Relationship Between Sail Area/Displacement to Boat Speed

[Goldencrab95]

Since sail area to displacement ratio greatly judges to determine how fast a boat would be, I figured that it could easily relate sailing speed to SA/D. Does anybody know how to calculate between the two factors? I tried looking up how to get convert SA/D to sailing speed but it is not specified. Perhaps maybe involving PHFR or a certain given wind speed(let's say 10 knots), would make the conversion connection link between SA/D and possible sailing speed more clarified and more likely to make the conversion really work.

[Oceanride007]

Upper speed is limited by hull speed which is related to Waterline length, you are unlikely to get past that in a monohull. There is a relationship between boat length and Displacement but only with similar vessels, for ships it is L=K*D^3. (Trying to remember my Naval Arch) so double the length Displacement increases 8 Times, but I reckon 2.7 may be a better than 3 as depth of yacht hull doesn't change much. Increasing displacement increases your surface area to the power of 2/3 SA=K*D^2/3 I think
It'll be a interesting relationship, but your vessel is going to change its hull shape as the wind increases, sails choke one another, to many variables, I reckon stay away from this calc.

Oceanrider

[RainDog]

Originally Posted by Goldencrab95

Since sail area to displacement ratio greatly judges to determine how fast a boat would be, I figured that it could easily relate sailing speed to SA/D. Does anybody know how to calculate between the two factors? I tried looking up how to get convert SA/D to sailing speed but it is not specified. Perhaps maybe involving PHFR or a certain given wind speed(let's say 10 knots), would make the conversion connection link between SA/D and possible sailing speed more clarified and more likely to make the conversion really work.

If you are looking for one number that you can use to compare the speed of different boats, I think PHRF is your best bet. It is the number specifically designed and refined over the years to try to compare the speed of two completely different boats.

If you want top speed, as already suggested it is purely a function of waterline length (in a normal monohull).

If you want more precise numbers for a single boat, you need to find the polars for that boat. Depending on the boat, they might be available on line.

[Adelie]

You are unlikely to average better than hull speed in a monohull in cruising trim. Loaded for racing, on a good wind day with the right boat, off the wind; sure no problem.

If you want to estimate your voyage length then

Average Daily Mileage = = 2.62 + 0.066*SA/D ratio + 0.051*LWL

LWL in ft
Keep in mind this in average you can expect to make over an extended period, probably good for estimating provisions on a long passage.

The following link explains how the equation came to be: http://www.bethandevans.com/pdf/200mile.pdf

[JazzyO]

Interesting.

My Baltic 38DP has a waterline of 31.5ft and 14,330lb of displacement.

Hull speed according to the regular formula is 7.52kts.

Using the formulas for my new wardrobe (arriving this week! yeeha!), we get:



For reference: Dale Parshall sailed the Transpac 1998 in a Baltic 38DP "Giggles". He averaged 6.69kts over 2120miles in 13 days and 5 hours, singlehandedly.

So I think the formula seems to work quite well.

Once I have done some decent passages on this boat I'll report back if it fits my experience. I have to say that she hits 7kts very, very easily and I've seen 10kts with old sails in 20kts wind or so, but of course average speed over long distance is a very different thing.


Onno

[Adelie]

I mis-stated the formula above, it should be:

Average Daily Mileage = 24 * (2.62 + 0.066*SA/D ratio + 0.051*LWL)

JazzyO, for your Baltic 38DP I get 133 nm/d. The formula uses SA/D for main and fore triangles, not actual sail areas.

The formula estimates mileage over the long term, in tropical and temperate waters on all points of sail in cruising trim. Consequently you will get significantly less mileage than you would expect from your PHRF rating, though there is a strong correlation between the two. See below.

From Latitude 38's description Dale Parshall's ride to HA was in pretty good conditions, though not as good as 1994's, and of course all down wind so his averaging 160nm/d is actually pretty good, not something to be expected regularly.

[cfarrar]

SA-to-Displacement indicates something useful about relative performance in light-air.

[JazzyO]

Originally Posted by Adelie

JazzyO, for your Baltic 38DP I get 133 nm/d. The formula uses SA/D for main and fore triangles, not actual sail areas.

I'm not following this. Can you elaborate?


Onno

[pdf27]

Originally Posted by JazzyO

Once I have done some decent passages on this boat I'll report back if it fits my experience. I have to say that she hits 7kts very, very easily and I've seen 10kts with old sails in 20kts wind or so, but of course average speed over long distance is a very different thing.

I should also point out that formula is based on point-to-point distances and total passage time, rather than speed through the water. So even if you travel everywhere at exactly 7 kts, your speed by that formula would be a bit lower.

[Adelie]

In general use sail area for SA/D is calculated from the main- and fore-triangles.
For the main that would be 1/2*P*E, the area of the roach is not included.
For the fore-triangle, 1/2*I*J, no overlap is included.
Displacement is the lightship displacement of the boat in lb.

These values are used in the equation because they are available for all boats. The amount of roach in a main may be defined by class rules, or it may be arbitrarily large or even negative for an owner who chooses not to follow class rules and just sail under PHRF. Overlap is not counted because because the overlap can be made arbitrarily large, I have a picture of a boat with a 264% drifter.

The goal of the formula is to indicate the power to weight potential of the rig as a whole in a standardized way that allows comparison across many types of boats.

I got the 19.95 SA/D value for your boat from BALTIC 38 DP sailboat specifications and details on sailboatdata.com.

The point of the equation was to estimate long term cruising speed. That means that on some passages you will exceed the estimate because the weather was consistently favorable, moderate to heavy winds reaching to running. On others you will not meet the estimate because the winds are light, or from the direction of the destination. Over say 10,000 nm with a crew of 2 and a mix of upwind, downwind, light and heavy weather the estimate should be approximately right, +/-10%.

I am working on an improved formula but that will be several month before I am done.

[barnakiel]

Originally Posted by JazzyO

For reference: Dale Parshall sailed the Transpac 1998 in a Baltic 38DP "Giggles". He averaged 6.69kts over 2120miles in 13 days and 5 hours, singlehandedly.

(...) I've seen 10kts with old sails in 20kts wind or so (...)

That year they were able to sail a nearly direct route and 6.7 in an otherwise 7.5 hull is a great result, even after we allow for any favourable currents. Great weather, great sails choice, good boat and good sailor.

b.

[barnakiel]

SA/D are pretty poor proxy for boats daily runs potential as both displacement and sail area can be distributed in various ways in any specific design.

Another pitfall is that SA/D do not allow for boat size. And as we know bigger is faster for more than pure LWL reasons.

But, off course, since our engine is in the SA and our brakes are in the D, hence there is a clean relationship in case of boats of similar length.

Just think two boats with same ratio may have vastly different speed potential and daily run records.

b.

[JazzyO]

Originally Posted by barnakiel

good sailor.

No doubt!

Originally Posted by Adelie

the area of the roach is not included.\no overlap is included.

Ah, thanks, all clear now.

This has been a very informative thread, although I see Barnakiel's point on the limitation of the formula. Of course cruising is not a science nor is it racing so it doesn't matter that much but it is nice to get an idea of the performance one can expect.


Onno

[Cheechako]

Originally Posted by cfarrar

SA-to-Displacement indicates something useful about relative performance in light-air.

Right... and a measure of ability to accelerate . So if you are drag racing it's useful... or if you are going to round in the roaring 40's it might be useful to get a boat with minimal SA!
A good measure (along with other numbers) to determine tenderness etc I 'spose...

[sailorboy1]

SA/D - maybe the only old ratio that still has meaning in the modern world