put it into words but if you work it out as math I think you'll see it's simple.
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19-01-2025, 12:13
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#10
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Moderator
Join Date: Sep 2014
Location: Channel Islands, CA
Boat: 1962 Columbia 29 MK 1 #37
Posts: 15,328
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Re: SA/Displ Ratio that Factors in Wind Speed?
__________________
DL
Pythagoras
1962 Columbia 29 MKI #37
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19-01-2025, 12:14
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#11
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Registered User
Join Date: May 2013
Location: Portland, ME
Boat: McCurdy & Rhodes 56
Posts: 260
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Re: SA/Displ Ratio that Factors in Wind Speed?
If I am understanding what you want to do correctly: assuming a monohull, when wind is forward of the beam, your heel angle will tell you when to reef. Downwind it's how big your balls are.
Some manufacturers publish SA/D ratios for upwind and downwind, downwind including a typical spinnaker, usually an S2 or A2. Upwind is usually using the fwd triangle, not the actual sail's sail area.
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19-01-2025, 12:14
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#12
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Registered User
Join Date: Oct 2014
Posts: 7,981
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Re: SA/Displ Ratio that Factors in Wind Speed?
When it comes to SA, it is mostly a Goldilocks assessment, too much, too little, just right.
And of course, it depends on which sails one is deploying at the moment and how much is deployed.
I have typically experienced that the words Spinnaker and Wind Speed do not pair well at upper limits.
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19-01-2025, 14:52
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#13
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Registered User
Join Date: Jul 2014
Location: Southeast US
Posts: 467
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Re: SA/Displ Ratio that Factors in Wind Speed?
This is interesting. Yes, it is for a monohull and I have't found a polar for a Pearson 367 yet. Teddy, I looked at your equation, but it makes SA2 too small. For example, with SA1 @ 600 sqft, AWS1 @ 10 knots, and AWS2 @18 knots, SA2= 185 sqft (unless I screwed up the algebra). I don't need this to know when to reef or anything like that; It's really just a mental activity because it's kinda cold out. I wanted to know the sheet loads, but beyond that, I was just chasing a rabbit until it disappeared.
A question I did come across with the SA/D ratio is specific to the foretriangle, but it's moot because once the winds are greater that "light winds", the SA/D value doesn't matter much. This questions was, for double headsail, how does the SA/D change when comparing fore triangle with the actual sail area (yankee and staysail), but that's a whole nother ball of thread to unravel and it doesn't much matter outside of Montanan's Goldilocks band anyway. And . . . It's warming a bit outside, so I'll step out and chase down different leporid.
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19-01-2025, 15:56
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#14
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Moderator
Join Date: Sep 2014
Location: Channel Islands, CA
Boat: 1962 Columbia 29 MK 1 #37
Posts: 15,328
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Re: SA/Displ Ratio that Factors in Wind Speed?
And when you look at ultralights they will typically have SA/D of 22 or more. Clearly they will do well in light air. But most cruisers don’t like the spartan interiors, little storage space and lack of heavy ballast.
__________________
DL
Pythagoras
1962 Columbia 29 MKI #37
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19-01-2025, 17:23
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#15
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Registered User
Join Date: May 2013
Location: Portland, ME
Boat: McCurdy & Rhodes 56
Posts: 260
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Re: SA/Displ Ratio that Factors in Wind Speed?
Here are polars for a Pearson 39. Maybe knock the numbers down 10% as a starting point?
https://jieter.github.io/orc-data/site/#USA/255
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