Following Commander Pete's suggestion, I went to //www.geocities.com/jvandry and clicked on Sailboat Math. This takes you to a neat calculator that gives you Hull Speed, minimum horsepower to achieve Hull Speed and the speed that your particular horsepower engine will drive the boat.
Using the following data for the Ariel / Commander
Displacement 5200 lbs
Waterline 18.5 feet
Beam 8.0 feet
Sail Area 305 square feet
Horsepower 5.0
Here are the results
Hull Speed 5.8 knots
Min Horsepower needed 7.7 hp
Speed with 5hp engine 4.6 knots
Displacement / Length Ratio 367
Sail Area / Displacement Ratio 16.3
Capsize Screening Ratio 1.85
(Below 2.0 recommended for off shore sailing)
This is another one of those calculators, this one to compare boats.
http://www.image-ination.com/sailcalc.html
Can't vouch for any of these calculators. There are probably too many factors invoved for them to be accurate. The data on the Commander in this one is wrong too.
As far as displacement for our boats, I've seen many different figures. I don't know if any of them account for engine, fuel, water, beer, crew, stores, ice, more beer, etc.
Interesting note at the bottom about hull speed, stability, and being able to carry sail. That's one reason why we get to torture bigger boats.
Bill Shaw indicated that the variations in displacement may result from the industry's shift to 50% from no load - ie., 1/2 fuel, 1/2 crew, etc.
Origianally the Ariel was shown at 5120 and the Commander 5100. Later (after the 1/2) the Ariel was shown at 5500. (There is a missprint in the manual showing 5320 for the Ariel.)
A quick look at http://www.image-ination.com/sailcalc.html
failed to show an Ariel. The Pearson 26 listed is a Shaw designed, spade keel boat.
Is there more?
I think the speed calculator is flawed , last Sunday with the new prop , we saw 6.2mph ( 5.63knots) using the GPS . That was with 6hp .
just asking, but if you use the waterline in calculations, wouldn't you use the beam at the waterline also?
Beam? That's a thought. Marine architects probably have a seven derivitive calculus to determine the "true" hull speed.
Too mush Jim Beam
The computer at this site uses beam in its computations:
http://www.image-ination.com/sailcalc.html
[The page is pretty slow to load]
The calculator is set up to make comparisons between boats, but it is not necessary to add another boat to the second window. Select the Pearson Commander in window #1, then move down the page to see the resulting input data and computations. Hull speed shown is about the same as with the other calculator.